Simulation of multiphase flow in porous media is crucial for the effective management of subsurface energy and environment-related activities. The numerical simulators used for modeling such processes rely on spatial and temporal discretization of the governing mass and energy balance partial-differential equations (PDEs) into algebraic systems via finite-difference/volume/element methods. These simulators usually require dedicated software development and maintenance, and suffer low efficiency from a runtime and memory standpoint for problems with multi-scale heterogeneity, coupled-physics processes or fluids with complex phase behavior. Therefore, developing cost-effective, data-driven models can become a practical choice, and in this work, we choose deep learning approaches as they can handle high dimensional data and accurately predict state variables with strong nonlinearity. In this paper, we describe a gradient-based deep neural network (GDNN) constrained by the physics related to multiphase flow in porous media. We tackle the nonlinearity of flow in porous media induced by rock heterogeneity, fluid properties, and fluid-rock interactions by decomposing the nonlinear PDEs into a dictionary of elementary differential operators. We use a combination of operators to handle rock spatial heterogeneity and fluid flow by advection. Since the augmented differential operators are inherently related to the physics of fluid flow, we treat them as first principles prior knowledge to regularize the GDNN training. We use the example of pressure management at geologic CO2 storage sites, where CO2 is injected in saline aquifers and brine is produced, and apply GDNN to construct a predictive model that is trained with physics-based simulation data and emulates the physics process. We demonstrate that GDNN can effectively predict the nonlinear patterns of subsurface responses, including the temporal and spatial evolution of the pressure and CO2 saturation plumes. We also successfully extend the GDNN to convolutional neural network (CNN), namely gradient-based CNN (GCNN), and validate its capability to improve the prediction accuracy. GDNN has great potential to tackle challenging problems that are governed by highly nonlinear physics and enable the development of data-driven models with higher fidelity.
Bibliographical noteKAUST Repository Item: Exported on 2022-05-12
Acknowledged KAUST grant number(s): BAS/1/1423-01-01.
Acknowledgements: The authors acknowledge the financial support by the US DOE through the Science-informed Machine Learning to Accelerate Real Time Decisions in Subsurface Applications (SMART) project. The SMART project is funded by US DOE Fossil Energy's Program Office's Carbon Storage Program and is managed by the National Energy Technology Laboratory (NETL). Bicheng Yan also thanks King Abdullah University of Science and Technology (KAUST) for the Research Funding through the grants BAS/1/1423-01-01. The authors also thank Dr. Seyyed A. Hosseini from University of Texas at Austin for providing part of the reservoir simulation data used for model development at the beginning, and Dr. Diana Bacon from Pacific Northwest National Laboratory for providing a parsing tool to process the simulation data. The authors at KAUST thank CMG Ltd. and Schlumberger for granting academic licenses for GEM simulator and Petrel, respectively.
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)
- Computer Science Applications