How does the particle size distribution of raw coke quantitatively affect the permeability of the material layer and the uniformity of calcination in the rotary kiln?

The quantitative impacts of the particle size distribution of raw material coke on the permeability of the material layer and the uniformity of calcination in a rotary kiln can be analyzed through the correlation between particle size parameters and process indicators as follows:

I. Quantitative Impact of Particle Size Distribution on the Permeability of the Material Layer

Particle Size Uniformity (PDI Value)

• Definition: Particle size distribution dispersion index (PDI = D90/D10, where D90 is the sieve size through which 90% of the particles pass, and D10 is the sieve size through which 10% of the particles pass).
• Impact Pattern:
  A smaller PDI value (indicating more uniform particle size) leads to a higher porosity of the material layer, with the permeability index (K value) increasing by approximately 15% to 20%.
• Experimental Data:
  When the PDI decreases from 2.0 to 1.3, the pressure drop inside the kiln decreases by 22%, and the gas flow rate increases by 18%, indicating a significant improvement in permeability.
• Mechanism:
  Uniform particle size reduces the phenomenon of small particles filling the gaps between large particles, avoiding the “particle bridging” effect and thus lowering the airflow resistance.

Fine Particle Content (<0.5 mm)

• Critical Threshold:
  When the proportion of fine particles exceeds 10%, the permeability deteriorates sharply.
• Quantitative Relationship:
  For every 5% increase in fine particles, the pressure drop inside the kiln rises by approximately 30%, and the gas flow rate decreases by 25%.
• Case Study:
  In a petroleum coke calcination kiln, when the fine particle content increases from 8% to 15%, the negative pressure at the kiln head rises from -200 Pa to -350 Pa, necessitating an increase in the induced draft fan power to maintain operation, resulting in a 12% increase in energy consumption.

Average Particle Size (D50)

• Optimal Range:
  The best permeability is achieved when D50 is between 8 and 15 mm.
• Deviation Impact:
  When D50 is less than 5 mm, the porosity of the material layer decreases to below 35%, and the permeability index drops by 40%;
  When D50 exceeds 20 mm, although the porosity is high, the contact area between particles decreases, reducing the heat transfer efficiency by 15% and indirectly affecting the calcination uniformity.

II. Quantitative Impact of Particle Size Distribution on the Uniformity of Calcination

Temperature Distribution Standard Deviation (σT)

• Definition:
  A statistical indicator of the fluctuation amplitude of the axial temperature inside the kiln, with a smaller σT indicating more uniform calcination.
• Impact of Particle Size:
  When the particle size is uniform (PDI < 1.5), σT can be controlled within ±15℃;
  When the particle size is non-uniform (PDI > 2.5), σT expands to ±40℃, leading to local overburning or underburning.
• Case Study:
  In an aluminum carbon rotary kiln, by optimizing the particle size distribution to reduce the PDI from 2.8 to 1.4, the standard deviation of the volatile content in the product decreases from 0.8% to 0.3%, significantly improving the calcination uniformity.

Reaction Front Movement Velocity (Vr)

• Definition:
  The propulsion speed of the calcination reaction interface in the material layer, reflecting the calcination efficiency.
• Correlation with Particle Size:
  For every 10% increase in the proportion of fine particles (<3 mm), Vr increases by approximately 25%, but it is prone to causing overly rapid reactions and local overheating;
  For every 10% increase in the proportion of coarse particles (>20 mm), Vr decreases by 15% due to increased heat transfer resistance.
• Equilibrium Point:
  When the particle size distribution is bimodal (e.g., a mixture of 3-8 mm and 15-20 mm particles), Vr can be maintained within the optimal range (0.5-1.0 mm/min) while ensuring uniformity.

Product Qualification Rate (Q)

• Quantitative Relationship:
  For every 0.5 unit increase in particle size uniformity (i.e., a decrease in PDI value), the product qualification rate increases by approximately 8%;
  For every 5% decrease in fine particle content, the waste rate due to underburning or overburning decreases by 12%.
• Industrial Data:
  In a titanium dioxide rotary kiln, by controlling the particle size of the raw material coke (D50 = 12 mm, PDI = 1.6), the standard deviation of the product whiteness decreases from 1.2 to 0.5, and the first-grade product rate increases from 75% to 92%.

III. Comprehensive Optimization Recommendations

Particle Size Control Objectives:

• D50: 8-15 mm (adjustable according to material characteristics);
• PDI: <1.5;
• Fine particle (<0.5 mm) content: <8%.

Process Adjustment Strategies:

• Adopt multi-stage crushing and screening processes to ensure a concentrated particle size distribution;
• Perform pre-forming treatment (e.g., briquetting) on fine particles to reduce flyaway losses;
• Optimize the particle size gradation according to the kiln type (length-to-diameter ratio, rotational speed), for example, using coarse particles as the main component for long kilns and supplementing with fine particles for short kilns.

Monitoring and Feedback:

• Install online particle size analyzers to monitor the particle size distribution of the material entering the kiln in real time;
• Combine with computational fluid dynamics (CFD) modeling of the temperature field inside the kiln to dynamically adjust the particle size parameters and calcination regime.