Browsing by Author "Helmig, Rainer (Prof. Dr.-Ing)"

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Open Access
Adaptive modelling of compositional multi-phase flow with capillary pressure
(2014) Faigle, Benjamin; Helmig, Rainer (Prof. Dr.-Ing)
Many technical as well as environmental applications in the field of multi-phase flow in porous media, such as CO2 storage in the subsurface, remediation of hazardous spills in the groundwater or gaseous infiltration from nuclear storage sites into the surrounding rock, take place on a huge spatial domain and occur over large time-scales. In most cases, however, complex flow regimes occur only in small regions of the whole domain of interest. Inside these regions, the quality of simulations benefits from highly resolved grids and from an in-depth description of the physics involved. Outside, in contrast, the grid can remain coarse and the relevant processes are already captured by a simpler model abstraction. To simulate such processes, numerical models have to be developed that mimic the relevant system properties and characteristics of flow. In this work, the sequential solution scheme is shown to be an efficient alternative to fully implicit formulations for compressible, compositional multi-phase systems; it even considers the often neglected gravitational effects and capillary pressure. An extension for non-isothermal flow is presented as well. Some numerical obstacles have to be mastered to model these numerically challenging systems in an efficient manner, avoiding costly iteration of the global solution. Two adaptive strategies are discussed: the multi-physics concept adapts the model complexity locally according to the underlying physical processes. Complicated physics are approached by complex models that differ from those applied in flow regimes that are simpler. The efficiency gain is flanked by the qualitative improvement to model each process not only with the fastest, but also with the most appropriate numerical model. As an example of such an adaptive modelling strategy, a large-scale CO2 injection scenario is presented. This example provides insights into the increased efficiency, as well as the decrease in modelling bias because the constraint on one numerical model per simulation is relaxed and the most appropriate available model is applied locally. In the quest for a good global solution, the physical and thermodynamic detail employed in complicated areas should be supported by a detailed resolution of the grid. Uniform refinement a priori is again avoided in favour of dynamic adaptation, resembling the second branch of adaptivity in this work. Detail and accuracy are gained in the region of interest while the global system remains coarse enough to be solved efficiently. The modification of the simulation grid should not be an additional source of error: for the complex systems considered, this requires careful transformation of the data while modifying the grid. Indicators have to be developed that steer the dynamic adaptation of the grid. These should be tailored to the specific problem at hand. Nevertheless, the stability of the numerical formulation applied is jeopardized by the types of indicators that would cause a back-coupling of modelling errors into the refinement process. On such adaptive grids, the standard approach to computing fluxes is known to fail. An alternative method, a multi-point flux approximation, is successfully applied and the improvements investigated. The combination with the standard flux expression yields a very efficient and potent solution to modelling compositional flow on adaptive grids. The proposed conceptual methods can only be successfully adapted if they are applicable to real problems. The large-scale simulations presented in this work are not intended to answer specific problem-related questions but to show the general applicability of the modelling concepts even for such complicated natural systems. At the same time, such large-scale real systems provide a good environment for balancing the efficiency potentials and possible weaknesses of the approaches discussed. The last example features four levels of complexity bonded together in the multi-physics setting: compositional single-phase flow with a simplified thermal approximation and under full non-isothermal consideration as well as compositional two-phase flow with and without full non-isothermal effects. Simulations are performed on an adaptively refined simulation grid.
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Coupling of porous media flow with pipe flow
(2011) Dogan, Mehmet Onur; Helmig, Rainer (Prof. Dr.-Ing)
Many flow problems in environmental, technical and biological systems are characterized by a distinct interaction between a flow region in porous medium and a free flow region in quasi-one-dimensional hollow structures. Examples for such systems are: (i) Mines: Methane released from unmined coal seams migrates through the porous rocks, but also through tunnels and shafts in the mine; (ii) Landslides: A sudden water infiltration through macropores may trigger landslides; (iii) Polymer electrolyte membrane fuel cells: The supply of reactive gases through free-flow channels into the porous diffusion layers interacts strongly with the evacuation process of the water, which is formed at the cathode reaction layer and flows from the porous diffusion layers into the free-flow channels; (iv) Cancer therapy: Therapeutic agents are delivered via the blood vessels into the tissue, targeting the tumor cells. The goal of this study is to introduce new coupling strategies and to develop coupled numerical models which can form a basis for further studies modeling the complex systems mentioned above. The focus is to present different new concepts for modeling three-dimensional flow in porous media coupled with one-dimensional pipe flow and to illustrate the characteristic behavior of such systems by numerical test examples. For the numerical modeling of coupled systems a special grid implementation is necessary, which is capable of representing one-dimensional network structures in a three-dimensional grid. Therefore, in the frame work of this study a special grid called 1D network grid in a 3D domain is developed. The dual-continuum concept is extended for coupling multi-phase porous media flow with lower-dimensional single-phase pipe flow. The complexity of the considered flow regimes is increased gradually. First, examples are given for a stationary, incompressible single-phase flow system, in which single-phase flow in porous media with Hagen-Poiseuille flow in pipe are coupled. Then, the complexity of the model is increased considering compressible and unsteady flow conditions. The single-phase coupling strategy is tested by comparing the results with results of the experiment done in controlled laboratory conditions. Furthermore, the coupling of Hagen-Poiseuille flow in pipe with a multi-phase flow based on Richards equation for the unsaturated soil zone is modeled, where the important role of capillary effects for the mass exchange rate between the two continua can be illustrated. The next model introduces a concept for a two-phase porous media flow coupled with a single-phase (gas) pipe flow problem, which reveals that the mobility exchange term can be decisive for the mass exchange rate. The final model presents a concept for coupling two-phase two-component porous media flow with single-phase two-component pipe flow. This model is able to simulate more complicated transport systems by accounting not only for the mobility exchange term but also for the concentrations of the exchanged components between the continua. It is shown that the concentration of the components in each continua play a significant role for the compositional ratio of the exchanged mass. The implemented numerical models and presented examples are kept as simple as possible to show the basic features and characteristics of the model concepts that address the processes of different complexity.