Mine Ventilation

Mine ventilation airflow and fan pressure

Mine ventilation moves fresh air through the workings to dilute gases and dust and to keep temperatures safe. The main fan must supply enough pressure to overcome the frictional and shock losses of the network. The airway resistance R is defined by h = RQ^2, where h is the pressure drop in Pa and Q is the quantity in m^3/s. Because the pressure varies with the square of the quantity, doubling the airflow in a fixed airway quadruples the pressure drop.

The natural ventilation pressure (NVP) arises from density differences between the intake and return columns. When the NVP aids the fan, the mine must absorb the sum of the fan pressure and the NVP, so the fan pressure required is h_f = RQ^2 - h_n. When the fan is stopped, the NVP alone drives the flow, so h_n = R'Q^2 for the resultant resistance R' of the network.

A regulator is a partial barrier installed in an airway to add resistance and control the split of air. Its added resistance varies inversely with the square of the free opening area, R \propto 1/A^2, so a small reduction in opening produces a large increase in resistance. The fan characteristic is the pressure a fan delivers against quantity. The actual static head curve rises to a peak, which is the stall point, and the operating point is where it meets the mine characteristic curve. A gradually expanding outlet duct can recover part of the outlet velocity pressure as static pressure, the recovered amount being the evasee efficiency times the velocity pressure difference.

Ventilation quantity is found from the oxygen balance. The air quantity is Q = \dot{V}_{O_2} / (c_{in} - c_{ret}), where c_{in} and c_{ret} are the oxygen fractions of intake and return air, and the return air must not fall below the minimum oxygen level prescribed by the regulations (19 % in Indian practice). Production per cycle is a different quantity: it is the coal won per metre of face multiplied by the panel width, and it does not enter the oxygen balance. Finally, a booster fan in one branch of a split must supply the pressure needed to raise that branch's flow with the main fan pressure held constant.

Parallel airway resistance equivalents

When airways are connected in parallel, they share the same pressure drop h, and their quantities add: Q = \sum Q_i. Since Q_i = \sqrt{h/R_i}, the equivalent resistance is obtained from the reciprocal square roots, not from the reciprocals of the resistances themselves: \dfrac{1}{\sqrt{R_{eq}}} = \sum_i \dfrac{1}{\sqrt{R_i}}. For two identical branches of resistance R, for example, 1/\sqrt{R_{eq}} = 2/\sqrt{R}, so R_{eq} = R/4. The equivalent resistance is always smaller than the smallest branch resistance.

In a split, the two districts carry the same pressure drop between the splitting and merging points. If a booster fan is placed in one branch to raise its flow from Q_B to Q'_B without changing the other branch, the pressure drop across that branch must rise by the fan pressure. Since the original drop is \Delta P = R_B Q_B^2, the booster pressure is P_B = \Delta P\left[(Q'_B/Q_B)^2 - 1\right]. The same reasoning gives the booster pressure needed when the branch flow is raised by a given percentage, where the new flow is compared with the original branch flow.

A common mistake is to use the series rule in a parallel network. Series resistances add directly, whereas parallel resistances combine through the reciprocal square root rule given above.

Airway frictional pressure drop

Frictional pressure loss in a roadway follows Atkinson's law, h = \dfrac{k P L V^2}{A}, where k is the friction coefficient in Ns^2 m^{-4}, P is the perimeter in m, L is the length in m, V is the mean velocity in m/s, and A is the cross-sectional area in m^2. Writing V = Q/A gives h = RQ^2 with R = kPL/A^3. The perimeter and area are computed from the cross-section shape, so a rectangular airway with side lengths a and b has P = 2(a+b) and A = ab. Unit checks help avoid errors: k P L/A^3 must have units of Ns^2/m^8.

For a circular airway of constant friction coefficient, P = \pi D and A = \pi D^2/4, so R \propto L/D^5. If the pressure loss is held fixed and the flow must change, the diameter must scale as D_2/D_1 = (Q_2/Q_1)^{2/5}. Doubling the flow therefore requires the diameter to increase by a factor of 2^{0.4} \approx 1.32.

Fan laws

Fan laws relate the performance of geometrically similar fans running at the same efficiency. The dimensionless coefficients are the flow coefficient, the pressure coefficient \psi = \dfrac{\Delta p}{\rho n^2 D^2}, and the power coefficient, where n is the rotational speed in rev/s and D is the impeller diameter. Because \psi is constant for similar fans, the pressure rise is proportional to \rho n^2 D^2.

The other laws follow from the same argument. The quantity varies as Q \propto nD^3 and the power varies as P \propto \rho n^3 D^5. Doubling the speed of a similar fan therefore doubles the flow, quadruples the pressure, and multiplies the power by eight.

Fan laws apply only to similar fans. Changing the speed of one fan keeps the same diameter, so the pressure changes with the square of the speed alone.

Atmospheric stability lapse rate

The dry adiabatic lapse rate (DALR) is about 9.8 °C per km, the rate at which a rising unsaturated air parcel cools by expansion. The ambient lapse rate is the actual rate of temperature decrease with height in the atmosphere. Comparing the two determines stability. If the ambient lapse rate is lower than the DALR, a displaced parcel becomes colder and denser than its surroundings and tends to return, so the atmosphere is stable. If the two are equal, the atmosphere is neutral. If the ambient lapse rate exceeds the DALR, a rising parcel remains warmer and lighter than its surroundings and keeps rising, so the atmosphere is unstable.

For example, an ambient lapse rate of 12 °C per km is steeper than the DALR, so the layer is unstable and vertical mixing of air is enhanced. An inversion, in which temperature increases with height, is a strongly stable condition that traps pollutants near the ground.

Controlled air recirculation

Controlled air recirculation returns part of the exhaust air to the working area after it has been cleaned, so that less fresh air needs to be conditioned. The main advantage is a reduction in heating and cooling loads and in overall ventilation cost. Recirculation can also raise the air velocity at a workplace where it is needed, since the redirected air is delivered to the face. Because the recirculation circuit adds resistance, an additional booster fan is often required to maintain the required flow.

Recirculation does not, by itself, cause a higher level of contaminants. The returned air must be filtered and monitored so that the concentration of dust, gas, or fumes at the workplace stays within limits. Without such control, contaminants would accumulate in the recirculated stream, which is why recirculation is always designed as a controlled system.

Coward flammability diagram

The Coward diagram is a triangular plot of methane, oxygen, and inert gas, used to judge the explosibility of a gas mixture. The apex representing pure inert gas lies at the origin of the composition space. Mixtures inside the explosive region are flammable, and the lower explosibility limit (LEL) of the region defines the composition below which the mixture cannot ignite.

When inert gas is injected into a sealed-off area, both methane and oxygen are diluted by the same factor, so the composition moves along a straight line toward the inert apex. If the dilution factor is f, the composition is multiplied by f, and the total volume becomes V/f. The volume of inert gas that must be added to a sealed area of volume V is therefore V_{in} = V(1/f - 1). For instance, a dilution factor of 0.5 means the total volume doubles, so a volume equal to V of inert gas is required.