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WELL PERFORMANCE INTRODUCTION Isabelle REY-FABRET isabelle.rey-fabret@ifp.fr

1


Psep

? PR

2


The Production System WELL HEAD

Pup

LINE

Pdown

Ps

SEPARATOR

WELL

Pr

Pwf

PAY ZONE

3


Pressure losses from the reservoir to the separator flow in the well head

P3

multiphase flow in the pipeline

Pdown Pup

P1

Ps

vertical and inclined multiphase flow

P2

Pr

P4

SEPARATOR

Pwf

flow in porous media

4


rate of production during the well life qp (Rate of production) build up

plateau rate

stop of the production

Time beginning of the production

production facilities to be installed 5


Aim of this course To foresee the different facilities of the production system (wells, artificial lift systems, pipelines, etc...)

for a given reservoir pressure (Pr) and a given separator pressure (Ps), to optimize the rate of production, qp 6


How to determine qp ? qp = intersection between IPR curve and VLP 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 the well to the separator 7


Ps

Pup

SEPARATOR

VLP curve

Pwf

Pr

P = Pwf IPR curve

For given Ps, Pr, and production facilities, there is a unique possibility of production rate = intersection between IPR and VLP

VLP

IPR

q

qp

8


To plot IPR and VLP curves, we have 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, ... 9


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 – VLP curve – application to flows in the pipelines

• Part 3 : Flow through the choke • Summary of the results 10


schedule date

Morning 8h – 11h30

11 dec

Afternoon 13h to 16h Introduction – IPR curve

12 dec

IPR curve (end) + tutorial 1 to 3

Introduction to PROSPER + Prosper tutorial 1 to 2

13 dec

Multiphase flow + VLP in the case of gas wells

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

14 dec

Tutorial 8 VLP analysis + pressure losses in a pipeline Sensitivities on Prosper

Choke and gas lift Nodal analysis Tutorial 9 and 11 Prosper : how to match a model ? ex : Well 4

15 dec

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

project

16 dec

project

project

17 dec

End of the project

Exam and conclusion

11


Pressure losses in the pay zone Part 1 Flow in porous media, IPR curve

12


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 13


WELL HEAD

Pup

LINE

Pdown

Ps

SEPARATOR

WELL

Pr

P1

Pwf

PAY ZONE

14


First conditions to flow ...

P1

P2

we open  No flow

P2

we open  flow

P1 = P2

P1 P1 > P2

flow only if difference between pressures

15


Pressure losses during production Pup

well

Abscissa

Pressure Drawdown = Pr – Pwf  ensures the production

FLOW

Pup

Pup

Pup new < Pup

Pr

reservoir

EQUILIBRIUM

Pwf P  P BH r Pwf < PBH

Pressure 16


first assumption ... â&#x20AC;˘ we consider that the flow in the reservoir is pseudo-permanent : â&#x20AC;&#x201C; sealed reservoir Pwf Pwf = bottom hole flowing pressure

transient zone

transition zone

pseudo-permanent zone

t 17


Productivity Index (PI) • Productivity Index = ratio of the rate of production per pressure drawdown q q PI  J   Prm  Pwf  P1

bbls / day / psi 

q = Production Rate (in bbls/day for an oil well) Prm = Static Reservoir Pressure (psi), calculated at the middle point of the reservoir Pwf = Flowing Bottom Hole Pressure (psi) 18


Inflow Performance Relationship Pwf

a relation between the production rate and the flowing down hole pressure (Pwf)

(psi)

 1 Pwf    q  Prm  J

Prm

first approximation

PI1

second approximation

not linear – due to 2 phase flow, turbulence, etc...

PI2 0

q1 qmax = maximum rate of production, obtained when Pwf = 0

q2

qmax

qth

q (bbls/day)

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

19


From IPR curve to PI PI = the productivity at a particular rate = f(q,Prm) = calculated by using the slope of the IPR curve at the considered point We have to determine the IPR curve corresponding to the reservoir which we are considering, in order to give PI at each flow rate 20


How to calculate the IPR ? - by using known quantities = the characteristics of the reservoir - by using theoretical models for flows in porous media = the Darcy's law - by using measurements = different well tests

21


characteristics of the reservoir known quantities

rw

Pr,Tr

h

re

k : absolute permeability ko,g : effective permeability of the rock to oil / to gas ď ­o,g : effective viscosity of oil / gas, at average pressure WC : water cut GOR = gas oil ratio

22


Case of oil wells Effective and relative permeabilities effects of water production (1/2) ko = effective permeability of the rock to oil

qo  o ko   AdPo dl

sw,o = water or oil saturation. For oil and water system, sw + so = 1 k = absolute permeability = single phase permeability

ko k ro  k

kw ; k rw  k

= relative permeabilities (oil ; water)

23


Case of oil wells Effective and relative permeabilities effects of water production (2/2) 1

oil

kro

krw

1

w er at

0 1 0

no oil flow

sor

swc sw so

no water flow

0 0 1

sor = residual oil saturation ; swc = connate water saturation

24


Models for flows in porous media : Darcy's law – experimental results Water injection (rate = q) A = r²

r P

L SAND

Pa = N/m²

kA P q  L Pa.s

where :

m

k = permeability of the sand µ = viscosity of the water

25


Darcy's law applied to petroleum production

- in field units

Prm = reservoir pressure at the outer boundary

q

0.00708 k .h

Pr

 f ( P) dP

  re  3  P  Pwf  ln    S '   r  4    w 

S '  S  FND q

f(P) = a function of pressure which depends on the state of the flow in the porous medium

S = skin factor FND q = turbulent flow term we have to distinguish between single phase flow and two phase flow

26


Hypothesis of IPR calculation concerning the reservoir • Homogeneous (permeability k and saturation s constant in all horizontal directions) • Horizontal h • Circular • The thickness h is constant • It is drained by a single fully penetrating well located at its centre 27


Different cases of flow Hydrocarbon phase diagram Critical point

De w

gas reservoir

po int

Joule-Thomson expansion Cricondentherm point

0%

5%

10 %

20 %

80

40 %

Reservoir Pressure

Undersaturated oil Oil reservoir reservoir generalization int o p saturatedbble Bu Oil reservoir %

condensate reservoir

lines of constant phase distribution (% = liquid volume)

Reservoir Temperature 28


IPR calculation versus type of flow

Type of flow

IPR Definition calculation

Oil (undersaturated reservoirs) Gas Oil and free gas (saturated reservoirs)

29


Oil – no free gas Pb  Pwf  Prm

oil reservoir

Prm Pb = bubble point pressure

0%

5%

10 %

20 %

% 80

40 %

Pwf Pb

Temperature

30


oil / no free gas Pb  Pwf  Prm

PB<Pwf<Prm

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

k ro f ( P)  B = viscosity of the fluid at average pressure

relative permeability of the rock to oil B = Formation Volume Factor of the fluid V ( Pr , Tr ) B  FVF  V ( Pstd , Tstd ) 31


oil / no free gas PB<Pwf<Prm

kro = 1 o

viscosity versus pressure

k ro f ( P)   o Bo

: t l n i a f o Bonst o o e c s Ca ost alm B PB

P

f(P) almost constant for P > PB

32


oil / no free gas PB<Pwf<Prm

Darcy's law in this case:

 qo  o Bo   re  3     S '   Prm Pwf  ln  0.00708 ko h   rw  4  P

qo 

0.00708 ko hPrm  Pwf    re  3   o Bo  ln    S '    rw  4 

Prm most of pressure losses near the wellbore

re

rw

33


oil / no free gas PB<Pwf<Prm

qo J  Prm  Pwf

0.00708 ko h  re 3   o Bo  ln   S '   rw 4 

ko h For a given system, J  const.  o Bo Non accurate, but gives a quick idea of J Note: if q in m3/d, h in m & P in bara (instead of bpd, ft & psia) replace 0.007082 by 0.053578

34


oil / no free gas case of oil and water flow

PB<Pwf<Prm

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

kw  0.00708 h  ko J    re 3  B  B o o w w  ln   S ' rw 4

Note: if q in m3/d, h in m & P in bara (instead of bpd, ft & psia) replace 0.007082 by 0.053578

oil

water

35


IPR calculation versus type of flow

Type of flow

IPR Definition calculation

Oil (saturated reservoirs) Gas Oil and free gas (undersaturated reservoirs)

36


Case of gas gas reservoir

Prm P

Pwf

0%

5%

10 %

20 %

40 %

% 80

Temperature

37


Case of gas 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

f ( P) 

kg  g Bg

If there are no condensation or liquid accumulation problems, kg = cte

 TZ  where : Z = gas compressibility B g  0.02827    P  Re s factor, which varies T = absolute T° 38


case of gas • an empirical method : use of well test results to elaborate a relation between q, Pwf and Pr. 1°) gas well tests 2°) back pressure equations

39


Different types of gas-well tests • drawdown : decrease of pressure during production at constant flow rate

• pressure buildup : increase of pressure with the well closed-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 40


Stabilized production point method • initially : close the well  buildup pressure  determination of Pi • four times : well flowed at a constant rate q for a sufficient time that Pwf stabilizes  four couples (q, Pwf ) • main disadvantage : unrealistically long test periods (to attain the stabilized Pwf)

41


Stabilized production point method Pwf Prm Pwf1 Pwf2 Pwf3

4 couples (q,Pwf) Pwf4 q

0

t1

q4

q3

q2

q1

t2

stabilized values

t3

t4

Time 42


Multiple-rate drawdown tests : isochronal procedures • in order to avoid the long delay necessary for a stabilized situation (stabilized production point method), before Pwf is recorded. • 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 43


Cullender's test Pwf

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

Pwf initial = Prm Pwf1

Prm Pwf2 stabilized pressure

Pwf3

Pwf4

q q2

q1 t1i t

t1f

t2i t2f t

q4

q3

t3i

t3f t

t4i

t4f t

Pwf5

q5

In this test, (q5,Pwf5) are the sole stable values Time 44


Katz's test Specific test condition : buildup period tbu is fixed

Pwf

Pwf initial = Prm

Prm

Pwf1

Pwf2

stabilized pressure Pwf3

Pwf5

Pwf4 q

q2

q1 t1i t

t2i t2f

t1f tbu

t

q4

q3

t3i tbu

In this test, (q5,Pwf5) are the sole stable values t4i

t3f t

q5

tbu

t4f

Time

t 45


case of gas – well tests 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

46


from these tests ... • 2 main types of gas well behaviours : – first back pressure equation : FND C q 2 C1 C1

 P 

2 rm

 Pwf2 q

 0

– second back pressure equation :

2 n wf

qg  C P  P 2 rm

47


ion t a tr s n o dem

Case of gas : first back pressure equation

Assumption : we consider the average of the different quantities. q

with

0.00708 k g .h

Pr

 f ( P) dP

  re  3  P  Pwf  ln    S '   r  4  w    

P f ( P)  0.02827  g ZT 48


case of gas : first back pressure equation

ion t a tr s n o dem

qg 

qg 

1.4066 *10 3 k g h

Prm

 

  re  3  ln    S '  Pwf  r  4  w    

PdP  g ZT

0.703 *10 3 k g h Prm2  Pwf2

(in Mscf/d)

  re  3   ga Z aTa  ln    S  FND q    rw  4 

for assumed average properties and pressures

term due to turbulent flow

Xa = average of the quantitiy, calculated at the average pressure 49


ion t a tr s n o dem

Case of gas First back pressure equation

If we consider C1 

we obtain

0.703.10 6 k g h  g Z aTa

and

 re  3 C2  ln    S  rw  4

FND q 2  C2 q  C1 Prm2  Pwf2  0

term due to turbulent flow

FND C2 q C1 C1

 P 

2 rm

 Pwf2 q

 0 50


Case of gas First back pressure equation

ion t a tr s n o dem

FND C q 2 C1 C1

 P 

2 rm

 Pwf2 q

 0

ax  b  y

straight line

xq y where :

Prm2  Pwf2 q

0.13.106 GZT a h 2 rw k 4 3

non Darcy coefficient (turbulent flow)

 1.422.106  ZT   re  3 b ln    S  kh   rw  4 

coefficient of Darcy effects

a and b are empirically determined by using well test regression

51


How to use the gas well tests to determine the equation parameters ? example of the second Back Pressure equation log-log plot n = slope of the straight line log qg

Case of stabilized data

log P  P 2 rm

2 wf

log q g  log C  n log Prm2  Pwf2

logC

logC = intersection between the straight line and the logq axis

52


How to use the gas well tests to determine the equation parameters ? example of the second Back Pressure equation

log q g  log C  n log P  P 2 rm

2 wf

2 n wf

qg  C P  P 2 rm

qg in MMscf/d

C = gas well performance coefficient n = exponent of the back pressure equation 0.5 < n < 1 High turbulent effect

Low turbulent effect

53


Use of Cullender or Katz's tests n and logC determination points obtained during drawdown periods (Pwfi,qi) , i = 1..4

log q

n

=

pe o sl

he t of

e lin

Case of only 1 stabilized data point obtained with (Pwf5,q5)

log Prm2  Pwf2

logC

2 n wf

qg  C P  P 2 rm

54


IPR determination for a gas-well example of second back pressure equation With tests, we measure q and Pwf



22 log P P rm wf

We calculate log q and log Prm  Pwf



22 log P P rm wf

2

We plot log q versus log Prm2  Pwf2

2

linear regression + use of stabilized (q,Pwf)

n and logC determination

IPR 55


Absolute Open Flow Potential qmax qmax represents the ideal case of production, where Pwf = 0. In this case, P1 is maximum, because : P1  PrShutIn  Pwf 0

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

can be written : qmax  C P

2 n wf

The back pressure equation : q g  C P  P 2 rm

n 2 rShutIn

56


IPR calculation versus type of flow

Type of flow

IPR Definition calculation

Oil (undersaturated reservoirs) Gas Oil and free gas (saturated reservoirs)

57


Two phase flow – oil and free gas Pwf  Prm  Pb oil reservoir

10 %

0%

Case of only 2 phase flow

5%

Pwf

20 %

Prm

% 80

40 %

Pb

Pb = bubble point pressure

Temperature

58


Two phase and single phase flow – oil and free gas Pwf  Pb  Prm oil reservoir

Prm

Pb = bubble point pressure

q1

Pb q2

Case of single phase and 2 phase flow 0%

5%

Pwf

Temperature

59


Two phase flow – oil and free gas Pwf  Prm  Pb oil reservoir

10 %

0%

Case of only 2 phase flow

5%

Pwf

20 %

Prm

% 80

40 %

Pb

Pb = bubble point pressure

Temperature

60


Two phase flow first case : PB > Prm

qo 

with

0.00708 k .h

PB > Prm

Prm

 f ( P) dP

  re  3  P  Pwf  ln    S '   r  4  w     f ( P) 

k ro  o Bo

not constant, function of pressure function of saturation

The equation can't be solved without the knowledge of the relation between kro/oBo and (Prm – Pwf) = P1 61


Two phase flow PB > Prm

kro can be estimated in lab with experience but is different at each level in the reservoir, for the same rock Prm varies  oil and gas saturations varie  kr varies

Prm

Pwf

k ro dP  o Bo

I1  I2

k ro  o Bo I2

I1 Pwf P

qo depends on the level of pressure. It depends on the GOR too (the curve is not the same).

Prm P

P

62


Two phase flow An empirical method Pwf Prm

PB > Prm

measurements Pressures and corresponding rates of production measured for different field cases are normalized by qmax and Prm resp. Curves of each field can be superposed. q qmax

measurements are used to establish an empirical equation = IPR equation

63


Two phase flow P

B

> Prm

IPR equations q qmax V=0:

J

 Pwf  1  1  V   Prm

q q  th Prm  Pwf Prm

  Pwf   V    Prm

PB > Prm

  

2

IPR = straight line Pwf

V = 0.8

VOGEL's equation Prm

V=1

IPR curves

FETKOVITCH's equation

q

qmax 2 2 ( P  P rm wf ) 2 Prm (qmax)F

(qmax)V

qth

64

q


Two phase flow relation between J* and qmax

PB > Prm

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

q J Prm  Pwf

q J

Prm  Pwf 1    Prm

  

Case of Vogel's equation :

qmax J Prm

  Pwf 1  0.8 P   rm 

    

J* 

1.8 qmax Prm

Case of Fetkovich's equation :

qmax J Prm

  Pwf 1    P   rm

    

2 qmax J*  Prm 65


Two phase flow IPR equations : How to determine qmax ?

PB > Prm

• if we know Prm, by using one result of well test (= one couple (q,Pwf)) or • without the knowledge of Prm, by using two results of well tests (= 2 couples (q,Pwf))

66


Two phase flow

PB > Prm

exercise 1.1 We 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's approach, and Vogel's one. 67


Oil and free gas Pwf < PB < Prm

Pwf  Pb  Prm oil reservoir

Pb = bubble point pressure

Prm Pb

Case of single phase and 2 phase flow 0%

5%

Pwf

Temperature

68


oil and free gas Pwf < PB < Prm

qo 

0.00708 k .h

Prm

 f ( P) dP

  re  3  P  Pwf  ln    S '   r  4  w     k ro and f ( P)  B 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

69


oil and free gas Pwf < PB < Prm Prm  Pb k  k   ro dP   ro dP  qo  B    re  3   P  Pwf B P  Pb    ln    S '   r  4  w    

0.00708 ko .h

Pwf < P < Pb two phase flow

Pb < P single phase flow

Pb  0.00708 ko .h Prm  Pb  kr    q dP  B    re  3   P  Pwf B    ln    S '   r  4  w    

part of the IPR curve given by Vogel's or Fetkovich's models 70


Oil and free gas IPR curve Pwf

Pwf < PB < Prm

Part of single phase flow Straight line  PI = J = cte

Prm

Physically, the transition from pure liquid flow to the presence of some free gas in the flowing stream is a continuous one  continuity and derivability of IPR at this point

Pb

q1

q2 Part of two phase flow curve qmax-qb qb

rate at bubble point pressure

qp

qmax (AOFP)

production rate

q

71


Oil and free gas Pwf < PB < Prm oil reservoir

Prm

q1

Pb

qp = q1 + q2

q2

0%

5%

Pwf

Temperature Pb = bubble point pressure

72


Two phase flow Fetkovich's approach to calculate

Pb

 f ( P)dP

Pwf < PB < Prm

Pwf

• assumption : f(P) is a linear function of pressure • we know the conditions of Pressure, viscosity, etc... at the bubble point  k ro   f ( P)   o Bo  P   f Pb   k ro Pb    B  o o b  P  k ro  f ( P)     B o o b Pb  73


Two phase flow

Pb

Fetkovich approach to calculate  f ( P)dP Pwf

 k ro  1   Pb2  Pwf2 2P   re  3   B  ln    S '   o o b b  r  4    w 

q

we can write :

0.00708 k .h

q

or

q  J ' Pb2  Pwf2

0.00708 ko .h 1 Pb2  Pwf2   re  3  2 Pb     o Bo  ln    S '    rw  4 

J q Pb2  Pwf2 2 Pb

Pwf < PB < Prm

where J is the PI in the case of single phase flow (q1 calculation) where J' is referred to a pseudo productivity index

74


Fetkovich approach IPR equation

Pwf < PB < Prm

q1  J Prm  Pb 

Pwf Prm gl n i s

Pb

q1

e as h ep

t

ion t r po

J q2  Pb2  Pwf2 2 Pb

rtion o p e as wo ph

q2

qmax-qb qb

Total rate :

qp

q  J Prm  Pb 

qmax (AOFP)

J Pb2  Pwf2 2 Pb

q

 

and qmax  J  Prm 

Pb  75 2


Two phase flow Vogel's approach

Pwf < PB < Prm

The two phase part of the curve can be written like in the case of two phase flow where Prm < Pb, with the assumption that PrmPb :

  Pwf q  qmax 1  0.2   Pb

  Pwf   0.8   Pb

  

2

  

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

  Pwf q  qb  qmax  qb 1  0.2   Pb

  Pwf   0.8   Pb

  

2

   76


Two phase flow – free gas relation between J* and qmax

Pwf < PB < Prm

Definition : If Pwf = Pb, we have J = J*=Jstraight line. Shift of the 2-phase curve Prm

0

J*

qmax

Prm

Pb

0 qmax- 0

qb

Case of Vogel's equation :

1.8 (qmax  qb ) J*  Pb

J*

Pb

qmax - qb

0

qb

qmax

Case of Fetkovich's equation :

J* 

2 (qmax  qb ) Pb 77


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

78


Horizontal wells - When to use them ? - How to calculate the flow rate ? - Influence of reservoir anisotropy - Case of slant wells 79


Why to use horizontal wells? Mainly : â&#x20AC;˘ To increase the surface of contact between the well and the reservoir â&#x20AC;˘ To enhance the productivity

80


Why to use horizontal wells ? RELIEF-WELL OFFSHORE

SHORELINE

MULTIPLE ZONES SIDETRACKING 81


Why to use horizontal wells? HEAVY OIL FRACTURED RESERVOIRS

THIN PAY-ZONES

LAYED RESERVOIR

WATER / GAS CONING

GAS WELLS


Drainage area in the case of a horizontal well L

drainage area of a vertical well

kv

drainage shape = ellipso誰dal

X X = large half-axis

kh 83


Surface of contact between the well and the reservoir re X

Vertical well

Horizontal well

L  X   2 

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

84


How to know the gain in 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 a single horizontal one

85


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 v  vertical

d  deviated 86


Flow rate estimation Several methods have been developed, and, more particularly the ones given by : â&#x20AC;&#x201C; Renard and Dupuy â&#x20AC;&#x201C; Joshi Assumption : reservoirs are isotropic (horizontal permeability = vertical one)

87


Renard and Dupuy’s model P  o Bo SI Units qh   h  1  2 X   h   ch      ln  L   L   2 rw  specific to 2k h h

where 2X = major axis of the drainage ellipse

this model

P  o Bo qh   h  1  2 X   h   ch      ln  L   L   2 rw  P 0.00708k h h  o Bo qh  1  2 X  ch   L   0.00708k h h

Field Units

If L>>h

88


Joshi’s model P 2kh h o Bo qh  SI Units 2   L  a  a²  2   h   h   ln    ln  L  L   2 rw    2 specific to  

   

this model

where :

If L>>h

L  2r  a 0.5  0.25   eh  2  L  qh 

4

field units : 2  0.00708 2rw  rw

2kh hP

   

2   L  a  a²  2  o Bo ln  L   2  

89


A model to compare horizontal and vertical PI Hyp : kv/kh = 1 h in feet

r  ln  ev  Jh  rw   2 Jv  L      1  1   2 reh    h   h   ln     L  ln  2 r  L w       2 reh    

0

Jh Jv

h  25 '

50 ' 200 '

400 '

if h <<L L

Conclusion : The gain of J in a thin reservoir is higher than for a thick zone 90


Case of anisotropic reservoirs Assumption : kv  kh (anisotropic reservoir) In this case, the anisotropy can be characterized by : 

kh kv

kh = permeability in the horizontal plane kv = vertical permeability

and the reservoir thickness is modified :

heff

kh h  h kv 91


Case of anisotropic reservoirs Jh Jv

h1 = cte

kh ď&#x201A;Ż kv

h2 = cte

h1 < h2

L

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

92


Case of anisotropic reservoirs anisotropy in the horizontal plane

case 1 : productivity = optimized larger horizontal anisotropy smaller horizontal anisotropy

case 2 : productivity = minimum

better = well drilled normal to the larger horizontal anisotropy

93


Case of anisotropic reservoirs • Joshi’s model : qh 

 a   ln   

p 0 . 00708 k h h  0 B0 2  L   a2      2     h    h    L  ln  2 r L  w  2 

where  

  

kh kv

and a defined as previously for Joshi's model

• Renard and Dupuy’s model : qh 

0 . 00708 k h h  p  0B0

where Rw  rw

1   2

1  2 X    h   h arcch    ln  L L      2 R w

   94


How to calculate the effective radius rw' ? rw' can be defined as the radius of a fictive vertical well which produces with the same flow rate as the considered horizontal well. Assumption :

r ev ď&#x20AC;˝ r eh

same drainage radius

Jv ď&#x20AC;˝ Jh

same productivity index

95


By using Joshi’s equation : 0 . 00708  a   ln   

=>

r w' 

a

2

 L     2  

L 2

 a  

khh

a

2

2

Jh  Jv 0 . 00708

oBo

   h h    L ln  2 r w   

 L  r eh   2   2  L     h    2     2 r w

  

   

  h  L  

khh

oBo  r  ln  e '  rw  



kh kv

(general relation, which takes into account the anisotropy) 96


Case of Slant wells ď Ś

h

pay-zone

well trajectory 97


Cinco, Miller and Ramey model assumption :  < 75° deviated thickness :

h hd  rw

kh kv

deviated inclination :

 kh  d  arctan  tan    kv 

effective wellbore radius :

rw'  rwe  sd  d  sd     41 

2.06

 d     56 

1.865

 hd  ln   100  98


Cinco, Miller and Ramey model Slant well / Vertical well comparison

 re  ln  rw  Jd   Jv  re  ln   r'w 

Jd Jv

h  400' 300' ' 200 ' 100

hyp : kv=kh

Conclusion : Jd/Jv increases with kv (as for horizontal wells) and with h (in contrast to horizontal well) 99


Van der Vlis’s model Assumption :   20° and kv=kh

rw    L  r    0.454 sin  360  h   4   ' w

h L

with :

 re  ln  r Then, we can apply : J d   w  Jv  re  ln   r'w 

L

h cos 

to compare Jd and Jv.

100


Conclusion Itâ&#x20AC;&#x2122;s only in the case of thick reservoirs that slant wells can be more interesting than horizontal ones. For thin pay-zones, horizontal wells are always better.

101


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

102


Skin factor

re

rw pay zone rs

ks

k

Zone of changed permeability SKIN EFFECT, characterized by the ÂŤ skin factor Âť, noticed S "S" takes into account the non homogeneity of the reservoir permeability .

103


â&#x20AC;˘ Why are there changes of the reservoir permeability near the wellbore ? FORMATION DAMAGE

104


Formation damage : definition Formation damage is any impairment of reservoir permeability around the wellbore It is a consequence of the drilling, completion, work-over, production, injection or stimulation operations Productivity or Injectivity are affected 105


Sources of Formation damage •Drilling •Cementing •Perforating •Completion and workover •Gravel packing •Production •Stimulation •Injection operations

106


Interface well-reservoir during drilling impermeable zone reservoir rock

Control of fluid loss through the wellbore cake

Filtration through the wellbore

ď&#x192;¨ understanding of the mechanisms of filtration and formation of cakes of complex well fluids with models 107


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 108


Virgin reservoir

Drilling operation

Shale

External mud cake

Quartz grains

1 m

Drilling mud with dispersed solids

109


Wellbore filtration Definition of the zones invaded by the filtrate Circulating drilling fluid

Well

External cake Internal cake Invaded zone

Non invaded zone

110


Near wellbore damage under overbalanced drilling • 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 under overbalanced pressure)

111


Drilling damages â&#x20AC;˘ Drilling mud solids

- solid penetration

â&#x20AC;˘ Water based mud filtrate - additive residues - formation sensitivity: pH, salinity - interactions with reservoir oil - fine migration

â&#x20AC;˘ Oil based mud filtrate

- oil + surfactant invasion : wettability, emulsion... 112


Dynamic Filtration Curves for Typical Mud Formulations

113


The importance of filter cake removal

114

Formation Damage 1999


Horizontal Well - 12000 BOPD Productivity Impairment due to Filtrate Invasion

Flow Rate (BOPD)

Permeability Reduction

Depth of invasion (inches)

115


Sources of Formation damage •Drilling •Cementing

•Perforating

•Completion and workover •Gravel packing •Production •Stimulation

•Injection operations 116


Well cementing

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

117


Perforations

Clearance

Cement

Formation Charge

Rp

Crushed zones

Casing

Lp

may create more damage than it overcomes : â&#x20AC;˘ fluids, debris â&#x20AC;˘ control : depth, geometry ...

118


119


Open hole or cased hole : different impact

120

J Alfenore


To summarize : Types of formation damage ONLY TWO TYPES !!! • Although there are a number of damage mechanisms, there are only two ways in which near wellbore permeability can be reduced: – Physical reduction in pore/pore throat size, – Relative permeability reduction. reduction 121


Classification of damage Process

fluid rock

fine Physical pore size reduction migration,

Relative permeability reduction

clay swelling, solid invasion, adsorption/ precipitation of polymers wettability

fluid fluid

P, T

mechanical

scale emulsion sludge

scale wax asphaltene

perforation plugging

fluid gas break saturation, out, fluid condensate blocking banking, (water, gas) water coning,

122


How to know the presence of skin ? â&#x20AC;˘ In this case, the actual production rate is different than expected from calculation Presence of (ď &#x201E;P)skin

123


Skin factor – ex. of oil field 0.00708 ko h  q  P    r 3  e   B ln  o o   r 4  S '   w   S '  S  FND q

(given by Darcy's equation)

   re  3    SB   DB  2 B  P  ln    q   q q   0.00708kh  rw  4   0.00708kh   0.00708kh    

P  PI ideal q  skin effect q  turb. effect q 2

124


Skin effect and pressure losses Change of pressure profile in the formation P PR

radius

Estimated Pwf for a given q Actual Pwf in the case of a positive skin factor

Pskin < 0

Actual Pwf in the case of a negative skin factor

Pwf Pskin > 0

Pskin  Pwf Estimated  Pwf Actual 125


Consequences of the skin effect on the IPR curve Pwf

Increase of skin effect

Ideal IPR

q 126


Models of skin factor calculation assumptions 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 permanent flow in the damaged area.

127


Models of skin factor calculation "Permanent skin" method first relation

0.00708hk P skin S qBo  o

S > 0 when the permeability near the wellbore is less than far from it : ks < k S = 0 when there is no change of permeability S < 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 test analysis). second relation

k  k s  rs  S ln  ks  rw 

s  skin w  well 128


Examples of skin factor calculation

Rw Rd Kd K

K= 500mD Kd= 50mD (1/10) Rw= 8 1/2 Rd= Rw + 30cm

 K   Rd  S    1 ln   Kd   Rw   qB  Pskin   *S  2kh  S = + 11.9 S = + 5.9 if Rd= Rw + 10cm S = + 5.3 if Kd= 100mD

129


Models of skin factor calculation Effective wellbore radius method (1/3) • The principle of this method is to create a fictive well which skin factor is 0 and which production rate is the same as the actual one. • The effective wellbore radius r’w is the theoretical radius of this well. • This method is available when the skin permeability and its radius are not too high. 130


Models of skin factor calculation Effective wellbore radius method (2/3) Flow rate :

0.00708kh q p  re   o Bo ln '   rw 

Productivity Index :

0.00708kh J  re   o Bo ln '   rw 

 re  3  re  ln '  replaces ln    S '  rw  4  rw 

131


Models of skin factor calculation Effective wellbore radius method (3/3)

r  rwe ' w

r’w = effective wellbore radius

S

s estimation

(k) (ks) rw

(k)

(k) rd

rd r’w

actual well : kd ≠ k

fictive well : kd = k

In this example, S<0  rw <r’w

132


Case of horizontal wells (1/2) Skin effect Vertical wells : (P)skin is proportional to the flow rate per unit length h of the wellbore in the payzone.

P skin

q   h

Horizontal wells : (P)skin is proportional to the flow rate per unit length L of horizontal part of the wellbore in the payzone. q P skin     L

Influence of damage in productivity less detrimental for horizontal 133 wells


Case of horizontal wells (2/2) Effective wellbore radius • In this case, the effective wellbore radius is the radius 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 well or – we write that both flow rates are equal (cf. "horizontal wells"). 134


Case of high permeability reservoirs In this case, (P)skin may be very large compared with other pressure drops. Therefore, we can write : Ptotal  Pskin q o Bo  Ptotal  S 0.00708kh 0.00708kh and J   o Bo S

J  cte 135


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

136


Prediction of the future IPR â&#x20AC;˘ In the previous part of the course, we have modeled the behavior of the flow in the reservoir today. â&#x20AC;˘ But what will happen in 3, 4 or 10 years ?

137


Prediction of the future IPR Prm < Pb Pwf PrmP

J = measured value of PI  actual value

JP*

PrmF JF*

?

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

How to calculate the future IPR, by using only J, and PrmP ?

qFmax

qPmax

q

P = present F = future 138


Prediction of the future IPR - Prm < Pb Fetkovich's procedure Fetkovich's model :

q  J * Prm2  Pwf2 J* 

where :

J 2 Prm

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

J F* PrmF  * J P PrmP  PrmF qF  J   PrmP * P

 2 2  PrmF  PwfF 

 139


Prediction of the future IPR - Prm < Pb Standing procedure (Based on Vogel's model) Assumption : The curvature of the IPR will be the same in the future.

We know that :

1.8 qmax J Prm

qmax and : J  Prm J* 

Pwf  1  0.8 Prm 

1.8 J Pwf  1  0.8 Prm 

  

(Vogel's model)

  

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

140


Prediction of the future IPR - Prm < Pb Standing procedure Then, the Vogel's equation can be written as follows :

 Pwf J * Prm  1  0.2 q 1 .8  Prm  

  Pwf   0.8   Prm

  

2

  

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

J *P qF  F rmF 1 .8 To be predicted

  PwfF 1  0.2   PrmF

  PwfF   0.8   PrmF

  

2

  

141


Prediction of the future IPR - Prm < Pb Standing procedure How to predict J*F ? J* can be calculated from the radial flow equation :

 k  J F*  J P*  ro    o Bo  F J P* 

J* 

0.00708ko h   re  3      o Bo  ln    S '    rw  4 

 k ro      o Bo  P

1.8 J P PwfP   1  0.8  PrmP  

JF* can be calculated and future IPR generated if kro, µo and Bo can be predicted from values of pressure and saturation today and in the future 142


Prediction of the future IPR Comparison of the procedures Pwf PrmP

IPR today future IPR  Standing proc. future IPR  Fetkovich's method

JP*

PrmF JF*

J

qPmax (qFmax)Fetk

(qFmax)Stand

q 143


Pr Pwf

ď &#x201E;P1

reservoir losses

IPR

qp

q'

q 144

Well performance  

Introduction to well performance

Well performance  

Introduction to well performance

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