Algebraic Dynamic Multilevel (ADM) Method for Immiscible Multiphase Flow in Heterogeneous Porous Media with Capillarity

Conference paper (2016)

Authors

M. Cusini Reservoir Engineering - CEG
H. Hajibeygi Reservoir Engineering - CEG
Research Group
Reservoir Engineering (CEG) (TU Delft)
Copyright: © 2016 M. Cusini, C.P.J.W. van Kruijsdijk, H. Hajibeygi
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Published Date

2016

Language

English

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Faculty

Civil Engineering & Geosciences

Department

Geoscience and Engineering

Research Group

Reservoir Engineering

Abstract

An
algebraic dynamic multilevel method (ADM) is developed for fully-implicit (FIM)
simulations of multiphase flow in heterogeneous porous media with strong
non-linear physics. The fine-scale resolution is defined based on the
heterogeneous geological one. Then, ADM constructs a space-time adaptive FIM system
on a dynamically defined multilevel nested grid. The multilevel resolution is
defined using an error estimate criterion, aiming to minimize the accuracy-cost
trade-off. ADM is algebraically described by employing sequences of adaptive
multilevel restriction and prolongation operators. Finite-volume conservative
restriction operators are considered whereas different choices for prolongation
operators are employed for different unknowns. The ADM method is applied to
challenging heterogeneous test cases with strong nonlinear heterogeneous
capillary effects. It is illustrated that ADM provides accurate solution by
employing only a fraction of the total number of fine-scale grid cells. ADM is
an important advancement for multiscale methods because it solves for all
coupled unknowns (here, both pressure and saturation) simultaneously on
arbitrary adaptive multilevel grids. At the same time, it is a significant step
forward in the application of dynamic local grid refinement techniques to
heterogeneous formations without relying on upscaled coarse-scale quantities

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