An intrusive Reduced Order Model (ROM) is developed for nonlinear porous media flow problems with transient and time-discontinuous fluid injection rates. The proposed ROM is significantly more computationally efficient than the Full Order Model (FOM). The training regime is generated using the FOM with constant injection rates during the offline stage. The trained ROM exhibits high accuracy for complex pumping schedules (rate vs time) simulated online. The proposed ROM uses the combination of Proper Orthogonal Decomposition and Discrete Empirical Interpolation Method (POD-DEIM), which is compared with the classical POD-Galerkin. The use of an approximated column-reduced Jacobian is shown to be vital to achieving a substantial speedup of ROM vs FOM run-times. An analysis of the trade-off between accuracy and run-time is conducted for ROMs of different sizes and hyper-parameters. The impact of the training regime on the performance of the presented ROM is assessed. The performance of the ROM is studied in the context of a two-dimensional analysis of time-varying injection into a two-well system in a layered porous media reservoir. The accuracy and efficiency of POD-DEIM motivate its potential use as a surrogate model in the real-time control and monitoring of fluid injection processes.

中文翻译：

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时变注入速率非线性瞬态多孔介质流的高效降阶模型


侵入式降阶模型 (ROM) 是针对具有瞬态和时间不连续流体注入速率的非线性多孔介质流动问题而开发的。所提出的 ROM 的计算效率明显高于全阶模型 (FOM)。训练制度是使用 FOM 在离线阶段以恒定的注入速率生成的。经过训练的 ROM 对于在线模拟的复杂泵送时间表（速率与时间）表现出高精度。所提出的ROM采用了本征正交分解和离散经验插值法（POD-DEIM）的组合，与经典的POD-Galerkin进行了比较。事实证明，使用近似列缩减雅可比行列式对于实现 ROM 与 FOM 运行时间的大幅加速至关重要。针对不同大小和超参数的 ROM，对准确性和运行时间之间的权衡进行了分析。评估训练制度对所提出的 ROM 性能的影响。在对层状多孔介质储层中的两井系统进行时变注入的二维分析的背景下，研究了 ROM 的性能。 POD-DEIM 的准确性和效率激发了其作为替代模型在流体注入过程的实时控制和监测中的潜在用途。