Xiao-Hong Wang

Adaptive Mesh Refinement for One-Dimensional Three-Phase Flow with Phase Change in Porous Media

This article presents a detailed analysis of the implementation of the adaptive mesh refinement (AMR) technique to one-dimensional three-phase flows in heterogeneous porous media, including phase change. Since this is a particularly complex, highly nonlinear problem, many difficulties had to be resolved. A specific refining procedure and refinement criterion are proposed to deal with discontinuous saturations across interfaces between different rock types. In addition, we propose an alternative numerical algorithm to avoid difficulties in applying previous multilevel or multigrid algorithms to advance the solution on the AMR grids. Numerical examples, focused on steam injection modeling, show that the AMR technique is fast and has good accuracy.

Adaptive Mesh Refinement for One-Dimensional Three-Phase Flows in Heterogeneous Fractured Porous Media

This article presents an analysis of the implementation of the adaptive mesh refinement (AMR) technique to one-dimensional three-phase flows in heterogeneous fractured media. Variations of matrix permeability and matrix–fracture transfer shape factor cause matrix saturation discontinuities. In order to avoid directly performing refining or coarsening operations on these matrix quantities, we suggest using two separated grid systems for the fracture and matrix equations, respectively. The fracture and matrix equations are decoupled by a special decomposition approach during the Newton-Raphson procedure for solving the resulting nonlinear equations. The numerical examples show that the proposed AMR technique is fast with good accuracy.

Statistical properties for two-dimensional fluid flow in percolation porous media

We study the statistical properties of fluid flows in percolation porous media at very low Reynolds number by numerical simulations for 20,000 different configurations. It is shown that there are some important differences between fluid flows in macroscopically homogeneous and fractal porous media. For fluid flows in macroscopically homogeneous media, the pressure is definite, but the velocity is random and depends on the structural details of porous media. The permeability k for fluid flows in fractal changes with the size L as k∼L−α where α≈1.0, not approaching the constant expected from Darcys law. The statistical distribution of pressure in fractal is independent of the size L and can be approximated by a function of the triangular shape.

FLUID PERMEABILITY IN TWO-DIMENSIONAL PERCOLATION POROUS MEDIA

The scaling relations for the fluid permeability in percolation structures are numerically studied using both of the coarse numerical grid and the refined numerical grid. We suggest that the permeability for viscous fluid flows in two-dimensional lattice percolation porous media be equivalent to the conductivity problem in percolation theory, independent of the simulation refinements. The refined numerical grid does not lead to the new universality.

Entropy fluctuations for directed polymers in 2+1 dimensions.

We find numerically that the sample to sample fluctuation of the entropy DeltaS is a more sensitive tool in distinguishing low from high temperature behaviors than the common corresponding fluctuation in the free energy. In 1+1 dimensions we find a single phase for all temperatures, since (DeltaS)(2) is always extensive. In 2+1 dimensions we find a behavior that at first sight might appear to be a transition from a low temperature phase where (DeltaS)(2) is extensive to a high temperature phase where it is subextensive. This is observed in spite of the relatively large system we use. The observed behavior is explained not as a phase transition but as a strong crossover behavior. We use an analytical argument to obtain (DeltaS)(2) for high temperature, and find that while it is always extensive it is also extremely small, and that the leading extensive part decays very quickly to zero as the temperature is increased.