In (dynamic) adaptive mesh refinement (AMR) an input mesh is refined or coarsened to the need of the numerical application. While the both DPDP solutions underestimate the matrix-fracture transfer rate, they agree well with each other and demonstrate a significant speedup as compared to the reference fine-scale solution. The performance of the DPDP model with both reference and predicted closures is compared to the reference DFM simulations of two-phase flows using a synthetic and a realistic fracture geometries. We demonstrate that once a trained CNN is available, it can provide the DPDP model closures for a wide range of modeling parameters, not only those for which the training dataset has been obtained. We alleviate these difficulties by pixelating the fracture geometries and predicting the upscaled parameters using a convolutional neural network (CNN), trained on precomputed fine-scale results. Obtaining these model closures from fine-scale discrete fracture-matrix (DFM) simulations is a lengthy and computationally expensive process.

In order to close the DPDP model, one needs to provide the upscaled fracture permeabilities and the parameters of the matrix-fracture mass transfer for every fractured coarse block in the domain. Upscaling methods such as the dual porosity/dual permeability (DPDP) model provide a robust means for numerical simulation of fractured reservoirs.

Gmsh list with step size