Dimensionless Diameter For Fluidized Reactors At G/S Contacting Regime Calculator

Dimensionless Diameter Formula:

\[ d'p = dp \times \left( \frac{\rho_{gas} \times (\rho_{solids} - \rho_{gas}) \times [g]}{\mu_L^2} \right)^{1/3} \]

Diameter of Particle:

Density of Gas:

kg/m³

Density of Solids:

kg/m³

Viscosity of Liquid:

Pa·s

Dimensionless Diameter (d'p):

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1. What is Dimensionless Diameter for Fluidized Reactors?

The Dimensionless Diameter is a parameter used to characterize the size of solid particles relative to the flow conditions of the Gas Phase in fluidized reactors. It provides a normalized measure that accounts for various physical properties affecting fluidization behavior.

2. How Does the Calculator Work?

The calculator uses the dimensionless diameter formula:

\[ d'p = dp \times \left( \frac{\rho_{gas} \times (\rho_{solids} - \rho_{gas}) \times [g]}{\mu_L^2} \right)^{1/3} \]

Where:

\( dp \) — Diameter of Particle (m)
\( \rho_{gas} \) — Density of Gas (kg/m³)
\( \rho_{solids} \) — Density of Solids (kg/m³)
\( \mu_L \) — Viscosity of Liquid (Pa·s)
\( [g] \) — Gravitational acceleration constant (9.80665 m/s²)

Explanation: The formula normalizes particle diameter by considering the balance between gravitational, buoyancy, and viscous forces in the fluidized system.

3. Importance of Dimensionless Diameter Calculation

Details: Accurate calculation of dimensionless diameter is crucial for predicting fluidization behavior, determining minimum fluidization velocity, and designing efficient gas-solid contacting reactors in chemical processes.

4. Using the Calculator

Tips: Enter particle diameter in meters, densities in kg/m³, and viscosity in Pa·s. All values must be positive and valid for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of dimensionless diameter in fluidized reactors?
A: Dimensionless diameter helps characterize particle behavior in fluidized beds, predicting fluidization patterns, mixing efficiency, and heat/mass transfer rates.

Q2: What are typical values for dimensionless diameter?
A: Values typically range from 0.1 to 1000, with different ranges corresponding to different fluidization regimes (bubbling, turbulent, fast fluidization).

Q3: How does particle density affect the dimensionless diameter?
A: Higher density solids increase the dimensionless diameter value, indicating stronger gravitational effects relative to fluid forces.

Q4: What is the role of viscosity in this calculation?
A: Viscosity appears squared in the denominator, meaning higher viscosity significantly reduces the dimensionless diameter by increasing resistance to particle motion.

Q5: Can this formula be used for liquid-solid fluidized systems?
A: While developed for gas-solid systems, the formula can be adapted for liquid-solid systems by using appropriate fluid properties, though specific correlations may differ.