Papers - Effects of Underground Stopping Leakage upon Mine-fan Performance (T. P. 1243, with discussion)

When calculating the pressure-volume characteristics of projected mine-ventilating circuits by orthodox methods, certain basic assumptions are required in order to employ the various available empirical data. It is assumed, for example, that the mine air is an incompressible fluid subjected to isothermal flow, an assumption sufficiently accurate for practical purposes since pressure and temperature differentials are small throughout the average circuit. A more erroneous assumption, however, is that all air is accounted for as it travels throughout the mine. No attempt is usually made to evaluate stopping leakage as it occurs; instead, the air volume required at the last crosscuts is assumed to enter the mine, travel the various intake air courses intact, sweep the workings and travel out by the return air courses to the point or points of exit from the mine. Actually, there is a leakage of air from intake to return at every stopping, the quantity of this leakage depending upon the tightness of the stopping and the pressure difference across the stopping. Unfortunately, a lack of empirical data and knowledge of the condition of individual stoppings makes an exact analysis of underground stopping leakage impossible. Generally, leakage is most severe through the old stoppings outbye the circuit. These are also subjected to higher pressure differences than the newer inbye stoppings. Therefore the circuit air volume diminishes at a decreasing rate progressing from outbye to inbye the circuit. Consider a simple mine circuit consisting of one intake and one return air course, each of equal and uniform section area and interconnected at regular intervals with crosscuts equipped with stoppings. At any point X inbye the circuit the air volume q on the intake air course equals that on the return air course and decreases with diminishing rate from outbye to inbye the circuit between the limits of Q1 completely outbye and Q completely inbye. Such a volume change is represented by curve a, Fig. I, which is computed with the aid of the equation q = Q1- (Q1- Q)(X + L)N. This equation results from the general algebraic equation of form q = k, — kXN after solving for kl and k with the knowledge that completely outbye X = o and q = QL, also completely inbye X = L and q = Q. Curves a, b and c, Fig. I, show values of q as ordinates versus values of X as abscissas, for values of N equal to 0.50, 1.00 and 2.00, respectively. Distribution of underground stopping 1eakage directly affects the air-volume distribution along the circuit, which in turn determines the circuit pressure gradient. To deliver any required air volume inbye a circuit or portion thereof requires a higher circuit-pressure differential if stoppings leak than is necessary with tight stoppings. Every mining engineer engaged in the analysis of projected mine-ventilation circuits is therefore confronted with the problem of making proper allowance for the effects of leaking stoppings. The purpose of this paper is to present evidence in support of the author's suggestion that circuit pressure increase (per cent)