Reduced-Order Models Based on POD-Tpwl for Compositional Subsurface Flow Simulation

Abstract:

A reduced-order modeling procedure applicable for compositional subsurface flow simulation will be described and applied. The technique combines trajectory piecewise linearization (TPWL) and proper orthogonal decomposition (POD) to provide highly efficient surrogate models. The method is based on a molar formulation (which uses pressure and overall component mole fractions as the primary variables) and is applicable for two-phase, multicomponent systems. The POD-TPWL procedure expresses new solutions in terms of linearizations around solution states generated and saved during previously simulated ‘training’ runs. High-dimensional states are projected into a low-dimensional subspace using POD. Thus, at each time step, only a low-dimensional linear system needs to be solved. Results will be presented for heterogeneous three-dimensional simulation models involving CO₂ injection. Both enhanced oil recovery and carbon storage applications (with horizontal CO₂ injectors) will be considered. Reasonably close agreement between full-order reference solutions and compositional POD-TPWL simulations will be demonstrated for ‘test’ runs in which the well controls differ from those used for training. Construction of the POD-TPWL model requires preprocessing overhead computations equivalent to about 3–4 full-order runs. Runtime speedups using POD-TPWL are, however, very significant – typically O(100–1000). The use of POD-TPWL for well control optimization will also be illustrated. For this application, some amount of retraining during the course of the optimization is required, which leads to smaller, but still significant, speedup factors.