Performance of Flowing Wells

Learning Objectives Production Technology

• Inflow Performance Relationship (IPR)

Performance of Flowing Wells

– Single phase – Two phase

• Vertical Lift Performance – Single phase – Two phase

Professor Bahman Tohidi Institute of Petroleum Engineering Heriot-Watt University Edinburgh EH14 4AS Scotland Tel: +44 (0)131 451 3672 Fax: +44 (0)131 451 3127 Email: [email protected] January 04

Performance of Flowing Wells

• Flow Through Chokes • Matching Inflow and Tubing Performances

1

1

January 04

Introduction

2

2

Introduction • Production is generally limited by the pressure in the reservoir and difficult to do something about it. • A major task is to optimise the design to maximise oil and gas recovery.

• Production by natural flow • Need for better understanding of various concepts which define well performance. • Pressure loss occurs in: – – – – – – –

Performance of Flowing Wells

the reservoir the bottom hole completion the tubing or casing the wellhead the flowline the flowline choke pressure losses in the separator and export pipeline to storage

January 04

Performance of Flowing Wells

3

3

Production Performance

5

4

4

– The nature of the fluid flow – Time taken for the pressure change in the reservoir – Fluid to migrate from one location to another

– Inflow performance of formation fluid flow from formation to the wellbore. – Vertical lift performance as the fluids flow up the tubing to surface. – Choke or bean performance as the fluids flow through the restriction at surface.

Performance of Flowing Wells

Performance of Flowing Wells

Fluid Flow Through Porous Media

• Production performance involves matching up the following three aspects:

January 04

January 04

– For any pressure changes in the reservoir, it might take days, even years to manifest themselves in other parts of the reservoir. – Therefore flow regime would not be steady state – Darcy’s law could not be applied – Time dependent variables should be examined

5

January 04

Performance of Flowing Wells

7

7

1

Characterisation and Modelling of Flow Patterns

Idealised Flow Pattern • They are: • Linear, Radial, Hemi-spherical, and Spherical

The actual flow patterns are usually complex, due to: 1. The shape of oil formations and aquifers are quite irregular 2. Permeability, porosity, saturations, etc are not homogeneous 3. Irregular well pattern through the pay zone 4. Difference in production rate from well to well 5. Many wells do not fully penetrate the pay zone, or not fully perforated.

• The most important cases are linear and radial models, both used to describe the water encroachment from an aquifer. • Radial model is used to describe the flow around the wellbore.

January 04

Performance of Flowing Wells

8

8

January 04

Well Inflow Performance P1

L

Definition One Darcy is defined as the permeability which will permit a fluid of one centipoise viscosity to flow at a linear velocity of one centimeter per second for a pressure gradient of one atmosphere per centimeter.

A

Darcy’s Law P1 − P2 A µ L

U=

Q K P1 − P2 K ∆P = =− A µ L µ ∆L

Q=K

Assumptions For Use of Darcy’s Law

P1 − P2 A L µ

Q∝

Performance of Flowing Wells

10

10

• Reservoir is horizontal and of constant thickness h. • Constant rock properties φ and K. • Single phase flow • Reservoir is circular of radius re • Well is located at the centre of the reservoir and is of radius rw. • Fluid is of constant viscosity µ. • The well is vertical and completed open hole

Performance of Flowing Wells

Steady flow Laminar flow Rock 100% saturated with one fluid Fluid does not react with the rock Rock is homogeneous and isotropic January 04 Performance of Flowing Wells Fluid is incompressible

12

12

Characteristics of the Flow Regimes

Radial Flow for Incompressible Fluids

January 04

9

9

Darcy’s Law

P2

Q

January 04

Performance of Flowing Wells

• Steady-State; the pressure and the rate distribution in the reservoir remain constant with time. • Unsteady-State (Transient); the pressure and/or the rate vary with time. • Semi-Steady State (Pseudo Steady-State); is a special case of unsteady state which resembles steady-state flow. • It is always necessary to recognise whether a well or a reservoir is nearest to one of the above states, as the working equations are generally different. 13

13

January 04

Performance of Flowing Wells

14

14

2

Coping with Complexities

Radial Flow for Incompressible Fluids

• There are essentially two possibilities:

Two cases are of primary interest: • Steady state: The reservoir conditions does not change with time.

1. The drainage area of the well, reservoir or aquifer is modelled fairly closely by subdividing the formation into small blocks. This results in a complex series of equations which are solved by numerical or seminumerical methods.

– Flow at r=re

• Semi steady state or pseudo steady state: Reservoir conditions changes with time, but dP/dr is fairly constant and does not change with time. – No flow occurs across the outer boundary – Fluid production of fluids must be compensated for by the expansion of residual fluids in the reservoir.

January 04

Performance of Flowing Wells

15

2. The drained area is represented by a single block in such a way that the global features are preserved. Inhomogeneities are averaged out or substituted by a simple pattern. Here the equations of flow can be solved analytically. 15

January 04

Steady State - Radial Flow of an Incompressible Fluid

16

qr µ dr q µ re dr = r ∫ 2πKh r 2πKh rw r [Pe − Pw ] = qr µ ln( re ) 2πKh rw

∫

Pe

Pw

18

dP = ∫

re

rw

[Pe - Pw ] is the total pressure drop across the reservoir and is denoted the drawdown. qr is the fluid flowrate at reservoir conditions. If the production rate measured at standard conditions at surface i.e. qs then qs.B = qr

Can be integrated between the limits of: inner boundary i.e. the wellbore sand face: r = rw P = Pw outer boundary i.e. the drainage radius: r = re P = Pe Performance of Flowing Wells

16

Steady State - Radial Flow of an Incompressible Fluid

A = 2πrh q q K dP U= r = r = A 2πrh µ dr q µ dr dP = r 2πKh r

January 04

Performance of Flowing Wells

[Pe − Pw ] = 18

Steady State - Radial Flow of an Incompressible Fluid

January 04

qsµB r ln( e ) 2πKh rw Performance of Flowing Wells

19

19

Steady State - Radial Flow of an Incompressible Fluid

If the production rate measured at standard conditions at surface i.e. qs then qs.B = qr

[Pe − Pw ] =

qsµB r ln( e ) 2πKh rw

In field units, i.e., P and qs in psi and STB/day

[Pe − Pw ] =

qsµB re 1 ln( ) 7.082 x10 −3 Kh rw

Highly supportive reservoir pressure maintenance with water injection or gas reinjection. Reservoir production associated with a substantial qsµB re 1 expanding gas cap. [P − P ] = ln( ) e

January 04

Performance of Flowing Wells

20

20

January 04

w

7.082 x10 −3 Kh

Performance of Flowing Wells

rw

21

21

3

Semi Steady State Radial Flow of a Slightly Compressible Fluid

Semi Steady State Radial Flow of a Slightly Compressible Fluid dP )r =r = 0 dr e dP ( )r P BPt . – The range of patterns developed will depend on the flow velocity and the GOR.

• Black Oil – A black oil has a very low GOR and accordingly is unlikely to progress beyond the bubble and slug flow regimes into annular flow.

• Heavy Oil – Heavy oil normally has a very low (or nonexistent) GOR and as such it will vary from single phase oil to the bubble flow regime. January 04

Performance of Flowing Wells

111

111

Fluid Parameters in Multiphase Flow: Slippage

Fluid Parameters in Multiphase Flow: Holdup

• If a gas-liquid mixture flows up a tubing string, the effects of buoyancy on the phases will not be equal. • The lighter of the phases will rise upwards at an incrementally higher rate compared to the oil. • The slip velocity, Vs, is defined as the difference in velocities of the two phases, ie, for a gas-oil system. Vs= Vg- Vo • Particularly in the flow slug regime, the impact of slippage is to assist in lifting the heavier phase (oil). • However if slippage is severe it can promote segregated flow particularly in the low velocity bubble flow regime. January 04

Performance of Flowing Wells

118

January 04

118

• Holdup is a term used to define the volumetric ratio between two phases which occupy a specified volume or length of pipe. • The liquid holdup for a gas-liquid mixture flowing in a pipe is referred to as HL:

• HL therefore has a value between zero and one. • Similarly, the gas holdup Hg is defined as:

January 04

Performance of Flowing Wells

119

119

14

Fluid Parameters in Multiphase Flow: Fluid Velocity

Practical Application of Multiphase Flow

• A difficulty arises as to how to define the velocity of a specific phase. There are two options: – The first option is to define velocity based upon the total cross-sectional area of the pipe. – The velocity in this case is termed the superficial velocity. – A more accurate value for the velocity of each phase is to correct for the holdup of each phase.

January 04

Performance of Flowing Wells

120

120

dP dP dP dP )Tot = ( )elev + ( )frict + ( )accel dL dL dL dL

January 04

123

123

A, B, C=Different Tubing Head Pressures

Flow regime

ρ ∆( v ) dP )accel = m dL 2gc dL 2 m

Performance of Flowing Wells

125

125

Pressure Transverse or Gradient Curves • By shifting the curves downwards, he found that, for a constant GLR, flowrate and tubing size, the curves overlapped • Then, a single curve could be utilised to represent flow in the tubing under assumed conditions. • The impact was in effect to extend the depth of the well by a length which, would dissipate the tubing head pressure. January 04

Performance of Flowing Wells

Hold up

(

(

January 04

Pressure Transverse or Gradient Curves

• Most of the multiphase flow correlations can be used with the following general procedure: • Use will be made of the general equation:

dP )elev = ρm dL f ρ v dP ( )frict = m m m dL 2gc d

• 1. Computer - recommended if time and location permits • 2. Working curves (pressure traverse or pressure gradient curves) - for initial estimation or when computer programme is not available.

Multiphase Flow Models

(

• There are two choices in conducting two phase flow calculations in calculating vertical lift performance of a well:

January 04

Performance of Flowing Wells

126

126

128

128

Gradient Curves Gilbert was then able to collect all the curves for a constant tubing size and flowrate on one graph, resulting in a series of gradient curves which would accommodate a variety of GLRs. He then prepared a series of gradient curves at constant liquid production rate and tubing size.

A, B, C=Different Tubing Head Pressures

Performance of Flowing Wells

127

127

January 04

Performance of Flowing Wells

15

Gradient Curves

January 04

Performance of Flowing Wells

129

129

January 04

Performance of Flowing Wells

130

130

132

132

134

134

Positive or Fixed Choke • This normally consists of two parts: – A choke which consists of a machined housing into which the orifice capability or "bean" is installed. – A "bean" which consists of a short length 1-6", of thick walled tube with a smooth, machined bore of specified size. January 04

Performance of Flowing Wells

131

131

January 04

Valve Seat with Adjustable Valve Stem

Performance of Flowing Wells

Rotating Disc Choke

• In this design, the orifice consists of a valve seat into which a valve stem can be inserted and retracted, thus adjusting the orifice size. • The movement of the valve stem can either be manual or automatic using an hydraulic or electrohydraulic controller. January 04

Performance of Flowing Wells

133

133

January 04

Performance of Flowing Wells

16

Choke Flow Characteristics

Critical Flow through Chokes

• Chokes normally operate in multiphase systems. Single phase can occur in dry gas wells.

January 04

Performance of Flowing Wells

135

R=P2/P1 The value of R at the point where the plateau production rate is achieved is termed the critical pressure ratio Rc.

135

January 04

Critical Flow through Chokes

Performance of Flowing Wells

137

136

136

Critical Flow through Chokes • For a two-phase compressible mixture, say, oil and gas, the sonic velocity will generally be lower than that for a gas system, i.e., Rc =0.5 - 0.6

• Critical flow behaviour is only exhibited by highly compressible fluid such as gases and gas/liquid mixtures. • For gas, which is a highly compressible fluid, the critical downstream pressure Pc is achieved when velocity through the vena contracta equals the sonic velocity • this means that a disturbance in pressure or flow downstream of the choke must travel at greater than the speed of sound to influence upstream flow conditions. • In general, critical flow conditions will exist when Rc=