How to Calculate the Capacity of a Rotary Dryer?

2025-11-11 08:39:00

How to Calculate the Capacity of a Rotary Dryer

Introduction

Rotary dryers are widely used in industrial processes for drying bulk materials such as minerals, chemicals, food products, and agricultural commodities. These cylindrical, rotating drums provide efficient heat transfer and material handling for continuous drying operations. Calculating the capacity of a rotary dryer is essential for proper equipment selection, process optimization, and energy efficiency. This comprehensive guide will explain the key factors and methodologies involved in determining rotary dryer capacity.

Understanding Rotary Dryer Capacity

The capacity of a rotary dryer refers to the amount of material it can process per unit time while achieving the desired moisture reduction. Capacity is typically expressed in terms of:

- Mass flow rate (kg/h or tons/h)

- Volumetric flow rate (m³/h)

- Evaporation rate (kg water/h)

Several interrelated factors influence dryer capacity, including:

- Physical dimensions of the dryer

- Operating parameters

- Material characteristics

- Heat transfer mechanisms

Key Parameters for Capacity Calculation

1. Dryer Dimensions

The physical size of the rotary dryer fundamentally determines its capacity:

- Diameter (D): Internal diameter of the rotating drum

- Length (L): Total length of the drying section

- Slope: Inclination angle (typically 1-5°)

- Rotation speed: Usually 2-10 rpm

The volume of the dryer cylinder is calculated as:

V = π × (D/2)² × L

2. Material Characteristics

Material properties significantly affect drying capacity:

- Initial moisture content (% wet basis)

- Final moisture content (% wet basis)

- Bulk density (kg/m³)

- Particle size distribution

- Thermal properties (specific heat, thermal conductivity)

- Heat sensitivity (maximum allowable temperature)

3. Operating Conditions

Process parameters that influence capacity:

- Inlet gas temperature

- Outlet gas temperature

- Gas flow rate

- Residence time

- Fill ratio (percentage of dryer volume occupied by material)

Step-by-Step Capacity Calculation Methods

Method 1: Volumetric Throughput Approach

This method estimates capacity based on the dryer's physical dimensions and material residence time:

1. Determine residence time (τ):

τ = (0.23 × L) / (N × D × S) + (0.6 × L × G) / (F)

Where:

- N = rotation speed (rpm)

- S = slope (m/m)

- G = gas mass velocity (kg/m²s)

- F = feed rate (kg/m²s)

2. Calculate volumetric loading:

Typical fill ratio ranges from 10-15% of dryer volume

3. Determine mass flow rate:

Capacity = (V × fill ratio × bulk density) / τ

Method 2: Heat and Mass Balance Approach

This more precise method involves energy calculations:

1. Calculate moisture to be removed:

ΔW = Feed rate × (X₁ - X₂) / (1 - X₂)

Where:

- X₁ = initial moisture content (decimal)

- X₂ = final moisture content (decimal)

2. Determine heat required for evaporation:

Q = ΔW × [λ + Cp,v × (Tout - Tin)] + m × Cp,s × (Tout - Tin)

Where:

- λ = latent heat of vaporization (kJ/kg)

- Cp,v = specific heat of vapor (kJ/kg°C)

- Cp,s = specific heat of dry solid (kJ/kg°C)

- m = mass flow rate of dry product (kg/h)

3. Calculate gas flow requirements:

mg = Q / [Cpg × (Tgin - Tgout)]

Where:

- Cpg = specific heat of gas (kJ/kg°C)

- Tgin = inlet gas temperature (°C)

- Tgout = outlet gas temperature (°C)

4. Verify dryer volume sufficiency:

Check against empirical data for similar materials

Method 3: Empirical Correlations

Industry-established correlations can provide quick estimates:

1. Evaporation capacity:

E = K × V × ΔT / L

Where:

- E = evaporation rate (kg water/h)

- K = empirical coefficient (typically 20-30 for direct heat dryers)

- ΔT = temperature difference between inlet and outlet gas (°C)

2. Specific evaporation rate:

Typically 5-80 kg water/m³h depending on material and conditions

Practical Considerations in Capacity Determination

1. Material Transport Considerations

The dryer must provide adequate residence time for moisture removal while maintaining proper material transport:

- Cascading action: Affected by lifters and rotation speed

- Gas velocity: Must be below particle entrainment velocity

- Slope and speed: Must be balanced for optimal throughput

2. Heat Transfer Mechanisms

Capacity depends on effective heat transfer through:

- Direct contact: Between hot gas and material particles

- Conduction: Through contact with dryer shell

- Radiation: From hot surfaces

The overall heat transfer coefficient (U) typically ranges from 30-150 W/m²°C

3. Moisture Removal Efficiency

The drying rate typically follows a falling rate period curve. Capacity calculations should account for:

- Constant rate period: Surface moisture evaporation

- Falling rate period: Internal moisture diffusion

Advanced Calculation Techniques

For more precise capacity determination:

1. Dimensionless Number Analysis

Using dimensionless groups to characterize drying:

- Sherwood number (Sh): Mass transfer

- Nusselt number (Nu): Heat transfer

- Reynolds number (Re): Flow regime

2. Computational Modeling

Advanced methods include:

- Discrete element modeling (DEM): For particle motion

- Computational fluid dynamics (CFD): For gas flow patterns

- Coupled heat and mass transfer models

Common Mistakes in Capacity Calculation

1. Overestimating heat transfer coefficients

2. Ignoring material property changes during drying

3. Underestimating gas flow requirements

4. Neglecting dust carryover limitations

5. Assuming constant drying rates throughout the process

Safety Factors in Design

Practical dryer sizing should include:

- 10-20% capacity margin for process variations

- Material characteristic variability (moisture, size distribution)

- Future capacity requirements

Case Study Example

Consider drying 10,000 kg/h of wet sand from 15% to 1% moisture (wet basis):

1. Moisture to remove:

ΔW = 10,000 × (0.15 - 0.01)/(1 - 0.01) = 1,414 kg water/h

2. Heat required (assuming 100°C outlet):

Q = 1,414 × [2,257 + 1.88×(100-25)] + 8,586 × 0.8×(100-25)

Q ≈ 3.8 × 10⁶ kJ/h

3. Air flow needed (500°C inlet, 100°C outlet):

mg = 3.8×10⁶ / [1.01 × (500-100)] ≈ 9,400 kg/h

4. Dryer size estimate (using K=25):

V = E × L / (K × ΔT)

For L/D=6 and ΔT=400°C:

V ≈ 1,414 × 6 / (25 × 400) ≈ 0.85 m³

D ≈ (0.85/(6×π/4))¹/³ ≈ 0.6 m

L ≈ 3.6 m

This preliminary calculation suggests a 0.6m diameter × 3.6m long dryer could potentially handle this capacity, though detailed design would require more precise parameters.

Conclusion

Calculating rotary dryer capacity involves understanding the complex interplay between equipment geometry, material properties, and process thermodynamics. While simplified methods can provide initial estimates, comprehensive design should incorporate detailed heat and mass balances, empirical correlations, and practical experience. Proper capacity calculation ensures efficient dryer operation, optimal energy utilization, and consistent product quality while allowing for future process requirements.