CSTR
A Continuously Stirred Tank Reactor (CSTR) is an idealised reactor in which perfect mixing is assumed, meaning concentration and temperature are uniform throughout the vessel and equal to the exit stream values. It operates at steady state with continuous feed and product streams, and is described by an algebraic design equation rather than a differential one. CSTRs are widely used in liquid-phase reactions, biological fermenters, and wastewater treatment due to their ease of temperature control and scale-up.
Key Formula
V = (F_A0 × X) / (−r_A)
LaTeX: V = \frac{F_{A0} \cdot X}{-r_A(X)}
| Symbol | Meaning | Unit |
|---|---|---|
| V | Reactor volume | L or m³ |
| F_A0 | Molar feed rate of reactant A | mol/min |
| X | Fractional conversion of A | dimensionless |
| −r_A | Rate of disappearance of A evaluated at exit conditions | mol/(L·min) |
Worked Example
Problem
A second-order liquid reaction A → P with k = 0.10 L/(mol·min), C_A0 = 1.0 mol/L, and v₀ = 50 L/min. Find the CSTR volume for 80% conversion.
Solution
Step 1: X = 0.80, C_A = C_A0(1−X) = 1.0 × 0.20 = 0.20 mol/L. Step 2: Rate at exit: −r_A = k·C_A² = 0.10 × (0.20)² = 0.10 × 0.04 = 4.0 × 10⁻³ mol/(L·min). Step 3: F_A0 = v₀ · C_A0 = 50 × 1.0 = 50 mol/min. Step 4: V = F_A0 · X / (−r_A) = 50 × 0.80 / (4.0 × 10⁻³) = 40 / 0.004 = 10,000 L.
Answer
CSTR volume = 10,000 L (10 m³)
CSTR Performance vs Conversion for First-Order Reaction (k = 0.05 min⁻¹, τ = V/v₀)
| Conversion X | C_A (mol/L) | Space Time τ (min) | Volume V (L) at v₀=100 L/min | Residence Time |
|---|---|---|---|---|
| 0.50 | 1.00 | 10 | 1,000 | 10 min |
| 0.70 | 0.60 | 23.3 | 2,333 | 23 min |
| 0.80 | 0.40 | 40 | 4,000 | 40 min |
| 0.90 | 0.20 | 90 | 9,000 | 90 min |
| 0.95 | 0.10 | 190 | 19,000 | 190 min |
Interactive Tools
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Related Terms
Chemical Reactor Design
Chemical reactor design is the discipline of selecting and sizing reactor vessels that achieve a desired chemical conversion at specified conditions of temperature, pressure, and flow rate. It integrates reaction kinetics, thermodynamics, and transport phenomena to predict concentration and temperature profiles within the reactor. Industrial applications range from petroleum refining and polymer synthesis to pharmaceutical manufacturing and environmental remediation.
Plug Flow Reactor
A Plug Flow Reactor (PFR) is an idealised tubular reactor in which fluid flows with a flat velocity profile (no axial mixing) so that all fluid elements have the same residence time. Concentration and temperature vary continuously along the reactor length, requiring a differential design equation for analysis. PFRs are preferred for gas-phase reactions, high-temperature processes, and situations where high conversion is required with minimum reactor volume compared to CSTRs.
Reaction Kinetics (engineering)
Reaction kinetics in engineering quantifies the rate at which reactants are converted to products under specified conditions of concentration, temperature, pressure, and catalyst presence. The rate expression (rate law) relates reaction rate to reactant concentrations via a rate constant, and the Arrhenius equation describes the temperature dependence of that constant. Engineering application of kinetics enables the sizing of reactors, optimisation of operating conditions, and prediction of yield and selectivity in industrial chemical processes.
Acronym for "Continuously Stirred Tank Reactor". The word "stirred" traces to Old English "styrian" (to move). The CSTR model was formalised in chemical engineering literature during the 1950s by Octave Levenspiel and colleagues at Oregon State University as part of the development of chemical reaction engineering as a discipline.