No abstract

No abstract

Reservoir models typically contain hundreds-of-thousands to millions of grid cells in which petrophysical properties such as porosity and permeability vary on a cell-to-cell basis. However, although the petrophysical properties of rocks do vary on a point-to-point basis, this variability is not equivalent to the cell-to-cell variations in models. We investigate the impact of removing cell-to-cell variability on predictions of fluid flow in reservoir models. We remove cell-to-cell variability from models containing hundreds of thousands of unique porosity and permeability values to yield models containing just a few tens of unique porosity and permeability values grouped into a few internally homogeneous domains. The flow behavior of the original model is used as a reference. We find that the impact of cell-to-cell variability on predicted flow is small. Cell-to-cell variability is not necessary to capture flow in reservoir models; rather, it is the spatially correlated variability in petrophysical properties that is important. Reservoir modelling effort should focus on capturing correlated geologic domains in the most realistic and computationally efficient manner.

Abstract. It is clear that none of the current available numerical schemes which may be adopted to solve transport phenomena in porous media fulfill all the required robustness conditions. That is while the finite difference methods are the simplest of all, they face several difficulties in complex geometries and anisotropic media. On the other hand, while finite element methods are well suited to complex geometries and can deal with anisotropic media, they are more involved in coding and usually require more execution time. Therefore, in this work we try to combine some features of the finite element technique, namely its ability to work with anisotropic media with the finite difference approach. We reduce the multipoint flux, mixed finite element technique through some quadrature rules to an equivalent cell-centered finite difference approximation. We show examples on using this technique to single-phase flow in anisotropic porous media.

Numerical solution of the equations governing multiphase porous media flow is challenging. A common approach to improve the performance of iterative non-linear solvers for these problems is to introduce artificial diffusion. Here, we present a mass conservative artificial diffusion that accelerates the non-linear solver but vanishes when the solution is converged. The vanishing artificial diffusion term is saturation dependent and is larger in regions of the solution domain where there are steep saturation gradients. The non-linear solver converges more slowly in these regions because of the highly non-linear nature of the solution. The new method provides accurate results while significantly reducing the number of iterations required by the non-linear solver. It is particularly valuable in reducing the computational cost of highly challenging numerical simulations, such as those where physical capillary pressure effects are dominant. Moreover, the method allows converged solutions to be obtained for Courant numbers that are at least two orders of magnitude larger than would otherwise be possible.