Kim and Finsterle (2002): Application of Automatic Differentiation for the simulation of nonisothermal, multiphase flow in geothermal reservoirs

Application of Automatic Differentiation for the simulation of nonisothermal, multiphase flow in geothermal reservoirs

Jong G. Kima and Stefan Finsterleb

Proceedings, Twenty-Seventh Workshop on Geothermal Reservoir Engineering
Stanford University, Stanford, California, January 28-30, 2002

a Argonne National Laboratory
Argonne, IL 60439

b Lawrence Berkeley National Laboratory, Earth Sciences Division
University of California, Berkeley, CA 94720

Abstract. Simulation of nonisothermal, multiphase flow through fractured geothermal reservoirs involves the solution of a system of strongly nonlinear algebraic equations. The Newton-Raphson method used to solve such a nonlinear system of equations requires the evaluation of a Jacobian matrix. In this paper we discuss automatic differentiation (AD) as a method for analytically computing the Jacobian matrix of derivatives. Robustness and efficiency of the AD-generated derivative codes are compared with a conventional derivative computation approach based on first-order finite differences.