Modeling of Multi Phase Flow in Porous Media: Operator Splitting, Front Tracking, Interfacial Area and Network Models
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In this work several new numerical methods and a new mathematical model related to multi phase flow in oil reservoirs have been developed, implemented and tested. The numerical difficulties in multi phase flow stem from the highly nonlinear nature of the equations. The solution can develop sharp fronts that travel through the reservoir. We have used front tracking to capture these fronts in our numerical methods. In addition corrected operator splitting for systems has been used and developed because of the advection dominated nature of the equations. The new mathematical model was developed to improve short comings of existing models and to include interfacial area as a new independent variable.
Paper A: Journal of Computational Physics 173(2), Operator splitting methods for systems of convection-diffusion equations: Nonlinear error mechanisms and correction strategies, pp. 636-663. Copyright 2001 Academic Press/ Elsevier.Paper B: Ask, A. K. ; Dahle, H. K.; Karlsen, K. H. and H. F. Nordhaug, A local streamline Eulerian-Lagrangian method for two-phase flow. In: Computational Methods in Water Resources 2, Bentley, L. R.; Sykes, J. F.; Brebbia, C. A.; Gray, W. G. and Pinder, G. F. (Eds.), pp. 645–650. Copyright 2000 Taylor & Francis.Paper C: Berre, Inga; Dahle, Helge K.; Karlsen, Kenneth H. and Hans F. Nordhaug, (2001), A streamline front tracking method for two- and three-phase flow including capillary forces. Preprint. Published in: Contemporary Mathematics: Fluid flow and transport in porous media: mathematical and numerical treatment 295, Zhangxin Chen and Richard E. Ewing (Eds.), pp. 49-61. Copyright 2002 American Mathematical SocietyPaper D: Nordhaug, Hans Fredrik; Dahle, Helge K. and Magne S. Espedal, Gray, William G., Celia, Michael A., Two phase flow including interfacial area as a variable. In: Computational Methods in Water Resources 1, Bentley, L. R.; Sykes, J. F.; Brebbia, C. A.; Gray, W. G. and Pinder G.F (Eds.), pp. 231–238. Copyright 2000 Taylor & Francis.Paper E: Nordhaug, H. F.; Celia, M. & H. K. Dahle, (2001), A pore network model for calculation of interfacial velocities. Preprint. Published in Advances in Water Resources, 26(10), pp. 1061-1074. Copyright 2003 Elsevier. Published version available at: <a href="http://dx.doi.org/10.1016/S0309-1708(03)00100-3"target=_blank>http://dx.doi.org/10.1016/S0309-1708(03)00100-3