Finite element method for coupled thermo-hydro-mechanical processes in discretely fractured and non-fractured porous media

Numerical analysis of multi-field problems in porous and fractured media is an important subject for various geotechnical engineering tasks such as the management of geo-resources (e.g. engineering of geothermal, oil and gas reservoirs) as well as waste management. For practical usage, e.g. for geothermal, simulation tools are required which take into account both coupled thermo-hydro-mechanical (THM) processes and the uncertainty of geological data, i.e. the model parametrization. For modeling fractured rocks, equivalent porous medium or multiple continuum model approaches are often only the way currently due to difficulty to handle geomechanical discontinuities. However, they are not applicable for prediction of flow and transport in subsurface systems where a few fractures dominates the system behavior. Thus modeling coupled problems in discretely fractured porous media is desirable for more precise analysis. The subject of this work is developing a framework of the finite element method (FEM) for modeling coupled THM problems in discretely fractured and non-fractured porous media including thermal water flow, advective-diffusive heat transport, and thermoporoelasticity. Pre-existing fractures are considered. Systems of discretely fractured porous media can be considered as a problem of interacted multiple domains, i.e. porous medium domain and discrete fracture domain, for hydraulic and transport processes, and a discontinuous problem for mechanical processes. The FEM is required to take into account both kinds of the problems. In addition, this work includes developing a methodology for the data uncertainty using the FEM model and investigating the uncertainty impacts on evaluating coupled THM processes. All the necessary code developments in this work has been carried out with a scientific open source project OpenGeoSys (OGS). In this work, fluid flow and heat transport problems in interactive multiple domains are solved assuming continuity of filed variables (pressure and temperature) over the two domains. The assumption is reasonable if there are no infill materials in fractures. The method has been successfully applied for several numerical examples, e.g. modeling three-dimensional coupled flow and heat transport processes in discretely fractured porous media at the Gross Schoenebck geothermal site (Germany), and three-dimensional coupled THM processes in porous media at the Urach Spa geothermal site (Germany). To solve the mechanically discontinuous problems, lower-dimensional interface elements (LIEs) with local enrichments have been developed for coupled problems in a domain including pre-existing fractures. The method permits the possibility of using existing flow simulators and having an identical mesh for both processes. It enables us to formulate the coupled problems in monolithic scheme for robust computation. Moreover, it gives an advantage in practice that one can use existing standard FEM codes for groundwater flow and easily make a coupling computation between mechanical and hydraulic processes. Example of a 2D fluid injection problem into a single fracture demonstrated that the proposed method can produce results in strong agreement with semi-analytical solutions. An uncertainty analysis of THM coupled processes has been studied for a typical geothermal reservoir in crystalline rock based on the Monte-Carlo method. Fracture and matrix are treated conceptually as an equivalent porous medium, and the model is applied to available data from the Urach Spa and Falkenberg sites (Germany). Reservoir parameters are considered as spatially random variables and their realizations are generated using conditional Gaussian simulation. Two reservoir modes (undisturbed and stimulated) are considered to construct a stochastic model for permeability distribution. We found that the most significant factors in the analysis are permeability and heat capacity. The study demonstrates the importance of taking parameter uncertainties into account for geothermal reservoir evaluation in order to assess the viability of numerical modeling

Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008

Fast Magnetic Flux Line Allocation Algorithm for Interactive Visualization Using Magnetic Flux Line Existence Probability

The visualization of magnetic flux lines is one of the most effective ways to intuitively grasp a magnetic field. The depiction of continuous and smooth magnetic flux lines according to the magnetic field is of paramount importance. Thus, it is important to adequately allocate the distribution of magnetic flux lines in the analyzed space. The authors have already proposed two methods of determining the allocation of magnetic flux lines in 3-D space. However, both methods exhibited a long computation time to determine the allocation of magnetic flux lines. For solving this problem, in this paper, we propose a new improved method for correct allocation of magnetic flux lines in 3-D space with modest computational cost. The main advantages of this method are shorter computation time, correct allocation of the magnetic flux lines, and especially short computation time for visualization of magnetic flux lines when changes in the number of depicted flux lines is requested

Multiscale mathematical models for simulation and scale-up of green processes in the perspective of industrial sustainability

The present work presents research studies aimed at developing tools useful to design engineering solutions moving in the direction of industrial sustainability. The investigations hereinafter discussed regard an extraction process of active compounds \u2013 polyphenols \u2013 from agro-food industry wastes (olive and grape pomaces) and a biorefinery exploiting waste frying oil, solid organic wastes and algal biomass to produce biofuels. In particular, for the former topic, a procedure aimed at the evaluation of the technological feasibility at pilot scale of said process is discussed. The proposed approach takes into consideration the extended kinetic route coupled with mathematical simulation. Detailed physically-based dynamic mathematical models, taking into account mass and energy balance equations, are adopted to describe both the lab-scale and the pilot-scale reactors. Chemical physical parameters appearing in the models are estimated from the experimental data at lab-scale or are partially taken from literature. Different heating systems are designed for the pilot scale reactor and their performance is tested by simulation. Characteristic times are evaluated also during start-ups and different control loops are analyzed in order to set-up the best process and operating variables. Average yields in polyphenols are finally evaluated for both the batch and the continuous operated pilot reactor, by considering feed variability and fluctuations of process parameters. For what concerns the biorefinery, special attention was devoted to the modeling of the airlift reactor, its most delicate and complex component. In fact, to optimize this interesting microalgae cultivation system, a precise description of the moving interfaces formed by the liquid and gas phase is critical. In this study, coupled front capturing methods (standard and conservative level set methods) and finite difference method are used to simulate gas bubbles dynamics in a pilot-scale external loop air-lift photobioreactor in which microalgae are used to capture CO2 from flue gas and to treat wastewater. Numerical simulations are carried out on rectangular domains representing different sections of the vertical axis of the riser. The data employed was either acquired from previous experimental campaigns carried out in the airlift reactor or found in the literature. The rise, shape dynamics and coalescence process of the bubbles of flue gas are studied. Moreover, for each analyzed applications, a procedure based on Buckingham \u3c0-theorem to perform a rigorous scale-up is proposed. In this way, scale-invariant dimensionless groups describing and summarizing the considered processes could be identified. For the research focused on the scale-up of photobioreactors used to cultivate Chlorella Vulgaris, an experimental campaign at three levels was designed and carried out to evaluate the characteristic dimensionless numbers individuated by the theoretical formulation. Since scale-up regards both geometrical dimensions and type of reactor, passing from lab-scale stirred tanks to pilot scale tubular and airlift, particular attention was devoted to define characteristic lengths inside the dimensionless numbers

The deal.II Library, Version 9.0

This paper provides an overview of the new features of the finite element library deal.II version 9.0

Optimization as a design strategy. Considerations based on building simulation-assisted experiments about problem decomposition

In this article the most fundamental decomposition-based optimization method - block coordinate search, based on the sequential decomposition of problems in subproblems - and building performance simulation programs are used to reason about a building design process at micro-urban scale and strategies are defined to make the search more efficient. Cyclic overlapping block coordinate search is here considered in its double nature of optimization method and surrogate model (and metaphore) of a sequential design process. Heuristic indicators apt to support the design of search structures suited to that method are developed from building-simulation-assisted computational experiments, aimed to choose the form and position of a small building in a plot. Those indicators link the sharing of structure between subspaces ("commonality") to recursive recombination, measured as freshness of the search wake and novelty of the search moves. The aim of these indicators is to measure the relative effectiveness of decomposition-based design moves and create efficient block searches. Implications of a possible use of these indicators in genetic algorithms are also highlighted.Comment: 48 pages. 12 figures, 3 table