Investigation Of Dust Produced During Blasting In Stopes

Respirable dust produced during blasting operations in underground mines exhibits both diffusion and convection properties of the airflow. However, the application of the mathematical model presently used to calculate the change in time in the concentration of blasting pollutants is mostly limited to a single drift and cannot be easily utilized for blasts taking place in stopes. This paper discusses an analytical solution based on considerations that enable us to reliably identify the initial condition. Such an approach may be used for any blasting area regardless of its position, its size, or the ventilation system in use during blasting. In addition, a test procedure using field data is established to determined those parameters not measured directly. As well, equations are derived to find the diffusion coefficient, and the position and size of a dust source from the field data. Mathematical considerations The convection-diffusion problem, for a one-dimensional case, is described by the following partial differential equation (PDE): ct. = Dcxx - Vcx + source - sink(1) where C = the concentration of a pollutant T = time V = the mean air velocity in x-direction D = the diffusion coefficient X = distance away from the pollutant source source = any additional pollutant source specified by an initial value problem sink = decay of a pollutant inside the region specified by the boundary conditions. Respirable dust produced during blasting is best considered as an initial value problem (IVP). To derive a mathematical model, the following assumptions are made: •At time zero (t = 0), the dust source is at point x = 0 of an infinite drift. •The problem is considered a one-dimensional case. •The mean velocity of air and the diffusion coefficient are constant. •There is no source or sink of dust other than specified at point x = 0 and time t = 0. We have to solve the following problem [PDE ct=Dcxx-Vcx-m<x...m;0<t<m(2)] ICc(x,0)=f(x)t=0, the initial condition Where c = dust concentration in mg/m3 V= the average mean velocity in a drift in m/s t= time in s D= the diffusion coefficient in m2 /S x = distance coordinate in m. We observe that in problem (2), we have moved the boundaries to[ -m and +m] in order to have an initial-value problem. We introduce new coordinates, s = t and z =x - Vt. To rewrite the PDE in terms of (z, s), we use the chain rule ct = czzt + csst = -Vcz + cs cx = czzx = cz cxx = (cz)x = czz. We now substitute our computed ct, cx. and cxx into the PDE to get new IVP in terms of z and s :