Critical pressure estimation

Pc = critical pressure estimated from group contributions Ti,r = reduced normal boiling point estimated from Eq. (2-9) Xp = log(l atm/P eas)... 

In most cases, the quality of the normal boiling point or, respectively, another given data point is decisive for the quality of the estimation. The comparably large error in the critical pressure estimation is often acceptable. 

Critical pressure estimation. The following procedure is used to estimate the critical pressure ... 

The estimation of the three parameters —pseudo-critical temperature, pseudo-critical pressure, and the acentric factor— should be done using the same method because these constants should be coherent. 

For simple fluids Nq is estimated to be about 0.01, and Kostrowicka Wyczalkowska et aJ [29] have vised this to apply crossover theory to the van der Waals equation with interesting resnlts. The critical temperature is reduced by 11% and the coexistence curve is of course flattened to a cvibic. The critical density is almost unchanged (by 2%), bnt the critical pressure p is reduced greatly by 38%. These changes redvice the critical... 

Critica.1 Properties. Several methods have been developed to estimate critical pressure, temperature, and volume, U). Many other properties can be estimated from these properties. Error propagation can be large for physical property estimations based on critical properties from group contribution methods. Thus sensitivity analyses are recommended. The Ambrose method (185) was found to be more accurate (186) than the Lyderson (187) method, although it is computationally more complex. The Joback and Reid method (188) is only slightly less accurate overall than the Ambrose method, and is more accurate for some specific substances. Other methods of lesser overall accuracy are also available (189,190) (T, (191,192) (T, P ),... 

Example 1 Estimate the Critical Temperature and Critical Pressure... 

Example 2 Estimate the Critical Temperature and Critical Pressure of 2-Butanol, Which Has an Experimental Normal Boiling Point... 

Example 1 Estimate the critical temperature and critical pressure of 2-butanol using the Ambrose method, Eqs. (2-1) and (2-6). The experimental normal boiling point is 372.7 K. 

Various methods are available for estimation of the normal boiling point of organic compounds. Lyman et al. review and give calcula-tional procedures for the methods of Meissner, Miller, and Lydersen/ Forman-Thodos. A more recent method that has been determined to be more accurate is the method of Pailhes, which reqmres one experimental vapor pressure point and Lydersen group contributions for critical temperature and critical pressure (Table 2-385). 

An analytical method for the prediction of compressed liquid densities was proposed by Thomson et al. " The method requires the saturated liquid density at the temperature of interest, the critical temperature, the critical pressure, an acentric factor (preferably the one optimized for vapor pressure data), and the vapor pressure at the temperature of interest. All properties not known experimentally maybe estimated. Errors range from about 1 percent for hydrocarbons to 2 percent for nonhydrocarbons. 

Chueh s method for calculating partial molar volumes is readily generalized to liquid mixtures containing more than two components. Required parameters are and flb (see Table II), the acentric factor, the critical temperature and critical pressure for each component, and a characteristic binary constant ktj (see Table I) for each possible unlike pair in the mixture. At present, this method is restricted to saturated liquid solutions for very precise work in high-pressure thermodynamics, it is also necessary to know how partial molar volumes vary with pressure at constant temperature and composition. An extension of Chueh s treatment may eventually provide estimates of partial compressibilities, but in view of the many uncertainties in our present knowledge of high-pressure phase equilibria, such an extension is not likely to be of major importance for some time. 

But it will also be seen that vapour pressure estimation methods provide critical analysis of all parameters involved in a fire hazard and thus allow refinement of the methods leading to a quantification of this risk. 

Prior work on the use of critical point data to estimate binary interaction parameters employed the minimization of a summation of squared differences between experimental and calculated critical temperature and/or pressure (Equation 14.39). During that minimization the EoS uses the current parameter estimates in order to compute the critical pressure and/or the critical temperature. However, the initial estimates are often away from the optimum and as a consequence, such iterative computations are difficult to converge and the overall computational requirements are significant. 

Example 15.4 A reboiler is required to supply 0.1 krnol-s 1 of vapor to a distillation column. The column bottom product is almost pure butane. The column operates with a pressure at the bottom of the column of 19.25 bar. At this pressure, the butane vaporizes at a temperature of 112°C. The vaporization can be assumed to be essentially isothermal and is to be carried out using steam with a condensing temperature of 140°C. The heat of vaporization for butane is 233,000 Jkg, its critical pressure 38 bar, critical temperature 425.2 K and molar mass 58 kg krnol Steel tubes with 30 mm outside diameter, 2 mm wall thickness and length 3.95 m are to be used. The thermal conductivity of the tube wall can be taken to be 45 W-m 1-K 1. The film coefficient (including fouling) for the condensing steam can be assumed to be 5700 W m 2-K 1. Estimate the heat transfer area for... 

Solutions in hand for the reference pairs, it is useful to write out empirical smoothing expressions for the rectilinear densities, reduced density differences, and reduced vapor pressures as functions of Tr and a, following which prediction of reduced liquid densities and vapor pressures is straightforward for systems where Tex and a (equivalently co) are known. If, in addition, the critical property IE s, ln(Tc /Tc), ln(PcVPc), and ln(pcVPc), are available from experiment, theory, or empirical correlation, one can calculate the molar density and vapor pressure IE s for 0.5 < Tr < 1, provided, for VPIE, that Aa/a is known or can be estimated. Thus to calculate liquid density IE s one uses the observed IE on Tc, ln(Tc /Tc), to find (Tr /Tr) at any temperature of interest, and employs the smoothing relations (or numerically solves Equation 13.1) to obtain (pR /pR). Since (MpIE)R = ln(pR /pR) = ln[(p /pc )/(p/pc)] it follows that ln(p7p)(MpIE)R- -ln(pcVpc). For VPIE s one proceeds similarly, substituting reduced temperatures, critical pressures and Aa/a into the smoothing equations to find ln(P /P)RED and thence ln(P /P), since ln(P /P) = I n( Pr /Pr) + In (Pc /Pc)- The approach outlined for molar density IE cannot be used to rationalize the vapor pressure IE without the introduction of isotope dependent system parameters Aa/a. 

Colorless gas density about 9.73 g/L at STP hquelies at -61.8°C density of liquid radon 4.4g/mL at -62°C sohdifies at -71°C to an opaque crystaUine solid density of sohd radon 4.0 g/cm critical temperature 104.4°C critical pressure 62.4 atm viscosity 2.13x10 poise at 0°C (estimated) strongly absorbed onto surfaces dissolves in water, 230 mL/L at 20°C slightly soluble in alcohol and other organic solvents. ... 

Pressure Dependencies Equation 3.95 predicts the binary diffusion coefficient to scale as p l, which is generally true except as the pressure approaches or exceeds the critical pressure. The Takahashi formula [392], which can be used to describe the high-pressure behavior, is discussed below. The Chapman-Enskog theory also predicts that Vji, increases with temperature as T3/2. However, it is often observed experimentally the temperature exponent is somewhat larger, say closer to 1.75 [332], An empirical expression for estimating T>jk is due to Wilke and Lee [433]. The Wilke-Lee formula is [332]... 

Rule 5. The length a may be estimated from the critical temperature Tc (K) and critical pressure pc (atm) as... 

Also estimate e/kg and o for Ar from the critical temperature Tc = — 122°C and critical pressure pc = 48 atm. Calculate the thermal conductivity as a function of temperature using these Lennard-Jones parameters. 

Above critical point, estimated or extrapolated. At saturation pressure, 288.72 K. 

EXAMPLE 2-2 Use Figure 2—10 to estimate the critical temperature and critical pressure of ethane. Also estimate the specific volumes of ethane liquid and gas at 70°F. 

Estimate the critical pressure of a mixture of methane and n-hexane if the critical temperature of the mixture is known to be 200°F. Compare your answer with the critical pressures of pure methane and pure n-hexane. 

Only the critical temperature ot accmldchydc is available in the literature The critical temperatures of other aldehydes were estimated by the method of Kicdcl.1 The critical pressures and densities were determined by (he method proposed hy Lyderscn et til 1... 

I he critical properties of phosgene have been determined expert menially. , x M The method of Vow les has been used to esilmatr the other critical temperatures with a probable ei for of less than 5 C. and live critical densities within 0.01 gramcmilliliter The critical pressures w-erc estimated by the method ol Lvdeison. C [Pg.26]

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