Abstract
Well placement optimization is important in reservoir management,but it is challenging to implement due to the high-dimensional solution space and large number of reservoir simulations required.Surrogate models may assist to alleviate the computational burden by efficiently approximating full-order models.Although deep learning has been proven to be effective for surrogate modeling,most deep learning surrogates are purely data-driven,and underlying physical principles or theories of subsurface flows are not considered.In this work,a theory-guided convolutional neural network(TgCNN)framework is extended as a surrogate for subsurface flows with position-varying sink/source terms(well locations),which is further utilized for well placement optimization.In TgCNN,the physical constraints are incorporated to guide the training process of the surrogate by adding the residual of governing equations(and boundary/initial conditions)into the loss function.Guided by theory,the TgCNN surrogate can achieve better accuracy and generalizability,even when trained with limited data.The trained TgCNN surrogate can be further used for well placement optimization by combining it with the genetic algorithm(GA).The TgCNN surrogate also achieves satisfactory extrapolation performance for scenarios with different well numbers,and thus joint optimization of well number and placement can also be implemented with the TgCNN surrogate.The performance of the proposed optimization strategy is compared with the optimization framework that uses the simulator directly,and the results verify the accuracy of the TgCNN surrogate-based GA.Moreover,using the TgCNN surrogate can improve the efficiency of optimization significantly compared with running the simulators repeatedly.The effect of geologic uncertainty for the optimization is also investigated,and the results demonstrate that the optimization results may deviate from the optimal well placements as the degree of uncertainty increases.
NSTL