Pressure, capillary

When two immiscible fluids (or a fluid and a gas) are in contact, molecular attractions between similar molecules in each fluid are greater than the attractions between the different molecules of the two fluids and a clearly defined interface exists between them. The force that acts on this interface is called interfacial tension (or surface tension in case of a gas-fluid contact). As a result of this force, a pressure difference exists across the interface. This pressure difference is known as capillary pressure and is given by the following equation (Dake, 1978)  

When an immiscible fluid or a gas is completely immersed in another fluid it assumes a spherical shape of minimum surface area. The curvature of the interface is spherical and (l/r + l/rg) in Equation 4.12 can be replaced by 2/r  

When two immiscible fluids are in contact with a rock surface, the capillary pressure is also influenced by the wettability of the rock. The wettability of a 

The displacement pressure is a rock property and is defined as the force required to replace water from a cylindrical pore with oil or gas. Hence the displacement pressure determines the minimum buoyancy pressure needed for migration. 

Secondary hydrocarbon migration generally occurs through water-saturated sedimentary rocks, i.e. through rocks that are water-wet. As water is generally considered a perfect wetting fluid (Schowalter, 1979), the contact angle 0 in Equation 4.14 for hydrocarbon-water-rock systems can be taken to be zero. If, in addition, the hydrocarbon-water interface is assumed to be spherical, then Equation 4.14 becomes identical with Equation 4.13. 

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Notice that the capillary pressure is greater for smaller capillaries (or throat sizes), and that when the capillary has an infinite radius, as on the outside of the capillaries in the tray of water, P, is zero. 

Inside the capillary tube, the capillary pressure (P ) is the pressure difference between the oil phase pressure (PJ and the water phase pressure (P ) at the interface between the oil and the water. 

The capillary pressure can be related to the height of the interface above the level at which the capillary pressure is zero (called the free water level) by using the hydrostatic pressure equation. Assuming the pressure at the free water level is PI ... 

This is consistent with the observation that the largest difference between the oil-water interface and the free water level (FWL) occurs in the narrowest capillaries, where the capillary pressure is greatest. In the tighter reservoir rocks, which contain the narrower capillaries, the difference between the oil-water interface and the FWL is larger. 

If a pressure measuring device were run inside the capillary, an oil gradient would be measured in the oil column. A pressure discontinuity would be apparent across the interface (the difference being the capillary pressure), and a water gradient would be measured below the interface. If the device also measured resistivity, a contact would be determined at this interface, and would be described as the oil-water contact (OWC). Note that if oil and water pressure measurements alone were used to construct a pressure-depth plot, and the gradient intercept technigue was used to determine an interface, it is the free water level which would be determined, not the OWC. 

Let us consider one more physical phenomenon, which can influence upon PT sensitivity and efficiency. There is a process of liquid s penetration inside a capillary, physical nature of that is not obvious up to present time. Let us consider one-side-closed conical capillary immersed in a liquid. If a liquid wets capillary wall, it flows towards cannel s top due to capillary pressure pc. This process is very fast and capillary imbibition stage is going on until the liquid fills the channel up to the depth l , which corresponds the equality pcm = (Pc + Pa), where pa - atmospheric pressure and pcm - the pressure of compressed air blocked in the channel. 

If the solid in question is available only as a finely divided powder, it may be compressed into a porous plug so that the capillary pressure required to pass a nonwetting liquid can be measured [117]. If the porous plug can be regarded as a bundle of capillaries of average radius r, then from the Laplace equation (II-7) it follows that... 

Bartell and co-workers report the following capillary pressure data in porous plug experiments using powdered carbon. Benzene, which wets carbon, showed a capillary pressure of 6200 g/cm. For water, the pressure was 12,000 g/cm, and for ben-... 

Capillary pressure gradients and Marongoni flow induce flow in porous media comprising glass beads or sand particles [40-42], Wetting and spreading processes are an important consideration in the development of inkjet inks and paper or transparency media [43] see the article by Marmur [44] for analysis of capillary penetration in this context. 

The key to understanding dewatering by air displacement is the capillary pressure diagram. Figure 6 presents an example typical for a fine coal suspension there is a minimum moisture content, about 12%, called irreducible saturation, which cannot be removed by air displacement at any pressure and a threshold pressure, about 13 kPa. 

Fig. 6. Typical capillary pressure curves in air displacement cake dewatering of a fine coal suspension at varying dewatering times from top curve down the...

The capillary retention forces in the pores of the filter cake are affected by the size and size range of the particles forming the cake, and by the way the particles have been deposited when the cake was formed. There is no fundamental relation to allow the prediction of cake permeabiUty but, for the sake of the order-of-magnitude estimates, the pore size in the cake may be taken loosely as though it were a cylinder which would just pass between three touching, monosized spheres. If dis the diameter of the spherical particles, the cylinder radius would be 0.0825 d. The capillary pressure of 100 kPa (1 bar) corresponds to d of 17.6 pm, given that the surface tension of water at 20°C is 12.1 b mN /m (= dyn/cm). 

The cross-sectional area of the wick is deterrnined by the required Hquid flow rate and the specific properties of capillary pressure and viscous drag. The mass flow rate is equal to the desired heat-transfer rate divided by the latent heat of vaporization of the fluid. Thus the transfer of 2260 W requires a Hquid (H2O) flow of 1 cm /s at 100°C. Because of porous character, wicks are relatively poor thermal conductors. Radial heat flow through the wick is often the dominant source of temperature loss in a heat pipe therefore, the wick thickness tends to be constrained and rarely exceeds 3 mm. 

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. 

If the driving pressure is taken to be the capillary pressure, 2yivCOS0/r, Eq. 23 may be integrated, assuming 9 and r] are constant to give the Washburn equation [43] which shows the penetration jCt is proportional to the square root of time t... 

Heterogeneity, nonuniformity and anisotropy are terms which are defined in the volume-average sense. They may be defined at the level of Darcy s law in terms of permeability. Permeability, however, is more sensitive to conductance, mixing and capillary pressure than to porosity. 

Coimectivity is a term that describes the arrangement and number of pore coimections. For monosize pores, coimectivity is the average number of pores per junction. The term represents a macroscopic measure of the number of pores at a junction. Connectivity correlates with permeability, but caimot be used alone to predict permeability except in certain limiting cases. Difficulties in conceptual simplifications result from replacing the real porous medium with macroscopic parameters that are averages and that relate to some idealized model of the medium. Tortuosity and connectivity are different features of the pore structure and are useful to interpret macroscopic flow properties, such as permeability, capillary pressure and dispersion. 

Lampinen, M. J. and Toivonen, K., Application of a Thermodynamic Theory to Determine Capillary Pressure and Other Fundamental Material Properties Affecting the Drying Process, DRYING 84, Springer-Verlag, 228-244, 1984. 

Kapiilar-analyse, /. capillary analysis, -an-ziehung, /. capillary attraction, -chemie, /. capillary chemistry, -druck, m. capillary pressure. 

The design factors to prevent blocking involve the use of low-viscosity fluids with minimum interfacial tension, minimum capillary pressure, and minimal fluid loss. 

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. 

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