Rapid simulation of Aquifer Thermal Energy Storage using Machine Learning

Aquifer Thermal Energy Storage (ATES) offers sustainable, low carbon heating and cooling to the built environment.  Optimising the design and operation of ATES installations requires numerical simulation of groundwater flow and heat transport in heterogeneous aquifers.  These simulations are typically computationally expensive: high spatial resolution is required to properly resolve pressure, flow and temperature fields; moreover, high temporal resolution may be necessary to control numerical diffusion and/or resolve frequent changes in injection flowrate and temperature.  Simulations of systems that utilize multiple boreholes, or when the interactions between neighbouring systems must be captured, are particularly challenging.  Multiple simulations may be required to quantify the impact of uncertain aquifer heterogeneity.  Yet the time available for aquifer modelling in many commercial projects is very limited.  Rapid but accurate approaches to simulate subsurface flow and heat transport in ATES and other shallow geothermal deployments are urgently required.

Machine Learning (ML) offers a rapid alternative to conventional numerical simulation of complex subsurface flow and transport processes.  Here we introduce the use of a Graph Neural Network (GNN)-based ML approach, on a purely data-driven basis, to significantly increase simulation efficiency whilst retaining its accuracy.   The ML proxy is trained using outputs from our in-house Imperial College Finite Element Reservoir Simulator (IC-FERST), an advanced code that uses dynamic mesh optimization to provide high solution accuracy at lower computational cost.  The practical consequence here is that the mesh changes between solution snap-shots used for training.  Conventional Convolutional Neural Network (CNN)-based models require a fixed mesh. Here, to enable a fast proxy under variable mesh, we implement a GNN-based model with auto-regressive approach.

We demonstrate that heat transport in the aquifer can be accurately captured by deploying an auto-regressive graph U-net architecture on the unstructured graph data. As a pioneer model in the field, it is proven to successfully replicate subsequent time steps on any given mesh topology of the current state. To further unleash the potential of our GNN-based approach, we further introduce a transformer-based Graph neural network to enable a stronger capability in capturing long range changes under continuous latent rollout. The model can take in the initial state of the reservoir in arbitrary mesh, perform prediction in latent rollout, and recover the latent representation of the prediction back to physical space on any given query mesh, allowing the integration of adaptive mesh refinement adjusted to fit the predicted solution on unstructured graphs.

Our results suggest a promising approach to rapid simulation of ATES, in which simulation times are reduced from tens of hours to a few minutes.