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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)

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Injectivity index II = q/ p

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Particle capture kinetics Permeability decline 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 k c – external cake formation

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Impedance J – reciprocal of II 3 equations: m(λ,β), t trans (α, λ) and m c (k c, λ,β, α) 1 equations is missing !!! Proposal: critical porosity ratio α=0.5 Mean α=0.1 α_β correlation is a missing equation M. Sharma, S. Pang, K. Wennberg, 1994, SPE & 1997, SPE Khatib, Z., 1995, SPE W.M.G.T. van den Broek, Bruin, J.N., Tran, T.K., 1999, SPE 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

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5 Injectivity Index and Impedance

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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

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Injectivity decline curve treatment and prediction Impedance curve

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

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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 Offshore A, Brazil

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

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12 Darcys law accounting for permeability damage

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

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14 Introduce dimensionless radius, time, rate and concentrations The dimensionless system is: 1d DBF: System of three equations for three unknowns Mass balance for suspended and retained particles Particle capture kinetics Darcys law with permeability damage Iwasaky, T., 1937 Herzig, J., Leclerc,D. and Goff, P Sharma M., et.al., 1987, 1994, 1997

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15 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.

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16 Profiles and histories as obtained from analytical solution

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17 Particle capture kinetics Permeability decline 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 k c – external cake formation

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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. :

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Combined Effect of Formation Damage and Mobility Variation on Injectivity Decline Mass balance for water (Buckley-Leverett) Darcys 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

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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

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Well AA016 Offshore A Brazil

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Well AA013 Offshore A Brazil

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Well AA002 Offshore A Brazil

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Injectivity damage characterization for history of wells

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Probabilistic distributions for injectivity impairment parameters Well data Coreflood data

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

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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

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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

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