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TOUGH2 is a widely used simulation package for solving groundwater flow related problems such as nuclear waste isolation, environmental remediation, and geothermal reservoir engineering. It solves a set of coupled mass and energy balance equations using a finite volume method. The parallel implementation first partitions the unstructured computational domain. For each time step, a set of coupled non-linear equations is solved with Newton iteration. In each Newton step, a Jacobian matrix is calculated and an ill-conditioned non-symmetric linear system is solved in parallel using a preconditioned iterative solver. Communication is required for convergence tests and data exchange across partitioning borders. A real problem with 17,584 blocks and 43,815 connections indicates good scalability properties. From 2 to 128 processors on Cray T3E, the solution time is reduced from 7984 to 126 seconds. Improved parallel performance is expected for larger problems with 105-106 blocks in a Yucca Mountain nuclear waste site study.