We present a novel control framework for the closed-loop operation of a hydraulic fracturing process. Initially, we focus on the development of a first-principle model of a hydraulic fracturing process. Second, a novel numerical scheme is developed to efficiently solve the coupled partial differential equations defined over a time-dependent spatial domain. Third, a reduced-order model is constructed, which is used to design a Kalman filter to accurately estimate unmeasurable states. Lastly, model predictive control theory is applied for the design of a feedback control system to achieve uniform proppant concentration across the fracture at the end of pumping by explicitly taking into account the desired fracture geometry, total amount of proppant injected, actuator limitations, and safety considerations. We demonstrate that the proposed control scheme is able to generate a spatial concentration profile which is uniform and close to the target concentration compared to that of the benchmark, Nolte's pumping schedule.

我们为水力压裂过程的闭环操作提出了一种新颖的控制框架。最初，我们专注于水力压裂过程的第一性原理模型的开发。其次，开发了一种新颖的数值方案来有效地求解在依赖于时间的空间域上定义的耦合偏微分方程。第三，构建降阶模型，该模型用于设计卡尔曼滤波器以准确估计不可测状态。最后，模型预测控制理论被用于反馈控制系统的设计，以便在泵送结束时通过明确考虑所需的裂缝几何形状，注入的支撑剂总量，执行机构限制和安全性，在整个裂缝中实现均匀的支撑剂浓度。注意事项。