## Plug flow reactor with a pressure drop

Posted February 18, 2013 at 09:00 AM | categories: ode | tags: fluids, reaction engineering

Updated March 06, 2013 at 04:39 PM

If there is a pressure drop in a plug flow reactor, ^{1} there are two equations needed to determine the exit conversion: one for the conversion, and one from the pressure drop.

Here is how to integrate these equations numerically in python.

import numpy as np from scipy.integrate import odeint import matplotlib.pyplot as plt kprime = 0.0266 Fa0 = 1.08 alpha = 0.0166 epsilon = -0.15 def dFdW(F, W): 'set of ODEs to integrate' X = F[0] y = F[1] dXdW = kprime / Fa0 * (1-X) / (1 + epsilon*X) * y dydW = -alpha * (1 + epsilon * X) / (2 * y) return [dXdW, dydW] Wspan = np.linspace(0,60) X0 = 0.0 y0 = 1.0 F0 = [X0, y0] sol = odeint(dFdW, F0, Wspan) # now plot the results plt.plot(Wspan, sol[:,0], label='Conversion') plt.plot(Wspan, sol[:,1], 'g--', label='y=$P/P_0$') plt.legend(loc='best') plt.xlabel('Catalyst weight (lb_m)') plt.savefig('images/2013-01-08-pdrop.png')

Here is the resulting figure.

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