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Accurate Discretization of Vertically-averaged Models of CO2 Plume Migration


When CO2 is injected into a deep formation, it will migrate as a plume that moves progressively higher in the formation, displacing the resident brine. The invasion front is driven by gravity, and the upward movement of the plume is limited by a low-permeable caprock. Several authors have recently proposed to make a sharp-interface assumption and only describe the plume migration in a vertically-averaged sense. For inhomogeneous permeability, the plume migration is then described by a system of conservation laws with spatially discontinuous flux. If one disregards dissolution and residual trapping, the system reduces to a scalar conservation law with a spatially dependent flux function, which may exhibit different solutions depending on the entropy condition that is enforced to pick a unique solution. We propose a certain set of assumptions that lead to the so-called minimum-jump condition and derive the corresponding solutions to the Riemann problem. Solutions to this problem are fundamental when developing accurate Godunov-type schemes. Here, we take a slightly different approach and present an unconditionally stable front-tracking method, which is optimal for this type of problem. Moreover, we verify the well-known observation that a standard upstream mobility discretization can give wrong solutions in certain cases.


Vitenskapelig foredrag





  • SINTEF Digital / Mathematics and Cybernetics

Presentert på

ECMOR XII - 12th European Conference on the Mathematics of Oil Recovery Oxford, UK


Oxford, UK


06.09.2010 - 09.09.2010





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