1887

Abstract

Summary

A common approach to stabilise the system arising from the discretisation of the advection equation is to introduce artificial diffusion. However, introducing artificial diffusion affects the result, therefore a balance has to be found so that the introduced artificial diffusion does not affects the final result.

Recently, a vanishing artificial diffusion was presented. In that method, the diffusion was controlled by the convergence of the non-linear solver by multiplying the artificial diffusion term by the difference between the most recent saturation estimation and the one obtained in the previous non-linear iteration. This approach showed that it is capable to help to reduce the computational effort required by the non-linear solver, as classical artificial diffusions do. However, this approach could lead to an introduction of an artificial source/sink in the system, therefore not conserving mass.

A conservative vanishing artificial diffusion is presented here. It improves the convergence and convergence rate of the non-linear solver by reducing the non-linearity of the equations. Moreover, it is tailored to specially help to deal with the capillary pressure. The vanishing artificial diffusion is introduced using the same model employed to introduce the capillary pressure, obtaining a vanishing artificial capillary pressure diffusion term. By solving this term implicitly in the saturation equation, a very efficient method to model multiphase porous media flow with physical capillary pressure is obtained. This is tested in real-size reservoir simulations with realistically high capillary numbers to prove its efficiency.

The presented method provides accurate results and significantly reduces the effort required by the non-linear solver to achieve convergence. It enables to carry out very demanding numerical simulations, e.g. when the physical capillary pressure effects are dominant, with Courant numbers that are at least two orders of magnitude bigger than without it.

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/content/papers/10.3997/2214-4609.201802118
2018-09-03
2020-04-09
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