Abstract
Compositional simulation can be very demanding computationally as a result of the potentially large number of system unknowns and the intrinsic nonlinearity of typical problems. In this work, we develop a reduced-order mod- eling procedure for compositional simulation. The technique combines trajectory piecewise linearization (TPWL) and proper orthogonal decomposition (POD) to provide a highly efficient surrogate model. The compositional POD-TPWL method represents new solutions in terms of linearizations around states generated (and saved) during previously simulated ‘training’ runs. High-dimensional states are projected (optimally) into a low-dimensional subspace using POD. The compositional POD-TPWL model is based on a molar formulation that uses pressure and overall component mole fractions as the primary unknowns. Several new features, including the use of a Petrov-Galerkin projection to reduce the number of equations (rather than the commonly used Galerkin projection), and a new procedure for determining which saved state to use for linearization, are incorporated into the method. Results are presented for heterogeneous three-dimensional reservoir models containing oil and gas phases with up to four hydrocarbon components. Reasonably close agreement between full-order reference solutions and compositional POD-TPWL simulations is demonstrated for the cases considered. Construction of the POD-TPWL model requires preprocessing overhead computations equivalent to about three full-order runs. Runtime speedups using POD-TPWL are, however, very significant – about a factor of 500 for the cases considered. The POD-TPWL model thus appears to be well suited for use in applications such as production optimization or uncertainty assessment, in which many simulations must be performed.
