Woods (1995b) provides different heat capacity and latent heat equations for phenol and naphthalene with different temperature ranges. Note that these are predicted values regardless of the existence of the compound as a liquid at \(25^{\circ} \mathrm{C}\).

Liquid heat capacities with \(\mathrm{C}_{\mathrm{p}}\left(25^{\circ} \mathrm{C}\right)\) in \(\mathrm{kJ} /(\mathrm{kg} \mathrm{K})\) and \(\mathrm{dC}_{\mathrm{p}} / \mathrm{dT} \mathrm{kJ} /\left(\mathrm{kg} \mathrm{K}^{2}\right)\) :

Naphthalene \(\mathrm{C}_{\mathrm{p}, \mathrm{L}}\left(25^{\circ} \mathrm{C}\right)=1.523 \mathrm{~kJ} /(\mathrm{kg} \mathrm{K}), \mathrm{dC}_{\mathrm{p}, \mathrm{L}} / \mathrm{dT}=0.00375 \mathrm{~kJ} /\left(\mathrm{kg} \mathrm{K}{ }^{2}\right)\), phenol \(\mathrm{C}_{\mathrm{p} . \mathrm{L}}\) \(\left(25^{\circ} \mathrm{C}\right)=2.2 \mathrm{~kJ} /(\mathrm{kg} \mathrm{K}), \mathrm{dC}_{\mathrm{p}, \mathrm{L}} / \mathrm{dT}=0.00176 \mathrm{~kJ} /\left(\mathrm{kg} \mathrm{K}{ }^{2}\right)\).

Heats of melting \(\lambda_{\mathrm{M}}\) and of evaporation \(\lambda_{\mathrm{V}}\) at \(25^{\circ} \mathrm{C}\) :

Naphthalene \(\lambda_{\mathrm{M}}=149 \mathrm{~kJ} / \mathrm{kg}, \lambda_{\mathrm{V}}=337 \mathrm{~kJ} / \mathrm{kg}\), phenol \(\lambda_{\mathrm{M}}=121 \mathrm{~kJ} / \mathrm{kg}, \lambda_{\mathrm{V}}=487 \mathrm{~kJ} / \mathrm{kg}\).
Woods does not provide the heat capacity of solid phenol, so use \(\mathrm{C}_{\mathrm{P}, \text { phenol,solid }}=220.9\)
\(\mathrm{kJ} /(\mathrm{kmol} \mathrm{K})\).
Use Woods's data to determine the total cooling requirement for the crystallization operation for Example 18-9 and compare with the result from the example. Note that a slightly different path for the energy balance may be required.

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Develop a conceptual design for a hybrid crystallization-distillation system to process 250.0 kmol/h of a 94.2 mol% phenol C6H5OH, 5.8 mol% naphthalene C10Hg mixture at 50C. The desired products are 99.05 mol% naphthalene and 99.70 mol% phenol stream. The concentration of the feed to the distillation column would need to be optimized, but for this example, the eutectic concentration is used. Operate distillation at L/D = 1.15 (L/D)min Reflux is a saturated liquid. Preheat the feed to the column to a saturated liquid, and use the optimum feed stage. The column has a total condenser and a partial reboiler. Operation is at 1.013 bar. Choose the basic flowsheet and the type of crystallizer to use. Determine the energy requirements for the crystallizer and distillation column in the hybrid system, and compare to the energy requirements for doing the entire separation by distillation. Estimate the energy costs from Table 11-9, and compare the hybrid energy costs to the distillation-only system energy costs. The data for the solid-liquid phase diagram are shown in Table 18-2 and are plotted in Figure 18-1. Other data are listed in Table 18-7. TABLE 11-9. Approximate energy costs Item Details Cost Reference Cooling water from 30.0C to $0.378/GJ Turton et al. (2018) cooling tower 40.0C or 45.0C Refrigeration 5.0C return 15.0C Turton et al. Luyben Turton et al. (2018); Luyben (2013) Chilled water -20.0C $4.77/GJ $4.43/GJ Low T -50.0C $8.49/GJ $7.89/GJ Very low T $14.12/GJ $13.11/GJ Electricity $18.72/GJ or Turton et al. (2018) $0.067/kWh Steam from boiler Latent heat only Turton et Luyben al. Low pressure 5.0 barg, 160.0C $4.54/GJ $7.78/GJ Reduced to 140C Medium pressure 10.0 barg, $4.77/GJ $8.22/GJ 184C Reduced to ~163C* High pressure 41.0 barg, $5.66/GJ $9.88/GJ 254C Reduced to -230C Definitions Barg = bar 1.0 GJ = 106 kJ = 10 absolute -1.0 J TABLE 18-2. Values for eutectic curve for phenol-naphthalene at 1.0 atm. (National Research Council, 1930, Vol. IV. p.136) Mol frac Xphenol,L 1.00 0.90 0.84 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.0 Crystals TC Pure phenol eutectic Pure naphthalene 40.5* 33.4 29.8 46.7 53.7 58.8 63.4 67.3 71.3 75.3 80.1 TC 80 70- 60- 50 40- 30- 0 0.2 0.4 0.6 0.8 1.0 Xphenol