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Product Type:. Publication Date newest to oldest Publication Date oldest to newest Relevance. ETDE Web. The principal task is to identify the number, location, and duty of fans and regulators for installation within a defined ventilation network to distribute the required fresh air- flow at minimum cost.
The successful implementation of these methods may produce a computational design tool to aid mine planning and ventilation engineers. This paper presents a review of the results of a series of recent research studies that have explored the use of mathematical methods to determine the optimum design of primary mine ventilation systems relative to fan power costs. Keywords: mine ventilation optimization; linear programming; nonlinear programming.
History: This paper was refereed. T he design of reliable mine ventilation systems is key to the safe and economical operation of underground mines. Governments of many countries repeated use of steady-state mine ventilation network programs to evaluate the airflow and pressure dis- tribution.
However, this method is time consuming recognize the important role of ventilation in the and may not always identify the solution that delivers safety of underground mines by imposing national the minimum fan power cost. The challenge for the mining laws and regulations. These rules specify engineer is to identify a practical subset of ventilation the minimum safety and environmental conditions arrangements and performance levels that deliver that a ventilation system must maintain within a the desired airflow distribution.
The use of any new working underground mine. The main objectives of ventilation arrangement needs to satisfy all mining, such a system are to sustain life and to ensure a health, and safety laws of the country in which the safe and acceptable working environment. Achieving mine operates. For example, in the United States, these aims requires the delivery of a sufficient quan- any significant changes to a mine ventilation sys- tity of fresh air to ensure the rapid dilution of mine pollutants to below statutory occupational exposure tem need the prior approval of the Mine Safety and levels OELs and their removal.
These pollutants may Health Administration—national mining laws can dif- include strata gases e. For example, the European eral dust and fumes, and particulates from diesel- Union allows booster fans in coal mines, whereas the powered equipment. United States prohibits them.
Roadways fitted with airlock doors intercon- 3 a review of the engineering components includ- nect these two flow circuits. The double D DD sym- ing fans and regulators that distribute the fresh air bol in Figure 1 represents airlock doors.
These doors within the mine network. We present a mathemat- prevent the short circuit of the fresh air to the con- ical formulation of the objective function and con- taminated return air circuit, and allow for the safe straints that define the optimization problem, and and efficient movement of workers, equipment, and follow this with a review of the optimization meth- supplies between the two airflow circuits.
To create a controlled flow of fresh air to all work- ing areas, engineers supplement any natural thermal The optimization problem seeks to minimize the ven- airflow drafts with large main fans, normally located tilation power consumption of a defined network, at or near the surface. These main fans either push subject to the conservation of mass flow and energy, fresh air into, or pull contaminated air out of, the the satisfaction of upper and lower airflow bounds, underground mine ventilation network.
Booster fans and any controls on the location of fans and regula- and air regulator doors divide the fresh airflow enter- tors Barnes Large mine networks can be com- ing the mine between the various mine workings. The plex; they often comprise hundreds of interconnected B and R symbols in Figure 1 represent the locations of roadways, which are ventilated by fans and regula- a booster fan and airflow regulators, respectively.
The tors positioned around the network. Minimizing the regulators throttle the airflow passing through a par- power costs of these systems is a challenging, practi- ticular airway and distribute the fresh airflow deliv- cal problem that may be examined as a solution to a ered by the main fan. Booster fans are added when the main fan s cannot deliver the pressure to transport the needed airflow Primary Mine Ventilation Systems quantities to the furthest locations in the mine.
This may occur when a mine ventilation network expands The layout of interconnected tunnels formed to access to exploit mineral reserves at an increased distance or and exploit the underground mineral deposits defines depth from the surface connections. Where local min- the topology of an underground mine ventilation net- ing laws and regulations allow, underground booster work. The design of a ventilation system is deter- fans may be installed within selected branches to mined principally by the location and rates of gen- deliver the energy to overcome the pressure losses eration of the contaminants within the mine circuit.
The correct design and installation of The working face is that portion of a tunnel in booster fans should minimize uncontrolled recircula- which minerals are actively extracted. Although the tion, but not adversely influence the performance of design of each individual mine ventilation system is other fans installed in the network.
Vertical shafts or inclined the pollutant necessitates a minimum airflow quantity tunnels, commonly termed ramps, connect the under- to dilute it below statutory OELs.
These working loca- ground network of tunnels to the surface. These sur- tions are termed specified airflow branches. The min- face connections serve as 1 egress routes for work- ing activities that produce pollutants include mineral ers, mobile machinery, and materials, 2 conveyance production faces, diesel maintenance workshops, bat- paths for the extracted mineral, and 3 entry or exit tery and fuel charging stations, and mineral crusher portals for the ventilation air.
McPherson For many mine ventila- nections between those paths. This new equation states that the volu- and ensure that the pressure drops and airflows in metric airflows entering a junction node are equal to each branch satisfy the Atkinson equation.
These laws ensure that the calculated airflow distribution com- the volumetric airflows leaving that junction. When plies with the principles of mass and energy conser- a flow is compressible, we consider the changes in vation McPherson , Lowndes and Tuck If the flow is incompress- Equations 2 — 15 in the appendix mathematically ible, density does not change or changes in density model these physical principles. Equation 15 represents the balance of change significantly. In a ventilation net- the frictional pressure loss Lj , the shock pressure work, the energy potentials are the pressure ener- loss of a regulator Rj , the fan pressure gain Fj , and gies delivered by the fans and the thermal drafts.
The frictional resistance and the shock losses cre- represents the total pressure drop in the jth branch. Changes in the roadway cross section, braic sum of all the total pressure drops experienced flow around a bend in the roadway, and flow around around the ith closed path in the network termed equipment within the roadway generate changes to the ith fundamental mesh Mi is equal to zero.
Equa- the flow direction or speed. The changes in the flow tion 8 represents this energy balance, as Figure 2 direction or speed result in energy losses, termed represents graphically. The shock pressure losses, caused by The arrow alongside each branch in Figure 2 shows changes in the flow direction or speed within the the direction of airflow.
The curved arrow at the cen- jth branch, are often estimated as the frictional pres- ter of the mesh indicates the chosen direction of the sure drop created by an equivalent length of the host flow in the mesh.
If Nb is the total number of branches equiv branch. The total resistance branch. The rates of mineral production divided by the cube of the cross-sectional area Aj of and transport define the levels of pollutants created the branch.
This knowledge allows the ventilation Equation 5 represents the shock pressure loss Rj engineer to determine the minimum and maximum because of a regulator within the jth branch.
We can airflow quantities delivered by the ventilation system also estimate Rj as the frictional pressure drop cre- reg ated by an equivalent length sj of the host branch. Thus, for an incompressible and turbu- Figure 2: This example of a closed path or fundamental mesh comprises lent airflow, the total pressure drop Hj , experienced three nodes and three branches in a network.
Equations 9 and 10 mathemat- Several commercial mine ventilation network pro- ically represent these constraints, where the range of grams are available to evaluate the steady state vol- the air quantity flowing through the jth branch Qj umetric flow and pressure distribution within a mine is restricted by a lower lj and an upper uj bound.
Table 1 ciency of the fan located in the jth branch of the net- summarizes examples of these programs Hardcas- work. However, practical constraints may preclude tle , Wallace , Widzyk-Capehart and Watson the installation of regulators or fans within certain , Marx and Belle The process repeats until consecutive solutions satisfy a chosen convergence criterion.
For Primary Mine Ventilation Network specified airflow branches, the method determines the value of the equivalent resistance or fan pressure Optimization Problem added to this branch to achieve the required mini- The PMVN optimization problem is defined by the mum airflow quantity. Calizaya et al. The objective is to mini- mine, while delivering the airflow requirements at all mize the fan power cost of a mine ventilation network, the locations fixed by engineers.
Equations 13 and 14 represent is defined, a number of variants of the optimiza- the nonnegativity and nature of the variables, respec- tion problem may be solved. These variants may tively. The PMVN optimization problem is nonlin- be categorized as 1 natural or free-flow splitting, ear and nonconvex, and the solution seeks to mini- 2 controlled flow splitting, and 3 semi-controlled mize the total air power delivered by the fans in the flow splitting.
The general formulation of the initially network Wu and Topuz The product of the defined PMVN corresponds to semi-controlled flow fan pressure Fj and the volumetric flow Qj pass- splitting. This variant has two types of subvariants, ing through the fan, divided by the fan efficiency depending on the solution method, that we explain in nj , in the jth branch of the network determines the this section.
The sum of all individual fan air powers variant, the natural or free-flow splitting FS , seeks determines the total air power consumed within a to find the airflow and pressure distribution cre- mine ventilation network. For branches that do not contain a fan, the fan pressure drop term is set to ated by fans, the natural ventilation pressure, and zero.
The energy contributed by fans, as Equation 12 the frictional and shock pressure losses within the represents, serves to generate the required airflow airways. The natural ventilation pressure is formed and pressure distribution through the mine ventila- by the difference in density caused by the different tion network.
In this The solution to the optimization problem identi- variant FS, Equation 16 is added to the PMVN to fies the number, location, and duty or operational guarantee that the regulators are not used to control point, which is a pressure and airflow combination of the flow distribution. In recent years, several studies have explored the The optimization problem that considers the sec- use of mathematical methods to minimize the power ond variant, the controlled flow splitting, is a different consumption of mine ventilation networks, includ- kind of problem.
Because the airflows are known for ing Wu and Topuz , Calizaya et al. The remaining deci- , Lowndes and Yang , Lowndes et al. The mathemat- resistances located in the mine ventilation network.
This variant is solved mization methods that solve the controlled and semi- using linear programming methods. All methods evaluate the minimum air semi-controlled flow-splitting problem variant, which power consumed to deliver a specified airflow dis- determines the installation of regulators and or tribution.
A controlled flow-splitting problem exists booster fans within a predefined subset of the net- when the airflow in all branches of a network is work branches, whereas the flows in the rest of the known. For semi-controlled splitting SC , there ods to solve the controlled flow-splitting variant of are two separate subvariants of the problem.
Type 1, the optimization problem: 1 linear programming semi-controlled 1 SC1 , allows regulators only within techniques, including the network simplex method, the specified airflow branches; Equation 17 is added 2 critical path crashing techniques, including appli- to the PMVN. Type 2, semi-controlled 2 SC2 , permits cations of the critical path method CPM , and 3 a regulators in any set of permissible branches of the combination of CPM and cut set i.
The CPM determines siders fans as the only means to regulate the airflow the longest path between two locations in the net- and pressure distribution. In the third variant, semi- work. For mine ventilation networks, the longest path controlled flow splitting, not only fans, but also reg- of connected branches corresponds to the path of ulators are considered for regulating the airflow and greatest resistance i.
These variants are the two most contribution to the total air power consumed by the common cases found in the mining industry. The sec- ventilation network. Thus, the solution may consist ond variant, in which the airflow is known and can of installing a booster fan within a high-resistance be regulated in all branches, is hard to find in the branch to compensate for the high frictional pres- industry, but it can be used to find solutions to the sure drop.
The method then recalculates the new total semi-controlled flow-splitting variant, as we show in air power consumed by the network. The process the next section. The third tors can reduce the overall energy consumed by the class of solution methods is a combination of CPM fans installed within semi-controlled flow networks.
A fundamental cut set is the The addition of regulators can change fan duty points, minimum number of branches whose removal defines reduce leakage, and create a more efficient airflow the tree of branches that connect all the nodes of the distribution. All proposed solution techniques use an iter- of the pressure value of a potential booster fan.
Thus, ative algorithm to determine the resistance values of this method first uses a CPM to identify the loca- the regulators needed in the network. The methods that Wang , Barnes fans required. Wu and Topuz describe the first mization problem, in which a regulator may be placed method, developed by Calizaya et al. The second method consists of five iterative consider the free-flow splitting variant of the opti- steps, which allow the evaluation of the air power mization problem, in which regulators are not permit- consumed by the network, considering changes of ted.
The core of the all the studies in Table 2 claim to achieve a local method is a gradient technique. The authors present optimal solution for the variant of the PMVN opti- a small network consisting of six junctions and eight mization problem considered. However, none of these branches. Wu and Topuz remark that 1 none of the Calizaya et al.
Controlled flow splitting is usually not applicable. They then on minimizing the airflow deviation from the require- determine the minimum fan power consumed from ments instead of minimizing the air power, as in a graphical solution of the intersection of the lin- other approaches. The technique defines the airflows ear approximations to the regulator resistance curves. As a result, the heuristic achieves the compared. However, the Newton-Raphson iterative method to solve the type 2 method cannot locate fans and or regulators.
The solution method permits the installa- multiple initial values. The objective function mini- tion of ventilation devices i. The authors provide a detailed description of the Barnes decomposes the type 2 semi- major computational steps involved in applying the controlled flow variant of the optimization problem GRG method, which are 1 the determination of a into two problems: 1 the determination of the air- search direction, and 2 the calculation of the step in flow distribution problem, and 2 the evaluation of the improvement direction.
In sim- tion of the solution for a small-scale mine ventilation ple terms, the method seeks an improvement solution network model, consisting of 18 branches and nine search direction, followed by the calculation of the nodes, illustrates the use of the method. The algo- Kumar et al. The first step determines the feasibility. The algorithm ends when no improvement best duty and location of the main surface fan s using direction is possible, as Barnes indicates.
The CPM determines the largest pressure Jacques presents a heuristic optimization drop of the network, which is used to calculate the approach to compute the operational duties for venti- pressure value of the fan s. The second step identifies lation devices e. The solution method can quickly respond to routines Bazaraa and Shetty , coupled with the the daily changes in the demands placed on a real use of a steady-state mine ventilation network pro- mine ventilation system.
The heuristic concentrates gram. The objective function minimizes the air power tial solution method proposed by Lowndes and Yang consumed by fans.
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