Moment Equations for Stochastic Immiscible Flow
BATTELLE PACIFIC NORTHWEST NATIONAL LABS RICHLAND WA
Pagination or Media Count:
We derive and analytically and numerically solve statistical moment differential equations for immiscible flow in porous media in the limit of zero capillary pressure, with application to secondary oil recovery. Closure is achieved by Taylor expansion of the fractional flow function and a perturbation argument. We reduce the equations by exploiting a relationship between saturation and velocity correlations that is unique to flow in one dimension. Mean and variance of water saturation exhibit a bimodal character two shocks replace the single shock front evident in the classical Buckley-Leverett saturation profile.
- Hydrology, Limnology and Potamology
- Statistics and Probability
- Fluid Mechanics