sonatrach's _well performance

7/29/2019 Sonatrach's _well Performance

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September October 2005abalt solutions limited - 2005

INTRODUCTION TO HYDROCARBON EXPLOITATION

Introduction to Hydrocarbon Exploitation

2005 Abalt Solutions Limited. All rights reserved

Well Performance

Pratap Thimaiah

WellPerformance


Content

Introduction to Reservoir Performance

Reservoir Characteristics

Fluid Flow Equations

Steady State Flow

Unsteady State Flow Pseudo-steady State Flow

Skin Factor

Turbulence Flow Factor

Principle of Superposition

Essentials of Well testing


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Introduction

Flow in porous media is a very complexphenomenon and as such can not be described

as flow through pipes or conduits.

Mathematical relationships that are designed todescribe the flow behaviour of the reservoir

fluids depend upon the characteristics of thereservoir such as:

Types of fluids in the reservoir

Flow regimes

Reservoir geometry

Number of flowing fluids in the reservoir

WellPerformance


Reservoir Characteristics Types ofFluids

Reservoir fluids can be classified into three

groups:

Incompressible fluids

Slightly compressible fluids

Compressible fluids

To identify the type of reservoir fluid, theisothermal compressibility coefficient is used.


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WellPerformance



Isothermal compressibility coefficient (c)

In terms of fluid volume

In terms of fluid density

V and are the volume and density of the fluidrespectively.

1 Vc

V p

1c

p

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Incompressible fluids

Fluid whose volume (or density) does not changewith pressure.

Incompressible fluids do not exist, however it isassumed to simplify the derivation and final form

of many flow equations.

0V

p

0p


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Slightly compressible fluids

Fluid who exhibit small changes in volume (ordensity) with changes in pressure.

Crude oil and water systems fit into the slightlycompressible category. Vref and ref are referencevalues of volume and density at reference (initial)pressure.

1ref ref V V c p p

1ref ref c p p

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Compressible fluids

Fluid who experience large changes in volume(or density) with changes in pressure.

All gases are considered compressible flows.

1 1g

T

c z p


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Volume and density changes as a function ofpressure for three types of fluids.

Compressible

Incompressible

Slightly Compressible

Incompressible

Slightly Compressible

Compressible

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Reservoir Characteristics Flow Regimes

There are three flow regimes that describe the

fluid behaviour and reservoir pressuredistribution as a function of time:

Steady-state flow

Unsteady-state flow

Pseudo steady-state flow

Steady state flow

Unsteady-state flow

Pseudo steady-state flow


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Steady-state flow

Pressure at every location in the reservoirremains constant. It does not change with time.

Steady-state flow condition can only occur whenthe reservoir is completely recharged andsupported by strong aquifer or pressure

maintenance operations.

0i

p

t

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Unsteady-state flow (transient flow)

Fluid flow condition at which the rate of changeof pressure with respect to time at any positionin the reservoir is not zero or constant.

Pressure derivative with respect to time isessentially a function of both position i and timet.

,p i tt


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Pseudo steady-state flow (semi steady-stateflow)

Pressure at different locations in the reservoir is

declining linearly as a function of time, like at aconstant declining rate.

constanti

p

t

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Reservoir Characteristics ReservoirGeometry

Shape of a reservoir has a significant effect on its flowbehaviour

Most reservoirs have irregular boundaries. Numericalsimulator are used for describing such complexboundaries.

The actual flow geometry may be represented by one ofthe following flow geometries:

Radial flow

Linear flow

Spherical and hemispherical flow


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Radial Flow

Absence of severe reservoir heterogeneitiesfacilities radial flow. Flow into or away from awellbore will follow radial flow lines from a

substantial distance from the wellbore.

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Linear Flow

Flow paths are parallel and the fluid flow in a singledirection, while the cross-sectional area to flow must beconstant.

A common application of linear flow equations is thefluid flow into vertical hydraulic fractures.

q

q

q

q

fracture

wellbore

q

q

wellbore

fracture


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Spherical and Hemispherical Flow

It depends upon the type of completion.

A well with a limited perforated interval could result inspherical flow in the vicinity of the perforations.

A well that only partially penetrates the pay zonecould result in hemispherical flow.

Hemispherical flow in a partially penetrating well Spherical flow due to limited entry

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Number of flowing fluids in the reservoir

Single-phase flow (oil, water, or gas)

Two-phase flow (oil-water, oil-gas, or gas-water)

Three-phase flow (oil, water, and gas)

Description of fluid flow and subsequent

analysis becomes more complicated as thenumber of mobile fluids increases.


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Fluid flow equations

Flow equations necessary to describe the flowbehaviour are developed from:

Conversation of mass equation

Transport equation (Darcys equation)

Equation of State

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Darcys Law

Fundamental law of fluid motion in porous media.

For a horizontal linear system

For a radial system

q k dp

v dx

r

rr

q k pv

r

2r rh

Apparent velocity

Volumetric flow rate at radius r

Cross-sectional area to flow at radius rPressure gradient at radius r

Apparent velocity at radius r


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Darcys Law

Only applies when the following conditionsexist:

Laminar (viscous) flow

Steady-state flow

Incompressible flow

Homogeneous formation

pressure

distance

Direction of flow

P1

P2

x

Pressure vs. distance in a linear flow

Direction of flow

rw

r re

pwf

pe

pressure

Pressure gradient in radial flow

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Steady State Flow

Linear flow of Incompressible Fluids

It is assumed the flow occurs through a constant

cross-sectional area A, where both ends areentirely open to flow.

It is assumed that no flow crosses the sides, top,

or bottom.

1 2kA p pq

L

1 20.001127 A p pqL

Field Units

[bbl/day]

[md][psia]

[cp][ft]

[ft2]


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Steady State Flow

Linear flow of compressible fluids (gases)

For a viscous (laminar) gas flow in a homogeneous- linearsystem, the real-gas equation of state can be applied to

calculate the number of gas moles n at pressure p,temperature T, and volume V:

Vn

RT sc sc

sc

pV p V

zT

21 2sc

0.111924

g

k p pq

TLz

2 2

1 2

2

p pp

qsc: gas flow rate at standard conditions, [scf/day]k: permeability, [md]

T: temperature, [R]

g: gas viscosity, [cp]A: cross-sectional area, [ft2]

L: total length of the linear system, [ft]

Z and g are a very strong function of pressure. The above equation is valid for applications when the pressure


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Steady State Flow

Radial flow of slightly compressible fluids ref ref 1

0.0011272

r

q c p pq k dp

rh dr

ref

ref

wf ref

10.00708ln

1ln

e

e

w

c p pkhq

r c p pcr

0.00708

ln 1

lno o e wf

eo o o

w

khq c p p

rB c

r

Separating the variables in the above equation and

integrating over the length of the porous medium

Choosing the bottom-hole flow pressure (pwf)as the reference pressure and expressing theflow rate in STB/day

co: isothermal compressibility coefficient, [psi-1]

qo: oil flow rate, [STB/day]k: permeability, [md]

WellPerformance


Unsteady-State Flow

Infinite acting reservoir

Radius of Investigation (r inv)

A pressure disturbance move from the wellbore at a rate that is

determined by:

Permeability

Porosity

Fluid viscosity

Rock and fluid compressibilities

pipi

Q = 0

re

re

re

re

re

re

p ip i

pi

pi

r1

r2

r3

r4

r1

r2

r3

r4

r1 r2 r3 r4r1r2r3r4

t1 t

2 t3 t4

t1 t2 t3 t4

pwf

Constant q

Shut in

Constant Flow Rate

Constant pwf


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Unsteady-State Flow

The transient (unsteady-state) flow is defined as thattime period during which the boundary has no effect onthe pressure behaviour in the reservoir and the reservoirwill behave as its infinite in size.

Steady-state flowing conditionUnsteady-state flowing condition

same quantity of fluid enters the flow system as leaves itthe flow rate into an element of volume of a porous mediamay not be the same as the flow rate out of that element

fluid content of theporous medium

changes with time

Steady-state flow variables

Time, TPorosity, Total compressibility, c

t

Unsteady-state f low variables

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Unsteady-State Flow

Basic Transient Flow Equation

Continuity equation

Transport equation

Compressibility equation

Initial and boundary conditions

The formation produces at a constant rate into the

wellbore

There is no flow across the outer boundary and the

reservoir behaves as if it were infinite in size (re=)


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Unsteady-State Flow

Basic Transient Flow Equationcenter ofthe well

pwf

rw

r

r

r+dr

dr

h

pe

(q)r

(q)r+dr

mass enteringvolume element

during interval t

mass leavingvolume element

during interval t

rate of massaccumulation

during interval t- =

WellPerformance


Unsteady-State Flow


Mass entering the volume element during timeinterval t:

Mass leaving the volume element:

Total accumulation of mass:

outMass 2 rh v

inMass 2 t h r drr dr v

Total mass accumulation = 2t dt t

rh dr


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Unsteady-State Flow


Continuity Equation

Provides the principle of conservation of mass inradial coordinates

1

r vr r t

: porosity: density, [lb/ft3]v: fluid velocity, [ft/day]

WellPerformance


Unsteady-State Flow


Transport Equation

Darcys law is essentially the basic motion

equation, which states that the velocity isproportional to the pressure gradient p

r

0.006328k p

v

k: permeability, [md]v: velocity, [ft/day]

: viscosity, [cp]


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Unsteady-State Flow

To describe the behaviour of radial flow of slightly compressiblefluids

o o w w g g f c S c S c S c Assuming permeability and viscosity are constant over pressure, time and distance ranges

The compressibility of any fluid is related to its density by:

Total compressibility (ct)t f

c c

Formation compressibility (cf)

1c

1

tf fc c

t

2

2

1 1p p

r r r t

.000264

tc

k: permeability, [md]r: radial position, [ft]p: pressure, [psia]

c t: total compressibility, [psi-1]

t: time, [hrs] : porosity, [fraction] : viscosity, [cp]

Diffusivity Equation Diffusivity constant

Assumptions and limitations:

1. Homogeneous and isotropic porous medium

2. Uniform thickness3. Single phase flow4. Laminar flow5. Rock and fluid properties independent of pressure

If the reservoir contains more than one fluid then

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Unsteady-State Flow

Generalised solutions to the diffusivity

equation:

Constant-terminal-pressure solution

Constant-terminal-rate solution

The Ei-function solution

The dimensionless pressure pD solution

Infinite-acting reservoir

Finite-radial reservoir


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Unsteady-State Flow

Generalised solutions to the diffusivity equation:

Constant-Terminal-Pressure Solution

Designed to provide the cumulative flow at anyparticular time for a reservoir in which the pressure atone boundary of the reservoir is held constant.

Frequently used in water influx calculations in gas and

oil reservoirs.

Flow rate is considered to be constant at certain radius(usually wellbore radius) and the pressure profile aroundthat radius is determined as a function of time andposition.

WellPerformance


Unsteady-State Flow


Constant-Terminal-Rate Solution

Solves for the pressure change throughout the radialsystem providing that the flow rate is held constant atone terminal end of the radial system, like at the

producing well.

Integral part of most transient test analysis techniques,such as with drawdown and pressure build up analyses.

Most of these tests involve producing the well at a

constant flow rate and recording the flowing pressure asa function of time like p(rw,t).


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Unsteady-State Flow



The Ei-function Solution (Matthews and Russell, 1967)

Based on the following assumptions:

1. Infinite acting reservoir (the reservoir is infinite in size)

2. The well is producing at a constant flow rate3. The reservoir is at a uniform pressure, p i, when production begins4. The well, with a wellbore radius of rw is centered in a cylindrical reservoir of radius re5. No flow across the outer boundary

70.6 948

, o o o o t i iq b c r

p r t p Ekh kt

2 3

n etc1! 2 2! 3 3!

u

i

x

e x x xE x du x

u

948 tc rx

t

10.9 0

0.01 3.0 ln 1.781

i

i

x E x

E x x

p(r,t): pressure at radius r from the well after t hourst: time, [hrs]k: permeability, [md]q

o: flow rate, [STB/day]

WellPerformance


Unsteady-State Flow



The Dimensionless pressure drop (Van Everdingen andHurst, 1949)

Based on the following assumptions:

1. Perfectly radial reservoir system2. The producing well is in the center and producing at a constant production rate of q3. Uniform pressure p

ithroughout the reservoir before production

4. No flow across the external radius re

p D: dimensionless pressure dropreD : dimensionless external radius

tD: dimensionless timerD

: dimensionless radiust: time, [hr]p(r,t): pressure at radius r and time t

k: permeability, [md] : viscosity, [cp]

2

2

1D D

D D D

p p

r r r t

,

0.00708

i

Do o o

p r tp

q B

h

2

.000264D

t w

tt

c r

D

w

reDw

rr


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Unsteady-State Flow



The Dimensionless pressure drop (Van Everdingen and

Hurst, 1949)

0.00708

i

D

o o o

p r tp

q B

h

2

0.000264D

t w

ktt

c r

eD

w

rrFor Infinite acting reservoir:

eDr

For 0.02 < tD


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Unsteady-State Flow

To describe the behaviour of radial flow of compressible fluids

There are three forms of the mathematical solution to thisdiffusivity equation

The m(p)-Solution Method (Exact Solution)

The Pressure-Squared Method (p 2-Approximation Method)

The Pressure Method (p-Approximation Method)

t o o w w g g f c S c S c S c

The compressibility of any fluid is related to its density by:

Total compressibility (ct) t fc c

Formation compressibility (cf)

1c

1

tf f

pc c

p t

Radial Diffusivity Equation for Compressible Fluids

If the reservoir contains more than one fluid then

1 1g

zc

p z dp For gas

22

1

0.000264

tp m p m pc

r r r k t

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Unsteady-State Flow

Describing the behaviour of radial flow of compressiblefluid with the diffusivity equation

The m (p) Solution Method (Exact Solution)

Written equivalent in terms of the dimensionless time tD

21637

og 3.23g

wf i

i ti w

q T ktm p m p

kh c r

1637 4

log1.781

g Dwf i

q T tm p m p

kh

2

0.000264D

i ti w

tt

r qg : gas flow rate, Mscf/day


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Unsteady-State Flow

Describing the behaviour of radial flow of compressible fluidwith the diffusivity equation

The Pressure-Squared Approximation Method (p 2-method)


qg : gas flow rate, Mscf/day

2 2 1637 4log

1.781

g Dwf i

q T z t p p

kh

2 2

2

1637log 3.23

g

wf i

i ti w

q T z kt p p

kh c r

2

2

wfp pp

The values of gas viscosity and deviation factor are evaluated at the average pressure

This effectively limit the applicability of the p2-method to reservoir pressures < 2000 psi

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Unsteady-State Flow

Describing the behaviour of radial flow of compressiblefluid with the diffusivity equation

The Pressure Approximation Method (treating the gasas a pseudo-liquid)


Gas properties are evaluated at the average pressure defined as:

The applicability of the pressure-approximation method is limited to reservoir pressures > 3000 psi

3

2

162.5 10

og 3.23

g g

wf it w

q B kt

p p kh c r

3162.5 10 4

log1.781

g g Dwf i

q B tp p

kh

2

wfp pp


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Pseudo steady-state flow Regime

The change in pressure with time becomes the samethroughout the drainage area.

constantr

p

t

P

No-Flow Boundary

No-Flow Boundary

t1t2 t3

t4

rerw

t1 t2 t3 t4

P

r

Pressure

p vs. r

p vs. time

time

WellPerformance



Behaviour of the pressure decline rate dp/dt during thesemisteady-state flow:

The reservoir pressure declines at a higher rate withan increase in the fluids production rate

The reservoir pressure declines at a slower rate forreservoirs with higher total compressibility coefficients

The reservoir pressure declines at a lower rate forreservoirs with larger pore volumes.

2

0.23396

t e

p q

t c r h


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constantr

p

t

Semisteady-state

condition

No flow across the wells drainage

areas boundaries

Pressure at every point inthe reservoir is changing atthe same rate

Reservoiraverage

pressurechanging at thesame rate also

rp pdpt t

:Volumetric average reservoir pressure

1 1 1, ,p V

2 2,q p V

3 3,p V

4 4 4, ,q p V

ri ii

r

i

i

q

pq

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Radial Flow ofslightly compressible fluids

Pseudo steady-state flow occurs regardless of the geometryof the reservoir.

Irregular geometries also reach this state when they havebeen produced long enough for the entire drainage area tobe affected.

0.00708

ln 0.5

wf

e

w

h p pQ

rB

r

0.00708

ln 0.75

wf

e

w

h p pQ

rB

r


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Radial Flow of slightly compressible fluids

The Shape Factor (CA) after Ramey and Cobb, 1971

4162.6 log1.781

r wf

A w

kh p pQ

ABC r

2

0.23396 162.6 4log

1.781wf i

t A w

QBt QB Ap p

h c kh C r

WellPerformance


Pseudo steady-state flow Regime Shape Factors Table

After Earlougher, R., Advances in Well Test Analysis. SPE, 1977


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Radial Flow of compressible fluids (gases)

The approximation to the above solution of the diffusivityequation are:

Pressure-squared approximation

Pressure-approximation

1422 ln 0.75

r wf

g

e

w

kh m p m pQ

rT

r

Q g: gas flow rate, [Mscf/day]T: temperature, [ R]

K: permeability, [md]

WellPerformance



Radial Flow ofcompressible fluids (gases)

Pressure-squared approximation: for p < 2000 psi

Pressure approximation: for p > 3000 psi

2 2

1422 ln 0.75

r wf

ge

w

kh p pQ

rT z

r

1422 ln 0.75

r wf

g

eg

w

kh p pQ

rB

r

2

2wfpp

2

wfp

p

0.00504gT

B


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Skin Factor

Skin effect: Altering the permeability aroundthe wellbore

rw

rskin

kskin

UndamagedZone

Damaged

Zone

Pressure Profile

rw

rskin

kskin

Undamaged

Zone

DamagedZone

k

k

Near Wellbore Skin Effect Center ofthe Well

Center ofthe Well

WellPerformance


Skin Factor

According to Hawkins (1956):

Permeability in the skin zone is uniform

Pressure drop across the zone can be approximatedby Darcys equation.

p < 0

p > 0

Improvedk

Reducedk

rw

rskin

Pressure Profile

Representation of positiveand negative skin effects

pskin =p in skin zone

due to kskin

p in skin zonedue to k

-


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Skin factor (s)

Positive Skin Factor, s > 0

Negative Skin Factor, s < 0

Zero Skin Factor, s = 0

actual actual

i wf i wf ideal skin skinidealp p p p p p p p

s

141.2 1 lno o o skinskin

kin w

Q B k r p s s

kh k r

WellPerformance


Skin Factor

Steady State Radial Flow

Unsteady State Radial Flow

For Slightly compressiblefluids:

For Compressible fluids:

2162.6 log 3.23 0.87o o o

i wf

t w

Q B kt p s

kh c r

0.00708

ln

wf

o

eo o

w

h p pQ

rB s

r

2 2

2

1037log 3.23 0.87

g

wf i

i ti w

Q T z ktp p s

kh c r


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Development Phase



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Skin Factor

Pseudo steady state Flow

For slightly compressible

fluids:

For compressible fluids:

0.00708

ln 0.75

r wf

o

eo o

w

kh p pQ

rB s

r

2 2

1422 ln 0.75

r wf

g

e

w

kh p pQ

rT z s

r

WellPerformance


Turbulent Flow Factor

Not always laminar flow conditions are observed duringflow.

During radial flow, the velocity increase as the wellbore isapproached and might result in the development of aturbulent flow around the wellbore.

If turbulent flow does exist, it is most likely to occur withgases and causes an additional pressure drop similar tothat caused by the skin effect.

Non-Darcy Flow


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Development Phase



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Referring to the additional real gas pseudo-pressure dropdue to non-darcy flow as , the total (actual) drop isgiven by:

Wattenburger and Ramey (1968)

Non-Darcy flow coefficient

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Unsteady-State RadialFlow

21637

log 3.23 0.87 0.87g

wf g

i ti w

Q T ktp m p s DQ

kh c r

Turbulent flow factor

Total Skin Factor


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Development Phase



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Semi-steady State Flow

Steady State Flow

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Oil Well Performance

Introduction

Vertical Oil Well Performance

Vogels method

Wiggins Method

Standings Method

Fetkovichs Method

The Klins-Clark Method

Horizontal Oil Well Performance

Method I

Method II

Horizontal Well Productivity under Steady-State Flow

Horizontal Well Productivity under Semi-Steady-StateFlow


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Introduction

Production performance of a well is affected byseveral factors that govern the flow of fluids

from the formation to the wellbore.

Production performance analysis is bases on:

Fluid PVT properties

Relative permeability data

Inflow performance relationship (IPR)

WellPerformance



Productivity Index (J)

Measure of the ability of the well to produce.Ratio of the total liquid flow rate to the pressuredrawdown.

For a water-free oil production, the productivityindex is given by:


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Development Phase



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Generally measured during a production test on thewell.

The well is shut-in until the static reservoir pressure isreached.

The well is then allowed to produce at constant flowrate of Q and a stabilized bottom-hole flow pressure of

pwf.

The productivity index is a valid measure of the well

productivity potential only if the well is flowing atpseudo steady-state conditions.

Productivity index during flow regimes

WellPerformance




The productivity index can be numerically calculated, butmust be defined in terms of semi steady-state flowconditions.


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Development Phase



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Productivity Index Features

Valuable methodology for predicting the futureperformance of wells

Useful for determining if a particular well has becomedamaged due to completion, workover, production,injection operations, or mechanical problems.

Good indicator of wells difficulties or damage during

completion through comparison between different wellsin the same reservoir.

In terms of relative permeability

WellPerformance



Productivity Index Normalization Specific Productivity Index

Productivity indexes may vary from well to well because of the

variation in thickness of the reservoir, therefore J is normalized bydividing each by the thickness of the well.

Qo

vs. p relationship

Assuming that the wells productivityindex is constant:


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Development Phase



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The Inflow Performance Relationship (IPR)

Graphical representation of the relationship that existbetween the oil flow rate and bottom-hole flowingpressure. IPR

WellPerformance



The Inflow Performance Relationship (IPR)

Features

When pwf equals average reservoir pressure, theflow rate is zero due to the absence of any

pressure drawdown.

Maximum rate of flow occurs when pwf is zero.(Absolute Open Flow - AOF)

The slope of the straight line equals thereciprocal of the productivity index.


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Development Phase



WellPerformance



Inflow into a well is directly proportional to the pressuredrawdown. The constant of proportionality is theproductivity index (J).

When the pressure drops below the bubble point pressure,the IPR deviates from that of the simple straight-linerelationship.

IPR below pb

WellPerformance



Variables that affect productivity index

Overall effect of changing the pressure on the term


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Development Phase



WellPerformance



Qualitative effect of reservoir depletion on theIPR

WellPerformance



Non-linearity behaviour of the IPR for solution gas drivereservoirs

Several empirical methods are designed too predictsuch behaviour, and most of them require at least onestabilized flow test in which Qo and pwf are measured;and all of them also include the following

computational steps:

Using the stabilized flow test data, construct the IPR

curve at the current average reservoir pressure

Predict future inflow performance relationships as to thefunction of the average reservoir pressures.


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Development Phase



WellPerformance



To generate the current and future inflowperformance relationships, the following

empirical methods have designed:

Vogels method

Wiggins Method

Standings Method

Fetkovichs Method

The Klins-Clark Method

WellPerformance


Vertical Oil Well Performance VogelsMethod

Used a computer model to generate IPRs for several hypotheticalsaturated-oil reservoirs that are producing under a wide range of

conditions.

Normalized the calculated IPRs and expressed the relationships ina dimensionless form by dimensionless parameters:

Plotted the dimensionless IPR curves for all the reservoir cases

and arrived at the following relationship:

Flow rate at zero wellbore pressure, i.e., AOF


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Development Phase



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Can be extended to account for water production byreplacing the dimensionless rate with where

The method requires the following data:

Current average reservoir pressure

Bubble-point pressure

Stabilized flow test data that include

The method can be used to predict IPR curve for thefollowing type of reservoirs:

Saturated oil reservoirs

Undersaturated oil reservoirs

WellPerformance



For Saturated Oil Reservoirs (when the reservoirpressure equals the bubble-point pressure)

The computational procedure is as follow:

1. Using the stabilized flow data, i.e., Qo

and pwf

,calculate:

2. Construct the IPR curve by assuming various valuesfor Pwf and calculating the corresponding Qo from:


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Development Phase



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For Under-saturated Oil Reservoirs

Beggs (1991) pointed out that in applying Vogelsmethod for undersaturated reservoirs, there are twopossible outcomes to the recorded stabilized flow testdata that must be considered.

Stabilized flow test data

- The recorded stabilized bottom-hole flowing pressureis greater than or equal to the bubble-point pressure,

i.e.

-The recorded stabilized bottom-hole flowing pressure

is less than the bubble-point pressure

WellPerformance




Case1: The Value of the Recorded Stabilized

1. Using the stabilized test data point (Qo and pwf)calculate the productivity index J:

2. Calculate the oil flow rate at the bubble-pointpressure:


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Case1: The Value of the Recorded Stabilized

3. Generate the IPR values below the bubble-pointpressure by assuming different values of p wf< pb andcalculating the correspond oil flow rates by applyingthe following relationship:

The maximum oil flow rate (Q o max or AOF) occurs when the bottom-hole flowing pressure

is zero, pwf = 0, which can be determined from the above expression as:

Note:When the IPR is l inear and:

WellPerformance




Case 2: The Value of the Recorded Stabilized pwf < pb

1. Using the stabilized well flow test data:

2. Calculate Qob

3. Generate the IPR for by assuming several valuesfor p wf above the bubble point pressure and calculatingthe corresponding Qo from:


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Case 2: The Value of the Recorded Stabilized pwf< pb

4. Calculate Qo at various values of pwf below pb, or:

WellPerformance



Predicting wells inflow performance for future time as the reservoirpressure declines.

Future well performance calculations require the developmentof a relationship that can be used to predict future maximum oil

flow rates.

Some prediction methods require the application of the materialbalance equation to generate future oil saturation data as a

function of reservoir pressure.

Without that data, there are two options:

First Approximation Method

Second Approximation Method


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WellPerformance



First Approximation Method

Provides a rough approximation of the future maximum oil

flow rate (Qomax)f at the specified future average reservoirpressure (pr)f

(Qomax)f can be used to predict the future inflow performancerelationships at

1. Calculate from:

2. Using the new calculated value of (Qomax)f and (pr)f generate theIPR by using:

Where the subscript f and p represent futureand present conditions, respectively.

WellPerformance



Second Approximation Method

Fetkovich (1973) proposed a simple

approximation for estimating future

Only to provide a rough estimation of future (Q o) max

The main disadvantage of Vogels methodology lies with its sensitivity to

the match point, i.e., the stabilized flow test data point, used togenerate the IPR curve for the well


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WellPerformance


Vertical Oil Well Performance WigginssMethod

Limited by the assumption that the reservoirinitially exists at its bubble-point pressure.

It propose generalized correlations that aresuitable for predicting the IPR during three-phase flow.

Data from a stabilized flow test on the well must be available in orderto determine (Qo)max and (Qw)max

WellPerformance


Vertical Oil Well Performance WigginssMethod

Predicting future performance

Estimating future maximum flow rates as afunction of:

Current (present) average pressure

Future average pressure

Current maximum oil flow rate

Current water flow rate


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Vertical Oil Well Performance Standings Method

Essentially an extended application of Vogelsmethod to predict future inflow performancerelationship of a well as a function of reservoirpressure.

Productivity index J Present (current) zero drawdown productivity index

For predicting the desired IPR expression

Estimating from the presentvalue of

If relative permeability data is not available,can be roughly estimated from:

WellPerformance


Vertical Oil Well Performance Fetkovichs Method

Attempt to account for the observed on-linear flowbehaviour (IPR) of wells.

By calculating a theoretical productivity index from thepseudo steady state flow equation.

Fetkovich (1973) suggests that the pressure functionf(p) can basically fall into one of the following tworegions:

Undersaturated Region

Saturated Region


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Region 1: Undersaturated Region

The pressure function f(p) falls into this region if p> pb.

Region 2: Saturated Region

P < pb

WellPerformance



Pressure Function Concept


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WellPerformance



In the application of the straight-line pressure

function, there are three cases that must beconsidered:

Case 1:

Case 2:

WellPerformance



Case 1:

The case of a well producing from anundersaturated oil reservoir where


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Case 2:

Both reservoir pressure and bottom-hole flowingpressure are below the bubble-point pressure.

: performance coefficient C

but

WellPerformance



Advantages over vertical wells: Large volume of the reservoir can be drained by each horizontal well.

Higher productions from thin pay zones.

Horizontal wells minimize water and gas zoning problems.

In high permeability reservoirs, where near-wellbore gas velocities ar

high in vertical wells, horizontal wells can be used to reduce near-wellbore velocities and turbulence.

In secondary and enhanced oil recovery applications, long horizontalinjection wells provide higher injectivity rates.

The length of the horizontal well can provide contact with multiplefractures and greatly improve productivity.


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Horizontal wells production features: Actual production mechanism and reservoir flow regimes around

the horizontal well are more complicated.

Flow geometry is a combination of linear and radial flow.

Well may behave in a manner similar to that of a well that hasbeen extensively fractured.

It has been reported that the shape of measured IPRs forhorizontal wells is similar to those predicted by the Vogel orFetkovich methods

Productivity gain from drilling 1,500 ft long horizontal wells is twoto four times that of vertical wells.

A horizontal well can be looked up as a number of vertical wellsdrilling next to each other and completed in a limited pay zonethickness.

WellPerformance



Horizontal well drainage area


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WellPerformance



Calculating the drainage area of a horizontalwell (Joshis Methods)

Method I:

Drainage area represented by two half circles ofradius b (equivalent to a radius of a well rev) ateach end and a rectangle, of dimensions L (2b), inthe centre.

Drainage area given by:

WellPerformance



Calculating the drainage area of a horizontal well(Joshis Methods)

Method II:

Assumed that the horizontal well drainage area is anellipse and given by:

half major

axis of an ellipse

Both methods give different values for the drainage area A and suggested

assigning the average value for the drainage of the horizontal well

Drainage radius of the horizontal well


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Development Phase



WellPerformance



Inflow performance calculations for horizontalwells

Flowing conditions:

Steady-state single-phase flow

Pseudo-steady state two-phase flow

WellPerformance



Horizontal Well Productivity under Steady-State Flow

The steady state solutions requires that the pressure atany point in the reservoir does not change with time.

Several methods are designed to predict the productivityindex from the fluid and reservoir properties:

Borisovs Method

The Giger-Reiss-Jourdan Method

Joshis Method

The Renard-Dupuy Method


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Development Phase





Gas Well Performance

WellPerformance


Introduction

Flow Regime and

conditions of flow in reservoir

Proper solution of

Darcys equation

Inflow Performance Relationship

Relationship between the inflow gas rate

and the sand-face pressure or flowing

bottom-hole pressure

Flow capacity of a gas well

Flow capacity of a Gas Well:

Determination Process


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Development Phase



WellPerformance


Introduction

Gas Well

Shut In

Unsteady-statebehaviour

Pressure drops atthe drainage boundary

of the well

Short transitionperiod

Pseudo-steady state

flow condition

Normalisation of flow of a Gas Well, right after production has been initiated

WellPerformance


Vertical Gas Well Performance

Exact solution to the differential form of Darcys

equation for compressible fluids under thepseudo-steady-state flow condition:


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Development Phase



WellPerformance



Productivity index (J) for a gas well:

Absolute open flow potential (AOF)

WellPerformance



Steady-state gas well flow


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WellPerformance


Integral Form


Exact solution to the differential form of Darcys equation for

compressible fluids under the pseudosteady-state flowcondition can also be written as:

1

g g g

p

z B

:

WellPerformance



Gas PVT data

Area below the curve betweenthe appropriated pressures


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Development Phase



WellPerformance



Region III: High-Pressure Region

Pressure functions are nearly constants, therefore:

Gas viscosity and formation volume factor should

be evaluated at the average pressure:

WellPerformance



Region II: Intermediate-Pressure Region

When the bottom-hole flowing pressure andaverage reservoir pressure are both between2000 and 3000 psi, the pseudo-pressure gas

pressure approach should be used to calculatethe gas flow rate:


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Region I: Low-Pressure Region

At low pressure, usually less than 2000 psi, pressurefunctions

and exhibit a linear relationship with pressure.

Golan and Whitson (1986) indicated that the productis essentially the same when evaluating any

pressure below 2000 psi.

Pressure-squared approximation method

WellPerformance



All presented before has been based on the assumption thatlaminar (viscous) flow conditions are observed during the gasflow.

During radial flow, flow velocity increases as the wellbore isapproached.

Increase of the gas velocity might cause the development of a

turbulent flow around the wellbore.

If turbulent flow does exist, it causes an additional pressuredrop similar to that caused by the mechanical skin effect.

The semisteady-state flow equation for compressible fluids canbe modified for the additional pressure drop due to turbulentflow by including the rate-dependent skin factor (DQg)


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Development Phase



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First Form: Pressure-Squared Approximation Form

Inertial or turbulent flow (D)

Non-Darcy flow coefficient (F)

10 1.47 0.531.88 10 k

10 1. 47 0 .5 31.88 10 k

WellPerformance



Second Form: Pressure Approximation Form

Third Form: Real Gas Potential (Pseudo pressure) Form


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Development Phase





Total System Analysis

Pratap Thimaiah

WellPerformance


Content

Introduction

Tubing Size Selection

Flowline Size Effect

Effect of Stimulation


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Development Phase



WellPerformance


Introduction

General procedure for applying total system or

nodal analysis to a producing well.

WellPerformance


Introduction

The system analysis procedure requires firstselecting a node and calculating the node

pressure, starting at the fixed or constantpressure existing in the system.

Fixed pressure are usually preserv_avg and eitherpwh or psep

The node may be selected at any point in thesystem, and the most commonly selectedpoints are:


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Development Phase



WellPerformance


Introduction

Location of various nodes

WellPerformance


Introduction

The expressions for the flow into the node and

for the flow out of the node can be expressedas:

Inflow:

Outflow:


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Development Phase



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Introduction

In most cases:

The two criteria that must be met are:

Flow into the node equals flow out of the node

Only one pressure can exist at the node for agiven flow rate

Finding the flow rate and pressure that satisfiesthe previous requirements can be accomplished

graphically by plotting node pressure versusflow rate.

WellPerformance


Introduction

The intersection of the inflow and outflow curves occursat the rate that satisfies the requirement that the inflowrate equals the outflow rate.

This rate will be the producing capacity for the system fora particular set of components.

To investigate the effect of changes in any of thecomponents on the producing capacity, new inflow oroutflow curves can be generated for each change.

If a change is made in an inflow or upstream componentsonly, the outflow curve will not change, and therefore willnot require re-calculation.


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Introduction

If the only change made is in a downstreamcomponent, the inflow will remain un-changed.

This allows isolation of the effect of a change in

any component on the total system capacity.

This method can be used for determining ifexisting systems are performing properly and

also designing new systems.

WellPerformance



Tubing String is one of the most important componentsin the production system.

It can represent as much as 80 percent of totalpressure loss in an oil well.

A common problem in well completions design is to select

a tubing size based on totally irrelevant criteria, such as:

What size tubing is on the pipe rack

What size has been installed in the past

Tubing size selection should be made before the well isdrilled, because tubing size dictates the casing size whichdictates the hole size.


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Selecting the tubing size prior drilling a well is notpossible in exploratory wells.

Once the first well has been drilled, enough data will beavailable to plan other wells in the field.

Selection can also be made using a possible range ofexpected conditions reservoir characteristics and thenrefined as more data become available.

There is an optimum tubing size for any well system.

WellPerformance



Tubing too small will restrict the production

rate because of excessive friction loss.

Tubing too large will cause a well to load up

with liquids and die.

A common problem that occurs in completing

large capacity wells is to install very largetubing to be safe, which often results in adecreased flowing life for the wells are reservoir

pressure declines and the wells begin to load.


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Development Phase



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To isolate the effect of tubing size, the wellhead pressureis considered constant in the particular case of study.

This might be the case for a short flow line discharginginto a fixed separator pressure.

The node selected in this case will corresponds to Node 6as picture previously shown.

The expressions for inflow and outflow are:

Inflow:

Outflow:

WellPerformance



Sometimes, it is necessary to run a small string of tubing in thebottom section of a well if the well is completed with a liner.

If the small tubing were run from the surface the producingcapacity would be too low, especially if the well is deep.

In such wells it is often advantageous to run larger tubing from thesurface to the top of the liner (tapered tubing string)

The effect of the size of the upper string on producing capacitycan be conveniently determined by selecting the point at whichthe tubing changes size as the node.

The inflow will then include the reservoir and the lower section ofthe tubing.

The outflow will include the flowline and the upper section oftubing.


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WellPerformance



Tampered strings

Effect of upper string size

WellPerformance


Tubing performance and gradient curves

Pressure drop required to lift a fluid through the production tubing at agiven flow rate is one of the main factors determining the deliverabilityof a well.

Having fixed either the wellhead or bottom-hole flowing pressure giventhe rates of oil, gas, and water, pressure drop along the productiontubing can be calculated by charts or correlations, and the resultingflowing pressure at the other end of the tubing can be determined.

With a wellhead pressure specified, a gradient curve can be used todetermine wellbore flowing pressure at several different oil rates.Resulting relationship between flowing pressure and oil rate is calledtubing performance relation (TPR); valid for the specified wellheadpressure.


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Pressure drop in tubing due to single-phase fluid (gas and highlyundersaturated oil wells) can be calculated by conventional pipe flow

equations.

However, a small quantity of free gas mixed with oil and/or water

create considerably more complicated flow conditions which require

empirical correlations.

For vertical flow of dry gas (Katz):

WellPerformance



The equation for vertical flow of dry gas (Katz) can only be

used for dry gas.

If water or condensate is produced as an entrained liquidphase (GOR greater than 7,000 scf/STB), then gas velocitymust generally exceed 18 to 20 ft/s in order to be able to

use the above equation.

At lower velocities it has been observed that liquidaccumulates, thereby increasing pressure loss considerablyabove that calculated from the above equation.

If velocity decreases to 10 to 12 ft/s, then the well will

probably die.


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Development Phase



WellPerformance



Pressure elements constituting the totalpressure at the bottom of the tubing:

Backpressure exerted at the surface from the

choke and wellhead assembly (wellheadpressure)

Hydrostatic pressure due to gravity and the

elevation change between the wellhead and the

intake to the tubing

Friction losses, which include irreversiblepressure loses due to viscous drag and slippage.

WellPerformance



Components of pressure loss in the tubing


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WellPerformance




In the case of single- phase liquid, density is assumedconstant and the hydrostatic pressure gradient (pressure

drop per unit length) is a constant.

Friction loss is rate-dependant, characterized by two flow

regimes (laminar and turbulent)

The rate dependence of friction-related pressure loss differswith the flow regime:

At low rates the flow is laminar and the pressure gradient

changes linearly with rate or flow velocity

At high rates the flow is turbulent and the pressure gradient

increases more than linearly with increasing flow rate.

WellPerformance




In gas wells, there is interdependence between flowrate, flow velocity, density, and pressure.

Increasing gas rates results in increasing totalpressure loss.

In multiphase mixtures, friction related andhydrostatic-pressure losses vary with rate in a muchmore complicated manner than for gas.

Increasing rate may change the governing pressureloss mechanism from predominantly gravitational topredominantly friction.


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WellPerformance


Pressure Traverse Curves

The pressure traverse curve is a pressure depth profile.

For a given flow rate, wellhead pressure, and tubing size,

there is a particular pressure distribution along the tubing,starting its traverse at the wellhead pressure and increasingdownward toward the intake to the tubing.

WellPerformance



The pressure traverse curve (pressure depth

profile)

Sometimes it is advantageous (when there is notcomputer applications available) to construct a

set of pressure traverse curves for hypotheticalvalues of variables such as qL, GLR, d, fw (watercut), etc.

These curves can be used to estimate pressure

drop that would occur in a well producing undersimilar conditions.


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Development Phase



WellPerformance



Preparation of pressure traverse curve

To prepare a curve, the following parameters are selected:

Pipe inside diameter, d

Liquid flow rate, q L Water fraction, fw Average flowing temperature, T

Oil, gas, and water gravities

A pressure traverse is calculated for several values of GLR, startingat zero pressure, zero well depth.

The maximum value of GLR used is the one that will give theminimum pressure gradient for the chosen conditions.

Figures will be prepared for the full range of pipe sizes, liquid rates,and water fractions expected to occur in the field underconsideration.

The average flowing temperature and fluid properties can beselected from fluid samples taken in the field.

WellPerformance



In single-phase liquid, both gravitational and frictionpressure gradients are constant along the tubing andtherefore the pressure traverse is linear with depth.

In gas, it is very nearly even though the friction andhydrostatic pressure gradients vary significantly withdepth.

In multiphase mixtures there is general trend of

increasing pressure gradient with depth. Unfortunately,we do not have analytical equations or simple proceduresfor calculating the pressure traverse of multiphasemixtures.

Using correlations based on experimental data limits theapplication to producing wells to the conditions of rate,geometry, GOR, and fluid properties used in theexperimental study.


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Development Phase



WellPerformance



Vertical flowing pressure traverses

WellPerformance



Procedure for estimating an unknown pressure

1. Select the chart that most closely correspondsto the known conditions of tubing ID, liquidproduction rate, and water fraction.

2. Enter the pressure axis at the known pressure.Proceed vertically from this pressure to theintersection of the appropriate GLR curve.Proceed horizontally to the left to theintersection of the depth axis. This locates the

number on the depth axis which represents theequivalent depth of which the known pressureexists, i.e. either the wellhead or bottom-hole.


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Development Phase



WellPerformance



Procedure for estimating an unknown pressure

3. If the known pressure is the wellhead pressure, addthe actual well depth to the equivalent depth locatedin step 2. This represents the axis depth which isequivalent to the actual well depth. If the knownpressure is bottom-hole pressure, subtract the actualwell depth from the number found in step 2. Thisgives the axis depth that is equivalent to the actualwellhead pressure.

4. From the point located in step 3, proceed horizontallyto the right to the intersection of the same GLR line.From this point proceed vertically upward to thepressure axis. Read the unknown pressure.

WellPerformance



The use of a gradient curve to determineflowing bottom-hole pressure and flowing

wellhead pressure in an oil well.


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WellPerformance



Remarks about the use of gradient curves:

1. The vertical axis represents distance travelledvertically from a given point where the pressure isknown. From a given point with known pressure it ispossible to determine the pressure at any other pointby moving along the gradient curve for a distancecorresponding to the distance between the twopoints. Alternatively, if the pressure at the secondpoint is known, it is possible to determine whichdistance corresponds to the pressure difference

between the two points by moving along the gradientcurve an interval corresponding to the pressurechange between the two points.

WellPerformance




2. The gradient dp/dH decreases with increasinggas/liquid ratio (GLR) until a minimum gradientis reached. Thereafter the trend reverses and

dp/dH increases with increasing gas/liquid ratio.The physical reason for this is a change in the

predominant pressure loss mechanism causedby an increasing gas/liquid ratio.

3. For convenience, the high-GLR gradient curves

are shifted down on the depth scale to avoidintersection with lower-GLR curves.


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WellPerformance




4. If production is water-free, then gas/liquid ratio,GLR equals gas/oil ratio, GOR. If water/oil ratio,WOR, is reported, then the relation between

GLR and GOR is GLR=GOR/(1+WOR), orFgl=R/(1+Fwo).

Where FgL is gas/liquid ratio (GLR), Fwo iswater/oil ratio (WOR), and R is gas/oil ratio

(GOR)

WellPerformance


Pressure Traverse Curves to construct the tubing performance

Constructing the tubing performance curve from the pressure traversecurves for an oil well producing through tubing with a given diameterand length at a specific gas/liquid ratio and wellhead pressure:

The wellhead pressure is specified as a constant

Selecting a gradient curve with the specified GLR, the point wherepressure equals wellhead pressure is found. This point correspondsto zero depth.

Moving down vertically a distance equal to the tubing length andthen horizontally until the same GLR curve is reached, the bottom-hole pressure is read on the x-axis scale. This pressure is theintake flowing pressure for the rate corresponding to the gradientcurve chosen.

Similarly intake pressures are determined for several other rates.

The rate-intake pressure points are then plotted to form the tubingperformance curve.


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Development Phase



WellPerformance


Pressure Traverse Curves to construct the

tubing performance

WellPerformance



If a well is producing into a flowline, thewellhead pressure is equal to the sum of theseparator pressure and the pressure drop in

the flowline, assuming there is no wellhead

choke.

A common cause of low producing capacity inmany wells, especially for wells with longflowlines, is the excessive flowline pressure

drop.


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Development Phase



WellPerformance



Many operators have a tendency to use anysize pipe that is convenient or, in some cases,

tie two or more wells into a common, smallflowline.

This can be very detrimental, specially for gaslifted wells, because the flowline pressure drop

increases as the gas rate increases.

In order to isolate the effect of flowline size it isusually recommended to use Node 3, or

sometimes Node 6.

WellPerformance



The effect of reducing the separator pressure is

small compared to the effect of increasingflowline size.

This results from the fact that as average

pressure in the flowline is decreased in aconstant area pipe, the fluid must move fasterbecause expansion.

This creates more frictional pressure drop.

This may not apply if the flowline is in a hillyterrain area, since the increased velocity may

decrease the pressure drop caused by the hills.


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WellPerformance


Effect of Stimulation

The systems analysis approach can be used to estimate theimprovement in well capacity due to fracturing or acidizing.

Even though the reservoir capacity may be increasedconsiderably by stimulation; in some cases the wells actualproducing capacity increase may be small due to restrictions inthe outflow.

Before a decision is made on what steps to take to increase theproducing capacity, the exact cause of the low productivityshould be determined.

This can be accomplish only through a total systemanalysis.

Large sums of money are often wasted on workover becausethe wrong component of the well system is changed.

sonatrach's _well performance

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