Monte Carlo Simulation of Linear Two-Phase Flow in Heterogeneous Media

Abstract

In this paper an algorithmic formulation is given for the synthesis of linear two-phase systems with inherent variability. It is assumed that uncertainties in the flow system arise due to the heterogeneities of the porous medium. Methods of stochastic mechanics are adopted to offer a novel approach, whereby the absolute permeability is taken as a spatial stochastic process with a log-normal distribution at each point of the flow domain. A correlation structure is built into the model so as to achieve a realistic representation. In addition, a constraint on the invariance of the harmonic means of the random permeabilities is attained by way of topological scaling. A computer-synthesized waterflooding experiment is conducted to explore the effect of heterogeneity on output variables such as the oil pressure head and cumulative recovery. It is observed that output uncertainties can become significant even when the heterogeneities are small. By employing a least-squares procedure, the sensitivity of relative permeabilities to induced stochastic variations is also qualitatively investigated.