The dehydrogenation of ethane (A) to ethene (B) is conducted in a 0.5-m³ PFR. The reaction is first-order with respect to A, with a rate constant of 15.2 min-¹ at 725°C. The feed contains pure ethane at 725°C 400 kPa, and a flow rate of 1 .O kmol min-¹. Compare the conversion predicted if isothermal

Question

The dehydrogenation of ethane (A) to ethene (B) is conducted in a 0.5-m³ PFR. The reaction is first-order with respect to A, with a rate constant of 15.2 [latex] min^{-1} [/latex] at 725°C. The feed contains pure ethane at 725°C 400 kPa, and a flow rate of 1 .O kmol [latex] min^{-1} [/latex]. Compare the conversion predicted if isothermal , isobaric conditions are assumed with that if the pressure drop is accounted for with isothermal flow. The diameter of the reactor tube is 0.076 m, and the viscosity of the gas is [latex] 2.5 imes 10^{-1} [/latex] Pa s

Accepted Answer

The reaction is [latex] A \rightarrow B + H_2 [/latex] . The reactor length corresponding to the reactor volume and diameter specified is 110 m. The [latex]f_A(x)[/latex] and P(x) profiles can be determined by simultaneously integrating the material-balance equation (15.2-4) and the pressure-drop equation (15.2-11) :

[latex] \frac {df_A}{dx} = \frac {\pi D^2( -r_A) }{4F_{Ao}} [/latex] (15.2-4)

where [latex] ( -r_A) = k_Ac_A = k_AF_A / q = k_AF_{Ao} ( 1 - f_A) /q [/latex] , and

[latex] \frac {dP}{dx} = \frac { -32f\rho q^2 }{\pi ^2D^5} [/latex] (15.2-11)

Assuming ideal-gas behavior, we can determine the volumetric flow rate (q) from [latex] q = F_tRT / P [/latex]

where [latex] F_t = F_{Ao}( 1 - f_A) [/latex] (obtained from a stoichiometric table).

The linear velocity (u) can be determined from [latex] u = 4q / \pi D^2 [/latex]

The friction factor,f, can be estimated using equation 15.2-12

[latex] f = 0.00140 + 0.125Re^{-0.32} [/latex] (15.2-12)

The density may be evaluated from the ideal-gas equation :

[latex] \rho = (P /RT )M_{av} [/latex]

where [latex] M_{av}[/latex] is the average molar mass of the gas mixture.

The E-Z Solve software can be used to integrate equations 15.2-4 and 15.2-11 numerically, while simultaneously updating q, U, p, Re, and f at each step (file exl5-8.msp). The predicted conversion for isothermal, nonisobaric conditions is 0.247; the calculated pressure drop is 114 kPa. If the pressure drop is ignored (i.e., P = 400 kPa throughout the reactor), the resulting conversion is 0.274. Thus, for this case, it is important that the pressure drop be accounted for

Question 15.8: The dehydrogenation of ethane (A) to ethene (B) is conducted...

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