This article describes approaches to computing second-order derivatives with automatic differentiation (AD) based on the forward mode and the propagation of univariate Taylor series. Performance results are given that show the speedup possible with these techniques relative to existing approaches. We also describe a new source transformation AD module for computing second-order derivatives of C and Fortran codes and the underlying infrastructure used to create a language-independent translation tool.

The authors have ported a fully implicit equation-of-state (EOS) compositional parallel reservoir simulator to run on clusters of PCs. They report on the performance of the code on two clusters, both in terms of scalability and in absolute performance relative to an IBM SP. The simulator scales well through 16 processors on the clusters and is comparable in execution time with the SP.

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractA fully implicit parallel equation-of-state (EOS) compositional simulator for large-scale reservoir simulation is presented. This simulator is developed under the framework named IPARS (Integrated Parallel Accurate Reservoir Simulator) and is constructed using a Newton-type formulation. The Peng-Robinson EOS is used for the hydrocarbon phase behavior calculations. The linear solvers from the PETSc package (Portable Extensible Toolkit for Scientific Computation) are used for the solution of the underlying linear equations. The framework provides input/output, table lookups, Fortran array memory allocation, domain decomposition, and message passing between processors for updating physical properties in mass-balance equations in overlapping regions. PETSc handles communications between processors needed for the linear solver.Many test runs were performed with up to four million gridblocks for a dry-gas injection process on an IBM SP machine and half a million gridblocks on a cluster of 16 PCs. Results indicate that the scalability of the simulator is very good. The linear solver takes around half of the total computational time for homogeneous reservoirs. For layered heterogeneous reservoirs, the linear solver took a larger fraction of the total computational time as the permeability contrast increased. The time for the communication between processors for updating the flow equations is insignificant.The PC cluster is roughly a factor of two slower than the SP for parallel runs, which is very encouraging. This factor is strongly related to the hardware configuration of the computers, which is detailed in the paper.

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