Coiled Stainless Steel Tubular Plug-Flow Reactor
15.3 m of 10 mm ID tube coiled compactly into a 1.20 L active reactor volume.
Chemical & Process Engineering / Tubular PFR Kinetics
FREE TO EXPLORELABORATORY 26 · CHEMICAL & PROCESS ENGINEERING
Plug-Flow Tubular Reactor (PFR) Residence Time & Isothermal Conversion Kinetics
Operate an isothermal tubular plug-flow reactor (PFR) conducting liquid-phase saponification, evaluate reactant conversion as a function of space time τ, and verify the first-order / linearized PFR performance model ln(1/(1 - X_A)) = k·τ. 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.
LINEARIZED PFR FACTOR LN(1/(1 - X_A))—
PROCESS & PILOT PLANT TELEMETRY
Ready to sample with Space Time τ = 4.5 min.
Adjust Space Time τ, 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 (1.5 to 9.0 min). Evaluated using a 1.2 L coiled tubular reactor (pipe ID 10.0 mm, length 15.3 m) submerged in a 25.0 °C bath. Linear regression models ln(1 / (1 - X_A)) versus space time τ to extract rate constant k = 0.1850 min^-1.
Process apparatus & industrial sensors.
Submerged Constant-Temperature Water Bath
Maintains tubular reactor isothermal at 25.00 ± 0.05 °C with high-flow circulation pump.
Dual Micro-Gear Metering Feed Pumps
Delivers pulsation-free reactant streams at combined flow rates from 0.133 to 0.800 L/min.
In-Line Flow-Through Optical Spectrophotometer Cell
Monitors effluent absorbance in real-time at reactor exit to determine conversion with 0.1% accuracy.
Rapid Mixing T-Junction Inlet Manifold
Mixes two feed streams within < 10 ms at the tube entrance to establish precise t = 0 reaction datum.
Digital Stopwatch & Analytical Volumetric Flasks
Calibrates pump discharge rates gravimetrically to establish exact space times τ.
FOLLOW THE METHOD
A reason behind every step.
Operate an isothermal tubular plug-flow reactor (PFR) conducting liquid-phase saponification, evaluate reactant conversion as a function of space time τ, and verify the first-order / linearized PFR performance model ln(1/(1 - X_A)) = k·τ. Standardized parameter settings: 1.5, 3.0, 4.5, 6.0, 7.5, 9.0 min.
01
Optical Sensor Calibration
Zero the spectrophotometer with pure solvent and record absorbance baseline for 0% and 100% conversion standards.
02
Bath Temperature Stabilization
Set bath temperature to 25.00 °C; circulate water for 15 minutes to ensure the coiled tube is isothermal.
03
Initial Flow Rate Setpoint
Set feed pumps to combined flow rate v_0 = 0.800 L/min (reactor space time τ = 1.20 L / 0.800 L/min = 1.50 min).
04
Steady-State Effluent Logging
Allow 3 residence times (4.5 minutes) for steady state; record effluent absorbance to calculate fractional conversion X_A.
05
Space Time Stepping Protocol
Step combined flow rate down through 0.400, 0.267, 0.200, 0.160, and 0.133 L/min to establish space times τ = 3.0, 4.5, 6.0, 7.5, and 9.0 min.
06
PFR Kinetic Regression Analysis
Calculate ln[1 / (1 - X_A)] for each run, plot versus space time τ, and fit a linear regression through the origin to determine rate constant k.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into chemical process engineering insight.
Points are your recorded observations. The solid regression line validates Tubular PFR Kinetics mathematical scaling.
LINEAR REGRESSION FIT · y = mx + b
ln(1 / (1 - X_A)) = k · τ = 0.1850 · τ
| # | PFR Space Time τ (min) | Linearized PFR Factor ln(1/(1 - X_A)) (ratio) | PFR space time τ (min) | Linearized PFR factor ln(1 / (1 - X_A)) | 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.
In an ideal Plug-Flow Reactor (PFR), axial mixing of fluid elements is assumed to be:
For a first-order reaction in an ideal PFR, the relationship between conversion X_A and space time τ is:
The Residence Time Distribution (RTD) curve E(t) for an ideal PFR is represented by:
For a series reaction A -> R -> S where R is the desired product, the reactor that maximizes yield of R is:
THEORY AND UNIT OPERATIONS CONTEXT
Process engineering background & physical principles.
Plug-flow reactors (PFRs or tubular reactors) represent the idealized opposite mixing extreme to the continuous stirred-tank reactor (CSTR). In an ideal PFR, fluid elements travel through an elongated conduit in orderly plug flow with zero axial mixing or back-dispersion, while exhibiting perfect radial mixing across any cross-section. Consequently, every fluid element resides in the reactor for exactly the same duration, equal to the space time τ = V / v_0. Reactants enter at maximum concentration, and reaction rate is highest at the entrance, declining progressively along the tube axis as reactants are consumed. This makes tubular PFRs substantially more efficient than CSTRs for positive-order reactions, requiring less reactor volume to achieve high fractional conversion. For a first-order or pseudo-first-order liquid reaction: -r_A = k · C_A = k · C_A0 · (1 - X_A), integrating the differential PFR design equation dX_A / dτ = -r_A / C_A0 yields the celebrated exponential relation: 1 - X_A = exp(-k · τ) -> ln[1 / (1 - X_A)] = k · τ. In this laboratory investigation, a coiled stainless steel tubular PFR submerged in a constant-temperature water bath is operated across space times from 1.5 to 9.0 min to measure conversion X_A, verify plug-flow kinetics, and evaluate rate constant k = 0.1850 min^-1.
ln(1 / (1 - X_A)) = k · τ = 0.1850 · τ
Evaluated using a 1.2 L coiled tubular reactor (pipe ID 10.0 mm, length 15.3 m) submerged in a 25.0 °C bath. Linear regression models ln(1 / (1 - X_A)) versus space time τ to extract rate constant k = 0.1850 min^-1.