Chapter 5, Problem 5.73P

Steam reforming is an important technology for converting re?ned natural gas, which we take here to be methane, into a synthesis gas that can be used to produce a variety of other chemical compounds. For example, consider a reformer to which natural gas and steam are fed in a ratio of 3.5 moles of steam per mole of methane. The reformer operates at 18 atm, and the reaction products leave the reformer in chemical equilibrium at 875°C. The steam reforming reaction is

   ${\text{CH}}_{\text{4}}{\text{+H}}_{\text{2}}\text{O}\rightleftharpoons {\text{CO+3H}}_{\text{2}}$(1)

and the water-gas shift reaction also occurs in the reformer.

   ${\text{CO+H}}_{\text{2}}\text{O}\rightleftharpoons {\text{CO}}_2{\text{+H}}_{\text{2}}$

(2)

The equilibrium constants for these two reactions are given by the expressions

   $\begin{array}{l}{K}_{\text{R}}=\frac{y_{\text{CO}}{y}_{{\text{H}}_{\text{2}}}^3}{y_{{\text{CH}}_{\text{4}}}{y}_{{\text{H}}_{\text{2}}\text{O}}}{P}^2\\ K_{\text{WG}}=\frac{y_{{\text{CO}}_{\text{2}}}{y}_{{\text{H}}_{\text{2}}}}{y_{\text{CO}}{y}_{{\text{H}}_{\text{2}}\text{O}}}\end{array}$

At 875°C, K_R= 872.9 atm²and K_WG, = 0.2482. The process is to produce 100.0 kmol/h of hydrogen. Calculate the feed rates (kmol/h) of methane and steam and the volumetric ?ow rate (m³/min) of gas leaving the reformer.