Corrections for compressibility

In order to calculate the true volume intrusion of mercury into the pores of a sample, a correction must be made to account for the compression of mercury, sample cell and sample [69]. The usual procedure is to carry out a blank experiment in the absence of a sample or with a non-porous sample [70]. During the course of calibration measurements on non-porous nylon it was found that a normal blank correction procedure led to erroneous mercury penetration volumes [71]. In particular it was found that the shape of the intrusion curve varied with the size of the sample. 

On Ailing the cell with mercury, a near-complete All is achieved, Vi-AVi. Using a mercury follower (i.e. an automatic calibrated screw probe moves down to die mercury surface where it short circuits and stops a digital counter measuring the probe movement) the small unAlled volume AVi is given by  

The true blank correction J = h-H where h is the probe count at pressure p is given by  

The Arst term accounts for the incompleteness of All ai the change in the cell factor with pressure and the second term the net compression. 

If a non-porous material of mass m, density p, and volume V at zero pressure and Vft at pressure p, is incorporated into the cell, the intrusion at pressure p is given by  

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Corrections for compressibility (Z) may be incorporated as described for the single-stage cylinder, handling this on a per-cylinder basis. 

If the capillary rheometer is used to compare different polymers, it is not necessary to go through the various correction procedures. However, if one wants to know the absolute values of the viscosity, it is important to apply the various correction factors. The most important corrections are the correction of the shear rate for non-Newtonian fluid behavior (often referred to as Rabinowitsch correction) and the correction of the shear stress for entrance effects (often referred to as Bagley correction). These are the most common corrections applied to capillary rheometers. Other corrections that are sometimes considered are corrections for viscous heating, corrections for the effect of pressure on viscosity, corrections for compressibility, correction for time effects, etc. If many corrections are applied to the data, the whole measurement and data analysis procedure can become very complex and time consuming. 

FIGURE 6 (E/N) m versus pressure P, corrected for compressibility, for SFe and l-CsFe the various symbols refer to measurements of different authors. [From Christophorou, L. G. (ed.). (1982). Gaseous Dielectrics III, Pergamon Press, New York Christophorou, L. G., and pace, M. O. (eds.). (1984). Gaseous Dielectrics IV, Pergamon Press, New York.]... 

Fig. 4.9 Pressurizing curve for nylon. Ouncorrected curve, corrected by a blank run [Equation (4.6)], corrected for compressibility of mercury and glass [Equation (4.7)], corrected for compressibility of mercury, glass and sample [Equation (4.9)].

For increased accuracy, a correction for pressure change can be made. Note that the number of moles of water vapor per mole of air (the mixing ratio of water vapor) must be constant during the descent of the air. However, as the pressure of the air increases, the partial pressure of water vapor increases in the same proportion. From Table 4.1, the air pressure at 4000 ft is approximately 0.89 atm at 1000 ft, it is approximately 0.97 atm. The partial pressure of water vapor can be corrected for compression during descent ... 

P(Pq. Tq) is the crude oil density at standard conditions, that is, 14.7 psia and 60°F Ap is the density correction for compressibility of oils (psia)... 

A key limitation of sizing Eq. (8-109) is the limitation to incompressible flmds. For gases and vapors, density is dependent on pressure. For convenience, compressible fluids are often assumed to follow the ideal-gas-law model. Deviations from ideal behavior are corrected for, to first order, with nommity values of compressibihty factor Z. (See Sec. 2, Thvsical and Chemical Data, for definitions and data for common fluids.) For compressible fluids... 

Liquids have relatively low compressibility compared with gases and, thus, the mobile phase velocity is sensibly constant throughout the column. As a consequence, elution volumes measured at the column exit can be used to obtain retention volume data and, unless extreme accuracy is required for special applications, there is no need for the retention volume to be corrected for pressure effects. 

Since non-ideal gases do not obey the ideal gas law (i.e., PV = nRT), corrections for nonideality must be made using an equation of state such as the Van der Waals or Redlich-Kwong equations. This process involves complex analytical expressions. Another method for a nonideal gas situation is the use of the compressibility factor Z, where Z equals PV/nRT. Of the analytical methods available for calculation of Z, the most compact one is obtained from the Redlich-Kwong equation of state. The working equations are listed below ... 

Note Once again the strain is less than 0.5% so no correction is needed for compressive loading). 

Table 2-12A is convenient for most air problems, noting that both free air (60°F and 14.7 psia) and compressed air at 100 psig and 60°F are indicated. The corrections for other temperatures and pressures are also indicated. Figure 2-37 is useful for quick checking. However, its values are slightly higher (about 10 percent) than the rational values of Table 2-11, above about 1000 cfm of free air. Use for estimating only. 

The Bureau of Mines report states that minor corrections for bends, tees, and even compressibility are unnecessary due to the greater uncertainties in actual line conditions. Their checks with the Weymouth relation omitted these corrections. The relation with pres-... 

Meters are accurate within close limits as legislation demands. However, gas is metered on a volume basis rather than a mass basis and is thus subject to variation with temperature and pressure. The Imperial Standard Conditions are 60°F, 30inHg, saturated (15.56°C, 1913.7405 mbar, saturated). Gas Tariff sales are not normally corrected, but sales on a contract basis are. Correction may be for pressure only on a fixed factor basis based on Boyle s Law or, for larger loads, over 190,000 therms per annum for both temperature and pressure using electronic (formerly mechanical) correctors. For high pressures, the compressibility factor Z may also be relevant. The current generation of correctors corrects for pressure on an absolute basis taking into account barometric pressure. 

In addition, the compression ratio has increased considerably and there must be a correction for loss of volumetric efficiency. 

An application of Eq. (19) is shown in Fig. 4, which gives the solubility of solid naphthalene in compressed ethylene at three temperatures slightly above the critical temperature of ethylene. The curves were calculated from the equilibrium relation given in Eq. (12). Also shown are the experimental solubility data of Diepen and Scheffer (D4, D5) and calculated results based on the ideal-gas assumption (ordinate scale is logarithmic and it is evident that very large errors are incurred when corrections for gas-phase nonideality are neglected. 

The release of steroids such as progesterone from films of PCL and its copolymers with lactic acid has been shown to be rapid (Fig. 10) and to exhibit the expected (time)l/2 kinetics when corrected for the contribution of an aqueous boundary layer (68). The kinetics were consistent with phase separation of the steroid in the polymer and a Fickian diffusion process. The release rates, reflecting the permeability coefficient, depended on the method of film preparation and were greater with compression molded films than solution cast films. In vivo release rates from films implanted in rabbits was very rapid, being essentially identical to the rate of excretion of a bolus injection of progesterone, i. e., the rate of excretion rather than the rate of release from the polymer was rate determining. 

Corrected Retention Volume V, Retention volume corrected for mobile phase compressibility V,- jv. 

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