Network models for two-phase flow in porous media Part 1. Immiscible microdisplacement of non-wetting fluids

Abstract

A theoretical simulator of immiscible displacement of a non-wetting fluid by a wetting one in a random porous medium is developed. The porous medium is modelled as a network of randomly sized unit cells of the constricted-tube type. Under creeping-flow conditions the problem is reduced to a system of linear equations, the solution of which gives the instantaneous pressures at the nodes and the corresponding flowrates through the unit cells. The pattern and rate of the displacement are obtained by assuming quasi-static flow and taking small time increments. The porous medium adopted for the simulations is a sandpack with porosity 0.395 and grain sizes in the range from 74 to 148 μrn. The effects of the capillary number, Ca, and the viscosity ratio, κ = μo/μw, are studied. The results confirm the importance of the capillary number for displacement, but they also show that for moderate and high Ca values the role of κ is pivotal. When the viscosity ratio is favourable (κ < 1), the microdisplacement efficiency begins to increase rapidly with increasing capillary number for Ca > 10−5, and becomes excellent as Ca → 10−3. On the other hand, when the viscosity ratio is unfavourable (κ > 1), the microdisplacement efficiency begins to improve only for Ca values larger than, say, 5 × 10−4, and is substantially inferior to that achieved with κ < 1 and the same Ca value. In addition to the residual saturation of the non-wetting fluid, the simulator predicts the time required for the displacement, the pattern of the transition zone, the size distribution of the entrapped ganglia, and the acceptance fraction as functions of Ca, κ, and the porous-medium geometry.

Uniqueness of Specific Interfacial Area–Capillary Pressure–Saturation Relationship Under Non-Equilibrium Conditions in Two-Phase Porous Media Flow

“…The pore-scale two-pressure algorithm of DYPOSIT model provides the distribution of local capillary pressures at the interfaces of (the discontinuous) phases. This approach is much more efficient than the other pore-scale approaches for mobilization such as the search algorithm proposed by Ng and Payatakes (1980) or the definition of single pressure as proposed by Dias and Payatakes (1986). As shown schematically in Fig.…”

Mass transfer from nonaqueous phase organic liquids in water‐saturated porous media

“…When Ca is less than 10 −6 , the upper limit in most aquifers, experiments have shown that residual saturation is independent of Ca [Morrow and Chatzis, 1982]. However, models have indicated that viscous forces may affect blob configuration at capillary numbers as low as 10 −7 [Dias and Payatakes, 1986]. This suggests that the residual saturation and ganglia configuration may change in response to a change in flow velocity that may occur during aquifer remediation.…”

Visualization and quantification of two-phase flow in transparent miniature packed beds

“…The frontal dynamics can affect the oil recovery efficiency, as well as mass transport between NAPL/aqueous interface. The frontal structure can vary from compact to fingering pattern, depending on capillary number and viscosity ratio between invading and defending fluid [11,15,18,19]. In particular, at low injection rate, where viscous force can be neglected and capillary force dominates, capillary fingering is manifested.…”