Physics-Informed ML Improves Forecasting, Connectivity Identification for CO2 EOR
Authors: Carpenter Chris 
Published: January 2025

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This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 221057, “Physics-Informed Machine Learning for Reservoir-Connectivity Identification and Production Forecasting for CO2 EOR,” by Masahiro Nagao, SPE, and Akhil Datta-Gupta, SPE, Texas A&M University. The paper has not been peer reviewed.

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Routine well injection and production data contain significant information that can be used for closed-loop reservoir management and rapid field decision-making. Traditional physics-based numerical reservoir simulation can be prohibitive computationally for short-term decision cycles. As an alternative, reduced physics models often have a limited range of applicability. Pure machine-learning (ML) models often lack physical interpretability and can have limited predictive power. To address these challenges, the authors propose hybrid models, combining ML and a physics-based approach, for rapid production forecasting and reservoir-connectivity characterization using routine injection, production, and pressure data.

Methodology
The study was focused on CO2 enhanced oil recovery (EOR) reservoirs with many producers and injectors. The producers featured three-phase fluid production. The available data consisted of multiphase production rate and CO2-injection rate. The proposed hybrid ML models were developed to rapidly identify correlation between the historical well measurements. If the historical bottomhole pressure (BHP) also was available, it could be incorporated in the hybrid models. The hybrid models are trained solely based on historical well measurements and can be used for two different purposes. First, production rates can be predicted by the models. Second, trained hybrid models can be used for estimating the reservoir connectivity between wells. Because the hybrid models are calibrated solely based on historical well measurements, it is not required to generate training data sets by running numerical simulations in the hybrid ML framework.
The authors propose two different hybrid modeling strategies: physics-based data preprocessing with a capacitance resistance model (CRM) and a physics-informed neural network (PINN) combined with a reduced physics model. These two hybrid model strategies were developed and applied to waterflooding cases. The complete paper extends the framework to CO2 miscible flooding that considers a three-phase flow system. The complete paper also briefly reviews the CRM and pure ML models before discussing the proposed hybrid models.

Validation Using a Synthetic Case
The proposed hybrid models were applied to a synthetic reservoir case. The prediction performance of the proposed hybrid models was compared with pure ML to analyze the prediction performance between different methodologies. The following three different approaches were applied in this study:
- Long short-term memory (LSTM) (a pure ML model)
- Physics-based data preprocessing with CRM
- PINN with a reduced physics model
Model Description.
The reservoir model had 69×69×10 grids, and the domain size was 5,175.0×5,175.0×100.0 ft. The porosity was uniformly distributed, and a heterogeneous permeability field was featured. Twelve producers and 12 injectors were completed in the reservoir, where continuous CO2 injection was performed for approximately 14 years. For initial conditions, water saturation was set at 0.5, gas saturation was 0.0, and initial reservoir pressure was 1,000 psi.
A commercial simulator was used to run flow simulation and create benchmark well histories. All producers had variable BHP constraints, and all injectors featured rate constraints in the simulation. The input data of the ML and hybrid models were composed of the CO2-injection rate of 12 injectors and BHP at 12 producers. A total of 2,000 days of historical well measurements was available from all wells, and prediction of multiphase production rate for 3,000 days was conducted.