Two-Dimensional Tubular Plug Flow Reactor

The eomponent mass balanee of speeies A entering the element longitudinally and radially per unit time is 

In assuming a steady state, the algebraie sum of the eomponents of mass entering (Equations 6-98, 6-99, and 6-100) and leaving (Equations 6-101, 6-102, 6-103, and 6-104) the element are zero. Expanding the terms evaluated at (1 -i- 61) and (r -i- 6r) in Taylor series about the points 1 and r, and negleeting the seeond order differenees, gives 

If the reaetion rate is a funetion of pressure, then the momentum balanee is eonsidered along with the mass and energy balanee equations. Both Equations 6-105 and 6-106 are eoupled and highly nonlinear beeause of the effeet of temperature on the reaetion rate. Numerieal methods of solution involving the use of finite differenee are generally adopted. A review of the partial differential equation employing the finite differenee method is illustrated in Appendix D. Eigures 6-16 and 6-17, respeetively, show typieal profiles of an exo-thermie eatalytie reaetion. 

Mass of component produced by chemical reaction = 2jrr6r6lpb(-rA) 

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