Numerical Simulation of Hysteretic Flow in Porous Media
Authors: Evrenos Attila I. , Comer A.G. 
Published: December 2007

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This paper is concerned with the simulation of multi-cycle drainage-imbibition processes in hydrophilic rock. The theory processes in hydrophilic rock. The theory of two-phase immiscible displacement is extended to cover the phenomena of dynamic hysteresis in residual phase saturations, relative permeability, and capillarity. Semi-empirical equations are given for the loci of the dynamic hysteresis envelopes and scanning loops spanning the domains of relative permeability and capillarity. An algorithm is presented to track the saturation history and to select the appropriate subset from the set of semi-empirical equations describing hysteretic relative permeability and capillarity. The application of the computational techniques is demonstrated by simulation of a semi-hypothetical reservoir.

Introduction

The purpose of this paper is to report a numerical simulator for the multi-dimensional, hysteretic flow of two compressible, immiscible fluids in hydrocarbon reservoirs. The simulator was developed as a performance evaluation-prediction tool for performance evaluation-prediction tool for cyclic gas movement in "aquifer storage" and, in particular, estimation of residual gas remaining in an aquifer-reservoir complex at abandonment.

The movement of natural gas in contact with underground water is a special case of multi-phase immiscible displacement in porous media. Hence, the central problem of porous media. Hence, the central problem of this paper is the extension of the theory of immiscible displacement to include multi-cycle drainage-imbibition processes involving two compressible fluids, and to develop a mathematical simulator of the flow system. Such a simulator is also applicable to oil-water systems in the vicinity and above the bubble-point, and to gas-oil systems subject to sufficiently small pressure gradients.

STATEMENT OF PROBLEM

The popular theory of immiscible displacement in porous media is based on the fundamental concepts of Darcy's Law, capillarity, relative permeability, equation of state, and material balance. Multi-cycle drainage-imbibition processes differ from the non-cyclic displacement in that dynamic hysteresis exhibited by phase relative permeability and capillarity must be considered. permeability and capillarity must be considered.