Directions

This simulation calculates the monetary profit as a function of reactor volume for a continuous stirred-tank reactor (CSTR) or a plug-flow reactor (PFR). The reaction is either first-order or autocatalytic; set the feed concentrations of reactant and product with sliders. Use sliders to set the value of the product and the costs of the reactant and reactor. Select "concentration" to view the reactant and product concentrations plotted versus reactor volume. The final volume corresponds to the volume at the black dot on the profit plot. Click and drag the black dot on the profit versus reactor volume plot. Check "optimize" to solve for the reactor volume with the highest profit. The separations cost is not considered in this simulation, but it can significantly affect profit.

Details

The rate of reaction r_A for a first-order reaction A → B is given by:

r_A = −k C_A,

and for an autocatalytic reaction it is:

r_A = −k C_A C_B,

where k is the rate constant (1/min) for a first-order reaction, and C_A and C_B are the reactant and product concentrations (mol/L).

A mass balance determines C_A and C_B for a continuous stirred-tank reactor (CSTR):

V = v₀ (C_A,0 − C_A) / (−r_A),

V = v₀ (C_B,0 − C_B) / r_A,

where V is the reactor volume (L), v₀ is the inlet volumetric flow rate (L/min) and C_A,0 and C_B,0 are the reactant and product feed concentrations (mol/L).

For a plug-flow reactor (PFR):

dC_A / dV = r_A / v₀,

dC_B / dV = −r_A / v₀.

Overall conversion x_A of reactant A to product and profit made p are calculated:

x_A = (C_A,0 − C_A) / C_A,0;

for a CSTR:

p = v₀ C_A,0 x_A (p_B − p_A) − V p_R,

for a PFR:

p = v₀ (C_B − C_B,0) p_B − v₀ C_A,0 x_A p_A − V p_R,

where p_A ($/mol) and p_R ($/[L min]) are the costs of the reactant and reactor and p_B ($/mol) is the value of the product.

About

This simulation was created in the Department of Chemical and Biological Engineering at University of Colorado Boulder for LearnChemE.com by John L. Falconer using Claude AI. It is a JavaScript/HTML5 implementation of a Mathematica simulation by Rachael L. Baumann and Garrison J. Vigil. It was prepared with financial support from the National Science Foundation (DUE 2336987 and 2336988). Address any questions or comments to LearnChemE@gmail.com.