CSTR and PFR Reactor Calculator
With k = 0.3 per hour and 8 hours of detention, a plug-flow reactor leaves 0.090718 of the inlet concentration (91 % removal) while a single CSTR leaves 29 %.
0.0907179532894125
Full answer, then cut to fewer decimals (not rounded):
- 0.0907179532894125
- 0.090717953289412
- 0.09071795328941
- 0.0907179532894
- 0.090717953289
- 0.09071795328
- 0.0907179532
- 0.090717953
- 0.09071795
- 0.0907179
- 0.090717
- 0.09071
- 0.0907
- 0.090
- 0.09
- PFR removal
- 90.92820467 %
- CSTR outlet C/C₀ = 1/(1 + kτ)
- 0.2941176471
- CSTR removal
- 70.58823529 %
- 3 CSTRs in series C/C₀
- 0.1714677641
Step-by-step solution
- PFR: C/C₀ = e^(−kτ) = e^(−2.4) = 0.09071795329
- CSTR: C/C₀ = 1 ÷ (1 + kτ) = 0.2941176471
- N tanks: C/C₀ = (1 + kτ/N)^(−N) = 0.1714677641
CSTR and PFR Reactor Formula
PFR: C/C₀ = e^(−kτ); CSTR: C/C₀ = 1/(1 + kτ)
N CSTRs in series: C/C₀ = (1 + kτ/N)^(−N), τ total
Worked Example
A first-order reaction with k = 0.3 per hour and 8 h detention:
- PFR: C/C₀ = e^(−kτ) = e^(−2.4) = 0.09071795329
- CSTR: C/C₀ = 1 ÷ (1 + kτ) = 0.2941176471
- N tanks: C/C₀ = (1 + kτ/N)^(−N) = 0.1714677641
CSTR outlet C/C₀ = 1/(1 + kτ): 0.2941176471 · CSTR removal: 70.58823529 % · 3 CSTRs in series C/C₀: 0.1714677641
GATE tip
For zero-order reactions PFR and CSTR need the same volume; for second-order the gap grows further. Always check the order before comparing reactors.
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Frequently asked questions
Why is a PFR more efficient?
In a CSTR the whole tank sits at the low outlet concentration, so a first-order reaction runs slowly everywhere; a PFR keeps high concentrations near the inlet.
Why put tanks in series?
Several CSTRs in series approach plug flow: for 90 % removal one CSTR needs about 3.9 times the PFR volume, three in series about 1.5 times.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). CSTR and PFR Reactor Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/reactor-design-calculator/
IEEE
Scientific Converters, "CSTR and PFR Reactor Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/reactor-design-calculator/