Chemical enhanced oil recovery by surfactant-polymer (SP) flooding has been studied in two space dimensions. A new global pressure for incompressible, immiscible, multicomponent two-phase porous media flow has been derived in the context of SP flooding. This has been used to formulate a system of flow equations that incorporates the effect of capillary pressure and also the effect of polymer and surfactant on viscosity, interfacial tension and relative permeabilities of the two phases. The coupled system of equations for pressure, water saturation, polymer concentration and surfactant concentration has been solved using a new hybrid method in which the elliptic global pressure equation is solved using a discontinuous finite element method and the transport equations for water saturation and concentrations of the components are solved by a Modified Method Of Characteristics (MMOC) in the multicomponent setting. Numerical simulations have been performed to validate the method, both qualitatively and quantitatively, and to evaluate the relative performance of the various flooding schemes for several different heterogeneous reservoirs.

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Physical systems governed by advection-dominated partial differential equations (PDEs) are found in applications ranging from engineering design to weather forecasting. They are known to pose severe challenges to both projection-based and non-intrusive reduced order modeling, especially when linear subspace approximations are used. In this work, we develop an advection-aware (AA) autoencoder network that can address some of these limitations by learning efficient, physics-informed, nonlinear embeddings of the high-fidelity system snapshots. A fully non-intrusive reduced order model is developed by mapping the high-fidelity snapshots to a latent space defined by an AA autoencoder, followed by learning the latent space dynamics using a long-short-term memory (LSTM) network. This framework is also extended to parametric problems by explicitly incorporating parameter information into both the high-fidelity snapshots and the encoded latent space. Numerical results obtained with parametric linear and nonlinear advection problems indicate that the proposed framework can reproduce the dominant flow features even for unseen parameter values.

Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. In a previous work [1], we explored the use of Neural Ordinary Differential Equations (NODE) as a non-intrusive method for propagating the latent-space dynamics in reduced order models. Here, we investigate employing deep autoencoders for discovering the reduced basis representation, the dynamics of which are then approximated by NODE. The ability of deep autoencoders to represent the latent-space is compared to the traditional proper orthogonal decomposition (POD) approach, again in conjunction with NODE for capturing the dynamics. Additionally, we compare their behavior with two classical non-intrusive methods based on POD and radial basis function interpolation as well as dynamic mode decomposition. The test problems we consider include incompressible flow around a cylinder as well as a real-world application of shallow water hydrodynamics in an estuarine system. Our findings indicate that deep autoencoders can leverage nonlinear manifold learning to achieve a highly efficient compression of spatial information and define a latentspace that appears to be more suitable for capturing the temporal dynamics through the NODE framework.

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In this paper, convergence of a characteristics-based hybrid method recently introduced in Daripa & Dutta (J. Comput. Phys., 335:249-282, 2017) has been proved. This method which combines a discontinuous finite element method and a modified method of characteristics (MMOC) has been successfuly applied to solve a coupled, nonlinear system of elliptic and transport equations that arise in multicomponent two-phase porous media flows. The novelty in this paper is the convergence analysis of the MMOC procedure for a nonlinear system of transport equations. For this purpose, an analogous single-component system of transport equations has been considered and possible extension to multicomponent systems has been discussed. Error estimates have been obtained and these estimates have also been validated by realistic numerical simulations of flows arising in enhanced oil recovery processes.

The goal of this study is to leverage emerging machine learning (ML) techniques to develop a framework for the global reconstruction of system variables from potentially scarce and noisy observations and to explore the epistemic uncertainty of these models. This work demonstrates the utility of exploiting the stochasticity of dropout and batch normalization schemes to infer uncertainty estimates of super-resolved field reconstruction from sparse sensor measurements. A Voronoi tessellation strategy is used to obtain a structured-grid representation from sensor observations, thus enabling the use of fully convolutional neural networks (FCNN) for global field estimation. An ensemble-based approach is developed using Monte-Carlo batch normalization (MCBN) and Monte-Carlo dropout (MCD) methods in order to perform approximate Bayesian inference over the neural network parameters, which facilitates the estimation of the epistemic uncertainty of predicted field values. We demonstrate these capabilities through numerical experiments that include sea-surface temperature, soil moisture, and incompressible near-surface flows over a wide range of parameterized flow configurations.