Adaptive-Implicit Method in Thermal Simulation

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Abstract
Summary: An adaptive-implicit method (AIM) for thermal simulation that provides different degrees of implicitness in various gridblocks is discussed. A special treatment of flow terms during appearance or disappearance of any particular phase is critical. This treatment creates a more stable Jacobian matrix, especially in cases where an implicit block is downstream of an explicit neighbor. The maximum eigenvalue of a local amplification matrix, which is related to a dimensionless front velocity, determines the switching between implicit and explicit treatment. The switching, which is automatic and problem-independent, is superior to classical threshold switching based on the magnitude of changes of key reservoir variables. Results from the simulation of several thermal recovery processes are presented. The saving in computer time over a fully implicit method ranges from 34 to 62%. The maximum savings can be achieved in the simulation of large field-scale problems in which the fronts are moving fairly slowly.