Reduced-order modeling of CO2 storage operations

Abstract

A POD-TPWL reduced-order modeling framework is developed to simulate and optimize the injection stage of CO2 storage operations. The method combines trajectory piecewise linearization (TPWL), where solutions with new sets of well controls are constructed based on linearization around previously simulated (training) solutions, and projection into a low-dimensional subspace using proper orthogonal decomposition (POD). The resulting representation is low-dimensional and linear, in contrast to the original nonlinear full-order flow simulations. Several new POD-TPWL treatments are introduced and demonstrated. These include the use of multiple derivatives, meaning that the linearizations are performed around different training solutions at different time steps, and the use of rate-controlled (rather than pressure-controlled) injection wells. Two example cases are presented, and the ability of the POD-TPWL model to accurately capture wellbore pressure, when time-varying CO2 injection rates are prescribed, is demonstrated. It is also shown that, for these examples, the reduced-order models can provide accurate estimates of CO2 molar fraction at particular locations in the domain. The POD-TPWL model is then incorporated into a mesh adaptive direct search optimization framework where the objective is to minimize the amount of CO2 reaching a target layer at the end of the injection period. The POD-TPWL model is shown to be well suited for this purpose and to provide optimization results that are comparable to those obtained using full-order simulations. The preprocessing computations needed to construct the POD-TPWL models entail a (serial) time equivalent of about 6.7 full-order simulations, though the resulting runtime speedups, relative to full-order simulation, are about 100–150 for the cases considered.