Mine Ventilation Network Optimization Using The Generalized Reduced Gradient Method

This paper describes the formulation of mine ventilation network optimization as a standard nonlinear programming problem and the solution of the problem using the generalized reduced gradient (GRG) method. In general, the GRG method is regarded as one of the most effective and efficient methods for solving large-scale nonlinear programming problems. The variables considered in the network optimization include air quantity, regulator pressure loss, and fan pressure for each branch. Each of the variables is constrained by lower and upper bounds. This facilitates proper assignments of ventilation requirements and provides a great flexibility to include various situations encountered in mine ventilation. The objective of the network optimization is to minimize the overall air power consumed by or supplied to the network; whereas the constraints are, in addition to the variable bounds, the two fundamental network laws: Kirchhoffs voltage law and Kirchhoffs current law. A computer program has been developed based on the GRG method for the network optimization. An example of network with 18 branches, 8 regulators and 3 fans is included for illustration.