Homogenization of a stochastic model of a single phase flow in partially fissured media

In this paper, we present new homogenization results of a stochastic model for flow of a single-phase fluid through a partially fissured porous medium. The model is a double-porosity model with two flow fields, one associated with the system of fissures and the other associated with the porous system. This model is mathematically described by a system of nonlinear stochastic partial differential equations defined on perforated domain. The main tools to derive the homogenized stochastic model are the Nguetseng’s two-scale convergence, tightness of constructed probability measures, Prokhorov and Skorokhod compactness process and Minty’s monotonicity method.

Constructing Dual-Porosity Models from High-Resolution Discrete-Fracture Models Using Deep Neural Networks

Detailed geological description of fractured reservoirs is typically characterized by the discrete-fracture model (DFM), in which the rock matrix and fractures are explicitly represented in the form of unstructured grids. Its high computation cost makes it infeasible for field-scale applications. Traditional flow-based and static-based methods used to upscale detailed geological DFM to reservoir simulation model suffer from, to some extent, high computation cost and low accuracy, respectively. In this paper, we present a novel deep learning-based upscaling method as an alternative to traditional methods. This work aims to build an image-to-value model based on convolutional neural network to model the nonlinear mapping between the high-resolution image of detailed DFM as input and the upscaled reservoir simulation model as output. The reservoir simulation model (herein refers to the dual-porosity model) includes the predicted fracture-fracture transmissibility linking two adjacent grid blocks and fracture-matrix transmissibility within each coarse block. The proposed upscaling workflow comprises the train-validation samples generation, convolutional neural network training-validating process, and model evaluation. We apply a two-point flux approximation (TPFA) scheme based on embedded discrete-fracture model (EDFM) to generate the datasets. We perform trial-error analysis on the coupling training-validating process to update the ratio of train-validation samples, optimize the learning rate and the network architecture. This process is applied until the trained model obtains an accuracy above 90 % for both train-validation samples. We then demonstrate its performance with the two-phase reference solutions obtained from the fine model in terms of water saturation profile and oil recovery versus PVI. Results show that the DL-based approach provides a good match with the reference solutions for both water saturation distribution and oil recovery curve. This work manifests the value of the DL-based method for the upscaling of detailed DFM to the dual-porosity model and can be extended to construct generalized dual-porosity, dual-permeability models or include more complex physics, such as capillary and gravity effects.

Computational Modeling of the Hydrological Processes in Caatinga and Pasture Areas in the Brazilian Semi-Arid

The semi-arid regions of northeastern Brazil have historically suffered from water shortage. In this context, monitoring and modeling the soil moisture’s dynamics with hydrological models in natural (Caatinga) and degraded (Pasture) regions is of fundamental importance to understand the dynamics of hydrological processes. Therefore, this work aims to evaluate the hydraulic parameters in Caatinga and Pasture areas using the Hydrus-1D inverse method. Thus, five soil hydraulic models present in Hydrus-1D were used, allowing the comparison of the single-porosity model with more complex models, which consider the dual porosity and the hysteresis of the porous medium. The hydraulic models showed better adjustments in the Caatinga area (RMSE = 0.01–0.02, R2 = 0.61–0.97) than in the Pasture area (RMSE = 0.01–0.03, R2 = 0.61–0.90). Regarding the hydraulic parameters, for all models, the Pasture showed smaller saturated hydraulic conductivity and water content values of the mobile region than the Caatinga. This fact demonstrates the negative impact of compaction and change in natural vegetation in the Brazilian semi-arid. The dual-porosity model presented the best fit to the data measured in the Pasture area. However, a single-porosity model could be considered representative of the Caatinga area. The results showed that Caatinga areas contribute to maintaining soil moisture and increasing the water storage in semi-arid regions.