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ΔH: Heat of reaction per mol of N2 (−26,000 kcal/kmol N2)

S2: Cross-sectional area of catalyst zone 0.78 m2

ra: Reaction rate (kmol N2, h m2)

cp,g: Heat capacity of the reacting gas 0.719 kcal/kg·K

Nitrogen mass balance:

$\begin{array}{l}ra=\frac{d{N}_{{\mathrm{N}}_{2}}}{dx}=-f\left[{K}_{1}\frac{{P}_{{\mathrm{N}}_{2}}·{P}_{{\mathrm{H}}_{2}}^{1.5}}{{P}_{{\mathrm{NH}}_{3}}}-{K}_{2}\frac{{P}_{{\mathrm{NH}}_{3}}}{{P}_{{\mathrm{H}}_{2}}}\right]\hfill \\ {K}_{1}=1.78954×{10}^{4}\mathrm{exp}\left(\frac{-20,800}{R{T}_{\mathrm{g}}}\right)\hfill \\ {K}_{2}=2.5714×{10}^{16}\mathrm{exp}\left(\frac{-47,400}{R{T}_{\mathrm{g}}}\right)\hfill \end{array}$

f: Catalyst activity

Pi: Partial pressure of the species

Ki: rate constants,

where

$\begin{array}{l}{P}_{{\mathrm{N}}_{2}}={P}_{\mathrm{o}}\left(\mathrm{atm}\right)·\left[\frac{{N}_{{\mathrm{N}}_{2}}}{{N}_{\mathrm{total}}}\right]\hfill \\ {P}_{{\mathrm{H}}_{2}}=3·{P}_{{\mathrm{N}}_{2}}\hfill \\ {P}_{{\mathrm{NH}}_{3}}={P}_{\mathrm{o}}\left(\mathrm{atm}\right)·\left[\frac{{N}_{{\mathrm{NH}}_{3}}}{{N}_{\mathrm{total}}}\right]\hfill \\ {N}_{{\mathrm{NH}}_{3}}={N}_{{\mathrm{NH}}_{3},\mathrm{o}}+2\left({N}_{{\mathrm{N}}_{2},\mathrm{o}}-{N}_{{\mathrm{N}}_{2}}\right)\hfill \\ {N}_{\mathrm{total}}={N}_{{\mathrm{N}}_{2}}+3·{N}_{{\mathrm{N}}_{2}}+{N}_{{\mathrm{NH}}_{3},\mathrm{o}}+{N}_{\mathrm{inertes}}+2\left({N}_{{\mathrm{N}}_{2},\mathrm{o}}-{N}_{{\mathrm{N}}_{2}}\right)\hfill \end{array}$

and the pressure drop ...

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