1 Multi-Phase Flow Analysis in Oil and Gas Engineering Systems and Its Model PDF

 

Multi-phase Flow Analysis in Oil and Gas Engineering Systems and its Modelling

F  l    o w  A n  a l    y   s  i    s 

a report by

Orl and o F A y al a , 1 L ui s F A y al a 2 and  Orl and o M A y al a 1 1. Universidad de Oriente; 2. Pennsylvania State University

Two-phase flow is very common in industrial processes and its applications were already in use in ages as remote as the era

consequence of their deformable nature, gas and liquid may adopt a wide variety of spatial configurations, usually referred to as

of Archimedes. At the present time, many industrial processes

flow patterns.

rely on multi-phase phenomena for the transport of energy and mass or for material processing. During the last century, the

Multi-phase flow phenomena can be found in a wide range of

nuclear, chemical and petroleum industries propelled intense

length scales of interest. Therefore, the most suitable approach to

research activity on the area. Their efforts have been aimed at the

study multi-phase flows will largely depend on the length scale of

demystification of the mechanisms taking place during this complex

interest. Typically, in the petroleum industry, attention is given to

flow situation.

large-scale phenomena in multi-phase flows, as no detailed flow behaviour is needed for routine design and operation. For instance,

In the petroleum industry, two-phase flow can be found in a variety

in pipeline networks we are interested only in the pressure drop and

of situations. The three more common working fluids (oil, natural

liquid hold-up. Other than the effect of the local flow pattern

gas and water) can have four different two-phase flow

variables, detailed flow phenomena are not important. However,

permutations: gas–liquid, liquid–liquid, solid–liquid and solid–gas

small-scale studies of multi-phase flows are very important because

flows. A solid phase can be incorporated to the flow either from the

large-scale phenomena are controlled by small-scale physics. For

reservoir itself (due to either drilling activities or sand formation during production) or from the formation of complex solid structures

instance, the transition from one flow pattern to another is driven by local small-scale phenomena. One of the most important problems

due to the prevailing production conditions (e.g. hydrates in natural

to be addressed by the scientific community is the development of

gas flow or waxes and asphaltenes in oil flow). Oil and natural gas

an improved understanding of transitions from one flow regime to

transportation typically deals with a gas–liquid system of flow. Due

another. This can be achieved only through small-scale studies of

to the deformable nature of fluids, the simultaneous flow of gas

multi-phase flows. In addition, for the improved understanding of

and liquid in a pipe represents a very complex process. As a

the operation of process equipment such as separators in the petroleum industry, it is necessary to understand the small-scale phenomena associated with separation.

Orlando F Ayala is a Consultant for the Venezuelan Petroleum Company. His research activities focus on the areas of natural gas, fluid mechanics, turbomachinery and heat transfer. He is a member of the National Association of Engineers of Venezuela. Professor Ayala holds an MSc degree in Mechanical Engineering from the University of Kansas. He was Professor of Mechanical Engineering at the Universidad de Oriente, Venezuela for 40 years before his retirement and chaired the Natural Gas Engineering graduate programme of Universidad de Oriente for 15 years.

Luis F Ayala is Assistant Professor of Petroleum and Natural Gas Engineering at the Pennsylvania State University, US. He has also been an Instructor in the Chemical Engineering and Petroleum Engineering Departments at Universidad de Oriente. Professor Ayala’s research activities focus on the areas of natural gas engineering, hydrocarbon phase behaviour, multi-phase flow, numerical modelling, and artificial intelligence. He is a Member of the Society of Petroleum Engineers), the American Chemical Society, the National Association of Engineers of Venezuela and the Canadian Petroleum Society. Professor Luis Ayala holds PhD and MSc degrees in petroleum and natural gas engineering from Pennsylvania State University and two engineering degrees with honours, one in chemical engineering ( summa  summa cum laude ) and one in petroleum engineering ( summa  summa cum laude ), from Universidad de Oriente.

The Growth of Multi-phase Flow Modelling The development of multi-phase flow large-scale analysis in the petroleum industry has been divided into three partially overlapping periods – the empirical period, the awakening years and the modelling period1 – which together encompass the second half of the past century. During the empirical period, all efforts were focused on correlating data from laboratory and field facilities in an attempt to encompass the widest range of operational conditions possible. The earliest attempt to empirically predict two-phase flow pressure drops for horizontal pipes is the well-known work of Lockhart and Martinelli. This correlation was followed by an innumerable number of new ones, which claimed to be progressively more applicable for a wider range of operational conditions. Being the first quantitative approach to two-phase flow modelling, Lockhart and Martinelli’s correlation became a classic against which subsequent correlations were compared. The fact is that most

Orlando M Ayala is Assistant Professor of Mechanical Engineering at the Universidad de Oriente. Professor Ayala’s research activities focus on the areas of multi-phase flows, turbulent flows, computational fluid analysis, direct numerical simulation and heat transfer. He is a Member of the American Society of Mechanical Engineers and the National Association of Engineers of Venezuela. Professor Orlando M Ayala holds PhD and MSc degrees in Mechanical Engineering from the University of Delaware and an engineering degree in Mechanical Engineering with honours (cum laude ) from Universidad de Oriente. He has also been working on several engineering projects for the Venezuelan Petroleum Company.

© TOUCH BRIEFINGS 2007

correlations are always best applicable for the conditions from which they were derived. It is worth mentioning the correlation developed by Beggs and Brill for predicting flow behaviour in inclined pipes. Along with a number of modifications applied to it, Beggs and Brill’s correlation became one of the most extensively used correlations. The correlation considers horizontal, vertical and inclined pipes, and the basic correlating parameter was the Froude number – a dimensional number that is considered a measure of the influence of

57

 

Multi-phase Flow Analysis in Oil and Gas Engineering Systems and its Modelling gravity on fluid motion. In general, the reliance on the empirical

introduce a fully phenomenological description of how transitions

approach was always limited by the uncertainty of their application

occur among the different flow patterns was the work developed

to systems operating under different conditions than those from

by Taitel and Dukler, which focused on horizontal and near-

which the correlations were originally proposed. Nonetheless,

horizontal pipes. The work of Taitel and Dukler is considered one

calculating and designing flow lines in multi-phase production

of the classic papers in multi-phase predictions that began to

facilities on the basis of empirical correlations was the norm until

incorporate more physical insight into analysis in the petroleum

well into the 1980s.

industry. This work led the way for subsequent research in the area, and most of their transition criteria are still in use in more

The advent of the personal computer during the 1980s dramatically

recent two-phase flow models. Few years after that initial work,

enhanced the capabilities of handling progressively more complex design situations, which is why this period has been called ‘the

Taitel and co-workers extended the model for the vertical and nearvertical case and Barnea extended the phenomenological approach

awakening years’.1 Much of the petroleum research on multi-phase

to the whole range of pipe inclinations in the 1980s. These three

flow during these years and the subsequent modelling period was

works are commonly referenced among researchers in the area, with

enriched by the progress already made by the nuclear industry.

a number of attempts at improvement.

Although the nuclear industry dealt with much simpler fluids (water and steam), it led the way towards more involved two-phase flow

Additional steady-state comprehensive mechanistic models for two-

analysis in the petroleum industry. More fundamental multi-phase

phase flow in vertical wells, horizontal pipes and deviated wells were

flow analysis approaches, such as two-fluid modelling, were already

presented by Ansari, Xiao, Kaya and co-workers in the 1990s. All

in use in the nuclear industry in the 1970s. These seed efforts are t he

these mechanistic models were developed at the Tulsa University

genesis of the well-known fast transient two-phase-flow codes –

Fluid Flow Projects and are usually referred to as TUFFP models.

State-of-the-art large-scale flow  modelling in the oil and gas multi-phase industry is largely  based on mechanisti mechanisticc models. RELAP4, RELAP5, RETRAN, MEKIN, COBRA, CATHARE and TRAC – in

Nowadays, there are also a number of commercially available two-

use today in the nuclear industry. Nowadays, the petroleum industry

phase flow packages, which include various features intended to

might be ready to explore new research avenues in multi-phase flow

accomplish specific tasks. Examples include OLGA, TACITE, PEPITE

analysis, with the incorporation of the increasingly sophisticated

and PIPESIM, among others.

modelling tools that have become available in the last few years. Modern multi-phase flow analysis models the flow of oil and gas The modelling period, which extends up to the present day, refers

through pipelines by invoking the basic principles of continuum

to the growing tendency of introducing more physically based (mechanistic or phenomenological) approaches into multi-phase

mechanics and thermodynamics. Depending on how these equations are applied and how the interactions between phases are

flow calculations. The main goal remains an attempt to reduce the

described, the most widely used two-phase models are the

impact of empirical correlations on multi-phase predictions. State-

homogeneous model (flow treated as a single phase with averaged

of-the-art multi-phase modelling efforts can be studied in two

fluid properties), drift-flux model (flow described in terms of an

different but interrelated fields of interest: small-scale and large-

averaged local velocity difference between the phases), separated

scale, depending on the length scale of interest to the modeller.

model (phases considered to be flowing in separated zones of the

During recent years, the oil and gas industry has paid particular

channel) and two-fluid model (a multi-fluid model that considers

attention to large-scale modelling of multi-phase flows. However,

two flowing phases and their interactions).

small-scale modelling promises to bring important physical insights into the quest for more accurate and reliable modelling of multi-

In the last decade, a great deal of attention has also been devoted

phase flow in the oil and gas industry in the foreseeable future.

to mechanistic or ‘phenomenological’ models – i.e. models trying to capture specific features of individual flow patterns – in which

58

Large-scale Interest

simplified conservation equations are invoked while the main focus

State-of-the-art large-scale multi-phase flow modelling in the oil and

is the prediction of pressure drop and hold-up. However, in previous

gas industry is largely based on mechanistic models. One of the distinguished features of a mechanistic model is the need for a

decades, the challenge of modelling two-phase flows by invoking such fundamental laws had been circumvented by

reliable tool for the prediction of flow pattern transitions for a given

reliance on empirical and semi-empirical correlations, especially in

set of operational conditions. Perhaps the earliest attempt to

the oil industry.

HYDROCARBON WORLD 2007

 

Multi-phase Flow Analysis in Oil and Gas Engineering Systems and its Modelling Perhaps one of the most fundamental and rigorous approaches to

are a continuum and invokes the basic laws of continuum mechanics

the study of large-scale multi-phase flow currently in use in the

in one dimension coupled with a thermodynamic phase behaviour

petroleum industry is the two-fluid model. In the two-fluid model,

model. In their work, the required semi-empirical relationships

separate conservation equations (mass, momentum and energy) are

needed to give mathematical closure to the model are discussed

written for each of the two phases for a total of six equations.

in detail.

These equations are coupled with terms describing the interaction between phases. In this two-phase flow method of analysis, as

Small-scale Interest and Computational Physics

well as in all the others, empiricism cannot be completely avoided,

The study of small-scale multi-phase flow has proved to be extremely

since additional closure relationships are needed. Empiricism

difficult for researchers due to the elusive nature of the phenomena

Perhaps one of the most fundamental and  rigorous approaches to the study of large-scale multi-phase flow currently in use in the  petrol  pet roleum eum ind indust ustry ry is the two two-fl -fluid uid mod model. el. comes into the picture during attempts to model the variety of

and the inherent limitations of experimental set-ups. A great deal of

constitutive relationships2 that show up in conservation equations. For instance, Ayala et al. have presented a unified two-fluid model

progress has been made on the development of useful small-scale experimental studies, but numerical experiments or models still

for the analysis of natural gas flow in pipeline in multi-phase flow

remain the most effective way of studying such detailed flow

regimes. Their formulation assumes that both gas and its condensate

behaviour. The challenge of modelling small-scale multi-phase flow

Engineering for mobility

Mubea is specialised in the production of high quality disc springs (Belleville Washers) Washers) for all different kinds of applications in the Oil and Gas Industry Industry..     m Specia materialss and geometrie geometriess up to 800 mm outside outside diamete diameterr can be offered to     o Speciall material     c yourr requ requirem irements ents.. Mube Mubea’ a’ss int intensi ensive ve know knowledg ledgee abou aboutt shot shot-peen -peening ing of   . suit you     a highly stressed springs guarantees a long fatigue life as well as reliability in     e      b perform performance. ance. Our complete complete in-house in-house process process and our well well equipped equipped test     u labora laboratories tories help to almost almost fulfill all all of our customer’s customer’s demands. Mubea’ Mubea’ss highly     m  . qualified engineering engineering team can offer offer you the best design and solution solution wherever  you u ne need ed hi high gh for force cess in a sm smal alll en envi viro ronm nmen entt .     w  yo

    w     w

engineering for mobility

 

Multi-phase Flow Analysis in Oil and Gas Engineering Systems and its Modelling resides in the finite nature of the computer power typically available

order to accurately capture the new fluid positions at each time-

to the modeller and the difficulty of tracking separated phases (and

step. At every time-step, the grid is refitted and adjusted to match

interfaces between them) with sharply different properties.

the location of the new, displaced boundaries. In the 1980s, Ryskin

The interplay of these two factors has historically limited the

and Leal used this method to study the steady rise of buoyant,

complexity of the systems that can be studied using small-scale

deformable, axisymmetric axisymmetric bubbles, while Oran and Boris studied the

simulation. However, during the last decade, major progress

break-up of a two-dimensional drop. A similar approach, called

has been achieved by implementing a variety of numerical

front tracking, is also used, where a separate front marks the

techniques, which typically depend upon the flow pattern type that

interface but a fixed grid is used for the fluid within each phase;

prevails under the conditions of the study. The study of small-scale

however, the fixed grid is modified near the front so a single grid

phenomena started when a group of scientists at the Los Alamos National Laboratory began to develop the basis of Computational

line follows the interface.

Fluid Dynamics (CFD) in the early and mid-1960s. In multi-phase

Small-scale modelling typically takes advantage of certain multi-

flow modelling within small-scale interest, the Navier-Stokes

phase flow conditions that can greatly simplify the modelling

equations – with the appropriate boundary conditions – are solved

process. For example, it is possible to simplify the Navier-Stokes

through a suitable numerical method – e.g. finite volumes,

equations by ignoring inertia completely (Stokes flow) or by ignoring

finite differences, finite elements or spectral methods. The

viscous effect (inviscid flows) in the limit of low and high Reynolds

main problem arises when considering that some boundary

numbers, respectively. These two limiting cases are typically

conditions are time-dependent, since they are located at phase

studied with boundary integral methods. The study of dispersed

boundaries, which are free to move, deform, break up or coalesce.

flows, for example, can be made especially amenable to small-scale

Different methods have been proposed; here we mention a few

simulation since the study of one of the phases (i.e. the dispersed

of them.

phase) can be greatly simplified. Two main methods are used to

Large-scale modelling includes the use of  transient and steady-state two-fluid models, as well as a variety of steady-state mechanistic models. The most common small-scale modelling approach discretises the

simulate dispersed flows: the Eulerian-Eulerian or the Eulerian-

flow domain using a regular and stationary grid – i.e. the well-

Lagrangian approach. In the Eulerian-Eulerian approach, separated

known Eulerian frame of reference for fluid motion. The first small-

equations are solved for the dispersed and the continuous

scale Eulerian method proposed was the marker-and-cell (MAC)

phase. No attempt is made to resolve the detailed motion

method, where marker particles distributed uniformly in each fluid

of the particles, and thus closure relations are necessary for

were used to identify each fluid. Using this method, in the late 1960s Harlow and Shanon studied the splash when a drop hits a liquid

the unresolved motion and the forces between the particle and the continuous phase. The closure relations are determined

surface. The MAC method has become obsolete since then and

through experimental correlations (similar to the computation of

has largely been replaced by others that use marker functions

turbulent flows using Reynolds average Navier-Stokes equations).

instead – e.g. the so-called volume-of-fluid (VOF) method. In the

In the Eulerian-Lagrangian approach, the dispersed phase is

VOF method, the transition between two fluids takes place within

represented by points moving inwards and otherwise constant-

the context of one grid cell. The main problem associated with this

density flow – i.e. the so-called point particle approximation.

is the difficulty of maintaining a sharply defined boundary between

The particles are followed using a Lagrangian approach and

two flowing fluids. In order to address this difficulty, level-set (LT)

the forces (such as drag forces) on the particle are specified

methods use continuous – rather than discontinuous – marker

by analytical and experimental models. In some cases, the particles

functions in order to identify the fluids. The use of continuous

are assumed to have no effect on the fluid flow, but in other

marker functions creates smooth transition zones between the two

cases the forces from the particles are added to the right-hand

fluids of interest and avoids the difficulty of maintaining a sharply

side of the Navier-Stokes equation of the continuous phase.

defined boundary.

However, none of these approaches can model the detailed flow around the particle that affects the interactions of nearby particles.

60

Some other small-scale modelling approaches use the Lagrangian frame of reference for fluid motion. In Lagrangian methods, the

These interactions are important to understand particle coalescence, which is the first step towards a possible flow pattern change.

numerical grid follows the fluid and deforms with it. In this

Ayala et al. 3 have recently developed a first attempt to

approach, the motion of the fluid interface needs to be modelled in

incorporate such interactions through a new hybrid direct numerical

HYDROCARBON

WORLD

2007

 

Multi-phase Flow Analysis in Oil and Gas Engineering Systems and its Modelling simulation (HDNS). This approach consists of direct numerical

much more heavily on empirical or semi-empirical correlations

simulation

flow

to model the phenomena than small-scale multi-phase analysis

and an analytical representation of local disturbance flows induced

does. Small-scale multi-phase flow analysis relies on the direct

by the particles.

solution of the most fundamental fluid dynamic equations, thus

of

the

undisturbed

continuous

phase

greatly reducing the need for empiricism. The limitation of In addition, a relatively new method in small-scale modelling is

small-scale multi-phase analysis resides in its scope, which is not

the Lattice Boltzmann method. Lattice Boltzmann methods are

currently amenable to the study of large industrial systems. The

based on kinetic theory and thus no Navier-Stokes equations are

oil and gas industry relies on large-scale analysis and does not

solved. Instead, the method considers a typical volume element of

currently use small-scale methods for the simulation and modelling

fluid to be composed of a collection of ‘particles’ that are represented by a particle velocity distribution function for each fluid

of oil and gas systems, but the physical insights that can be obtained by small-scale simulation are invaluable. It is widely

component at each grid point. In this novel approach, the rules

expected that the demystification of small-scale intricacies of

governing the motion and collisions of these ‘particles’ are designed

multi-phase flow phenomena can greatly help large-scale modelling

in such a way that the time-average motion of the particles is

in the foreseeable future. The simultaneous implementation of

consistent with the Navier-Stokes equation.

large-scale and small-scale simulation represents a powerful combination that can significantly improve our understanding

Concluding Remarks

of multi-phase flow phenomena. Small-scale simulation, for

The most popular modelling approach nowadays in the oil and

example, could play an important role in significantly improving the

gas industry – above and beyond the use of long-established,

nature and reliability of the semi-empirical relationships needed

fully empirical equations – is large-scale mechanistic modelling.

by large-scale simulation models. Small-scale simulation can also

Large-scale modelling includes the use of transient and steady-state

define more reliable flow pattern transition models, which are the

two-fluid models, as well as a variety of steady-state mechanistic

backbone of the large-scale multi-phase flow simulators in

models. However, large-scale multi-phase flow modelling relies

use today. ■

1. Brill J, Ariracha Arirachakaran karan S, State State of the Art Art in Multiphase Multiphase Flow, Flow,  J P et Tec h , 1992;44(5):538–41 1992;44(5):538–41.. 2. Ayala LF, LF, et al., Low-li Low-liquid quid Loading Loading Multipha Multiphase se Flow in in

3.

natural Gas Pipelines,  J E ner gy Res our ces and Tec h , 2003;125:284–93. Ayala OM, OM, et al., A Hybrid Hybrid Approach Approach for Simulat Simulating ing Turbulent Turbulent

Collisions of Hydrodynamically-interacting Particles,  J C omp ut  Phys , 2007;doi:10.1016/j.jcp.200 2007;doi:10.1016/j.jcp.2006.11.016. 6.11.016.

NEPTUNE OCEANOGRAPHICS LTD PROVIDING SERVICES TO THE OFFSHORE INDUSTRY

Leaks in your subsea pipeline installations? Neptune Oceanographics can find them Techniques available include: Fluorescence Acoustics Direct hydrocarbon detection (oil and gas) Differential temperature NOL maintain a continuous programme of development of new techniques for subsea leak detection Neptune Oceanographics Ltd, Sapharey House, Charlbury, Oxon, OX7 3SX, UK Tel +44 8453 707177. Fax +44 8704 581979. Email [email protected] www.neptune.gb.com Neptune Oceanographics ltd is an ISO 9001 : 2000 certified company First Point Registration 20436