Data-Driven Model Reduction for Coupled Flow and Geomechanics Based on DMD Methods

Abstract

Learning reservoir flow dynamics is of primary importance in creating robust predictive models for reservoir management including hydraulic fracturing processes. Physics-based models are to a certain extent exact, but they entail heavy computational infrastructure for simulating a wide variety of parameters and production scenarios. Reduced-order models offer computational advantages without compromising solution accuracy, especially if they can assimilate large volumes of production data without having to reconstruct the original model (data-driven models). Dynamic mode decomposition (DMD) entails the extraction of relevant spatial structure (modes) based on data (snapshots) that can be used to predict the behavior of reservoir fluid flow in porous media. In this paper, we will further enhance the application of the DMD, by introducing sparse DMD and local DMD. The former is particularly useful when there is a limited number of sparse measurements as in the case of reservoir simulation, and the latter can improve the accuracy of developed DMD models when the process dynamics show a moving boundary behavior like hydraulic fracturing. For demonstration purposes, we first show the methodology applied to (flow only) single- and two-phase reservoir models using the SPE10 benchmark. Both online and offline processes will be used for evaluation. We observe that we only require a few DMD modes, which are determined by the sparse DMD structure, to capture the behavior of the reservoir models. Then, we applied the local DMDc for creating a proxy for application in a hydraulic fracturing process. We also assessed the trade-offs between problem size and computational time for each reservoir model. The novelty of our method is the application of sparse DMD and local DMDc, which is a data-driven technique for fast and accurate simulations.

CFD-Based Computational Studies of Quantum Dot Size Control in Slug Flow Crystallizers: Handling Slug-to-Slug Variation

“…An alternative approach is to use subspace-identification methods, viz., (MOESP), 53,54 and support vector regression (SVR) 55 to consider the SFC as a black-box model. Also, the newly emerging dynamic mode decomposition 56 and extended dynamic mode decomposition 57 methods have demonstrated good performance in describing various processes with nonlinear dynamics and could be utilized to generate a reduced order model for the SFC. The inputs to these subspace models can be the fluid velocities and the precursor concentration, while the outputs can be the CSD and the QD size profile.…”

Vehicular Applications of Koopman Operator Theory—A Survey

“…For this category, the most common studies employing Koopman operator-based methods were found for the application of hydraulic fracturing, which included [108], [109], [110] and [111]. However, these studies were deemed to fall outside the scope of this review due to their non-vehicular nature.…”

Application of offset‐free Koopman‐based model predictive control to a batch pulp digester

“…However, when the system exhibits highly nonlinear large‐scale dynamics or broad operational range, it is difficult to represent the entire local dynamics only with a single EDMD model. In that case, multiple model identification methods are commonly employed to accurately capture the local dynamics 51,73 …”