Capillary pressure determination

Studies on displacement dynamics and interfacial tensions were carried out to establish and improve recovery efficiencies of acidic crudes by alkaline agents. Displacement tests were carried out on restored state oil-field cores and on synthetic Ottawa sand-packs with permeabilities ranging from 100 to 3,500 millidarcies. Concomitant experiments were carried out with a spinning-drop tensiometer and a contact angle goniometer capillary pressure-determined wettability indices were measured and the type and stability of emulsions were characterized. These experiments indicate that the recovery mechanisms cited in the literature are valid under specific conditions of pH, electrolyte type and con-... 

In this chapter we present a brief overview of the results obtained so far by the FTT with various oils and surfactants in relation to antifoaming. As shown here, the critical capillary pressure, determined in the FTT experiments, has a close relation to the actual process of foam destruction by oil drops. Several conclusions about the mechanism of antifoaming and the antifoam activity of the oils have been drawn and presented in quantitative terms by using the concept of the critical capillary pressure, P , and the FTT results. 

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. 

Important physical properties of catalysts include the particle size and shape, surface area, pore volume, pore size distribution, and strength to resist cmshing and abrasion. Measurements of catalyst physical properties (43) are routine and often automated. Pores with diameters <2.0 nm are called micropores those with diameters between 2.0 and 5.0 nm are called mesopores and those with diameters >5.0 nm are called macropores. Pore volumes and pore size distributions are measured by mercury penetration and by N2 adsorption. Mercury is forced into the pores under pressure entry into a pore is opposed by surface tension. For example, a pressure of about 71 MPa (700 atm) is required to fill a pore with a diameter of 10 nm. The amount of uptake as a function of pressure determines the pore size distribution of the larger pores (44). In complementary experiments, the sizes of the smallest pores (those 1 to 20 nm in diameter) are deterrnined by measurements characterizing desorption of N2 from the catalyst. The basis for the measurement is the capillary condensation that occurs in small pores at pressures less than the vapor pressure of the adsorbed nitrogen. The smaller the diameter of the pore, the greater the lowering of the vapor pressure of the Hquid in it. 

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. 

The present analysis is based on the assumption that the interfacial temperature is constant and the capillary pressure is determined by the following expression... 

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. 

In this section, we describe our experimental and analysis methods to determine spatially dependent porosity and saturation distributions, permeability functions and saturation-dependent multiphase flow properties the relative permeability and capillary pressure functions. 

Relative permeability and capillary pressure functions, collectively called multiphase flow functions, are required to describe the flow of two or more fluid phases through permeable media. These functions primarily depend on fluid saturation, although they also depend on the direction of saturation change, and in the case of relative permeabilities, the capillary number (or ratio of capillary forces to viscous forces). Dynamic experiments are used to determine these properties [32]. 

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. 

While capillary pressure can be determined independently through experiments implementing a series of equilibrium states, this can be very time consuming, particularly if the entire capillary pressure function is to be reconciled. Furthermore, as there can be difficulties in re-establishing identical states of initial saturation, it is most desirable to determine capillary pressure and relative permeability functions simultaneously, from the same experiment. 

We present a general approach for estimating relative permeability and capillary pressure functions from displacement experiments. The accuracy with which these functions are estimated will depend on the information content of the measurements, and hence on the experimental design. We determine measures of the accuracy with which the functions are estimated, and use these measures to evaluate different experimental designs. In addition to data measured during conventional displacement experiments, we show that the use of multiple injection rates and saturation distributions measured with MRI can substantially increase the accuracy of estimates of multiphase flow functions. 

Figure 15.7 Starling principle a summary of forces determining the bulk flow of fluid across the wall of a capillary. Hydrostatic forces include capillary pressure (Pc) and interstitial fluid pressure (PJ. Capillary pressure pushes fluid out of the capillary. Interstitial fluid pressure is negative and acts as a suction pulling fluid out of the capillary. Osmotic forces include plasma colloid osmotic pressure (np) and interstitial fluid colloid osmotic pressure (n,). These forces are caused by proteins that pull fluid toward them. The sum of these four forces results in net filtration of fluid at the arteriolar end of the capillary (where Pc is high) and net reabsorption of fluid at the venular end of the capillary (where Pc is low).

Glomerular capillary pressure is determined primarily by renal blood flow (RBF). As RBF increases, PGC and therefore GFR increase. On the other hand, as RBF decreases, PGC and GFR decrease. Renal blood flow is determined by mean arterial pressure (MAP) and the resistance of the afferent arteriole (aff art) ... 

Pressure regulator. The split inlet is back pressure regulated to ensure a constant head pressure, therefore, a steady flow through the column. For capillary columns, the inlet pressure determines the column flow, as per Eq. (14.11). As the inlet operates, the split vent can be opened or closed or upstream gas flow may change the regulator maintains the desired pressure, therefore the desired column flow. 

The behavior of solids is, of course, quite different. Their present shape and their internal stresses and strains greatly depend on their pre-treatment. Thus we can measure the capillary pressure existing in a given liquid sample simply by measuring the shape of the sample in an external force field, such as one due to gravitation but a determination of the capillary pressure in a solid is an almost impossible task. Chapter III deals with this difficulty. 

The determination of the capillary pressure of a diffusion layer is critical, not only to have a better understanding of the mass transport mechanisms inside DLs but also to improve their design. In addition, the accuracy of mafhemafical models can be increased with the use of experimental data obtained through reliable techniques. Both Gostick et al. [196] and Kumbur et al. [199] described and used the MSP method in detail to determine the capillary pressures of differenf carbon fiber paper and carbon cloth DLs as a function of the nonwetting phase saturation. Please refer to the previous subsection and these publications for more information regarding how the capillary pressures were determined. 

Nguyen et al. [205] designed a volume displacement technique that was used to measure the capillary pressures for both hydrophobic and hydrophilic materials. One requirement for this method is that the sample material must have enough pore volume to be able to measure the respective displaced volume. Basically, while the sample is filled wifh water and then drained, the volume of water displaced is recorded. In order for the water to be drained from fhe material, it is vital to keep the liquid pressure higher than the gas pressure (i.e., pressure difference is key). Once the sample is saturated, the liquid pressure can be reduced slightly in order for the water to drain. From these tests, plots of capillary pressure versus water saturation corresponding to both imbibitions and drainages can be determined. A similar method was presented by Koido, Furusawa, and Moriyama [206], except they studied only the liquid water imbibition with different diffusion layers. 

Upon capillary condensation of water in PEMs, the relative humidity, f /P, determines capillary pressure, P , and capillary radius, via the Kelvin-Laplace equation ... 

The corresponding capillary pressure, P% Equation (6.11), and the external gas pressure, Ps, determine the liquid pressure, P via Equation (6.14). 

The quality of the support is especially critical if the formation of the top layer is mainly determined by capillary action on the support (see Section 2.3.2). Then, besides a narrow pore size distribution the wettability of the support system plays a role (see Equation 2.1). An example of the synthesis of a two-layer support and ultrafUtration membrane is given in the French Patent 2,463,636 (Auriol and Trittcn 1973). In many cases an intermediate layer, whose pore sizes and thickness lie between those of the main support and the top layer (see Figure 2.2), is used. This intermediate layer can be used to improve the quality of the support system. If large capillary pressures are used to form such an intermediate layer, defects (pinholes) in the support will be transferred to this layer. This can be avoided by decreasing the acting capillary pressures or even by eliminating them. This can be done in several ways. 

To determine the saturation for any of the models, the capillary pressure must be known at every position within a diffusion medium. Hence, the two-phase models must determine the gas and liquid pressure profiles. In typical two-phase flow in porous media, the movement of both liquid and gas is determined by Darcy s law for each phase and eq 47 relates the two pressures to each other. Many models utilize the capillary pressure functionality as the driving force for the liquid-water flow... 

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