Olaf Kolditz

Variable-density flow and transport in porous media: approaches and challenges

We review the state of the art in modeling of variable-density flow and transport in porous media, including conceptual models for convection systems, governing balance equations, phenomenological laws, constitutive relations for fluid density and viscosity, and numerical methods for solving the resulting nonlinear multifield problems. The discussion of numerical methods addresses strategies for solving the coupled spatio-temporal convection process, consistent velocity approximation, and error-based mesh adaptation techniques. As numerical models for those nonlinear systems must be carefully verified in appropriate tests, we discuss weaknesses and inconsistencies of current model-verification methods as well as benchmark solutions. We give examples of field-related applications to illustrate specific challenges of further research, where heterogeneities and large scales are important.

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.

Coupled groundwater flow and transport: 1. Verification of variable density flow and transport models

Abstract This work examines variable density flow and corresponding solute transport in groundwater systems. Fluid dynamics of salty solutions with significant density variations are of increasing interest in many problems of subsurface hydrology. The mathematical model comprises a set of non-linear, coupled, partial differential equations to be solved for pressure/hydraulic head and mass fraction/concentration of the solute component. The governing equations and underlying assumptions are developed and discussed. The equation of solute mass conservation is formulated in terms of mass fraction and mass concentration. Different levels of the approximation of density variations in the mass balance equations are used for convection problems (e.g. the Boussinesq approximation and its extension, fully density approximation). The impact of these simplifications is studied by use of numerical modelling. Numerical models for nonlinear problems, such as density-driven convection, must be carefully verified in a particular series of tests. Standard benchmarks for proving variable density flow models are the Henry, Elder, and salt dome (HYDROCOIN level 1 case 5) problems. We studied these benchmarks using two finite element simulators - ROCKFLOW, which was developed at the Institute of Fluid Mechanics and Computer Applications in Civil Engineering and FEFLOW, which was developed at the Institute for Water Resources Planning and Systems Research Ltd. Although both simulators are based on the Galerkin finite element method, they differ in many approximation details such as temporal discretization (Crank-Nicolson vs predictor-corrector schemes), spatial discretization (triangular and quadrilateral elements), finite element basis functions (linear, bilinear, biquadratic), iteration schemes (Newton, Picard) and solvers (direct, iterative). The numerical analysis illustrates discretization effects and defects arising from the different levels of the density of approximation. We contribute new results for the salt dome problem, for which inconsistent findings exist in literature. Applications of the verified numerical models to more complex problems, such as thermohaline and three-dimensional convection systems, will be presented in the second part of this paper.

Reactive transport codes for subsurface environmental simulation

A general description of the mathematical and numerical formulations used in modern numerical reactive transport codes relevant for subsurface environmental simulations is presented. The formulations are followed by short descriptions of commonly used and available subsurface simulators that consider continuum representations of flow, transport, and reactions in porous media. These formulations are applicable to most of the subsurface environmental benchmark problems included in this special issue. The list of codes described briefly here includes PHREEQC, HPx, PHT3D, OpenGeoSys (OGS), HYTEC, ORCHESTRA, TOUGHREACT, eSTOMP, HYDROGEOCHEM, CrunchFlow, MIN3P, and PFLOTRAN. The descriptions include a high-level list of capabilities for each of the codes, along with a selective list of applications that highlight their capabilities and historical development.

Coupled groundwater flow and transport: 2. Thermohaline and 3D convection systems

Abstract This work continues the analysis of variable density flow in groundwater systems. It focuses on both thermohaline (double-diffusive) and three-dimensional (3D) buoyancy-driven convection processes. The finite-element method is utilized to tackle these complex non-linear problems in two and three dimensions. The preferred numerical approaches are discussed regarding appropriate basic formulations, balance-consistent discretization techniques for derivative quantitites, extension of the Boussinesq approximation, proper constraint conditions, time marching schemes, and computational strategies for solving large systems. Applications are presented for the thermohaline Elder and salt dome problem as well as for the 3D extension of the Elder problem with and without thermohaline effects and a 3D Benard convection process. The simulations are performed by using the package FEFLOW. Conclusions are drawn with respect to numerical efforts and the appropriateness for practical needs.

Surface‐subsurface model intercomparison: A first set of benchmark results to diagnose integrated hydrology and feedbacks

There are a growing number of large-scale, complex hydrologic models that are capable of simulating integrated surface and subsurface flow. Many are coupled to land-surface energy balance models, biogeochemical and ecological process models, and atmospheric models. Although they are being increasingly applied for hydrologic prediction and environmental understanding, very little formal verification and/or benchmarking of these models has been performed. Here we present the results of an intercomparison study of seven coupled surface-subsurface models based on a series of benchmark problems. All the models simultaneously solve adapted forms of the Richards and shallow water equations, based on fully 3-D or mixed (1-D vadose zone and 2-D groundwater) formulations for subsurface flow and 1-D (rill flow) or 2-D (sheet flow) conceptualizations for surface routing. A range of approaches is used for the solution of the coupled equations, including global implicit, sequential iterative, and asynchronous linking, and various strategies are used to enforce flux and pressure continuity at the surface-subsurface interface. The simulation results show good agreement for the simpler test cases, while the more complicated test cases bring out some of the differences in physical process representations and numerical solution approaches between the models. Benchmarks with more traditional runoff generating mechanisms, such as excess infiltration and saturation, demonstrate more agreement between models, while benchmarks with heterogeneity and complex water table dynamics highlight differences in model formulation. In general, all the models demonstrate the same qualitative behavior, thus building confidence in their use for hydrologic applications.

A parallel finite element scheme for thermo-hydro-mechanical (THM) coupled problems in porous media

Many applied problems in geoscience require knowledge about complex interactions between multiple physical and chemical processes in the sub-surface. As a direct experimental investigation is often not possible, numerical simulation is a common approach. The numerical analysis of coupled thermo-hydro-mechanical (THM) problems is computationally very expensive, and therefore the applicability of existing codes is still limited to simplified problems. In this paper we present a novel implementation of a parallel finite element method (FEM) for the numerical analysis of coupled THM problems in porous media. The computational task of the FEM is partitioned into sub-tasks by a priori domain decomposition. The sub-tasks are assigned to the CPU nodes concurrently. Parallelization is achieved by simultaneously establishing the sub-domain mesh topology, synchronously assembling linear equation systems in sub-domains and obtaining the overall solution with a sub-domain linear solver (parallel BiCGStab method with Jacobi pre-conditioner). The present parallelization method is implemented in an object-oriented way using MPI for inter-processor communication. The parallel code was successfully tested with a 2-D example from the international DECOVALEX benchmarking project. The achieved speed-up for a 3-D extension of the test example on different computers demonstrates the advantage of the present parallel scheme.

Numerical simulation of flow and heat transfer in fractured crystalline rocks: Application to the Hot Dry Rock site in Rosemanowes (U.K.)

Abstract This study examines heat transfer during forced water circulation through fractured crystalline rock using a fully 3-D finite-element model. We propose an alternative to strongly simplified single or multiple parallel fracture models or porous media equivalents on the one hand, and to structurally complex stochastic fracture network models on the other hand. The applicability of this “deterministic fracture network approach” is demonstrated in an analysis of the 900-day circulation test for the Hot Dry Rock (HDR) site at Rosemanowes (U.K.). The model design with respect to structure, hydraulic and thermal behavior is strictly conditioned by measured data such as fracture network geometry, hydraulic and thermal boundary and initial conditions, hydraulic reservoir impedance, and thermal drawdown. Another novel feature of this model is that flow and heat transport in the fractured medium are simulated in a truly 3-D system of fully coupled discrete fractures and porous matrix. While an optimum model fit is not the prime target of this study, this approach permits one to make realistic long-term predictions of the thermal performance of HDR systems.

Enhanced biodegradation by hydraulic heterogeneities in petroleum hydrocarbon plumes

In case of dissolved electron donors and acceptors, natural attenuation of organic contaminant plumes in aquifers is governed by hydrodynamic mixing and microbial activity. Main objectives of this work were (i) to determine whether aerobic and anaerobic biodegradation in porous sediments is controlled by transverse dispersion, (ii) to elucidate the effect of sediment heterogeneity on mixing and biodegradation, and (iii) to search for degradation-limiting factors. Comparative experiments were conducted in two-dimensional sediment microcosms. Aerobic toluene and later ethylbenzene degradation by Pseudomonas putida strain F1 was initially followed in a plume developing from oxic to anoxic conditions and later under steady-state mixing-controlled conditions. Competitive anaerobic degradation was then initiated by introduction of the denitrifying strain Aromatoleum aromaticum EbN1. In homogeneous sand, aerobic toluene degradation was clearly controlled by dispersive mixing. Similarly, under denitrifying conditions, microbial activity was located at the plumes fringes. Sediment heterogeneity caused flow focusing and improved the mixing of reactants. Independent from the electron accepting process, net biodegradation was always higher in the heterogeneous setting with a calculated efficiency plus of 23-100% as compared to the homogeneous setup. Flow and reactive transport model simulations were performed in order to interpret and evaluate the experimental results.

Impacts of the use of the geological subsurface for energy storage: an investigation concept

New methods and technologies for energy storage are required to make a transitionto renewable energy sources; in Germany this transition is termed “Energiewende”. Subsurface georeservoirs, such as salt caverns for hydrogen, compressed air, and methane storage or porous formations for heat and gas storage, offer the possibility of hosting large amounts of energy. When employing these geological storage facilities, an adequate system and process understanding is essential in order to characterize and to predict the complex and interacting effects on other types of subsurface use and on protected entities. In order to make optimal use of georeservoirs, a comprehensive use planning of the subsurface is required that allocates specific uses to appropriate subsurface locations. This paper presents a generic methodology on how subsurface use planning can be conducted and how its scientific basis can be developed. Although synthetic, realistic scenarios for the use of the geological underground for energy storage are parameterized and numerically simulated, accounting for other kinds of subsurface use already in place. From these scenario analyses, the imposed coupled hydraulic, thermal, mechanical and chemical processes, as well as mutual effects and influences on protected entities are assessed and generalized. Based on these, a first methodology for large-scale planning of the geological subsurface considering different surface and subsurface usage scenarios may also be derived.