Isothermal Tubular Catalytic Microreactor
12.7 mm ID quartz tube housed in an electric three-zone furnace with ±0.2 °C temperature uniformity.
Chemical & Process Engineering / Heterogeneous Catalysis & Thiele Modulus
FREE TO EXPLORELABORATORY 29 · CHEMICAL & PROCESS ENGINEERING
Heterogeneous Catalytic Fixed-Bed Kinetics & Thiele Modulus Internal Diffusion
Measure the reaction conversion of a gas-phase reactant over porous cylindrical catalyst pellets in a packed-bed microreactor across varying pellet diameters d_p, evaluate the internal effectiveness factor η, and determine the diffusion-limitation slope S relating 1/η to d_p. 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.
RECIPROCAL EFFECTIVENESS 1/Η—
PROCESS & PILOT PLANT TELEMETRY
Ready to sample with Pellet Dia d_p = 3.0 mm.
Adjust Pellet Dia d_p, 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 (1.0 to 6.0 mm). Evaluated using porous alumina-supported platinum pellets (d_p = 1.0 to 6.0 mm, pore diameter 8 nm, D_eff = 2.4e-6 m^2/s) catalyzing hydrocarbon isomerization in an isothermal microreactor at 200.0 °C. Linear regression models 1/η versus d_p to extract slope S = 0.3500 mm^-1.
Process apparatus & industrial sensors.
Calibrated Porous Catalyst Pellet Batches
Six monodisperse batches of porous Pt/Al2O3 pellets with calibrated diameters d_p = 1, 2, 3, 4, 5, 6 mm.
Thermal Mass Flow Controller (MFC) Gas Manifold
Delivers reactant vapor in carrier helium at precise space velocity with 0.1 mL/min precision.
Online Gas Chromatograph with Flame Ionization Detector
Analyzes reactor effluent every 5 minutes to quantify reactant conversion with 0.05% resolution.
Internal Multi-Point Thermocouple Well
Monitors catalyst bed centerline temperature to verify strictly isothermal operation at 200.0 °C.
Micromeritics BET Physisorption Surface Area Analyzer
Measures catalyst specific surface area (210 m^2/g) and average pore diameter (8.2 nm).
FOLLOW THE METHOD
A reason behind every step.
Measure the reaction conversion of a gas-phase reactant over porous cylindrical catalyst pellets in a packed-bed microreactor across varying pellet diameters d_p, evaluate the internal effectiveness factor η, and determine the diffusion-limitation slope S relating 1/η to d_p. Standardized parameter settings: 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 mm.
01
Furnace Heating & Isothermal Baseline
Heat microreactor furnace to 200.0 °C under helium purge; allow 30 minutes for temperature controllers to stabilize to within ±0.1 °C.
02
Pellet Bed Packing (d_p = 1.0 mm)
Pack 2.00 g of 1.0 mm catalyst pellets into the reactor tube between quartz wool plugs; verify bed depth and zero bypass channeling.
03
Reactant Introduction & Steady Conversion
Introduce reactant feed at space velocity WHSV = 2.0 h^-1; allow 20 minutes to reach chemical steady state and log effluent conversion via GC-FID.
04
Intrinsic Baseline Normalization
Establish the intrinsic rate from the finest 1.0 mm pellets (minimal diffusion resistance, η ≈ 0.74) to normalize observed rates into effectiveness factor η.
05
Pellet Diameter Progression Protocol
Repeat tests under identical temperature and space velocity using catalyst batches of d_p = 2.0, 3.0, 4.0, 5.0, and 6.0 mm, logging conversion at each plateau.
06
Thiele Modulus Regression Analysis
Calculate internal effectiveness factor η for each pellet size, plot 1/η versus pellet diameter d_p, and fit a linear regression to determine slope S.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into chemical process engineering insight.
Points are your recorded observations. The solid regression line validates Heterogeneous Catalysis & Thiele Modulus mathematical scaling.
LINEAR REGRESSION FIT · y = mx + b
1 / η = S · d_p + 1.0000 = 0.3500 · d_p + 1.0000
| # | Catalyst Pellet Diameter d_p (mm) | Reciprocal Effectiveness 1/η (ratio) | Catalyst pellet diameter d_p (mm) | Reciprocal internal effectiveness factor 1 / η | 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 Thiele modulus φ for a porous catalyst pellet is defined as the ratio of:
Under strong internal pore diffusion resistance (Thiele modulus φ >> 3), the effectiveness factor η scales with pellet diameter d_p as:
When strong pore diffusion resistance dominates, the apparent activation energy measured experimentally is approximately:
To minimize expensive precious metal usage in diffusion-limited reactions, industrial catalysts are formulated as:
THEORY AND UNIT OPERATIONS CONTEXT
Process engineering background & physical principles.
Heterogeneous solid-catalyzed reactions represent the backbone of the chemical and petrochemical industries, accounting for more than 80% of all chemical manufacturing processes (including ammonia synthesis, catalytic reforming, Fischer–Tropsch fuels, and automotive emissions catalytic converters). In heterogeneous catalysis, porous catalyst pellets provide enormous internal active surface area (100 to 500 m^2/g) inside an intricate network of microscopic pores. A gaseous reactant molecule must undergo five sequential transport and chemical steps: (1) external convective mass transfer across the fluid boundary layer to the external pellet surface, (2) internal Knudsen and molecular diffusion through fluid-filled pores to interior catalytic sites, (3) chemisorption onto active metal sites, (4) intrinsic surface chemical reaction, and (5) desorption and back-diffusion of products. When internal pore diffusion is slower than intrinsic surface kinetics, a steep reactant concentration gradient develops inside the pellet: reactant molecules are consumed before they can penetrate into the deep pellet core, leaving interior catalyst unutilized. Ernest W. Thiele (1939) formulated the celebrated Thiele modulus: φ = L_p · sqrt(k_v / D_eff), where L_p = R_p / 3 is the characteristic diffusion length, k_v is the intrinsic volumetric reaction rate constant, and D_eff is effective pore diffusivity. The ratio of actual overall reaction rate to the ideal rate that would occur if the entire pellet interior were exposed to surface concentration C_s is termed the internal effectiveness factor: η = tanh(φ) / φ. Under strong pore diffusion limitations (φ > 3), the effectiveness factor scales inversely with pellet diameter: η ≈ 1 / φ ∝ 1 / d_p, meaning reciprocal effectiveness scales linearly with pellet diameter: 1 / η = S · d_p + 1.0. In this laboratory investigation, an isothermal packed-bed microreactor is tested with catalyst pellets of diameters d_p from 1.0 to 6.0 mm to measure 1/η vs d_p, verify Thiele pore diffusion theory, and determine the diffusion limitation slope S = 0.3500 mm^-1.
1 / η = S · d_p + 1.0000 = 0.3500 · d_p + 1.0000
Evaluated using porous alumina-supported platinum pellets (d_p = 1.0 to 6.0 mm, pore diameter 8 nm, D_eff = 2.4e-6 m^2/s) catalyzing hydrocarbon isomerization in an isothermal microreactor at 200.0 °C. Linear regression models 1/η versus d_p to extract slope S = 0.3500 mm^-1.