Plexiglas Packed Test Column with Calming Sections
50 mm ID column packed to 600 mm with 6 mm glass beads; equipped with flow calming grids.
Chemical & Process Engineering / RTD & Axial Dispersion
FREE TO EXPLORELABORATORY 28 · CHEMICAL & PROCESS ENGINEERING
Residence Time Distribution (RTD) & Axial Dispersion Modeling in Packed Columns
Perform pulse tracer injection of a salt electrolyte in a liquid-flowing packed column, record the exit age distribution E(t), evaluate mean residence time t_mean and variance σ^2, and determine the vessel Peclet number Pe via the axial dispersion model. 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.
MEAN RESIDENCE TIME RECIPROCAL 1/T_MEAN—
PROCESS & PILOT PLANT TELEMETRY
Ready to sample with Flow Q = 150.0 mL/min.
Adjust Flow Q, 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 (50.0 to 300.0 mL/min). Evaluated using a 50 mm ID column packed with 6 mm glass beads (total volume 600 mL, bed voidage ε = 0.40, liquid pore volume V_p = 240 mL; calibrated to V_p = 400.0 mL system hold-up). Linear regression models 1/t_mean versus Q to extract slope S = 0.00250 min^-1/(mL/min).
Process apparatus & industrial sensors.
Fast-Actuating Septum Tracer Injection Valve
Delivers 1.0 mL Dirac pulse of 2.0 M KCl tracer in < 0.1 s without disturbing main flow.
High-Speed Micro-Flow Conductivity Probe
Monitors effluent salt concentration at column exit with 10 Hz sampling rate and 0.01 mS/cm resolution.
Precision Dual-Piston HPLC Liquid Metering Pump
Delivers pulsation-free deionized water carrier flow from 20 to 400 mL/min with 0.1% accuracy.
Digital Data Acquisition System with Chronometer
Integrates C(t) curves in real-time to compute zeroth, first, and second moments automatically.
Thermostatically Controlled Water Reservoir
Maintains carrier water at 25.0 ± 0.1 °C to ensure constant liquid density and tracer diffusivity.
FOLLOW THE METHOD
A reason behind every step.
Perform pulse tracer injection of a salt electrolyte in a liquid-flowing packed column, record the exit age distribution E(t), evaluate mean residence time t_mean and variance σ^2, and determine the vessel Peclet number Pe via the axial dispersion model. Standardized parameter settings: 50.0, 100.0, 150.0, 200.0, 250.0, 300.0 mL/min.
01
Baseline Conductivity Zeroing
Circulate deionized water at 150 mL/min through the packed column until baseline effluent conductivity reads stable at < 0.02 mS/cm.
02
Initial Flow Rate Establishment
Set metering pump to Q = 50.0 mL/min; allow pressure and flow to achieve steady state for 10 minutes.
03
Tracer Pulse Injection Execution
Rapidly inject 1.0 mL of 2.0 M KCl solution through the inlet septum valve; trigger data acquisition timer at t = 0.
04
RTD Curve Data Acquisition
Log effluent conductivity continuously at 10 Hz until the tracer concentration returns to baseline (< 1% of peak height).
05
Flow Rate Progression Protocol
Step carrier flow rate through 100.0, 150.0, 200.0, 250.0, and 300.0 mL/min, executing pulse injections and acquiring RTD curves at each plateau.
06
Moments & Dispersion Regression Analysis
Numerically integrate each RTD curve to determine t_mean and variance σ^2; plot 1/t_mean versus Q to extract slope S, and evaluate Peclet number Pe.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into chemical process engineering insight.
Points are your recorded observations. The solid regression line validates RTD & Axial Dispersion mathematical scaling.
LINEAR REGRESSION FIT · y = mx + b
1 / t_mean = S · Q = 0.0025 · Q
| # | Superficial Liquid Flow Q (mL/min) | Mean Residence Time Reciprocal 1/t_mean (min^-1) | Volumetric liquid flow rate Q (mL/min) | Reciprocal mean residence time 1 / t_mean (min^-1) | Remove |
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No readings yet. Execute a process trial and record it.
Calculate it yourself.
CHECK YOUR UNDERSTANDING
Explain what the process engineering metrics mean.
The total area under an exit age distribution curve E(t) from t = 0 to t = ∞ equals:
In the axial dispersion model, an infinite Peclet number (Pe → ∞) corresponds to:
The first moment of the residence time distribution curve represents:
If a reactor exhibits a substantial volume of stagnant dead zones, the measured mean residence time t_mean will be:
THEORY AND UNIT OPERATIONS CONTEXT
Process engineering background & physical principles.
In real chemical reactors, packed absorption towers, and tubular contactors, fluid flow never achieves the idealized extremes of pure plug flow or perfect backmixing. Instead, non-ideal flow phenomena—such as velocity profile shearing, molecular diffusion, turbulent eddy mixing, stagnant dead zones, and channeling—cause fluid elements to spend varying amounts of time inside the vessel. P. V. Danckwerts (1953) formulated the foundational theory of Residence Time Distribution (RTD) to diagnose and quantify these non-idealities. When a narrow Dirac delta pulse of an inert non-adsorbing tracer (e.g., concentrated potassium chloride solution) is injected at the reactor inlet at t = 0, the exit tracer concentration curve C(t) defines the exit age distribution: E(t) = C(t) / ∫ C(t) dt. The first moment of E(t) yields the mean residence time: t_mean = ∫ t · E(t) dt = V_p / Q, where V_p is the internal liquid pore volume and Q is volumetric throughput. Consequently, the reciprocal mean residence time scales strictly linearly with flow rate: 1 / t_mean = (1 / V_p) · Q = S · Q. The second central moment gives the distribution variance σ^2 = ∫ (t - t_mean)^2 · E(t) dt, which quantifies the degree of axial backmixing. Fitting the one-dimensional Taylor-Aris axial dispersion model determines the dimensionless vessel Peclet number Pe = u · L / D_ax: σ^2 / t_mean^2 = 2 / Pe - 2 / Pe^2 · [1 - exp(-Pe)]. In this laboratory investigation, an instrumented packed column is tested with pulse tracer injections across flow rates from 50.0 to 300.0 mL/min to measure RTD curves, verify 1/t_mean = 0.00250 · Q (V_p = 400.0 mL), and determine the Peclet number Pe.
1 / t_mean = S · Q = 0.0025 · Q
Evaluated using a 50 mm ID column packed with 6 mm glass beads (total volume 600 mL, bed voidage ε = 0.40, liquid pore volume V_p = 240 mL; calibrated to V_p = 400.0 mL system hold-up). Linear regression models 1/t_mean versus Q to extract slope S = 0.00250 min^-1/(mL/min).