Skin Factor due to Injectivity Decline Injection Well History Analysis and Interpretation Bedrikovetsky, P., Fonseca, D. R., da Silva, M. J. (North Fluminense.

Skin Factor due to Injectivity DeclineSkin Factor due to Injectivity Decline

Injection Well History Analysis and Interpretation Injection Well History Analysis and Interpretation

Bedrikovetsky , P., Fonseca, D. R., da Silva, M. J. (North Fluminense State

University, Rio de Janeiro )

Furtado, C., Serra de Souza, A.L. & Siqueira, A.G. (Petrobras, Cenpes)

Injectivity indexII = q/p

Waterfl ooding

CAP TURE MECHANISMS OF SOL ID & L IQU ID PART ICLES

Straining

Gravity

Bridging

Electricforces

Van Der Waalsforces

Sorption

Gravity

-+

+ ++

++- -

- --

DEEP BED FILTRATION

EXTERNAL CAKE

INJECTIVITY INDEX vs TOTAL WATER INJECTED

0

10

20

30

40

50

60

70

80

90

100

0 500 1000 1500 2000 2500 3000Wi

II fi

nal

/ II

inic

ial

(%)

POÇO A POÇO B POÇO C

POÇO D POÇO E POÇO F

POÇO G POÇO H PÇO H_ PDG

Potência (PÇO H_ PDG)

2

qc

t r

1

0kk

DEEP BED FILTRATION

EXTERNAL CAKE Particle capture kinetics

Permeability decline

0,2w

w

qr t c t

r

trt

Inlet plugging at the transition time

Deposition at core inlet

Transition time 4 deep bed filtration parameters: λ – filtration coefficient β – formation damage coeficient α – critical porosity ratio kc – external cake formation

c

0cUt tr

Impedance J – reciprocal of II

TII

TII)T(J

0

0

1.0External cakedevelopm ent

D eep bedfiltration

arctg m c

arctg m

tttrans

3 equations:

m(λ,β), ttrans(α, λ)

and mc(kc, λ,β, α)

1 equations is missing !!!

Proposal:critical porosity ratio α=0.5Mean α=0.1

α_β correlation is a missing equation

( ) 1J T mT

)1(k

ckm

cc

00

c

)TT(m)T(J)T(J trctr

•M. Sharma, S. Pang, K. Wennberg, 1994, SPE 28489 & 1997, SPE 38181

•Khatib, Z., 1995, SPE 28488

20

1,

ln

wc rw

c w

w

c Rm e ei r

R rr

0,4195

•W.M.G.T. van den Broek, Bruin, J.N., Tran, T.K., 1999, SPE 54769

•Bedrikovetsky, P., Tran, P. , Van den Broek, et.al, 2003, J SPE PF, No 3

•Da Silva, M., Bedrikovetsky, P., Van den Broek, W.M.G., 2004, SPE 89885

5

Injectivity Index and Impedance

reswf ppp

tqtp

tptq

tII

tII

0

0

0

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1T (VPI)

II(T

)

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1T (VPI)

J(T

)

)(

)0()(

tII

tIItJ

6

ASSUMPTIONS OF THE INJECTIVITY IMPAIRMENT MODEL

      Water incompressibility

      Small particle concentration -> the suspension density is equal to water density

      No diffusion

      Linear law for particle capture kinetics

      Constant filtration coefficient

      No particle penetrates after the transition time

•Incompressible external filter cake

0

0,2

0,4

0,6

0,8

1

1,2

0 0,5 1 1,5 2

T (10-2 p.v.i)

II (

T)

DBF CAKE PREDICTION

J(T) = 32.01T + 1.000

Jc(T) = 368.38T - 2.64

0

1

2

3

4

0 0,5 1 1,5 2

T (10-2 p.v.i)

J (

T)

DBF CAKEMODELLING PREDICTION

Injectivity decline curve treatment and prediction

Impedance curve

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

0.01

0.02

50.

050.

075

0.1

0.15 0.

20.

25 0.3

0.35

Alfa

Fre

qu

en

cy

Alfa-3 Point

Alfa-Cor

0.00%

5.00%

10.00%

15.00%

20.00%25.00%

30.00%

35.00%

40.00%

45.00%

200 400 600 800 1000 1200 1400 1600

Beta

Fre

qu

en

cy

Beta-3 Point

Beta-Cor

0.00%5.00%

10.00%15.00%20.00%

25.00%30.00%35.00%40.00%45.00%

10 30 60 90 120

150

180

210

240

270

300

Lambda (1/m)

Fre

qu

ency

Lambda-3 Point

Lambda-Cor

Treatment of 27 routine lab test data from SPE by the α(β) correlation

Bedrikovetsky, P., Tran, P. , Van den Broek, et.al, 2003, J SPE PF, No 3

Wells /, m-1 kc (md) SH_A09_2 131 272 0.076 0.047 SH_A10_2 5.3 620 0.01 0.33 SH_A10_3 8.0 256 0.088 1.19 SH_A36_2 1.88 553 0.013 3.4

Injectivity damage parameters as calculated from well history

Sharma, M., Pang, S., Wennberg, K.E., 2000, J SPE P& F

Contents:•Introduction: •Analytical model for injectivity impairment accounting for varying Oil-Water mobility•Effect of varying O-W mobility•Injection well impairment – prediction results•Conclusions

0,0

20,0

40,0

60,0

80,0

100,0

120,0

140,0

0 0,02 0,04 0,06 0,08

T(p.v.i.)

II(T

)

1.0

T, p.v.i.

II(T)II(0)

T tr

externalcake

form ationdeepbed

filtration

0

Offshore A, BrazilW orO wi

10

1. Deep bed filtration of injected particles

c

h

m0,xhx,

Ucht

t,xm0,xht,xh

0

0

Physics meaning of filtration coefficient

tlA

tUAc

t

l

11

c= *c*U

Filtration Coefficient Determ ines the Intensity of Deposition

d td

12

Formation Damage Function

1

0

k( )k(0)

k( ) = k(0)

Darcy’s law accounting for permeability damage

( )kU p

13

2

c q c

t r r t

Uct

0

1rwork k p

Ur

Mass balance for suspended

and retained particles

Particle capture kinetics

Darcy’s law with permeability damage

One Dimensional Deep Bed Filtration:

System of three equations for three unknowns

14

Introduce dimensionless radius, time,

rate and concentrations

The dimensionless system is:

1d DBF: System of three equations for three unknowns

0

2

1

c q c

t r r t

U ct

k pU

r

0

2

2

1 2

1

C C C

T X X

S C

T X

P

X Xc

22

00 0

; ;

; ;

c c

r q tT X

R R

Q cq C S

H c c

00

2 1; ln

2 w

k pP X P

q

2

0 : 0

: 1ww

c

T C S

rX X C

R

Mass balance for suspended and retained particles Particle capture kinetics

Darcy’s law with permeability damage

•Iwasaky, T., 1937•Herzig, J., Leclerc,D. and Goff, P. 1970•Sharma M., et.al., 1987, 1994, 1997

15

0 x

tc(x,t)(x,t)

L

c= =0c=c inj

1D injection of particle suspension into a “clean” core

Tm1xdx

p

TUL

k)T(J

L

0

Impedance versus time T, p.v.i. TII

TII)T(J

0

t 1 t 2 t 3

X

P

qII

, ,wX X

wC X T e T X X

, ,2

wX X

w w

eS X T T X X T X X

X

20

1

ln

wc rw

c w

w

c Rm e ei r

R rr

( )y

x

eei x dy

y

ln2

cf

w

RmS T

r

Skin factor

During constant rate injection into an injection well during T=0.0001 pvi, pressure drop increases 5 times. Calculate the pressure drop increase for T=0.0005 pvi.

16

0 X

T

c (X,T) (X,T)

1c= =0

c= =0c=1

CONCENTRATIONS PROFILES ON THE PLANE (X,T) PROFILES FOR SUSPENDED CONCENTRATION

AT DIFFERENT MOMENTS

0

1

c ( X , T )

1 2

3

1XT T

T

DEPOSITED CONCENTRATION ON EDGES OF THE CORE

0

1

1 T, p.v.i.

X = 0 X = 1

Profiles and histories as obtained from analytical solution

17

0

2 w

qc

t r h

1

0kk

DEEP BED FILTRATION

EXTERNAL CAKE Particle capture kinetics

Permeability decline

0cUt tr

0,wr t Uc t trt

Inlet plugging at the transition time

Deposition at core inlet

Transition time 4 deep bed filtration parameters: λ – filtration coefficient β – formation damage coeficient α – critical porosity ratio kc – external cake formation

c

Injectivity Increase During Damage-Free Waterflooding

During the particle-free water injection into a reservoir saturated by oil that is less mobile than water, the total mobility ratio increases M times due to displacement of less mobile fluid by more mobile one

1rowi

o

w

rwor

k

kM

M

TJBL1

0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

1

1.2

T (p.v.i.)

JBL

(T)

M=1

M=3

M=250 2.510 5 5 10 5

0.6

0.8

1

T (p.v.i.)

JBL

(T)

M=1

M=3

M=25

The increase happens during (1-5)10-5 p.v.i.

0

1 2

f

or

s1 - s

s

XDT 1 DT 2

:

Combined Effect of Formation Damage and Mobility Variation on Injectivity Decline

trtrc

trBL

trBL

TTTTM

mT

M

mTJ

TTTM

mTJ

TJ

,

,

,0

f ss

T X

W orO wi

Q Ps

X X

( ) ( )( , )

1rw ro w

o

k s k ss

cs cf s

T X T

,

2

s cf s

T X

Mass balance for water (Buckley-Leverett)

Darcy’s law for total oil-water flux

Total oil-water mobility accounting for

particle retention in swept zone

Mass balance for suspended

and retained particles

Kinetics of particle retention

0 0.007 0.0140

0.5

1

1.5

T (p.v.i.)

J(T

)

0 2.510 5 5 10 5

0.6

0.8

1

T (p.v.i.)

J(T

)

11

2

2

3

3

4

5

4

65

6

Impedance curve behaviour for M=1, 3 and 25 for high and low formation damage (curves 1,2,3 and 4,5,6 respectively); a)for time scale 0.01 p.v.i.; b) zoom for time scale 0.00001 p.v.i.

The effect is particularly significant for heavy oil reservoirs and for relatively low formation damage

If during the short initial waterflooding stage in a heavy oil reservoir the injectivity does not change, the reservoir suffers large formation damage which will cause a significant injectivity decrease

Well AA016

Offshore A

Brazil

0

0,2

0,4

0,6

0,8

1

1,2

1,4

1,6

0 0,02 0,04 0,06 0,08

T(p.v.i.)

II(T

)

Real data analytical model

0

0,5

1

1,5

2

2,5

3

3,5

0 0,02 0,04 0,06 0,08

raw data pure damage data analytical model

0

0,2

0,4

0,6

0,8

1

1,2

0 0,02 0,04 0,06 0,08 0,1 0,12 0,14

T (p.v.i)

II (

T)

raw data analytical model

0

1

2

3

4

5

6

7

0 0,02 0,04 0,06 0,08 0,1 0,12 0,14

T (p.v.i)

J (

T)

raw data pure damage data analytical model

Well AA013

Offshore A

Brazil

0

0,2

0,4

0,6

0,8

1

1,2

0 0,02 0,04 0,06 0,08

T (p.v.i)

II (T

)

raw data analytical model

0

1

2

3

4

56

7

8

9

10

0 0,02 0,04 0,06 0,08

T (p.v.i)

J (

T)

raw data pure damage data analytical model

Well AA002

Offshore A

Brazil

Injectivity damage characterization for history of 28-6- wells

m mc Wells m kc (md)

85 AA001 4,6 35 305 AA002 8 133 0,44 1,38

594 1632 AA003 17,6 196 0,17 0,4 85,2 350 AA004 5,5 132 0,445 2,45

98,5 AA005 4 20,5 AA006 19,2

166 530 AA007 14 158 0,286 0,746 35 171 AA008 9,8 114 0,64 2,3

6,8 22,6 AA009 0,5 404 0,029 13,6 19,8 AA011 19,7

46 194,5 AA012 3,36 304 0,058 2,023 14,7 109 AA013 2,7 115 0,6 3,6 9,51 28 AA014 1,057 153 0,3 14

9,8 AA015 40 25 146,5 AA016 4,36 138 0,39 2,7

1485 5818 SH_A09_1 114 294 0.065 0.091 477 1412 SH_A36_1 116 209 0.15 0.1

1108 15755 SH_A39 103.7 257 0.087 0.016 35 53 N1 32.7 115 0.6 1.22 58 62 N2 49.3 139 0.4 1.7 34 45 N3 23 117 0.6 1.5

239 1760 SA1 100 493 0.018 0.07 175 671 SA2 148 245 0.1 0.074 5.7 9.7 TEX 76.6 116 0.6 2.49 86 919 Gulf 5 218 0.13 0.8

153 481 Prudhoe Bay 15.7 168 0.25 1.7 848 4612 Forties5 15.7 180 0.21 1.07 9.9 84.2 Forties6 12.1 140 0.37 0.25

0%

5%

10%

15%

20%

25%

30%

35%

1-5 5-10 10-50 50-100 100-150

Filtration coefficient, 1/m

FR

EQ

UE

NC

Y

0%

5%

10%

15%

20%

25%

30%

35%

0-0,1 0,1-0,2 0,2-0,3 0,3-0,4 0,4-

Critical porosity fraction

FR

EQ

UE

NC

Y

0%

5%

10%

15%

20%

25%

30%

35%

40%

100-150 150-200 200-250 250-300 300-

Formation damage coefficient

FR

EQ

UE

NC

Y

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

Alfa

Fre

qu

ency

Alfa-3 Point

Alfa-Cor

0.00%

5.00%

10.00%

15.00%

20.00%25.00%

30.00%

35.00%

40.00%

45.00%

200 400 600 800 1000 1200 1400 1600

Beta

Fre

qu

ency

Beta-3 Point

Beta-Cor

0.00%5.00%

10.00%15.00%20.00%

25.00%30.00%35.00%40.00%45.00%

10 30 60 90 120

150

180

210

240

270

300

Lambda (1/m)

Fre

qu

ency

Lambda-3 Point

Lambda-Cor

Probabilistic distributions for injectivity impairment parametersWell data Coreflood data

0

0,2

0,4

0,6

0,8

1

1,2

0 0,005 0,01 0,015 0,02 0,025

T(p.v.i.)

II(T

)

DBF, IICake, IIPrediction without mobility effectPrediction with mobility effect

Jd(T)= 86,18T + 1

Jc(T)= 919,28T - 10,895

0

1

2

3

4

0 0,006 0,012 0,018T (p.v.i.)

J(T

)

DBF,Jd CAKE, Jd DBF, J

Cake, J JBL Modelling Jd

Shumbera, D. A. et.al, 2003, SPE 84416 Paige, R. W. et al, 1995, SPE 29774

0

0,2

0,4

0,6

0,8

1

1,2

0 0,1 0,2 0,3 0,4 0,5 0,6T (p.v.i.)

II (T

)

DBF, IICake, IIPrediction without mobility effectPrediction with mobility effect

Jd(T) = 9,9241T + 1

JC(T)= 84,159T - 8,4996

0

1

2

3

4

5

6

0 0,05 0,1 0,15 0,2 0,25T (p.v.i.)

J(T

)

DBF, Jd CAKE,Jd DBF, J

Cake, J JBL Modelling Jd

Well-history-based Injectivity Predictionwith and without varying O_W mobility effect

Conclusions

•Some injectivity index increase before the injectivity impairment is explained by displacement of more viscous oil by less viscous water from injector vicinity

•The analytical model for injectivity impairment accounts for particle deep bed filtration, external cake formation and for varying oil-water mobility during waterflood

•The analytical model allows determination of the injectivity impairment coefficients – filtration and formation damage coefficients, critical porosity fraction and cake permeability - from well injectivity decline curve

•The injectivity impairment coefficients as obtained from treatment of xxx injectors vary in the same intervals as that obtained from lab coreflood

•Injector A7 data were treated. Prediction. Well fracturing was anticipatedAcidification was anticipated in case of well A13.

Reservoir B is similar to reservoir A. Well injectivity was predicted.Finally, it was recommended to drill 37 wells instead of 26 wells

Horizontal injector N23 data have been treated, and penetration radius 1/ was found to be xxx cm. Acidification was planned based on this radius. It allows to economise xxx cu m of acid

Vertical well N13 data have been treated, and penetration radius 1/ was found to be xxx cm. It allows recommending xxx cm depth of perforation instead of xx cm planned before