Equation experimental pressures

Vugacity Coefficients. An exact equation that is widely used for the calculation of fugacity coefficients and fugacities from experimental pressure—volume—temperature (PVT) data is... 

If the experimental values P and w are closely reproduced by the correlating equation for g, then these residues, evaluated at the experimental values of X, scatter about zero. This is the result obtained when the data are thermodynamically consistent. When they are not, these residuals do not scatter about zero, and the correlation for g does not properly reproduce the experimental values P and y . Such a correlation is, in fact, unnecessarily divergent. An alternative is to process just the P-X data this is possible because the P-x -y data set includes more information than necessary. Assuming that the correlating equation is appropriate to the data, one merely searches for values of the parameters Ot, b, and so on, that yield pressures by Eq. (4-295) that are as close as possible to the measured values. The usual procedure is to minimize the sum of squares of the residuals 6P. Known as Barkers method Austral. ]. Chem., 6, pp. 207-210 [1953]), it provides the best possible fit of the experimental pressures. When the experimental data do not satisfy the Gibbs/Duhem equation, it cannot precisely represent the experimental y values however, it provides a better fit than does the procedure that minimizes the sum of the squares of the 6g residuals. 

There are few reported comparisons to experimental pressure drop data taken by the same workers. An exception is Calis et al. (2001) who compared CFD, the Ergun correlation and experimental data for N — 1-2. They found 10% error between CFD and experimental friction factors, but the Ergun equation... 

Milton et al. [1.136] used this methods and refer to it as manometric temperature measurement. They used times of pressure rises of up to 30 s. During this time, the ice temperature will increase, mainly due to continued heat flow. Therefore, an equation has been developed to transform the experimental pressure data, including three other corrections, into the true vapor pressure of the ice. If the valve is closed for only a very short time, < 3 s, and the pressure is measured and documented 60 to 100 times/s, these data can be recorded as shown in Fig. 1.78.1. The automatic pressure rise measurements (1) can then be plotted... 

There is evidence in the work reported in Chapter 5 on sedimentation 5) to suggest that where the particles are free to adjust their orientations with respect to one another and to the fluid, as in sedimentation and fluidisation, the equations for pressure drop in fixed beds overestimate the values where the particles can choose their orientation. A value of 3.36 rather than 5 for the Carman-Kozeny constant is in closer accord with experimental data. The coefficient in equation 6.3 then takes on the higher value of 0.0089. The experimental evidence is limited to a few measurements however and equation 6.3, with its possible inaccuracies, is used here. 

This equation can be derived by supposing that the wall is in contact with liquid only, and that shearing forces are equal at the gas-liquid interface. Experimental pressure drops were predicted to +50% to —30% on the average, although larger individual variations existed. An attempt was made by Marchaterre (Ml) to refine this method by expressing the mechanical-energy balance in terms of... 

The IBM machines were used to set up the Antoine constants from determined data. A preliminary C value was obtained from the equation C = 239. — 0.19 /,. A and B were then obtained and new C values either side of the first C used and new A and B values found. In each case above, the boiling points at the experimental pressures were calculated and compared with the determined boiling points. 

In Equations 3.7a and b, Ag4 is the isothermal compression of hydrate from equilibrium to experimental pressure, in which the hydrate is assumed incompressible. 

In this latter equation, Pq is the reference pressure and P is the experimental pressure. Obviously, Eq. (8.41) reduces to the WLF equation when P = Pq. 

Calculation of the entropy of a perfect gas. The calculation of w in terms of quantities which can be measured experimentally (pressure, volume, temperature), and of the number and mass of the molecules, is accompanied in the general case by very serious difl culties. For a perfect monatomic gas Boltzmann has succeeded in solving the problem, thus calculating the entropy S. For a perfect monatomic gas he deduces from equation (1) the expression t... 

This equation was first deduced by Nernst in a different manner. Bose confirmed the equation experimentally for the special case of rectihnear vapour pressure curves, f In this case the left-hand side of the equation becomes... 

In bubbling fluidized beds under ambient pressure and low gas velocity conditions where the bubble size increases with the gas velocity, the bubble size may be estimated by various correlation equations, such as those developed by Mori and Wen, Barton et al., ° and Cai et al. There is a similarity in the rise behavior of a single bubble in gas-solid and liquid media. The rise velocity of a single spherical cap bubble in an infinite liquid medium can be described by the Davies and Taylor equation. Experimental results indicate that the Davies and Taylor equation is valid for large bubbles with bubble Reynolds numbers greater than Whereas for bubbles in fluidized... 

Equation (288) results in a straight line when P is plotted against T, which fits the experimental pressure-temperature data usually obtained during melting of solids or freezing of liquids. 

Equation (1.11) is the definition of the Kelvin temperature scale from the experimental pressure-volume properties of a real gas. 

Figure 20 shows the calculated pressure drop factor and the experimental values. We observe that the model of Liu et al. (32) predicts the experimental pressure drop both in the Darcy s flow regime, the transition, and the Forchheimer regimes. The two-dimensional model gives a much better prediction than that using the one-dimensional model. The Ergun equation significantly overpredicts the experimental data. 

Water Solute in Hydrocarbon-Rich Vapor and Liquid. The pure component parameters of water solute AP(TC) and a were determined by using Equations 5 and 16 to fit the gas-phase volumetric properties of steam (5) and the second virial cross coefficients of steam and light gases such as methane, ethane, and nitrogen (6). The least-squares minimization technique was used to find the parameters that gave the minimum deviations between calculated and experimental pressures and second virial cross coefficients. (Table I lists the parameters for pure steam and of other compounds used in this study.)... 

The number of moles of the reagents, the product and the catalyst were obtained from amounts added and the yield measurements. The number of moles of CO2 was obtained by increasing the value used until the pressure calculated from the P-R equation in a 20 mL cell equalled the experimental pressure. At pressures below 100.6 bar, the calculation showed the presence of two phases. Experimentally the existence of two phases was observed at 106 bar and 109 bar. Thus predicted and observed phase behaviour did not exactly agree, but there was approximate agreement. 

For a given experimental pressure (or corresponding reduced pressure) and introducing the explicit expressions for the two free-energy derivatives, a partial differential equation for y ensues. Its solution provides the E T dependence of the free volume. It will be noted that y does not freeze at Tg but only exhibits a reduced temperature coefficient [McKinney and Simha, 1976]. In subsequent discussion, as in most applications, an approximation has been used that avoids the complications attendant on to Eq. (4.2a). That is, the first term on the right-hand side has been used together with an experimental pressure to solve for y as an adjustable quantity. A comparison with the result obtained from the full Eq. (4.2a) for the case of two poly(vinyl acetate) (PVAc) glasses shows this to be an acceptable approximation not too far below Tg. 

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