New Optimization Approach to Multiphase Flow

A. J. Kearsley, L. C. Cowsar, R. Glowinski, M. F. Wheeler and I. Yotov
Additional contact information
A. J. Kearsley: Carnegie Mellon University
L. C. Cowsar: Lucent Technologies
R. Glowinski: University of Houston
M. F. Wheeler: University of Texas at Austin
I. Yotov: University of Pittsburgh

Journal of Optimization Theory and Applications, 2001, vol. 111, issue 3, No 1, 473-488

Abstract: Abstract A new optimization formulation for simulating multiphase flow in porous media is introduced. A locally mass-conservative, mixed finite-element method is employed for the spatial discretization. An unconditionally stable, fully-implicit time discretization is used and leads to a coupled system of nonlinear equations that must be solved at each time step. We reformulate this system as a least squares problem with simple bounds involving only one of the phase saturations. Both a Gauss–Newton method and a quasi-Newton secant method are considered as potential solvers for the optimization problem. Each evaluation of the least squares objective function and gradient requires solving two single-phase self-adjoint, linear, uniformly-elliptic partial differential equations for which very efficient solution techniques have been developed.

Keywords: Multiphase flow; mixed methods; cell-centered finite differences (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1023/A:1012689626027

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