Capillary pressure, effect

Conventionally, the sample is initially saturated with one fluid phase, perhaps including the other phase at the irreducible saturation. The second fluid phase is injected at a constant flow rate. The pressure drop and cumulative production are measured. A relatively high flow velocity is used to try to negate capillary pressure effects, so as to simplify the associated estimation problem. However, as relative permeability functions depend on capillary number, these functions should be determined under the conditions characteristic of reservoir or aquifer conditions [33]. Under these conditions, capillary pressure effects are important, and should be included within the mathematical model of the experiment used to obtain property estimates. 

Capillary pressure effects appear to explain the very important 1964 discovery of Bernard and Holm that dispersions could make the mobility of the nonwetting phase essentially independent of the absolute permeability of the porous medium (52). (See above.) Indeed, the theoretical analysis of Khatib, et al., which was corroborated by experiments, gave dispersed-phase mobilities at the upper limiting capillary pressure (for coalescence) that were nearly constant for absolute permeabilities ranging from 7D to ca. 1,000D (41). 

Another theory of the reason for increased friction in the presence of moisture was proposed by Gao et al . They found that in a humid environment molybdenum disulphide films were more readily thinned by sliding contact, due to increased ease of interlamellar slip. They suggested that adsorption of water softened the films, and that resulting increased deformation by plowing in sliding contact led to a poorly oriented film and thus to increased friction. However, they considered that this was a short-term reversible effect which was not in conflict with theories of chemical breakdown. Gao et al also poiinted out the possibility that an increase In friction is caused by capillary pressure effects of moisture at asperity contacts. 

Haas JA, Osswald H. Adenosine Induced fall in glomerular capillary pressure effect of ureteral obstruction and aortic constriction in the Munich-Wistar rat kidney. Naunyn Schmiedebergs Arch Pharmacol 1981 317 86-89. 

The initial water level ho in the capillary is set so as to form a convex meniscus in puncture 4 when disc 1 is offloaded. Once disc 1 is installed on the meniscus, water from capillary 8 flows to the junction under study and spreads under the capillary pressure effect over the surface under consideration. The new level hi of water in capillary 8 and the height decrease A/i = ho — hi of the water column are recorded. The kinetic dependence A/i has the form of an exponent. The installation time of disc 1 before hi measurement is taken is 5 min, corresponding to the exponent approach to a constant value. 

Thus, it is clear that the finite difference numerical solutions offered by some authors are not really necessary because problems without capillary pressure can be solved analytically. Actually, such computational solutions are more damaging than useful because the artificial viscosity and numerical diffusion introduced by truncation and round-off error smear certain singularities (or, infinities) that appear as exact consequences of Equation 21-17. Such numerical diffusion, we emphasize, appears as a result of finite difference and finite element schemes only, and can be completely avoided using the more labor-intensive method of characteristics. For a review of these ideas, refer to Chapter 13. As we will show later, capillary pressure effects become important when singularities appear modeling these correctly is crucial to correct strength and shock position prediction. 

Fortran implementation. Equation 21-77 is easily programmed in Fortran. Because the implicit scheme is second-order accurate in space, thus rigidly enforcing the diffusive character of the capillary pressure effects assumed in this formulation, we do not obtain the oscillations at saturation shocks or the saturation overshoots having S > 1 often cited. The exact Fortran producing the results shown later is displayed in Figure 21-5 and in several function statements given later. For convenience, the saturation derivatives F (Sy ) and G (Sy ) are denoted FP and GP (P indicates prime for derivatives). 

Surfactants aid dewatering of filter cakes after the cakes have formed and have very Httle observed effect on the rate of cake formation. Equations describing the effect of a surfactant show that dewatering is enhanced by lowering the capillary pressure of water in the cake rather than by a kinetic effect. The amount of residual water in a filter cake is related to the capillary forces hoi ding the Hquids in the cake. Laplace s equation relates the capillary pressure (P ) to surface tension (cj), contact angle of air and Hquid on the soHd (9) which is a measure of wettabiHty, and capillary radius (r ), or a similar measure appHcable to filter cakes. 

The capillary flow with distinct evaporative meniscus is described in the frame of the quasi-dimensional model. The effect of heat flux and capillary pressure oscillations on the stability of laminar flow at small and moderate Peclet number is estimated. It is shown that the stable stationary flow with fixed meniscus position occurs at low wall heat fluxes (Pe -Cl), whereas at high wall heat fluxes Pe > 1, the exponential increase of small disturbances takes place. The latter leads to the transition from stable stationary to an unstable regime of flow with oscillating meniscus. 

Chapter 11 consists of following Sect. 11.2 deals with the pattern of capillary flow in a heated micro-channel with phase change at the meniscus. The perturbed equations and conditions on the interface are presented in Sect. 11.3. Section 11.4 contains the results of the investigation on the stability of capillary flow at a very small Peclet number. The effect of capillary pressure and heat flux oscillations on the stability of the flow is considered in Sect. 11.5. Section 11.6 deals with the study of capillary flow at a moderate Peclet number. 

Effect of Capillary Pressure and Heat Flux Oscillations... 

We estimate the effect of the velocity fluctuations on the capillary pressure, using the Hoffman-Voinov-Tanner law which is valid at 9d < 135° and Ca < 0 (0.1)... 

The simplest device for measuring ECC at mercury is Gouy s capillary electrometer (Eig. 10.5). Under the effect of a mercury column of height h, mercury is forced into the slightly conical capillary K. In the capillary, the mercury meniscus is in contact with electrolyte solution E. The radius of the mercury meniscus is practically equal to the capillary radius at that point. The meniscus exerts a capillary pressure Pk = directed upward which is balanced by the pressure = ftpegg of... 

R. L. Kleinberg 1996, (Utility of NMR T2 distributions, connections with capillary pressure, day effect, and determination of the surface relaxivity parameter n >). Magn. Reson. Imaging 14 (7/8), 761—767. 

We can conclude that the stability of static foam in porous media depends on the medium permeability and wetting-phase saturation (i.e., through the capillary pressure) in addition to the surfactant formulation. More importantly, these effects can be quantified once the conjoining/disjoining pressure isotherm is known either experimentally (8) or theoretically (9). Our focus... 

Figure 7 reports calculations of the effect of flow velocity on the critical capillary pressure for the constant-charge electrostatic model and for different initial film thicknesses. 

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