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Abstract Two finite difference algorithms suitable for long‐time simulation of the exploitation of a two‐phase geothermal reservoir are presented. One is based on the hopscotch method proposed by Saul'yev 1 and analysed further by Gordon 2 and Gourlay. 3 The other is based on the well‐known ADI method. Both methods use a Newton–Raphson iterative technique in order to obtain accurate solutions of the non‐linear difference equations involved. Rapid convergence of the iterative schemes occurs both for single‐phase and two‐phase reservoir problems. One‐ and two‐dimensional model problems are presented.
Zyvoloski et al. (Mon,) studied this question.