Norbert Böttcher

Evaluation of thermal equations of state for CO2 in numerical simulations

Three commonly used thermal equations of state for carbon dioxide, as well as the ideal gas law, have been compared against a large number of measurement data taken from the literature. Complex equations of state reach a higher accuracy than simple ones. The inaccuracy of the density function can cause large errors in fluid property correlations, such as heat capacity or viscosity. The influence of this inaccuracy on the results of numerical simulations have been evaluated by two examples: The first one assumes isothermal gas expansion from a volume, while the second one considers heat transport along a fracture. For both examples, different equations of state have been utilized. The simulations have been performed on the scientific software platform OpenGeoSys. The difference among the particular simulation results is significant. Apparently small errors in the density function can cause considerably different results of otherwise identical simulation setups.

Are upwind techniques in multi-phase flow models necessary?

Two alternatives of primary variables are compared for two-phase flow in heterogeneous media by solving fully established benchmarks. The first combination utilizes pressure of the wetting fluid and saturation of the non-wetting fluid as primary variables, while the second employs capillary pressure of the wetting fluid and pressure of the non-wetting fluid. While the standard Galerkin finite element method (SGFEM) is known to fail in the physical reproduction of two-phase flow in heterogeneous media (unless employing a fully upwind correction), the second scheme with capillary pressure as a primary variable without applying an upwind technique produces correct physical fluid behaviour in heterogeneous media, as observed from experiments.

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

Thermo-mechanical investigation of salt caverns for short-term hydrogen storage

\mathrm {CO}_2

Evaluation of Geo-processes

CO2 storage research site: Ketzin, in Germany.

Simulation of Laboratory Tests

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.

Simulating Gas Storage in Salt Caverns

Abstract To investigate the temperature influence on the cavern capacity, a numerical model was developed in order to simulate the thermo-mechanical behaviour of salt caverns during cyclic hydrogen storage. The model considers the thermodynamic characteristics of the storage medium as well as the heat transport and the temperature-dependent material properties of the host rock. Therefore, a well-known visco-elastic constitutive model was modified to describe temperature effects of rock salt and implemented into the freely available simulator OpenGeoSys. Thermal and mechanical processes are solved using a finite element approach, connected via a staggered coupling scheme. Numerical analyses were performed and evaluated using basic criteria for cavern safety and convergence. The results show that large temperature amplitudes in the working gas may lead to tensile stresses at the cavern boundary. Reducing the frequency of the cyclic loading is a way to reduce temperature variations and to avoid tensile failure. Furthermore, the influence of cavern shape was investigated. Narrow cylindrical caverns converge faster than spherical ones of the same volume and are subjected to a higher risk of structural failure.