An Optimization Problem For Coal-Mine Ventilation Shafts ? Introduction

Optimal sizing of a ventilation shaft is a classical subject in mine ventilation economics.. The shaft size is optimized by minimizing the sum of shaft-construction and ventilation-power costs, or owning and operating costs. The length and air quantity of the shaft are held constant, and the location of the shaft, affecting its depth, and construction and ventilation power costs, is not considered (Hartman, 1961; Lambrechts, 1974; Wang et al., 1978). This paper proposes an approach by which the location and size for a new pair of shafts (intake and return shafts) are optimized for a coal-mine ventilation network. Specifically, the problem is to determine the location and size for a new pair of shafts, and the distribution of air between the new and old shafts so that the combined cost of shaft construction and ventilation power is minimized. The shaft length or depth corresponds to the height of overburden at any shaft location. To simplify the problem, the shaft locations will be limited to the line along the main or submain entries, and the connection entries at the shaft bottom neglected. In order to calculate the ventilation-power cost, the air power of the system should be determined. This in turn requires the calculations of the air quantity and pressure of each fan in the network, satisfying Kirchhoff's laws and Atkinson equation. After obtaining the air power, the cost calculation is straightforward. In the following, we shall assume that the resistances of all airways, and the quantity for each mining section, which is controlled by adjusting the air regulator, are all known. The resistances for the shafts are determined from the estimated friction factors, and shaft dimensions and lengths. Furthermore, it will be assumed that the fans can be selected to meet the duties called for by any network solutions.