Reactor Design Economics
The rate of reaction rA for a first-order reaction A → B is given by: rA = -kCA, and for an autocatalytic reaction it is rA = -kCACB, where k is the rate constant (1/min), and CA and CB are the reactant and product concentrations (mol/L).

A mass balance determines CA and CB for a CSTR:  where V is the reactor volume (L), vo is the inlet volumetric flow rate (L/s) and CA,0 and CB,0 are the reactant and product feed concentrations (mol/L).

For a plug-flow reactor (PFR):  Overall conversion xA of reactant A to product and profit made p are calculated: 
for a CSTR:
for a PFR: 
where pA ($/mol) and pR ($/[L min]) are the costs of the reactant and reactor and pB ($/mol) is the value of the product.

This Demonstration 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. When the concentration plot is selected, the reactant and product concentrations are plotted versus reactor volume, and the final volume corresponds to the volume at the black dot. 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 Demonstration, but it can significantly affect profit.

Download the CDF file to view the simulation using the free Wolfram CDF player.