# On the Interaction of Heterogeneity and Multiphase Flow in Porous Media

Thursday, January 10, 2002 - 2:00pm - 3:00pm

Keller 3-180

Frederico Furtado (University of Wyoming)

Most (if not all) existing stochastic theories for two-phase flow in heterogeneous porous media hinge on two basic assumptions: (1) that the total fluid velocity depends weakly on the (evolving) spatial distribution of the fluid phases; and (2) that the heterogeneity is weak.

The first assumption is used to justify the decoupling of the pressure equation, which determines the total fluid velocity, from the saturation equation, which determines how the distinct phases are transported. Thus, under this assumption, the total velocity field is stationary (not time-dependent), and its stochasticity is entirely due to the stochasticity of the underlying geology. The second assumption is usually an important ingredient in the justification of the closure procedure adopted in the stochastic theory for the (decoupled) saturation equation.

In this talk, the speaker will discuss the limitations of both assumptions, in the case of two-phase, immiscible flow in petroleum reservoirs, and the associated issue of accuracy of the predictions provided by the stochastic theories. The discussion is based on results of high-resolution numerical simulations of such flows.

The first assumption is used to justify the decoupling of the pressure equation, which determines the total fluid velocity, from the saturation equation, which determines how the distinct phases are transported. Thus, under this assumption, the total velocity field is stationary (not time-dependent), and its stochasticity is entirely due to the stochasticity of the underlying geology. The second assumption is usually an important ingredient in the justification of the closure procedure adopted in the stochastic theory for the (decoupled) saturation equation.

In this talk, the speaker will discuss the limitations of both assumptions, in the case of two-phase, immiscible flow in petroleum reservoirs, and the associated issue of accuracy of the predictions provided by the stochastic theories. The discussion is based on results of high-resolution numerical simulations of such flows.