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

Inhaltsverzeichnis

1. Frontmatter

2. Introduction

   1. Frontmatter

   2. Chapter 1. Introduction

      Olaf Kolditz, Thomas Nagel, Hua Shao

      Abstract

      In this section we discuss recent literature in thermo-hydro-mechanical-chemical (THMC) analysis particularly in fractured-porous media.

3. Single Processes

   1. Frontmatter

   2. Chapter 2. H Processes

      Tao Chen, Jobst Maßmann, Peter Vogel

      Abstract

      This section presents a set of examples which are standard practice in groundwater hydraulics. We focus on the closed form solutions. The associated simulation exercises have been checked by OGS; they may serve as verification test. Throughout this section we are concerned with the evaluation of pressure distributions. For the underlying theory of groundwater movement see Freeze and Cherry (Freeze RA, Cherry JA, Groundwater, Prentice-Hall, Englewood Cliffs) (1979), for more advanced examples see Polubarinova-Kochina (Polubarinova-Kochina PY, Theory of Groundwater Movement, Princeton University Press, Princeton) (1962).

   3. Chapter 3. M Processes

      Xing-Yuan Miao, Jobst Maßmann, Thomas Nagel, Dmitri Naumov, Francesco Parisio, Peter Vogel

      Abstract

      This section presents problems on bending of elastic plates. Most of the material is based on ideas outlined by Timoshenko and Goodier, Theory of elasticity. McGraw-Hill Book Company, New York, 1951, Timoshenko and Goodier (1951), the last exercise of this section has been adopted from Woinowsky-Krieger, Ing-Arch, 4(203–226):305–331, 1933, Woinowsky-Krieger (1933). We focus on the closed form solutions. The associated simulation exercises have been checked by OGS; they may serve as verification tests. For the underlying theory of linear elasticity see Gurtin, Encyclodedia of physics. Springer, Berlin, 1972, Gurtin (1972).

   4. Chapter 4. T Processes

      Vinay Kumar, Jobst Maßmann, Rainer Helmig

      Abstract

      Thermal processes in porous media involve both conduction and convection. In low conducting media, or under very low Peclet numbers, the contribution of thermal conduction to the total heat transport might be just as or even more important than the contribution of thermal convection. For a purely diffusive system, the equation for pure conduction gives the total heat flux \(q_\mathsf {T}\) through a given area of the domain

      $$\begin{aligned} q_\mathsf {T} = -\lambda _\mathsf {pm} \nabla T \end{aligned}$$

4. Coupled Processes

   1. Frontmatter

   2. Chapter 5. HH Processes

      Aaron Peche, Thomas Graf, Lothar Fuchs, Insa Neuweiler, Jobst Maßmann, Markus Huber, Sara Vassolo, Leonard Stoeckl, Falk Lindenmaier, Christoph Neukum, Miao Jing, Sabine Attinger

      Abstract

      OpenGeoSys was coupled to the pipe flow model HYSTEM-EXTRAN [HE, version 7.7 or newer] (itwh, Kanalnetzberechnung - Hydrodynamische Abfluss-Transport- und Schmutzfrachtberechnung. HYSTEM-EXTRAN 7 Modellbeschreibung, 2014, itw 2010) in order to simulate pipe leakage in a variably saturated subsurface. The newly developed weak coupling scheme is applicable for the Richards flow process in a modified version of OGS 5 that can be downloaded from the custom branch available at https://github.com/APeche/OGS-HYSTEM-EXTRAN.git. The shared-memory-based coupling was implemented using the interprocess communication method Named Pipes, which is considered a cost-effective and easy-to-implement push-migration solution (Laszewski and Nauduri, Migrating to the Cloud, pp. 1–19, 2012, Laszewski and Nauduri 2012). The implementation of the coupling scheme is based on a timestep-wise update of boundary conditions and source terms. Bidirectional interprocess data transfer is realized using in total two Named Pipes. First pipe is the server pipe, mainly used to send the HE-calculated pipe water level \(H_{\text {PW}}\) [L] to OGS. In OGS, \(H_{\text {PW}}\) is used as a Dirichlet-type boundary condition assigned to the pipe defect surface. It is converted to a hydrostatic pressure p [\(M L^{-1} T^{-2}\)] using fluid density \(\rho \) [\(M L^{-3}\)] and gravitational acceleration g [\(L T^{-2}\)] in the form of \(p=H_{\text {PW}}\cdot \rho \cdot g\). The second Named Pipe is the client pipe used to send the OGS-calculated leakage flow \(Q_{\text {leak}}\) [\(L^3 T^{-1}\)] to HE, where it is used as a source term. The coupled model will be referred to as OGS-HE.

   3. Chapter 6. H Processes

      Yonghui Huang, Haibing Shao

      Abstract

      The Richards flow model has been implemented in the newly developed OGS-6 version. In this section, we will use the single continuum model benchmark to demonstrate the correctness of the implementation.

   4. Chapter 7. HT (Convection) Processes

      Fabien Magri, Mauro Cacace, Thomas Fischer, Dmitri Naumov, Wenqing Wang, Norihiro Watanabe, Tianyuan Zheng, Xing-Yuan Miao, Thomas Nagel, Marc Walther

      Abstract

      In a geothermal system, unstable fluid density profiles due to temperature variations can trigger the onset and development of free thermal convective processes (J.W. Elder. Transient convection in a porous medium. (Elder in J Fluid Mech 27: 609–623 , 1967, Elder 1967). Early studies on the problem showed that the development of free thermal convection in the Earth’s crust require a relatively high permeability of the porous rocks (Lapwood in Math Proc Camb Philos Soc, 44:508–52, 1948, Lapwood 1948). Since the permeability inside the damaged area of major fault zones can far exceed the permeability of the enclosing rocks (Wallace, Morris in PAGEOPH, 124:107–125, 1986, Wallace and Morris 1986), one can expect the development of free thermal convective instabilities to occur in such tectonically perturbed rocks. The onset of thermal convection of a single-phase fluid in a vertical fault enclosed in impermeable rocks was considered in a full 3D approximation by Wang, Kassoy, Weidman (Int J Heat Mass Trans, 30:1331–1341, 1987, Wang et al. (1987)). A fundamental result of those investigations was that highly permeable faults allow for onset of free thermal convection even under a normal (e.g. 30 \(^{\circ }\mathrm{C}\cdot \mathrm{km}^{-1}\)) geothermal gradient. In contrast to simple homogenous 1D and 2D systems, no appropriate analytical solutions can be derived to test numerical models for more complex 3D systems that account for variable fluid density and viscosity as well as permeability heterogeneity (e.g. presence of faults). Owing to the efficacy of thermal convection for the transport of thermal energy and dissolved minerals in the moving fluid, a benchmark case study for density/viscosity driven flow is crucial to ensure that the applied numerical model accurately simulates the physical processes.

   5. Chapter 8. HM Processes

      Gesa Ziefle, Jobst Maßmann, Norihiro Watanabe, Dmitri Naumov, Herbert Kunz, Thomas Nagel

      Abstract

      This section focuses on coupled hydraulic–mechanical processes in a fault zone. The presented benchmark is motivated by the “Fault Slip (FS)” experiment of the Mont Terri Project. In this experiment, a fluid injection into a fault zone is carried out and the resulting hydraulic and mechanical effects are monitored. The fault zone is characterized by a range of minor and major faults and the experiment comprises several steps where various locations are influenced by an injection. More information about this experiment as well as similar approaches can be found in Guglielmi et al. (2015b), and Guglielmi et al. (2015a), and Derode et al. (04/2015).

   6. Chapter 9. TM Processes

      Peter Vogel, Jobst Maßmann, Xing-Yuan Miao, Thomas Nagel

      Abstract

      This section presents problems on thermal stresses in beams. We focus on the closed form solutions. The associated simulation exercises have been checked by OGS; they may serve as verification tests. For the underlying theory of linear thermoelasticity see Carlson (Encyclodedia of physics, Springer, Berlin, pp. 297–345, 1972), for more details on thermoelastic beams see Hetnarski and Eslami (Thermal stresses - advanced theory and applications, Springer Science, Berlin, 2009).

   7. Chapter 10. THM Processes

      Peter Vogel, Jobst Maßmann, Tianyuan Zheng, Xing-Yuan Miao, Dmitri Naumov, Thomas Nagel

      Abstract

      This section presents problems on permeable elastic beams subject to liquid pressure and temperature changes. We focus on the closed form solutions. The associated simulation exercises have been checked by OGS; they may serve as verification tests. For the underlying theory of porothermoelasticity and for more advanced examples see Cheng (2016) (Poroelasticity, Springer International Publishing, Switzerland, 2016).

   8. Chapter 11. RTM Processes

      Renchao Lu, Norihiro Watanabe, Eunseon Jang, Haibing Shao

      Abstract

      Fluid-mineral interaction, taking place over the fracture surface, renders a permanent change of fracture surface geometry. Hydraulic characteristic of fracture is consequently altered in response to the geometric change. For the sake of simplicity, the hydraulic process is assumed to be decoupled from the surface weathering. The dissolution-induced change of fracture surface geometry is neglected accordingly. Following this presumption, a benchmark is carried out. In the benchmark, we focus on the water-granite interaction in a flow-through undeformable fracture under confining stress, with highlights on the enhanced mineral dissolution at grain contacts where pressure solution is operative.

   9. Chapter 12. THC-Processes

      Thomas Nagel, Peter Ostermeier, Gabriele Seitz, Holger Class, Rainer Helmig

      Abstract

      The operation of thermochemical heat storage devices in open mode by permeating a reactive porous body or particle bed by a compressible heat-transfer fluid which in turn transports a reactive fluid component constitutes a strongly coupled problem of multiple physical processes. High reaction rates associated with a rapid release of significant amounts of heat and a complicated dependence of processes and material properties on the physical and chemical state of the system add to the level of complexity. It is the purpose of this chapter to (i) define a suitable benchmark for a suitable process model and (ii) perform such a comparison by using the simulation platforms OpenGeoSys, DuMux and ANSYS Fluent.

5. Backmatter