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McNaught, J M, Macdonald equation, for fixed-bed pressure drop, Mach number, Macleod-Sugden method for surface tension Macrolayer consumption model for critical heat flux in pool boiling, Maddox, R N Magnetic fields, effect on properties of rheologically complex materials, Magnetic devices, for fouling mitigation, Magnetohydrodynamcs, inaugmentation of heat transfer in microfluidic systems, Margarine manufacture, crystallization of edible oils and fats in, scraped surface heat exchangers for, Marlotherm, heat transfer media, Martensitic stainless steels, Martin, H Martinelli and Boelter equations for combined free and forced convection, Martinelli and Nelson correlations: Mass absorption coefficient, Mass extinction coefficient, Mass fraction, in multicomponent mixtures, Mass scattering coefficient, Mass transfer: Mass transfer coefficient: Materials of construction, for heat exchangers, Low temperature operation, ASME VIII code guidelines for, Matovosian, Robert, Matrix inversion techniques, in radiative heat transfer, Maximum drag reduction Maximum velocities (in shell-and-tube heat exchangers) Maxwell model, for non-Newtonian fluid, Maxwell-Stefan equations, for multicomponent diffusion, Maxwell's equations, for electromagnetic radiation, Mean beam length concept, in radiative heat transfer: Mean phase content, Mean temperature difference: Measurement of fouling resistance, Mechanical design of heat exchangers: Mechanical draft cooling towers, Mechanical loads, specifications in EN13445, Mechanical vapour compression cycles in refrigeration, Mediatherm, heat transfer medium, Melo, L F, Melting, thermal conduction in, Melting point: Mercury: Merilo correlation, for critical heat flux in horizontal tubes, Merkel's equation, in cooling tower design, Mertz, R, Metais and Eckert diagrams, for regimes of convection: Metals: Metallurgical industry, kilns and furnaces for, Metastable equilibrium, of vapor and liquid, Methane: Methanol: Methyl acetate: Methylacetylene: Methyl acrylate: Methyl amine n-Methylaniline: Methyl benzoate: 2-Methyl-1,3-Butadiene (Isoprene): 2-Methylbutane (isopentane): Methylbutanoate: 2-Methyl-2-butene: Methylcyclohexane: Methylcyclopentane: Methylethylketone: Methyl formate: Metallurgical slag, use of submerged combustion in reprocessing of, Methyl fluorate: 2-Methylhexane: Methylisobutylketone: Methylmercaptan: 1-Methylnaphthalene: 2-Methylnaphthalene: 2-Methylpentane: 3-Methylpentane: 2-Methylpropane (isobutane): 2-Methylpropene: Methyl propionate: Methylpropylether: Methylpropyl ketone: Methyl salicylate: Methyl-t-butyl ether: Microbubbles, for drag reduction, Microchannels (see also microfluidics) Micro-fin tubes: Microfluidics, enhancement of heat transfer in, Mie scattering, in pulverized coal combustion, Miller, C J Miller, E R Mineral oils, as heat transfer media, physical properties of, Mineral wool production, submerged combustion systems for, Minimum fluidization velocity, Minimum heat flux in pool boiling: Minimum tubeside velocity, in shell-and-tube heat exchangers, Minimum velocity for fluidization, Minimum wetting rate, for binary mixtures, Mirror-image concept, in radiative heat transfer, Mirrors, spectral characteristics of reflectance from, Mishkinis, D, Mist flow: Mitigation of fouling, Mixed convection occurrence in horiozntal circular pipe, Metais and Eckert diagram for, Mixing (shell-side), in twisted tube heat exchangers, Mixing length, in turbulent flow, Mixtures: Modelling, of fouling: Models, theory of, Modulus of elasticity: Moffat, R S M, Molecular gas radiation properties, Molecular weight: Mollier chart, for humid air, Momentum equation: Monitoring, on line, of fouling, Monochloroacetic acid: Monte Carlo methods, in radiative heat transfer, Moody chart: Morris, M Mostinski correlations: Moving bed, heat transfer to, Muchowski, E, Mueller, A C Muller-Steinhagen, H Multicomponent mixtures: Multidimensional systems, heat conduction in, Multiflux methods, for radiative heat transfer in nonisothermal gases, Multipass shell-and-tube heat exchangers, Multiphase fluid flow and pressure drop: Multiple duties, in plate heat exchangers, Multiple effect evaporation, Multiple hairpin heat exchanger, Multistage flash evaporation (MSF) Multizone model, for furnaces,
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Thermodynamic Properties

DOI 10.1615/hedhme.a.000504

5.1 PROPERTIES OF MIXTURES FLUIDS
5.2.2 Thermodynamics properties

A. Light hydrocarbons

There are reasonably reliable charts available from which equilibrium constants for light hydrocarbons can be obtained. Perhaps the best, and most widely used, are those published by the Gas Processors Association (GPSA, 1972). Values from the charts, if properly used, will agree closely with the values obtained from a good equation of state. In addition, they are easily and quickly used and ideal for hand calculations.

If more accurate equilibrium constants are desired, or if equilibrium conditions are being predicted by computer, an equation of state is used for estimating the equilibrium constant values. The most widely used equations of state for light hydrocarbons are the Soave version of the Redlich-Kwong (SRK) (Redlich and Kwong, 1949; Soave, 1972; Erbar, 1973), the Starling version of the Benedict-Webb-Rubin (BWR) (Starling and Han, 1972), and the Peng-Robinson (PR) (Peng and Robinson, 1976). Each has advantages and disadvantages, proponents and opponents. More importantly, different computer solutions for each equation may yield equilibrium constants that are significantly different. Erbar and Maddox (1977) have made comparison calculations for simple equilibrium flash calculations that differed by as much as 20%. The same equation of state was used for all calculations the programming of the solution was different.

Equilibrium coefficients are calculated from the equation of state using one of the Equation 503.8, Equation 503.9, Equation 503.10 and Equation 503.11. All thermodynamic quantities may be related to each other by mathematical manipulation. The fugacity coefficient is related to pressure, volume, temperature, and compressibility factor by

\[\label{eq1} \ln \gamma_{g_i}=\dfrac1{\tilde{R}T}\int_{v}^{\infty}\left[\left(\dfrac{\alpha P}{\alpha n_i}\right)_{\!T,V, n_j}\!\!-\dfrac{\tilde{R}T}{V}\right]dV-\ln Z \tag{1}\]

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