Three-Stage CSTR Cascade Rig
Three identical 1.0 L glass CSTRs in cascade with gravity overflow weirs and 4 wall baffles.
Chemical & Process Engineering / CSTR Cascade in Series
FREE TO EXPLORELABORATORY 27 · CHEMICAL & PROCESS ENGINEERING
Continuous Stirred-Tank Reactor (CSTR) Cascade in Series & Multi-Stage Conversion
Operate a three-stage CSTR cascade in series, measure inter-stage concentration profiles at steady state across total space times τ_tot from 6.0 to 36.0 min, and evaluate conversion enhancement approaching plug-flow behavior. Explore interactive transport phenomena, unit operations simulation, and chemical engineering telemetry.
TRANSPORT PHENOMENA · UNIT OPERATIONS · PROCESS CONTROL · REACTION ENGINEERING
Your virtual chemical and process engineering laboratory.
CASCADE ROOT CONCENTRATION FACTOR (C_A0/C_A3)^(1/3)—
PROCESS & PILOT PLANT TELEMETRY
Ready to sample with Cascade τ_tot = 18.0 min.
Adjust Cascade τ_tot, then execute chemical process trial.
Chemical and process engineering telemetry is evaluated rigorously using 64-bit IEEE 754 precision. Residuals reflect ordinary least-squares regression across successive observations. Continuous data structures support high-fidelity transport phenomena and unit operations modeling.
Process engineering assumptions and boundary condition limits
The transport and thermodynamic models apply within the specified calibrated operating window (6.0 to 36.0 min). Evaluated using three 1.0 L jacketed glass CSTRs in series (V_tot = 3.0 L, N = 3) with Rushton impellers at 350 RPM and 25.0 °C. Linear regression models (C_A0 / C_A3)^(1/3) versus τ_tot to extract S = 0.0450 min^-1.
Process apparatus & industrial sensors.
Independent Variable-Speed Impeller Drives
Three 6-blade Rushton turbines driven at 350 RPM to ensure ideal mixing in each stage.
Master Peristaltic Feed Metering Pump
Delivers reactant feed at steady flow rates from 0.083 to 0.500 L/min to set τ_tot = 6 to 36 min.
Three In-Line Flow-Through Conductivity Probes
Measures effluent conductivity at exit of Tank 1, Tank 2, and Tank 3 with 0.01 mS/cm precision.
Common Thermostatic Circulation Jacket Loop
Maintains all three reactors at uniform temperature 25.00 ± 0.05 °C.
Automated Multi-Channel Data Acquisition System
Logs real-time inter-stage conversion profiles X_A1, X_A2, and X_A3.
FOLLOW THE METHOD
A reason behind every step.
Operate a three-stage CSTR cascade in series, measure inter-stage concentration profiles at steady state across total space times τ_tot from 6.0 to 36.0 min, and evaluate conversion enhancement approaching plug-flow behavior. Standardized parameter settings: 6.0, 12.0, 18.0, 24.0, 30.0, 36.0 min.
01
Cascade Sensor Calibration
Calibrate all three conductivity probes using standardized 0% and 100% conversion solutions to verify identical cell constants.
02
Jacket Thermal Equilibration
Circulate 25.0 °C water through all three reactor jackets; fill tanks to their 1.0 L overflow levels with deionized water and start impellers at 350 RPM.
03
Initial Flow Rate Setpoint
Set feed pump to v_0 = 0.500 L/min (total cascade space time τ_tot = 3.0 L / 0.500 L/min = 6.0 min, τ_i = 2.0 min per tank).
04
Inter-Stage Steady-State Logging
Allow 4 cascade residence times (24 minutes) for steady state; record conductivity and compute concentrations C_A1, C_A2, and C_A3.
05
Space Time Progression Protocol
Step feed flow down through 0.250, 0.167, 0.125, 0.100, and 0.083 L/min to establish τ_tot = 12.0, 18.0, 24.0, 30.0, and 36.0 min, recording inter-stage data at each plateau.
06
Cascade Kinetic Regression Analysis
Compute (C_A0 / C_A3)^(1/3) for each run, plot versus τ_tot, and fit a linear regression to extract slope S and evaluate rate constant k.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into chemical process engineering insight.
Points are your recorded observations. The solid regression line validates CSTR Cascade in Series mathematical scaling.
LINEAR REGRESSION FIT · y = mx + b
(C_A0 / C_A3)^(1/3) = S · τ_tot + 1.0000 = 0.0450 · τ_tot + 1.0000
| # | Total Cascade Space Time τ_tot (min) | Cascade Root Concentration Factor (C_A0/C_A3)^(1/3) (ratio) | Total cascade space time τ_tot (min) | Cascade root concentration factor (C_A0 / C_A3)^(1/3) | Remove |
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Calculate it yourself.
CHECK YOUR UNDERSTANDING
Explain what the process engineering metrics mean.
As the number of equal-sized CSTRs in series N approaches infinity for a fixed total volume, the cascade behaves as:
For a first-order reaction in N equal-volume CSTRs in series, the overall concentration ratio is given by:
To achieve a given conversion for a positive-order reaction, the total volume required by a 3-CSTR cascade compared to a single CSTR is:
For a first-order reaction, the optimal volume distribution among N CSTRs in series that minimizes total volume is:
THEORY AND UNIT OPERATIONS CONTEXT
Process engineering background & physical principles.
In industrial chemical reaction engineering, connecting multiple continuous stirred-tank reactors in series (a CSTR cascade or tank battery) is one of the most effective strategies for overcoming the low conversion efficiency of a single backmix vessel while preserving excellent temperature control and slurry handling capabilities. In a single CSTR, feed is immediately diluted to the final product concentration, forcing the entire vessel to operate at the slowest reaction rate. In contrast, in a cascade of N equal-volume tanks in series, reactant concentration drops in discrete stages from tank to tank. The first tank operates at a high intermediate concentration and high reaction rate, the second at a moderate rate, and only the final tank operates at the exit concentration. Mathematically, as the number of stages N approaches infinity while total volume V_tot is held constant, the discrete staircase concentration profile approaches the smooth continuous exponential decay of an ideal plug-flow reactor (PFR). For an equimolar first-order or pseudo-first-order reaction (-r_A = k · C_A) conducted across N identical CSTRs each having individual space time τ_i = τ_tot / N, mass balances across each tank yield: C_Ai = C_A,i-1 / (1 + k · τ_i). Cascading across N stages gives: C_A0 / C_AN = (1 + k · τ_tot / N)^N. For a three-stage cascade (N = 3): (C_A0 / C_A3)^(1/3) = 1 + (k / 3) · τ_tot = S · τ_tot + 1.0. In this laboratory investigation, an instrumented three-tank CSTR cascade is operated across total space times from 6.0 to 36.0 min to measure inter-stage concentrations, verify the N-stage power law, and evaluate kinetic slope S = k / 3 = 0.0450 min^-1 (k = 0.1350 min^-1).
(C_A0 / C_A3)^(1/3) = S · τ_tot + 1.0000 = 0.0450 · τ_tot + 1.0000
Evaluated using three 1.0 L jacketed glass CSTRs in series (V_tot = 3.0 L, N = 3) with Rushton impellers at 350 RPM and 25.0 °C. Linear regression models (C_A0 / C_A3)^(1/3) versus τ_tot to extract S = 0.0450 min^-1.