Isothermal Chemical Reactor Design

Isothermal Chemical Reactor Design

Designing a chemical reactor involves determining the size (volume) required to achieve a specific conversion of reactants into products. When a reactor operates isothermally (at a constant temperature), the rate constant (kk) remains constant throughout the reactor volume, greatly simplifying the design calculations.

1. Design Equations for Isothermal Operation

For a given reaction rate −rA-r_A (which is a function of concentration, e.g., −rA=kCA-r_A = k C_A for a first-order reaction), the volume required can be calculated using the ideal reactor design equations.

Continuous Stirred-Tank Reactor (CSTR)

In a CSTR, the concentration and temperature are uniform throughout the vessel and are identical to the exit conditions. The required volume VV is evaluated at the exit conditions:

V=FA0X−rAexitV = \frac{F_{A0} X}{-r_A}_{exit}

Where:

  • FA0F_{A0} is the molar feed rate of reactant A.
  • XX is the fractional conversion.
  • −rA∣exit-r_A|_{exit} is the reaction rate evaluated at the outlet concentration CA=CA0(1−X)C_A = C_{A0}(1-X).

Plug Flow Reactor (PFR)

In a PFR, the concentration changes continuously as the fluid flows down the length of the tube. The required volume is found by integrating the design equation over the conversion profile:

V=FA0∫0XdX−rAV = F_{A0} \int_0^X \frac{dX}{-r_A}

2. First-Order Reaction Sizing

For a simple first-order liquid-phase reaction (constant density), −rA=kCA0(1−X)-r_A = k C_{A0}(1-X).

Substituting this into the design equations yields the required residence time τ=V/v0\tau = V / v_0:

For a CSTR: τCSTR=Xk(1−X)\tau_{CSTR} = \frac{X}{k(1-X)}

For a PFR: τPFR=−1kln⁡(1−X)\tau_{PFR} = -\frac{1}{k} \ln(1-X)

3. Comparison of Volumes

For reaction orders greater than zero, the rate of reaction decreases as the reactants are consumed.

  • Because a CSTR operates entirely at the lowest concentration (the exit concentration), its reaction rate is the lowest possible.
  • A PFR operates at a high rate initially, which gradually decreases.
  • Consequently, to achieve the same conversion under isothermal conditions, a CSTR always requires a larger volume than a PFR for reactions with n>0n > 0.