Surrogate models for Rock-Fluid Interaction: A Grid-Size-Invariant Approach

Abstract

Modelling rock-fluid interaction requires solving a set of partial differential equations (PDEs) to predict the flow behaviour and the reactions of the fluid with the rock on the interfaces. Conventional high-fidelity numerical models require a high resolution to obtain reliable results, resulting in huge computational expense. This restricts the applicability of these models for multi-query problems, such as uncertainty quantification and optimisation, which require running numerous scenarios. As a cheaper alternative to high-fidelity models, this work develops eight surrogate models for predicting the fluid flow in porous media. Four of these are reduced-order models (ROM) based on one neural network for compression and another for prediction. The other four are single neural networks with the property of grid-size invariance; a term which we use to refer to image-to-image models that are capable of inferring on computational domains that are larger than those used during training. In addition to the novel grid-size-invariant framework for surrogate models, we compare the predictive performance of UNet and UNet++ architectures, and demonstrate that UNet++ outperforms UNet for surrogate models. Furthermore, we show that the grid-size-invariant approach is a reliable way to reduce memory consumption during training, resulting in good correlation between predicted and ground-truth values and outperforming the ROMs analysed. The application analysed is particularly challenging because fluid-induced rock dissolution results in a non-static solid field and, consequently, it cannot be used to help in adjustments of the future prediction.

Figures (9)

• Figure 1: Diagrams for the two different options of the prediction neural network compared. In the UNet++ diagram, each block $B^{i,j}$ corresponds to the sequence of operations highlighted in "Conv Block B1" in the UNet diagram.
• Figure 2: Rollout training: strategy used to improve multiple timesteps inference in grid-size-invariant framework.
• Figure 3: Workflow for training the ROMs. The dashed box indicates the adversarial training extra steps, used only in Adversarial Autoencoder (AAE). After training the compression network, a prediction network is trained using latent space of compression.
• Figure 4: Workflow for inference using one of the reduced-order surrogate models. The compression module produces an initial condition, the predictor uses the latent solution at three previous timesteps to generate a prediction for the next timestep, time marching is used to generate a sequence of predictions in latent space and, finally, the predictions are reconstructed to the original space.
• Figure 5: Surrogate model using compression - Autoregressive prediction after 100 timesteps in the carbon storage dataset, which contains four fields: concentration of CO2, porosity, and velocities in X- and Y-direction. Comparison of the results considering compression with an autoencoder or an adversarial autoencoder and prediction considering a UNet or a UNet++.