Abstract
Immiscible two-phase flow of Newtonian fluids in porous media exhibits a power law relationship between flow rate and pressure drop when the pressure drop is such that the viscous forces compete with the capillary forces. When the pressure drop is large enough for the viscous forces to dominate, there is a crossover to a linear relation between flow rate and pressure drop. Different values for the exponent relating the flow rate and pressure drop in the regime where the two forces compete have been reported in different experimental and numerical studies. We investigate the power law and its exponent in immiscible steady-state two-phase flow for different pore size distributions. We measure the values of the exponent and the crossover pressure drop for different fluid saturations while changing the shape and the span of the distribution. We consider two approaches, analytical calculations using a capillary bundle model and numerical simulations using dynamic pore-network modeling. In case of the capillary bundle when the pores do not interact to each other, we find that the exponent is always equal to 3/2 irrespective of the distribution type. For the dynamical pore network model on the other hand, the exponent varies continuously within a range when changing the shape of the distribution whereas the width of the distribution controls the crossover point.
Highlights
Multiphase flow is relevant for a wide variety of different applications which deal with the flow of multiple immiscible fluids in single capillaries to more complex porous media (Bear, 1988; Dullien, 1992)
Many studies on the steady-state two phase flow on Newtonian fluids have revealed a non-trivial rheology, that is, in the regime where capillary forces are comparable to viscous forces, the relation between the total flow rate Q in a sample and the global pressure drop P across it differs from a linear Darcy law (Darcy, 1856; Whitaker, 1986)
We present a detailed study on how the distribution of pore sizes controls the effective rheology of the two-phase flow in the steady state
Summary
Multiphase flow is relevant for a wide variety of different applications which deal with the flow of multiple immiscible fluids in single capillaries to more complex porous media (Bear, 1988; Dullien, 1992). Many studies on the steady-state two phase flow on Newtonian fluids have revealed a non-trivial rheology, that is, in the regime where capillary forces are comparable to viscous forces, the relation between the total flow rate Q in a sample and the global pressure drop P across it differs from a linear Darcy law (Darcy, 1856; Whitaker, 1986). They used x-ray micro-tomography measurements and for a fractional flow of 0.5 they found the exponent in the non-linear regime to be equal to 1.67 (≈ 1/0.6) They reported a regime with linear Darcy type behavior at lower capillary numbers where the conductance does not change significantly. There the variation in exponent in the non-linear regime and the transition point is studied by varying three parameters: the saturation of the wetting fluid, and the span and shape related to the pore-size distribution. With a twodimensional plane of the non-linear exponent vs. the transition point, we show how the above three parameters control the effective rheology of two-phase flow
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