1. Skin Factor due to Injectivity Decline
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)

2. Injectivity index
II = q/Dp

3. Particle capture kinetics
Deposition at
core inlet
Inlet plugging at
the transition time
Permeability decline
4 deep bed filtration parameters:
λ – filtration coefficient
β – formation damage coeficient
α – critical porosity ratio
kc – external cake formation
Transition time

4. Impedance J – reciprocal of II 3 equations: m(λ,β), ttrans(α, λ)
and mc(kc, λ,β, α)
1 equations is missing !!!
Proposal:
critical porosity ratio α=0.5
Mean α=0.1
M. Sharma, S. Pang, K. Wennberg, 1994, SPE & 1997, SPE 38181
Khatib, Z., 1995, SPE 28488
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
α_β correlation is a missing equation

5. Injectivity Index and Impedance

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

7. Injectivity decline curve treatment and prediction
Impedance curve

8. Injectivity damage parameters as calculated from well history
Sharma, M., Pang, S., Wennberg, K.E., 2000, J SPE P& F
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

9. Contents: Conclusions Introduction:
Offshore A, Brazil
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

10. 1. Deep bed filtration of injected particles
Physics meaning of filtration coefficient

12. Darcy’s law accounting for permeability damage

13. One Dimensional Deep Bed Filtration:
System of three equations for three unknowns
Mass balance for suspended and retained particles
Particle capture kinetics
Darcy’s law with permeability damage

14. 1d DBF: System of three equations for three unknowns
Mass balance for suspended and retained particles
Particle capture kinetics
Darcy’s law with permeability damage
Introduce dimensionless radius, time, rate and concentrations
The dimensionless system is:
Iwasaky, T., 1937
Herzig, J., Leclerc,D. and Goff, P. 1970
Sharma M., et.al., 1987, 1994, 1997

15. Skin factor 1D injection of particle suspension into a “clean” core
Impedance versus time T, p.v.i.
Skin factor
During constant rate injection into an injection well during T= pvi, pressure drop increases 5 times. Calculate the pressure drop increase for T= pvi.

16. Profiles and histories as obtained from analytical solution

17. Particle capture kinetics
Inlet plugging at
the transition time
Permeability decline
Deposition at
core inlet
4 deep bed filtration parameters:
λ – filtration coefficient
β – formation damage coeficient
α – critical porosity ratio
kc – external cake formation
Transition time

18. 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
M=1
M=3
M=25
M=1
M=3
M=25
The increase happens during (1-5)10-5 p.v.i. :

19. 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
Combined Effect of Formation Damage and Mobility Variation on Injectivity Decline

20. 1 1 4 4 2 5 3 6 2 5 3 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 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

21. Well AA016
Offshore A
Brazil

22. Well AA013
Offshore A
Brazil

23. Well AA002
Offshore A
Brazil

24. Injectivity damage characterization for history of 28-6- wells

25. Probabilistic distributions for injectivity impairment parameters
Well data
Coreflood data

26. Well-history-based Injectivity Prediction
with and without varying O_W mobility effect
Shumbera, D. A. et.al, 2003, SPE 84416
Paige, R. W. et al, 1995, SPE 29774

27. 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

28. Injector A7 data were treated. Prediction
Injector A7 data were treated. Prediction. Well fracturing was anticipated
Acidification 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