Dimethyl ether production is performed in a PBR reactor filled with alumina catalyst. The reaction consists of methanol dehydration and the kinetics of the reaction can be obtained at reference 1 2CH3OH = CH3OCH3 + H20, AH298 = -23.4 = -23.4 (kJ/mol) The parameters of the reactor, catalyst and heat exchanger are presented in the Table below. Parameter Value Reactor Catalyst void fraction Specific surface area of catalyst pellet Catalyst diameter (m) Ratio of void fraction to tortuosity of catalyst particle Reactor Length (m) Reactor diameter (m) Bed void fraction Catalyst density (kg m-3) Density of bed (kg m-3) Heat exchanger Tube side diameter (m) Tube thickness (m) Shell diameter (m) Overall heat transfer coefficient (Wm-'-') Heat exchanger length (m) 0.2 673 0.3175 x 10-2 0.066 8 4 0.5 2010 1005 1.905 x 10-2 2.11 x 10-3 0.615 325 4.57 Consider feeding the reactor at a pressure of 20 bar and temperature of 260 oC and a flow rate 51 kg/s of a mixture containing the following mass fraction: 94% methanol, 1% water and 5% dimethyl ether. Consider the pressure drop in the catalytic bed. A) Show the equations of the molar and energy balances and the Ergun equation; B) Graph the molar flow of each component as a function of the length of the reactor; C) Graph the conversion as a function of the length of the reactor; D) Make a temperature graph as a function of the length of the reactor; E) Vary the feed flow and determine the conversion (Calculate the conversion with 10 different flows); F) Vary the feed temperature and determine the conversion; Reference 1: G. Bercic, J. Levec, Intrinsic and global reaction rate of methanol dehydration over A1203 pellets, Industrial and Engineering Chemistry Research 31 (1992) 10351040