Well performance

1

WELL PERFORMANCE

INTRODUCTION

Isabelle [email protected]

2

PR

Psep

?

3

The Production System

SEPARATOR

PrPPwfwf

Pup

Pdown Ps

PAY ZONE

WELL

WELLHEAD LINE

4

Pressure losses from the reservoirto the separator

SEPARATOR

P1flow in porous media

P2vertical and inclinedmultiphase flow

Pr Pwf

Pup

Pdown Ps

multiphase flowin the pipeline

P4

flow in thewell head P3

5

rate of productionduring the well life

Time

qp (Rate ofproduction)

beginningof the

production

build up

production facilities tobe installed

plateau rate

stop ofthe production

6

Aim of this course

To foresee the different facilities of theproduction system

(wells, artificial lift systems, pipelines, etc...)for a given reservoir pressure (Pr) and a

given separator pressure (Ps),

to optimizethe rate of production, qp

7

How to determine qp ?

qp = intersection between IPR curve andVLP curve

• IPR curve = Index of Productivity Relationship– description of the flow in the reservoir

• VLP curve = Vertical Lift Performance –description of the flow from the bottom of thewell to the separator

8

SEPARATOR

Pr

Ps

q

IPR curve

IPR

qp

PPPPwfwf

== PPwfwf

For given Ps, Pr, and productionfacilities,

there is a unique possibility ofproduction rate

=intersection between IPR and VLP

VLP curve

VLP

Pup

9

To plot IPR and VLP curves, wehave to estimate pressure losses

• by using models dedicated to :– flows in porous media– vertical and inclined flows– flows in the choke

• we have to distinguish between :– single phase flows and two phase flows– vertical wells and deviated wells– gas or oil reservoirs,– isotropic or anisotropic reservoirs,– ...

10

Plan of this course• Part 1 : Flow in the porous media, IPR

curve, horizontal wells• Part 2 : Multiphase flow

– application to vertical flows in the well – VLPcurve

– application to flows in the pipelines• Part 3 : Flow through the choke• Summary of the results

11

schedule

Exam and conclusionEnd of the project17 dec

projectproject16 dec

projectProsper : how to design a gas lift system ? ex : Well 5Summary of the course + questions

15 dec

Choke and gas liftNodal analysisTutorial 9 and 11Prosper : how to match a model ? ex : Well 4

Tutorial 8VLP analysis + pressure losses in a pipelineSensitivities on Prosper

14 dec

VLP in the case of oil wells – correlationsTutorial 4 to 7Prosper tutorial 3

Multiphase flow+ VLP in the case of gas wells

13 dec

Introduction to PROSPER+ Prosper tutorial 1 to 2

IPR curve (end)+ tutorial 1 to 3

12 dec

Introduction – IPR curve11 dec

Afternoon 13h to 16hMorning 8h – 11h30date

12

Pressure lossesin the pay zone

Part 1Flow in porous media, IPR curve

13

Plan of this course• Part 1 : Flow in the porous media, IPR

curve• Part 2 : Multiphase flow

– application to the vertical flow in the well –VLP curve

– application to the flow in the pipelines• Part 3 : Flow through the choke• Summary of the results

14

Pr Pwf PAY ZONE

SEPARATOR

Pup

Pdown Ps

WELL

WELLHEAD LINE

P1

15

First conditions to flow ...

flow only if difference between pressures

P1 P2

P1 P2

we open No flow

P1 = P2

P1 > P2

we open flow

16

Pressure losses during production

reservoir

wel

l

Pup

Pr

Pressure

Abscissa

PBH PrPup

EQUILIBRIUMFLOW

Pressure Drawdown = Pr – Pwf ensures the production

Pwf

Pwf < PBHPup new < Pup

Pup

17

first assumption ...

• we consider that the flow in the reservoir ispseudo-permanent :– sealed reservoir

t

Pwf

pseudo-permanentzone

transitionzone

transientzonePwf = bottom hole

flowing pressure

18

Productivity Index (PI)

• Productivity Index = ratio of the rate ofproduction per pressure drawdown

psidaybblsP

q

PP

qJPI

wfrm

//1

q = Production Rate (in bbls/day for an oil well)Prm = Static Reservoir Pressure (psi),

calculated at the middle point of the reservoirPwf = Flowing Bottom Hole Pressure (psi)

19

Inflow Performance Relationshipa relation between the production rate

and the flowing down hole pressure (Pwf)

rmwf PqJ

P

1

Pwf(psi)

qthqmax

first approximation

Prm

second approximation

q(bbls/day)

qth = pseudo qmax,in the case of no free gas

qmax = maximum rate of production,obtained when Pwf = 0

PI1

PI2

q2q10

not linear – due to2 phase flow, turbulence, etc...

20

From IPR curve to PI

PI = the productivity at a particular rate= f(q,Prm)= calculated by using the slope of theIPR curve at the considered point

We have to determine the IPR curvecorresponding to the reservoir which weare considering, in order to give PI at eachflow rate

21

How to calculate the IPR ?

- by using known quantities = thecharacteristics of the reservoir

- by using theoretical models for flows inporous media = the Darcy's law

- by using measurements = different welltests

22

characteristics of the reservoirknown quantities

Pr,Tr

rw

reh

k : absolute permeabilityko,g : effective permeability of the rock to oil / to gaso,g : effective viscosity of oil / gas, at average pressureWC : water cutGOR = gas oil ratio

23

Case of oil wellsEffective and relative permeabilities

effects of water production (1/2)

dlAdPq

ko

ooo

ko = effective permeability of the rock to oil

sw,o = water or oil saturation.For oil and water system, sw + so = 1

k = absolute permeability = single phase permeability

k

kk

k

kk w

rwo

ro ; = relative permeabilities (oil ; water)

24

Case of oil wellsEffective and relative permeabilities

effects of water production (2/2)

oil

watersw

so

1

0 0

1

swcsor

010 1

k rw

k ro

no oilflow

no waterflow

sor = residual oil saturation ; swc = connate water saturation

25

Models for flows in porous media :Darcy's law – experimental results

SAND

A = r²

L P

Water injection(rate = q)

L

PkAq

r

k = permeability of the sandµ = viscosity of the water

where :

m² Pa = N/m²

Pa.sm

26

Darcy's law applied topetroleum production

dPPf

Sr

r

hkq

r

wf

P

PP

w

e

)(

'43

ln

.00708.0

qFSS ND'S = skin factorFND q = turbulent flow term

f(P) = a function of pressurewhich depends on the state

of the flow in the porous medium

Prm = reservoir pressure atthe outer boundary

we have to distinguish betweensingle phase flow and two phase flow

- in field units

27

Hypothesis of IPR calculationconcerning the reservoir

• Homogeneous (permeability k andsaturation s constant in all horizontaldirections)

• Horizontal• Circular• The thickness h is constant• It is drained by a single fully penetrating

well located at its centre

h

28

Different cases of flowHydrocarbon phase diagram

80%40

%

20%

0%

10%

5%

Reservoir Temperature

Res

ervo

irP

ress

ure

Criticalpoint

Dew pointBubble point

Cricondenthermpoint

lines of constantphase distribution(% = liquid volume)

gas reservoircondensatereservoir

Joule-Thomsonexpansion

oilreservoir

generalization

UndersaturatedOil reservoir

saturatedOil reservoir

29

IPR calculation versus type of flow

Oil (undersaturated reservoirs)Gas

Oil and free gas (saturatedreservoirs)

Type of flow DefinitionIPR

calculation

30

Oil – no free gas

80%40

%

20%

0%

10%

5%

Temperature

oilreservoir

Pb Pwf Prm

Pb

Prm

Pwf

Pb = bubble point pressure

31

oil / no free gas

B

kPf ro

)(

B = Formation Volume Factorof the fluid

relative permeabilityof the rock to oil

= viscosity of the fluidat average pressure

Pb Pwf Prm

Specific assumptions :- the oil satures completely the formation (no free gas)- the flow rate is low no turbulence

),(

),(

stdstd

rr

TPV

TPVFVFB

PB<Pwf<Prm

32

oil / no free gas

PPB

o

Bo

oo

ro

B

kPf

)(

kro = 1

viscosity versus pressure

f(P) almost constant for P > PB

Case of oil :

B almost constant

PB<Pwf<Prm

33

oil / no free gas

'43

ln

00708.0

Sr

rB

PPhkq

w

eoo

wfrmoo

rmw

e

o

ooowf PS

r

r

hk

BqP

'

4

3ln

00708.0

Darcy's lawin this case:

P

Prm

w

er

r

most of pressure lossesnear the wellbore

PB<Pwf<Prm

34

oil / no free gas

'

43

ln

00708.0

Sr

rB

hk

PP

qJ

w

eoo

o

wfrm

o

For a given system,oo

o

B

hkconstJ

.

Non accurate, but gives a quick idea of J

PB<Pwf<Prm

Note: if q in m3/d, h in m & P in bara(instead of bpd, ft & psia) replace0.007082 by 0.053578

35

oil / no free gascase of oil and water flow

If both oil and water are flowing,we use the Darcy's law for each fluid :

ww

w

oo

o

w

e B

k

B

k

Sr

rh

J'

43

ln

00708.0

oil water

PB<Pwf<Prm

Note: if q in m3/d, h in m & P in bara(instead of bpd, ft & psia) replace0.007082 by 0.053578

36


Oil (saturated reservoirs)Gas

Oil and free gas(undersaturated reservoirs)


calculation

37

Case of gas

80%40

%

20%

0%

10%

5%

Temperature

Prm

Pwf

gas reservoir

P

38

Case of gas

gg

g

B

kPf

)( If there are no condensation or

liquid accumulation problems,kg = cte

sg P

TZB

Re

02827.0

Z = gas compressibility

factor, which variesT = absolute T°

where :

Specific assumptions :- the compressibility and the viscosity of the fluid can’t be

considered as constant- the flow rate is high turbulence more pressure losses- the liquid fraction is neglected

39

case of gas

• an empirical method : use of well testresults to elaborate a relation between q,Pwf and Pr.1°) gas well tests2°) back pressure equations

40

Different types of gas-well tests

• drawdown : decrease of pressure during production atconstant flow rate

• pressure buildup : increase of pressure with the wellclosed-in

Gas-well tests– stabilized production point test– multiple-rate drawdown tests : non stabilized

flow conditions– multiple-rate drawdown tests : isochronal and

p²-plot methods

41

Stabilized production point method

• initially : close the well buildup pressure determination of Pi

• four times : well flowed at a constant rateq for a sufficient time that Pwf stabilizes four couples (q, Pwf )

• main disadvantage : unrealistically longtest periods (to attain the stabilized Pwf)

42

Stabilized productionpoint method

Time

Pwf

PPrmrm

q

q1q2

q3q4

Pwf1

Pwf2

Pwf3

Pwf4

t1 t2 t3 t40

4 couples (q,Pwf)

stabilized values

43

Multiple-rate drawdown tests :isochronal procedures

• in order to avoid the long delay necessary for a stabilizedsituation (stabilized production point method), before Pwf isrecorded.

• 2 examples : Cullender test and Katz test common test conditions :

- generally 4 different flow rates q1<q2<q3<q4- same fixed delay t for the 4 sequencies of production :sufficiently short to assume transient flow conditions

- a last test period of production with Pwf stabilization

44

Cullender's test

In this test, (q5,Pwf5) arethe sole stable values

Specific test conditions : we wait until the pressures build upto the static value with the well closed-in

stabilized pressure

q

Pwf initial = Prm

t1f t2i t3i t3f Time

Pwf

t2f

t t t

PPrmrm

t4i t4f

t

q1

q2

q3q4

q5

Pwf1 Pwf2Pwf3 Pwf4 Pwf5

t1i

45

Katz's test

t1f t2i t3i t3f Time

Pwf

t2f

t t t

PPrmrm

t4i t4f

t

q

q1q2

q3q4

q5

Pwf1 Pwf2

Pwf3Pwf4

Pwf5

t1i

Pwf initial = Prm

tbu tbutbu

Specific test condition : buildup period tbu is fixed

stabilized pressure

In this test, (q5,Pwf5) arethe sole stable values

46

Conditions for using these methods

• in the case of a low permeability k :– tests don't allow stabilized conditions.

inaccurate measurements

• for a good k :– the period of stabilization is short

good accuracy of the method

case of gas – well tests

47

from these tests ...

• 2 main types of gas well behaviours :– first back pressure equation :

– second back pressure equation :

0

22

1

2

1

q

PP

C

Cq

C

F wfrmND

nwfrmg PPCq 22

48

Case of gas :first back pressure equation

dPPf

Sr

r

hkq

r

wf

P

PP

w

e

g

)(

'43

ln

.00708.0

ZT

PPf

g02827.0)( with

Assumption : we consider the averageof the different quantities.

demonstration

49

rm

wf

P

P g

w

e

gg ZT

PdP

Sr

r

hkq

'

43

ln

10*4066.1 3

case of gas :first back pressure equation

qFSr

rTZ

PPhkq

NDw

eaaga

wfrmgg

43

ln

10*703.0 223

for assumed average properties and pressuresXa = average of the quantitiy, calculated at the average pressure

term due toturbulent flow

(in Mscf/d)

demonstration

50

aag

g

TZ

hkC

6

1

10.703.0

Sr

rC

w

e

4

3ln2

02212

2 wfrmND PPCqCqF

If we consider and

we obtain

0

22

1

2

1

q

PP

C

Cq

C

F wfrmND

Case of gas -First back pressure equation

term due toturbulent flow

demonstration

51

0

22

1

2

1

q

PP

C

Cq

C

F wfrmND ybax straight line

Sr

r

kh

ZTb

krh

GZTa

q

PPy

qx

w

e

w

wfrm

4

3ln

10.422.1

10.13.0

6

342

6

22

non Darcy coefficient(turbulent flow)

coefficient of Darcy effects

where :

Case of gas -First back pressure equation

• a and b are empirically determinedby using well test regression

demonstration

52

How to use the gas well tests to determinethe equation parameters ?

example of the second Back Pressure equation

22logloglog wfrmg PPnCq 22log wfrm PP

log qg

logC

n = slope of the straight line

logC = intersection between the straight lineand the logq axis

log-log plot

Case of stabilized data

53

How to use the gas well tests to determinethe equation parameters ?

example of the second Back Pressure equation

nwfrmg PPCq 22

C = gas well performance coefficientn = exponent of the back pressure equation

0.5 < n < 1

High turbulent effect

qg inMMscf/d

Low turbulent effect

22logloglog wfrmg PPnCq

54

Use of Cullender or Katz's testsn and logC determination

22log wfrm PP

log q

logC

nn == slope

slope ofof thethe lineline

pointpoint obtainedobtainedwithwith ((PPwf5wf5,q,q55))

pointspoints obtainedobtainedduringduring drawdowndrawdown periodsperiods

((PPwfiwfi,,qqii) , i = 1..4) , i = 1..4

nwfrmg PPCq 22

Case of only 1stabilized data

55

IPR determination for a gas-wellexample of second back pressure equation

With tests, we measure q and Pwf

22log wfrm PP We calculate log q and22logwfrmPP

22logwfrmPP

We plot log q versus 22log wfrm PP

linear regression + use of stabilized (q,Pwf)

n and logC determination IPR

56

Absolute Open Flow Potential qmax

nrShutInPCq 2max

qmax represents the ideal case of production, where Pwf = 0.

nwfrmg PPCq 22

In this case, P1 is maximum, because :

wfrShutIn PPP 1

0

Then, the production is maximum(by considering only the reservoir point of view).

The back pressure equation :

can be written :

57


Oil (undersaturated reservoirs)Gas

Oil and free gas (saturatedreservoirs)


calculation

58

Two phase flow – oil and free gas

80%40

%

20%

0%

10%

5%

Temperature

oilreservoir

Pwf Prm Pb

Pb

Prm

Pwf


Case of only2 phase flow

59

Two phase and single phase flow –oil and free gas

0%

5%

Temperature

oilreservoir

Pwf Pb Prm

Pb

Prm

Pwf


Case of single phase and2 phase flow

q1

q2

60

Two phase flow – oil and free gas

80%40

%

20%

0%

10%

5%

Temperature

oilreservoir

Pwf Prm Pb

Pb

Prm

Pwf


Case of only2 phase flow

61

Two phase flow

dPPf

Sr

r

hkq

rm

wf

P

PP

w

e

o

)(

'43

ln

.00708.0

first case : PB > Prm

not constant,function of pressure

The equation can't be solved without the knowledgeof the relation between kro/oBo and (Prm – Pwf) = P1

oo

ro

B

kPf

)(with

function of saturation

PB > Prm

62

Two phase flow

oo

ro

B

k

kro can be estimated in lab with experience

but

is different at each level in the reservoir, for the same rockPrm varies oil and gas saturations varie kr varies

P P

Pwf Prm

I1 I2

P

I1 I2dPB

krmP

Pwf oo

ro

qo depends on the levelof pressure.It depends on the GORtoo (the curve is not thesame).

PB > Prm

63

Two phase flowAn empirical method

rm

wf

P

P

maxq

q

measurements

measurements are usedto establish an empirical equation

=IPR equation

PB > Prm

Pressures and corresponding rates of productionmeasured for different field cases are normalized

by qmax and Prm resp.

Curves of each fieldcan be superposed.

64

Two phase flow PB > Prm

IPR equations

2

max

11

rm

wf

rm

wf

P

PV

P

PV

q

q

rm

th

wfrm P

q

PP

qJ

V = 0 : IPR = straight line

V = 0.8 VOGEL's equation

V = 1 FETKOVITCH's equation

)( 222

maxwfrm

rm

PPP

qq

PB > Prm

q

Pwf

(qmax)F (qmax)V qth

PrmIPR curves

65

Two phase flowrelation between J* and qmax

wfrm PP

qJ

rm

wf

rm

P

P

Pq

J

1

J is defined by :

rm

wf

rm P

P

P

qJ 8.01max

rmP

qJ max8.1

*

Definition : If Pwf = Prm, we have J = J*.

Case of Vogel's equation :

rm

wf

rm P

P

P

qJ 1max

rmP

qJ max2

*

Case of Fetkovich's equation :

PB > Prm

66

Two phase flowIPR equations : How to determine qmax ?

• if we know Prm, by using one result of welltest (= one couple (q,Pwf))

or• without the knowledge of Prm, by using two

results of well tests (= 2 couples (q,Pwf))

PB > Prm

67

Two phase flow PB > Prm

exercise 1.1We consider an oil well, which produces in the

following conditions :– Prm = 2500 psi– qi = 3000 bbls/d– Pwfi = 1800 psi– Prm < Pb

Question : Give the IPR curve using Fetkovich'sapproach, and Vogel's one.

68

Oil and free gas

0%

5%

Temperature

oilreservoir

Pwf Pb Prm

Pb

Prm

Pwf


Case of single phase and2 phase flow

Pwf < PB < Prm

69

oil and free gas

B

kPfand

dPPf

Sr

r

hkq

ro

P

PP

w

e

o

rm

wf

)(

)(

'43

ln

.00708.0

when Pwf > Pb, single phase f(P) almost constant

when Pwf < Pb , two phase flow (oil + gas) f(P) is a function of saturation and pressure

Pwf < PB < Prm

70

oil and free gas

dPB

kdP

B

k

Sr

r

hkq

rm

b

b

wf

P

PP

ro

P

PP

ro

w

e

oo

'43

ln

.00708.0

B

PPdP

B

k

Sr

r

hkq brm

P

PP

r

w

e

ob

wf

'43

ln

.00708.0

part of the IPR curve given by Vogel's or Fetkovich's models

Pwf < P < Pbtwo phase flow

Pb < Psingle phase flow

Pwf < PB < Prm

71

Oil and free gasIPR curve

Part of single phase flowStraight line PI = J = cte

rate at bubblepoint pressure

Part of two phase flowcurve

q1 q2

qqmax(AOFP)

qb

qmax-qb

Pwf

Prm

Pb

qp

production rate

Physically, the transition from pure liquidflow to the presence of some free gas

in the flowing stream is a continuous one continuity and derivability

of IPR at this point

Pwf < PB < Prm

72

Oil and free gas

0%

5%

Temperature

oilreservoir

Pb

Prm

Pwf


q1

q2

Pwf < PB < Prm

qp = q1 + q2

73

Two phase flowFetkovich's approach to calculate

b

boo

ro

oo

ro

b P

P

Bk

Bk

Pf

Pf

)(

boo

ro

bB

kP

PPf

)(

• we know the conditions of Pressure, viscosity, etc...at the bubble point

• assumption : f(P) is a linear function of pressure

b

wf

P

P

dPPf )( Pwf < PB < Prm

74

Two phase flowFetkovich approach to calculate

22

2

1

'43

ln

.00708.0wfb

bboo

ro

w

e

PPPB

k

Sr

r

hkq

22

2

1

'43

ln

.00708.0wfb

b

w

eoo

o PPP

Sr

rB

hkq

where J is the PI in the case of single phase flow (q1 calculation)

22

2 wfbb

PPP

Jq we can write : or 22' wfb PPJq

where J' is referred to a pseudo productivity index

Pwf < PB < Prmb

wf

P

P

dPPf )(

75

Fetkovich approachIPR equation

q1

qqmax(AOFP)

qb

qmax-qb

Pwf

Prm

Pb

q2

qp

brm PPJq 1

single phase portion

222 2 wfb

b

PPP

Jq

two phase portion

22

2 wfbb

brm PPP

JPPJq Total rate : and

2maxb

rm

PPJq

q2

qp

Pwf < PB < Prm

76

2

max 8.02.01b

wf

b

wf

P

P

P

Pqq

The two phase part of the curve can be written likein the case of two phase flow where Prm < Pb, with the assumption thatPrmPb :

To obtain the real equation of IPR in the case of two phase flow wherePwf < PB < Prm, we have to shift this curve by introducing the bubble flow rate qb :

2

max 8.02.01b

wf

b

wfbb P

P

P

Pqqqq

Pwf < PB < Prm

Two phase flowVogel's approach

77

Two phase flow – free gasrelation between J* and qmax

Definition : If Pwf = Pb, we have J = J*=Jstraight line.

b

b

P

qqJ

)(2* max

b

b

P

qqJ

)(8.1* max

Case of Vogel's equation : Case of Fetkovich's equation :

Pwf < PB < Prm

Prm Pb

0 qb

qmax- 0 qmax - qb

ShiftShift ofof thethe 22--phasephase curvecurve

qmax0 qb

Pb

0 qmax

PrmJ* J*

78

Changes of IPR curve ...

• Case of horizontal and deviated wells• Modification due to the skin factor• Evolution of IPR

– IPR in the future, during the field life

79

Horizontal wells

- When to use them ?- How to calculate the flow rate ?- Influence of reservoir anisotropy- Case of slant wells

80

Why to use horizontal wells?

Mainly :• To increase the surface of contact

between the well and the reservoir

• To enhance the productivity

81

SIDETRACKINGSIDETRACKING

OFFSHOREOFFSHORE SHORELINESHORELINE

RELIEFRELIEF--WELLWELL

MULTIPLE ZONESMULTIPLE ZONES

Why to use horizontal wells ?

HEAVY OIL

THIN PAY-ZONES

LAYED RESERVOIR

FRACTURED RESERVOIRS

WATER / GAS CONING

GAS WELLS

Why to use horizontal wells?

83

drainage areaof a vertical well

Drainage area in the case of ahorizontal well

L

X

drainage shape = ellipsoïdal

X = large half-axis

kv

kh

84

Surface of contact betweenthe well and the reservoir

re

Vertical well Horizontal well

X

2

LX

Examples :For 1000 ft : Horizontal area = 2 * Vertical areaFor 2000 ft : Horizontal area = 3 * Vertical area

85

How to know the gainin productivity by drilling

a horizontal well ?

• By doing a comparison between :– Horizontal well PI and vertical well PI– The number of vertical wells required to

obtain the same level of productivity as asingle horizontal one

86

Quantities used in this part• L = Horizontal well length• h = Thickness of the pay-zone• rw = Wellbore radius• re = Drainage radius• q = Flow rate• k = permeability

• subscripts :h horizontal d deviatedv vertical

87

Flow rate estimation

Several methods have been developed,and, more particularly the ones given by :– Renard and Dupuy– Joshi

Assumption : reservoirs are isotropic (horizontalpermeability = vertical one)

88

Renard and Dupuy’s model

w

ooh

h

r

h

L

h

L

Xch

B

Phk

q

2ln

2

2

1

SI Units

Field Units

w

ooh

h

r

h

L

h

L

Xch

B

Phk

q

2ln

2

00708.0

1

where 2X = major axisof the drainage ellipse

L

Xch

B

Phk

q ooh

h 2

00708.0

1

If L>>h

specific tothis model

89

Joshi’s model

If L>>h

w

ooh

h

rh

Lh

L

Laa

BP

hkq

2ln

2

2²ln

2

2

where :

42

25.05.02

L

rLa eh

SI Units

field units :2 0.00708

2rw rw

2

2²ln

22

L

LaaB

Phkq

oo

hh

specific tothis model

90

A model to comparehorizontal and vertical PI

w

eh

eh

w

ev

v

h

rh

Lh

rL

rL

r

r

J

J

2ln

2

211

ln

ln

2

0 if h <<L

v

h

J

J'25h

'50'200

'400

L

Conclusion : The gain of J in a thin reservoiris higher than for a thick zone

h in feet

Hyp : kv/kh = 1

91

Case of anisotropic reservoirsAssumption : kv kh (anisotropic reservoir)

and the reservoir thickness is modified :

hk

khh

v

heff

In this case, the anisotropy can be characterized by :

v

h

k

k kh = permeability in the horizontal plane

kv = vertical permeability

92

Case of anisotropic reservoirs

Conclusions :- The gain of PI is higher for reservoirs of good vertical permeabilities,- this impact is relaxed in the case of thin reservoirs.

v

h

J

J

v

h

k

k

L

h1 < h2

h1 = cte

h2 = cte

93

Case of anisotropic reservoirsanisotropy in the horizontal plane

largerlarger horizontalhorizontal anisotropyanisotropy

smallersmaller horizontalhorizontal anisotropyanisotropy

case 1 : productivity = optimized case 2 : productivity = minimum

better = well drilled normal tothe larger horizontal anisotropy

94

Case of anisotropic reservoirs• Joshi’s model :

• Renard and Dupuy’s model :

w

h

h

r

h

L

hL

Laa

B

phk

q

2ln

2

2ln

00708.0

22

00

w

hh

R

h

L

h

L

Xarcch

B

phkq

2ln

2

100708.0

00

v

h

k

kwhere

2

1 ww rRwhere

and a defined aspreviouslyfor Joshi's model

95

How to calculatethe effective radius rw' ?

Assumption : ehev rr

hv JJ

rw' can be defined as the radius of a fictivevertical well which produces with the sameflow rate as the considered horizontal well.

same drainage radius

same productivity index

96

By using Joshi’s equation : vh JJ

'

22 ln

00708.0

2ln

2

2ln

00708.0

w

e

oo

h

w

oo

h

rr

Bhk

r

h

L

hL

Laa

Bhk

L

h

w

eh

w

r

hLaa

Lr

r

22

22

2

'

v

h

k

k=>

(general relation, which takes into account the anisotropy)

97

Case of Slant wells

h pay-zone

well trajectory

98

Cinco, Miller and Ramey modelassumption : < 75°

v

h

wd k

k

r

hh deviated thickness :

tanarctan

v

hd k

kdeviated inclination :

dsww err 'effective wellbore radius :

100ln

5641

865.106.2

dddd

hs

99

Cinco, Miller and Ramey modelSlant well / Vertical well comparison

w

e

w

e

v

d

r

r

r

r

JJ

'ln

ln

Conclusion : Jd/Jv increases with kv (as for horizontal wells)and with h (in contrast to horizontal well)

v

d

J

J

'400h'300

'200'100

hyp : kv=kh

100

Van der Vlis’s modelAssumption : 20° and kv=kh

L

h

ww h

rLr

360sin454.0

4'

cos

hL with :

Then, we can apply :

w

e

w

e

v

d

r

r

r

r

JJ

'ln

ln

to compare Jd and Jv.

101

Conclusion

It’s only in the case of thick reservoirs thatslant wells can be more interesting than

horizontal ones.

For thin pay-zones, horizontal wells arealways better.

102




103

pay zone kks

Zone of changed permeability

SKIN EFFECT, characterized by the « skin factor », noticed S

rw

rs

re

Skin factor

"S" takes into account the non homogeneity of the reservoir permeability .

104

• Why are there changes of the reservoirpermeability near the wellbore ?

FORMATION DAMAGE

105

Formation damage is any impairment ofFormation damage is any impairment ofreservoirreservoir permeabilitypermeability around thearound the wellborewellbore

It is a consequence of the drilling, completion,work-over, production, injection or stimulation

operationsProductivity orProductivity or InjectivityInjectivity

are affectedare affected

Formation damage :Formation damage :definitiondefinition

106

•Drilling•Cementing•Perforating•Completion and workover•Gravel packing•Production•Stimulation•Injection operations

Sources of Formation damage

107

Interface well-reservoir during drilling

cakecake

reservoir rock

Filtration through the wellbore

Control of fluid lossthrough the wellbore

understanding of themechanisms of filtration andformation of cakes of complexwell fluids with models

impermeable zone

108

Fluid characterization• Density control,• Suspension stability,• Rheological properties,• Filtration properties :

Static : V = a' + b' t 1/2

where b' = ( 2 k P A2/ h)1/2

Dynamic : V = a + b t

V filtration volume, k cake permeability, A area of filtration, filtrate viscosity, P differential pressure , h cake thickness

109

Drillingmud withdispersed

solids

Externalmud cake

Shale

1m

Drilling operationVirgin reservoir

Quartzgrains

110

Wellbore filtration

Definition of the zones invaded by the filtrate

Circulating drilling fluid Well

External cake

Internal cake

Invaded zone

Non invaded zone

111

Near wellbore damage under overbalanceddrilling

• Whole mud invasion(spurt period):– Internal and then

external filter cakes• Filtrate invasion

(filtrate displacing oil):– Dynamic period

(mud is circulating)– Static period

(well is left underoverbalanced pressure)

112

Drilling damages

• Drilling mud solids - solid penetration

• Water based mud filtrate - additive residues- formation sensitivity: pH,salinity- interactions with reservoir oil- fine migration

• Oil based mud filtrate - oil + surfactant invasion :wettability, emulsion...

113

Dynamic Filtration Curves for Typical Mud Formulations

114

The importance of filter cake removal

Formation Damage 1999

115

Horizontal Well - 12000 BOPDProductivity Impairment due to Filtrate Invasion

Depth of invasion (inches)

Flow

Rat

e (B

OPD

)

PermeabilityReduction

116

•Drilling•Cementing

•Perforating

•Completion and workover•Gravel packing•Production•Stimulation

•Injection operations

Sources of Formation damage

117

Well cementing

Source of damage :• fluid lost• fine particle cement,• spacer fluid

118

Clearance

Charge

Casing

Cement

Rp

Formation

Lp

Crushed zones

Perforations

may create more damage than it overcomes :• fluids, debris• control : depth, geometry ...

120

Open hole or cased hole : different impact

J Alfenore

121

To summarize :Types of formation damage

ONLY TWO TYPES !!!ONLY TWO TYPES !!!

• Although there are a number of damagemechanisms, there are only two ways inwhich near wellbore permeability can bereduced:–– Physical reduction in pore/pore throat size,Physical reduction in pore/pore throat size,–– Relative permeability reductionRelative permeability reduction.

122

Process fluid rock fluidfluid

P, T mechanical

Physical poresize reduction

finemigration,

clayswelling,

solidinvasion,

adsorption/precipitationof polymers

scaleemulsion

sludge

scalewax

asphaltene

perforationplugging

Relativepermeability

reduction

wettability fluidsaturation,

fluidblocking

(water, gas)

gas breakout,

condensatebanking,

waterconing,

Classification of damage

123

How to know the presence of skin ?

• In this case, the actual production rate isdifferent than expected from calculation

Presence of (P)skin

124

Skin factor – ex. of oil field

qFSS

P

Sr

rB

hkq

ND

w

eoo

o

'

'43

ln

00708.0

2

00708.000708.04

3ln

00708.0q

kh

BDq

kh

BSq

r

r

kh

BP

w

e

2. qeffectturbqeffectskinqPIP ideal

(given by Darcy's equation)

125

Skin effect and pressure lossesChange of pressure profile in the formation

PPR

radius

Pwf

Pskin > 0

Pskin < 0

Estimated Pwf for a given q

Actual Pwf in the case of a positive skin factor

Actual Pwf in the case of a negative skin factor

ActualwfEstimatedwfskin PPP

126

Consequences of the skin effect onthe IPR curve

Pwf

q

Increase ofskin effect

Ideal IPR

127

Models of skin factor calculationassumptions

Assumptions concerning the damaged area :• Fluids are considered as uncompressible• At any time, the volume of incoming fluid is

equal to the volume of outgoing fluid.

• All these conditions suppose a permanentflow in the damaged area.

128

Models of skin factor calculation"Permanent skin" method

skinoo

PqB

hkS

00708.0

S > 0 when the permeability near the wellbore is less than far from it :ks < kS = 0 when there is no change of permeabilityS < 0 in the case of ks > k (after an acidizing process for example)

S can be determined by using well tests (cf course about well testanalysis).

first relation

w

s

s

s

r

r

k

kkS ln s skin

w wellsecond relation

129

Rw

Rd

KdK

K= 500mDKd= 50mD (1/10)Rw= 8 1/2

Rd= Rw + 30cm

S = + 11.9S = + 5.9 if Rd= Rw + 10cmS = + 5.3 if Kd= 100mD

Examples of skin factor calculation

Skh

qBP

R

R

K

KS

skin

w

d

d

*2

ln1

130

Models of skin factor calculationEffective wellbore radius method (1/3)

• The principle of this method is to create afictive well which skin factor is 0 and whichproduction rate is the same as the actual one.

• The effective wellbore radius r’w is thetheoretical radius of this well.

• This method is available when the skinpermeability and its radius are not too high.

131


p

r

rB

khq

w

eoo

'ln

00708.0

'ln

00708.0

w

eoo r

rB

khJ

'

lnw

e

r

r

Flow rate :

Productivity Index :

'4

3ln S

r

r

w

e

replaces

132


rdrd

rw r’w

In this example, S<0 rw <r’w

Sww err '

r’w = effectivewellbore radius

(ks)(k) (k)(k)

actual well : kd ≠ k fictive well : kd = k

s estimation

133

Case of horizontal wells (1/2)Skin effect

Vertical wells :(P)skin is proportional

to the flow rate perunit length h of thewellbore in the pay-zone.

h

qP skin

Horizontal wells :(P)skin is proportional

to the flow rate perunit length L ofhorizontal part of thewellbore in the pay-zone.

L

qP skin

Influence of damage in productivity less detrimental for horizontal wells

134

Case of horizontal wells (2/2)Effective wellbore radius

• In this case, the effective wellbore radius is theradius of a fictive vertical well which verifies :– its PI is the same as the PI of the considered

horizontal well,– Its skin is 0.

• To calculate the effective wellbore radius :– we convert the horizontal well Productivity Index to

that of the equivalent vertical wellor

– we write that both flow rates are equal (cf. "horizontalwells").

135

Case of high permeability reservoirs

In this case, (P)skin may be very largecompared with other pressure drops.Therefore, we can write :

SB

khJand

Skh

BqP

PP

oo

oototal

skintotal

00708.000708.0

J cte

136




137

Prediction of the future IPR

• In the previous part of the course, we havemodeled the behavior of the flow in thereservoir today.

• But what will happen in 3, 4 or 10 years ?

138

Prediction of the future IPRPrm < Pb

JP*

qqPmax

J

J = measured value of PI actual value

J* = initial value of J= the value of PI when q 0i.e. Pwf Prm

Pwf

PrmP

JF*

qFmax

PrmF

P = presentF = future

?How to calculate the future IPR,

by using only J, and PrmP ?

139

Prediction of the future IPR - Prm < Pb

Fetkovich's procedure

22* wfrm PPJq

22*wfFrmF

rmP

rmFPF PP

P

PJq

rmP

rmF

P

F

P

P

J

J

*

*

Assumption : J* declines in proportion to the decline in pressure.

Fetkovich's model :

where :rmP

JJ

2*

140


Standing procedure

rm

wf

P

P

JJ

8.01

8.1*

rmP

qJ max8.1

J* is in terms of J. It can be calculated from it, which is measured.

We know that :(Vogel's model)

and :

rm

wf

rm P

P

P

qJ 8.01max

(Based on Vogel's model)

Assumption : The curvature of the IPR will be the same in the future.

141


Standing procedure

2

8.02.018.1

*

rm

wf

rm

wfrm

P

P

P

PPJq

Then, the Vogel's equation can be written as follows :

This equation can be applied as the IPR's one in the future, with :Prm = PrmF ; J* = JF*

2

8.02.018.1

*

rmF

wfF

rmF

wfFrmFFF P

P

P

PPJq

To be predicted

142

Prediction of the future IPR - Prm < PbStanding procedure

Poo

ro

Foo

roPF B

k

B

kJJ

**

'43

ln

00708.0*

Sr

rB

hkJ

w

eoo

o

J* can be calculated from the radial flow equation :

How to predict J*F ?

rmP

wfP

PP

P

PJ

J

8.01

8.1*

JF* can be calculated and future IPR generated if kro, µo and Bo can be predictedfrom values of pressure and saturation today and in the future

143

Prediction of the future IPRComparison of the procedures

JP*

qqPmax

J

Pwf

PrmP

JF*PrmF

future IPR Standing proc.future IPR Fetkovich's method

IPR today

(qFmax)Stand(qFmax)Fetk

144

qpqq'

P1Pwf

Pr

reservoir losses

IPR

Well performance

Documents

Transcript of Well performance