Use a thermal swing adsorption process to remove traces of toluene from liquid n-heptane using silica gel as adsorbent. Adsorber operates at \(1.0 \mathrm{~atm}\). Feed is \(0.11 \mathrm{wt} \%\) toluene and \(99.89 \mathrm{wt} \% \mathrm{n}\)-heptane at \(35^{\circ} \mathrm{C}\). Superficial velocity of feed is \(5.50 \mathrm{~cm} / \mathrm{min}\). Adsorber is 0.85 meters long and during feed step is at \(35^{\circ} \mathrm{C}\). Feed is continued until toluene breakthrough occurs. Thermal regeneration/purge is done with counterflow of pure n-heptane at \(80^{\circ} \mathrm{C}\) continued until all xylene is removed. Superficial velocity during thermal regeneration/purge is \(9.0 \mathrm{~cm} / \mathrm{min}\). Data are in problem 20.D21. Use solute movement theory to

a. determine breakthrough time for toluene during feed step.

b. determine thermal breakthrough time during both purge and feed steps.

c. determine xylene outlet concentration profile during regeneration/purge.

Data From Problem 20.D21

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D21. Isotherms for dilute amounts of toluene and xylene adsorbed on silica gel from n-heptane are linear = at low concentrations (Matz and Knaebel, 1991). For toluene, Tol = K'Tol (T)X Tol where a Tol is g toluene/g adsorbent and XTol is in g toluene/g solution (mass fraction) (Matz and Knaebel, 1991). The linear constants are functions of temperature. For toluene, Tol = 17.46 XTol at 0C, Q Tol = 7.77 XTol at 30C, a Tol = 5.16 XTol at 35C, and QTol 1.23 XTol at 80C. Isotherms for xylene at low concentrations have similar form to those for toluene, qxy = K'xy(T)XTxyl where qxy is g xylene/g adsorbent and Xxy is in g xylene/g solution (mass fraction). Isotherms for xylene: qxy = 22.36 xxy at 0C, qxy = 12.03 Xxy at 30C, qxy = 6.28 xxy at 35C, and qxy = 2.01 xxy at 80C. Wall heat capacities can be ignored, heat of adsorption is negligible, and no adsorption of n-heptane. Find appropriate zone, product, and desorbent interstitial velocities (based on column diameter) for an SMB separating toluene and xylene if interstitial feed velocity VF = 1.0 cm/min and temperature is 30C. Switching time is 100.0 min and L = 15.0 cm. Physical properties: &= 0.43, p = 0.48, p = 2100 kg/m, pf = 684 kg/m, Kd = 1.0, Cps = 920 J/kg C, and Cpf = 1841 J/(kg C).