Conversion as a Function of Rate Laws and Feed Composition

Conversion as a Function of Rate Laws and Feed Composition 

One of the simplest models used to describe the performance of tubular reactors is the well-known isothermal one-dimensional plug flow tubular reactor (PFTR) model. The mass balance of this model for steady-state conditions, the simultaneous occurrence of M reactions and a constant volumetric flow rate V is  

the oq are the elements of the stoichiometric matrix, Ar represents the cross-section area of the tube, and z is the axial coordinate. This system of ordinary differential equations can be integrated numerically for arbitrary rate laws, provided that appropriate initial conditions c = q(z = 0) are provided. 

If only one reaction needs to be considered, and conversion Xa is chosen to be the state variable of interest, using Eqs. (5) and (7), the mass balance of the PFTR, Eq. 8, can be expressed as follows  

Integration from 0 to the reactor length L and from 0 to Xa(L) leads to the well-known dimensionless mass balance of the PFTR  

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