Reduced-order Modeling for Thermal Recovery Processes

Thermal recovery typically entails higher costs than conventional oil recovery, so the application of computational optimization techniques may be beneficial. Optimization, however, requires many simulations, which incurs substantial computational cost. Here we apply a model-order reduction technique, which aims at large reductions in computational requirements. The technique considered, trajectory piecewise linearization (TPWL), entails the representation of new solutions in terms of linearizations around previously simulated (and saved) training solutions. The linearized representation is projected into a low-dimensional space, with the projection matrix constructed through proper orthogonal decomposition of solution `snapshots' generated in a training step. We consider two idealized problems, specifically primary production of oil driven by downhole heaters, and a simplified model for steam assisted gravity drainage, where water and steam are treated as a single `effective' phase. The strong temperature dependence of oil viscosity is included in both cases. TPWL test-case results for these systems demonstrate that the method can provide accurate predictions relative to full-order reference solutions. The overhead associated with TPWL model construction is equivalent to the computation time for several full-order simulations (the precise overhead depends on the number of training runs). Observed runtime speedups are very substantial -- over two orders of magnitude.