Browsing by Author "Faigle, Benjamin"

Now showing 1 - 1 of 1

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.