Chapter 9, Problem 9.43P

You are checking the performance of a reactor in which acetylene is produced from methane in the reaction

   $2C{H}_4\left(g\right)\to C_2{H}_2\left(g\right)+3H_2\left(g\right)$

An undesired side reaction is the decomposition of acetylene:

   $C_2{H}_2\left(g\right)\to 2C\left(s\right)+H_2\left(g\right)$

Methane is fed to the reactor at 1500°C at a rate of 10.0 mol CH4/S. Heat is transferred to the reactor at a rate of 975 kW. The product temperature is 1500°C and the fractional conversion of methane is 0.600. A flowchart of the process and an enthalpy table are shown below.

References: C(s), H₂(g), at 25°C, 1 atm

Substance	${\stackrel{\dot{}}{n}}_{in}$(mol/s)	${\hat{H}}_{in}$(kJ/mol)	${\stackrel{\dot{}}{n}}_{out}$(mol/s)	${\hat{H}}_{out}$(kJ/mol)
$C{H}_4$	10.0	41.65	${\stackrel{\dot{}}{n}}_1$	${\hat{H}}_1$
$C_2{H}_2$	—	—	${\stackrel{\dot{}}{n}}_2$	${\hat{H}}_2$
$H_2$	—	—	${\stackrel{\dot{}}{n}}_3$	${\hat{H}}_3$
C	—	—	${\stackrel{\dot{}}{n}}_4$	${\hat{H}}_4$

(a) Using the heat capacities given below for enthalpy calculations, write and solve material balances and an energy balance to determine the product component flow rates and the yield of acetylene (mol C₂H₂produced/mol CH₄consumed).

   $\begin{array}{l}C{H}_4\left(g\right):C_p\approx 0.079kJ/\left(mol\cdot °C\right)\\ C_2{H}_2\left(g\right):C_p\approx 0.052kJ/\left(mol\cdot °C\right)\\ H_2\left(g\right):C_p\approx 0.031kJ/\left(mol\cdot °C\right)\\ C\left(s\right):C_p\approx 0.022kJ/\left(mol\cdot °C\right)\end{array}$

For example, the specific enthalpy of methane at 1500°C relative to methane at 25°C is [0.079 kJ/(mol·°C)](1500°C - 25°C) = 116.5 kJ/mol.

(b) The reactor efficiency may be defined as the ratio (actual acetylene yield/acetylene yield with no side reaction). What is the reactor efficiency for this process?

(c) The mean residence time in the reactor [ $\tau$(s)] is the average time gas molecules spend in the reactor in going from inlet to outlet. The more $\tau$increases, the greater the extent of reaction for every reaction occurring in the process. For a given feed rate, $\tau$is proportional to the reactor volume and inversely proportional to the feed stream flow' rate.

If the mean residence time increases to infinity, what would you expect to find in the product stream? Explain.

Someone proposes running the process with a much greater feed rate than the one used in Part (a), separating the products from the unconsumed reactants, and recycling the reactants. Why would you expect that process design to increase the reactor efficiency? What else would you need to know to determine whether the new design would be cost-effective?