Abstract : Porous media flow and transport is important in wide applications, including carbon sequestration, subsurface hydrogen storage, and geothermal reservoirs. This mini-symposium seeks to highlight newest developments of porous media flow and transport both in physical models and numerical methods, to exchange ideas and to promote collaborations. Specific topics of interest include, but are not limited to: advanced physical models of porous media flow and transport; novel numerical methods for its simulation; its machine learning and deep learning algorithms; multiphase and multiphysics simulation; its error estimation, cross-scale analysis, and uncertainty quantification; applications especially in geological carbon sequestration and energy storage.
[03292] Stabilized enhancement for large time computation using exponential spectral process method
Author(s) :
Xiang Wang (Jilin University)
Abstract : We propose an exponential spectral process (ESP) method for time discretization of spatial-temporal equations. The proposed ESP method uses explicit iterations at each time step, which allows us to use simple initializations at each iteration. This method has the capacity to obtain high accuracy (up to machine precision) with reasonably large time step sizes. Theoretically, the ESP method has been shown to be unconditionally energy stable for arbitrary number of iteration steps for the case where two spectral points are used. To demonstrate the advantages of the ESP approach, we consider two applications that have stability difficulties in large-time simulations. One of them is the Allen-Cahn equation with the symmetry breaking problem that most existing time discretizations face, and the second one is about the complex Ginzburg-Landau equation, which also suffers from large-time instabilities.
[03294] A pressure robust solver for Stokes flow based on a lifting operator
Author(s) :
Ruishu Wang (Jilin University)
Abstract : We presents novel finite element solvers for Stokes flow that are pressure-robust due to the use of a lifting operator. Weak Galerkin (WG) finite element schemes are developed for the Stokes problem on quadrilateral and hexahedral meshes. Local Arbogast-Correa or Arbogast-Tao spaces are utilized for construction of discrete weak gradients. The lifting operator lifts WG test functions into 𝐻(div)-subspaces and removes pressure dependence of velocity errors.
[03331] Numerical Approaches and Analysis for The Generalized Maxwell-Stefan Equations
Author(s) :
Xiuping Wang (King Abdullah University of Science and Technology)
Shuyu Sun (King Abdullah University of Science and Technology)
Abstract : This talk presents an analysis of the thermodynamic properties of the generalized Maxwell-Stefan equations for the diffusion process in multi-component systems and proposes a corresponding numerical scheme. Detailed proofs show that the model satisfies Onsager's principle and the second law of thermodynamics. An energy-stable numerical scheme is established by a mixed finite element method and the backward Euler scheme.
[03419] The Undrained Split Phase Field Method for Modeling Hydraulic Fracture Propagation
Author(s) :
Tameem Almani (Saudi Aramco)
Abstract : In this work, we present and analyze the undrained split iterative coupling scheme for coupling flow with geomechanics applied to the fracture propagation problem. In the undrained split scheme, the mechanics problem is solved first, followed by the flow problem, and the fluid content of the medium (i.e., porosity) is assumed to be constant during the mechanics solve. This sequential coupling approach was shown to be convergent in an earlier work, and has the advantage of being easier to integrate with legacy reservoir simulators compared to the standard fixed-stress split scheme. This is due to the fact that in the undrained split scheme, the regularization terms are added to the mechanics equation and not the flow equation. In this work, we will establish the convergence of this scheme when applied to the fracture prograpation problem using the phase field method. To the best of our knowledge, this is the first time in literature the undrained split scheme is applied to the fracture propagation problem using the phase field method, and the convergence of the combined scheme is established.
[03443] Accelerating Pressure-Temperature Flash Calculations with Physics-informed Neural Networks
Author(s) :
Yuanqing Wu (Dongguan University of Technology)
Abstract : Pressure-Temperature (PT) flash calculations are a performance bottleneck of compositional-flow simulations. With physics-informed neural networks, the two heavy-burden routines of PT flash calculations: the successive substitution technique and stability analysis are be avoided in the offline stage, and therefore the computing burden in the offline stage is removed. After training, the phase condition and the compositions can be output by the neural network, which costs much less time than the PT flash calculations.
[03499] The numerical CFD-DEM model for polymer flooding in weakly consolidated porous media
Author(s) :
Yerlan Amanbek (Nazarbayev Univesity)
Daniyar Kazidenov (Nazarbayev Univesity)
Sagyn Omirbekov (Nazarbayev Univesity)
Abstract : The study of sand production from the oil and gas reservoirs is an essential for ensuring the long-term viability and profitability of hydrocarbon production operations. In this talk, we present numerical model of polymer flooding using CFD coupled DEM for sand production in 3D. The Navier-Stokes equation is solved using CFD approach, and the DEM approach is based on the second Newton’s law to simulate the behavior of individual particles in the porous medium. The modified JKR model is used to represent the weakly consolidated sandstone. The rheology of the injected polymer is described by the power law model. The laboratory experiment was conducted considering the polymer flooding. Numerical model was validated by the sand production rate of the laboratory experiment in the normalized setting.
[03503] Physics-Preserving Semi-Implicit Schemes for Porous Media Flow with Capillary Heterogeneity
Author(s) :
Shuyu Sun (KAUST)
Abstract : Two-phase flow commonly occurs in environmental engineering and petroleum industry. We present our work on semi-implicit algorithms for two-phase flow in porous media with capillary heterogeneity; in particular, different capillary pressure functions are used for different rock types. Our proposed algorithms, derived from our novel splitting of variables, are locally conservative for both phases, handle capillary heterogeneity well, and are unbiased. The algorithms are also numerically more stable than classical approaches, demonstrated using numerical examples.
[04169] Efficient numerical methods for thermodynamically consistent model of two-phase flow in porous media
Author(s) :
Huangxin Chen (Xiamen University)
Abstract : In this talk we will introduce a thermodynamically consistent mathematical model for incompressible and immiscible two-phase flow in porous media with rock compressibility. An energy stable numerical method will be introduced, which can preserve multiple physical properties, including the energy dissipation law, full conservation law for both fluids and pore volumes, and bounds of porosity and saturations. Numerical results are given to verify the features of the proposed methods.
[05155] Geothermal management with an integrated optimization method accelerated by a general thermal decline model and deep learning
Author(s) :
Bicheng Yan (King Abdullah University of Science and Technology )
Manojkumar Gudala (King Abdullah University of Science and Technology )
Shuyu Sun (KAUST)
Abstract : Geothermal modeling is complex due to the coupled thermo-hydro-mechanical physics, which brings computational challenges for geothermal management.
To tackle with this, we developed a parsimonious thermal decline model to capture the early thermal breakthrough and the later decline behavior. Further, a forward neural network maps the reservoir parameters to the decline model parameters, and it is integrated with a multi-objective optimizer, which considers reservoir uncertainties and subjects engineering constraints for robust reservoir optimization.
[05424] Gym-preCICE: Reinforcement Learning Environments for Active Flow Control
Author(s) :
Ahmed H. Elsheikh (Heriot-Watt University)
Mosayeb Shams (Heriot-Watt University)
Abstract : We introduce Gym-preCICE, a Python adapter to facilitate designing and developing Reinforcement Learning (RL) environments for single- and multi-physics Active flow control (AFC) applications. In an actor-environment setting, Gym-preCICE takes advantage of preCICE, an open-source coupling library for partitioned multi-physics simulations, to handle information exchange between a controller (actor) and an AFC simulation environment. The developed framework results in a seamless non-invasive integration of realistic physics-based simulation toolboxes with RL algorithms.
[05495] Ensemble schemes for the numerical solution of a random transient heat equation with uncertain inputs
Author(s) :
Xianbing Luo (Guizhou University)
Meng Li (Guizhou University)
Tingfu Yao (Guizhou University)
Changlun Ye (Guizhou University)
Abstract : Ensemble-based time stepping schemes are applied to solving a transient heat equation with random Robin boundary and diffusion coefficients. (1) By introducing ensemble mean, we use HDG method to obtain optimal convergence order for random diffusion coefficient problem. (2) By introducing two ensemble means of Robin boundary and diffusion coefficients, we propose a new ensemble Monte Carlo (EMC) scheme for the transient heat equation. (3) By introducing two Max ensemble for Robin boundary and diffusion coefficients problem, we propose a unconditional stability ensemble method. Stability analysis and error estimates are derived. Numerical examples verify the theoretical results and the validity of the ensemble method.
[05657] Robust globally divergence-free Weak Galerkin finite element methods for incompressible Magnetohydrodynamics flow
Author(s) :
Xiaoping Xie (Sichuan University)
Abstract : We develop a class of weak Galerkin (WG) finite element methods for the steady incompressible
Magnetohydrodynamics equations. The methods yield globally divergence-free approximations of velocity and
magnetic fields. We establish the Well-posedness and optimal a priori error estimates and present an
unconditionally convergent iteration algorithm. Numerical experiments are provided.
