4. The continuity equation for the reaction A(g)+catProducts in a fixed bed catalytic reactor based on a simple pseudo-homogeneous one dimensional plug flow model can be represented as dxd(ucA)+p(rA)=0 where cA= concentration of A u= flow velocity p= particle density rA= reaction rate x= bed depth (a) Starting from this equation derive the expression for the catalyst holdup, W, in terms of conversion XA, at bed depth x. [9 marks] (b) Compare the derived equation in part (a) to the design equation for the volume of a Plug Flow Reactor (PFR) and explain briefly how the rate terms, rA, are related in the two equations. [4 marks] (c) Discuss briefly the operational advantages of the following reactors: (i) Biological reactors (ii) Membranes reactors (iii) Biomass reactors (iv) Microscale reactors