A constrained pressure-temperature residual (CPTR) method for non-isothermal multiphase flow in porous media
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In petroleum reservoir simulation, the standard preconditioner, the Constrained Pressure Residual (CPR) method, is a two-stage process which involves solving a restricted pressure system. Initially designed for isothermal models, this approach is often used in the thermal case. However, its treatment of the temperature variable does not incorporate heat diffusion, which is often dominant in thermal cases. In this paper, we present an extension of CPR: the Constrained Pressure-Temperature Residual (CPTR) method, where a restricted pressure-temperature system is solved in the first stage. In previous work, we introduced a block preconditioner with an efficient Schur complement approximation for a pressure-temperature system. Here, we extend this method for multiphase flow as the first stage of CPTR. The algorithmic performance of different two-stage preconditioners is evaluated for reservoir simulation test cases.
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