13304 PRODUCTION ENGINEERING I PETROLEUM ENGINEERING FACULTY OF EXPLORATION AND PRODUCTION TECHNOLOGY

13304

PRODUCTION ENGINEERING I

PETROLEUM ENGINEERING

FACULTY OF EXPLORATION AND PRODUCTION TECHNOLOGY

Previous Meeting

• IPR multiphase for Oil Well

• Composite IPR

FUTURE IPR

• Predicting future production rate of a well is very important, especially for

designing artificial lift equipment specification, production allocation for each well, and to estimate the production rate or flowing bottom hole pressure.

• The changing of two-phase IPR curve is represented by the changing of slope of the curve, that means the productivity index, J.

• For two-phase IPR, the productivity index could be represented by dq/dP_wf = J

• This statement could be applied to predict the future two-phase IPR

The Valid Assumption in the Application of Future IPR

• The well producing from solution gas drive reservoir

• The well have not changed the producing formation

• The well had never been stimulated (acidizing or fracturing)

VOGEL’S METHOD

o p o

ro o f o

ro f

B k

B k

Jp J



 







 





=





𝑞 =

^𝐽_1.8^{𝑓𝑃𝑓 1−0.2 𝑝}_𝑃^𝑤𝑓

𝑓 −0.8 𝑝_𝑤𝑓 𝑃_𝑓

2

𝐽_𝑓: productivity index in a future time 𝑃_𝑓: reservoir pressure in a future time

( ) ( )

o p o

ro o f o

ro

p f

B k

B k J

J



 







 





=





Fetkovich Formulation

• Assuming that k

_ro

/

_o

B

_o

is linear to pressure, therefore k

_ro

/

_o

B

_o

ratio of mobility at two different pressure is equal to the pressure ratio.

• Therefore the productivity index ratio is equal to the reservoir

pressure ratio.

2 1 2

1

r r

P P C

C =

ri r

o P o

ro o P o

ro

P P B

k B k

ri

r =



 







 









Persamaan Fetkovich

rf ri

P P C

C

f

i =

Pr Pr

(

_{rf wf}

)

ⁿ

o

C P P

q

f

2 2

Pr

−

=

(

rf wf

)

ⁿ

ri rf i

o P P

P C P

q = _Pr ² − ²

ri rf

P C P

CPrf = Pri

The value of C and n are obtained from isochronal test

Using Fetkovich’s Equation, and by assuming J and n are constants through time

Eckmeir’s Equation to Predict IPR

• Assuming “n” equal to 1.0, the ratio of maximum flow rate of two reservoir pressure could be represented as follows:

3

1 r

2 r 1

max o

2 max o

P P Q

Q 



 



=  ³

ri rf i

max o f

max

o P

Q P

Q 









= 

The Changing of IPR Curve Due to The Changing of Reservoir Pressure

0 200 400 600 800 1000 1200 1400 1600 1800 2000

0 1000 2000 3000 4000 5000 6000

Laju Produksi, stb/d Tekanan Alir dasar Sumur, psi Aw al

Np= 8601 Np=17202 Np=25804 Np=34405 Np=43006

0 200 400 600 800 1000 1200 1400 1600 1800 2000

0 10000 20000 30000 40000 50000

Produksi Kumulatif, stb

Tekanan Reservoir, psi

Persamaan peramalan kurva ipr

3 ri i rf max o f

max

o P

Q P

Q 



 



= 

0 200 400 600 800 1000 1200 1400 1600 1800 2000

0 1000 2000 3000 4000 5000 6000

Laju Produksi, stb/d Tekanan Alir dasar Sumur, psi Aw al

Np= 8601 Np=17202 Np=25804 Np=34405 Np=43006

Q-max-f Q-max-i Pr-i

Pr-f

Exercise 5. Future IPR

• Determine IPR for a well at the time when average reservoir pressure will be 1800 psi. The following data are obtained from laboratory tests of well fluid samples:

• Using Fetkovich’s method, plot the IPR curve for a well in

which reservoir pressure initial is 3,000 psia and C

_i

= 4x10

^-4

stb/d-psi2. Predict the IPRs of

the well at well shut-in static

pressures of 2,500 psia, 2,000

psia, 1,500 psia, and 1,000 psia.

Horizontal Well

• Joshi (1988) presented the following relationship

considering steady-state flow of oil in the horizontal plane and pseudo–steady- state flow in the vertical

plane: Half length of drainage ellipse in

horizontal well Anisotropy ratio

HEAVY OIL

THIN PAY-ZONES LAYED RESERVOIR

FRACTURED RESERVOIRS

WATER / GAS CONING

WHEN TO USE HORIZONTAL OR

SLANTED WELLS?

Horizontal Well

• Moderate significance of the vertical to horizontal

permeability anisotropy for a moderate thickness

formation

• Great significance of

permeability anisotropy for thicker reservoir.

• But how is it if we compare to vertical well?

EXERCISE 8: INFLUENCE OF THE LENGTH OF A HORIZONTAL DRAIN ON THE PRODUCTIVITY

Data:

• reservoir pressure : 2900 psi

• thickness : 80 ft

• permeability: 100 mD

• kh/kv: 10

• porosity: 0.2 fraction

• viscosity: 0.5 cP

• FVF: 1.5

• total compressibility: 0.00002069 psi^-1

• well radius: 0.328 ft

• production rate: 3150 b/d

• drainage radius: 4900 ft

• horizontal permeability of damaged zone: 30 mD

• horizontal radius of damaged zone:

1 ft

• length of the drain: 1640 ft

1. Compare PI between a vertical well and a horizontal well without skin, and the following lengths of the horizontal drain: 50, 100, 200, 500, 1500 or 2000 ft. Conclusion?

2. Now, change the thickness of the reservoir: 50, 80, 100, or 150 ft. Conclusion?

Horizontal Well

• If the trajectory of a well is deviated or horizontal, the surface of contact between the pay zone and the well is increased, and thus its productivity.

• In the case of an horizontal well, the drain is generally open hole. It is crucial to clean the cake as efficiently as possible for a good productivity of the well.

• The productivity of an horizontal well is all the more high that the reservoir is thin and a vertical permeability is high.

• The productivity of a deviated well is all the more high that the reservoir is thick and a vertical permeability is high.

Vertical & horizontal wells: sensitivity to skin

RATIO IP (skin)/ IP (skin=0)

0 0,5 1 1,5 2 2,5

-10 -5 0 5 10 15 20 25

Skin

Puits Vertical Puits Horizontal

27

GEOMETRIC SKIN : HORIZONTAL WELL

DASHED HORIZONTAL WELLS

CASE 1 CASE 2 CASE 3 CASE 4 CASE 5 CASE 6

CASE 7 Vertical

1000 m

250 m 250 m

500 m

175 m 150 m 175 m

100 m

50 m DASHED HORIZONTAL WELLS

Productivity index

0 50 100 150 200 250 300

case 1 case 2 case 3 case 4 case 5 case 6 case 7

PI m3/d/bar

-8 -7 -6 -5 -4 -3 -2 -1 0 1

Geometr ic skin

Quiz

• A horizontal well is all the more interesting because

• the pay zone is thick / thin

• the vertical permeability is high / low

• the middle part / the ends of the drain are well connected with the reservoir

• The formation damage is more detrimental in the case of vertical wells / horizontal wells.

• A slanted well is all the more interesting because

• the pay zone is thick / thin

• the vertical permeability is high / low

The comparison between the vertical PI and the Horizontal one has to be done to justify the interest of a horizontal well trajectory.

GAS WELL

• Darcy’s Law for Oil flow is also used in equation of gas flow

• The solution of partial differential equation from combination of The Continuity and Darcy’s Law for radial flow

• The unit of variables:

• P_r : reservoir pressure, psia

• P_wf : flowing bottom hole pressure, psia

• k = permeability, md

• h = formation thickness, ft

• T_R : reservoir temperature, ^oR

GAS WELL

Temperature

P_r

P_wf

gas reservoir

Pressure 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

GAS WELL

Qs, in SCF/day (standard conditions)

Basic Equation Gas Flow in Porous Medium

• Z : gas compressibility

• r_e : draiange radius, ft

• r_w : wellbore radius, ft

• q_sc : gas production rate, MMSCF/d

• C : performance constant of well

( )



 



  −



 



 

= ⁻ −

75 . r 0

ln r Z T

P P

kh 10

x 703 .

q 0

w e R

g

2 wf 2

r 6

sc



 



  −



 



 

= ⁻

75 . r 0

ln r Z T

kh 10

x 703 .

C 0

w e R

g

6

(

_r² _wf²

)

sc

C P P

q = −

• In a case of a gas well, the IPR is a curve. Mainly two models can be used to represent the behaviour of the gas flowing in the reservoir : the 2 back pressure equations.

• The parameters of these models can be determined with help from isochronal well test results. The most adequate model is the one which is the closest to the measurements.

• The default model is the second back pressure equation. In this equation, n is all the more close to 0.5 that the flow is turbulent.

IPR curve (gas well)

MODELS

2 parameters to characterize the well behaviour:

(a ; b) or (C ; n) determined from well tests

In the case of stabilized high flow rates, 2 main types of gas well behaviours:

( )

0

2 2

− =

− +

g wf r

q P b P

aq_g

First back pressure Equation Second back pressure Equation

(

r wf

)

ⁿ

g C P P

q = ² − ²

KATZ’S TEST

t_1f t_2i t_3i t_3f Time

P_wf

t_2f

t 

t

t

P_rm

t_4i t_4f

t

q

q₁ q₂ q₃ q₄ q₅

P_wf1

P_wf2

P_wf3

P_wf4 P_wf5

t_1i P_{wf initial} = P_r

t_bu t_bu t_bu

In this test, P_wfi and q are unstable values

stabilized pressure

IDENTIFICATION OF BOTH BACK PRESSURE EQUATIONS FROM WELL TESTS

( )

0

2 2

− =

−

+ q

P b P

aq ^{r wf}

can be written as linear functions

First Back Pressure Equation

( )

q P b P

aq ^{r wf}

2 2 −

= +

(

^{2 2}

)

log log

log q_g = C + n P_r − P_wf

(

_{r wf}

)

ⁿ

g C P P

q = ² − ²

Second Back Pressure Equation

CASE OF STABILIZED WELL TEST

(

^{2 2}

)

log log

log q_g = C + n P_r − P_wf

(

^{2 2}

)

log P_rm − P_wf

log q_g

logC

n = slope of the linear regression

logC= intersection between the linear regression and the logq axis

log-log plot

example of the identification of the second back pressure equation

n

CASE OF NON STABILIZED WELL TESTS

(

^{2 2}

)

log P_rm − P_wf

log q

logC

point obtained

with (P_wf5,q₅) = stabilized point points obtained

during drawdown periods (P_wfi,q_i) , i = 1..4

(

r wf

)

ⁿ

g C P P

q = ² − ²

example of the identification of the second back pressure equation

METHOD TO IDENTIFY MODEL PARAMETERS WITH WELL TESTS MEASUREMENTS

( )22logwfrm PP−( )22logwfrm PP− ( )22logwfrm PP−( )22logwfrm PP−

With well tests, we measure 4 or 5 times q and P_wf

Back Pressure 1

( )

q P P_r² − _wf²

We calculate

model 1

We plot q versus

( )

q P P_r² − _wf²

linear regression (+ use of stabilized (q,P_wf))

aand b determination

Back Pressure 2

We calculate log q and

model 2

We plot log q versus

linear regression (+ use of stabilized (q,P_wf))

n and logCdetermination

(

^{2 2}

)

log P_rm −P_wf

(

^{2 2}

)

log P_rm − P_wf

ABSOLUTE OPEN FLOW POTENTIAL

(

^P

)

ⁿ

C AOFP = ²

(

r wf

)

ⁿ

g

C P P

q =

²

−

²

AOFP represents the case of production where P_wf = 0.

In this case, P₁ is maximum, because :

wf rShutIn P P

P = −

 ₁

0

Then, the production rate is maximum

(by considering only the reservoir point of view).

example : The 2nd back pressure equation : can be written :

INFLOW – EXERCISE7 : MODELING OF A GAS WELL BEHAVIOUR

Flow rate (Mcfd) Bottom hole pressure (psia)

Shut in 3120

7800 2870

10590 2750

13960 2588

17615 2389

A dry gas well was tested at various flow rates with back pressure tests :

questions:

•By using the back pressure equations, build both models and give the AOFP of the well. Choose the adequate model.

•The well is flowed at 25% of the AOFP. In this case, what is the bottom hole pressure?

•The reservoir pressure declines to 2980 psia, what is the new AOFP ? Assume n and C in the back pressure equation remain constant.

Back pressure 1: (P_r² – P_wf²) / q = aq + b

plot (P_r² – P_wf²)/q versus q and directly determine a and b

Back pressure 2: q = C (P_r² – P_wf²)ⁿ => log q = log C + n log (P_r² – P_wf²) plot log q vs. log (P_r² – P_wf²) and directly determine n and logC, hence C

Plot Test Data Pr (psi) = 3120

X mod1 q (Mcfd) 7800 10590 13960 17615

Pwf (psi) 2870 2750 2588 2389

Pr² - Pwf² 1497500 2171900 3036656 4027079

Y mod1 (Pr² - Pwf²)/q 192 205 218 229

X mod2 log(Pr² - Pwf²) 6.18 6.34 6.48 6.60

Y mod2 log(q) 3.89 4.02 4.14 4.25

mod1 = Back pressure 1 model plot mod2 = Back pressure 2 model plot

INFLOW – EXERCISE7 : MODELING OF A GAS WELL BEHAVIOUR

43 43

Back pressure 1 model: does not yield a perfect fit

Plot determines directly (P_r² - P_wf²)/q = 0.0037q + 164.5 q @ Pwf = 0 => AOFP = 33.7 MMscfd

Back pressure 2 model achieves a better fit with test data in this case y = 0.8236x –1.1937 => log q = 0.8236 log (P_r² – P_wf²) –1.1937

n = 0.8236 and logC =-1.1937 => C = 0.064 Back pressure 1 model

y = 0,0037x + 164,5

190 200 210 220 230

5000 10000 15000 20000

q

(Pr2 - Pwf2)/q

Data

Linear (Data)

Back pressure 2 model

y = 0,8236x - 1,1937

3,8 3,9 4,0 4,1 4,2 4,3

6,1 6,2 6,3 6,4 6,5 6,6 6,7

Log (Pr2 – Pwf2)

Log q

Data

Linear (Data)

INFLOW – EXERCISE7 : MODELING OF A GAS WELL BEHAVIOUR

(

^{31202 2}

)

^0.8236

064 .

0 P_wf

q = −

IPR relationship:

INFLOW – EXERCISE7 : MODELING OF A GAS WELL BEHAVIOUR

• Absolute Open Flow Potential

• P_wf for the well flowing at 25% AOFP

• AOFP after depletion

( )

MMscf d

AOFP= 0.064 9734400^0.8236 = 36.4 /

d MMscf q = 0.25*36.4 = 9.1 /

C psia P q

P_{wf r} ⁿ 2815

064 . 0

3120 9114 ^0.8236

1 2

1

2  =



 



−

 =



 



−

=

( )

^{MMscf d}

AOFP = 0.064 2980^{2 0.8236} =33.8 /

IPR Gas Well

• In the case of gas wells, the velocity of the flow generates turbulences, which are represented in the models by a specific skin.

• Consequently, the relationship between the production rate and the drawdown isn't linear.

• We dispose on different models, and more particularly the two back pressure equations.

These models are generic, and can be adapted to each case of well by estimating their 2 parameters (a and b, or C and n) with help from well test analysis.

• The model used by default is the second back pressure equation, which is more often the most representative of the actual behaviour of the gas well. In this model, n is the factor of turbulence : when it is close to 0.5, the flow is very turbulent. When it is close to 1, the

turbulences are very low.

45

INFLOW PERFORMANCE RELATIONSHIP

P_wf

(psi)

P_r

q

(Mscf/day)

0

not linear – mainly due to turbulence

case of gas wells

AOFP

Reservoir Deliverability

• Reservoir pressure

• Pay zone thickness and permeability

• Reservoir boundary type and distance

• Wellbore radius

• Reservoir fluid properties

• Near-wellbore condition

• Reservoir relative permeability

THE RESERVOIR WELLBORE INTERFACE

Data:

reservoir thickness : 25 ft

reservoir permeability: 120 mD viscosity: 2.5 cP

FVF: 1.25 bbl/STB

well radius: 0.25 ft skin: 0

production rate: 600 STB/d

dP P f r S

r

h k q C

r

wf

P

P P w

e

=







 − +



 



=  ( )

4 ' ln 3

. 









 − +

 



= 

− '

4

ln 3 S

r r Ckh

P qB P

w e o

o wf

r



case of oil well one phase flow

Question:

Calculate the pressure profile and list the pressure drop across the following 1 ft intervals: [rw;1.25] [4;5] [19;20]

[99;100] [744;745]. Conclusion ?

EVALUATING SKIN

• Positive skin factor, S>0 K

_skin

< K

• Negative skin factor, S<0 K

_skin

> K

• Zero skin factor, S=0

K

_skin

= K

THE SKIN EFFECT

GLOBAL SKIN

q g

m

S S

S

S ' = + +

mechanical skin

Turbulences geometric skin

Skin factor

• The global skin is the sum of the skin due to formation damage

(mechanical skin) + geometric skin + skin linked with turbulences.

• The global skin can be estimated from well test interpretation,

• the geometric skin is the result of technical choices and is given by models (ex : trajectory of the well, number of perforations),

• the skin due to turbulences is neglected excepted in the case of gas wells or in the case of very high oil production rates.

• the skin due to formation damage can sometimes be estimated from well tests, but can also be estimated by the difference between the global skin and the geometric one.

• The smaller the skin, the higher the productivity.

• The knowledge of the mechanical skin allows to take decisions for extra jobs (acidizing job, reperforation) before starting production to finally obtain a lower global skin, and a better productivity index.

THE SKIN FACTOR IN PRACTICE

q g

m

S S

S

S ' = + +

can be estimated with well tests

the part of the skin we can act on

has to be estimated

can be estimated with models

can be estimated with well tests

54

Drilling pump

Mud tank

+ mud treatment injection line high pressure

BOP

casing

open hole drilling bit

High Pressure Circulation Low Pressure Circulation

landing collar

• Main roles of the mud :

• To balance formation pressure by hydrostatic pressure,

• To clean the hole and transport cuttings,

• To stabilize the wellbore,

• To cool and lubricate the bit.

• Main kinds of mud :

• water based mud

• oil based mud

Example of the formation damage

due to the drilling process

55

Interface well-reservoir during the drilling process

cake

reservoir rock

Filtration through the wellbore

impermeable zone Non invaded zone

Circulating mudWell External cake Internal cake Invaded zone

The penetration depends mainly on the filtration properties of the mud.

Formation Damage and Formation Skin

• In terms of productivity of the well, an adequate mud is a mud

• which cake is generated very rapidly, and seals very efficiently the reservoir from the well,

• which the filtrate is compatible with the fluid in place,

• which cake can be removed easily.

• The granulometry of the solid part of the mud is chosen in order to minimize the internal cake thickness.

• The good removal of the cake is one of the main conditions for a good production of the well when produced open hole (case of horizontal drains)

Formation damage

• In the case of a cased hole, the perforations must have a sufficiently deep penetration to allow the effluent to bypass the damaged zone.

• In the case of an open hole, the cake has to be well removed for a good connection between the reservoir and the well.

57

MECHANICAL SKIN

Zone of changed permeability due to FORMATION DAMAGE

k_s r_s

pay zone k

r_w r_e

s → skin w → well Formation damage is any impairment

of reservoir permeability around the wellbore.

HAWKINS FORMULA

 

 



− 

=

w s s

s

m

r

r k

k

S k ln

_{s → skin}

w → well

K = 500 mD ; D_w = 8^1/2"

K_s = 50 mD ; R_s = R_w + 30 cm

S = +11.9 If K_s = 100 mD

→ S = ?

If R_s = R_w + 10 cm

→ S = ?

Rw

R_s K_s

K

INFLOW EXERCISE: EXAMPLES OF SKIN FACTOR CALCULATION

( )

( )

3 . 5

10795 . 0

40795 . ln 0 4

0254 . 0

* 2 / 5 . 8

3 . 0 0254 . 0

* 2 / 5 . ln 8 100

100 500

+





 



= 



 



 +

= −

S S S

 

 



− 

=

w s s

s

m

r

r k

k

S k ln

inches →m

diam. to radius Case 1: K = 500 mD ; D_w = 8"^1/2

K_s = 100 mD ; R_s = R_w + 30 cm

INFLOW EXERCISE: EXAMPLES OF SKIN FACTOR CALCULATION

( )

( )

9 . 5

10795 . 0

20795 . ln 0 9

0254 . 0

* 2 / 5 . 8

1 . 0 0254 . 0

* 2 / 5 . ln 8 50

50 500

+





 



= 



 



 +

= −

S S S

 

 



− 

=

w s s

s

m

r

r k

k

S k ln

Case 2: K = 500 mD ; D_w = 8"^1/2

K_s = 50 mD ; R_s = R_w + 10 cm

GEOMETRIC SKIN

q g

m

S S

S

S ' = + +

frac pp

g

S S S

S = +

_

+

mechanical skin

Turbulences geometric skin

Partial penetrating

Completion hydraulic

fracturing well trajectory

Skin from Partial Completion and Slaint

How to derive the skin factor

How to derive the skin factor

PBU tests (shut-ins) should share the same stabilization on the

derivative, indicative of radial flow regime.

Blockage or plugging can be caused by:

- Fine accumulation - Scale deposition - Hydrates

- Wax

- Debris, etc

Remember that it can occur during ...

The mechanical skin, S_m, is the parameter for integrating all sources of damage in the reservoir-wellbore interface model.

• Drilling, cementing

• Completion, workover

• Gravel packing, perforating

• Production, stimulation or injection ...

ONLY TWO WAYS to impair the near wellbore permeability :

- Physical reduction in pore/pore throat size,

- Reduction of the relative permeability to oil (with WBM)

The formation damage is any impairment of the reservoir permeability near the wellbore.

Formation damage

Review

Section A. True/false

• Skin can be negative or positive with units of feet

• Skin depends on the depth of penetration of formation damage

• Production tubing is routinely cemented to the borehole wall Section B.

• Use Hawkin’s formula to estimate the skin of a damaged zone around a well with radius of 4 in., k = 20 md, and kd = 2 md. The damaged zone extends 2 in.

beyond the radius of the well.

• Estimate the skin for a well if the damaged zone extends 4 in. beyond the radius of the well, which is 3 in. The native formation permeability is 10 md, and the permeability of the damaged zone is 3 md.

INFLOW EXERCISE1 : NEAR WELLBORE PRESSURE PROFILE

( )( )( )

( )( )( ) ^_^{ }_^

+

= ln 0.25

25 120 00708 .

0

600 25

. 1 5 .

1800 2 r

P



 

 + 

=

w o

o

wf r

r Ckh

P qB

P  ln



 

 + 

=1800 88.28ln 0.r25 P

r (ft) p (psi) radius interval

pressure drop (psi)

0.25 1800

1.25 1942

4 2045

5 2064

19 2182

20 2186

99 2328

100 2329

744 2506.1

745 2506.2

744ft - 745ft

142

19

4

1

0.1 0.25ft - 1.25ft

4ft - 5ft

19ft - 20ft

99ft - 100ft

pressure profile (psi)

0 500 1000 1500 2000 2500 3000

0 100 200 300 400 500 600 700 800

pressure (psi)

p (psi)

logarithmic shape

Conclusion

The near wellbore area plays a major role on the well productivity.

SKIN EFFECT ON THE PRESSURE DROP

near wellbore zone

near wellbore zone

P P_R

radius

P_wf

Estimated pressure profile without disturbance

P_skin > 0

Actual pressure profile in the case of a positive skin factor

P_skin < 0 Actual pressure profile in the case of

a negative skin factor

( )

wf nodisturb

( )

wf _Actual

skin P P

P = −



well

well

reservoir

Well Performance Analysis

Well Performance Analysis

P_r, P_s, Q_p

IPR

VLP

Well

deliverability

Natural Flow well ?

Yes, but … no

Artificial lift

Q_p

yes

Artificial Lift

(start/restart, optimize)