Uwe-Jens Görke

OpenGeoSys: an open-source initiative for numerical simulation of thermo-hydro-mechanical/chemical (THM/C) processes in porous media

In this paper we describe the OpenGeoSys (OGS) project, which is a scientific open-source initiative for numerical simulation of thermo-hydro-mechanical-chemical processes in porous media. The basic concept is to provide a flexible numerical framework (using primarily the Finite Element Method (FEM)) for solving multifield problems in porous and fractured media for applications in geoscience and hydrology. To this purpose OGS is based on an object-oriented FEM concept including a broad spectrum of interfaces for pre- and postprocessing. The OGS idea has been in development since the mid-eighties. We provide a short historical note about the continuous process of concept and software development having evolved through Fortran, C, and C++ implementations. The idea behind OGS is to provide an open platform to the community, outfitted with professional software-engineering tools such as platform-independent compiling and automated benchmarking. A comprehensive benchmarking book has been prepared for publication. Benchmarking has been proven to be a valuable tool for cooperation between different developer teams, for example, for code comparison and validation purposes (DEVOVALEX and CO2 BENCH projects). On one hand, object-orientation (OO) provides a suitable framework for distributed code development; however, the parallelization of OO codes still lacks efficiency. High-performance-computing efficiency of OO codes is subject to future research.

A material model for finite elasto-plastic deformations considering a substructure

Abstract Developing further the substructure models proposed by Mandel and Dafalias a thermodynamically consistent system of differential and algebraic equations is derived to describe anisotropic elasto-plastic material behavior at finite deformations. Based on the multiplicative split of the deformation gradient an appropriate material law is formulated applying the principle of the maximum of plastic dissipation. Generalized basic relations of this material model containing a relation of hyperelasticity, evolutional equations for the internal variables describing different kinds of hardening, and the yield condition are presented. The capacity of the proposed material model is demonstrated on the example of a sheet with a hole. Presenting the evolution of yield surfaces the capability of the model to describe anisotropic hardening behavior is shown.

Numerical analysis of thermal effects during carbon dioxide injection with enhanced gas recovery: a theoretical case study for the Altmark gas field

Prediction about reservoir temperature change during carbon dioxide injection requires consideration of all, often subtle, thermal effects. In particular, Joule–Thomson cooling (JTC) and the viscous heat dissipation (VHD) effect are factors that cause flowing fluid temperature to differ from the static formation temperature. In this work, warm-back behavior (thermal recovery after injection completed), as well as JTC and VHD effects, at a multi-layered depleted gas reservoir are demonstrated numerically. OpenGeoSys (OGS) is able to solve coupled partial differential equations for pressure, temperature and mole-fraction of each component of the mixture with a combination of monolithic and staggered approaches. The Galerkin finite element approach is adapted for space discretization of governing equations, whereas for temporal discretization, a generalized implicit single-step scheme is used. For numerical modeling of warm-back behavior, we chose a simplified test case of carbon dioxide injection. This test case is numerically solved by using OGS and FeFlow simulators independently. OGS differs from FeFlow in the capability of representing multi-componential effects on warm-back behavior. We verify both code results by showing the close comparison of shut-in temperature profiles along the injection well. As the JTC cooling rate is inversely proportional to the volumetric heat capacity of the solid matrix, the injection layers are cooled faster as compared to the non-injection layers. The shut-in temperature profiles are showing a significant change in reservoir temperature; hence it is important to account for thermal effects in injection monitoring.

Thermo-Hydro-Mechanical-Chemical Processes in Fractured Porous Media: Modelling and Benchmarking

The present book provides guidance to understanding complicated coupled processes based on the experimental data available and implementation of developed algorithms in numerical codes. Results of selected test cases in the fields of closed-form solutions (e.g., deformation processes), single processes (such as groundwater flow) as well as coupled processes are presented. It ispart of the Open Geo Sysinitiative - an open source project to share knowledge and experience in environmental analysis and scientific computation with the community.

A Large Strain Material Model for Soft Tissues With Functionally Graded Properties

The reaction of articular cartilage and other soft tissues to mechanical loads has been characterized by coupled hydraulic (H) and mechanical (M) processes. An enhanced biphasic material model is presented, which may be used to describe the load response of soft tissue. A large-strain numerical approach of HM coupled processes has been applied. Physical and geometrical nonlinearities, as well as anisotropy and intrinsic rate-dependency of the solid skeleton have been realized using a thermodynamically consistent approach. The presented material model has been implemented into the commercially available finite element code MSC MARC. Initial verification of the model has been conducted analytically in tendonlike structures. The poroelastic and intrinsic viscoelastic features of the model were compared with the experimental data of an unconfined compression test of agarose hydrogel. A recent example from the area of cartilage research has been modeled, and the mechanical response was compared with cell viability. All examples showed good agreement between numerical and analytical/experimental results.

Energy storage in the geological subsurface: dimensioning, risk analysis and spatial planning: the ANGUS+ project

New techniques and methods for energy storage are required for the transition to a renewable power supply, termed “Energiewende” in Germany. Energy storage in the geological subsurface provides large potential capacities to bridge temporal gaps between periods of production of solar or wind power and consumer demand and may also help to relieve the power grids. Storage options include storage of synthetic methane, hydrogen or compressed air in salt caverns or porous formations as well as heat storage in porous formations. In the ANGUS+ project, heat and gas storage in porous media and salt caverns and aspects of their use on subsurface spatial planning concepts are investigated. The optimal dimensioning of storage sites, the achievable charging and discharging rates and the effective storage capacity as well as the induced thermal, hydraulic, mechanical, geochemical and microbial effects are studied. The geological structures, the surface energy infrastructure and the governing processes are parameterized, using either literature data or own experimental studies. Numerical modeling tools are developed for the simulation of realistically defined synthetic storage scenarios. The feasible dimensioning of storage applications is assessed in site-specific numerical scenario analyses, and the related spatial extents and time scales of induced effects connected with the respective storage application are quantified. Additionally, geophysical monitoring methods, which allow for a better spatial resolution of the storage operation, induced effects or leakages, are evaluated based on these scenario simulations. Methods for the assessment of such subsurface geological storage sites are thus developed, which account for the spatial extension of the subsurface operation itself as well as its induced effects and the spatial requirements of adequate monitoring methods.

Numerical simulation of two-phase flow in deformable porous media

In this paper, conceptual modeling as well as numerical simulation of two-phase flow in deep, deformable geological formations induced by CO2 injection are presented. The conceptual approach is based on balance equations for mass, momentum and energy completed by appropriate constitutive relations for the fluid phases as well as the solid matrix. Within the context of the primary effects under consideration, the fluid motion will be expressed by the extended Darcys law for two phase flow. Additionally, constraint conditions for the partial saturations and the pressure fractions of carbon dioxide and brine are defined. To characterize the stress state in the solid matrix, the effective stress principle is applied. Furthermore, the interaction of fluid and solid phases is illustrated by constitutive models for capillary pressure, porosity and permeability as functions of saturation. Based on this conceptual model, a coupled system of nonlinear differential equations for two-phase flow in a deformable porous matrix (H2M model) is formulated. As the displacement vector acts as primary variable for the solid matrix, multiphase flow is simulated using both pressure/pressure or pressure/saturation formulations. An object-oriented finite element method is used to solve the multi-field problem numerically. The capabilities of the model and the numerical tools to treat complex processes during CO2 sequestration are demonstrated on three benchmark examples: (1) a 1-D case to investigate the influence of variable fluid properties, (2) 2-D vertical axi-symmetric cross-section to study the interaction between hydraulic and deformation processes, and (3) 3-D to test the stability and computational costs of the H2M model for real applications.

A parallel finite element method for two-phase flow processes in porous media: OpenGeoSys with PETSc

In past decades, high performance computing has became a valuable tool in many fields of environmental science and technology to utilize computational power for better characterization of the complexity of environmental systems as well as predicting their evolution in time. In this work, a parallel computing technique is presented for the numerical simulation of two-phase flow processes in porous media. The Galerkin finite element method (FEM) is used to solve the initial boundary value problem arising from the underlying mathematical model. The PETSc package is utilized for parallelization of the computational task in both the global assembly of the system of linear equations and the linear solver. In order to parallelize the global assembly of the linear equation system, the overlapping domain decomposition method is used. The preset parallel FEM approach is realized within the framework of OpenGeoSys, an open source C++ finite element code for numerical simulation of thermal, hydraulic, mechanical and chemical processes in fractured porous media. The computational efficiency of the approach has been tested with three examples of increasing complexity, the five spot benchmark, dense non-aquaeous phase liquid infiltration into a inhomogeneous porous medium and a real-world application to the

Development of a generalized material interface for the simulation of finite elasto-plastic deformations

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