Phase non-wetting

The solution of these dynamic nonlinear differential equations is considerably more complex than the previous systems considered. In particular, stable solution methods are based on physically realistic multiphase flow functions that have the following properties relative permeability functions are non-negative, monotoni-cally increasing with their respective saturation, and are zero at vanishing saturations, and capillary pressure is monotonically increasing with respect to the saturation of the non-wetting phase. It is necessary that any iterative scheme for estimating the multiphase flow functions retain these characteristics at each step. 

Flow properties of macroemulsions are different from those of non-emulsified phases 19,44). When water droplets are dispersed in a non-wetting oil phase, the relative permeability of the formation to the non-wetting phase decreases. Viscous energy must be expended to deform the emulsified water droplets so that they will pass through pore throats. If viscous forces are insufficient to overcome the capillary forces which hold the water droplet within the pore body, flow channels will become blocked with persistent, non-draining water droplets. As a result, the flow of oil to the wellbore will also be blocked. 

Since water must be forced into a dry GDM regardless of PTFE-content, water is effectively the non-wetting phase. This process has the characteristics of primary drainage, for which invasion percolation30 is an adequate model.6,31 Invasion percolation describes... 

U2 and p-2 are the non-wetting phase velocity and dynamic viscosity respectively a is the surface tension and g is the gravitational acceleration. Similarly, the afore-mentioned non-dimensional parameters exhibit significantly low values in the GDL within comparable order of magnitude variations. It should be noted that for the hydrophobic CL and GDL representative of a typical PEFC, water is the non-wetting phase (NWP) and air the wetting phase (WP). 

The displacement of a non-wetting phase by a wetting phase in a porous medium or a gel the reverse of drainage. 

Capillary sealing effects take place at the interface between the non-wetting phase in a reservoir and the wetting phase within a top seal. The capillary forces exerted at this interface are in no way related to the thickness of the seal above. Therefore the existence of a relationship between top seal thickness and sealing capacity is not expected in the field. Thicker seals may be better equipped to resist breaching by faults, but will not retain greater columns by capillary resistance. 

It is reported that gas flow as a separate phase through a seal is given if the pressure of a non-wetting phase (gas) can displace the connate water out of the pore space, or in other words if the buoyancy forces created by the gas column exceed the capillary pressure within the seal. It is important to state that the most relevant factor controlling capillary pressure is the effective interconnected pore radius and that the pore radius does not depend on seal thickness (Zieglar, 1992 Antonellini and Aydin, 1994). 

Phc-water consists of a fluid flux (Darcy) component and a non-wetting phase capillary entry-pressure... 

Fig. 55. Surface phase diagram in the plane of variables g, and <)> for three values of g. The region where the surface is non-wet (at small gj is separated from the wet region by a phase boundary which describes the wetting transition. For > (second-order wetting) this is just the straight line giril = — g(l—) The region of first order wetting is shown for symmetrical mixtures with Na = NB = N = 10 and N = 100, respectively, and the first-order transitions are shown by dash-dotted curves. In this regime metastable wet and non wet phases are possible up to the stability limits ( surface spinodals ) denoted by dashed curves. Assuming that g, and g are essentially independent of temperature T, variation of T essentially means variation of <)>, . From Schmidt and Binder [125],...

Seal properties Rock seal properties are usually described in terms of their capillary pressure characteristics, primarily wettability, entry and displacement pressures, and irreducible wetting phase saturation. Wettability defines which fluids will preferentially occupy the smallest rock pores. Entry pressure is the capillary pressure at which the non-wetting phase first displaces the wetting phase, while displacement pressure is the capillary pressure at which the non-wetting phase first forms a continuous network within the pore structure. The irreducible wetting phase saturation describes the initial connate fluid saturation at the top of the capillary column. 

Capillary blockage occurs when the non-wetting phase is blocked at a pore throat by the interfacial tension (Y ) with the wetting phase (Fig. 11). 

Here, and g refer to the water and gas phases, respectively. Usually, a wetting and a non-wetting phase are considered, but in the context here, these denominations would be ambiguous. 

In interfacial contact reactors, a selectively wetted porous membrane is used to maintain an organic-aqueous interface in the plane of the membrane, while allowing for interfacial contact between the substrate and the biocatalyst (Fig. 3). Bulk mass transfer limitation, common in conventional heterogeneous emulsion systems, could thus be reduced [125]. Once more, the two liquid phases acted as a reservoir for substrates and/or products. To keep the interface in the plane of the membrane, a slight positive pressure in the non-wetting phase was needed [126,127]. 

Fig. 11. Ratio of "true" to "false" non-wetting phase exponents vs. dimensionless rate.

Fig. 13. Ratio of "true" to "false" endpoint non-wetting phase relative permeability vs. rate.

In the case of drainage, the end-point relative permeability and saturation exponent for the non-wetting phase can be related to the dimensionless rate. These parameters increase as the dimensionless rate increases. 

J = least squares error function to be minimized K = absolute permeability Kr = relative permeability /Cr = relative permeability of non-wetting phase Kr = relative permeability of wetting phase... 

Viscous dissipation in the non-wetting phase (air in the classical forced wetting problem) is usually neglected, but has to be considered here, because of the significance of the liquid viscosity i/l with respect to i/ak- Indeed, both viscous forces in the wetting phase (air) comer Fair(u) = (3f i/air/i t - 0dl) and in the non-wetting one (liquid) Fl Cri v are of the same order (C 1 a numerical factor), because a = 3f l air/ L F... 

In the course of measuring imbibition capillary pressures, Morrow (20) also determined residual non-wetting phase saturations as a function of the intrinsic contact angle. For systems which spontaneously imbibe, he found that the residual oil values in- creased as the intrinsic contact angle was increased from 0° to 62°, the limit at which spontaneous imbibition occurs. Therefore, for systems which imbibe, the best recovery should be obtained from strongly water-wet systems. 

The work of Dombrowski and Brownell (53) shows that it is much harder to displace the residual wetting phase from a porous medium (in this case, small glass beads). Figure 3 indicates that the capillary number required for their displacement of the wetting phase is two orders of magnitude higher than that required for the displacement of most non-wetting phases. Jenks et al. (54)... 

The effects of increasing surface roughness were experimentally determined to give reductions in non-wetting phase contact angles and reductions in the mobilization forces requirement. When composite surfaces form, roughened surfaces reduce the mobilization requirements when compared with those for smooth surfaces. This behavior could occur in porous media that has first been exposed to the wetting brine phase. 

One point meriting discussion is the magnitude of the minimum saturation at which the non-wetting phase will flow, sometimes referred to as "critical saturation". According to Geffen et al. (6) the critical saturation to gas or oil is approximately 1 percent. The lowest reported non-wetting phase saturations at which measurable relative permeabilities were found in drainage tests, however, have been between about 5% and 35% pore volume. 

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