MATHEMATICAL MODELS FOR THE SIMULATION OF MINE VENTILATION NETWORKS (PIPE FLOW, HARDY CROSS, KIRCHHOFF'S LAWS)

Network analysis plays a crucial role in designing, monitoring, and controlling of mine ventilation systems. Physical flow networks, such as the ventilation systems, are guided by two laws; the conservation of flow and the conservation of energy. Solving for the flow distribution that satisfies these laws for certain boundary conditions, constitutes network analysis. The relationships governing these laws happen to be a combination of linear and nonlinear sets of equations. The Hardy Cross iterative procedure is routinely used in ventilation systems to solve these equations.;For the methods chosen, mathematical models applicable to mine ventilation systems are developed, flow charts or algorithms are presented, computer implementation is discussed, programs are presented in Fortran, and some cases of flow distribution are analyzed. The application of separable programming piecewise linearization method resulted in no definitive conclusion regarding its usefulness. Some numerical analysis problems remain to be addressed to establish the suitability of the method. The ability to accommodate sensitivity analysis and gains, make this method a potential contender. The linear theory flow rate equations model is compact, converges rapidly, and can include a number of network features but it is less attractive in storage requirements. Out of the three models developed, the best appears to be the linear theory method of nodal head equations. It offers the most elegant and straightforward approach to ventilation network analysis, providing simplicity, ease of programming, and superior storage and solution features. (Abstract shortened with permission of author.).;The research was initiated with an objective of identifying efficient and simpler alternatives to the Hardy Cross algorithm from the information available in graph theory, nonlinear network programming, and water distribution systems analysis. A large variety of techniques are noted to be applicable for ventilation network analysis. They are grouped into nonlinear equation solvers, nonlinear network programming methods, and linear theory techniques. A number of factors led to the choice of separable programming piecewise linearization, linear theory method based on flow rates as unknowns, and linear theory method based on nodal heads as unknowns for further study. All the three methods involve a linearization of the network flow problem without requiring gradients and initialization.