A lattice Boltzmann study on the impact of the geometrical properties of porous media on the steady state relative permeabilities on two-phase immiscible flows |
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| Institution: | 1. Xi’an Jiaotong-Liverpool University, No. 111 Ren’ai Road, Suzhou Dushu Lake Higher Education Town, Suzhou 215123, China;2. The School of Engineering, University of Liverpool, Brownlow Hill, Liverpool L69 7ZX, United Kingdom;3. Chemical and Process Engineering, University of Surrey, Guildford, Surrey GU2 7XH, United Kingdom;1. CEMSE, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia;2. DISAT, Politecnico di Torino, Torino, Italy;3. ICES, The University of Texas at Austin, USA;4. Mathematics Institute, University of Warwick, UK;1. Department of Earth Sciences, Uppsala University, Uppsala, Sweden;2. Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA;3. Institute of Fluid Mechanics and Environmental Physics in Civil Engineering, Leibniz University Hannover, Germany;4. Université de Rennes 1, Geosciences Géosciences Rennes (UMR CNRS 6118), Rennes, France;1. Institute of Chemical Process Engineering, University of Stuttgart, Stuttgart 70199, Germany;2. Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Stuttgart 70569, Germany |
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| Abstract: | In the current paper, the effect of the geometrical characteristics of 2-D porous media on the relative permeability in immiscible two-phase flows is studied. The generation of the different artificial porous media is performed using a Boolean model based on a random distribution of overlapping circles/ellipses, the size and shape of which are chosen to satisfy the specific Minkowski functionals (i.e. volume fraction, solid line contour length, connectivity). The study aims to identify how each different Minkowski functional affects the relative permeability of each phase at various saturations of the non-wetting phase. A 2-D multi-relaxation time (MRT) lattice Boltzmann model (LBM) that can handle high density ratios is employed in the simulation. The relationship between the driving forces G and the relative permeabilities of the two phases for every artificial structure is quantified. It is found that for high non-wetting phase saturations (fully connected flow), a non-linear relationship exists between the non-wetting phase flow rate and the driving force, whilst this relationship becomes linear at higher magnitudes of the latter. The force magnitude required to approach the linear region is highly influenced by the pore size distribution and the connectivity of the solid phase. For lower non-wetting phase saturation values, its relative permeability in the linear regime decreases as the fraction of small pores in the structure increases and the non-wetting phase flow becomes disconnected. A strong influence of the solid phase connectivity is also observed. |
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