A Physics-Constrained Deep Learning Model for Simulating Multiphase Flow in Fully Three-Dimensional Heterogeneous Reservoirs

Given the complexity of coupled nonlinear physics for fluid flow in porous media, physics-based multiphase porous flow simulators usually require a high cost for product development, constant maintenance, and domain expertise. Hence, there exists a huge demand for fast multiphase flow modeling in subsurface processes including carbon storage, hydrocarbon and geothermal recovery.

In this work, a novel and efficient Physics-Constrained Deep Learning Model is developed for solving 3D multiphase porous media flow problems. The model architecture fully leverages the spatial topology predictive capacity of deep convolutional neural networks , specifically U-Net, and marches temporal evolution by a finite difference scheme. Similar to physics-based reservoir simulators , the model is fed with multiple data sources such as permeability and porosity fields, rock-fluid relations, fluid PVT and time series of surface well operation control, and generates pressure and saturation snapshots at arbitrary time steps. With maintaining flow locality in porous media, those three-dimensional reservoir models are decomposed into manageable sub-grids for cheaper model training cost, and this novel partition scheme freely brings gains of dataset augmentation and better modeling scalability.

The Physics-Constrained Deep Learning Model is tested on 3D cases for modeling CO₂ storage into saline aquifer formations. T rained from a very small number of simulation runs (24 in our case), the model predicts pressure and saturation with a speedup of 100x compared to a fu ll-physics reservoir simulator , and the error of predicted pressure and saturation snapshots continuously decreases with time and stays stabilized at a low level between 0.01% and 1.0% as the flow regime falls into a pseudo-steady-state. T his level of performance is extremely rare in regular data-driven approaches. Based on the high fidelity of pressure and saturation snapshots, well rates are efficiently calculated with rock-fluid and PVT data, with errors less than 3% on average. Therefore, with its unique scheme to cope with temporal and spatial dimensions, the Physics-Constrained Deep Learning Model can become an efficient forward model for data assimilation and optimization, and also has the potential to be extended to predict highly nonlinear physics processes with more degrees of freedom, e.g. porous flow-geomechanics coupling, which usually requires high CPU cost in fully physics-based simulations.