RESERVOIR ENGINEERING - Determination of Oil and Gas Reserves.pdf

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INTRODUCTION TO RESERVOIR ENGINEERING RESERVOIR PRESSURES AND TEMPERATURES RESERVOIR FLUIDS COMPOSITION PHASE BEHAVIOUR OF HYDROCARBON SYSTEMS BEHAVIOUR OF GASES PROPERTIES OF RESERVOIR LIQUIDS FUNDAMENTAL PROPERTIES OF RESERVOIR ROCKS ROCK PROPERTIES MEASUREMENT PERMEABILITY-ITS VARIATIONS FLUID FLOW IN POROUS MEDIA DRIVE MECHANISMS VAPOUR LIQUID EQILIBRIA EQUILIBRIUM RATIO PREDICTION AND CALCULATION PVT ANALYSIS MATERIAL BALANCE EQUATION MATERIAL BALANCE EQUATION APPLICATION WATER INFLUX IMMISCIBLE DISPLACEMENT EXAMINATION AND MODEL SOLUTIONS

RESERVOIR ENGINEERING

RE

This Reservoir Engineering module covers material presented in a range of reservoir engineering texts and a number of the figures and examples are based on these texts and copyright is currently being sought. The student may find the more detailed analysis in these texts supportive when going through these notes. The following books are considered useful in building up a reservoir engineering library. 1.Fundamentals of Reservoir Engineering.

L.P.Dake. Elsevier. 1978 ISBN:0-444-41667-6

2.The Practise of Reservoir Engineering.

L.P.Dake. Elsevier. 1994. ISBN: 0-444-82094-9

3.Principles of Petroleum Reservoir Engineering.

G.H.Chierici. Springer-Verlag 1994. ISBN:3-540-56037-8

4.Fundamental Principles of Petroleum Reservoir Engineering

B.F. Towler. Society of Petroleum Engineers Inc ISBN:55563-092-8

5.Applied Reservoir Engineering

B.C.Craft & M.F.Hawkins. Prentice Hall. 1959.

6.The Properties of Petroleum Fluids 2nd Ed

W.D.McCain Pennwell Books . 1990 ISBN:0-87814-335-1

7.Petroleum Engineering Principles and Practise.

J.S.Archer & C.Wall.Graham & Trotman. 1986. ISBN:0-86910-715-9

8.Petroleum Reservoir Engineering.

J.W.Amyx,D.M.Bass & R.L.Whiting. McGraw-Hill. 1960. ISBN:07-001600-3

9.PVT and Phase Behaviour of Petroleum Reservoirs A. Danesh. Elsevier. ISBN: 0-444-82196-1

Adrian C Todd

All rights reserved no part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise without the prior permission of the Copyright owner.

Reservoir Engineering notes cover an extensive amount of material. They are support material for the examination in this topic but are also considered to be useful material in subsequent career use. Not all the material in the text can be covered in a limited time examination. In the context of the examination a student should consider the learning objectives at the front of each section which should help in the level of detail and analysis which is required in relation to an examination covering the various topics. Detailed below is a graded analysis of each section which should help the candidate in examination preparation. These should be considered alongside the learning objectives. Grading structure: 5 4 3 2 1

-

Core material for examination purposes Core material less analytical than 5 - examinable. Between 4 & 2 General awareness. Not so examinable with respect to analysis of detail. Other information not examinable.

OM- Material covered in another module not for examination purposes in Reservoir Engineering. Equations – It is not necessary to memorise complicated equations. Equations unless asked to be derived will be given. Clearly some basic equations one should know and would not be given e.g. Darcy’s Law, PV = nzRT STOOIP equation Equilibrium Ratio K=y/x

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4

Chapter 3 Reservoir Composition 1 5 2 5 3 4 4 5 5.1 5 5.2 2 5.3 2

Chapter 2 Reservoir Pressures 1 5 2 5 3 5 4 5 5 5 6 4

Chapter 1 Introduction Section – grading 1.1 4 1.2 4 1.3 4 2 4 3 – 3.1 4 3.2 4 3.3 4 3.4 4 4 OM 5 OM 6 4 7 4 8 4 9 4

Chapter 7 Reservoir Rocks 1 3 2 4 3 3 4.1 5 4.2 5 4.3 3 4.4 3 4.5 5 4.6 5 4.7 4 4.8 5 4.9 2 4.10 2 5 3 6 5 7.1 5 7.2 5 7.3 5 8.1 5 8.2 5 8.3 5

Chapter 6 Liquids 1 5 2 5 3 5 4 5 5 5 6 5 7 3 note there is an error in some texts with another 7 heading 8.1 5 8.2 5 9 5 10 3 11 1 12 5

Chapter 5 Gases 1.1 5 1.2 5 1.3 5 1.4 5 1.5 5 1.6 5 1.7 5 1.8 5 1.9 5 2.1 5 2.2 5 2.3 5 2.4 1 2.5 5 3 5 4 3 5 3 6 2

Chapter 4 Phase Behaviour All material 5

Chapter 10 Fluid Flow 1 3 2 3 3.1 3 3.2 3 3.3.1 3 3.3.2 3 3.3.3 3 3.3.3.1 5 3.3.4 5 3.4 5 3.4.1 3 3.5 5 4 1 5 5 5.2 5 5.3 5 6 5

Chapter 9 - Permeability Variations 1 3 2 5 3 5

Chapter 8 Rock Measurement 1.1 2 2.1 2 2.2 2 3.1 2 3.2 2 4.1 3 4.2 3 4.3 3 4.4 3 5 2 6.1 5 6.2 3 6.3 5 6.4 5 7 2

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Vapour Liquid Equilibrium 2 2 Eq 11 – 5 5 5 5 5 3 3 3 3

Chapter 14 PVT 1 4 2 2 3.1 5 3.2 5 3.3 5 3.4 2 3.5 2 4 5 5 2 6 5 7 3 8.1 2 8.2 2 9 5 10 5 11 5 12 5 13 3 14 3 15 1

Chapter 13 Equilibrium Ratio 1 3 2 3 3 2 4 2

Chapter 12 1 2 3 4.1 4.2 4.3 5.1 5.2 5.3 5.4

Chapter 11 Drive Mechanisms All sections 5

MB Application 5 5 5 4 5 (5.1.2.2 Eq46 -1 ) 4 4 2 5 5 2 2 1 3 1

Chapter 17 Water Influx 1 5 2.1 3 2.2 3 2.3 3 2.4 3 2.5 5 3 5 4 4 5 3 6 2 7 2

Chapter 16 1 2 3 4 5.1 5.2 5.3.1 5.3.2 5.3.3 5.3.4 5.3.5 5.4 5.5 5.6 6

Chapter 15 Material Balance 1 5 2 3 3 5 4 5 5 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5

Chapter 18 Immiscible Displacement 1 5 2 5 3.1 3 3.2 5 3.3 3 ( Eqn 1 – 5 -should be expected to know ) 3.4 4 ( post equation 14 – 5 ) 4 5 5.1 2 5.2 5 ( from equation 72+ - 2) 6.1 3 6.2 3 6.3 3 6.4 5 6.5 5 6.6 1 6.7 5 7 5 8.1 2 8.2 2 8.3 2 8.4 1 8.5 1

Introduction To Reservoir Engineering

CONTENTS 1 INTRODUCTION

8. PRODUCTION OPERATIONS OPTIMISATION 8.1 Development Phase 8.2 History Matching 8.3 Phases of Development

2 RESERVOIR ENGINEERING TECHNIQUES

9. THE UNIQUENESS OF THE RESERVOIR

3 RESERVE ESTIMATING 3.1 Definitions 3.2 Proven Reserves 3.2.1 Exercises - Reserve Definitions 3.3 Unproved Reserves 3.3.1 Probable Reserves 3.3.2 Possiible Reserves 3.4 Reserve Status Categories 3.4.1 Developed: 3.4.1.1 Producing 3.4.1.2 Non-producing: 3.4.2 Undeveloped Reserves:

10. CONCLUSIONS

1.1 1.2 1.3

Reserves Estimation Development Planning Production Operations Optimsation

4 PROBABILISTIC REPRESENTATION OF RESERVES 5 VOLUME IN - PLACE CALCULATIONS 5.1 Volume of Oil and Gas in-Place 5.2 Evolution of Reserve Estimate 5.3 Reservoir Area 5.4 Reservoir Thickness 5.5 Reservoir Porosity 5.6 Water Saturation 5.7 Formation Volume Factors 5.8 Recovery Factors 5.9 Production Capacity 5.10 Hydrocarbon Pore Volume Map 6 OTHER APPRAISAL ROLES 7 DEVELOPMENT PLANNING 7.1 Reservoir Modelling 7.2 Technoconomics 7.3 Coping with Uncertainty

LEARNING OBJECTIVES Having worked through this chapter the Student will be able to: • Show using a block diagram the integration of reservoir engineering with other petroleum engineering and other subjects. • Define the SPE definitions of reserves; proven reserves, unproved reserves; probable reserves and possible reserves. • Calculate given the prerequisite data proved, probable and possible reserves. • Describe in general terms reserve estimation. • Sketch a diagram showing the probability versus recoverable reserves indicating, proven, proven + probable and proven + probable + possible reserves. • Present a simple equation for volumes of oil and gas in-place. • Describe in general terms the evolution of reserves through successive exploration wells. • Describe briefly with the aid of a sketch the various maps used to represent reservoir; area, thickness porosity, saturation. • Describe briefly the use of the production (well0 test to determine reservoir flowability and properties. • Describe briefly the various elements of development planning: reservoir modeling technoeconomics and uncertainty. • Illustrate with a sketch the impact of different technical parameters on the associated uncertainties on a project. • Describe in general terms in the context of production operations, optimization in history matching. • Draw a sketch showing the various phases of production from build up to economic limit. • Draw a sketch illustrating the various recovery scenarios from primary to tertiary recovery.



Introduction To Reservoir Engineering

1 INTRODUCTION With the petroleum industry’s desire to conserve and produce oil and gas more efficiently a field of specialisation has developed called Petroleum Reservoir Engineering. This new science which can be traced back only to the mid 1930’s has been built up on a wealth of scientific and practical experience from field and laboratory. In the 1959 text of Craft & Hawkins1 on Applied Reservoir Engineering it is commented that “as early as 1928 petroleum engineers were giving serious consideration to gas-energy relationships and recognised the need for more precise information concerning physical conditions as they exist in wells and underground reservoirs. Early progress in oil recovery methods made it obvious that computations made from wellhead or surface data were generally misleading.” Dake2, in his text "The Practise of Reservoir Engineering", comments that “Reservoir Engineering shares the distinction with geology in being one of the ‘underground sciences’ of the oil industry, attempting to describe what occurs in the wide open spaces of the reservoir between the sparse points of observation - the wells” The reservoir engineer in the multi-disciplinary perspective of modern oil and gas field management is located at the heart of many of the activities acting as a central co-ordinating role in relation to receiving information processing it and passing it on to others. This perspective presented by Dake2 is shown in the figure below. Exploration Geophysics/ Geology

Petrophysics

Reservoir Engineering

Economics (Project viability)

Production Process Egineering General Engineering Platform Topsides Design

2

Figure 1 Reservoir Engineering in Relation to Other Activities (adapted Dake )

Dake2 has usefully specified the distinct technical responsibilities of reservoir engineers as: • Contributing, with the geologists and petrophysicists , to the estimation of hydrocarbons in place. • Determining the fraction of discovered hydrocarbons that can be recovered. • Attaching a time scale to the recovery. Insitute of Petroleum Engineering, Heriot-Watt University



• Day-to-day operational reservoir engineering throughout the project lifetime. The responsibility of the first is shared with other disciplines whereas the second is primarily the responsibility of the reservoir engineer. Attaching a time scale to recovery is the development of a production profile and again is not an exclusive activity. The day-to-day operational role is on going through the duration of the project. A project can be conveniently divided into two stages and within these the above activities take place, the appraisal stage and the development phase. The appraisal phase is essentially a data collection and processing phase with the one objective of determining the ‘viability’ of a project. The development phase covers the remaining period if the project is considered viable from the time continuous production commences to the time the field is abandoned. Reservoir engineering activity in various forms takes place during both of these stages. The activities of reservoir engineering fall into the following three general categories: (i) Reserves Estimation (ii) Development Planning (iii) Production Operations Optimisation

1.1 Reserves Estimation

The underground reserves of oil and gas form the oil company’s main assets. Quantifying such reserves forms therefore a very important objective of the practising reservoir engineer but it is also a very complex problem, for the basic data is usually subject to widely varying interpretations and on top of that, reserves may be affected significantly by the field development plan and operating practice. It is an on-going activity during, exploration, development planning and during production. It is clearly a key task of the appraisal phase for it is at the heart of determining project viability. Before any production has been obtained, the so-called ‘volumetric estimate of reserves’ is usually made. Geological and geophysical data are combined to obtain a range of contour maps with the help of a planimeter and other tools the hydrocarbon bearing rock volumes can be estimated. From well log petrophysical analysis, estimates of an average porosity and water saturation can be made and when applied to the hydrocarbon rock volume yield an estimate of oil in place (STOIIP). Since it is well known that only a fraction of this oil may in fact be ‘recoverable’, laboratory tests on cores may be carried out to estimate movable oil. The reserve estimate finally arrived at is little more than an educated guess but a very important one for it determines company policy. In 1987 the Society of Petroleum Engineers in collaboration with the World Petroleum Congress published definitions with respect to reserves and these are now accepted world-wide 3. These definitions have been used in the summary of reserve definitions which follow.



Introduction To Reservoir Engineering

1.2 Development Planning

Oilfield development, particularly in the offshore environment, is a ‘front loaded’ investment. Finance has to be committed far in advance not only of income guaranteed by the investment, but frequently also of good definitive data on the character of the field. Much of the responsibility for this type of activity falls on the reservoir engineers because of their appreciation for the complex character of sub-surface fluid behaviour under various proposed development schemes.

1.3 Production Operations Optimisation

Producing fields will seldom behave as anticipated and, of course, by the very nature of this sort of activity, the balance of forces in the reservoir rock gets severely upset by oil and gas production. The reservoir engineer is frequently called upon to ‘explain’ a certain aspect of well performance, such as increasing gas-oil ratio, sand and/or water production and more importantly will be asked to propose a remedy. The actual performance of the reservoir as compared to the various model predictions is another ongoing perspective during this phase.

2 RESERVOIR ENGINEERING TECHNIQUES In the past the traditionally available reservoir engineering tools were mainly designed to give satisfactory results for a slide rule and graph paper approach. For many problems encountered by reservoir engineers today this remains a perfectly valid approach where the slide rule has been replaced by the calculator. Increasingly, however, the advance of computing capability is enabling reservoir engineering modelling methods (‘simulations’) to be carried out at the engineers desk, previously considered impossible. The basis of the development of the 'model' of the reservoir are the various data sources. As the appraisal develops the uncertainty reduces in relation to the quality of the forecasts predicted by the model. Building up this ‘geological’ model of the reservoir progresses from the early interpretation of the geophysical surveys, through various well derived data sets, which include drilling information, indirect wireline measurements, recovered core data, recovered fluid analysis, pressure depth surveys, to information generated during production.

3. RESERVE ESTIMATING The Society of Petroleum Engineers SPE and World Petroleum Congress WPO1987 agreed classification of reserves3 provides a valuable standard by which to define reserves, the section below is based on this classification document.

3.1 Definitions

Reserves are those quantities of petroleum which are anticipated to be commercially recovered from known accumulations from a given date forward. All reserve estimates involve some degree of uncertainty. The uncertainty depends chiefly on the amount of reliable geologic and engineering data available at the time Insitute of Petroleum Engineering, Heriot-Watt University



of the estimate and the interpretation of these data. The relative degree of uncertainty may be conveyed by placing reserves into one of two principal classifications, either proved or unproved. Unproved reserves are less certain to be recovered than proved reserves and may be further sub-classified as probable and possible reserves to denote progressively increasing uncertainty in their recoverability. Estimation of reserves is carried out under conditions of uncertainty. The method of estimation is called deterministic if a single best estimate of reserves is made based on known geological, engineering, and economic data. The method of estimation is called probabilistic when the known geological, engineering, and economic data are used to generate a range of estimates and their associated probabilities. Identifying reserves as proved, probable, and possible has been the most frequent classification method and gives an indication of the probability of recovery. Because of potential differences in uncertainty, caution should be exercised when aggregating reserves of different classifications. Reserves estimates will generally be revised as additional geologic or engineering data becomes available or as economic conditions change. Reserves do not include quantities of petroleum being held in an inventory, and may be reduced for usage or processing losses if required for financial reporting. Reserves may be attributed to either natural energy or improved recovery methods. Improved recovery methods include all methods for supplementing natural energy or altering natural forces in the reservoir to increase ultimate recovery. Examples of such methods are pressure maintenance, gas cycling, waterflooding, thermal methods, chemical flooding, and the use of miscible and immiscible displacement fluids. Other improved recovery methods may be developed in the future as petroleum technology continues to evolve.

3.2 Proven Reserves

Proven reserves are those quantities of petroleum which, by analysis of geological and engineering data, can be estimated with reasonable certainty to be commercially recoverable, from a given date forward, from known reservoirs and under current economic conditions, operating methods, and government regulations. Proved reserves can be categorised as developed or undeveloped. If deterministic methods are used, the term reasonable certainty is intended to express a high degree of confidence that the quantities will be recovered. If probabilistic methods are used, there should be at least a 90% probability that the quantities actually recovered will equal or exceed the estimate. Establishment of current economic conditions should include relevant historical petroleum prices and associated costs and may involve an averaging period that is consistent with the purpose of the reserve estimate, appropriate contract obligations, corporate procedures, and government regulations involved in reporting these reserves. In general, reserves are considered proved if the commercial producibility of the reservoir is supported by actual production or formation tests. In this context, 

Introduction To Reservoir Engineering

the term proved refers to the actual quantities of petroleum reserves and not just the productivity of the well or reservoir. In certain cases, proved reserves may be assigned on the basis of well logs and/or core analysis that indicate the subject reservoir is hydrocarbon bearing and is analogous to reservoirs in the same area that are producing or have demonstrated the ability to produce on formation tests. The area of the reservoir considered as proved includes (1) the area delineated by drilling and defined by fluid contacts, if any, and (2) the undrilled portions of the reservoir that can reasonably be judged as commercially productive on the basis of available geological and engineering data. In the absence of data on fluid contacts, the lowest known occurrence of hydrocarbons controls the proved limit unless otherwise indicated by definitive geological, engineering or performance data. Reserves may be classified as proved if facilities to process and transport those reserves to market are operational at the time of the estimate or there is a reasonable expectation that such facilities will be installed. Reserves in undeveloped locations may be classified as proved undeveloped provided (1) the locations are direct offsets to wells that have indicated commercial production in the objective formation, (2) it is reasonably certain such locations are within the known proved productive limits of the objective formation, (3) the locations conform to existing well spacing regulations where applicable, and (4) it is reasonably certain the locations will be developed. Reserves from other locations are categorised as proved undeveloped only where interpretations of geological and engineering data from wells indicate with reasonable certainty that the objective formation is laterally continuous and contains commercially recoverable petroleum at locations beyond direct offsets. Before looking at further detail we will carry out some tests to help emphasise the above definition.

3.2.1 Exercises - Reserve Definitions

The section on Reserve Definitions as put together by the SPE and the World Petroleum Congress, defines the various aspects of reserve definitions. These definitions, are important both to companies and countries, and they can have very significant commercial impact. The following tests are presented to help understand the working of these earlier definitions. Test 1 There are 950 MM stb ( million stock tank barrels) of oil initially in place in a reservoir. It is estimated that 500 MM stb can be produced. Already 100 MM stb have been produced. In the boxes below, identify the correct answer. 950

500

400

MM stb

The Reserves are: 450

400

500

MM stb

STOIIP is:

Turn to page 9 for answers

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Test 2 Before starting production it was estimated that there was a 90% chance of producing at least 100 MM stb, 50% chance of producing 500 MM stb and 10% chance of producing 700MM stb. That is we are sure we can produce at least 100MM stb, and we will probably produce as much as 500 MM stb, and we will possibly produce as much as 700 MM stb. Tick the correct answers. Proved reserves (MM stb): 400

500

600

700

200

400

500

600

700

Possible reserves 200 100

400

500

600

700

100

200

Probable reserves 100

Turn to page 9 for answers Test 3 What is wrong with the following definitions? 1. Reserves are those quantities of petroleum which are anticipated to be recovered from a petroleum accumulation.

Test 4 1. We have a structure in our licence area which we intend to explore. We anticipate it to contain a STO IIP of 2000 MM stb, and recovery factor of 65% using primary methods (30%), secondary (25%) and tertiary (10%) recovery methods. What are the reserves?

Test 5 A reservoir has been discovered by drilling a successful exploration well, and drilling a number of producing wells. We have even produced some 200 MM stb of oil. STOIIP = 2000MM stb What are the reserves?



Recovery factor = 35%

Introduction To Reservoir Engineering

Test 1 answer There are 950 MM stock tank boards in place. It is estimated that 500 MM stb can be produced and 100 MM stb have been produced then 400 recoverable reserves remain. 950

√

500 X

400

X

MM stb

The Reserves are: 450

X

400 √

500

X

MM stb

STOIIP is:

Test 2 answer

Proved : Probable : Possible : Proved : Proved & Possible Proved & Probable & Possible :

100 MM stb 500 - 100 = 400 MM stb 700 - 500 = 200 MM stb 100 MM stb 500 MM stb 700 MM stb

Test 3 answer Reserves are those quantities of petroleum which are anticipated to be commercially recovered from a petroleum accumulation. Clearly economics is a very important aspect of the definition. Economic Variables What economic factors are used in the calculations? What oil and gas price do we use for proved reserve estimates? Is inflation taken into account? Do we predict future price trends? Do we apply discount factors to calculate present value of the project? Are all these used in proved reserve calculations? The current economic conditions are used for the calculations, with respect to prices, costs, contracts and government regulations. Test 4 answer 1. Answer is zero by SPC/WPC definition. 2. Intentions and anticipations are not the basis for reserves. In this case no well has yet been drilled. Note: Some companies allocate potential reserves for internal use but these cannot be used for public and government figures. Reserves are those quantities of petroleum which are anticipated to be commercially recovered from a known accumulation. Requirements for “Proved” include The following sources are required for proved reserves. Maps (from seismic and/ geological data). Petrophysical logs. Well test results and rock properties from core analysis tests on recovered core. Insitute of Petroleum Engineering, Heriot-Watt University



Facilities An important perspective which might be forgotten by the reservoir engineer, is that for reserves to be classified as “proven”, all the necessary facilities for processing and the infrastructure for transport must either be in place or that such facilities will be installed in the future, as backed up by a formal commitment. Contribution to the Proved Reservoir Area This comes from drilled and produced hydrocarbons, the definition of the gas and oil and water contacts or the highest and lowest observed level of hydrocarbons. Also the undrilled area adjacent to the drilled can be used. Test 5 answer Ultimate recovery = 2 000 x 0.35 = 700 MM stb Minus production to date = 200 Reserves = 500 MM stb Reserves are those quantities of petroleum which are anticipated to be commercially recovered from known accumulations from a given date forward. i.e. Reserves refer to what can be produced in the future.

RESERVE CATEGORIES Probability Levels

Figure 2 gives a schematic of reserves showing the progression with time. P10

Potential

SPE / WPC Definitions Possible

Possible

Probable

Probable

P50

Provan

P90

Cumulative Production

Provan Time

Seismic Discovery of Start of Dev Start of Data Well Planning Production PERIOD TYPE OF DATA METHOD

Before Drilling Exploration Well Geophysical and Geological

Prior and During Delineation, Evaluation, Appraisal Development Geophysical, Geological, Petrophysical and Well Test Data

Mostly Probabilistic

Abandonment Production

Geophysical, Reservoir Performance Geological, and Production Data Petrophysical and Well Tests and Production Data

Deterministic and Probabilistic

Figure 2 Variations of Reserves During Field Life

What are the amounts termed that are not recoverable? The quantity of hydrocarbons that remains in the reservoir are called remaining hydrocarbons in place, NOT remaining reserves! Reserves which are to be produced through the application of established improved recovery methods are included in the proved classification when : 10

Introduction To Reservoir Engineering

(i) Successful testing by a pilot project or favourable response of an installed program in the same or an analogous reservoir with similar rock and fluid properties provides support for the analysis on which the project was based, and, (ii) It is reasonably certain that the project will proceed. Reserves to be recovered by improved recovery methods that have yet to be established through commercially successful applications are included in the proved classification only: (i) After a favourable production response from the subject reservoir from either (a) A representative pilot or

(b) An installed program where the response provides support for the analysis on which the project is based and

(ii) It is reasonably certain the project will proceed.

3.3 Unproved Reserves

Unproved reserves are based on geologic and/or engineering data similar to that used in estimates of proved reserves; but technical, contractual, economic, or regulatory uncertainties preclude such reserves being classified as proved. Unproved reserves may be further classified as probable reserves and possible reserves. Unproved reserves may be estimated assuming future economic conditions different from those prevailing at the time of the estimate. The effect of possible future improvements in economic conditions and technological developments can be expressed by allocating appropriate quantities of reserves to the probable and possible classifications.

3.3.1. Probable Reserves

Probable reserves are those unproved reserves which analysis of geological and engineering data suggests are more likely than not to be recoverable. In this context, when probabilistic methods are used, there should be at least a 50% probability that the quantities actually recovered will equal or exceed the sum of estimated proved plus probable reserves. In general, probable reserves may include : (1) Reserves anticipated to be proved by normal step-out drilling where subsurface control is inadequate to classify these reserves as proved, (2) Reserves in formations that appear to be productive based on well log characteristics but lack core data or definitive tests and which are not analogous to producing or proved reservoirs in the area, (3) Incremental reserves attributable to infill drilling that could have been classified as proved if closer statutory spacing had been approved at the time of the estimate,

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(4) Reserves attributable to improved recovery methods that have been established by repeated commercially successful applications when;

(a) a project or pilot is planned but not in operation and (b) rock, fluid, and reservoir characteristics appear favourable for commercial application,

(5) Reserves in an area of the formation that appears to be separated from the proved area by faulting and the geologic interpretation indicates the subject area is structurally higher than the proved area, (6) Reserves attributable to a future workover, treatment, re-treatment, change of equipment, or other mechanical procedures, where such procedure has not been proved successful in wells which exhibit similar behaviour in analogous reservoirs, and (7) Incremental reserves in proved reservoirs where an alternative interpretation of performance or volumetric data indicates more reserves than can be classified as proved.

3.3.2. Possible Reserves

Possible reserves are those unproved reserves which analysis of geological and engineering data suggests are less likely to be recoverable than probable reserves. In this context, when probabilistic methods are used, there should be at least a 10% probability that the quantities actually recovered will equal or exceed the sum of estimated proved plus probable plus possible reserves. In general, possible reserves may include: (1) reserves which, based on geological interpretations, could possibly exist beyond areas classified as probable, (2) reserves in formations that appear to be petroleum bearing based on log and core analysis but may not be productive at commercial rates, (3) incremental reserves attributed to infill drilling that are subject to technical uncertainty, (4) reserves attributed to improved recovery methods when

(a) a project or pilot is planned but not in operation and (b) rock, fluid, and reservoir characteristics are such that a reasonable doubt exists that the project will be commercial, and

(5) reserves in an area of the formation that appears to be separated from the proved area by faulting and geological interpretation indicates the subject area is structurally lower than the proved area.

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Introduction To Reservoir Engineering

3.4 Reserve Status Categories

Reserve status categories define the development and producing status of wells and reservoirs.

3.4.1. Developed:

Developed reserves are expected to be recovered from existing wells including reserves behind pipe. Improved recovery reserves are considered developed only after the necessary equipment has been installed, or when the costs to do so are relatively minor. Developed reserves may be sub-categorised as producing or non-producing.

3.4.1.1 Producing:

Reserves subcategorised as producing are expected to be recovered from completion intervals which are open and producing at the time of the estimate. Improved recovery reserves are considered producing only after the improved recovery project is in operation.

3.4.1.2. Non-producing:

Reserves subcategorised as non-producing include shut-in and behind-pipe reserves. Shut-in reserves are expected to be recovered from (1) completion intervals which are open at the time of the estimate but which have not started producing, (2) wells which were shut-in for market conditions or pipeline connections, or (3) wells not capable of production for mechanical reasons. Behind-pipe reserves are expected to be recovered from zones in existing wells, which will require additional completion work or future recompletion prior to the start of production.

3.4.2. Undeveloped Reserves:

Undeveloped reserves are expected to be recovered: (1) From new wells on undrilled acreage, (2) From deepening existing wells to a different reservoir, or (3) Where a relatively large expenditure is required to

(a) Recomplete an existing well or (b) Install production or transportation facilities for primary or improved recovery projects.

4. PROBABILISTIC REPRESENTATION OF RESERVES Whereas in the deterministic approach the volumes are determined by the calculation of values determined for the various parameters, with the probalistic statistical analysis is used, using tools like Monte Carlo methods. The curve as shown in the figure 3 below presents the probability that the reserves will have a volume greater or equal to the chosen value.

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Probability that the reserve is at least as large as indicated.

1.0 'Proven'

0.9

0.5

'Proven + Probable'

'Proven + Proable + Possible'

0.1 0

Recoverable Reserve

Figure 3 Probabilistic Representation of Recoverable Reserves.

On this curve: The proven reserves represent the reserves volume corresponding to 90% probability on the distribution curve. The probable reserves represent the reserves volume corresponding to the difference between 50 and 90% probability on the distribution curve. The possible reserves represent the reserves volume corresponding to the difference between 10 and 50% probability on the distribution curve. As with the deterministic approach there is also some measure of subjectivity in the probalistic approach. For each of the elements in the following equation, there is a probability function expression in low, medium and high probabilities for the particular values. A schematic of a possible distribution scenario for each of the elements and the final result is given below in the figure 4. Net rock volume.

Net rock average porosity

Connate Formation Estimated water volume recovery saturation factor factor

[ Vnr x φ x (1 - Swc) / Bo ] x RF Uniform

P

Triangular

= Reserves

Gaussian Uniform

=

Figure 4 Probablistic Reserve Estimates. 14

p90 p50 p10

Introduction To Reservoir Engineering

The resulting calculations result in a probability function for a field as shown in the figure 5 below, where the values for the three elements are shown Proven = 500 MM stb the P90 figure. Probable = 240 MM stb which together with the proven makes up the P50 figure. of 740MMstb Possible = 120 MM stb which together with the proven and probable makes up the P10 value of 860MMstb Reserves distribution for a new field.

100

P90

90

P10 = 860 MMstb P50 = 740 MMstb P90 = 500 MMstb

Probability / %

80 70 60

Proven 500 MMstb

50

Probable 240 M

40 30

P+P+P = 860 MMstb

20

120

10 0

P50

Proven 0

200

Probable 400 600 Reserves / MMstb

P10

Possible 800

1000

Figure 5 Reserves Cummulative Probability Distribution.

As a field is developed and the fluids are produced the shape of the probability curve changes. Probability figures for reserves are gradually converted into recovery leaving less uncertainty with respect to the reserves. This is illustrated in figure 6.

Insitute of Petroleum Engineering, Heriot-Watt University

15

100

P90

90

Probability / %

80 70 60

P50

50 40

Proved ultimate recovery.

30 20 10 0

Production 0

200

P10

Proved reserves 400 600 Reserves / MMstb

800

1000

Figure 6 Ultimate Recovery and Reserves Distribution For a Mature Field.

5. VOLUME IN-PLACE CALCULATIONS 5.1 The volume of oil and gas in-place depends on a number of parameters : The aerial coverage of the reservoir. A The thickness of the reservoir rock contributing to the hydrocarbon volume. hn The pore volume, as expressed by the porosity ,φ , the reservoir quality rock. The proportion of pore space occupied by the hydrocarbon ( the saturation ). 1-Sw The simple equation used in calculation of the volume of fluids in the reservoir, V, is V=Ahnφ(1-Sw):













(1)

where: A= average area hn = nett thickness. nett thickness = gross thickness x nett: gross ratio φ = average porosity Sw = average water saturation. When expressed as stock tank or standard gas volumes, equation above is divided by the formation volume factor Bo or Bg. V = Ahnφ (1 − Sw ) / Bo











(2)

To convert volumes at reservoir conditions to stock tank conditions formation volume factors are required where Bo and Bg are the oil and gas formation volume factors. These are defined in subsequent chapters. The expression of original oil in place is termed the STOIIP. 16

Introduction To Reservoir Engineering

The recovery factor, RF, indicates the proportion of the in-place hydrocarbons expected to be recovered. To convert in place volumes to reserves we need to multiply the STOIIP by the recovery factor so that: Reserves = STOIIP x RF

(3)

The line over the various terms indicates the average value for these spatial parameters. The reservoir area A, will vary according to the category; proven, probable or possible, that is being used to define the reserves. Before examining the contributions of the various parameters it is worthwhile to give consideration of the evolution of the reserve estimate during the exploration and development stage.

5.2 Evolution of the Reserve Estimate

Figure 7 gives a cross section view of a reservoir structure as suggested from seismic and geological data.

Oil

Suggested 0il and water contact Figure 7 Cross Section Interpretation From Seismic and Geological Data.

Using this data and possible suggested structure we can carry out some oil in place calculations and estimate reserves. These figures however are not admissible in public reserve estimates. They are useful inside the company to justify project expenditure! The question is where do we locate the first exploration well and get involved in large exploration expenditure costs. Figure 8 suggest three alternatives

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17

Suggest this location.

Oil

Suggested oil and water contact Figure 8 Alternative locations of Exploration Wells

In figure 9 an exploration well has been drilled and a core recovered and the structure of the field with respect to formations and contacts redefined. The redefined structure can now be used to provide an estimate of reserves according to the three, proven, probable and possible perspectives. Figure 10

Oil

Oil and water contact

Cored interval

Figure 9 Interpretation After Exploration Well Drilled and Cored.

18

P

Oil

e bl

si os

ba

ble

Proved

Pr o

Pr ob ab l

e

Introduction To Reservoir Engineering

ible

s Pos

Figure 10 After The Exploration Well Was Drilled.

Subsequent appraisal wells are now drilled to give better definition of the reserves of the field. Well 2 aimed at defining the field to the left identifies some additional isolated hydrocarbon structure with its own oil water contact. Figure 11. The well, as well as increasing the proven reserves, further identifies previous unknown reserves. The next appraisal well is aimed at defining the reserves in the other direction. During well testing on wells 1or 2 indications of faulting are also helping to define the flowing nature of the accumulation. Figure 12 for the further appraisal well confirms the accumulation to the right and also identifies the impact of the fault with a new oil water contact. Subsequent appraisal wells and early development give greater definition to the field description. Figure 13 Well 2.

ven

Pro

Well 1.

Proven

Proposed delineation well 3.

Oil

Initial appraisal stage. Figure 11 Further Delineation Well.

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19

Well 2.

Well 1.

Well 3.

Gas

ven

Pro

Proven

Oil New oil water contact.

Figure 12 After Further Appraisal.

Well 1. Well 4.

Well 2.

Well 3.

Gas

ven

Pro

Proven

Oil New oil water contact.

Figure 13 Final Appraisal Well.

From a deterministic perspective the various reserve estimates, that is, proven, probable and possible can be further determined. The indication of the various elements based on the top structure map are shown. Figure 14

20

Introduction To Reservoir Engineering

Probable 1

Proved 2

3

4

Possible

Figure 14 Reserves Uncertainties by Deterministic Method.

5.3 Reservoir Area

The reservoir area can be obtained by separately evaluating the individual units making up the reservoir as obtained from various reservoir maps. These maps are derived from the evidence given from seismic and subsequent drilled wells. The maps generally indicate the upper and lower extent of the reservoir section or sections and the aerial extent as defined by faults or hydrocarbon contacts. Figure 15 shows an aerial section with the defined limits. The contour lines are lines of constant subsea depths. Figure 16 gives a cross section of a reservoir unit. The combination of the two representations of the unit(s) can be used to calculate the gross rock volume. Fault B

ounda

ry

Porosity Boundary

Fluid Contact

ry

unda

Bo Fault

Figure 15 Structure Contour Map.

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7

21

Heighest Elevation on Top Structure

To p

Contour Elevation (units ss)

Heighest Elevation on Base Structure

St R r Ro ese uctu re ck rvo Ba Vo ir se lu St m ru e c

tu

re

Hydrocarbon Water Contact Elevation

o

Area Contained by Contour

Figure 16 Reservoir cross section.

7

Figures 17 & 18 show an example of a top structure map and cross section of the Rough Gas field in the North Sea. 47/2 47/3 Completed Producers Gw C

Proposed Well Locations

C

C.I. = 50ft.

960

47/7 47/8

G

0

w

9 95500 00

x Abandoned Wells

955000 8 95 50 8 94 00 94 50 93 00 8 8 8 93 8 B 250 9 A2 00 8 92 8 A

47/8-1x 8

A

8

8 A A5

A A4

A

Platform A A3

9100

A6

93

00 93 50 92 9200

50

91

50

x 47/8-2

Figure 17 Top Sand Structure Map Rough Gas Field.

22

5

Introduction To Reservoir Engineering

Depth (ft) subsea 9000

A5

Unc

Rot

onf

orm

ity es onfo rmit y

lieg

Fault

9400

A2

A4

Unc

end

Fault

9200

A1

A3

Tentative hydrocarbon/ water contact

9600 9800 Carboniferous Sands

Figure 18 Schematic Cross Section of The Rough Field.

5

5.4 Reservoir Thickness

Another representation of the reservoir formations is the reservoir thickness map. Where the areal contour maps show the thickness normal to the plane of the reservoir the contours are called isopachs. When the thickness is mapped as a vertical thickness then the contour is called an isochore. Not all the reservoir thickness will contribute to fluid recovery and will include non-productive strata. Those contours which include these non-productive material are called gross reservoir isopach and those where non-productive material is excluded are called net reservoir isopach maps. Those intervals contributing to flow are termed pay. The ratio of net to gross, hn/ht , is an important aspect in reservoir evaluation. Figure 19 shows a net pay thickness isopach and the isopach map for the Rough field is shown in figure 20

75 0

150

125

Isopach C I 25 Units

100

7

Figure 19 Net Pay Thickness Isopach.

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23

47/2 47/3 GwC

140

130

Gw

C

120

0 11

0

10

A2

47/7 47/8

47/8-1 x

A5

A4 80

A1

0 11

100

90

A3

6 11

70

A6 x 47/8-2

Figure 20 Rough Field Isopach.

5

The isopach map can also be used to calculate reservoir volume. For example in figure 21 the area under a plot of net pay thickness vs. area contained within the contour provides a net pay volume. These plots can be generated for each section or rock type. The thickness plots for each section are called isoliths. 0

Net Pay Isopach Value

40

Area Enclosed = Net Rock Volume

80 120 140 180

OWC Area Contained by Contour

7

Figure 21 Hydrocarbon Volume From Net Pay Isopach.

5.5 Reservoir Porosity

The variation of porosity can also be represented . The average porosity, φ, in a well can be calculated from the thickness-weighted mean of the porosities 4 .

24

Introduction To Reservoir Engineering

m



φw =

∑φ h k =1

k n, k

hn















(4)

where φk is the average porosity derived from the log over a small thickness hn,k within the net pay thickness, hn. These values of porosity can then be plotted to generate an isoporosity map as illustrated in figure 22. The example of an isoporosity map for the Rough Field is shown in figure 23.

5

10

25

20

15

Porosity C I 5%

Figure 22 Iso Porosity Map.

7

47/2 47/3

G

w

C

C

Gw

x

A5

A

A1

A6

6%

A3

A4

10 % 8%

47/8-1

12%

47/7 47/8

14%

A2

47/8-2

x

7

Figure 23 Rough Field Iso Porosity Map. Insitute of Petroleum Engineering, Heriot-Watt University

25

5.6 Water Saturation, Sw

The water saturation in a reservoir is influenced by the characteristics of the reservoir rock and the location with respect to the position above the free water level near the oil-water or gas-oil contact (see section Reservoir Rock Properties Chapter 7). The average water saturation Sw,w , can be calculated in a similar way to porosity by calculating the volume weighted mean across the producing elements of the formation, the pay. m



Sw,w =

∑S k =1

w, k

φ k h n,k

φwh n













(5)

The values of Sw,w can be plotted and contours of constant saturation (isosaturation) presented. Figure 24.

Shale 15

20

25

30 35 40

WOC

4

Figure 24 Iso Saturation (sw) Map.

A more detailed description together with exercises are given in the mapping section of the geology module.

5.7 Formation Volume Factors Oil, Bo and Gas, Bg

These properties of the oil and gas which convert reservoir volumes to surface volumes, are generated from measurements made on fluid samples from the reservoir. They do not vary significantly across the reservoir when compared to the other rock related parameters. These parameters are covered in the gas properties and oil properties chapters. In some reservoirs where the formations are thick there is a compositional gradient over the depth. This variation in composition from heavier (less volatile components) to lighter components at the top results in a variation of the oil formation volume factor, Bo over the thickness. In such cases an average value based on values measured or calculated at depth would be a preferred value.

26

Introduction To Reservoir Engineering

5.8 The Recovery Factor, ER

The proportion of hydrocarbons recovered is called the recovery factor. This factor is influenced by a whole range of factors including the rock and fluid properties and the drive mechanisms. The variability of the formation characteristics, the heterogeneity can have a large influence on recovery. The development process being implemented and the geometries and location of wells again will also have a large influence. Calculating recovery therefore in the early stages is not feasible and many assumptions have to be included in such calculations. It is in this area that reservoir simulation can give indications but the quality of the calculated figure is limited by the sparse amount of quality data on which the simulation is based. The American Petroleum Institute6 has analysed the recoveries of different fields and correlations have been presented for different reservoir types and drive mechanisms. Figures 25 and 26 give the residual saturations and oil recovery efficiences for different drive mechanisms. The API also presents correlations for recoveries,ER, For sandstone and carbonate reservoirs with solution gas drive

ER, o

 φ (1 − Sw )  = 0.4185   Bob 

0.1611

 k     µob 

0.0979

(Sw )

0.3722

 pb     pa 

0.1741



(6)

For sandstone reservoirs with water drive

ER, o

 φ (1 − Sw )  = 0.54898   Boi 

0.0422

 k µ wi     µoi 

0.0770

p  a

(Sw )− o.1903  pi  − 0.2159

(7)

b refers to bubble point conditions, i is the initial condition and a, refers to abandonment pressure.

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27

2

5

10

20

30

40

50

60

70

80

95

98

RESIDUAL SATURATIONS 1.00

Sor In Water Drive Reservoirs

0.50

0.50

Sgr In Solution Gas Drive Reservoirs 0.10

0.10

0.05

0.05

−σ

0

+σ MEDIAN

Sor (OR Sgr) as Fraction of Total Pore Space

1.00

2

5

10

20

30

40

50

60

70

80

95

98

0

PERCENTAGE OF CASES LARGER THAN

Figure 25 Log - Probability Residual Oil Saturation For Water Drive and Solution Gas 6 Drive Reservoirs. (API )

5

OIL RECOVERY EFFICIENCY AT FIELD ABANDONMENT IN PERCENT OF OIL PLACE

2

10

20

30

40

50

60

70

80

95

98

RESIDUAL SATURATIONS

1.00

1.00

Water Drive Gas Cap Drive

0.50

0.50

Gas Cap Drive + Water Injection

0.10

0.10

Solution Gas Drive

0.05

0.05

0

+σ MEDIAN

−σ

2

5

10

20

30

40

50

60

70

80

95

98

0

PERCENTAGE OF CASES LARGER THAN

6

Figure 26 Log - Probability of Oil Recovery For Various Drive Mechanisms. (API )

28

Introduction To Reservoir Engineering

5.9 Production Capability

Another concept, isocapacity, is used to signify production capability. Isocapacity denotes equal values of permeability-net thickness product. This product can be mapped instead of permeability. The figure 27 shows an isocapacity map where the absolute permeability has been obtained as an arithmetic average in the zone.

4 0.5

5

4

3

2

1

123

0.25

7

Figure 27 Isocapacity Map.

The permeability map for the Rough Field is given in figure 28

G

w

C

C

Gw

47/2

47/7 47/8

120 A2 100 80

47/8-1 x

A4

A5

Platform B

60 40

A3 0

A6 x 47/8-2

Contour Intervals 20 millidarcies

5

Figure 28 Rough Field Permeability Map.

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29

5.10 The Hydrocarbon Pore Volume Map

The hydrocarbon pore volume can be obtained by combining the net rock volume with a mean porosity and a mean hydrocarbon saturation. An alternative is the mapping of hydrocarbon thickness (HPT) at each well. HPT at a well in a given zone is: _

_

HPT = φ .hn . Sh











(8)

where: _

_

Sh = 1 − Sw Figure 29 gives an HPT map and the Rough Field HPT map is given in figure 30

12 11 0 10 14

15

14

13

13 12 10 0

11

9

7

Figure 29 Hydrocarbon Pore Thickness Map.

0 10

A2

9

8 A5

A4

7

A1

6 A3

5 4

A6

5

Figure 30 Rough Field Hydrocarbon Pore Thickness. 30

Introduction To Reservoir Engineering

6. OTHER APPRAISAL ROLES In building up the ‘picture’ to enable the reserves estimates and recoveries to be determined the reservoir engineer will be involved in an number of aspects. One of the most powerful tools is the production test. In a well test an exploration or appraisal well is converted to a short term producing well, with all the associated facilities put in place to handle the produced fluids and monitor fluid rates. A downhole pressure monitoring device is also located in the well. Figure 31. The well is flowed at a constant rate , and sometimes two rates as illustrated in figure 32a, a two rate test. The downhole pressure device responds to the production and pressure declines. After a short or longer time period depending on the nature of the test, the well is “shut in”, i.e. the flow is stopped. In the well the pressure builds up and eventually as monitored by the downhole pressure device, recovers to the original pressure. Figure 32b. It is in the analysis of the pressure drawn down and build up curves and the rates that the reservoir engineer is able to determine the flowability of the reservoir. If the flowing interval thickness is known, the permeability can be calculated. The presence of faults can also be detected. A considerable amount of reservoir data can be obtained from these well tests sometimes called DST’s ( drill stem tests). It has been the practise over recent years for the produced fluids to be flared since there is unlikely to be an infrastructure to collect these fluids. Now that companies are moving to a zero or reduced hydrocarbon emission policy the nature and facilities required for these tests are changing. A feature of the flaring approach is a public demonstration of the productivity of the well being tested.

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31

Surface casing

Production casing Production tubing Cement

Packer

Perforations Down hole pressure monitor

Figure 31 Production Test Assembly.

32

q bbls / day

Introduction To Reservoir Engineering

Flow 1

Flow 2

Well shut in

t

Pf. psig

Pi Pressure draw down Pressure build up

t

Figure 32 Production Test Analysis. Two Rate Test.

Well test analysis is a powerful reservoir engineering tool and is treated in depth in a subsequent module of the Petroleum Engineering course. The nature of the fluids is key to reservoir behaviour and also subsequent processing in any development. The collection and analysis of these fluids is an important role and is at the focus of PVT analysis. This topic is covered in Chapter 14 PVT Analysis. The pressure profile in a well is another important aspect of reservoir characterisation and can be used to identify fluid contacts. When used during the early stages of production it can be a powerful means of refining the structure and hydrodynamic continuity characteristics of the reservoir. This is covered in the next chapter. Like PVT analysis where the information is based on samples removed from the reservoir, core analysis is based on recovered core from the formation. Various tests on this material and its reaction to various fluids provides many of the reservoir engineering parameters important in determining the viability of a project. Core analysis also provides a cross check for indirect measurements made downhole. These core analysis perspectives are covered in chapters 7 and 8. It is clear from what we have discussed that reservoir engineering is an important function in the appraisal of the reservoir. The focus for this appraisal so far has concentrated on determining the characteristics and potential flow behaviour of a reservoir under development. Clearly there could be a whole range of possibilities with respect to the plan that could be used to develop the field. This development planning perspective is an important part of the reservoir engineers role. Again it is a team effort Insitute of Petroleum Engineering, Heriot-Watt University

33

involving the geological community who understand the ‘reservoir’ and the various engineers who have the responsibilities of designing and operating the hardware to enable production. An important part of any future development are the facilities that would be required for sustained production and its is therefore an important part of the appraisal stage to provide data for those who would have responsibility for good quality data predictions which will enable optimised facility design. In any project new data is always being generated. Indeed for a reservoir, its characteristics are unlocked over the whole lifetime of the project. The duration of the appraisal stage clearly is a techno economic decision related to the confidence to go ahead based on a good foundation of quality data and forecasts. Fine tuning can always be carried out but this is costly if this delays the development stage. It is important to identify and fill the gaps for the largest uncertainties, and having sufficient information to design a system which is safe and cost effective. The difficulty is making the decision on the data under which a line is drawn which defines the basis for field development design. In reservoir development the reservoir is always revealing its properties, indeed it is in the production phase that the true characteristics are revealed.

7 DEVELOPMENT PLANNING 7.1 Reservoir Modelling

Given appraisal well data, and test results the reservoir engineer can consider some alternative development plans, relying heavily on experience and insight. Since the 80’s computer based reservoir simulation has played a major role. The starting point will invariably be a reservoir map used to calculate reserves, but in addition use will be made of the material balance equation (chapter 15), together with some drive concepts (chapter 11), to predict reservoir behaviour. One of the problems faced in making predictions is to adequately take into account knowledge about geological trends and, although individual well models can be adjusted to reflect local conditions, there is no practical ‘desk calculator’ technique for using say, the material balance equation and well models to come up with a predictive reservoir performance. Displacement models such as those derived by Buckley and Leverett (chapter 18), mainly from observations in the laboratory, give some insight into reservoir behaviour but again do not significantly assist in allowing the engineer to study the effect of alternative development plans on a heterogeneous reservoir. With insight and ingenuity, the reservoir can be divided into a number of simple units that can be analysed by the traditionally available techniques but such an approach remains unsatisfactory. Over recent years the integration of geological and geophysical perspectives is contributing considerably to the ‘confidence’ in reservoir modelling.

7.2 Technoeconomics

For hydrocarbon accumulations found on dry land the traditional reservoir engineering techniques available for field development planning were, in fact, quite adequate. This is mainly so because land development operations offer a high degree of planning 34

Introduction To Reservoir Engineering

flexibility to oil companies and hence allow them to make optimal use of the latest information. In an offshore environment this is not the case; once platforms have been ordered most development options are closed. It is with respect to offshore field development planning that reservoir simulation models have found their greatest application potential.

7.3 Coping with Uncertainty

The challenge to the exploration & production business of the oil & gas industry is considerable. The looking for the “needle in the haystack” scenario is not too far from the truth, when compared to other industrial sectors. With the challenge of reserves being found in technically challenging areas and the oil price moving in response to political as well as demand scenarios, there is the need to define more accurately forecasts of production and recovery. Reducing uncertainty is the message of the current decade and not least in reservoir engineering and its related disciplines. It is clear from what we have overviewed in this chapter and the topics which will be covered in the subsequent chapters that there are many parameters which contribute to the viability of the various aspects of successful oil and gas production. It is also clear that the various forms of data required, the confidence in the absolute values vary according to the type, and therefore the final impact on the final result will vary according to the particular parameter. The following list summarises some of the principal uncertainties associated with the performance of the overall reservoir model. The type of data can for example be subdivided into two aspects “static” and “dynamic” data . Static Properties • Reservoir structure • Reservoir properties • Reservoir sand connectivity • Impact of faults • “thief” sands Dynamic Properties • Relative permeability etc • Fluid properties • Aquifer behaviour • Well productivity (fractures, welltype, condensate drop out etc.) The impact of each of these parameters will vary according to the particular field but it is important that the company is not ignorant of the magnitude of the contributing uncertainties, so that resources can be directed at cost effectively reducing specific uncertainties. Figure 33 illustrates an outcome which might arise from an analysis of various uncertainties for a particular field. It demonstrates for this particular field and at the time of analysis the impact of the various data has on the final project cost. Clearly in this case the aquifer behaviour uncertainties has the least impact whereas reservoir structure and well productivity uncertainties had the most significant. Another field would result in different impact perspectives, and therefore a different strategy to reduce overall project uncertainty would be required.

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35

Q

Reservoir area

P

Well production

Project Cost

Reservoir structure

Sand conectives Aquifer behaviour Fluid properties Relative permeabilities etc. Thief zones

Faults

-

Changes

+

Figure 33 Impact on a Project of Different Uncertainties

8 PRODUCTION OPERATIONS OPTIMISATION 8.1 The Development Phase

The development phase covers the period from the time continuous production starts until the production from the field stops i.e. abandonment. The decision when to stop production clearly is a techno-economic decision based to a large extent on the costs of the development. Low volume producers can be allowed to continue in an onshore development where well operating costs might be low but the high costs associated with for example in an expensive offshore operation sets a much higher economic limit for the decision to abandon a field. During the development phase Dake2 has identified a number of roles for the Reservoir Engineering which are targeted at optimising production. It is an irony that some of the best data is generated during the production phase. Through production the reservoir unveils more of its secrets. Some of these may cause modifications to the development, perhaps in defining new well locations. The nature of the hydrodynamic continuity of the reservoir is mainly revealed through pressure surveys run after a period of production. This may define zones not being drained and therefore modifications to the well completions might result. As production progresses fluid contacts rise and therefore these contacts need to be monitored and the results used to decide, for example, to recomplete a well as a result of, for example excessive water production. As is pointed out in the chapter on reservoir pressure, development wells before they are completed provide a valuable resource to the reservoir engineer to enable surveys of pressure to be run to provide a dynamic pressure-depth profile. 36

Introduction To Reservoir Engineering

8.2 History Matching

Throughout the production phase the comparison of the actual performance with that predicted during the appraisal stage and more recent predictions is made. It is during this stage that the quality of the reservoir simulation model comes under examination. The production pressure decline is compared to that predicted and the reservoir simulation model adjusted to match. This process is called history matching. Clearly if the simulation cannot ‘predict’ what has happened over the recent past it cannot be used with much confidence to forecast the future! More simple approaches not requiring the resources of a complex simulator can also be used to up date early predictions, for example material balance studies. Once production has been obtained, the additional data becomes available and makes an important contribution to the refining of the initial reserves estimates. Two techniques historically used are decline curve analysis and material balance studies. In material balance studies, the pressure-volume behaviour of the entire field is studied assuming an infinite permeability for the reservoir. By assuming an initial oil-in-place from volumetric calculations, the pressure is allowed to decline following fluid withdrawal. This decline is matched against the observed pressure behaviour and, if necessary, the original oil-in-place figure is modified until a match is obtained. In the presence of a water drive, additional variables are included by allowing water influx into the ‘tank’. Water influx is governed by mathematical relationships such as van Everdingen and Hurst (These concepts are covered in Chapters 11, 12, and 13 MB/MB Applications and Water Influx). Decline curves are plots of rate of withdrawal versus time or cumulative withdrawal on a variety of co-ordinate scales. Usually a straight line is sought through these observations and extrapolated to give ultimate recovery and rates of recovery. Decline curves only use rates of withdrawal and pay relatively little attention to the reservoir and flowing pressures. A change in the mode of operation of the field could change the slope of the decline curve; hence, this is one of the weaknesses of this technique. A noteworthy feature of these two approaches is that the engineer in fact ‘fits’ a simple model to observe data and uses this model to predict the future by extrapolation. As more data becomes available the model gets ‘updated’ and predicted results are adjusted. Decline curve analysis has not been used to the same extent as in the 60’s and 70’s. With the power of computing and the efforts made to integrate geological understanding , the physics of the flow and behaviour of rock and fluid systems into reservoir simulation, the ‘fitting” and the uncertainty of earlier methods are being superseded by integrated reservoir simulation modelling. The routine company function will generate the need for on going production profile updates. The generation of these is generally the responsibility of the reservoir engineer, who might chose simple analytical approaches to the more costly reservoir simulation methods.

8.3 Phases of Development

During the development there are a number of phases. Not all of these phases may be part of the plan. There is the initial production build up to the capacity of the facilInsitute of Petroleum Engineering, Heriot-Watt University

37

ity as wells are brought on stream. There is the plateau phase where the reservoir is produced at a capacity limited by the associated production and processing facilities. Different companies work with different lengths of the plateau phase and each project will have its own duration. There comes a point when the reservoir is no longer able to deliver fluids at this capacity and the reservoir goes into the decline phase. The decline phase can be delayed by assisting the reservoir to produce the fluids by the use of for example ‘lifting’ techniques such as down-hole pumps and gas lift. The decline phase is often a difficult period to model and yet it can represent a significant amount of the reserves. These phases are illustrated in figure 34

Production rate

Plateau phase Artificial lift Decline phase

Build up phase Economic limit Time - years

Figure 34 Phases of Production.

The challenge facing the industry is the issue of the proportion of hydrocarbons left behind. The ability to extract a greater proportion of the in-place fluids is obviously a target to be aimed at and over recent years recoveries have increased through the application of innovative technology. Historically there have been three phases of recovery considered. Primary recovery, which is that recovery obtained through the natural energy of the reservoir. Secondary recovery is considered when the energy is supplemented by injection of fluids, for example gas or water, to maintain the pressure or partially maintain the pressure. The injected fluid also acts as a displacing fluid sweeping the oil to the producing wells. After sweeping the reservoir with water or gas there will still be remaining oil; oil at a high saturation where the water for a range of reasons, for example; well spacing, viscosity, reservoir characteristics to name just a few, has by-passed the oil. The oil which has been contacted by the injected fluid will not be completely displaced from the porous media. Because of characteristics of the rock and the fluids a residual saturation of fluid is held within the rock. Both of these unrecovered amounts, the by-passed oil and the residual oil are a target for enhanced recovery methods, EOR. Much effort was put into enhanced oil recovery (EOR) research up until the mid seventies. Sometimes it is termed tertiary recovery. When the oil price has dropped the economics of many of the proposed methods are not viable. Many are based on 38

Introduction To Reservoir Engineering

the injection of chemicals which are often oil based. The subject of EOR has not been forgotten and innovative methods are being investigated within the more volatile oil price arena. Figure 35 gives a schematic representation of the various phases of development and includes the various improved recovery methods. More recently a new term has been introduced called Improved Oil Recovery (IOR). IOR is more loosely defined and covers all approaches which might be used to improve the recovery of hydrocarbons in place. Clearly it is not as specific as EOR but provides more of an achievable target than perhaps some of the more sophisticated EOR methods. As we have entered into the next millennium it is interesting to note that a number of major improved recovery initiatives are being considered particularly with respect to gas injection. One perspective which make a project more viable is that of the disposal of gas for example which is an environmental challenge in one field can be the source of gas for another field requiring gas for a gas injection improved oil recovery process. Primary Recovery Natural Flow

Artifical Lift

Pump gas lift etc.

Secondary Recovery Pressure Maintenance

Natural Flow

C O N V E N T I O N A L

Water, gas injection

Tertiary Recovery E O R

Thermal

Gas

Steam In-situ combustion.

Hydrocarbon miscible, CO2 N2 immiscible gas

Chemical

Microbial

Polymer surfactant/ polymer

Figure 35 Oil Recovery Mechanisms.

9. THE UNIQUENESS OF THE RESERVOIR As we have discussed the role of the reservoir engineer in combination with other disciplines is to predict the behaviour of the reservoir. Whereas in the early years of oil exploration little attention was paid to understanding the detailed characteristics of the reservoir, it is now recognized that detailed reservoir properties associated with often complex physical and chemical laws determine field behaviour. The unlocking of these characteristics and understanding the laws enable engineering plans to be put in place to ensure optimised developments are implemented. This is schematically illustrated in figure 36. Insitute of Petroleum Engineering, Heriot-Watt University

39

Reservoir Behaviour Development Plan

Reservoir Description Unique Dynamic and Static

Figure 36 Relationship between Reservoir Description, and Reservoir Behaviour.

At one extreme for example in a blow - out situation, a reservoir produces in an uncontrolled manner only restricted by the size of the well through which is producing. Optmised development however based on a thorough understanding of the reservoir enables the reservoir to be produced in a controlled, optimised manner. In many other industries the effort expended on one project can be utilised in engineering a duplicate or a similar size unit elsewhere. Such opportunities are not possible in the engineering of a reservoir. Reservoirs are unique in many aspects. The composition of the fluids are unique, the rock characteristics and related properties are unique, the size and shape are unique and so on. From our perspective this reservoir description is dynamic as the reservoir over a period of time gives up its secrets. From the reservoir’s perspective however the description is static, except with the changes resulting from the impact of fluid production or injection. The challenge to those involved is reducing the time it takes for our dynamic description to match, our static description known only to the reservoir or whoever was responsible for its formation! The answer perhaps is more of a philosophical nature. The reality is shown in figure 37 where the top structure map for a North Sea gas field with a ten year gap shows the impact of knowledge gained from a number of wells as against that interpreted from the one well. Considerable faulting is shown not as a result of major geological a activity over the ten years but knowledge gained from the data associated with the new wells.

40

Introduction To Reservoir Engineering

2°00

2°10

2°20

100

0

00

200 0

21

53°10

SHELL/ESSO 49/26

2200

20

21

00

00

Gas /water contact Depths in metres scale 1 100,000

21

00

49/26.1

53°05

00

12

53°05

53°10

AMOCO 49/27

0 80

100

0

00

20 10 00

00

00

20

20

0 210

20 100 00 0

10

00

100

0

2000

2°00

2°20

Present interpretation of Leman Gas-field, showing contours on top of Rotliegendes in feet below sea-level

Figure 37 (a) The Leman Field as it Appeared to be When The Exploration Well Was The Leman field as it appeared to be when the exploration well was drilled Drilled.

2°00

2°10

53°10

2°20

2°30 53°10

SHELL/ESSO 49/26 AMOCO 49/27

Depth in feet Miles 0 1 0 1 2 KMS 70 00

Gas /water contact A permanent platform

63 00

00 63

53°05

53°05 6400 6300

620

0

69

00

610

0

6900

690

00

69

70

53°00

2°00

69

00

6300 6 90

0

0 64 0

00

6300 6400

2°10

0

53°00

2°20

2°30

Present interpretation of Leman Gas-field, showing contours on top of Rotliegendes in feet below sea level.

Leman field ten years discovery Figure 37b Leman Field Tenafter Years After Discovery

The coverage of the reservoir has also changed effecting the equity associated with the blocks. This illustrates the early benefits to be gained from drilling a number of exploration wells. These equity agreements, are called unitisation agreements and such agreements are shortened when good quality and comprehensive reservoir description data is available. Clearly there can never be sufficient description, however the Insitute of Petroleum Engineering, Heriot-Watt University

41

economics of project management will determine when decisions have to be taken based on description to date. The value of extra information has to be balanced by the cost of delay in going ahead with a project.

10. CONCLUSION In order to accomplish these objectives the Petroleum Reservoir Engineer should have a broad fundamental background both theoretically and practically in the basic sciences and engineering. The basic areas are: (i) The properties of petroleum reservoir rocks (ii) The properties of petroleum reservoir fluids (iii) The flow of reservoir fluids through reservoir rock (iv) Petroleum reservoir drive mechanisms It is also important that the Petroleum Reservoir Engineer has a thorough basic understanding in general, historical and petroleum geology. The influence of geological history on the structural conditions existing in a reservoir should be known and considered in making a reservoir engineering study. Such a study may also help to identify and characterise the reservoir as to its aerial extent, thickness and stratification and the chemical composition, size distribution and texture of the rock materials. In his latest text, Dake2 comments on some of the philosophy of approach to reservoir engineering, and identifies the importance of pinning down interpretation and prediction of reservoir behaviour to well grounded laws of physics. Reservoir forecasting has moved on considerably since wells were drilled with little interest and concern into the production and forecasting of what was happening in the reservoirs thousands of feet below. The approach to coping with uncertainty as jokingly reflected in the cartoon below, (Figure 38) is no longer the case as sophisticated computational tools enable predictions to be made with confidence and where uncertainty exists the degree of uncertainty can be defined.

42

Introduction To Reservoir Engineering

"We feed the geological data for the area, the computer produces a schematic topological overview designating high probability key points, then we stick the printout on the wall and Lever throws darts at it."

Figure 38 A Past Approach to Uncertainty!

REFERENCES 1. Craft, B.C. and Hawkins, M.F. Applied Reservoir Engineering, Prentice-Hall Inc. 1959 2. Dake, L.P., The Practise of Reservoir Engineering. Elsevier. 1994 3. Society Of Petroleum Engineers. Reserves Definitions 1995. 4. Chierici,G.L. Principles of Petroleum Reservoir Engineering. Vol 1 Springer Verlag 1994 5. Hollois,A.P. Some petroleum engineering considerations in the change over of the Rough Gas field to the storage mode. Paper EUR 295 Proc Europec. 1982, pg 175 6. API. A Statistical Study of the Recovery Efficiency. American Petroleum Institute. Bull D14, 1st Edition ,1967 7. Archer,J.S. and Wall,C.G. Petroleum Engineering Principles and Practise, Graham and Trotman ,1986.

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43

Reservoir Pressures and Temperatures

CONTENTS 1 INTRODUCTION 2 ABNORMAL PRESSURES 3 FLUID PRESSURES IN HYDROCARBON SYSTEMS 4 PRESSURE GRADIENTS AROUND WATER- OIL CONTACT 5. TECHNIQUES FOR PRESSURE MEASUREMENT 6. RESERVOIR TEMPERATURE





LEARNING OBJECTIVES Having worked through this chapter the Student will be able to: • Having worked through this chapter the student will be able to: • Define the terms; lithostatic pressure, hydrostatic pressure and hydrodynamic pressure. • Draw the normal hydrostatic pressure gradient for water systems. • Define normal pressured reservoirs, overpressured reservoirs and underpressured reservoirs • Describe briefly and sketch the pressure gradients associated with overpressured and underpressured reservoirs. • Describe briefly , sketch and present equations for the pressures in a water supported oil and gas bearing formation. • Illustrate how a downhole formation pressure device can be used to discriminate permeability layers after production has commenced. • Comment briefly what geothermal gradient is in a reservoir where flow processes occur at constant reservoir temperature.





Reservoir Pressures and Temperatures

1. INTRODUCTION Determining the magnitude and variation of pressures in a reservoir is an important aspect in understanding various aspects of the reservoir, both during the exploration phase but also once production has commenced. Oil and gas accumulations are found at a range of sub-surface depths. At these depths pressure exists as a result of the depositional process and from the fluids contained within the prous media. These pressures are called lithostatic pressures and fluid pressures. These pressures are illustrated in figure 1. The lithostatic pressure is caused by the pressure of rock which is transmitted through the sub-surface by grain-to grain contacts. This lithostatic or sometimes called geostatic or overburden pressure is of the order of 1 psi/ft. The lithostatic pressure gradient varies according to depth, the density of the overburden, and the extent to which the rocks are supported by water pressure. If we use this geostatic pressure gradient of 1 psi/ft. then the geostatic pressure Pov, in psig at a depth of D feet is pov = 1.0D















(1)

The geostatic pressure is balanced in part by the pressure of the fluid within the pore space, the pore pressure, and also by the grains of rock under compaction. In unconsolidated sands, loose sands, the overburden pressure is totally supported by the fluid and the fluid pressure Pf is equal to the overburden pressure Pov . In deposited formations like reservoir rocks the fluid pressure is not supporting the rocks above but arises from the continuity of the aqueous phase from the surface to the depth D in the reservoir. This fluid pressure is called the hydrostatic pressure. The hydrostatic pressure is imposed by a column of fluid at rest. Its value depends on the density of the water ρw, which is affected by salinity. In a sedimentary basin, where sediment has settled in a region of water and hydrocarbons have been generated and trapped, we can expect a hydrostatic pressure. For a column of fresh water the hydrostatic pressure is 0.433 psi/ft. For water with 55,000 ppm of dissolved salts the gradient is 0.45 psi/ft; for 88,000 ppm of dissolved salts the gradient is about 0.465 psi/ft. Its variation with depth is given by the equation. Pf = ρwDg















(2)

where g is the acceleration due to gravity. There is another fluid pressure which arises as a result of fluid movement and that is called the hydrodynamic pressure. This is the fluid potential pressure gradient which is caused by fluid flow. This however does not contribute to in-situ pressures at rest.

Institute of Petroleum Engineering, Heriot-Watt University



Depth (Ft.)

14.7 0

Pressure (psia)

FP

GP Overpressure

Overburden Pressure (OP)

Normal

Underpressure

(FP = Fluid Pressure, GP = Grain Pressure)

Figure 1 Gives the relationship between the lithostatic pressure and the hydrostatic 1 pressure.

Fluid pressure in hydrocarbon accumulations are dictated by the prevailing water pressure in the vicinity of the reservoir. In a normal situation the water pressure at any depth is:

dP Pw =   x D + 14.7psia  dD  water









(3)

where dP/dD is the hydrostatic pressure gradient This equation assumes continuity of water pressure from the surface and constant salinity. In most cases even though the water bearing sands are divided between impermeable shales, any break of such sealing systems will lead to hydrostatic pressure continuity, but the salinity can vary with depth. Reservoirs whose water pressure gradient when extrapolated to zero depth give an absolute pressure equivalent to atmospheric pressure are called normal pressured reservoirs.

EXERCISE 1 If the average pressure gradient in a region is 0.47 psi/ft, calculate the pore pressure in a normally pressurised formation at 7400ft. Convert the pressure from psi to KPa, then express the pressure in MPa. What is the pressure gradient in KPa/m?



Reservoir Pressures and Temperatures

2. ABNORMAL PRESSURE Under certain conditions, fluid pressures may depart substantially from the normal pressure. Overpressured reservoirs are those where the hydrostatic pressure is greater than the normal pressure and underpressured reservoirs are below normal pressure. Figure 1. They are called abnormal pressured reservoirs and can be defined by the equation:

dP Pw =   x D + 14.7 psia + C  dD  water







(4)

where C is a constant, being positive for overpressured and negative for an underpressured system. For abnormally pressured reservoirs, the sand is sealed off from the surrounding strata so that there is not hydrostatic pressure continuity to the surface. Conditions which cause abnormal fluid pressure in water bearing sands have been identified by Bradley 2 and include (Figure 2): FP-Too High Upthrust (a)

(b)

Original Deposition

Dense Shale Reservoir

Shale deposited too quickly to allow fluid equilbrium

North Sea (c)



Glacier Normal Surface

Greenland 3 km thick 1300 psi/1000 m ice

Figure 2 Causes of overpressurring

• Thermal effects, causing expansion or contraction of water which is unable to escape ; an increase in temperature of 1˚F can cause an increase of 125 psi in a sealed fresh water system.

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• Rapid burial of sediments consisting of layers of sand and clay. Speed of burial does not allow fluids to escape from pore space. • Geological changes such as uplifting of the reservoir, or surface erosion both of which result in the water pressure being too high for the depth of the burial. The opposite occurs in a down thrown reservoir. • Osmosis between waters having different salinity, the sealing shale acting as a semi-permeable membrane. If the water within the seal is more saline than the surrounding water, the osmosis will cause a high pressure and vice versa. Overpressured reservoirs are common in Tertiary deltaic deposits such as the North Sea, Niger delta and the Gulf Coast of Texas. In the North Sea one mechanism for overpressure is the inability to expel water from a system of rapidly compacted shales. With abnormally pressured reservoirs a permeability barrier must exist, which inhibit pressure release. These may be lithological or structural. Common lithological barriers are evaporates and shales. Less common are the impermeable carbonates and sandstones. Structure permeability barriers may result from faults which, in some cases, seal. The subject on of abnormal pressures is covered more fully in the Geology Module If reservoirs are all normal pressured systems then the pressure gradient for these reservoirs would be virtually all the same, other than from the influence of salinity. The figure below shows the water pressure gradients for a number of reservoirs in the North Sea and indicates the significant overpressuring in this region. Often these overpressuring show regional trends. For example the fields depicted in figure 3 show an increase in abnormal pressure in the south east direction. Clearly if all these reservoirs were normally pressured then the pressure depths values would lie on the same gradient line with a zero depth pressure value of atmospheric pressure.



Reservoir Pressures and Temperatures

8,000

Statfjord OWC

Brent OWC

9,000

Thistle OWC

Cormorant OWC 4

Subsea Depth (Feet)

10,000

11,000

1

2

Heather OWC

Ninian OWC

3 Lyell 5

12,000

Alwyn N.W. Alwyn S.W> Ninian

13,000

Note:

Water gradient lines drawn through known or projected oil/water contacts

5000

6000

7000

8000

9000

10,000

Pressure, psig

3

Figure 3 Examples of overpressured reservoirs in the North Sea

3. FLUID PRESSURES IN HYDROCARBON SYSTEMS Pressure gradients in hydrocarbon systems are different from those of water systems and are determined by the oil and gas phase in-situ specific gravities, ρo and ρg of each fluid. The pressure gradients are a function of gas and oil composition but typically are:

 dP  = (0.45 psi / ft)  dD  water









 dP  = (0.35 psi / ft)  dD  oil









 dP  = (0.08 psi / ft)  dD  gas













(5) (6)

Institute of Petroleum Engineering, Heriot-Watt University

(7) 

For a reservoir containing both oil and a free gas cap a pressure distribution results, as in the Figure 4 As can be seen, the composition of the respective fluids gives rise to different pressure gradients indicated above. These gradients will be determined by the density of the fluids which result from the specific composition of the fluids. Depth (Ft.) 13

8500

12

Depth (Ft.)

8600

11 10 9 Gas-Oil Contact

0.17 psi/ft ρf = 0.39 gm/cc 8

7

6

0.29 psi/ft ρf = 0.67 gm/cc 5

8700

Oil-Water Contact 4

0.47 psi/ft ρf = 1.09 gm/cc

3

8800 4000

2 1

4050

4100

4150

Formation Pressure (PSI)

Figure 4 Pressure distribution for an oil reservoir with a gas cap and an oil-water contact.

The nature of the pressure regime and the position and recognition of fluid contacts are very important to the reservoir engineer in evaluating reserves, and determining depletion policy. The data used for these fluid contacts comes from:

(i) (ii) (iii) (iv) (v) (vi) (vii)

Pressure surveys Equilibrium pressures from well tests Flow of fluid from particular minimum and maximum depth Fluid densities from reservoir samples Saturation data from wireline logs Capillary pressure data from cores Fluid saturation from cores

EXERCISE 2 If the pressure in a reservoir at the OWC is 3625 psi, calculate the pressure at the top if there is a 600ft continuous oil column. If a normal pressure gradient exists outwith the reservoir, calculate the pressure differential at the top of the reservoir. Redo the calculations for a similar field, but this time containing gas.



Reservoir Pressures and Temperatures

4. PRESSURE GRADIENTS AROUND THE WATER-OIL CONTACT Water is always present in reservoir rocks and the pressure in the water phase Pw and the pressure in the hyrocarbon phase Po are different . If P is the pressure at the oil/water contact where the water saturation is 100%, then the pressure above this contact for the hydrocarbon and water are : Po = P - ρogh













(8)

Pw = P - ρwgh













(9)

The difference between these two pressures is the capillary pressure Pc: see Chapter 8. In a homogenous water-wet reservoir with an oil-water contact the variation of saturation and phase pressure from the water zone through the capillary transition zone into the oil is shown in Figure 5). In the transition zone the phase pressure difference is given by the capillary pressure which is a function of the wetting phase saturation. (Chapter 8). Oil Zone

Sw h=

Vertical Depth D

Oil Phase Pressure po = pFWL - ρogh Oil Gradient

Capilliary Transition Zone

pc

pc (Sw) ∆ρg

WOC

Water Gradient

FWL

(pc = o) Water Phase Pressure pw = pFWL - ρwgh

Water Zone 0

Swc



1

pFWL

Water Saturation, Sw

Pressure, P

Figure 5 Pressure Gradients around the Water-Oil Contact

Pc = Po - Pw













(10)

at hydrostatic equilibrium Pc(Sw) = ∆ρgh ∆ρ = ρw-ρo h = height above free water level

Institute of Petroleum Engineering, Heriot-Watt University



The free water level, FWL, is not coincident with the oil-water contact OWC. The water contact corresponds to the depth at which the oil saturation starts to increase from water zone. The free water level is the depth at which the capillary pressure is zero. The difference in depth between the oil-water contact and the free water level depends on the capillary pressure which in turn is a function of permeability, grain size etc. Providing the phase is continuous the pressures in the respective phases are: Po = PFWL - ρogh













(11)

Pw = PFWL - ρwgh













(12)

On the depth-pressure diagram the intersection of the continuous phase pressure line occurs at the free water level.

5. TECHNIQUES FOR PRESSURE MEASUREMENT Earlier tests for vertical pressure logging have been replaced by open-hole testing devices that measure the vertical pressure distribution in the well, and recover formation samples. One such device which was introduced in the mid seventies which has established itself in reservoir evaluation is the repeat formation tester RFT (Schlumberger trade name). It was initially developed as a device to take samples. Over the years however its main application is to provide pressure -depth profiles over reservoir intervals. The device places a probe through the well mud cake and allows small volumes of fluid to be taken and pressure measurements to be made (Figure 6). It can only be operated therefore in an open hole environment. The unit can be set at different locations in the well and the pressure gradient thereby obtained. This device has been superseded by different tools provided by a number of wireline service providers. The principle is the same of measuring with a probe in open hole the pressure depth profile.

10

Reservoir Pressures and Temperatures

Packer

Mud Cake Packer Filter

Flow Line Equalising Valve (To Mud Column)

Piston Pressure Guage

Formation

Flow Line Chamber 1

Probe Closed

Chamber 2

Seal Valve to Upper Chamber

Seal Valve to Upper Chamber

Probe Open and Sampling

Figure 6 Original Schematic of the RFT Tool

These open hole pressure measurements have proved valuable at both the appraisal stage and can be used to establish fluid contacts. It has also proved particularly valuable during the development stage in accessing some of the dynamic characteristics of the reservoir. The pressure changes in different reservoir layers resulting from production reveal the amount of interlayer communication and these pressure measurements can be a powerful tool in understanding the characteristics of the reservoir formation. By comparing current pressure information with those obtained prior to production, important reservoir description can be obtained which will aid reservoir depletion, completion decisions and reservoir simulation. In 1980 Amoco3 published a paper with respect to the Montrose Field in The North Sea which illustrates the application of pressure-depth surveys. Figure 7 shows the pressure depth survey in 1978 of a well after production since mid 1976. Only the top 45ft of the 75ft oil column had been perforated. The initial pressure gradient indicates the oil and water gradients at the condition of hydrostatic equilibrium. The second survey shows a survey after a period of high production rate, and reveals the reservoir behaviour under dynamic conditions. The various changes in slope in the pressure profile reveal the partial restricted flow in certain layers. Similar surveys in each new development wells (Figure 8) show the similar profiles and enable the detailed layered structure of the reservoir to be characterised which is important for reservoir simulation purposes.

Institute of Petroleum Engineering, Heriot-Watt University

11

Gr% 0 100

Sw% 100 0

Reservoir pressure - psig

θ% 0 50

2500

3000

3500

4000

Top paleocene

Layer 1 Layer 2

True vertical subsea depth - metres

2500

8100

Original pressure gradient

8200

Layer 3

8300

2550 8400

Layer 4

8500

2600

8600 Layer 5

2650

8700

True vertical subsea depth - feet

Perforations

8800 14



26

24 18 22 16 20 Reservoir pressure - MPa

Figure 7 RFT Pressure Survey in Development Well of Montrose Field 3.

Reservoir pressure - psig 3000 3400 3200 A15 A11 A17 A18

2500

A6

A8

Original pressure gradient

8100 8200 8300

2550

8400 8500

2600

8600

2650

symbol

2700



8000

18

?Well number 22/17-A6 A8 A11 A15 A17 A18

20

Date 05/04/77 27/01/78 20/12/77 15/08/78 02/11/78 28/03/79

26 22 24 Reservoir pressure - MPa

8700 8800

True vertical subsea depth - feet

True vertical subsea depth - metres

2450

8900 28

9000

Figure 8 RFT Pressure Syrveys on a number of Montrose Wells3. 12

Reservoir Pressures and Temperatures

6. RESERVOIR TEMPERATURE

The temperature of the earth increases from the surface to centre. The heat flow outwards through the Earth’s crust generates a geothermal gradient, gc. This temperature variation conforms to both a local and regional geothermal gradient, resulting from the thermal characteristics of the lithology and more massive phenomenon associated with the thickness of the earth’s crust along ridges, rifts and plate boundaries. In most petroleum basins the geothermal gradient is of the order of 1.6˚F/100 ft. (0.029 K/m) The thermal characteristics of the reservoir rock and overburden give rise to large thermal capacity and with a large surface area in the porous reservoir one can assume that flow processes in a reservoir occur at constant reservoir temperature. The local geothermal gradient will be influenced by associated geological features like volcanic intrusions etc. The local geothermal gradient can be deduced from wellbore temperature surveys . However they have to be made under stabilised conditions since they can be influenced by transient cooling effects of circulating and injected fluids. During drilling the local thermal gradient can be disturbed and by analysis of the variation of temperature with time using a bottom hole temperature (BHT) gauge the local undisturbed temperature can be obtained. Without temperature surveys the temperature at a vertical depth can be estimated using a surface temperature of 15 oC (60 oF) at a depth D. T(D) = 288.2 + gcD (K)

Solutions to Exercises EXERCISE 1 If the average pressure gradient in a region is 0.47 psi/ft, calculate the pore pressure in a normally pressurised formation at 7400ft. Convert the pressure from psi to KPa, then express the pressure in MPa. What is the pressure gradient in KPa/m? Multiply KPa by 0.145 to get psi. 1 US foot = 0.3048m. SOLUTION Pressure in formation = 0.47 * 7400 = 3478 psi Converting to KPa = 3478 / 0.145 = 23986 Kpa Converting to MPa = 23986 / 1000 = 23.99 MPa Pressure gradient = 0.47 psi/ft = (0.47 / 0.145) KPa/ft = 3.2414 KPa/ft = (3.2414 /0.3048) KPa/m = 10.63 KPa/M

Institute of Petroleum Engineering, Heriot-Watt University

13

EXERCISE 2 If the pressure in a reservoir at the OWC is 3625 psi, calculate the pressure at the top if there is a 600ft continuous oil column. If a normal pressure gradient exists outwith the reservoir, calculate the pressure differential at the top of the reservoir. Redo the calculations for a similar field, but this time containing gas. SOLUTION Typical pressure gradients are (psi/ft): Water – 0.45 Oil – 0.35 Gas – 0.08 Pressure at seal = 3625 - (600*0.35) = 3415 psi To calculate the pressure differential across seal, look at fluid gradient differential from OWC to seal 600ft above… Differential = (0.45-0.35) * 600 = 60 psi If the reservoir is gas then the differential becomes… (0.45 – 0.08) * 600 = 222 psi higher in the reservoir than surrounding area

REFERENCES 1. Dake,L.P. Fundamentals of Reservoir Engineering. Elsevier 1986 2. Bradley,J.S. Abnormal Formation Pressure. The American Association of Petroleum Geologists Bulletin. Vol 59, No6, June 1975 3. Bishlawi,M and Moore,RL: Montrose Field Reservoir Management. SPE Europec Conference, London,(EUR166) Oct.1980

14

Reservoir Fluids Composition

CONTENTS 1 INTRODUCTION 2 HYDROCARBONS 2.1 Chemistry of Hydrocarbons 2.2 Alkanes or Paraffinic Hydrocarbons 2.3 Isomerism 2.4 Unsaturated Hydrocarbons 2.5 Napthene Series 2.6 Aromatics 2.7 Asphalts 3 NON-HYDROCARBON COMPOUNDS 4 COMPOSITIONAL DESCRIPTION FOR RESERVOIR ENGINEERING 4.1 Definitions of Composition in Reservoir Engineering 5 GENERAL ANALYSIS 5.1 Surface Condition Characterisation 5.2 Refractive Index 5.3 Fluorescence of Oil

LEARNING OBJECTIVES Having worked through this chapter the Student will be able to: • Describe briefly the origin, nature and appearance of petroleum fluids • Be aware that the principal components of petroleum fluids to be hydrocarbons. • Draw a diagram illustrating the classification of hydrocarbons and to identify; paraffin’s (alkanes ), aromatics and cyclic aliphatics ( napthas). • List the non- hydrocarbon compounds which might be present in small qualities in reservoir fluids. • Define the black oil model description of the composition of a reservoir fluid. • Explain briefly what PNA analysis is and its application. • Describe briefly the concept of pseudo components in fluid composition characterization. • Be aware of general analysis descriptors for petroleum fluids e.g. oAPI, refractive index and flourescence. • Be able to calculate the API gravity given the specific gravity • Calculate given the prerequisite data proved, probable and possible reserves. • Describe in general terms reserve estimation.



Reservoir Fluids Composition

1 INTRODUCTION Petroleum deposits vary widely in chemical composition and depending on location have entirely different physical and chemical properties. The very complex characteristics are evident from the many products which can be produced from oil and gas. What is petroleum? Petroleum is a mixture of naturally occurring hydrocarbons which may exist in the solid, liquid or gaseous states, depending on the conditions of temperature and pressure to which it is subjected.1 Petroleum deposits occurring as a gaseous state are termed natural gas, in the liquid state as petroleum oil or crude oil and in the solid state as tars, asphalts and waxes. For a mixture with small molecules it will be a gas at normal temperature and pressure (NTP). Mixtures containing larger molecules will be a liquid at NTP and larger molecules as a solid state, for example, tars and asphalts. The exact origin of these deposits is not clear but is considered to be from plant, animal and marine life through thermal and bacterial breakdown. The composition of crude oil consists mainly of organic compounds, principally hydrocarbons with small percentages of inorganic non-hydrocarbon compounds. such as carbon dioxide, sulphur, nitrogen and metal compounds. The hydrocarbons may include the lightest (C1 methane ) to napthenes and polycyclics with high molecular weights. The appearance varies from gases, through very clear liquids, yellow liquids to a dark, often black, highly viscous material, the variety obviously being a function of composition. Although the principal elements are carbon (84-87%), and hydrogen (11-14%), crude oil can vary from a very light brown liquid with a viscosity similar to water to a very viscous tar like material . Water is always present in the pore space of a reservoir, since the original depositional environment for the rocks was water. This water has subsequently been displaced by the influx of hydrocarbons but not totally since surface tension forces acting in the rock pore space cause some of the water to be retained. For reservoir engineering purposes the description of the composition is an important characterisation parameter for the determination of a range of physical parameters important in various reservoir volumetric and flow calculations. It is not the concern of the reservoir engineer to determine the composition with respect to understanding the potential to separate the material to a range of saleable products. For this reason therefore simplistic characterisation approaches are used. The two compositional characterisation approaches used are the compositional model and the black oil model. The basis of the compositional model is a multicomponent description in terms of hydrocarbons and the black oil model is a two component description in terms of produced oil, stock tank oil and produced gas, solution gas. The compositional model is the topic covered in this chapter and the black oil model is covered in the liquid properties chapter. Institute of Petroleum Engineering, Heriot-Watt University



2 HYDROCARBONS 2.1 Chemistry of Hydrocarbons

The compositional model uses hydrocarbons as the descriptor since hydrocarbons represent the largest proportion in petroleum fluids. It is important to review briefly the chemistry of hydrocarbons. The hydrocarbon series is represented in figure 1 below Hydrocarbons Aliphatic Alkanes

Alkenes

Aromatics Alkynes

(Paraffins)

Cyclic Aliphatics (Napthenes)

Figure 1 Classification of Hydrocarbon.

The hydrocarbons divide into two groupings with respect to the arrangement of the carbon molecules and the bonds between the carbon molecules. The arrangement of the molecules are open chain or cyclic and the bonds between the carbon are saturated (single) bonds or unsaturated or (multiple) bonds.

2.2 Alkanes or Paraffinic Hydrocarbons

The largest series is the alkanes or paraffins which are open chain molecules with saturated bonds. Carbon has a valance of four and therefore the formula for these compounds is CnH2n+2. These saturated hydrocarbons include all the paraffins in which the valence of the carbon atoms is satisfied by single covalent bonds. This type of structure is very stable. Unsaturated hydrocarbons are those where the valence of some of the carbon atoms is not satisfied with single covalent bonds so they are connected by two or more bonds which make them less stable and more prone to chemical change. The paraffin series begins with methane (CH4), and its basic formula is CnH2n+2. Pentane to pentadecane are liquids and the chief constituents of uncracked gasoline. Its higher members are waxy solids. In a given bore hole the wax may clog the pore space next to the hole as gas expands and cools. The paraffins are the largest constituent of crude oil and are characterised by their chemical inertness. Clearly they would not have remained as they are if this were not so.

2.3 Isomerism

From methane to propane there is only one way to arrange the branched chains however above propane there are alternative arrangements and these are called isomers.



Reservoir Fluids Composition

Structural formulae do not represent the actual structure of the molecules. Isomers are substances of the same composition that have different molecular structure and therefore different properties, for example, normal butane and isobutane. normal butane isobutane

CH3CH2CH2CH3

CH3CH CH3 CH3



-

B.Pt. 31.1˚F

-

B.Pt. 10.9˚F

Pentane has three structures (isomers). Clearly the number of isomers increase as the number of carbon atoms increases. Hexane has 5 isomers and heptane 9. Table 1 below gives some of the basic physical properties of the more common hydrocarbons of the paraffin series and Table 2 lists the state of the various pure components demonstrating that components which might be solid on their own contribute to liquid states when part of a mixture. Figure 2 gives some structural formula for three paraffin compounds. Name



Chemical Formula

Molecular Weight

Boiling Point (°C) at normal

Critical Temp °C

Density Gas Liquid (air = 1) (water = 1) conditions sp.gr.

Methane

CH4

16.04

-161.4

-82.4

0.554

0.415 (-614°)

Ethane

C 2H6

30.07

-89.0

32.3

1.038

0.54 (-88°)

Propane

C 3H8

44.09

-42.1

96.8

1.522

0.585 (-44.5°)

n-butane

C4H10

58.12

0.55

153.1

2.006

0.601 (0°)

Isobutane

C4H10

58.12

-11.72

134.0

2.006

0.557

n-pentane

C5H12

72.15

36.0

197.2

2.491

0.626

Isopentane

C5H12

72.15

27.89

187.8

2.491

0.6197

n-hexane

C6H14

86.17

60.30

228.0

2.975

0.6536

Table 1 Physical properties of common hydrocarbons.

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ALKANES or PARAFFIN HYDROCARBONS Cn H 2n+2

No of carbon atoms 1

Name

State (ntp)

Methane

Gas

2

Ethane

Gas

3 4

Propane Butane

Gas Gas

5 6

Pentane Hexane

Liquid Liquid

7

Heptane

Liquid

8

Octane

Liquid

9 10 C5-C17

Nonane Decane

Liquid Liquid Liquid

C18+

Solid

Table 2 Alkanes or Paraffin Hydrocarbons Cn H 2n + 2 H

PARAFFINS H H

C

H

H

Methane

H

H H

C

H H

C

C

C

H

H

H

H

Iso-butane

H

H

H

H

H

H

H

H

H

C

C

C

C

C

C

C

C

H

H

H

H

H

H

H

H

H

n-octane

Figure 2 Gives some standard formula for saturated hydrocarbons

2.4 Unsaturated Hydrocarbons

These are hydrocarbons which have double or triple bonds between carbon atoms. They have the potential to add more hydrogen or other elements and are therefore termed unsaturated. There are termed the olefins, and there are two types, alkenes, for example ethylene, CH2=CH2, which have a carbon-carbon double bond and alkynes, for example acetylene,CH=CH which have a carbon carbon triple bond. Both compound types being unsaturated are generally very reactive and hence are not found in reservoir fluids.

2.5 Napthene Series

The napthene series (CnH2n) sometimes called cycloparaffins or alicyclic hydrocarbons are identified by having single covalent bonds but the carbon chain is closed and is saturated. They are very stable and are important constituents of crude oil. Their chemical properties are similar to those of the paraffins. A crude oil with a high napthene content is referred to as an napthenic based crude oil. An example is cyclohexane C6H12. Figure 3 gives the structural formula for two napthenic compounds.



Reservoir Fluids Composition

NAPHTHENES H

H

H

C

H

C

H H

C

H

C

H H

H

C

H

H

C

C

C

H

H

C

C

H

H H

C C

H

H H H

H

H

Methyl Cyclopentane

H

Cyclohexane

Figure 3 Structural formula for two naphenic compounds.

2.6 Aromatics

The aromatic series (CnH2n-6) is an unsaturated closed-ring series, based on the benzene compound and the compounds are characterised by a strong aromatic odour. Various aromatic compounds are found in crude oils. The closed ring structure gives them a greater stability than open compounds where double or triple bonds occur. Figure 4 gives the structural formula for two aromatic compounds. AROMATICS H

H

H

C

C

C

H

C

C

H

H

C

C

C

H

H

C

C

H

H

C

C

C

H

C H



Benzene

C

C

H

H

Naphthalene

Figure 4 Structural formula for two aromtic compounds.

The aromatic-napthene based crudes are usually associated with limestone and dolomite reservoirs such as those found in Iran, the Arabian Gulf and Borneo. Some crude oils used to be described, more from a refining perspective, according to the relative amount of these non paraffin compounds. Crude oils would be called paraffinic, napthenic or aromatic. It is not a classification of value in reservoir engineering.

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Physical Properties of some Common Petroleum Reservoir Fluid Constituents Component Paraffins Methane Ethane Propane n-Butane Iso-Butane n-Pentane n-Hexane Iso-octane n-Decane Naphthenes Cyclopentane Methyl cyclo-pentane Cyclohexane Aromatics Benzene Toluene Xylene Naphthalene

Formula

Melting Point (˚C)

Normal Boiling Point (˚C)

Density (g/cm3) at 1 atm and 15˚C

CH4 C2H6 C3H8 C4H10 C4H10 C5H12 C6H14 C8H18 C10H22

-184 -172 -189.9 -135 -145 -131.5 -94.3 -107.4 030

-161.5 -88.3 -42.2 -0.6 -10.2 36.2 69.0 99.3 174.0

0.626 0.659 0.692 0.730

C5H10 C6H12 C6H12

-93.3 -142.4 6.5

49.5 71.8 81.4

0.745 0.754 0.779

C6H6 C7H8 C8H10 C10H8

5.51 -95 -29 80.2

80.1 110.6 144.4 217.9

0.885 0.867 0.880 0.971

Table 3 Physical properties of some common petroleum reservoir fluid constituents

2.7 Asphalts

Asphalt is not a series by itself. Asphalts are highly viscous to semi-solid, brownblack hydrocarbons of high molecular weight usually containing a lot of sulphur and nitrogen, which are undesirable components, and oxygen. Asphalts are closely related to the napthene series and because of their high nitrogen and oxygen content they may be considered juvenile oil, not fully developed.

3 NON-HYDROCARBON COMPOUNDS Although small in volume, generally less than 1%, non-hydrocarbon compounds have a significant influence on the nature of the produced fluids with respect to processing and the quality of the products. The more common non-hydrocarbon constituents which may occur are: sulphur, oxygen, nitrogen compounds, carbon dioxide and water. Sulphur and its associated compounds represent 0.04% - 5% by weight. These corrosive compounds include sulphur, hydrogen sulphide (H2S ),which is very toxic, and mercaptans of low molecular weight ( these are produced during distillation and require special metals to avoid corrosion). Non-corrosive sulphur materials include sulphides. Sulphur compounds have a bad smell and both the corrosive and noncorrosive forms are undesirable. On combustion these products produce S02 and S03 which are undesirable from an environmental perspective. 

Reservoir Fluids Composition

Oxygen compounds, up to 0.5% wt., are present in some crudes and decompose to form napthenic acids on distillation, which may be very corrosive. Nitrogen content is generally less than 0.1% wt., but can be as much as 2%. Nitrogen compounds are complex . Gaseous nitrogen reduces the thermal quality of natural gas and needs to be blended with high quality natural gas if present at the higher levels. Carbon Dioxide is a very common constituent of reservoir fluids, especially in gases and gas condensates. Like oxygen it is a source of corrosion. It reacts with water to form carbonic acid and iron to form iron carbonate. Carbon dioxide like methane has a significant impact on the physical properties of the reservoir fluids. Other compounds. Metals may be found in crude oils at low concentration and are of little significance. Metals such as copper, iron, nickel, vanadium and zinc may be present. Produced natural gas may contain helium, hydrogen and mercury. Inorganic compounds The non-oil produced fluids like water will clearly contain compounds arising from the minerals present in the rock, their concentration will therefore vary according to the reservoir. Their composition however can have a very significant effect on the reservoir behaviour with respect to their compatibility with injected fluids. The precipitation of salts, scale, is a serious issue in reservoir management. Many of these salts need to be removed on refining as some generate HC1 when heated with water.

4. COMPOSITIONAL DESCRIPTION FOR RESERVOIR ENGINEERING 4.1 Definitions of Composition in Reservoir Engineering

In petroleum engineering, and specifically in reservoir engineering, the main issue is one of the physical behaviour and characteristics of the petroleum fluids. The composition of the fluid clearly has a significant impact on the behaviour and properties. In petroleum engineering therefore the description of the composition is a key to determine the physical properties and behaviour. For the oil refiner or chemical manufacturer the composition of the fluid is the key to determine what chemical products can be extracted or processed from the material. The petroleum engineer is not concerned with the fact that the oil might contain, albeit in small concentrations, hundreds of different components. The petroleum engineer wants as simple a description as possible which still enables the determination of the physical properties and behaviour under different temperature and pressure conditions. Two models are used in this industry to describe the composition for physical property prediction purposes, the black-oil model and the compositional model. The black-oil model is a 2 component description of the fluid where the two components are, the fluids produced at surface, stock tank oil and solution gas. Associated with this model are black-oil parameters like solution gas-oil ratio and the oil formation volume factor. These parameters are discussed in the chapter on liquid properties. Institute of Petroleum Engineering, Heriot-Watt University



The compositional model is a compositional description based on the paraffin series CnH2n+2. The fluid is described with individual compositions of normal paraffins up to a limiting C number. Historically C6, more common now to go up to C9, or even higher. Components greater than the limiting C number are lumped together and defined as a C+ component. Isomers, normal and iso are usually identified up to pentane. Non paraffinic compounds are assigned to the next higher paraffin according to its volatility. The material representing all compounds above the limiting carbon number are called the C+ fraction , so C7+ for a limiting value of C6 and C10+ for a limiting value of C9. The physical properties of paraffins up to the limiting C number are well known and documented. The C+ component is however unique to the fluid and therefore two properties are used to characterise it, apparent molecular weight and specific gravity. The behaviour of some fluids are complex and the paraffin based description may have difficulty in predicting properties under certain conditions. Consideration may be required to also identify napthenic and aromatic compounds, (PNA analysis), which could be contributing to complex behaviour. This is particularly the case for gas condensates existing at high pressures and high temperatures. Figure 4 illustrates the compositional model and its application as reservoir fluids are produced to surface. Although the individual components contribute to a single liquid reservoir phase for an oil, when the fluids are produced to surface they produce a gas phase, solution gas, and a liquid phase, stock tank oil. The distribution characteristics of the individual components is complex and not just a function of temperature and pressure. For reservoir fluids the composition is also an influence on the distribution. This makes it a difficult task to predict this distribution perspective since reservoir fluid compositions are unique. This topic is further dealt with in the chapter on vapour liquid equilibrium. Improved methods of chemical analysis make it possible to describe the oil up to a C value of C29. Although such definitions provide a very accurate description, the associated computer effort in using such a comprehensive description does lead to the use of pseudo components. Pseudo components are obtained by grouping the various C number compositions, thereby reducing the description to 4 or 5 "pseudo components". A number of methods exist to group the various C values and other components.

10

Reservoir Fluids Composition

Reservoir Fluid

Gas at Surface Conditions

Oil at Surface Conditions

C1

C2

C3

C4

C5

C6

C7+

The relative amounts of C1 - C7+ are a function of :

Temperature, Pressure, Composition (particularly at high temperature) Figure 5 Compositional Model

5. GENERAL ANALYSIS 5.1 Surface condition characterisation

Reservoirs as well as having unique compositions also exist at specific pressures and temperatures. It is important therefore to provide a common basis for describing the quantities of fluids in the reservoir and throughout the production process. The basis chosen is the fluids at surface conditions, the surface conditions being 14.7 psia or 101.3 kPa and 60oF or 298K. These conditions are called standard conditions. For gas therefore this yields standard cubic feet SCF or standard cubic meters SCM. It is useful to consider these expression not as volumes but as mass, the volume of which will vary according to density. For liquids we express surface conditions as stock tank volumes either stock tank barrels STB or stock tank cubic meters STM3. The relative amount of gas to oil is expressed by the gas-oil ratio GOR SCF/STB. Since there are so many types of oil, each with a wide range of specific gravity, an arbitrary non-linear relationship was developed by the American Petroleum Institute (API) to classify crude oils by weight on a linear-scaled hydrometer. The observed readings are always corrected for temperature to 60oF, by using a prepared table of standard values. Institute of Petroleum Engineering, Heriot-Watt University

11

Degrees API = 141.5 -131.5 Sp.Gr.at 60ºF







(1)

Sp.Gr = specific gravity relative to water ar 60oF. The API gravity of water is 10º. A light crude oil would have an API gravity of 40º, while a heavy crude would have an API gravity of less than 20º. In the field, the API gravity is readily measured using a calibrated hydrometer. There are no definitions for categorising reservoir fluids, but the following table 5 indicates typical GOR, API and gas and oil gravities for the five main types. The compositions show that the dry gases contain mostly paraffins, with the fraction of longer chain components increasing as the GOR and API gravity of the fluids decrease. In chapter 4 we give a classification for the various reservoir fluid types in the context of phase behaviour. Type

Dry Gas

Appearance Colourless at surface Gas

Initial GOR (scf/stb)

WetGas

Gas Condensate

Volatile Oil

Black Oil

Colourless Gas + clear liquid

Colourless + significant clear/straw Colour

Brown liquid Some Red/Green Liquid

Black Viscous Liquid

No Liquids

>15000

3000-15000

2500-3000

100-2500

-

60-70

50-70

40-50

Tc

SINGLE PHASE

1 Liquid state-rapid change of pressure with small volume change

First Gas Bubble

Pressure

Last Drop of Liquid

T < Tc

Pressure remains constant while both gas and liquid are present

4 Dew Point Gas

Bubble Point

T2 > Tc

2

TWO PHASE REGION All Gas Volume

Figure 5 Pressure-Volume diagram for a Single-Component System

For a pure substance vapour pressures at bubble point and dew point are equal to the vapour pressure of the substance at that temperature. Above the critical point, ie 3 - 4 , the PV behaviour line shows no abrupt change and simply shows an expansion of the substance and no phase change. This fluid is called a super critical fluid. A series of expansions can be performed at various constant temperatures and a pressure volume diagram built up and the locus of the bubble point and dew point values gives the bubble point and dew point lines which meet at the critical point. Conditions under the bubble point and dew point lines represent the conditions where two phases coexist whereas those above these curves represent the conditions where only one phase exists. At the critical temperature the P,T curve goes through the critical point. Figure 6

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3

T = Tc

Liquid state rapid change of temperature with small volume change T > Tc

1

SINGLE PHASE T < Tc 4

De

Curve

Bubble

Point

Pressure

Critical Point

w

Po

in t Pressure remains constant while Cur ve both gas and liquid are present

2

TWO PHASE REGION Volume

Figure 6 Series of PV lines for a pure component

The pressure volume curve for pure component ethane is given in figure 7 The locus of the bubble points and dew points form a three-dimensional diagram when projected in to a P-T diagram give the vapour pressure line (Figure 8).

900

Pressure - PSIA

800 C

700

90

600

A

400 0

ºF

Two Phase Region

Liquid 500

11 0

B

D

0.05

0.10

0.15

ºF

Vapor 60 º F

0.20

0.25

Specific Volume - Cu. Ft. per lb.

Figure 7 Pressure-Volume Diagram of Ethane

10

Phase Behaviour of Hydrocarbon Systems

Bubble Point Line

uid

Liq

Critical Point

G as

an d

Vo lu

s

Ga

me

id

e

tur

ra pe m Te



Critical Point

u Liq

Pressure

Pressure

Li qu id

Dew Point Line

Vapor Pressure Curve

s Ga ure rat pe m Te

Figure 8 Three Dimensional Phase Diagram for a Pure Component System

4 TWO COMPONENT SYSTEMS

Reservoir fluids contain many components but we will first consider a system containing two components, such a system is called a binary.

4.1 Pressure Volume Diagram

The behaviour of a mixture of two components is not as simple as for a pure substance. Figure 9 shows the P-V diagram of a two-component mixture for a constant temperature system.

Pressure

Liquid Bubble Point

Liquid

and

Gas

Dew Point

Ga

s

Volume

Figure 9 Pressure-Volume Line for a Two-Component System at Constant Temperature

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11

The isotherm is very similar to the pure component but the pressure increases as the system passes from the dew point to the bubble point. This is because the composition of the liquid and vapour changes as it passes through the two-phase region. At the bubble point the composition of the liquid is essentially equal to the composition of the mixture but the infinitesimal amount of gas is richer in the more volatile component. At the dew point the composition of vapour is essentially the mixture composition whereas the infinitesimal amount of liquid is richer in the less volatile component. Breaks in the line are not as sharp as for pure substances. The pressure-volume diagram for a specific n-pentane and n-heptane mixture is given in Figure 10. Clearly a different composition of the two components would result in a different shape of the diagram.

600

500 45

400

300

200

100 0

Bubble Point Line

Pressure - PSIA

0º

Critical point 45 4º F

425

º

400

º

350

º

300

º

0.1

Dew Point Line

0.2

0.3

0.4

0.5

Specific Volume - Cu. Ft. per lb.

Figure 10 Pressure-Volume Diagram for N-Pentane and N-Heptane (52.4 mole % Heptane) ref. 4

4.2 Pressure Temperature Diagram

Compared to the single line representing the vapour pressure curve for pure substances there is a broad region in which the two phases co-exist. The two-phase region of the diagram is bounded by the bubble point line and the dew point line, and the two lines meet at the critical point. Points within a loop represent two-phase systems (Figure 11). Consider the constant temperature expansion of a particular mixture composition. At 1 the substance is liquid and as pressure is reduced liquid expands until the bubble point is reached. The pressure at which the first bubbles of gas appear is termed the bubble point pressure. As pressure is decreased liquid and gas co-exist until a minute amount of liquid remains at the dew point pressure. Further reduction of pressure causes expansion of the gas. 12

Phase Behaviour of Hydrocarbon Systems

By carrying out a series of constant temperature expansions the phase envelope is defined and within the envelope contours of liquid to gas ratios obtained. These are called quality lines and describe the pressure and temperature conditions for equal volumes of liquid. The quality lines converge at the critical point.

4.3 Critical Point

In the same way as pure components, when more than one component is present liquid and gases cannot coexist, at pressures and temperatures higher than the critical point. The critical point for a more than one component mixture is defined as a point at which the bubble point line and dew point line join, ie. it is also the point at which all the intensive properties of the liquid are identical. This aspect is a very severe test for physical property prediction methods. If the vapour pressure lines for the pure components are drawn on the P-T diagram then the two-phase region for the mixture lies between the vapour pressure lines. In the figure 11 the critical temperature of the mixture TcAB lies between TcA and TcB whereas the critical pressure PcAB lies above PcA and PcB. It is important to note that the PcAB and TcAB of the mixture does not necessarily lie between the Pc & Tc of the two pure components.

1 Critical Point

PCAB

PCA

% Liq.

Liquid

CA

100 75 50

PCB

Pressure

b Bu

ble

P

t o in

e Li n

0

t Poin Dew

Temperature

CB

25

TCA

2

Gas

TCAB

TCB

Figure 11 Pressure-Temperature Diagram for a Two Component System

A specific mixture composition will give a specific phase envelope lying between the vapour pressure lines. A mixture with different proportions of the same components will give a different phase diagram. The locus of the critical point of different mixture compositions is shown in Figure 12 for the ethane and n-heptane system, and in Figure 13 for a series of binary hydrocarbon mixtures. Figure 13 demonstrates that for binary mixture e.g. Methane and n-decane two phases can coexist at conditions of pressure considerably greater than the two phase limit, critical conditions for the separate pure components. Methane is a significant component of reservoir fluids. Institute of Petroleum Engineering, Heriot-Watt University

13

1400 C2

Composition No Wt % Ethane C 100.00 C1 90.22 C2 50.25 C3 9.78 C7 N-Heptane

1200

C1 800 C

C3 A1

an e

600

A

le

bb

Bu

i Po

e

in

L nt

C7

A3 0

i

100

B3

B2

B1

De

w

Po

an

e

nt

A2

200

0

li n

e

400

E th

Pressure, lbs./Sq. In. ABS

1000

N-

He

pt

B 200

300

400

500

600

Temperature º F

Figure 12 Pressure-Temperature Diagram for the Ethane-Heptane System 2

14

Phase Behaviour of Hydrocarbon Systems

6000

Single Phase

5000

Pressure Lbs. (psia)

4000

Two Phases

3000

2000

et ha ne

1000

M

0 0

-100

Eth

e an

0

pa Pro

ne

100

e an xane ptane ne ut a ent ane N-B N- P N-He N-He N-Dec

200

300

400

500

600

700

Temperature º F

Figure 13 Critical Point Loci for a Series of Binary Hydrocarbon Mixtures 2

4.4 Retrograde Condensation

Within the two phase region our two component system there can be temperatures and pressures higher than the critical temperature where two phases exist and similarly pressures. These limiting temperatures and pressures are the cricondentherm and cricondenbar . The cricondentherm can be defined as the temperature above which liquid cannot be formed regardless of pressure, or expressed differently, as the maximum temperature at which two phases can exist in equilibrium. The cricondenbar can be defined as the pressure above which no gas can be formed regardless of temperature or as the maximum pressure at which two phases can exist in equilibrium. (Figure 14). These limits are of particular significance in relation to the shape of the diagram in figure 14. Consider a single isotherm on Figure 14. For a pure substance a decrease in pressure causes a change of phase from liquid to gas. For a two-component system below Tc a decrease in pressure causes a change from liquid to gas. We now consider the constant temperature decrease in pressure, 1-2-3 , in figure 14 at a temperature between the critical temperature and the cricondentherm. As pressure is decreased from 1 the dew point is reached and liquid forms, i.e., at 2 the system is such that 5% liquid and 95% vapour exists, i.e. a decrease in pressure has caused a change from gas to liquid, opposite to the behaviour one would expect. The phenomena is termed Retrograde Condensation. From 2 - 3, the amount of liquid decreases Institute of Petroleum Engineering, Heriot-Watt University

15

and vaporisation occurs and the dew point is again reached where the system is gas. Retrograde condensation occurs at temperatures between the critical temperature and cricondentherm. The retrograde region is shown shaded in the figure. Region of retrograde condensation

Cricondenbar Liquid

1

% Liq.

Pressure

100

10 5 0

2

e Dew Point Lin

3 Gas

Cricondentherm

25

Po

e

50

Bu bb l

in t

Li

ne

75

Temperature

Figure 14 Phase Diagram Showing Conditions for Retrograde Considerations



5. MULTI-COMPONENT HYDROCARBON Using two component systems we have examined various aspects of phase behaviour. Reservoir fluids contain hundreds of components and therefore are multicomponent systems. The phase behaviour of multicomponent hydrocarbon systems in the liquid-vapour region however is very similar to that of binary systems however the mathematical and experimental analysis of the phase behaviour is more complex. Figure 15 gives a schematic PT & PV diagram for a reservoir fluid system. Systems which include crude oils also contain appreciable amounts of relatively non-volatile constituents such that dew points are practically unattainable.

16

Phase Behaviour of Hydrocarbon Systems

PVT CELL

PHASE DIAGRAM

All Liquid

Liqu id

"a"

Critical Point

First Gas Bubble

Bubble Point uid Liq

% % 40

%

20

%

w De

int Po

Lin

Pressure

60

e

Bu bb le

Pressure

Last Drop of Liquid

Po in

Gas / 40% Liquid

80

tL i ne

Bubble Point

Dew Point

Dew Point

All Gas

Temperature

Volume

Figure 15 Phase Diagrams for Multicomponent Systems

We will consider the behaviour of several examples of typical crude oils and natural gases:





Low-shrinkage oil (heavy oil - black oil) High-shrinkage oil (volatile oil) Retrograde condensate gas Wet gas Dry Gas

Figure 16 is a useful diagram to illustrate the behaviour of the respective fluid types above. However it should be emphasised that for each fluid type there will be different scales. The vertical lines help to distinguish the different reservoir fluid types. Isothermal behaviour below the critical point designates the behaviour of oil systems and the fluid is liquid in the reservoir, whereas behaviour to the right of the critical point illustrates the behaviour of systems which are gas in the reservoir.

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17

Single Phase Region (Gas)

Single Phase Region (Liquid) Black Oil P

Pressure

Bu

% Liquid 100 75

b

int Po ble

Volatile Gas Oil Condensate

P m

b

Gas

CP

e Lin

2

Two Phase Region

TM Where: P = Bubble point pressure b at indicated temperature P = Maximum pressure at which m two phases can coexist

50 25 20 15 10 5 0

Dew

Poin

T = Maximum temperature at m which two phases can coexist

e t Li n

Single Phase Region

C = Critical conditions

Gas

X5

X = Cricondentherm 5

Temperature

Figure 16 Phase diagram for reservoir fluids

5.1 Oil Systems ( Black Oils and Volatile Oils)

Figures 17&18 illustrate the PT phase diagrams for black and volatile oils. The two-phase region covers a wide range of pressure and temperature. Tc is higher than the reservoir temperature. In figure 17 the line 1-2-3 represents the constant reservoir temperature pressure reduction that occurs in the reservoir as crude oil is produced for a black oil. These oils are a common oil type. The dotted line shows the conditions encountered as the fluid leaves the reservoir and flows through the tubing to the separator. If the initial reservoir pressure and temperature are at 2, the oil is at its reservoir bubble point and is said to be saturated, that is, the oil contains as much dissolved gas as it can and a further reduction in pressure will cause formation of gas. If the initial reservoir pressure and temperature are at 1, the oil is said to be undersaturated, i.e. The pressure in the reservoir can be reduced to Pb before gas is released into the formation. For an oil system the saturation pressure is the bubble point pressure.

18

Phase Behaviour of Hydrocarbon Systems

1 Undersaturated Mole % Liq. 100

Lin e

2 Saturated

Critical Point

Pb

3 75

De

50

w

Po

int

Sep.

line

Po int

Bu bb le

Pressure

Liquid

Gas

25 0



Temperature

Figure 17 Phase Diagram for a Black Oil

As the pressure is dropped from the initial condition as a result of production of fluids, the fluids remain in single phase in the reservoir until the bubble point pressure corresponding to the reservoir temperature is reached. At this point the first bubbles of gas are released and their composition will be different from the oil being more concentrated in the lighter ( more volatile) components. When the fluids are brought to the surface they come into the separator and as shown on the diagram, the separator conditions lie well within the two phase region and therefore the fluid presents itself as both liquid and gas. The pressure and temperature conditions existing in the separator indicate that around 85% liquid is produced, that is a high percentage and as a result the volume of liquid at the surface has not reduced a great amount compared to its volume at reservoir conditions. Hence the term low-shrinkage oil. As the pressure is further reduced as oil is removed from the reservoir, point 3 will be reached and 75% liquid and 25% gas will be existing in the reservoir. Strictly speaking once the reservoir pressure has dropped to the bubble point, beyond that the phase diagram does not truly represent the behaviour of the reservoir fluid. As we will see in the chapter on drive mechanisms, below the bubble point gas produced flows more readily than the associated oil and therefore the composition of the reservoir fluid does not remain constant. The system is continually changing in the reservoir and therefore the related phase diagram changes. The summary characteristics for a black oil sometimes termed a heavy oil or low shrinkage oil are as follows.

Broad-phase envelope High percentage of liquid High proportion of heavier hydrocarbons GOR < 500 SCF/STB

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Oil gravity 30˚ API or heavier Liquid - black or deep colour Volatile oil contains a much higher proportion of lighter and intermediate hydocarbons than heavier black oil and therefore they liberate relatively large volumes of gas leaving smaller amounts of liquid compared to black oils. For this reason they used to be called high shrinkage oils. The diagram in figure 18 shows similar behaviour to the black oil except that the lines of constant liquid to gas are more closely spaced. Points 1 and 2 have the same meaning as for the black oil. As the pressure is reduced below 2 a large amount of gas is produced such that at 3 the reservoir contains 40% liquid and 60% gas. At separator conditions 65% of the fluid is liquid, i.e. less than previous mixture. The summary characteristics for a volatile sometimes termed a heavy oil or high shrinkage oil when compared to black oils are as follows.

Not so broad phase envelope as black oil Fewer heavier hydrocarbons Deep coloured API < 50˚ GOR < 8000 SCF/STB

1 2

Liquid

Critical Point

Mole % Liq. 100

3

50 40

e

Sep.

Gas

w

po

in t

lin

Bu b

ble

po int

lin e

Pressure

75

De

25 0



Temperature

Figure 18 Phase Diagram for a Volatile Oil

Clearly, for these fluids, it is the composition of the fluid that determines the nature of the phase behaviour and the relative position of the saturation lines, (bubble point and dew point lines), the lines of constant proportion of gas/liquid and the critical point. 20

Phase Behaviour of Hydrocarbon Systems

For both of these fluids types one can prevent the reservoir fluid going two phase by maintaining the reservoir pressure above its saturation pressure by injecting fluids into the reservoir. The most common practise is the use of water as a pressure maintenance fluid.

5.2 Retrograde Condensate Gas

If the reservoir temperature lies between the critical point and the cricondentherm a retrograde gas condensate field exists and Figure 19 gives the PT diagram for such a fluid. Above the phase envelope a single phase fluid exists. As the pressure declines to 2 a dew point occurs and liquid begins to form in the reservoir. The liquid is richer in heavier components than the associated gas. As the pressure reduces to 3 the amount of liquid increases. Further pressure reduction causes the reduction of liquid in the reservoir by re-vaporisation. It is important to recognise that the phase diagram below for a retrograde condensate fluid represents the diagram for a constant composition system. Before production the fluid in the reservoir exists as a single phase and is generally called a gas. It is probably more accurate to call it a dense phase fluid. If the reservoir drops below the saturation pressure the dew point, then retrograde condensation occurs within the formation. The nature of this condensing fluid is only in recent years being understood. It was previously considered that the condensing fluid would be immobile since its maximum proportion was below the value for it to have mobility. It was considered therefore that such valuable condensed fluids would be lost to production and the viability of the project would be that from the ‘wet’ gas.

1

Mole % Liq.

B

Pressure

Liquid

e bl ub

P

tL oin

ine

Critical Point 2

3

100 75

Sep.

50 25 10 5 0

De

t oin wP

e Lin

Gas

Temperature

Figure 19 Phase Diagram for a Retrograde Condensate Gas

One of the development options for such a field therefore is to set in place a pressure maintenance procedure whereby the reservoir pressure does not fall below the saturation pressure. Water could be used as for oils but gas might be trapped behind the water as the water advances through the reservoir. Gas injection, called gas Institute of Petroleum Engineering, Heriot-Watt University

21

cycling ( Figure 20 ), is the preferred yet very expensive option. In this process the produced fluids are separated at the surface and the liquid condensates, high value product relative to heavy oil, are sent for export, in an offshore situation probably by tanker. The ‘dry’ gas is then compressed and reinjected into the reservoir to maintain the pressure above the dew point. Clearly with this process the pressure will still decline because the volume occupied by the gas volume of the exported liquid is not being replaced. Full pressure maintenance is obtained by importing dry gas equivalent to this exported volume from a nearby source. Eventually the injected dry gas displaces the ‘wet’ gas and then the field can be blown down as a conventional dry gas reservoir, if a suitable export route for the gas is then in place. The process described is very costly and carries with it a number of risks not least the possibility of early dry gas breakthrough. Imported Gas

Gas

Dry Gas Reinjection

Surface Separation Condensate Sales

Injection Well

Production Well Gas Water Contact

Figure 20 Gas cycling process

Recent research has shown that the nature of oil forming in porous media by this retrograde process may not be as first considered. The isolation of condensing liquids in porous rock is dependant on the relative strength of the interfacial tension and viscous forces working in the rock. If the relative magnitude of these is high then the fluid will be trapped however if they are low as a result of low interfacial tension, which is the case nearer the critical point, then the condensing liquids may be mobile and move as a result of viscous and gravity forces. Condensate liquids have been able to flow at saturations well below the previously considered irreducible saturation proportion. Established relative permeability thinking is having to be reconsidered in the context of gas condensates. The phenomena just described may give explanation to the observation sometimes made of an oil rim below a gas condensate field. Looking at the PT phase diagram one might consider that "blowing the reservoir down" 22

Phase Behaviour of Hydrocarbon Systems

quickly might be an option and as a result vaporise the condensed liquids in the formation. This is not a serious option since once the reservoir pressure falls below the dew point the impact of the increasing liquid proportion remaining in the reservoir causes the phase diagram to move to the right relative to reservoir conditions, and any vaporising will be of the lightest components which are likely to be in good supply and therefore not of significant value. The summary characteristics for a retrograde gas condensate fluid are as follows. Contains more lighter HC’s and fewer heavier HC’s than high-shrinkage oil API up to 60˚ API GOR up to 70,000 SCF/STB Stock tank oil is water-white or slightly coloured

5.3 Wet Gas

The phase diagram for a mixture containing smaller hydrocarbon molecules lies well below the reservoir temperature. Figure 21. The reservoir conditions always remain outside the two-phase envelope going from 1 to 2 and therefore the fluid exists as a gas throughout the reduction in reservoir pressure. For a wet gas system, the separator conditions lie within the two-phase region, therefore at surface heavy components present in the reservoir fluid condense under separator conditions and this liquid is normally called condensate. These liquid condensates have a high proportion of light ends and sell at a premium. The proportion of condensates depend on the compositional mix of the reservoir fluid as represented by the iso-volume lines on the PT diagram.

Liquid

1

Pressure

Critical Point

Mole % Liq. 100 75 50 25 5 0



2 Sep.

Gas

Temperature

Figure 21 Phase Diagram for a Wet Gas

The reference wet gas, clearly does not refer to the system being wet due to the presence of water but due to the production condensate liquids. Institute of Petroleum Engineering, Heriot-Watt University

23

In some locations where there are natural petroleum leakages at the surface, when condensates are produced they are sometimes called white oil. The summary characteristics for wet gas are as follows. GOR < 100,000 SCF/STB Condensate liquid > 50˚ API

5.5 Dry Gas

The phase envelope of the dry gas, which contains a smaller fraction of the C2-C6 components, is similar to the wet gas system but with the distinction that the separator also lies outside the envelope in the gas region (Figure 22). The term dry indicates therefore that the fluid does not contain enough heavier HC’s to form a liquid at surface conditions. The summary characteristics for a dry gas are as follows. GOR > 100,000 SCF/STB

Pressure

1

Critical Point

Liquid



75 50 25

2 Sep. Gas

Temperature

Figure 22 Phase Diagram for a Dry Gas

6 COMPARISON OF THE PHASE DIAGRAMS OF RESERVOIR FLUIDS Figure 16 gave a rather simplistic representation of the various types of fluids with respect to the relative position of reservoir temperature with respect to the phase diagram. In reality it is the phase diagram which changes according to composition and the relative position of the reservoir temperature and separator conditions, and these determine the character of the fluid behaviour. Figure 23 gives a better indication of the various reservoir types with respect to a specific pressure and temperature 24

Phase Behaviour of Hydrocarbon Systems

Pressure

scales. As the proportion of heavier components in the respective fluids increases the phase envelope moves to the right.

Separator

Dry Gas

Gas Wet Gas Condensate

Volatile Oil

Black Oil

Temperature (ºC) Critical Point

Figure 23 Relative positions of phases envelopes

7 RESERVOIRS WITH A GAS CAP Figure 24 illustrates a simplification of the phase diagrams associated with an oil reservoir with a gas cap. The phase diagram for the gas cap fluid, the oil reservoir fluid and for a fluid representing the combination fluid of a mixture of gas and liquid in the same proportions as they exist in the reservoir are presented.

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Reservoir Temperature Reservoir Gas

Total Reservoir Fluid

CG

C Reservoir Liquid

Pd=Pb Pressure

Initial Reservoir Pressure

CL

Separator

Temperature

Figure 24 Phase Diagram for an Oil Reservoir with a Gas Cap

The diagram illustrates that at the gas-oil contact the gas is at its dew pressure, the oil is at its bubble point pressure and the combination fluid lies on the constant proportion quality line representing the ratio of the gas and oil as they exist in the reservoir system. The gas cap may be dry, wet or condensate depending on the composition and phase diagram of the gas.

8 CRITICAL POINT DRYING Although not part of the topic of phase behaviour in the context of reservoir fluids it is useful to illustrate the application in a very practical application in the context of the evaluation of rock properties. Critical point drying has been used by a number of sciences to prepare specimens of delicate materials for subsequent micro visual analysis where conventional preparation techniques will destroy delicate fabric. Critical point drying takes advantage of the behaviour of fluids around the critical point where one can go from one phase type, like liquid to gas without a visually observed phase change. In the 1980’s it was observed in a UK offshore field that the interpreted permeability for a well sand in the zone where water injection was proposed was different from well injectivity tests when compared to the core analysis value where the value was many times more. The extent of this difference was such that permeabilities from the well test gave values which would prevent injection to take place whereas those from the core tests would result in practical injectivities. Clearly the difference was important.

26

Phase Behaviour of Hydrocarbon Systems

The company concerned embarked on a more sophisticated core recovery and analysis process suspicious that perhaps the fabric of the rock was being affected by core preparation methods. They resorted to critical point drying. The core recovered from the water zone of the reservoir from a subsequent new well was immersed and transferred to the test laboratory submerged in ‘formation water’. At the laboratory a core plug sample was extracted, cut to size and loaded into a core holder still submerged in the water. The core was then mounted in a flow rig (figure 25) and an alcohol which is miscible with water displaced the water in the core. Carbon dioxide at a pressure and temperature where it is in the liquid state was then introduced which miscible displaced the alcohol. The temperature and pressure was then adjusted taking them around the critical point rather than across the vapour pressure line of the PT phase diagram (figure 26) ending up with a temperature and pressure below the vapour pressure line with the fluid now in a gaseous state. After this process the permeability was measured to be of the same order as that interpreted from the well injectivity test. The reason for this difference was subsequently demonstrated to be a very fragile clay which during conventional core recovery and cleaning was damaged to an extent that its pore blocking structure was destroyed.

T

P

Core In Holder

Figure 25 Critical point drying system

Pressure

Critical Point Drying Route

Critical Point LIQUID

Vapour Pressure Line GAS Temperature



Figure 26 Critical point drying

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REFERENCES 1. Fig 1 Daniels, F Farrington: “Outlines of Physical Chemistry,” John Wiley & Sons,Inc New York, 1948 2. Fig 2 Brown,GG et al. “ Natural Gasoline and Volatile Hydrocarbons,” Natural Gasoline Association of America, Tulsa, Okl., 1948. Fig 10 Sage, S.G.,Lacy,W.N. Volumetric and Phase Behaviour of Hydrocarbons, Gulf Publishing Co.Houston 1949

28

Behaviour of Gases

CONTENTS 1 IDEAL GASES 1.1 Boyle's Law 1.2 Charles' Law 1.3 Avogadro's Law 1.4 The Equation of State For an Ideal Gas 1.5 The Density of an Ideal Gas 1.6 Standard Conditions 1.7 Mixtures of Ideal Gases 1.7.1 Dalton's Law of Partial Pressures 1.7.2 Amagat's Law 1.8 Apparent Molecular Weight 1.9 Specific Gravity of a Gas 2 BEHAVIOUR OF REAL GASES 2.1 Compressibility Factor For Natural Gases 2.2 Law of Corresponding States 2.3 Pseudocritical Properties of Natural Gases 2.4 Impact of Nonhydrocarbon Components on z Value 2.5 Standard Conditions For Real Reservoir Gases 3 GAS FORMATION VOLUME FACTOR 4 COEFFICIENT OF ISOTHERMAL COMPRESSIBILITY OF GASES



5 VISCOSITY OF GASES 5.1 Viscosity 5.2 Viscosity of Mixtures 6 EQUATIONS OF STATE 6.1 Other Equations-of-State 6.2 Van de Waals Equation 6.3 Benedict - Webb - Rubin Equation (BWR) 6.4 Redlich - Kwong Equation 6.5 Soave, Redlich Kwong Equation 6.6 Peng Robinson Equation of State 6.7 Application to Mixtures

LEARNING OBJECTIVES Having worked through this chapter the Student will be able to: • Present the ideal equation of state, PV=nRT. • Calculate the mass of an ideal gas given PV 7T values. • Derive an equation to calculate the density of an ideal gas. • Convert a mixture composition between weight and mole fraction. • Present an equation and calculate the apparent molecular weight of a mixture. • Define and calculate the specific gravity of a gas. • Present the equation of state, EOS, for a ‘real gas’ and explain what ‘Z’ is, PV=ZnRT. • Define the pseudocritical pressure and psuedocritical temperature and be able to use them to determine the ‘Z’ value for a gas mixture. • Express and calculate reservoir gas volumes in terms of standard cubic volumes. • Define the gas formation volume factor and derive an equation fore it using the EOS. • Calculate the volume of gas in a reservoir in terms of standard cubic volumes given prerequisite data. • Calculate the viscosity of a gas of a specific composition given perquisite equations and figures. • Be aware of the development of EOS’s to predict reservoir fluid properties.



Behaviour of Gases

INTRODUCTION A gas is a homogenous fluid that has no definite volume but fills completely the vessel in which it is placed. The system behaviour of gases is vital to petroleum engineers and the laws governing their behaviour should be understood. For simple gases these laws are straightforward but the behaviour of actual hydrocarbon gases particularly at the conditions occurring in the reservoir are more complicated. We will review the laws that relate to the pressure, volume and temperatures of gases and the associated equations. These relationships were previously termed gas laws; it is now more common to describe them as equations of state.

1 IDEAL GASES The laws relating to gases are straightforward in that the relationships of pressure, temperature and pressure are covered by one equation. First consider an ideal gas. An ideal gas is one where the following assumptions hold: • Volume of the molecules i.e. insignificant with respect to the total volume of the gas. • There are no attractive or repulsive forces between molecules or between molecules and container walls. • There is no internal energy loss when molecules collide. Out of these assumptions come the following equations.

1.1 Boyle’s Law

At constant temperature the pressure of a given weight of a gas is inversely proportional to the volume of a gas. i.e.

V α

1 or PV = constant, T is constant P





(1)

P = pressure, V = volume, T = temperature.

1.2 Charles’ Law

At constant pressure, the volume of a given weight of gas varies directly with the temperature: i.e.

V α T or

V = constant, P is constant T







(2)

The pressure and temperature in both laws are in absolute units.

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1.3 Avogadro’s Law

Avogadro’s Law can be stated as: under the same conditions of temperature and pressure equal volumes of all ideal gases contain the same number of molecules. That is, one molecular weight of any ideal gas occupies the same volume as the molecular weight of another ideal gas at a given temperature and pressure. Specifically, these are: (i) 2.73 x 1026 molecules/lb mole of ideal gas. (ii) One molecular weight (in lbs) of any ideal gas at 60˚F and 14.7 psia occupies a volume of 379.4 cu ft.



One mole of a material is a quantity of that material whose mass in the unit system selected is numerically equal to the molecular weight. eg. one lb mole of methane CH4 = 16 lb one kg mole of methane CH4 = 16kg

1.4 The Equation of State for an Ideal Gas

By combining the above laws an equation of state relating pressure, temperature and volume of a gas is obtained.

PV = constant T













(3)

R is the constant when the quantity of gas is equal to one mole. It is termed the Universal Gas Constant and has different values depending on the unit system used, so that;

10.732

cu ft psia lb mole  R

R in oilfield units = Table 1 gives the values for different unit systems. p



psia atm atm atm atm mm Hg in.Hg

V

T

n

cu ft cu ft cc litre cu ft litre cu ft

R K K K R K R

lb - mole lb - mole gm - mole gm - mole lb - mole gm - mole lb - mole

R 10.73 1.3145 82.06 0.08206 0.730 62.37 21.85

Table 1 Values of R for different unit systems



Behaviour of Gases

For n moles the equation becomes: PV = nRT















(4)

T= absolute temperature oK or oR where ºK=273 +oC and oR=460 +oF To find the volume occupied by a quantity of gas when the conditions of temperature and pressure are changed from state 1 to state 2 we note that:

n =

PV PV PV is a constant so that 1 1 = 2 2 RT T1 T2



EXERCISE 1.

A gas cylinder contains methane at 1000 psia and 70°F. If the cylinder has a volume of 3 cu.ft assuming methane is an ideal gas calculate the mass of methane in the cylinder.

1.5 The Density of an Ideal Gas

Since density is defined as the weight per unit volume, the ideal gas law can be used to calculate densities.

ρg = weight / volume =

where ρg is the gas density For 1 mole m = MW

V =



m V

MW = Molecular weight





RT P

∴ ρg =

MW.P RT









(5)

EXERCISE 2. Calculate the density of the gas in the cylinder in exercise 1.

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1.6 Standard Conditions

Oil and gas at reservoir conditions clearly occur under a whole range of temperatures and pressures. It is common practice to relate volumes to conditions at surface, ie 14.7 psia and 60˚F. ie

Pres Vres P V = sc sc Tres Tsc











(6)

sc - standard conditions res - reservoir conditions This relationship assumes that reservoir properties behave as ideal. This is NOT the case as will be discussed later.

EXERCISE 3. Assuming methane is at the conditions of exercise 1, calculate the volume the gas would occupy at standard conditions.

1.7 Mixtures of Ideal Gases

Petroleum engineering is concerned not with single component gases but mixtures of a number of gases. Laws established over early years governing ideal gas mixtures include Dalton’s Law and Amagat’s Law.

1.7.1 Dalton’s Law of Partial Pressures

The total pressure exerted by a mixture of gases is equal to the sum of the pressures exerted by its components. The partial pressure is the contribution to pressure of the individual component. Consider a gas made up of components A, B, C etc The total pressure of the system is the sum of the partial pressures ie P = PA + PB + PC + ..... where A, B and C are components. therefore 









(7)

Behaviour of Gases

P = n A

RT RT RT + n B + nC V V V

i.e. P =



∴

RT Σn j V

Pj n = j = y j P n









th where yj = mole fraction of j component.







(8)



The pressure contribution of a component, its partial pressure, is the total pressure times the mole fraction.

1.7.2 Amagat’s Law

Amagat’s Law states that the volume occupied by an ideal gas mixture is equal to the sum of the volumes that the pure components would occupy at the same temperature and pressure. Sometimes called the law of additive volumes. i.e. V = VA + VB + VC

V = n A

V =



i.e.











(9)







(10)

RT RT RT + n B + n C P P P

RT Σn j P

Vj n = j = y j V n



i.e, for an ideal gas the volume fraction is equal to the mole fraction. It is conventional to describe the compositions of hydrocarbon fluids in mole terms. This is because of the above laws. In some circumstances however weight compositions might be used as the basis and it is straight forward to convert between the two.

EXERCISE 4. A gas is made up of the following components; 25lb of methane, 3 lb of ethane and 1.5 lb of propane. Express the composition of the gas in weight and mole fractions.

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1.8 Apparent Molecular Weight

A mixture does not have a molecular weight although it behaves as though it had a molecular weight. This is called the apparent molecular weight. AMW If yj represents the mole fraction of the jth component:

(

AMW = Σ y j × MWj

)

AMW for air = 28.97, a value of 29.0 is usually sufficiently accurate.

EXERCISE 5. What is the apparent molecular weight of the gas in exercise 4



1.9 Specific Gravity of a Gas

The specific gravity of a gas, γg is the ratio of the density of the gas relative to that of dry air at the same conditions.



γ g =

ρg ρair













(11)









Assuming that the gases and air are ideal.

MgP M M γ g = RT = g = g M air P M air 29 RT



Mg = AMW of mixture, Mair = AMW of air.

EXERCISE 6. What is the gas gravity of the gas in exercise 4 ?

2 BEHAVIOUR OF REAL GASES The equations so far listed apply basically to ideal systems. In reality, however, particularly at high pressures and low temperatures the volume of the molecules are no longer negligible and attractive forces on the molecules are significant.



Behaviour of Gases

The ideal gas law, therefore, is not too applicable to light hydrocarbons and their associated fluids and it is necessary to use a more refined equation. There are two general methods of correcting the ideal gas law equation: (1) By using a correction factor in the equation PV = nRT (2) By using another equation-of-state

2.1 Compressibility Factor for Natural Gases

The correction factor ‘z’ which is a function of the gas composition, pressure and temperature is used to modify the ideal gas law to: PV = znRT













(12)

where the factor ‘z’ is known as the compressibility factor and the equation is known as the compressibility equation-of-state or the compressibility equation. The compressibility factor is not a constant but varies with changes in gas composition, temperature and pressure and must be determined experimentally (Figure 1). To compare two states the law now takes the form:

P1V1 PV = 2 2 z 2 T2 z1T1













(13)

z is an expression of the actual volume to what the ideal volume would be.













(14)

co ns ta nt

Vactual Videal

at ur e

=

1.0 pe r

Compressibility factor, Z



z =

Te m

i.e.

0.5

0

0

PRESSURE, P

Figure 1 Typical plot of the compressibility factor as a function of pressure at constant temperature. Institute of Petroleum Engineering, Heriot-Watt University



Although all gases have similar shapes with respect to z the actual values are component specific. However through the law of corresponding states all pure gases are shown to have common values.

2.2 Law of Corresponding States

The law of corresponding states shows that the properties of many pure liquids and gases have the same value at the same reduced temperature (Tr) and pressure (Pr) where:



Tr =

T P and Pr = Tc Pc











(15)

Where, Tc and Pc are the pure component critical temperature and pressure. The compressibility factor ‘z’ follows this law. It is usually presented vs Tr and Pr. Although in many cases pure gases follow the Law of Corresponding States, the gases associated with hydrocarbon reservoirs do not. The Law has however been used to apply to mixtures by defining parameters called pseudo critical temperature and pseudocritical pressure . For mixtures a pseudocritical temperature and pressure, Tpc and Ppc is used such that:

Tpc = Σy jTcj and Ppc = Σ y j Pcj











(16)

where y is the mole fraction of component j and Tcj and Pcj are the critical temperature and pressure of component j. It should be emphasised that these pseudo critical temperature and pseudocritical pressures are not the same as the real critical temperature and pressure. By definition the pseudo values must lie between the extreme critical values of the pure components whereas the actual critical values for mixtures can be outside these limits, as was observed in the Phase Behaviour chapter.

EXERCISE 7. Calculate the pseudo critical temperature and pseudocritical pressure of the mixture in exercise 4 .

For mixtures the compressibility factor (z) has been generated with respect to natural gases 1, where ‘z’ is plotted as a function of pseudo reduced temperature, Tpr and pseudo reduced pressure Ppr where

10

Behaviour of Gases

Compressibility Factors for Natural Gases as a Function of Pseudoreduced Pressure and Temperature.

1.1

0

Pseudo Reduced Pressure, Pr

1

2

3

4

5

6

8

Pseudo Reduced Temperature 3.0 2.8 2.6 2.4 2.2 2.0 1.9 1.8

1.0

0.9

5

1. 4

1.0 1.05 1.2 0.95

1.

1.5

05

1.6

1.

1.7

1

0.8

1.3 1.1

1.1

1.

1.7

1.45

0.7

0.6

1. 3

1.2

1.6 1.8

1.15

0.4

2.0

3.0

2.8

1.1

1.3

2.6

1.2

3.0

2.2 2.0 1.8 1.7 1.6

0.9 7

1.9

1.1

Compressibility of Natural Gases (Jan. 1, 1941)

2.6 2.4 1.2

1.0

1.1 1.4 1.3

8

1.4

2.2

1.05

0.25

1.0

1.7 1.9

2.4

1.1

0.3

1.5

4 1. 1.5

1.25

0.5

1.6

2

1.4 1.35 1.3

1.

Compressibility Factor, z

7

1.05

0.9 9

10

11

12

13

Pseudo Reduced Pressure, Pr

14

15

Figure 2 Compressibility factors for natural gas1 (Standing & Katz, Trans AIME, 1942)

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Tpr =



T P and Ppr = Tpc Ppc











(17)

The use of this chart , figure 2 ,has become common practise to generate z values for natural gases. Poettmann and Carpenter 2 have also converted the chart to a table. Various equations have also been generated based on the tables.

EXERCISE 8. For the gas of exercise 4 determine the compressibility factor at a temperature of 150°F and a pressure of 3500psia.

2.3 Pseudocritical Properties of Natural Gases

Pseudocritical Pressure, psia

The pseudocritical properties of gases can be computed from the basic composition but can also be estimated from the gas gravity using the correlation presented in Figure 3. Pseudocritical Properties of Natural Gases

700

Condens

650

Miscellaneous ate Wel

l Fluid

Gases

s

600

550

Pseudocritical Temperature, R

500

450

400 n Co

s

se

Ga

e

an

ell

sc Mi

s ou

ids Flu ell W e sat den

350

300

0.5

0.6

0.7

0.8

0.9

1.0

1.1

Gas Gravity (air = 1)

Figure 3 Pseudocritical properties of natural gases 3 12

1.2

Behaviour of Gases

2.4 Impact of Nonhydrocarbon Components on z value.

Components like hydrogen sulphide, and carbon dioxide have a significant impact on the value of z. If the method previously applied is used large errors in z result. Wichert and Aziz 4 have produced an equation which enables the impact of these two gases to be calculated. T'pc = Tpc - e











(18)

Tpc + yH 2 S 1 − yH 2 S e









(19)

and

p′pc =



p pc Tpc′

(

)

T'pc and p'pc are used to calculate Tpr and ppr. The value for ε is obtained from the figure 4 from the Wichert and Aziz paper

80



15

70

PER CENT C02

60

50

20

40

E

25

30

30

20 30

25

10 20 15

0

5

0

10

10

20

30

40

34.5

50

60

70

80

PER CENT H2S

Figure 4 Adjustment factors for pseudocritiacl properties for non hydrocarbon gases(Wichert & Aziz)

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EXERCISE 9.

Calculate the pseudo critical properties of the gas in exercise 4 if it also contained 3 lb of hydrogen sulphide, 10lb of carbon dioxide and 2.5lb of nitrogen Gas Components 1 2 3 4 5 6



Methane Ethane Propane Hydrogen sulphide Carbon Dioxide Nitrigen Total

Weight

Wgt Mol fraction weight

lb moles

Mole fraction

pc-psi

Tc °R

ppc psia

Tpc 255.70 26.17 10.81 28.25

25 3 1.5 3

0.56 0.07 0.03 0.07

16.04 30.07 44.09 34.08

0.035 0.002 0.001 0.002

0.743 0.048 0.016 0.042

667.00 708.00 616.00 1306

344 550 666 673

495.8 33.7 10.0 54.8

10

0.22

44.01

0.005

0.108

1071

548

116.1 59.38

2.5 45

0.06 1.00

28.02

0.002 0.0466

0.043 1.000

493

227

21.0 731

9.66 390

From Wichert & Azis chart for compositions of H2S and CO2 ε = 19

Tpc′ = Tpc - e = 371o R p′pc =

p pc Tpc′

(

)

Tpc + yH 2 S 1 − yH 2 S e

Ppc′ = 694.3

2.5 Standard Conditions for Real Reservoir Gases

As indicated in section 1.6 for ideal gases it is convenient to describe the quantity of gas to a common basis and this is termed the standard conditions, giving rise to the standard cubic foot and the standard cubic metre. The petroleum engineer is primarily interested in volume calculations for gaseous mixtures. Throughout the industry gas volumes are measured at a standard temperature of 60˚F (15.6˚C) and at a pressure of 14.7 psia (one atmosphere). These conditions are referred to as standard temperature and pressure STP. Standard Cubic Feet, the unit of volume measured under these conditions is sometimes abbreviated SCF or scf (SCM is Standard Cubic Metres). It is helpful to consider these expressions not as volumes but as an alternate expression of the quantity of material. For example a mass of gas can be expressed as so many standard cubic feet or metres.

EXERCISE 10. Express the quantity of 1 lb mole of a gas as standard cubic feet.

14

Behaviour of Gases

EXERCISE 11. Express the mass of gas in exercise 4 as standard cubic feet.

3 GAS FORMATION VOLUME FACTOR The petroleum industry expresses its reservoir quantities at a common basis of surface conditions which for gases is standard cubic volumes. To convert reservoir volumes to surface volumes the industry uses formation volume factors. For gases we have Bg, the gas formation volume factor, which is the ratio of the volume occupied at reservoir temperature and pressure by a certain weight of gas to the volume occupied by the same weight of gas at standard conditions. The shape of Bg as a function of pressure is shown in figure 5.



Bg =

volume occupied at reservoir temperature and pressure volume occupied at STP

The gas formation volume factor can be obtained from PVT measurements on a gas sample or it may be calculated from the equations-of-state discussed previously. One definition of the gas formation volume factor is: it is the volume in barrels that one standard cubic foot of gas will occupy as free gas in the reservoir at the prevailing reservoir pressure and temperature. Depending on the definition the units will change and the units will be; rb free gas/scf gas or rm3 free gas/scm gas

.008 .006 Bg rb/scf .004 .002 1000

2000

3000

PRESSURE (psig)

Figure 5 Gas Formation Volume Factor, Bg

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For example Bg for a reservoir at condition 2 is;

Bg =



V2 P Tz = sc 2 2 Vsc P2 Tsc zsc











(20)

‘sc’ refers to standard conditions. z at standard conditions is taken as 1.0 The reciprocal of Bg is often used to calculate volumes at surface so as to reduce the possibility of misplacing the decimal point associated with the values of Bg being less than 0.01, ie:

volume at surface 1 = =E volume in formation B g E is sometimes referred to as the expansion factor. Usually the units of Bg are barrels of gas at reservoir conditions per standard cubic foot of gas, ie bbl/SCF or cubic metres per standard cubic metre.

Bg =



VR Vsc















(21)

R and sc are reservoir and standard conditions respectively.

VR =



znRT P













(22)











(23)











(24)

T and P at reservoir conditions:

Vsc =



zsc nRTsc Psc



z = 1 for standard conditions



∴ Bg = z

T Psc cu. ft . . Tsc P SCF

Since Tsc = 520˚Rm Psc = 14.7 psia for most cases

Bg = 0.0283

zT cu. ft P SCF

Bg = 0.0283

16

or

zT cu. ft bbl × P SCF 5.615 cu ft

zT res bbl Bg = 0.00504 P SCF



Behaviour of Gases Bg = 0.0283 or

zT cu. ft bbl × P SCF 5.615 cu ft

Bg = 0.00504

zT res bbl P SCF









(25)

EXERCISE 12. Calculate the gas formation factor for a gas with the composition of exercise 4 existing at the reservoir conditions given in exercise 8.

EXERCISE 13. A reservoir exists at a temperature of 150°F (as for exercise 8) suitable for storing gas. It has an areal size of 5 miles by 2 miles and is 200ft thick. The average porosity is 20% and there is no water present. How much gas of the composition of exercise 4 can be stored at a pressure the same as in exercise 8 i.e. 3500 psia ? (1 mile= 5280 ft.)



4 Coefficient of Isothermal Compressibility of Gases The compressibility factor, z, must not be confused with the compressibility which is defined as the change in volume per unit volume for a unit change in pressure, or

cg = −

1  ∂V  1  ∂Vm    or = −   V  ∂P  Vm  ∂P 

Vm is the specific volume or volume per mole. cg is not the same as z, the compressibility factor.





(26)





(27)

For an ideal gas: PV = nRT or:

 dV  = − nRT  dP  P2 1 − nRT  1 cg =    = 2     V P P





For real gases:



V =

znRT P

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dz P −z  ∂V    = nRT dP2  ∂P  T P cg = −



cg =

P  nRT  ∂z  P − z  2    nRTz  P  ∂P

1 1 ∂z − . P z ∂P











(28)

dz/dP can be obtained from the slope of the z vs P curve. The Law of Corresponding states can be used to express the above equation in another form

P = Ppc Ppr

∂z  ∂Ppr   ∂z  =  ∂P  ∂P   ∂Ppr  ∂Ppr 1 = ∂P Ppc ∂z  1   ∂z  = ∂P  Ppc   ∂Ppr  Combining this equation with eqn 28 above yields

cg =

1 1  ∂z  − Ppc Ppr zPpc  ∂Ppr  Tpr

c g Ppc =

1 1  ∂z  − Ppr z  ∂Ppr  Tpr







Units of cg = P-1, and cgPc is dimensionless cpPpc is called pseudo reduced compressibility, cpr

18





(29)

Behaviour of Gases

Since the pseudo reduced compressibility is a function of ‘z’ and pseudo reduced pressure, the graph of Figure 2 can be used with Equation 29 to calculate values of cpr.

5 VISCOSITY OF GASES 5.1 Viscosity

Viscosity is a measure of the resistance to flow. It is given in units of centipoise. A centipoise is a gm/100 sec.cm. The viscosity term is called dynamic viscosity whereas kinematic viscosity is the dynamic viscosity divided by the density.



kinematic vis cos ity =

dynamic viscosity density

Kinematic viscosity has units of cm2/100 sec and the term is called centistoke.

Viscosoty, micropoises

Gas viscosity reduces as the pressure is decreased. At low pressures an increase in temperature increases gas viscosity whereas at high pressures gas viscosity decreases as the temperature increases. Figure 6 gives the values for pure component ethane.

1000 900 800 700 600 500

Viscosity of ethane

Pressure, psia 5000

400

3000

300

4000

2000 15000

200 750

1000

600

100 90 80 70 50

14.7

100

150

200

250

300

350

400

Temperature, deg F

Figure 6 Viscosity of ethane

The viscosity of gases at low pressures can be obtained from correlations presented by different workers.

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0.024

m liu He

0.022

Air

0.020

e x id Dio n rbo Ca

0.018

0.016 Viscosity, cp

en rog Nit

nS ge dro y H

0.014

id ulf

e

han M et e ylen Eth

0.012

e

ane Eth

e pan pr o n ta e i-Bu t ane n-Bu

0.010

0.008

e ntan n-pe a x ne n-He tane p e n-H

ane n-Oct ane n o N nne n-Deca

0.006

0.004

50

100

150

200

250

300

350

400

Temperature, ?ºF

Figure 7 Viscosity of paraffin hydrocarbon gases at one atmosphere

Figure 7 and Figure 8 give the viscosities of individual components and paraffin hydrocarbons at one atmosphere. For systems greater than 1 atmos the viscosities can be obtained from the literature. Another way is by calculating the reduced temperature and reduced pressure and use the chart developed by Carr6 which gives a ratio of µ at reservoir conditions. This is given in Figure 9 in terms of pseudo reduced conditions.

20

Behaviour of Gases

1.0

Gas Gravity (Air = 1) 2.0 2.5

1.5

Correction added to Viscosity, c.p.

0.015

0.013 0.012 0.011 0.010 0.009 0.008 0.007 0.006 0.005

Correction added to Viscosity, c.p.

Viscosity, at 1 atm, µ1, centipoise

0.014

0.0010 G = 20

1.5 1.0

G = 20

0.0010 G = 06

0.0005 0 0

400

ºF

300

º F

200

º F

100

º F

5 10 15 Mole per cent N2

3.5 CO2

0.0015

0.0005 0 0

1.5 1.0

G = 20

0.0010

G = 06 5 10 15 Mole per cent CO2

1.5 1.0

0.0005

G = 06 5 10 15 Mole per cent H2S

0 0

0.004 10

N2

0.0015

H2S

0.0015

3.0 Correction added to Viscosity, c.p.

0.016

0.5

20

30

40

50 60 70 Molecular Weight

80

90

100

Figure 8 Viscosity of gases at atmospheric pressure6

6.0 5.0

µ =

Viscosity at operating temperature and pressure, centipoises

µA =

Viscosity at 14.7 psia (1atm) and operating temperatures, centipoises

4.0

Viscosity, µ / µA

3.5 3.0

20 15

2.5

ps eu do red

10

uc ed

8

2.0

pre s

su re

6

,p

R

4 3

1.5

2 1

1.0 0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

Pseudoreduced Temperature, TR

Figure 9 Viscosity ratio vs pseudo reduced temperature and pseudo pressure.

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5.2 Viscosity of Mixtures

Another formula that is used for mixtures is:

µ mix =





Σµ j y j M j Σy j M j













(30)

j = 1, n

where:

y j = mole fraction of jth component M j = molecular weight of component µ j = the viscosity of jth component n = number of components The presence of other gases can also make a significant difference on the viscosity (Figure 7).

EXERCISE 14. Calculate the viscosity of the gas mixture in exercise 4 at 200°F and a pressure of one atmosphere.

EXERCISE 15. Use the gas gravity method to calculate the viscosity of the gas in exercise 4

EXERCISE 16. Determine the viscosity of the gas in exercise 4 at 150°F and 3500 psia (ref ex 4, 7, &8)

22

Behaviour of Gases

6 EQUATIONS OF STATE 6.1 Other Equations-of-State

As indicated at the start of section 2 the compressibility factor evolved out of the need to use an equation derived out of ideal gas behaviour and incorporating it into it a correction factor to suit real gas behaviour. One of the difficulties of the compressibility equation: PV = ZnRT to describe the behaviour of gases is that the compressibility factor is not constant and therefore mathematical manipulations cannot be made directly but must be carried out through graphical or numerical techniques. Rather than use this modified equation of state many have developed equations specifically to represent the behaviour of real gases. It is an irony however that because of the long use of the equation above incorporating z many of the real gas equation of states have been worked to calculate z for use in the above equation.

6.2 Van de Waals Equation 1873

The well known van der Waal’s equation was one of the earliest equations to represent the behaviour of real gases. This most basic EOS, which corrects for the volume of the molecules and attractive and collision forces using empirical constraints a and b. (P + a/V2) (V-b) = RT











(31)

The two corrective terms to overcome the limiting assumptions of the ideal gas equation are: (i) The internal pressure or cohesion term , which accounts for the cohesion forces, is a/V2. (ii) The co-volume b, which represents the volume occupied by one mole at infinite pressure and results from the repulsion forces which occur when the molecules move close together. The equation can also be written as: V3 - (+ b) V2 + (a/P)V - ab/P = 0 Such equations are therefore called cubic equations of state. The equation written to solve for z, the compressibility factor , becomes: Z3 - Z2 (1 + B) + Z A - AB = 0









(32)









(33)

where



A=

aP bP and B = 2 ( RT ) RT



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Values of a and b are positive constants for a particular fluid and when they are zero the ideal gas equation is recovered. One can calculate P as a function of V for various values of T. Figure 10 is a figure of 3 isotherms. Also drawn is the curve for saturated liquid and saturated vapour. Isotherm T1 is the single phase isotherm, Tc is the critical isotherm and T2 gives the isotherm below the critical temperature.

c

T1>Tc

P

Tc

Psat

T2>P) then the set of charts nearest to calculated Pic may be used. Otherwise, a crossplot of K values versus PK all at constant temperature and pressure, must be constructed for interpolation. For those components characterised as a C7+ fraction Katz has suggests using a K value of 15% of that of C7+. Danesh3 makes reference to other correlations to estimate the critical properties of C7+ fractions. McCain6 has also presented pseudo critical properties of C7+ as a function of molecular weight and specific gravity, his correlation figures are shown below in figure 7. 10

Equilibrium Ratio Prediction and Calculation

1700 Pseudocritical temperature, °R

1600 1500

Specific gravity of heptanes plus = 1.0

1400

.95

1300

.85

1200

.75

.90 .80 .70

1100

1000 900 100

150 200 250 Molecular weight of heptanes plus

300

500

Pseudocritical pressure, °R

450 400

1.0 = Specific gravity of heptanes plus

350

.95 .90

300

.85 .80

250

.75 .70

200 150 100

100

150 200 250 Molecular weight of heptanes plus

300

Figure 7 Pseudocritical properties of Heptane Plus6. 5

The following example has been presented by McCain in his text . and is helpful as a worked example in determining the appropriate convergence pressure charts Example: McCain5. The gas-liquid equilibrium of a high-shrinkage crude oil has been calculated. The composition of the liquid phase formed at 75˚F and 100 psia is given below. A convergence pressure of 2000 psia was used to determine the equilibrium ratios for the calculations. What value of convergence pressure should have been used for this mixture?

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Component

Composition of liquid mole fraction

Methane Ethane Propane i-butane n-butane i-pentane n-pentane Hexane Heavier*

0.0356 0.0299 0.0919 0.0170 0.0416 0.0198 0.0313 0.0511 0.6818 1.0000

* Molecular weight and gravity of C7+ assumed to be 263 and 0.886

Solution First, the composition of the liquid must be expressed as weight fraction. Component

Composition of liquid mole

C1 C2 C3 i-C4 n-C4 i-C5 n-C5 *C6 *C7+

0.0356 0.0299 0.0919 0.0170 0.0416 0.0198 0.0313 0.0511 0.6818 1.0000

Molecular weight Mj

16.0 30.1 44.1 58.1 58.1 72.2 72.2 86.2 263

Weight xMj

0.5696 0.9000 4.0528 0.9877 2.4170 1.4296 2.2599 4.4048 179.3134 196.3348

Composition of liquid, weight fraction xjMj/ΣxjMj 0.0029 0.0046 0.0206 0.0050 0.0123 0.0073 0.0115 0.0224 0.9133 0.9999

* Molecular weight and gravity of C7+ assumed to be 263 and 0.886 respectively

Second, adjust weight fraction to exclude methane and calculate weighted-average critical properties. Component Composition excluding

Critical °R temperature wjtcj °R Tcj

psia pressure, wjpcj psia pc psia pcj

C2 C3 i-C4 n-C4 i-C5 n-C5 C6 *C7+

549.8 665.7 734.7 765.3 828.8 845.4 899.3 1360

707.8 616.3 529.1 550.7 490.4 488.6 445.4 240

methane, wj

0.0046 0.0207 0.0050 0.0123 0.0073 0.0115 0.0225 0.9160 0.9999

* Critical properties of C7+ from figure 7.

12

2.53 13.78 3.67 9.41 6.05 9.72 20.23 1245.76 wt avg Tc= 1311°R, 851°F

Critical

3.26 12.76 2.65 6.77 3.58 5.623 10.02 219.84 wt avg pc= 265 psia

Equilibrium Ratio Prediction and Calculation

The calculated values of weight averaged Tc and Pc are close to Kensol and the mid continent crude point of figures 5 and 6. The location of the temperature 75°F with the methane - component (Kensol or mid - continental crude) is at a convergence pressure of around 10,000 psia, a value much greater than the assumed value of 2,000. The calculator needs to be repeated using the higher convergence pressure related K value data. The calculation procedure will converge when the estimated convergence pressure is the same as the calculated convergence pressure.

3 EQUATION OF STATE BASED EQUILIBRIUM CALCULATIONS 3.1 Methods Based on Empirical Equations of State of Fluid Phase Theory

The thermodynamic properties of a pure fluid may be represented by an equation of state of the generalised form: f (P,V,T) = 0 where the pressure P, temperature T and molar volume V are related by a mathematical function. Most equations of state have been developed by fitting an analytical expression to pure component PVT data. To extend the application of the developed equation to mixtures, the parameters of the equation must take into account the composition of the mixture and for simplicity require only the insertion of pure component data. Since most equations are effectively only mathematical models, the equations tend in general to be more complex, that is contain a large number of parameters, as the required level of accuracy increases. The basic assumption in the development of an equation of state is that at a critical point:

 ∂2 P   ∂P    =  2 = 0  ∂V  T  ∂V  T

Equations of state can be used for the following purposes: 1 representation of PVT data to assist data smoothing and improve interpolation; 2 prediction of vapour-liquid equilibria of mixtures especially at high pressures; 3 prediction of gas phase properties of pure fluids and their mixtures using a minimum amount of experimental data. In the gas property chapter we reviewed the topic of equations of state. Currently although a number of different equations could be used, the industry favours two, the Peng Robinson equation of state and the Soave modification of the Redlich Kwong equation of state.

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3.2 Prediction of Vapour-Liquid Equilibrium

An equation of state capable of predicting behaviour in the liquid phase and vapour phase is sufficient in itself for vapour-liquid equilibrium predictions. Unfortunately as we have indicated although modifications to the Van der Waals type equation have predicted vapour properties the equations in general have not been so accurate in predicting the liquid behaviour. Many vapour-liquid prediction methods have therefore gone to an equation of state, for example the Redlich-Kwong equation, for the prediction of the vapour phase fugacity and have employed a liquid theory to evaluate the liquid phase properties. We will now go through the steps in the application of equation of states in vapour liquid equilibrium calculations. It is worth noting that the steps described are those which would be taking place within each grid block of a compositional reservoir simulator. The implication therefore is a very large computational load for large numbers of grid blocks. The application of equation of states is based on the fact that at equilibrium, the fugacity of the gas and liquid phases are identical i.e: fiv = fiL















(2)

where fiv and fiL are the fugacities of component in the vapour and liquid phases respectively. The ratio of the fugacity to pressure is called the fugacity coefficient where φi = fi/(pzi) (3) where zi is the composition of the component in the system. The fugacities can be expressed for a vapour and liquid therefore by: fiL = φi xip and: fiv = φi yip p yi & xi

- is the system pressure; - are the mole fractions of i in the vapour and liquid phase.

Therefore:

fiL xp φ y Ki = iL = i = i fig φig ni ( ) y p i

The fugacity coefficients for the liquid and gas can be calculated using the following equation 14

Equilibrium Ratio Prediction and Calculation

ln φi =

V  1  RT  ∂p    dV − ln z −   RT ∫∞  V  ∂ni  T , V , n  i  





(4)

McCain5 and also Ahmed6 give good descriptions of the application of EOS in equilibrium calculations. At the present time the preferred EOS are the 3 parameter Peng-Robinson (PR) 8,9 and the Soave-Redlich Kwong (SRK)10. Other equations exist and are more accurate in predicting some properties. The considerable investment in binary interaction parameters for the preferred equations is such that there is a reluctance to use some recently developed EOS’s. Danesh's3 text gives a good review of the EOS. Since the applications of the equations are applied to mixtures, mixing rules are required to determine the values for the parameters in the particular EOS being used. We will use the Peng Robinson equation as our basis but others could be used. The Peng Robinson equation is



p=

RT aT − Vm − b Vm (Vm + b) = b(Vm − b)







(5)

The equation is set up for both liquid and gas using the following mixing rules to calculate b, and aT . The rules are presented in the context of gas ie. y, clearly for liquids, x values are used. and





b = ∑ yi bi i







aT = ∑ ∑ yi y j (aTi aTj )0.5 (1 − kiy ) i

j











(6)









(7)

where kij are the binary interaction coefficients, and kii = kjj = o and kij = kji. The value of bi and aTi for the individual components are calculated as follows



bi = 0.07780

and



RTci Pci

aTi = aciαi and

ac i = 0.45724



R2 T 2 ci Pci











(8)











(9)











(10)

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αi is a temperature dependant factor where

α i 0.5 = 1 + m(1.0 − Tri0.5 )













(11)







(12)

where 2 m = 0.37476 + 1.54226ω i − 0.26992ω i

The Peng Robinson equation can be written as a cubic equation in terms of z, the compressibility factor, z3 - (1-B)z2 + (A-2B -3B2)z - (AB - B2 -B3) =0





(13)





(14)

where



A=

aP R2 T 2

B=

bP RT







The solution to the above equation gives three roots for z. The highest value is the liquid phase z factor and when the equation is solved using vapour compositions then the lowest root is the z factor for the vapour. If the Peng Robinson equation is combined with the fugacity coefficient equation the following equation results for the fugacity coefficient of each component.

 z + (21.5 + 1) B  A ln φi = − ln( z − B) + ( z − 1) Bi′ − 1.5 ( Ai′ − Bi′) ln  1.5  2  z − (2 + 1) B 

(15)

Where B'i = bi/b













(16)









(17)

and



Ai′ =

1 aT

 0.5 0.5 2 aTi ∑ yi aTi 1 − kij 1 

(

)

Following all these steps independently for the liquid and gas phases the fugacities of the gas and liquid phases can be calculated. fLi = xipφLi and fvi = yipφvi When fLi=fvi then equilibrium is achieved and calculations are complete. Having presented these equations we will now describe the process to calculate K values , vapour liquid equilibrium ratios and compositions given a system composition, temperature and pressure.

16

Equilibrium Ratio Prediction and Calculation

Step 1: Estimate the K values of the system. The Wilson11 equation is good for this purpose.

p  T   Ki =  ci  exp 5.37(1 + ω i )1 − ci     p T  







(18)

wi = acentric factor for component i Step 2: Carry out vapour equilibrium calculations using estimated K values using the iterative procedure outlined previously. That is estimate the V/L ratio and iterate until convergence is obtained, that is when compositions sum to unity. We now have liquid and vapour compositions to use in equation of state calculations. Step 3: Using liquid compositions, calculate the A & B values for the EOS and then solve the z-value form of the EOS, to determine z. The lowest root (value) is the z value for the liquid. Step 4: Calculate the compositional coefficients A'i and B'i for the liquid components and calculate the fugacity coefficients of the components of the liquid Step 5: Repeat steps 3 & 4 using the vapour phase compositions. Step 6: Calculate fgi and fLi fgi=yipφi and fLi= xipφI . Check if fgi= fLi. If this value is greater than 10-12 then the whole process has to be repeated from step 1, except that the K values used are the calculated K values arising from step 5 i.e. Rather than set up the tolerance check on fugacity equivalence the tolerance can be εi = fLi - fgi based on K values. A value of ε of 0.001 can be used for the sum of the errors.



Ki =

εi =

φ Li φ gi 2 ( KiE − KiC ) KiE KiC















(19)













(20)

The iteration is complete when these tolerance limits are met and the compositions of the respective phases are those which have been been determined at the last iteration. Calculations can then proceed to provide volumetric and density data for the respective phases. Danesh3 has given a flow diagram for the above flash calculation. An example follows to illustrate the calculation process. Institute of Petroleum Engineering, Heriot-Watt University

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Start Input zi, P, T, Component Properties Estimate Ki, Using Eq.(18) Calculate xi, yi, Using Figs. 20-22 (Ch 12) Set-Up EOS For Liquid

Set-Up EOS For Vapour

Calculate ZL

Calculate ZV

Calculate fiL

Calculate fiV

Adjust Ki = Ki old (fiL/fiV) NO NO Is Σ(1- fiL/fiV)2