A new semi-analytical mathematical model (IMOD) is developed as a part of a multidisciplinary study1-5  to investigate the potential of imbibition carbonated waterflood in low-permeability, naturally-fractured reservoirs. The model is based upon the concept of Buckley-Leverett type flow6,7  in a fracture surrounded by matrix blocks. The rate of water imbibition with varying water saturation at the imbibition boundary is represented by a convolution integral. The numerical iteration technique determines the fracture and matrix water saturation distributions in Laplace space. Stehfest's numerical Laplace inversion algorithm7  inverts the solutions to real domain.

Laboratory flow test data2,4  are used to check the validity of IMOD. Core face flushing technique is used in the imbibition experiments conducted on chalk cores. The test temperatures are 70 °F, 110 °F, and 150 °F. Concentrations of carbonated water solutions are 0.0, 2.3, 4.0 and 5.5 percent by weight of CO2, respectively.

The significant achievements of IMOD are: (1) it can provide the nonlinear solutions for a range of oil to water viscosity ratios and (2) the same model can be used for both plain and carbonated water imbibition recovery by adjusting the maximum recoverable oil (R) and imbibition recovery constant (λ). Results of the analysis show that: (1) the computed oil recoveries match the laboratory performance very well; (2) the computed oil recovery and phase saturation distribution in the fracture and matrix are greatly influenced by the magnitude of viscosity ratio; and (3) the imbibition recovery constant λ has a significant effect on the rate of imbibition oil recovery, thus, must be checked with laboratory data before modeling the reservoir performance.

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