Dehydrogenation of Ethanol

Consider the heterogeneously catalyzed reaction:

The first-order (surface) reaction rate coefficient is $k_{r} = 0.45~\mathrm{m~s^{-1}}$. The (zero flux) binary mass-transfer coefficients are: $k_{12} = 0.07~\mathrm{m~s^{-1}}$, $k_{13} = 0.23~\mathrm{m~s^{-1}}$, and $k_{23} = 0.23~\mathrm{m~s^{-1}}$. These values are given at the operating conditions $p = 1.0 \cdot 10^{5}~\mathrm{Pa}$ and $T = 548~\mathrm{K}$. The bulk gas phase composition is:
$x_{1} = 0.60$, $x_{2} = 0.20$, $x_{3} = 0.20$.

Assume ideal gases and that a film model is appropriate.

Questions:

1. Write down the Maxwell-Stefan equations.

2. Solve this system by direct numerical integration. What are the molar fluxes?

3. Solve this system using the exact “matrix method.”

4. Make a linear approximation of the concentration profiles and solve the resulting algebraic equations.

5. Solve this system using the approximate “matrix method” in a mass-average reference frame.

6. Compare the accuracy of the different methods.

Note that all numerical implementations should be consistent with the provided equations and parameter values.