Institute for Modeling Hydraulic and Environmental Systems
University of Stuttgart
"A Decoupled Model for Compositional Multiphase Flow in Porous Media and Multi-Physics, Multi-Scale Approaches for Two-Phase Flow"
In many practical applications of porous media flow simulators, the most complex processes are confined to a small part of the model domain. The demands of a simulator on computational resources increase with the physical complexity of the model. Thus, a trade-off between physical accuracy and the computational demands of a model has to be made. Either great complexities are neglected in favor of a lean model or all processes are captured with a complex model which is superfluous in large parts of the domain. As a compromise between these options, a consistent transfer concept is introduced. It couples simple and complex models and adapts the resulting multiscale model to the physical processes actually occurring. As a basis for this, a decoupled formulation for non-isothermal compositional multiphase flow is discussed. It has the advantage that the size of the linear system of equations does not grow with the number of phases or components involved.
One part of the presentation reviews common concepts for the description of multiphase flow in porous media and provides a consistent derivation of the conservation equations of non-isothermal compositional flow and transport processes. Based on these equations, decoupled formulations for isothermal and non-isothermal compositional flow are derived, using the concept of the local conservation of total fluid volume. The implementation of the derived formulations into a finite volume method with an implicit pressure, explicit concentration time discretization is presented. The resulting simulation tool is tested and verified with results from various experimental and computational investigations and its range of applicability is considered.
Based on the decoupled formulations derived before, an isothermal and a non-isothermal multiphysics concept for the transition of complexity within a porous media domain are presented. Furthermore, a simple and robust subdomain control scheme is developed which ensures optimal adaption of the model complexity to the occurring processes at any time. Both models are implemented and tested towards their accordance with the globally complex decoupled models. It is shown that the computational demands of a simulator can be decreased by incorporating the multi-physics schemes.
Ideas for the extension of the multiphysics towards more complex systems and possible interfaces with multiscale methods are discussed. In the presentation, we want to introduce and distinguish two types of multi-scale approaches which have proven to model this simplified system very efficiently and accurately. We combine an adaptive grid method based on multi-point flux approximation with various local up-scaling techniques. Resulting effective parameters like relative permeabilities can be full second-order tensors. The method is tested on different examples
Fritz, J., Flemisch, B. and R. Helmig: Decoupled and multiphysics models for non-isothermal compositional two-phase flow in porous media. International Journal of Numerical Analysis & Modeling 9, 1 (2011) 17-28.
Helmig, R., Flemisch, B., Wolff, M., Ebigbo, A. and H. Class: Model coupling for multiphase flow in porous media. Advances in Water Resources 51 (2013) 52-66.
Helmig, R., Niessner, J., Flemisch, B., Wolff, M. and J. Fritz: Efficient modelling of flow and transport in porous media using multi-physics and multi-scale approaches. In: Freeden, W., Nashed, Z., and T. Sonar (eds.): Handbook of Geomathematics. Springer-Verlag, 2010, 417-458.
Wolff, M., Flemisch, B., Helmig, R. and I. Aavatsmark: Treatment of tensorial relative permeabilities with multipoint flux approximation. International Journal of Numerical Analysis & Modeling 9 (2011) 725-744.
Wolff, M., Cao, Y., Flemisch, B., Helmig, R. and B. Wohlmuth: Multi-point flux approximation L-method in 3D: Numerical convergence and application to two-phase flow through porous media, De Gruyter, (2013).
M. Darcis: Coupling Models of Different Complexity for the Simulation of CO2 Storage in Deep Saline Aquifers. PhD thesis, University of Stuttgart, 2012.
PDF of Abstract.