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.

翻译：模拟岩石-流体相互作用需要求解一组偏微分方程（PDEs），以预测流体在界面处的流动行为及其与岩石的反应。传统的高保真数值模型需要高分辨率才能获得可靠结果，导致巨大的计算开销。这限制了此类模型在多查询问题（如不确定性量化和优化）中的应用，因为这些应用需要运行大量情景。作为高保真模型的低成本替代方案，本研究开发了八种用于预测多孔介质中流体流动的替代模型。其中四种是基于一个用于压缩的神经网络和另一个用于预测的神经网络的降阶模型（ROM）。另外四种是具有网格尺寸无关特性的单一神经网络；我们使用该术语指代能够在比训练时更大的计算域上进行推理的图像到图像模型。除了新颖的网格尺寸无关替代模型框架外，我们比较了UNet和UNet++架构的预测性能，并证明对于替代模型而言，UNet++优于UNet。此外，我们表明网格尺寸无关方法是减少训练期间内存消耗的可靠途径，能在预测值与真实值之间实现良好的相关性，并优于所分析的ROMs。所分析的应用尤其具有挑战性，因为流体诱导的岩石溶解导致固体场非静态，因此无法用于辅助未来预测的调整。