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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