Overview
This lecture covers the sizing of continuous flow reactors, focusing on graphical methods (Levenspiel plots) to determine reactor volumes for CSTR and PFR, and includes a worked example using experimental data.
Recap of Design Equations
- Design equations exist for batch reactors, CSTR (Continuous Stirred-Tank Reactor), PFR (Plug Flow Reactor), and PBR (Packed Bed Reactor).
- The rate of reaction (−rₐ) is a function of the conversion (X), making sizing dependent on conversion.
Conversion and Rate Relationship
- For a first-order reaction: −rₐ = k·Cₐ, with Cₐ expressed as Cₐ₀·(1−X).
- The conversion (X) links the moles of reactant to concentration and reaction rate.
Reactor Sizing Cases
- Two main sizing cases: known reactor volume (find conversion) or known conversion (find volume).
- Sizing requires understanding how −rₐ changes with X.
Levenspiel Plot Method
- Sizing is often done with a Levenspiel plot: X vs 1/(−rₐ) or X vs Fₐ₀/(−rₐ).
- For a CSTR, reactor volume is the area of a rectangle at a given X under the curve.
- For a PFR, reactor volume is the area under the curve up to the desired X.
Example: Isothermal Isomerization of A → B
- Experimental data of X and −rₐ are given for a gas-phase reaction at 500 K and 830 kPa, with Fₐ₀ = 0.4 mol/s.
- Calculated values of 1/(−rₐ) and Fₐ₀/(−rₐ) are used to construct Levenspiel plots.
- Trends are consistent between the two plot types; only the y-axis scale differs.
Calculating Reactor Volumes
- For CSTR, volume at a target conversion is the area of a rectangle from the plot (X × Fₐ₀/(−rₐ)).
- Example: At X = 0.8, volume = 0.8 × 8 = 6.4 m³.
- For PFR, the volume is the area under the curve (to be discussed in the next lecture).
Key Terms & Definitions
- CSTR — Continuous Stirred-Tank Reactor, a reactor where contents are well mixed.
- PFR — Plug Flow Reactor, a reactor with continuous flow and no back-mixing.
- Conversion (X) — Fraction of reactant converted to product.
- Levenspiel Plot — A plot of conversion vs 1/(−rₐ) or Fₐ₀/(−rₐ), used for graphical reactor sizing.
- −rₐ — Rate of disappearance of reactant A.
- Fₐ₀ — Molar flow rate of reactant A entering the reactor.
Action Items / Next Steps
- Practice drawing Levenspiel plots using provided data and Excel.
- Calculate CSTR volumes at various conversions from the plot.
- Prepare for the next lecture on PFR volume calculation using numerical integration methods.