Flow of Two Immiscible Fluids

Each restoration situation would have a specific set of curves to define these relationships. For other materials, the curves may vary in shape, but the concept is similar. Mixed flow substantially reduces the relative permeability. This concept can be very important during the removal of NAPFs by the use of a large drawdown 

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FIGURE 5.9 Relative permeability relationships controlling the flow of two immiscible fluids. (After Leverett, 1939.)... 

Pressure Flow of Two Immiscible Fluids with Different Viscosities... 

Pressure flow of two immiscible fluids with different viscosities that flow as separate layers between parallel plates are often encountered inside dies during co-extrusion when producing multi-layer films. Such a system is schematically depicted in Fig. 6.16, which presents two layers of thickness h/2 and viscosities m and //,2, respectively. 

The two-phase flow option in FLAG allows numerical modelling of the flow of two immiscible fluids through porous media. A description of the concepts involved in the mathematical description of multi-phase flow may be found in reference books such as Fundamentals of Numerical Reservoir Simulation (Peaceman, D. W., 1977). Some of these concepts are addressed below. 

Countercurrent flow of two immiscible fluids in porous media is strongly influenced by the competition of the two fluids for the available pore space. 

Pressure-driven two-phase flows are flows of two immiscible fluids in the same micro- or nanofluidic conduit driven by a pressure gradient. The fluids can be of different chemical compositions, liquid-liquid, or in different physical states, gas-liquid. 

Consider stratified flow of two immiscible fluids a and b in a horizontal (or slightly inclined) conduit. The flow configuration and coordinates are described in Figure 1. Detailed derivations of the transient one-dimensional averaged two-fluid equations can be found in many studies (e.g., Yadigaroglou and Lahey [54], Hancox et al. [55], Banerjee and Chan [56], Banerjee [57,58], Andron [59], Kocamustafaogullari [60]). 

We consider an unsteady laminar flow of two immiscible fluids. Both fluids are assumed to be viscous and Newtonian. Moreover, we suppose that the flow is isothermal, thus neglecting the viscosity and density variations due to changes of a temperature field. We assume also that the fluids are incompressible. Presuming, in addition, the fluids to be homogeneous, we may infer that the densities and viscosities are constant within each fluid. We utilize the sharp-interface (zero interfacial thickness) approach the density and viscosity have, therefore, a jump discontinuity at the interface (see, e.g., (Batchelor 1967)). We assume that the interface has a surface tension. We also suppose that there is no mass transfer through the interface (i.e. the interface is impermeable), and there are no surfactants present in the fluids (hence, there is no species transport along the interface). The surface tension coefficient is, thus, assumed constant. 

Fines Migration in Multiphase Flow. Most of the preceding discussion was concerned with flow of brine at 100% brine saturation. From a petroleum engineering perspective this brine staturation represents a condition that is rarely encountered in the field. A more relevant situation would be flow of brine at residual oil saturation and commingled flow of oil and brine. When fines migration occurs in the presence of two immiscible fluids, additional factors such as the wettability of the medium and that of the fines and the relative permeability characteristics become important. Therefore, it is important to consider the effect of the presence of a second immiscible fluid on fines migration and permeability damage. 

Let us consider a three-phase system composed by an elastic body with large pores where a mixture of two immiscible fluids (or a suspension of solid particles in a fluid or a fluid component carrying an adsorbate) flows through. 

Ozen O, Aubry N, Papageorgiou DT, Petropoulos PG (2006) Electrohydrodynamic linear stability of two immiscible fluids in channel flow. Electrochim Acta 51 5316-5323... 

Numerical Techniques for Free Surface Flows Inter- domain composed of two immiscible fluids and (b) grid... 

Numerical Techniques for Free Surface Flows Interface Capturing and Interface Tracking, Figure 11 Immersed boundary method (a) computational domain composed of two immiscible fluids (b) grid points considered for the interface velocity around the marker X [12]... 

Verma, P.D., Bhatt, B.S., 1973. Plane Couette flow of two immiscible incompressible fluids with uniform suction at the stationary plate. Proc. Indian Acad. Sci. India A 78, 108-120. 

Two immiscible fluids A and B, of viscosities p./t and fin, flow under streamline conditions between two horizontal parallel planes of width b, situated a distance 2a apart (where a is much less than b), as two distinct parallel layers one above the other, each of depth a. Show that the volumetric rate of flow of A is ... 

When two immiscible fluids flow relative to each other along an interface of separation, there is a maximum relative velocity above which a small disturbance of the interface will amplify and grow and thereby distort the flow. This phenomenon is... 

To compute the motion of two immiscible and incompressible fluids such as a gas liquid bubble column and gas-droplets flow, the fluid-velocity distributions outside and inside the interface can be obtained by solving the incompressible Navier-Stokes equation using level-set methods as given by Sussman et al. (1994) ... 

Interfacial rheology deals with the flow behavior in the interfacial region between two immiscible fluid phases (gas-liquid as in foams, and liquid-liquid as in emulsions). The flow is considerably modified by surface active agents present in the system. Surface active agents (surfactants) are molecules with an affinity for the interface and accumulate there forming a packed structure. This results in a variation in physical and chemical properties in a thin interfacial region with a thickness of the order of a few molecular diameters. These... 

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