Effect of back mixing on the performance of tubular-flow reactors

In chemical reaction engineering; Plug-Flow-Reactor (PFR) and Continuous-Stirred-Tank-Reactor (CSTR) are ideal reactors and are based on extremely simplified assumptions. One can predict the performance of these ideal reactors easily, but this prediction may deviate from reality considerably. In a tubular-flow reactor, dispersion-model can be used to predict the performance of real reactors. Degree of dispersion is represented by Peclet (Pe =uL/D) number. In a PFR, Pe  ∞, and in a CSTR, Pe = 0. In real reactors, degree of backmixing is between those of PFR and CSTR. From mole balance one could get the following equation in terms of conversion of limiting component A, XA for an nth -order reaction. D/uL (d^2 X_A)/(dz^2 )-(dX_A)/dz+kτC_Ao^(n-1) (1-X_A )^n=0 Where, z = dimensionless distance along the reactor, D = dispersion coefficient, L = length of reactor, u = linear velocity, k = reaction rate constant, τ=space time, n = order of reaction. If Pe (uL/D) number = ∞, the above equation reduces to PFR equation. n = 1 and n = 2 were selected with Pe = 0.1, 0.3, 0.5, 1, 3, 5, 10, 100 as parameters. The model equation was solved symbolically by MATLAB. For positive orders, backmixing has an adverse effect on the fractional conversion. In this study, for variety of Pe numbers’ effect on backmixing is simulated for 1st and 2nd order reactions. This study has indicated that in a tubular-flow reactor, dispersion has negative effects on performance of tubular-flow reactor. Larger the Pe number, the more conversion is obtained for a fixed reactor size and dimensions. These findings are presented in tabular and graphical forms.