GeoDIN - Geoscience-Based Deep Interaction Networks for Predicting Flow Dynamics in Reservoir Simulation Models
Authors: Maucec Marko , Jalali Ridwan 
Published: February 2022

Summary
Network graphs represent a general language for describing complex systems and a framework for knowledge discovery. Graph learning is a new concept with applications emerging in biomedicine, pharmacology, smart mobility, and physical reasoning. When applied to petroleum systems, such as reservoir models, graphs provide unique differentiators for the abstraction of reservoir connectivity to facilitate “reservoir-centric” machine learning (ML) applications.
In this paper, we demonstrate, for the first time, the application of geoscience-based deep interaction networks (GeoDIN) to learn complex physics relationships from 3D reservoir models for fast and accurate prediction of subsurface spatio-temporal flow dynamics. We build the network graph with embedded subsurface and physics representations and train the ML model to “act like the reservoir simulator.”
We use a simulation benchmark model for two-phase incompressible flow, with approximately 1.1 million grid size, one central injector, and four corner producers. Static 3D grid properties include porosity and permeability. We use full-physics simulation output to construct the interaction network (IN) graph, where graph nodes objects (nodes) represent reservoir grid cells. We embed the feature vector combining pore, oil and water volumes, and pressure and relative permeability. The graph objects representing wells are connected with well completion factors. The producing wells have embedded oil and water production rates, while the objects representing injecting wells have embedded water injection rates. We represent graph relations (edges) with bidirectional transmissibility of the source cell. To preprocess the data for ML, we scale the graph object attributes using “min-max” normalization and we normalize the graph relation attributes using Box-Cox transformation.
We train the GeoDIN framework to predict oil and water saturation dynamics in space and time. When benchmarked with full-physics simulation, the INs ran on two V100 graphics processing units and substantially accelerated the prediction phase compared to the physics-based simulator running on 70 Intel Xeon E5 CPU cores. On average, the error in GeoDIN predicted spatio-temporal distribution of oil saturation remains within 5% of full-physics simulation for 90% of model grid cells, while the error in water saturation remains within 2.5% of full-physics simulation. The spatio-temporal propagation of pressure is more sensitive to local embeddings of INs, which communicate on node-to-node information transfer. This results in a larger prediction error of the GeoDIN model when benchmarked to full-physics simulation. On average, the error distribution suggests that the great majority (90 to 95%) of grid cells fall within 10 to 30% error bound relative to full-physics simulation.
The presented GeoDIN approach to network learning carries a game-changing potential for the prediction of subsurface flow dynamics. As the way forward, we will investigate the implementation of graph neural networks with automated feature learning, generalization, and scaleup.