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In this paper we consider a modification to Darcy equation by taking intoaccount the dependence of viscosity on the pressure. We present a stabilizedmixed formulation for the resulting governing equations. Equal-orderinterpolation for the velocity and pressure is considered, and shown to bestable (which is not the case under the classical mixed formulation). Theproposed mixed formulation is tested using a wide variety of numericalexamples. The proposed formulation is also implemented in a parallel setting,and the performance of the formulation for large-scale problems is illustratedusing a representative problem. Two practical and technologically importantproblems, one each on enhanced oil recovery and geological carbon-dioxidesequestration, are solved using the proposed formulation. The numericalexamples show that the predictions based on Darcy model are qualitatively andquantitatively different from that of the predictions based on the modifiedDarcy model, which takes into account the dependence of the viscosity on thepressure. In particular, the numerical example on the geological carbon-dioxidesequestration shows that Darcy model over-predicts the leakage into anabandoned well when compared to that of the modified Darcy model. On the otherhand, the modified Darcy model predicts higher pressures and higher pressuregradients near the injection well. These predictions have dire consequences inpredicting damage and fracture zones, and designing the seal, whose integrityis crucial to the safety of a geological carbon-dioxide sequestrationgeosystem.

A mixed formulation for a modification to Darcy equation based on Picard linearization and numerical solutions to large-scale realistic problems