Portfolio 05: Multiple reactions

CHEN3010/ CHEN5040: chemical reaction engineering

Introduction

The direct vapor phase oxidation route to produce ethylene oxide (EO) from ethylene (E)

$$\ce{C2H4 + 1/2 O2 -> C2H4O} \qquad \Delta H_{rxn, 1} = -103.246 \ kJ/mol \tag{1}$$

is usually accompanied by two main side reactions.

Ethylene combustion:

$$\ce{C2H4 + 3O2 -> 2CO2 + 2H2O} \qquad \Delta H_{rxn, 2} = -1321.716 \ kJ/mol \tag{2}$$

Ethylene oxide combustion:

$$\ce{C2H4O + 5/2 O2 -> 2CO2 + 2H2O} \qquad \Delta H_{rxn, 3} = -1218 \ kJ/mol \tag{3}$$

At reactor operating conditions (below 250 °C), EO combustion (Equation 3) is negligible.

The reaction rate expressions and their parameters for ethylene oxidation over silver catalyst on an alumina support were given by Borman and Westerterp (1992).

The rates of reactions ($r_i$) for reactions 1 and 2 are expressed using semi-empirical relations as:

$$r_i = \frac{k^i_r P_E P_O^{n_i}} {1 + K^i_E P_E + K^i_C P_C + K^i_W P_W + K^i_{EO} P_{EO}} \tag{4}$$

Where, $r_i$ is the rate of production of EO or $\ce{CO2}$ in $mol/(kg-cat\ s)$. $k^i_r$ is reaction rate constant for reaction $i$ (in $mol/kg-cat\ s\ bar$); $K^i_j$ is absorption rate constant for component $j$, reaction $i$, $P_j$ is the partial pressure of component $j$ in Pa, $T$ is the temperature in K.

The subscripts $E, O, C, W$, and $EO$ denote ethylene, oxygen, carbon dioxide, ethylene oxide, and water respectively. The values of all the constants is given in Table 1.

Table 1: Reaction rate data

	Reaction 1	Reaction 2
$k_r$	$0.2572 \exp(-8068/T)$	$178 \exp(-11381/T)$
$n$	0.13	0.14
$K_E$	0.30 $\times 10^{-3}$	0.49 $\times 10^{-3}$
$K_C$	0.87 $\times 10^{-3}$	1.14 $\times 10^{-3}$
$K_{EO}$	0.90 $\times 10^{-3}$	0.49 $\times 10^{-3}$
$K_W$	3.68 $\times 10^{-6} \exp(2370/T)$	4.04 $\times 10^{-7} \exp(3430/T)$

The reaction is carried out in vertical tubular packed bed reactor. Shell catalyst S882, which is silver impregnated on aluminum, in the form of Raschig rings of size 8mm $\times$ 8mm, is used. The tube diameter ($d_t$) is 0.0389 m and length ($L$) is 12.8 m. Catalyst density ($\rho_s$) is 890 $kg/m^3$ and void fraction ($\epsilon$) is 0.6. Inlet superficial gas velocity ($v$) is 1 $m/s$ (volumetric flow rate $\upsilon_0 = v a_c = 1.188 \times 10^{-3} m^3/s$) and the feed enters at 180 °C.

The gases enter the reactor at the top and leave from the bottom. The shell side of the reactor has boiling kerosene. About top one third has kerosene vapour and the bottom has liquid kerosene. The vapour heats up the entering gases while the liquid at the bottom removes the heat generated in the exothermic reactions.

Inlet gas composition is given in Table 2.

Table 2: Inlet gas composition

Gas	volume fraction at inlet (%)
$\ce{C2H4}$	31.36
$\ce{O2}$	6.30
$\ce{C2H4O}$	0.03
$\ce{CO2}$	2.35
Inert	59.96

Questions

1. Write expressions for (6 marks)

   1. instantaneous and overall yield of EO,
   2. instantaneous and overall selectivity of EO w.r.t. $\ce{CO2}$, and
   3. conversion of $\ce{C2H4}$.

   You may use just $r_i$ instead of expanding the expressions.

2. Comment on reactor selection and operating conditions to maximize yield of EO. Explain your answer with relevant equations. (6 marks)

3. Yield and selectivity of EO. (12 marks)

   1. Based on inlet conditions, calculate instantaneous yield and selectivity of EO.
   2. For the outlet composition given in Table 3 calculate instantaneous yield and selectivity of EO. The outlet temperature is 220 °C. Comment on the results.

Table 3: Outlet gas composition

Gas	volume fraction at outlet (%)
$\ce{C2H4}$	28.84
$\ce{O2}$	4.26
$\ce{C2H4O}$	2.45
$\ce{CO2}$	3.14
Inert	61.31

4. Write complete set of governing equations for calculating the conversion in the reactor. (6 marks)

References

Borman, P. C., and K. R. Westerterp. 1992. “An Experimental Study of the Selective Oxidation of Ethene in a Wall Cooled Tubular Packed Bed Reactor.” Chemical Engineering Science, Twelfth International Symposium on Chemical Reaction Engineering Today, 47 (9): 2541–46. https://doi.org/10.1016/0009-2509(92)87090-D.