MULTIPHASE FLOW IN HETEROGENEOUS POROUS-MEDIA FROM A STOCHASTIC DIFFERENTIAL GEOMETRY VIEWPOINT

Multiphase flow of immiscible fluids is studied by means of a stochast ic flow path approach. This approach is based on a differential geomet ric formulation that replaces the partial differential equations (PDEs ) of flow by a set of ordinary differential equations (ODEs) that dete rmine the flow paths and impose conservation of flux. It is shown that flux conservation along the flow paths involves a space transform. Ot her formulations of the multiphase flow equations involve Jacobian map pings. Flow realizations as well as statistical flow moments can be de rived by means of the stochastic flow path method. Advantages of the s tochastic flow path method include: reduction of a PDE to an ODF syste m, independence from perturbation approximations and Green's functions , and the freedom to use random initial conditions at the boundary. Us ing the stochastic flow path method, closed-form expressions are obtai ned for two-phase flow in uniaxially heterogeneous media. Two-phase fl ow in a heterogeneous two-dimensional medium is also investigated usin g numerical simulations.