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.

开发了POD-TPWL降阶建模框架来模拟和优化CO ₂的注入阶段存储操作。该方法结合了轨迹分段线性化（TPWL），其中基于围绕先前模拟的（训练）解的线性化来构造具有新的井控集的解决方案，并使用适当的正交分解（POD）投影到低维子空间中。与原始的非线性全阶流模拟相反，结果表示是低维的和线性的。介绍并演示了几种新的POD-TPWL处理。这些包括使用多个导数，这意味着在不同的时间步长周围围绕不同的训练解决方案执行线性化，以及使用速率控制（而不是压力控制）的注入井。给出了两个示例案例，以及POD-TPWL模型准确捕获井眼压力的能力，_{说明了2种}注射速率。还显示，对于这些示例，降阶模型可以提供域中特定位置的CO ₂摩尔分数的准确估计。然后将POD-TPWL模型合并到网格自适应直接搜索优化框架中，该框架的目标是最大程度地减少CO ₂的量在注入周期结束时到达目标层。POD-TPWL模型显示非常适合此目的，并提供了与使用全阶模拟获得的结果可比的优化结果。构造POD-TPWL模型所需的预处理计算需要约6.7个（完整）模拟时间（串行）时间，尽管对于所考虑的情况，相对于完整模拟，运行时加速约为100-150。