Plug flow reactor with a pressure drop

Name: Put your name here

The performance of a plug flow reactor with a pressure drop is defined by these two coupled ODEs:

\(\frac{dX}{dW} = \frac{k'}{F_{A0}}\frac{1 - X}{1 + \epsilon X} y\)

\(\frac{dy}{dW} = - \frac{\alpha (1 + \epsilon X)}{2 y}\)

Where \(X\) is the conversion, \(y\) is the dimensionless pressure, and \(W\) is the weight of catalyst in the reactor. The constants are described below.

kprime = 0.0266  # rate constant
Fa0 = 1.08       # inlet molar flow
alpha = 0.0166   # pressure drop parameter
epsilon = -0.15  # mole change parameter

At the beginning of the reactor you have \(X=0\) and \(y=1\). Use this information to determine how much catalyst weight is required to reach a conversion of 0.5. What is the dimensionless pressure at that catalyst weight?

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