Pressure correction

The properties of real gases and liquids under pressure are calculated by adding a pressure correction to the properties determined for the ideal gas or the saturated liquid. 

Properties of mixtures as a real gas or as a liquid under pressure are determined starting from the properties of mixtures in the ideal gas state or saturated liquid after applying a pressure correction determined as a function of a property or a variable depending on pressure )... 

The specific heat of gases at constant pressure is calculated using the principle of corresponding states. The for a mixture in the gaseous state is equal to the sum of the C g of the ideal gas and a pressure correction term ... 

Expected errors for this method are 4-5 percent. At higher pressures, a pressure correction using Eq. (2-130) may be used. The mixture is treated as a hypothetical pure component with mixture critical properties obtained via Eqs. (2-5), (2-8), and (2-17) and with the molecular weight being mole-averaged. 

The average error in the pressure correction alone is typically 3 percent. 

Another pressure correction for percent loss can also be applied, as described in the ASTM test method. 

Consequently, as the inlet pressure increases, the mean flow rate will be reduced according to the pressure correction function and the expected decrease in elution rate will not be realized. Consider an open tubular column. 

Now, applying the pressure correction factor from chapter 2,... 

All relief valves are affected by reaching critical flow, which corre-spond.s to a back-pressure of about 50% of the set pressure. Pilot-operated relief valves can handle up to 50% back-pressure without any significant effect on valve capacity. Back-pressure correction factors can be obtained from the relief valve manufacturers for back-pre.ssures above 50%. API RP 520 gives a generic method for sizing a pilot-operated relief valve for sub-critical flow. 

T = flowing temperature, "R K(, = back-pressure correction factor... 

Kj = valve coefficient of discharge = 0.92 Pi = flowing pressure, psia MW = molecular weight of gas = 17,4 Z = compres-sibility factor = 0.9561 C = gas constant based on ratio of specific heats Cp/C T = flowing temperature, R Kb = back-pressure correction factor... 

The point of all this is simply that we must not use the apparent plate height or the apparent plate number as performance criteria in the unified chromatography techniques on the justification that they already work well for LC and that they work well for GC when a pressure correction is applied. A considerable expansion of theory and an effective means for evaluating equations (7.4) or (7.5) are required first. Likewise, as we consider multidimensional chromatography involving techniques existing between the extremes of LC and GC, we must not build judgments of the multidimensional system on unsound measures of the individual techniques involved. 

Apply the tube size multiplier from table associated with Figure 10-108 and also the multiplier for pressure correction from Figure 10-109. Note that for high pressure systems a pressure can become quite large, and some designers limit it to an arbitrary value of about 3,000. 

Figure 10-109. Pressure correction factor. (Used by permission Chen, Ning Hsing. Chemical Engineering, V. 66, No. 5, 1959. McGraw-Hill, Inc. All rights reserved.)...

When a Mollier chart is available for the gas involved the first method, which is illustrated by Figure 12-12A is the most convenient. On the abscissa of Figure 12-12A four enthalpy differences are illustrated. (Hg — Hj) is the enthalpy difference for the isentropic path. (Hg — Hi°) is the ideal gas state enthalpy difference for the terminal temperatures of the isentropic path. The other AH values are the isothermal pressure corrections to the enthalpy at the terminal temperatures. A generalized chart for evaluating these pressure corrections was presented previously. 

Later, we will make equilibrium calculations that involve activities, and we will see why it is convenient to choose the ideal gas as a part of the standard state condition, even though it is a hypothetical state/ With this choice of standard state, equations (6.94) and (6.95) allow us to use pressures, corrected for non-ideality, for activities as we make equilibrium calculations for real gases.s... 

By demanding that the new velocity w field fulfils both the momentum and the mass conservation equation, the following equations for the velocity and pressure correction are derived ... 

A pressure correction scheme based on such an approximation is known as the SIMPLEC algorithm [89]. The SIMPLEC algorithm does not require under relaxation of the pressure correction, is efficient and has found widespread applications. 

The effect of pressure is negligible. These epithermal Au-Ag vein-type deposits have formed in a shallow and low-pressure environment and pressure correction, such that any correction to the homogenization temperatures will be small (probably less than 20°C). 

The good correlation between homogenization temperatures and electrum-sphalerite temperatures suggests several points (1) the uncertainties of electrum-sphalerite temperatures are less than 20° to 30°C, even at temperatures from ca. 180° to 300°C, (2) the electrum-sphalerite-pyrite-argentite assemblage was formed close to equilibrium in Japanese epithermal Au-Ag vein-type deposits, and (3) the pressure corrections to homogenization temperatures for Japanese epithermal Au-Ag vein-type deposits is small, less than 20°C to 30°C. 

Edmister (1948) published a generalised plot showing the isothermal pressure correction for real gases as a function of the reduced pressure and temperature. His chart, converted... 

As with materials of construction correction factors, the pressure correction factors in Table 2.5 are average and only approximate and will vary, amongst other things, according to the type of equipment. Finally, its operating temperature also influences equipment capital cost. This is caused by, amongst other factors, a decrease in the allowable stress for materials of construction as the temperature increases. Table 2.6 presents typical factors to account for the operating temperature. 

Fig. 1.30. Typical pressure correction for a Pirani gage for different gas species (courtesy of Alcatel).

By analysis and by measurement, we can determine H2 — H and express it in terms of values at 25 °C and 1 atm. Since Q is large for combustion reactions, these pressure corrections usually have a small effect on the accuracy of the heat of combustion determined in this way. 

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