A reversible reaction, A ⇌ B, takes place in an adiabatic plug-flow reactor (PFR). Select either an exothermic ($\mathrm{\Delta }H<0$) or an endothermic ($\mathrm{\Delta }H>0$) reaction. The black curve is the equilibrium conversion as a function of temperature from the Van't Hoff equation. The blue line is conversion as a function of temperature from the adiabatic energy balance. The intersection of the curve and the line is the conversion at equilibrium ($X_e$) and the adiabatic temperature at equilibrium ($T_e$). You can vary the feed temperature and the molar ratio of inert to reactant in the feed using the sliders.

For the reversible reaction A ⇌ B with both reactant A and inert component I in the adiabatic PFR feed, the equilibrium constant is: $$K_e=K_m\exp [\frac{\mathrm{\Delta }H}{R}(\frac{1}{T_m}-\frac{1}{T})]$$ where K_m is the equilibrium constant at temperature T_m (K), ∆H is the heat of reaction (J/mol), R is the ideal gas constant (J/[mol K]), and T is the temperature of the reaction (K).

The equilibrium conversion is obtained from the equilibrium constant: $$X_e=\frac{K_e}{1+K_e}$$ $$X_{EB}=\mathrm{\Sigma }\frac{\alpha C_p(T-T_f)}{-\mathrm{\Delta }H}$$ where $X_e$ is the equilibrium conversion, $X_{EB}$ is the conversion calculated from the energy balance, $\alpha$ is the ratio in the feed of (total moles)/(moles of reactant), $C_p$ is the heat capacity (J/[mol K]) of both the reactant and the inert, and $T_f$ is the feed temperature (K).

References:

[1] H. S. Fogler, Essentials of Chemical Reaction Engineering, Upper Saddle River, NJ: Prentice Hall, 2011 pp. 503 - 505.

[2] Reversible Reaction in an Adiabatic Plug-Flow Reactor. https://learncheme.com/simulations/kinetics-reactor-design/reversible-reaction-in-an-adiabatic-pfr/

This simulation was created in the Department of Chemical and Biological Engineering at University of Colorado Boulder for LearnChemE.com by Drew Smith and Jason Horst under the direction of Professor John L. Falconer. This simulation was prepared with financial support from the National Science Foundation. It is based on a Mathematica simulation on the Wolfram Demonstration Project website prepared by Rachael L. Baumann (Reversible Reaction in an Adiabatic Plug-Flow Reactor). Address any questions or comments to learncheme@gmail.com. All of our simulations are open source, and are available on our LearnChemE Github repository.

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