Chapter 5, Problem 5.74P

A ?owchart of a methanol synthesis process is shown below.

The following speci?cations apply to the labeled streams and process units:

A. Fresh feed—a mixture of CO, H₂, N₂, and CO₂

B. Feed to the reactor—30.0 mole% CO, 63.0% H₂, 2.0% N₂, and 5.0% CO₂.

Reactor. Two reactions occur and proceed to equilibrium at 200°C and 4925 kPa absolute:

   $\begin{array}{c}{\text{CO+2H}}_{\text{2}}\rightleftharpoons {\text{CH}}_{\text{3}}\text{OH}\left(\text{M}\right)\\ {\text{CO+3H}}_{\text{2}}\rightleftharpoons {\text{CH}}_{\text{3}}{\text{OH+H}}_{\text{2}}\text{O}\end{array}\begin{array}{c}{\left(K_p\right)}_1=\frac{p_{\text{M}}}{p_{\text{CO}}{p}_{\text{H}}^2{}_2}=3.49\times {10}^{-6}{\text{kPa}}^{\text{-2}}\\ {\left(K_p\right)}_2=\frac{p_{\text{M}}{p}_{{\text{H}}_{\text{2}}\text{O}}}{p_{{\text{CO}}_2}{p}_{\text{H}}^3{}_2}=5.19\times {10}^{-8}{\text{kPa}}^{\text{-2}}\end{array}$

C. Reactor effluent—contains all feed and product species at the reactor temperature and pressure. Species partial pressures satisfy the two given equations.

Sep1. Condenses all methanol and water in reactor ef?uent.

D. Liquid methanol and water, (These species will be separated by distillation in a unit not shown.)

E. Gas containing N₂and unreacted CO, H₂, and CO₂.

Sep2. Multiple-unit separation process.

F. All of the nitrogen and some of the hydrogen in Stream E.

G. Recycle stream—CO, CO₂, and 10% of the hydrogen fed to Sep2.

(a) Taking 100 kmol/h of Stream B as a basis of calculation, calculate the molar ?ow rates (kmol/h) and molar compositions of the remaining six labeled streams.

(b) The process is to be used to provide 237 kmol/h of methanol. Scale up the ?owchart of Part (a) to calculate the required fresh feed rate (SCMH), the ?ow rate of the reactor ef?uent (SCMH), and the actual volumetric ?ow rate of the reactor ef?uent (m³/h), assuming ideal-gas behavior.

(c) Use the rule of thumb for a diatomic gas given in Equation 5.2-3 to test the ideal-gas assumption at the reactor outlet. If the assumption is invalid, which of the values calculated in Part (b) are in error?