Dust Collection System Efficiency

Dust collection system efficiency quantifies the ability of a collector to remove particulate matter from an air stream. Efficiency varies significantly with particle size, making accurate characterization essential for regulatory compliance and system design.

Collection Efficiency Definitions

Overall Collection Efficiency represents the total mass fraction of particulate removed:

$$\eta_{\text{overall}} = \frac{m_{\text{collected}}}{m_{\text{inlet}}} \times 100%$$

Where:

• $m_{\text{collected}}$ = mass of dust collected (lb/hr or kg/hr)
• $m_{\text{inlet}}$ = mass of dust entering collector (lb/hr or kg/hr)

Alternatively, using concentration measurements:

$$\eta_{\text{overall}} = \frac{C_{\text{in}} - C_{\text{out}}}{C_{\text{in}}} \times 100%$$

Where:

• $C_{\text{in}}$ = inlet dust concentration (gr/ft³ or mg/m³)
• $C_{\text{out}}$ = outlet dust concentration (gr/ft³ or mg/m³)

Penetration expresses the fraction passing through:

$$P = 1 - \eta = \frac{C_{\text{out}}}{C_{\text{in}}}$$

Penetration is particularly useful when dealing with high-efficiency collectors where small differences matter.

Particle Size Distribution Effects

Dust collection efficiency strongly depends on particle aerodynamic diameter. Fine particles (< 1 μm) are difficult to collect due to:

• Low inertial forces
• Increased influence of Brownian motion
• Reduced gravitational settling velocity

Stokes Diameter characterizes particle behavior:

$$d_{\text{Stokes}} = \sqrt{\frac{18 \mu V_{\text{terminal}}}{\rho_p g}}$$

Where:

• $\mu$ = air viscosity (lb/ft·s or Pa·s)
• $V_{\text{terminal}}$ = terminal settling velocity (ft/s or m/s)
• $\rho_p$ = particle density (lb/ft³ or kg/m³)
• $g$ = gravitational acceleration (32.2 ft/s² or 9.81 m/s²)

Particle size distributions typically follow log-normal patterns. The mass median diameter (MMD) and geometric standard deviation characterize the distribution.

Fractional Efficiency Curves

Fractional efficiency (grade efficiency) shows collection performance across particle size ranges:

$$\eta(d_p) = \frac{m_{\text{collected}}(d_p)}{m_{\text{inlet}}(d_p)}$$

Characteristic Efficiency Parameters:

The relationship between fractional and overall efficiency:

$$\eta_{\text{overall}} = \int_0^\infty \eta(d_p) \cdot f(d_p) , dd_p$$

Where $f(d_p)$ is the particle size distribution function normalized to unity.

Overall System Efficiency Calculation

For practical calculations with discrete size fractions:

$$\eta_{\text{overall}} = \sum_{i=1}^{n} \eta_i \cdot w_i$$

Where:

• $\eta_i$ = fractional efficiency for size range $i$
• $w_i$ = weight fraction in size range $i$
• $n$ = number of size fractions

Example Calculation:

Emission Testing Requirements

graph TD
    A[Emission Testing Program] --> B[Isokinetic Sampling]
    A --> C[Particle Size Analysis]
    A --> D[Concentration Measurement]

    B --> E[EPA Method 5]
    B --> F[EPA Method 17]

    C --> G[Cascade Impactor]
    C --> H[Optical Particle Counter]

    D --> I[Gravimetric Analysis]
    D --> J[Real-time Monitoring]

    E --> K[Particulate Matter <10 mg/dscm]
    F --> L[Visible Emissions <20%]

    G --> M[Size Distribution Data]
    H --> M

    I --> N[Compliance Verification]
    J --> N
    M --> N
    K --> N
    L --> N

    N --> O[Efficiency Calculation]
    O --> P{Meets Standards?}
    P -->|Yes| Q[Operational Approval]
    P -->|No| R[System Modification Required]

EPA Method 5 (Particulate Emissions):

• Isokinetic sampling required
• Filter temperature 120°C ± 14°C
• Minimum sample volume 0.6 dscm
• Reporting in mg/dscm corrected to standard conditions

EPA Method 201A/202 (PM₁₀ and PM₂.₅):

• Includes particle sizing
• More stringent for fine particulate
• Required for many industrial sources

EPA and OSHA Compliance Standards

EPA Emission Standards:

OSHA Workplace Standards (29 CFR 1910):

Required Minimum Efficiency by Application:

Monitoring and Documentation:

Facilities must maintain:

• Continuous opacity monitoring (COMS) or periodic visible emission observations
• Annual stack testing for major sources
• Pressure drop monitoring across collectors
• Particulate loading calculations
• Maintenance and inspection logs

Performance Verification:

$$\text{Required Testing Frequency} = f(\text{Source Category, Emission Rate, Compliance History})$$

Typical requirements:

• Initial performance test upon startup
• Annual testing for major sources
• Semi-annual for problematic operations
• After any process modifications

Properly designed systems operating within design parameters consistently achieve specified efficiency. Regular monitoring, preventive maintenance, and prompt corrective action ensure sustained compliance and protect worker health and environmental quality.