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.
Highlights
Discovering the dynamics of the fluid flow through a reservoir based on production data is paramount to the development of fast predictive models for reservoir management
We focus on the development of reduced-order models based on the dynamic mode decomposition (DMD) family of methods
Many of the tools used in this paper have been developed in different settings, the novelty of this work is threefold: (1) the application of sparsity-promoting DMD to multiphase flow in porous media and its comparison to proper orthogonal decomposition (POD)-based methods; (2) the application of Local DMD with control (DMDc) to coupled flow and geomechanics (PKN) with added complexities accounting for hydraulic fracturing dynamics, and to the author’s knowledge, this is the first publication in this area; (3) in addition, in this paper, we proposed a new Global optimum search (GOS) clustering algorithm which facilitates optimal clustering of the data based on their dynamical behavior
Summary
Discovering the dynamics of the fluid flow through a reservoir based on production data is paramount to the development of fast predictive models for reservoir management. Provide the four algorithms considered here for constructing the projection basis, namely, POD, standard DMD, sparse DMD, and local DMDc. we demonstrate the benefits of the DMD family by applying the methods to a 3D reservoir simulation based on the SPE10 benchmark and with a hydraulic fracturing process. Many of the tools used in this paper have been developed in different settings, the novelty of this work is threefold: (1) the application of sparsity-promoting DMD to multiphase flow in porous media and its comparison to POD-based methods; (2) the application of Local DMDc to coupled flow and geomechanics (PKN) with added complexities accounting for hydraulic fracturing dynamics, and to the author’s knowledge, this is the first publication in this area; (3) in addition, in this paper, we proposed a new GOS clustering algorithm which facilitates optimal clustering (both the number of clusters and the cluster configuration) of the data based on their dynamical behavior
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