Data at higher pressures

In this section we will discuss only the effect of pressure on solid phases, i.e., minerals. The evaluation of the pressure integral is done in quite a different way for gases, water, and aqueous solutes, and will be treated in later chapters. 

As shown previously (Equation 4.43), the derivative of G with respect to P is V, i.e.. 

When substance i is a solid phase and thus has relatively small variation of V with both P and T (relative that is to liquids and gases), the errors introduced by the assumption that V is not affected by P or r tend to cancel one another, and very little error is introduced by assuming that V, is a constant at all P, T values. As a result, the assumption of constant V for solids is often adopted for minerals, and results in 

If we are dealing with a mineral reaction (that is, a reaction involving only solid phases for which (4.43) is valid) instead of a pure compound, we substitute A. Af for AJ-, and A,b, and A,c for and c where A,a, etc. are the usual product-reactant terms, just as we did in Equation (5.30). Equation (5.33) then becomes 

Alternatively, some attempt at modeling the temperature and pressure effects on mineral volumes can be attempted (see Helgeson et al., 1978, and Berman, 1988 for lengthy discussions of this topic). The only attempt at this to find its way into a widely used database is that of Berman (1988). Berman fit the available data for rock-forming minerals to the expression 

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Reference data for the adsorption of benzene, dichloromethane and methanol have been used to construct as plots for the adsorption of these vapoius on Carbosieve, Takeda molecular sieve carbons, Maxsorb superactivated carbons and a charcoal cloth. It is shown that the as method can give satisfactory results when applied to organic adsorptives provided that good quality adsorption data at higher pressures is available. It is also shown how analysis of the as plots can lead to useful information about the pore structure of the different types of carbon, and some of the difficulties associated with the use of nitrogen adsorption at 77K for the characterisation of microporous carbons are discussed. 

Fig. 6 includes full-scale capacify dafa for 3, 4, and 6 in. caps at low pressure obtained by FRI and by Shell for 6 in. caps only (Fractionation Research, Tulsa, Oklahoma, U.S.A., private communication). Both sets of data for 6 in. caps show a capacity deficit compared to the smaller caps however, the Shell data show approximately 80% of the capacity found by FRI. The difference may be caused by system properties or by the more conservative definition of flood point used by Shell. Data at higher pressure with the butane-isobutane system at the 4 ft diameter were also obtained by FRI (Fig. 8). 

COMMENT. It is unlikely that low-pressure data can be used to obtain an accurate value of the volume corresponding to complete coverage. See Problem 25,6 for adsorption data at higher pressures,... 

UCST and LCST values depend somewhat on pressure. LCST values in the table are usually given at the vapor pressure of the solvent at this temperature. UCST values are measured in most cases at normal pressure data at higher pressures are neglected here. The interested reader can find such information, for example, in Refs. 76, 84,104,157, 165, 177,185-187, or 192. 

For the flux data (Fig. 4.5 A, A ), the calculated values correspond better with the experimental data at higher pressures. When activity coefficients are taken as unity, the model predicts almost no flux at pressures lower than 8 bar for... 

Because of the vast amount of data on refractive indices, in comparison to the former collection in the Landolt-Bornstein series a specialization for this new volume was necessary. Only data for pure liquids and binary liquid mixtures at normal pressure (sometimes at the saturation vapour pressure) were taken into account. In some cases the user will find a footnote if data at higher pressures are available in the original source. Emphasis was laid on the wavelength dependence of the refractive index to fill the gap stated above. No data for the gaseous state are included here. For mixtures, this data collection is restricted to binary liquid mixtures, i.e. no solutions of any solids are included here (e.g., for polymer solutions, a recent compilation was prepared by Huglin [89H1]). 

Figure 6. Temperature dependence of 5 (see the text on its definition) determined by the fitting of our prediction to the experimental data of p, Kj, and Cp at various pressures. Open squares, triangles, and circles represent, respectively, data onp.Ax.andCpat ambient pressure. All the other symbols are data at higher pressures. The dashed line is our theoretical prediction for S. The values of S determined from the 23 sets of data of bulk liquid water are all collapsed on the master curve, which is described by the single Boltzmann factor. The figure is reproduced from Fig lb of [25]...

The less-than-satisfactory agreement with experimental data at higher pressures of the Temkin-Pyzhev rate equation has been mentioned. In 1950, Temkin modified the original equation by introducing fugacities instead of partial pressures [34]. Furthermore, the original equation, Eq. (21), was multiplied by a term... 

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