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Question 3 (18 marks) The following equations describe a dynamic model for adsorptive reactors. The component material balances for the packed adsorptive reactor can be described at ac 2010) 1-6 =D 29. Pal + PDU, R Equation 1 Oz oz E at where i = 1....Nc gas components, and I are the axial and temporal co-ordinates respectively. C is the gas-phase molar concentration of component i (mol/m?). Pat is the adsorbent density (kg/m),q is the solid-phase concentration of adsorbate i (mol/ kg). v is interstitial gas velocity (m/s). D. is the axial dispersion coefficient (m/s), Ry is the reaction rate for component i in the reaction j. the variation of fluid velocity through the column, The overall mass balance equation, which giv takes the form: ca. AC ac at OCY O: +. , R, MC P , R, The energy balance for the reactor, including the heat-transfer to the column wall, is described as (Rawadich and Gomes, 2009: Ding and Alpay, 2000a: Xiu et al., 2002b); ar OT =ke at (6.C.C., +3C, -C.Cul cq at -]{ar... - Pas (14, R)-(7-10) 4U d where K is the effective thermal conductivity. (J/ms K). C is the total molar concentration in the bulk phase (mol/m), Cyx is the gas-phase heat capacity (J/mol.K), C is the solid-phase heat capacity, (J/kg.K), U is the overall bed-wall heat-transfer coefficient. (J/m.K), AHans is the adsorption heat of componenti (on the adsorbent surface). (J/mol), AHR reaction heat of reaction j. (J/mol), and T. is the wall temperature. (K). Diffusion-controlled kinetics may be satisfactorily approximated as. dy =klg -a) di e) What would be the equation 1 if there is no reaction happening in the bed? What would be the equation 1 if there are no adsorbent particles in the bed (only reaction)