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Publications [#287422] of John A. Trangenstein

Papers Published

  1. Bell, JB; Trangenstein, JA; Shubin, GR, Conservation Laws of Mixed Type Describing Three-Phase Flow in Porous Media, Siam Journal on Applied Mathematics, vol. 46 no. 6 (December, 1986), pp. 1000-1017, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1399 [Gateway.cgi], [doi]
    (last updated on 2021/10/21)

    In this paper we examine the mathematical structure of a model for three-phase, incompressible flow in a porous medium. We show that, in the absence of diffusive forces, the system of conservation laws describing the flow is not necessarily hyperbolic. We present an example in which there is an elliptic region in saturation space for reasonable relative permeability data. A linearized analysis shows that in nonhyperbolic regions solutions grow exponentially. However, the nonhyperbolic region, if present, will be of limited extent which inherently limits the exponential growth. To examine these nonlinear effects we resort to fine grid numerical experiments with a suitably dissipative numerical method. These experiments indicate that the solutions of Riemann problems remain well behaved in spite of the presence of a linearly unstable elliptic region in saturation space. These results are relevant to modeling fluid flow in petroleum reservoirs.

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