Embed-to-Control Reservoir Surrogate Used To History-Match Geological Models

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 228029, “History-Matching Geological Models Using an Embed-to-Control Observe Deep-Learning Reservoir Surrogate,” by Usman Abdulkareem, SPE, Ahmed Adeyemi, SPE, and Mustafa Onur, SPE, The University of Tulsa. The paper has not been peer-reviewed. _ In this study, the authors propose the use of a deep-learning (DL) reduced-order surrogate model that can lower computational costs significantly while maintaining high accuracy for data assimilation or history-matching (HM) problems. The fundamental component is the Embed-to-Control Observe (E2CO) DL architecture. It serves as a reduced-order model mimicking the trajectory piecewise linearization (TPWL) coupled with proper orthogonal decomposition (POD) to simulate subsurface flow by using blocks of neural networks trained with the snapshots generated from a high-fidelity model or simulator. Methodology, Results, and Discussion An initial section of the complete paper outlines the theories, methods, and mathematical equations that support the proposed E2CO-HM. These subsections of the complete paper include discussions of POD-TPWL formulation and E2CO-HM formulation. In this section of the synopsis, the authors describe the synthetic reservoir model, SPE10, used to apply the E2CO-HM-based approach and discuss the results obtained. Reservoir Model. A section of the oil/water SPE10 benchmark model with grid dimensions 60×60×4 was used in the proposed E2CO-HM. This channelized reservoir model consists of four layers with permeability values measured in mD for each layer. This model represents one of the 1,000 SPE10 models generated using the Stanford Geostatistical Modeling Software (SGeMS) and is considered the “true” model for HM applications. It features a total of 40 control timesteps, each spanning 60 days, resulting in a reservoir lifespan of 2,400 days. The model includes eight wells: three bottomhole pressure (BHP)-controlled production wells and five rate-controlled injection wells. Generation of Realizations of the SPE10 Model for HM. A suite of 1,000 SPE10 models was generated using the sequential Gaussian simulation algorithm implemented in the SGeMS geostatistical software. These models were conditioned to hard data (horizontal permeability) created by randomly applying 35 and 50% dropouts to the permeability field while ensuring that permeability values at the well locations were preserved across all layers. The spatial structure of the permeability fields was characterized by an exponential semi-variogram with ranges of 1,690, 1,147, and 60 ft. E2CO-HM Proxy-Models Data Generation and Training. The data set (600/1,000) -generated model is partitioned into a training set of 450 realizations, a validation set of 50 realizations, and a test set of 100 realizations from the suite of realizations generated. Each geological realization includes 40 control timestep state variables (pressure and water saturation in each gridblock) and well output (oil-production rates, water-production rates, and BHPs), simulated using the Intersect reservoir simulator with an average of 27 seconds per model realization run. This results in a total of 450×40 = 18,000 data points for training the E2CO-HM model. The training of the E2CO-HM is divided into two steps. First, the model parameters are fed into the transition and transition-output network in m-space (vector of geological model parameters) for proxy training by following a linear transition rule. Second, the model parameters are fed into the transition and transition output network in β-space (vector of scaled model parameters) with a 95% energy criterion. These low-dimensional parameters are then fed into the transition and transition-output networks for proxy training, following a linear transition rule.