Pressure saturation curve

To use Equation 6.4, one must measure or calculate hc dr for a given aquifer material. A mathematical formula for the water pressure-saturation curve during drainage is needed to calculate the average water pressure head. The Brooks-Corey model of the drainage curve can be used as follows (Corey, 1986) ... 

Equation (46) assumes that the liquid is uniformly distributed in the agglomerate. The product can be calculated from the capillary pressure/saturation curve (Figure 64(b)). 

Figure 5. (a) Primary drainage and (b) primary imbibition two-phase (water/PCE) capillary pressure-saturation curves for water-, intermediate-, and... 

Modified Leverett Function Appropriate for Fuel Cell Media The standard Leverett function has been found to be appropriate for qualitative matching of the flow characteristics through the media however, actual measurements of PEFC diffusion media show different quantitative behavior. Kumbur et al. [47] presented a modified Leverett function appropriate for thin-film fuel cell DM to estimate the capillary pressure as a function of liquid saturation and hydrophobic additive content This empirical fit was derived from the direct measurement of capillary pressure-saturation for different types of DMs (cloth and paper) with PTFE content ranging from 0 to 20% of weight and a nnicrop-orous layer. Figure 5.35 depicts the measured capillary pressure (Pc) versus nonwetting liquid saturation for carbon paper DM tailored with 20% PTFE content. The nature of the capillary pressure-saturation curves exhibits a continuous S shape, rather than J shape, and yields four inflection points. For saturation leads under 0.5, the capillary pressure in the DM was fit to a modified Leverett function, appropriate for the hydrophobic pores ... 

Two additional illustrations are given in Figures 6 and 7 which show fugacity coefficients for two binary systems along the vapor-liquid saturation curve at a total pressure of 1 atm. These results are based on the chemical theory of vapor-phase imperfection and on experimental vapor-liquid equilibrium data for the binary systems. In the system formic acid (1) - acetic acid (2), <() (for y = 1) is lower than formic acid at 100.5°C has a stronger tendency to dimerize than does acetic acid at 118.2°C. Since strong dimerization occurs between all three possible pairs, (fij and not... 

This equation follows from equation 66, because vaporization occurs at the constant pressure Moreover, the heat of vaporization is related to the slope of the vapor—Hquid saturation curve through the Clapeyron equation ... 

Next we draw the saturation curve in the hj -x coordinate system. Vapor pressures can be calculated with Eqs. (4.106) and (4.108) or taken directly from the tables. The humidity x corresponding to the saturation pressure pi,(t) is calculated with Eq. (4.83) noting that p = 0.875 bar. The enthalpy of humid saturated air is calculated with Eq. (4.94) ... 

The total pressure thus has no importance. If this result is. sought from a Mollier diagram by finding the intersection of the humidity line (jr = humidity of air = constant) and the saturation curve, which gives the dewpoint temperature, a diagram constructed for a pressure of 9.S0 mbar should be used. A decent ap-proximation can be found from a diagram constructed for pressure p 1 bar. 

If, instead, the air is damped adiabatically with the wet cloth, so that the state of the air varies, the cloth will settle to a slightly different temperature. Each state of air (0, x) is represented by a certain wet bulb temperature 6, which can be calculated from Eq. (4.116) or its approximation (4.123), when the partial pressures of water vapor are low compared with the total pressure. When the state of air reaches the saturation curve, we have an interesting special case. Now the temperatures of the airflow and the cloth are identical. This equilibrium temperature is called the adiabatic cooling border or the thermodynamic wet bulb temperature (6 ). 

Eable 4.7)Draw in the Mollier diagram at the 14 °C point of the saturation curve (a) the state change line of the adiabatic humidification and (b) an auxiliary line, associated with the wet bulb temperature measurement, by means of which the state can be defined. The pressure of air is p = 1 bar. 

In this form, Alhas the units of torr.) The relationship defined by Equation (A15.4) plots as a hyperbola. That is, the MbOg saturation curve resembles an enzyme substrate saturation curve. For myoglobin, a partial pressure of 1 torr for jbOg is sufficient for half-saturation (Figure A15.1). We can define as the partial pressure of Og at which 50% of the myoglobin molecules have a molecule of Og bound (that is, F= 0.5), then... 

It is difficult to measure partial molar volumes, and, unfortunately, many experimental studies of high-pressure vapor-liquid equilibria report no volumetric data at all more often than not, experimental measurements are confined to total pressure, temperature, and phase compositions. Even in those cases where liquid densities are measured along the saturation curve, there is a fundamental difficulty in calculating partial molar volumes as indicated by... 

The different capillary pressure, saturation, and permeability relationships of the different models can be compared. To do this, the effective permeabilities from some of the different models are plotted as a function of the capillary pressure in Figure 8. In the figure, the capillary pressure at which the effective permeability no longer changes is where the medium is fully saturated. Also, the values of the effective permeability are dependent on the diffusion media being tested. Furthermore, the value of the effective permeability at the right end of the curves corresponds to the saturated permeability, except for the model of Weber and Newman, who use a gas-phase residual saturation. 

Within the PV region delimited by the two saturation boundary curves, liquid and vapor phases coexist stably at equilibrium. To the right of the vapor saturation curve, only vapor is present to the left of the liquid saturation curve, vapor is absent. Let us imagine inducing isothermal compression in a system composed of pure H2O at T = 350 °C, starting from an initial pressure of 140 bar. The H2O will initially be in the gaseous state up to P < 166 bar. At P = 166 bar, we reach the vapor saturation curve and the liquid phase begins to form. Any further... 

Binding of O2 to one of the subunits of the T form leads to a local conformational change that weakens the association between the subunits. Increasing O2 partial pressure thus means that more and more molecules convert to the higher-af nity R form. This cooperative interaction between the subunits increases the O2 af nity of Hb with increasing O2 concentrations—i. e., the O2 saturation curve is sigmoidal (see p. 282). 

Phase diagram for hydrogen, showing the conditions under which hydrogen changes from molecular (H2) to metallic (H+). Below the gray He saturation curves, He and H are immiscible. Adiabats for Jupiter and Saturn cross the saturation curve once H becomes metallic, but the Uranus (and presumably Neptune) adiabats do not reach such high pressures. 

For continuous systems, molar flow rates Q can be used instead of n. The thermodynamic activity (ax) can be calculated according to Equation 2, but requires knowledge of the saturation pressure of the pure compound (Ppsatx). This data can be obtained from the saturation curves (vapor-liquid equilibrium curves) and is taken at the working temperature of the gas stream. The thermodynamic activity is then calculated using the following equation ... 

Elevation can also play a role, for at reduced atmospheric pressure the saturation curve will be higher. This causes an increase in the potential and... 

The Clapeyron equation is most often used to represent the relationship between the temperature dependence of a pure liquid s vapor pressure curve and its latent heat of vaporization. In this case, dPat/dT is the slope of the vapor pressure—temperature curve, A His the difference between the volume of the saturated vapor, H, and the saturated liquid, and AEFap is the latent heat of vaporization. Commonly, T) is small in comparison to V and the ideal gas law is assumed for the vapor phase. 

The liquid solvent is in equilibrium with its vapour alone along the saturation curve (denoted by subscript a), but when an external pressure is imposed, the liquid boils only when its vapour pressure equals the external pressure. The normal boiling point, 7 b, is reached at standard atmospheric pressure,... 

VL(L) E measurements for binaries involving water with alcohol and acid have been done, as described elsewhere [2]. Figure 8.6 presents experimental vapor pressure data for 2-ethylhexyl laurate. The normal boiling point (nbp) is 607.6 K, close to the prediction by Gani s method. On the other hand, the prediction of the whole saturation curve by Riedel s method (noted estimation in Figure 8.6) is in large error at lower pressures. This fact can affect the accuracy of chemical equilibrium calculation, but fortunately the errors compensate each other [2]. 

The clearest results were obtained with the normal, saturated fatty acids and alcohols. These formed stable films, which would stand considerable compression laterally, and (at room temperature on distilled water) gave a very clearly marked critical area at which the surface pressure first appeared, this point being of course Pockels s critical point of the first diminution of surface tension. As the area was reduced from large initial areas no surface pressure could be detected until the area had reached about 22 sq. A. per molecule and at 20 5 sq. A. the pressure increased very rapidly indeed with further increase of pressure. The curve I of Fig. 15 shows the relation between surface pressure and area per molecule, which is obtained with accurate apparatus for the fatty acids on water curve III is that obtained with the alcohols.3... 

Thus, project along the 100-psia (689.5-kPa) pressure curve until it intersects the saturation curve, point g. From here project horizontally to the left-hand scale and read the enthalpy of 100-psia (689.5-kPa) saturated steam as 1187 Btu/lb (2761.0 kJ/kg). (The Mollier diagram in Fig. 19.1 has fewer grid divisions than large-scale diagrams to permit easier location of the major elements of the diagram.)... 

Determine the vapor properties in the final state. Sketch the process on P-V, H-S, or T-S diagrams (Fig. 19.6). Note that the expanded steam is wet in the final state because the 2-psia (13.9-kPa) pressure line is under the saturation curve on the H-S and T-S diagrams. Therefore, the vapor properties in the final state must be corrected for the moisture content. However, the actual final enthalpy cannot be determined until after the expansion efficiency (Hi — H2)/(Hi — H2s) is evaluated. 

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