Solving mine ventilation networks with fixed and non-fmed branches

Editor's Note: Y.J. Wang's paper appeared in the September Technical Papers section. There were some inadvertent editorial errors in it. So we are reprinting it here. Abstract - This paper examines the ventilation network problem from a view point of solving a system of B equations in B unknowns, where B is the number o f branches in the network. Based on Kirchhoff s current and voltage laws, the solution to the general ventilation network problem must satisfy B network equations. In this paper, the air quantities and control-device pressures are chosen as variables and are grouped into B dependent variables (unknowns) and B independent variables, resulting in a system of B equations in B unknowns. Based on whether their variables are dependent or independent, the network branches are classified into f our types: five d, non-fixed, p-fixed, and q fixed. The ventilation network problem may include all four types of branches. There are .some conditions under which the problem as defined in this manner does not have a unique solution. To have a unique solution, the Jocabian matrix of the equations m us! he nonsingular. It then follows that: • the number of branches with independent air quantities must be less than or equal to the number of chords with respect to a spanning tree; •the subnetwork of branches with independent air quantities must not contain any cutset; and •the suhnetwork of branches with dependent control-device pressures must not contain any cutset. These three conditions must be met regardless of the values for the variables. In addition to the problem formulation, a solution procedure applying the Newton (or Newton-Raphson) method is outlined and illustrated with an example problem.