PFR (integral)
CSTR (rectangle)
Directions
This simulation shows how the choice of reactor type affects the volume needed to reach a target conversion, using a Levenspiel plot of \(F_{A0}/(-r_A)\) versus conversion \(X\).
- Choose a kinetics scenario. Use the "Normal decay" or "Autocatalytic" buttons to switch between the two rate expressions.
- Set the conversion. Click and drag anywhere on the chart to move the black dot along the curve. The dot's horizontal position sets the conversion \(X\).
- Read the areas. The red rectangle is the volume of a CSTR operating at the exit conversion; the blue shaded region under the curve is the volume of a PFR reaching the same conversion.
- Check the numbers. The panel on the right updates live with \(V_{CSTR}\), \(V_{PFR}\), and their ratio as you move the point.
- Dig deeper. Open the Details panel for the governing equations and symbol definitions, or download the Guided Inquiry worksheet for a structured set of questions to work through.
Details
Design equations
\( \displaystyle V_{CSTR} = \frac{X \cdot F_{A0}}{-r_A}\bigg|_{exit} \)
\( \displaystyle V_{PFR} = F_{A0}\int_0^{X} \frac{dX}{-r_A} \)
Kinetics used to generate the curve
Normal decay (Scenario 1):
\( \displaystyle \frac{F_{A0}}{-r_A} = \frac{20}{1.05 - X} \)
Autocatalytic (Scenario 2):
\( \displaystyle \frac{F_{A0}}{-r_A} = 150(X-0.3)^2 + 15 \)
Symbols
| \(X\) | Conversion of reactant A (dimensionless) |
| \(F_{A0}\) | Molar feed rate of reactant A entering the reactor |
| \(-r_A\) | Rate of consumption of reactant A, a function of \(X\) |
| \(V_{CSTR}\) | Volume of a continuous stirred-tank reactor (area of the red rectangle, evaluated at the exit conversion) |
| \(V_{PFR}\) | Volume of a plug-flow reactor (area under the curve from \(X=0\) to the exit conversion) |
About
This simulation was generated by Professor David L. Silverstein and Dr. Loyal Murphy of the University of Mississippi using Google Gemini. It was modified for LearnChemE using Claude AI.