Title: Using exact Jacobians in an implicit Newton method for solving multiphase flow in porous media

Authors: Henrik Büsing; Johannes Willkomm; Christian H. Bischof; Christoph Clauser

Addresses: Institute for Applied Geophysics and Geothermal Energy, E.ON Energy Research Center, RWTH Aachen University, 52074 Aachen, Germany ' Scientific Computing Group, TU Darmstadt, 64293 Darmstadt, Germany ' Scientific Computing Group, TU Darmstadt, 64293 Darmstadt, Germany ' Institute for Applied Geophysics and Geothermal Energy, E.ON Energy Research Center, RWTH Aachen University, 52074 Aachen, Germany

Abstract: We present a new numerical approach to solve the fully coupled equations for two-phase flow in porous media with exact Jacobians. The method is based on a space and time discretisation and a linearisation of the arising non-linear algebraic system with Newton's method, where the required Jacobians are obtained with automatic differentiation (AD), providing the exact derivatives. We compare the forward AD differentiation mode to the standard finite difference method and the complex variable method in terms of precision and performance. It turns out that AD performs favourably compared to both methods. We also illustrate the advantages of exact Jacobians in a test example for two-phase flow in porous media investigating the evolution of pressure and saturation in a CO₂ sequestration scenario.

Keywords: multiphase flow; porous media; implicit Newton method; exact Jacobians; automatic differentiation; CO2; carbon dioxide; carbon sequestration; pressure; saturation.

DOI: 10.1504/IJCSE.2014.064535

International Journal of Computational Science and Engineering, 2014 Vol.9 No.5/6, pp.499 - 508

Received: 02 Feb 2012
Accepted: 13 Sep 2012
Published online: 22 Sep 2014 *

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