Formula for calculating the relationship between the inner diameter of a vertical kiln and its output
The production output of lime vertical kiln is positively correlated with the inner diameter of the kiln body. Under the conditions of constant height to diameter ratio, calcination process, and raw material quality, the output is proportional to the square of the inner diameter, which is the core basis for the design of vertical kiln production capacity. By combining industrial production standards and thermal principles, accurate calculation formulas for inner diameter and output can be derived, which are suitable for conventional circular section lime vertical kilns.
The general calculation formula is: Q=24 × π× d ² × H × G × η/(4 × 0.9 × T). In the formula, Q is the daily output of the vertical kiln (t/d); D is the effective inner diameter of the kiln body (m); H is the effective calcination height of the kiln body (m); G is the volumetric bulk density of limestone (t/m ³); η is the qualified rate of calcined products, with a conventional value of 0.85-0.95; T is the residence time (h) of the material in the kiln, and the standard value for ordinary vertical kilns is 10-12 hours.
After fixing the height to diameter ratio of the kiln body (the optimal range in the industry from 5.0 to 6.0) and the process parameters, the formula can be simplified as Q=K × d ², where K is the comprehensive coefficient of the operating conditions, determined by the fuel calorific value, ventilation conditions, and raw material particle size. Under normal operating conditions, the K value remains stable at 18-22.
In actual production, expanding the inner diameter will increase the effective calcination cross-sectional area inside the kiln, directly increasing production capacity. However, excessive inner diameter can easily lead to uneven ventilation, incomplete calcination, and other problems, resulting in a decrease in K value. Therefore, industrial design needs to match a reasonable inner diameter, taking into account both production capacity and finished product quality. This formula can accurately guide vertical kiln selection, expansion and renovation, and production capacity accounting.
