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CHEMECAT / ENGINEERING TOOLS

Cat Lab

Catalyst Bed / Reactor Calculator

Connect geometry, gas flow, and catalyst inventory. Examine every result.

Illustrative example loaded. Values are demonstration inputs, not validated gas or catalyst property data. No data is saved after refresh.

Packed-bed volume

7.85mL

Includes particles + interparticle voids

Superficial velocity

0.0412m/s

At operating conditions

GHSV at reference conditions

764h⁻¹

Reference gas / packed-bed volume

Ergun pressure drop

88.7Pa

Ergun · constant-property estimate

Inputs

INPUT

Leave unknown values blank. Unit changes preserve the entered physical quantity.

01Bed geometry & inventory

Bed diameter

Packed-bed length

Catalyst mass

Optional if bulk density and bed volume are known.

Bed bulk density

Mass per packed-bed volume, including interparticle voids.

Geometry defines bed volume when diameter and length are supplied. Otherwise mass ÷ bulk density can define it.

02Bed voidageVoidage source

Interparticle void fraction

Strictly between 0 and 1 (or 0–100%).

03Gas flow & operating stateVolumetric flow basis

Gas volumetric flow

Operating temperature

Operating / inlet pressure

Absolute pressure; convert gauge readings before entry.

Ideal gas (Z = 1). Absolute pressure and kelvin are used internally.

04Reference gas state

Defines the supplied flow and is needed for conversion.

Reference temperature

Reference pressure

Absolute pressure. The reference state is explicit, not universal.

05Gas mass properties

Gas molecular weight

Mixture-average value. Needed for density, mass flow, WHSV, and full Ergun.

06Ergun pressure drop

Calculate pressure drop

Sphere particle diameter

Uniform spheres assumed; arbitrary pellet width is not a validated equivalent diameter.

Dynamic viscosity

Supply a defensible value at operating temperature and pressure.

Also uses diameter, length, voidage, flow, operating state, and molecular weight.

Cylindrical packed bed · SI scientific core

Calculated results

3 significant figures

Reference gas basis: 273.15 K · 101.325 kPa absolute
GHSV uses packed-bed volume. WHSV uses total inlet gas mass.

Geometry & inventory

Quantity / calculation	Value	Unit
Cross-sectional area Show Calculation CALCULATED RESULT A = πD² / 4 Substitution in SI ((3.141592653589793 × (0.01 m)^2) / 4) = 7.85e-5 m² Display conversion: divide the SI value by 0.000100000 → 0.785 cm². Assumptions The packed region is a uniform cylinder. Dimensions checked against the declared SI output unit.	0.785	cm²
Packed-bed volume Show Calculation CALCULATED RESULT V_b = AL Substitution in SI (0.0000785398 m² × 0.1 m) = 7.85e-6 m³ Display conversion: divide the SI value by 0.00000100000 → 7.85 mL. Assumptions The packed region is a uniform cylinder. Dimensions checked against the declared SI output unit.	7.85	mL
Catalyst massDERIVED Show Calculation DERIVED VALUE m_c = ρ_b V_b Substitution in SI (600 kg/m³ × 0.00000785398 m³) = 0.00471 kg Display conversion: divide the SI value by 0.00100000 → 4.71 g. Assumptions The packed region is a uniform cylinder. Dimensions checked against the declared SI output unit.	4.71	g
Catalyst loading / bulk densityINPUT Show Calculation INPUT ρ_b = supplied packed-bed bulk density Substitution in SI 600 kg/m³ = 600 kg/m³ Mass per packed-bed volume; not particle density. Dimensions checked against the declared SI output unit.	600	kg/m³
Bed void fractionINPUT Show Calculation INPUT ε = supplied interparticle void fraction Substitution in SI 0.4 1 = 0.4 1 Assumptions Void fraction describes only interparticle space in a uniformly packed bed. Dimensions checked against the declared SI output unit.	0.4	1
Interparticle void volume Show Calculation CALCULATED RESULT V_v = ε V_b Substitution in SI (0.4 1 × 0.00000785398 m³) = 3.14e-6 m³ Display conversion: divide the SI value by 0.00000100000 → 3.14 mL. Assumptions Void fraction describes only interparticle space in a uniformly packed bed. The packed region is a uniform cylinder. Dimensions checked against the declared SI output unit.	3.14	mL

Flow & contact

Quantity / calculation	Value	Unit
Operating volumetric flow Show Calculation CALCULATED RESULT Q_op = Q_ref (T_op/T_ref)(P_ref/P_op) Substitution in SI ((0.00000166667 m³/s × (523.15 K / 273.15 K)) × (101325 Pa / 100000 Pa)) = 3.23e-6 m³/s Display conversion: divide the SI value by 1.66667e-8 → 194 mL/min. Assumptions The gas obeys PV = nRT (Z = 1); no reaction or change in composition between flow states. Dimensions checked against the declared SI output unit.	194	mL/min
Reference volumetric flowINPUT Show Calculation INPUT Q_ref = supplied volumetric flow at the declared reference state Substitution in SI 0.00000166667 m³/s = 1.67e-6 m³/s Display conversion: divide the SI value by 1.66667e-8 → 100 mL/min. Dimensions checked against the declared SI output unit.	100	mL/min
Superficial velocity Show Calculation CALCULATED RESULT u_s = Q_op / A Substitution in SI (0.00000323438 m³/s / 0.0000785398 m²) = 0.0412 m/s Assumptions The gas obeys PV = nRT (Z = 1); no reaction or change in composition between flow states. The packed region is a uniform cylinder. Dimensions checked against the declared SI output unit.	0.0412	m/s
Interstitial velocity Show Calculation CALCULATED RESULT u_i = u_s / ε Substitution in SI (0.0411813 m/s / 0.4 1) = 0.103 m/s Assumptions Void fraction describes only interparticle space in a uniformly packed bed. The gas obeys PV = nRT (Z = 1); no reaction or change in composition between flow states. The packed region is a uniform cylinder. Dimensions checked against the declared SI output unit.	0.103	m/s
Empty-bed space time Show Calculation CALCULATED RESULT τ_b = V_b / Q_op Substitution in SI (0.00000785398 m³ / 0.00000323438 m³/s) = 2.43 s Assumptions Gas flow and voidage are spatially uniform and constant. The packed region is a uniform cylinder. The gas obeys PV = nRT (Z = 1); no reaction or change in composition between flow states. Dimensions checked against the declared SI output unit.	2.43	s
Nominal void residence time Show Calculation CALCULATED RESULT τ_v = ε V_b / Q_op Substitution in SI (0.00000314159 m³ / 0.00000323438 m³/s) = 0.971 s Excludes intraparticle hold-up; not a measured residence-time distribution. Assumptions Gas flow and voidage are spatially uniform and constant. Void fraction describes only interparticle space in a uniformly packed bed. The packed region is a uniform cylinder. The gas obeys PV = nRT (Z = 1); no reaction or change in composition between flow states. Dimensions checked against the declared SI output unit.	0.971	s
Operating space velocity Show Calculation CALCULATED RESULT SV_op = Q_op / V_b Substitution in SI (0.00000323438 m³/s / 0.00000785398 m³) = 0.412 s⁻¹ Display conversion: divide the SI value by 0.000277778 → 1,480 h⁻¹. Operating gas volume per packed-bed volume. Assumptions The gas obeys PV = nRT (Z = 1); no reaction or change in composition between flow states. The packed region is a uniform cylinder. Dimensions checked against the declared SI output unit.	1,480	h⁻¹
GHSV at reference conditions Show Calculation CALCULATED RESULT GHSV_ref = Q_ref / V_b Substitution in SI (0.00000166667 m³/s / 0.00000785398 m³) = 0.212 s⁻¹ Display conversion: divide the SI value by 0.000277778 → 764 h⁻¹. Reference gas volume per packed-bed volume. No universal standard state is implied. Assumptions The packed region is a uniform cylinder. Dimensions checked against the declared SI output unit.	764	h⁻¹

Gas & loading

Quantity / calculation	Value	Unit
Gas density at operating state Show Calculation CALCULATED RESULT ρ_g = P_op M / (R T_op) Substitution in SI ((100000 Pa × 0.028 kg/mol) / (8.31446 J/(mol·K) × 523.15 K)) = 0.644 kg/m³ Assumptions The gas obeys PV = nRT (Z = 1); no reaction or change in composition between flow states. Dimensions checked against the declared SI output unit.	0.644	kg/m³
Molar flow Show Calculation CALCULATED RESULT ṅ = PQ / (RT), at the entered flow state Substitution in SI ((101325 Pa × 0.00000166667 m³/s) / (8.31446 J/(mol·K) × 273.15 K)) = 7.44e-5 mol/s Display conversion: divide the SI value by 0.0000166667 → 4.46 mmol/min. Assumptions The gas obeys PV = nRT (Z = 1); no reaction or change in composition between flow states. Dimensions checked against the declared SI output unit.	4.46	mmol/min
Total inlet gas mass flow Show Calculation CALCULATED RESULT ṁ = ṅ M Substitution in SI (0.0000743584 mol/s × 0.028 kg/mol) = 2.08e-6 kg/s Display conversion: divide the SI value by 2.77778e-7 → 7.5 g/h. Assumptions The gas obeys PV = nRT (Z = 1); no reaction or change in composition between flow states. Dimensions checked against the declared SI output unit.	7.5	g/h
WHSV · total inlet gas Show Calculation CALCULATED RESULT WHSV = ṁ / m_c Substitution in SI (0.00000208203 kg/s / 0.00471239 kg) = 4.42e-4 s⁻¹ Display conversion: divide the SI value by 0.000277778 → 1.59 h⁻¹. Total inlet gas mass per catalyst mass; not reactant-only WHSV. Assumptions The gas obeys PV = nRT (Z = 1); no reaction or change in composition between flow states. The packed region is a uniform cylinder. Dimensions checked against the declared SI output unit.	1.59	h⁻¹

Pressure drop

Quantity / calculation	Value	Unit
Viscous contribution Show Calculation CALCULATED RESULT ΔP_v = 150 μ L (1−ε)² u_s / (ε³ d_p²) Substitution in SI (((((150 × 0.000025 Pa·s) × 0.1 m) × ((1 − 0.4 1))^2) × 0.0411813 m/s) / ((0.4 1)^3 × (0.001 m)^2)) = 86.9 Pa Assumptions Steady single-phase flow through a fixed bed of uniform spheres; constant viscosity and density. Void fraction describes only interparticle space in a uniformly packed bed. The gas obeys PV = nRT (Z = 1); no reaction or change in composition between flow states. The packed region is a uniform cylinder. Dimensions checked against the declared SI output unit.	86.9	Pa
Inertial contribution Show Calculation CALCULATED RESULT ΔP_i = 1.75 ρ_g L (1−ε) u_s² / (ε³ d_p) Substitution in SI (((((1.75 × 0.643721 kg/m³) × 0.1 m) × (1 − 0.4 1)) × (0.0411813 m/s)^2) / ((0.4 1)^3 × 0.001 m)) = 1.79 Pa Assumptions Steady single-phase flow through a fixed bed of uniform spheres; constant viscosity and density. The gas obeys PV = nRT (Z = 1); no reaction or change in composition between flow states. Void fraction describes only interparticle space in a uniformly packed bed. The packed region is a uniform cylinder. Dimensions checked against the declared SI output unit.	1.79	Pa
Ergun pressure drop Show Calculation CALCULATED RESULT ΔP = ΔP_v + ΔP_i Substitution in SI (86.8669 Pa + 1.79105 Pa) = 88.7 Pa Constant-property estimate at the entered operating/inlet state. Assumptions Steady single-phase flow through a fixed bed of uniform spheres; constant viscosity and density. The gas obeys PV = nRT (Z = 1); no reaction or change in composition between flow states. Void fraction describes only interparticle space in a uniformly packed bed. The packed region is a uniform cylinder. Dimensions checked against the declared SI output unit.	88.7	Pa

— indicates missing prerequisites or a withheld result. Inspect its calculation for details. Numerical precision does not establish physical accuracy.

First-principles checks

PASS11WARNING1FAIL0NOT CHECKED5

Active input bounds & signsPASS

Input validation · Active finite inputs are checked against physical sign and range constraints. Invalid inputs suppress dependent results.

Mass / density / geometry agreementNOT CHECKED

Mass consistency · Supply independent catalyst mass, bulk density, diameter, and length to check their agreement.

Voidage magnitudePASS

Magnitude screening · The 0.2–0.8 interval is a broad screening heuristic, not a validated packing range. Independently verify the actual bed voidage.

Tube / particle diameterPASS

Model applicability · D/d_p = 10. A ratio ≤ 1 cannot represent this packed-bed model. Below 10, review wall effects; 10 is a screening heuristic, not a universal validity limit.

Bed length / particle diameterPASS

Model applicability · L/d_p = 100. A bed shorter than one sphere cannot contain it. Below 10, examine shallow-bed and entrance effects; 10 is a screening heuristic.

Pressure-drop / inlet-pressure ratioPASS

Physical bounds · ΔP/P_in = 0.0887%. Above 10%, constant-density Ergun needs a compressible model review (screening heuristic). At or above 100%, the implied outlet pressure is nonpositive and the total is withheld.

Dimensional consistencyPASS

Dimensions · 21 evaluated expressions match their declared SI dimensions. Dimensions propagate through the same operations that compute the values.

Canonical SI unitsPASS

Units · The engine accepts SI only. The interface checks field dimensions and converts explicitly; pressure is absolute and gas-law temperature is kelvin.

ṁ = ρ_g Q_op = ṅ MPASS

Equation consistency · An algebraic implementation check only; this does not independently establish a physical stream balance.

Reference / operating molar-flow identityPASS

Equation consistency · An algebraic implementation check only; this does not independently establish a physical stream balance.

Mass balanceNOT CHECKED

Conservation · No independent inlet/outlet, generation, or accumulation evidence is supplied by this module.

Mole balanceNOT CHECKED

Conservation · No independent inlet/outlet, generation, or accumulation evidence is supplied by this module.

Elemental balanceNOT CHECKED

Conservation · No independent inlet/outlet, generation, or accumulation evidence is supplied by this module.

Energy balanceNOT CHECKED

Conservation · No independent inlet/outlet, generation, or accumulation evidence is supplied by this module.

Model assumptionsWARNING

Assumption tracking · 5 model assumptions need independent verification. Three displayed significant figures do not imply 0.1% accuracy; measurement uncertainty and model limits may dominate.

Finite results & stable arithmeticPASS

Numerical stability · Nonfinite and underflow arithmetic is intercepted. Singular physical states are rejected; undefined zero-flow time ratios are not rendered as Infinity.

Explicit input-unit conversionPASS

Units · 12 active input values converted to SI with field-dimension validation. Blank values stay missing.

Engineering Review

Model, assumptions & sources

What model is being evaluated?

A nonreacting, uniform cylindrical packed bed at one operating state. Geometry and flow ratios come from their definitions. Gas properties and flow-state conversions use the ideal-gas law. The optional Ergun model is an empirical pressure-drop estimate.

Each result’s Show Calculation view exposes its equation, SI substitutions, display conversion, and relevant assumptions. Units are checked by dimensional arithmetic in the calculation engine.

What assumptions were made?

ASSUMPTION · UNVERIFIEDThe packed region is a uniform cylinder.
A single diameter and packed length define bed geometry.
ASSUMPTION · UNVERIFIEDThe gas obeys PV = nRT (Z = 1); no reaction or change in composition between flow states.
Required for gas density and flow-state conversion. No gas property database or real-gas correction is used.
ASSUMPTION · UNVERIFIEDVoid fraction describes only interparticle space in a uniformly packed bed.
Envelope density includes particle pores; skeletal density cannot be substituted.
ASSUMPTION · UNVERIFIEDGas flow and voidage are spatially uniform and constant.
Times are nominal kinematic ratios, excluding dispersion and intraparticle hold-up.
ASSUMPTION · UNVERIFIEDSteady single-phase flow through a fixed bed of uniform spheres; constant viscosity and density.
Ergun is empirical. Wall, entrance, support losses, nonsphericity, fluidization, and axial compressibility are not modeled; no universal validity range is asserted.

Are conservation laws satisfied?

The first-principles panel checks applicable equation identities and redundant inventory data. A physical reactor mass, mole, elemental, or energy balance is NOT CHECKED because independent streams, reaction, accumulation, and heat/work data are absent. An algebraic identity passing is not independent evidence of conservation.

What should an engineer independently verify?

Flowmeter reference temperature and absolute pressure, mixture molecular weight, and operating viscosity.
Actual packed length, diameter, catalyst inventory, packing uniformity, and interparticle voidage.
Whether ideal-gas behavior, uniform flow, and sphere-packing assumptions apply.
Whether compressibility, wall effects, reaction, fluidization, or distributor/support losses require a more detailed model.
Input measurement uncertainty and its impact on useful significant figures.

Screening thresholds are product heuristics, not published guarantees of model validity. No universal Ergun validity range is asserted.

Constants & provenance

REFERENCE DATA Molar gas constant: 8.31446261815324 J/(mol·K), from NIST SI constants.
EMPIRICAL VALUE Ergun coefficients: 150 (viscous) and 1.75 (inertial), dimensionless.

Inputs are user-supplied values; the initial example is illustrative, not a property dataset. Derived inventory and voidage values are labelled DERIVED. Formula outputs are CALCULATED RESULT.

Active inputs in canonical SI

Bed diameter: 0.01 m
Packed-bed length: 0.1 m
Bed bulk density: 600 kg/m³
Sphere particle diameter: 0.001 m
Interparticle void fraction: 0.4 1
Gas volumetric flow: 0.00000166666666667 m³/s
Operating temperature: 523.15 K
Operating / inlet pressure: 100000 Pa
Reference temperature: 273.15 K
Reference pressure: 101325 Pa
Gas molecular weight: 0.028 kg/mol
Dynamic viscosity: 0.000025 Pa·s

Scientific sources

Ideal-gas equation of state · NASA
Ideal-gas density and flow-state conversion.
SI constants · NIST CODATA
Molar gas constant R.
Packed-bed pressure drop · Fogler, University of Michigan
Ergun equation and superficial-velocity convention.
Density definitions · Micromeritics
Bulk, envelope, and skeletal density distinctions.
Reference space velocity · da Silva Jr. et al. (2024)
Equations 35–37: gas reference-state and bed-volume basis.

Cat Lab

Catalyst Bed / Reactor Calculator

Inputs

Calculated results

Geometry & inventory

Substitution in SI

Assumptions

Substitution in SI

Assumptions

Substitution in SI

Assumptions

Substitution in SI

Substitution in SI

Assumptions

Substitution in SI

Assumptions

Flow & contact

Substitution in SI

Assumptions

Substitution in SI

Substitution in SI

Assumptions

Substitution in SI

Assumptions

Substitution in SI

Assumptions

Substitution in SI

Assumptions

Substitution in SI

Assumptions

Substitution in SI

Assumptions

Gas & loading

Substitution in SI

Assumptions

Substitution in SI

Assumptions

Substitution in SI

Assumptions

Substitution in SI

Assumptions

Pressure drop

Substitution in SI

Assumptions

Substitution in SI

Assumptions

Substitution in SI

Assumptions

First-principles checks

Engineering Review

What model is being evaluated?

What assumptions were made?

Are conservation laws satisfied?

What should an engineer independently verify?

Constants & provenance

Active inputs in canonical SI

Scientific sources