Analysis of connecting a forcing fan to a multiple fan ventilation network of a real-life mine

Accepted Manuscript Title: Analysis of Connecting a Forcing Fan to a Multiple Fan Ventilation Network of a Real-Life Mine Authors: Nikodem Szl˛azak, Dariusz Obracaj, Marek Korzec PII: DOI: Reference:

S0957-5820(17)30067-8 http://dx.doi.org/doi:10.1016/j.psep.2017.03.001 PSEP 992

To appear in:

Process Safety and Environment Protection

Received date: Revised date: Accepted date:

6-9-2016 4-2-2017 1-3-2017

Please cite this article as: Szl˛azak, Nikodem, Obracaj, Dariusz, Korzec, Marek, Analysis of Connecting a Forcing Fan to a Multiple Fan Ventilation Network of a Real-Life Mine.Process Safety and Environment Protection http://dx.doi.org/10.1016/j.psep.2017.03.001 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Analysis of Connecting a Forcing Fan to a Multiple Fan Ventilation Network of a Real-Life Mine Nikodem Szlązak*, Dariusz Obracaj*, Marek Korzec* * AGH University of Science and Technology, Faculty of Mining & Geoengineering, Department of Underground Mining, Mickiewicz Avenue 30, 30-059 Cracow, Poland Highlights

   

Increase in primary ventilation capacity of the multi-fan ventilation network. Change from exhaust ventilation system to the push-pull system. Benefits depending on location of a forcing fan in the multi-fan ventilation network. Improvement in ventilation of working areas located close to the shaft with a connected forcing fan.

Abstract The important role of ventilation in underground mines is to guarantee safety and proper environmental conditions in all accessible areas of a mine by applying national mining laws and regulations. A mining ventilation network changes all the time as a result of moving working areas. It frequently results in an increased length of primary intake and return routes, which in turn increases the equivalent resistance of a complex ventilation network. It is necessary to undertake activities to maintain needed airflow rates in branches of ventilation network. In the conditions that prevail in copper mines in Poland, the number of downcast shafts is usually greater than that of upcast shafts. Developing new mining areas in a mine is released by subsurface roadways. If developing of mining areas is realised by shafts the most commonly used ones are downcast shafts. It is difficult to obtain demanded air distribution in ventilation network of the mine due to the large distance between the downcast and upcast shafts. In one of the Polish copper mines, installing a subsurface main fans’ station at a downcast shaft, aimed at increasing airflow rates in the ventilation network, is being considered. The paper is devoted to the analysis of the possibility of increasing airflow rate in a ventilation network in this mine. The first example of building in a forcing fan in the ventilation system with a single downcast shaft and one upcast shaft is shown to illustrate the complexity of the issues in the real ventilation network of the mine. Then the impact of embodying the forcing fan to the ventilation network of the real copper mine with a multiple-fan network is analysed. Computer software can be used to solve the ventilation system for such an analysis. Most of the software is based on the model of air distribution in the ventilation network known as The Hardy Cross procedure. The principles governing such a procedure have been discussed in the article. The results of the analysis let us draw a conclusion that a significant increase in the total air supplied to the mine with a complex structure of the ventilation network is difficult to obtain using underground forcing fans. The only tangible benefit of the presented solution is a change in air distribution in excavations located a short distance from the downcast shaft at which a forcing fan could be installed. An increase in airflow rates in mining districts located near this shaft is possible. However, it must be remembered that connecting the forcing fan in one downcast shaft of the multi-shaft network decreases airflow into other downcast shafts.

Keywords: mine ventilation; push-pull ventilation network; main fan station; ventilation network analysis.

1. Introduction Copper ore is extracted in Polish mines by employing the room-and-pillar mining method. Mines of this kind are characterised by a large demand for air in mining districts. Extracting ore in several or a dozen or so mining districts entails the necessity to supply considerable volumetric flow rates of air to the mine. Polish mines use exhaust ventilation systems and the main ventilation fans operating from the surface. Fresh air enters the mine through the downcast shafts. The air flows along intake airways to the mining districts and next the air passes back along return airways to the station of exhaust fans on the surface. Depletion of ore beds makes it necessary to shift production areas to other mining fields. 1

Consequently, it becomes necessary to adapt the ventilation network of a mine to direct airflow into newly-opened districts. For economic reasons, opening new ore beds is often achieved via underground workings. If new beds are accessed via shafts, usually downcast shafts are used for this purpose for technological reasons, whereas the main fan stations at the upcast shafts are only modernised. As a result, the possibility of implementing some changes in the ventilation system is reduced as the resistance of the lengthened primary returns increases. As workings proceed further away from upcast shaft bottoms, the cost of passing air along the lengthening airways rises. In Polish mines where extraction does not entail gas-related effects, there is a possibility of implementing a push-pull ventilation system in order to supplement airflows to newly developed mining fields. This is achieved by installing subsurface fan stations with forcing fans at the bottom of the downcast shaft. Such a solution is currently being considered for one of the copper mines in Poland. In push-pull systems with multiple main fans, it is vital to select forcing fans with characteristic curves matching those of the existing exhaust fans to prevent undesirable mutual interaction. In complex ventilation networks it is necessary to calculate distribution of airflow, especially in networks with a large number of installed fans (McPherson, 1993; Pawiński et al., 1995; Szlązak et al, 1999; von Glehn et al., 2008; Luo et al., 2014; Suvar et al., 2014). In order to perform the calculations, one can use a model of network structure in the form of canonical diagrams (Wala and Altman, 1987; Szlązak et al., 1998). In these diagrams, ventilation districts consisting of many branches with serial, parallel and diagonal connections to one another can be represented by a single branch with an equivalent resistance (Budryk, 1961; Burrows et al., 1981; McPherson, 1993; Lilic and Kuzmanovic, 1994; Pawiński et al., 1995; Szlązak et al., 1998). Methods of complex ventilation network analysis can be employed for the calculations. 2. Airflow distribution in the ventilation network of a mine - theoretical foundations of the calculations The distribution of airflow in the ventilation networks of underground mines is described using the four basic equations of fluid dynamics: continuity equation, movement equation, energy equation and equation of gas state (McPherson, 1993; Pawiński et al., 1995). For these networks, one-dimensional flow is assumed for simplification. The continuity equation for steady state flow takes the following form: 𝜌 ∙ 𝑉̇ ∙ 𝐹 = constant (1) while the movement equation for steady state and non-viscous airflow is as follows: 1

∙ 2𝑔

𝑑𝑣 2 𝑑𝑠

𝑑𝑧

1 𝑑𝑝

+ 𝑑𝑠 + 𝛾 ∙ 𝑑𝑠 + 𝑓 + ∑𝑗 𝑤𝑗 ∙ 𝛿(𝑠 − 𝑠𝑗 ) = ∑𝑘

∆𝑝𝑚𝑘 𝛾

∙ 𝛿(𝑠 − 𝑠𝑘 )

where: 𝜌 – air density; 𝑉̇ – volumetric flow rate of air; 𝐹 – cross-section of an excavation; 𝑔 – acceleration due to gravity; 𝑣 – air speed; 𝑠 – current coordinate (the length of the flow path); 𝑧 – vertical axis pointing upwards; 𝛾 – specific weight of air; 𝑝 – barometric pressure; 𝑓 – frictional pressure drop represents energy losses per unit weight;

2

(2)

𝑤𝑗 –shock pressure losses per unit weight, resulting from energy losses of the flow within local resistance jth in coordinate 𝑠𝑗 ; ∆𝑝𝑚𝑘 – total pressure increase across the fan, for the point with coordinate 𝑠𝑘 ; 𝛿(𝑠 − 𝑠𝑗 ) and 𝛿(𝑠 − 𝑠𝑘 ) – Dirac’s delta functions. A ventilation network is usually mapped into a graph composed of nodes and edges, termed junctions and branches (Scott and Hinsley , 1951; McPherson, 1993; Pawiński et al., 1995; ElNagdy, 2013; Luo, 2014; Maleki, 2016). Edges represent different paths airflow, which connected by junctions form closed paths termed as fundamental meshes. Ventilation meshes are expressed by junction-branch and mesh-junction matrixes, junction and mesh equations, termed as Kirchhoff’s first and second circuit laws, can take the following form: ̇ ∑𝑁 (3) 𝑖=1 𝜀𝑘𝑖 ∙ 𝜌𝑖 ∙ 𝑉𝑖 = 0 or, assuming constant density of air throughout the branch i: ̇ ∑𝑁 (4) 𝑖=1 𝜀𝑘𝑖 ∙ 𝑉𝑖 = 0 and ∑𝑁 (5) 𝑖=1 𝛼𝑚𝑖 ∙ (𝑊𝑖 − ℎ𝑖 ) = 0 where: 𝑘 = 1, 2, … 𝑃 – number of independent junctions, where 𝑃 is the number of all independent junctions in the ventilation network; 𝑖 = 1, 2, … 𝑁 – number of independent ventilation branches ending with an independent junction 𝑘 of the network, where 𝑁 is the number of all branches 𝑖; 𝜀𝑘𝑖 – character-oriented constant of the junction-branch matrix of the network, for which the value of +1 is assumed when airflow enters a junction 𝑘 via the 𝑖 branch, whereas the value of -1 is assumed when air flows out of a junction 𝑘 via an 𝑖 branch; 𝛼𝑚𝑖 – character-oriented constant of a mesh-branch matrix of a network, for which a value of +1 is assumed when branch 𝑖 belongs to the mesh 𝑚 and is oriented positive to mesh orientation (the flow within this branch is in the same direction as that defined for the mesh), whereas a value of -1 is assumed when branch 𝑖 is not oriented positive to mesh orientation; 𝑚 = 1, 2, … 𝑀 – number of the fundamental mesh 𝑚 of the network, where 𝑀 is the number of all fundamental meshes (closed paths) present in the network; 𝑊𝑖 – sum of frictional pressure drop and shock pressure losses in a branch 𝑖, whereas ℎ𝑖 = ∆𝑝𝑚𝑖 + ℎ𝑛𝑖 denotes a sum of the increase in total pressure across the fan ∆𝑝𝑚𝑖 and the natural ventilation pressure gain ℎ𝑛𝑖 in branch 𝑖; 𝜌𝑖 – air density in branch 𝑖; 𝑉̇𝑖 –volumetric flow rate of air in branch 𝑖. According to Kirchhoff’s second circuit law, total pressure drop in a ventilation mesh according to Atkinson's equation (Atkinson, 1854; McPherson, 1993), which consists of branches 𝑖 with the Atkinson’s resistance, termed as the total equivalent of branch 𝑅𝑖 and constant values of air density, can be calculated with the following formula: 2 𝑁 ̇ 𝑊𝑖 = ∑𝑁 (6) 𝑖=1 𝛼𝑚𝑖 ∙ 𝑅𝑖 ∙ 𝑞𝑖 ∙ 𝑠𝑔𝑛(𝑉𝑖 ) = ∑𝑖=1 𝛼𝑚𝑖 ∙ ℎ𝑖 where: 𝑅𝑖 – the equivalent resistance of branch i (Atkinson’s resistance); 𝑠𝑔𝑛(𝑉̇𝑖 ) – positive or negative value depending on the airflow direction within ith branch to the direction defined for the mesh. Equations (4), (5) (6) form a system of equations with fundamental meshes. The non-lineral programming technique or the Linear Theory are employed in order to solve this system of equations (Wang, 1984; Maleki and Mozaffari, 2016). 3

The earliest numerical method is that of Hardy-Cross method (Cross, 1936; Scott and Hinsley, 1951). This method is an example of a widely known Newton-Raphson numerical scheme (Acuna and Lowndes, 2014; Maleki and Mozaffari, 2016), which consists in finding roots of the system of equations by applying procedures of successive approximation in accordance with the following formula: 𝑁

𝑀

𝑖=1

̅ =1 𝑚

̅̇ (𝑟)| ∙ 𝛼 ∙ ∆𝑉̅̇ (𝑟) − 𝑑ℎ𝑖 (𝑟) ∙ 𝛼 ∙ ∆𝑉̅̇ (𝑟)} = ∑ 𝛼𝑚𝑖 ∙ {2𝑅𝑖 ∙ | ∑ 𝛼𝑖𝑚 ̅ ∙ 𝑉𝑚 ̅ ̅ ̅ ̅ ̅ 𝑖𝑚 𝑚 𝑖𝑚 𝑚 𝑑𝑉̇𝑖 𝑀 ̅̇ (𝑟)| ∙ ∑𝑀 𝛼 ∙ 𝑉̅̇ (𝑟)} = ∑𝑁 ̅ ∙ 𝑉𝑚 ̅ ̅ ̅ 𝑚 ̅ =1 𝛼𝑖𝑚 ̅ =1 𝑖𝑚 𝑚 𝑖=1 𝛼𝑚𝑖 ∙ {ℎ𝑖 − 𝑅𝑖 ∙ |∑𝑚

(7)

where: 𝑚 ̅ − mesh in which all airflows in branches are replaced by airflow of a basic branch, called mesh airflow; 𝛼𝑖𝑚̅ − character-oriented constant of a transpose of a mesh-branch matrix of the network, for replacing airflows in branches by airflows in basic branches (mesh airflows) where value of +1 is assumed when direction of mesh 𝑚 is oriented positive to basic branch 𝑖 orientation, whereas value of -1 is assumed when direction of mesh 𝑚 is not oriented positive to basic branch orientation; 𝑟 − subsequent approximation (iteration step). In equation (7), airflows in branches are replaced with airflows in the basic branches in the mesh 𝑀 𝑚: 𝑉̇ = ∑ 𝛼 ∙ 𝑉̅̇ (𝑟). The correction to the airflow ∆𝑉̇ (𝑟) for the basic branch is 𝑖

̅ =1 𝑚

̅ 𝑖𝑚

̅ 𝑚

𝑖

replaced with equivalent correction for mesh 𝑚: ∆𝑉̇𝑖 (𝑟) = 𝛼𝑖𝑚̅ ∙ ∆𝑉̅̇𝑚̅ (𝑟). In Hardy Cross method, having considered that 𝛼𝑚𝑖 − 𝛼𝑖𝑚 = |𝛼𝑚𝑖 | and 𝑚 = 𝑚 ̅ in approximation 𝑟, correction of airflow in mesh 𝑚 ̅ is calculated in accordance with the following formula: ̅ (𝑟)|∙[∑𝑀 𝛼 ∙𝑉 ̅ (𝑟)]} ∑𝑁 𝛼 ∙{ℎ −𝑅 ∙|∑𝑀 ̅̅̅ ̅̅̅ ̅̅̅ ∙𝑉̇𝑚 ̅̅̅ ̇ 𝑚 ̅̅̅=1 𝛼𝑖𝑚 ̅̅̅=1 𝑖𝑚 𝑚 ∆𝑉̅̇ (𝑟) = 𝑖=1 𝑚𝑖 𝑖 𝑖 𝑚 (8) ̅ 𝑚

𝑀 ̅ (𝑟)|−𝑑ℎ𝑖 (𝑟)} ∑𝑁 ̅̅̅ ̅̅̅ ∙𝑉̇𝑚 ̅̅̅=1 𝛼𝑖𝑚 𝑖=1 𝛼𝑚𝑖 ∙{2𝑅𝑖 ∙|∑𝑚 ̇ 𝑑𝑉𝑖

The method determines the airflow corrections needed to balance the calculated pressure losses around each mesh in the network and calculates the airflow changes needed to the estimates. The process of successive approximation (r) repeats until consecutive solutions satisfy a chosen convergence criterion. The analysis of a ventilation network can be realised by different simulation packages which allow showing easily the effect of adding a forcing fan to the exhaust ventilation network. Computer programmes such as VentSim (Widzyk-Capehart and Watson, 2001), Vuma 3D (Marx and Belle, 2002), 3D-Canvent (Hardcastle et al., 1995), VNetPC2007 (Wallace, 2001) or Polish Ventgraph (Dziurzyński and Kruczkowski, 2007) are best known among several commercial mine ventilation network programmes. Commercial software is mainly used to optimize a mine ventilation network. To optimize the method it is necessary to identify a number, location, duty of fans and regulators to minimize the total fan air power or energy consumption of the mine (Glehn et al., 2008; Acuna and Lowndes, 2014; Bluhm et al., 2014; Suvar et al., 2014). Trace gases techniques are the one of the methods for assessing air distribution in airways with low flow velocity of air (Patterson and Luxbacher, 2012; Widiatmojo et al., 2015; Xu et al., 2015; Xu et al., 2016). These techniques are usually use for determination of air leakages or recirculation in the complex network. They may also be used for verification of input data of ventilation network in commercial software. Commercial software can be employed to analyze the impact of the addition of a forcing fan to an exhaust ventilation system, but it is better to do it in an analytical way to understand it. The impact of adding a forcing fan will be discussed with reference to a simple ventilation network and to the structure of a ventilation network in the real-life mine. 4

If there are two main exhaust fans in a mesh, they cannot have the same orientation in relation to mesh orientation. Using the method for calculating airflow distribution outlined above, it is possible to assess the impact of adding two fans in a mesh, whose orientation is consistent with the already existing exhaust fans. 3. The impact of adding a forcing fan on air distribution along primary airways in a simple ventilation network with one exhaust fan Ventilation networks of underground mines can consist of either only two shafts (downcast and upcast) or of many shafts. In multi-shaft networks, two or more main fan stations can be installed. In a ventilation network consisting of only one downcast and one upcast shaft with an exhaust fan, the possibility of increasing primary ventilation capacity in a system after installing another forcing fan can be proven by an analysis. The object of the analysis is a sample single-fan network, represented by a canonical diagram in Figure 1a. Activating another forcing fan Wt2 in the downcast shaft (at the bottom of the shaft) is tantamount to simplifying the network to the form presented in Figure 1b with known values of branch resistance 𝑅1 and 𝑅2 . Increasing the airflow in the ventilation network from 𝑉𝑜̇ (P0 in Figure 2) to 𝑉̇2 (P1 in Figure 2) is connected with a certain value of fan pressure depending on the significance of branch resistance. Both fans will be passed by the same amount of airflow 𝑉1̇ = 𝑉̇2 . If 𝑅𝑧 signifies the supplementary resistance of the system, then: 𝑅𝑧 = 𝑅1 + 𝑅2 (9) If 𝑉̇2 > 𝑉𝑜̇ , and forcing fan Wt2 is supposed to overcome resistance 𝑅2 , then: ∆𝑝𝑊1 = 𝑅1 ∙ 𝑉12 = 𝑅1 ∙ 𝑉̇22 (10) and ∆𝑝𝑊𝑡2 = 𝑅2 ∙ 𝑉̇22 = 𝑅2 ∙ 𝑉1̇ 2 (11) Consequently, the total pressure of fan 𝑊𝑡2 equals: 𝑅 ∆𝑝𝑊𝑡2 = ∆𝑝𝑊1 ∙ 𝑅2 (12) 1

Assuming that 𝑅1 = 𝑅2 is ∆𝑝𝑊1 = ∆𝑝𝑊𝑡2, both fans should have the same characteristic curves. If 𝑅1 > 𝑅2 or 𝑅1 < 𝑅2 , the characteristic curve of Wt2 must include fan pressure ∆𝑝𝑊𝑡2 for specified capacity 𝑉̇2 (P2 in Figure 2). For real ventilation networks, the probability of fan misalignment is very low provided that the above-mentioned methodology of selecting their place of installation is employed. Forcing fans installed in a ventilation network should be equipped with a controlling device to regulate the rotational speed of the impeller. In summary, it should be concluded that in order to increase primary ventilation capacity in an existing ventilation network, it is necessary to specify the places of installation of the forcing fans and calculate their fan pressure in accordance with formulas (9)-(12). It should be emphasised that there is an increase in total airflow in the analysed ventilation network. The value of total fan pressure decreases for the main fan at the cost of installing another fan in the system. The characteristic curve of forcing fan Wt2 in the specified operating point needs to be compared with the characteristic curve of the existing exhaust fan. The impact of connecting another forcing fan to ventilation networks with a greater number of downcast and upcast shafts located in various parts of the mining area is much harder to estimate. Complex multiple-fan networks may be represented by using a subsystem approach. Each subsystem (for each fan) has its own subsystem curve, which is the relation between the 5

airflow through it and the pressure drop across it (Budryk, 1961; Pawiński et al., 1995; Wang, 1992; El-Nagdy, 2013). In such networks, it is necessary to calculate the distribution of airflow using the methods of ventilation network analysis in a real complex ventilation network. The Hardy Cross procedure may be used for this purpose. The remainder of the article is devoted to a proper selection of forcing fan parameters for the real copper ore mine in Poland. The purpose of the analysis is to check the possibility of increasing airflow rate in the ventilation network. 4. The impact of adding the forcing fan on airflow distribution in the ventilation network of the real-life mine 4.1. P-S Copper Ore Mine In Poland, copper ore is currently mined in three mines in the southwest part of the country, in the Legnica–Glogow Copper District situated in the area of the Fore-Sudetic Monocline. In the P-S mine, the exploited ore deposit has a form of an ore bed, which declines gently towards the northeast. Mining the deposit takes place at the depth ranging from 900 to 1350 m (Mrozek et al., 1996). Initially, the form and stratification of the deposit enforced using a mining infrastructure in which processing units were located at the centre, while peripheral shafts at the boundaries of the mining field performed auxiliary functions related to ventilation, employees' transfer and material supply. The distance between the peripheral shafts and the main shafts is about 3 to 5 km (Mrozek et al., 1996). Because of the large area covered by the mining fields, the number of shafts in a mine varied from several to about a dozen. A single shaft covered an area of 4-10 km2. Over the years, working districts moved forward and organizational structures changed, which resulted in merging the mining fields into complex mines. The underground mine layout consists of multiple development roadways, drilled in the ore bed. The room-and-pillar mining method with roof sagging is employed. The mine is characterised by harsh microclimate conditions. At present, there are seven shafts in the mining field. Fresh air enters the system via five downcast shafts. The return air passes back to the surface via two upcast shafts, each with its own surface station of exhaust fans. In the P-S mine, the mining districts are ventilated using a through-flow ventilation system (McPherson, 1993). The localisation of shafts in the mining field and distances between them are presented in Figure 3. Until now, the mining activities have been conducted mainly between shafts SZ2 and W1 and between shafts SZ2 and W2. The ventilation network is an extensive system, in which the main ventilation fans have an occasional impact on the ventilation subsystems of both upcast shafts.

In addition, air is supplied to the mine via shafts from SZ1 to SZ4 and the recently drilled shaft SZ5, situated in a newly developed part of the mining field. Following the partial depletion of the ore bed in the area of shaft W1 (in the southern part of the mining field), the working front is expected to move towards the north of the mining field during the next few years. In the northern part of the field, there is no upcast shaft, but only two downcast shafts, SZ4 and SZ5 respectively. The number of mining districts is not expected to change, but their site within the mining field will be modified. Consequently, it has been proposed to install the subsurface main fan station at the bottom of downcast shaft SZ4. For this reason, it becomes necessary to investigate the possibility of increasing the airflow in the ventilation network. 4.2. Model of mine ventilation network Figure 4 presents a simplified layout of the ventilation network of the P-S mine. It presents resistances of particular network branches. The ventilation network can be classified as a highly 6

complex one. It consists of 57 branches (i=57) and 33 junctions (k=33), forming 25 fundamental ventilation meshes (m=25). For the ventilation system under analysis, it has been proposed to connect the main fan station to the bottom of downcast shaft SZ4 (Fig. 4) in order to increase airflow through this shaft. Table 1 presents the branch input data for the ventilation network. The resistance values of individual branches of the network presented in the table were calculated on the basis of the data acquired during ventilation surveys in primary airways. The resistance values were calculated for individual branches, based on the measured values of airflow, barometric pressure and bulb temperatures. In the table there are also presented measured volumetric flow rate, average density of air and natural ventilation pressure in each branch. Air is supplied to subsurface excavations via five downcast shafts and returned via two upcast shafts with stations of main fans on the surface. The network covers eight mining districts and functional chambers indicated in Figure 4. The figure also shows airways with regulators. At shaft W1, a main fan station consists of 3 fans working in a parallel way; its combined characteristic curve is described by the following equation: ∆𝑝 = −0.0058 ∙ 𝑉̇ 2 + 9.12 ∙ 𝑉̇ + 2419 (13) At shaft W2, the combined characteristic curve of the working fans is described by the following equation: ∆𝑝 = −0.0786 ∙ 𝑉̇ 2 + 68.48 ∙ 𝑉̇ − 10617 (14) 3 ̇ where 𝑉 is the volumetric airflow rate (m /s). The airflow distribution can be manually calculated using the Hardy Cross algorithm, but it is practically impossible to meet for 25 fundamental ventilation meshes with three fans. The Ventgraph software is used for calculations. In the code of this software, the Hardy Cross method was employed. The following approximation equations for the characteristic curves of the forcing fans Wt3 were applied for the particular variants:  variant No. 2: ∆𝑝 = −0.01 ∙ 𝑉̇ 2 − 0.55 ∙ 𝑉̇ + 5000, (15) 2 ̇ ̇  variant No. 3: ∆𝑝 = −0.0025 ∙ 𝑉 − 0.28 ∙ 𝑉 + 5000, (16) 2 ̇ ̇  variant No. 4: ∆𝑝 = −0.0011 ∙ 𝑉 − 0.18 ∙ 𝑉 + 5000. (17) 4.3. Results and discussion The calculations of airflow distribution were done for fixed-quantity branches in the ventilation network of the mine. Four alternative variants were considered. Variant 1 represents mine ventilation using only exhaust fans at shafts W1 and W2 (Table 1 and Figure 4). In variants 2, 3 and 4, it has been assumed that a forcing fan Wt3 will be installed at the bottom of downcast shaft SZ4. The particular variants differ in the characteristics of the fan installed in the shaft. The calculations were done for three different characteristic curves of fan Wt3, reflecting the functioning of this type of a fan as a single device and in parallel cooperation with two and three fans. Table 2 presents the total airflows in primary airways in particular variants, divided into downcast shafts, upcast shafts and fan pressures. Figure 3.4 shows the characteristic curves of fans with operating points for particular subsystems of the upcast shafts and for the forcing fan.

The analysis of the obtained results reveals that installing a forcing fan in upcast shaft SZ4 causes a slight increase in the total airflow in the ventilation network of the mine. The values of the increase obtained for the particular variants (No. 2, No. 3, No. 4) were 0.8%, 1.0% and 1.1% respectively compared with the existing situation (variant No. 1). Also, adding a forcing fan to 7

the network decreased the pressure of exhaust fans installed at upcast shafts (the decreases ranged from 0.5% to 18.3%). The greatest reduction in fan pressure was possible for the main ventilation fan characterized by the lowest equivalent resistance of its own subsystem (W2). As for the downcast shaft with an installed fan, in each variant higher values of airflow in the shaft were obtained. Despite that, only a slight increase in the total airflow supplied to the mine was observed. It is a consequence of insignificant changes in the equivalent resistance of the subsystems of both upcast shafts. Increasing the airflow passing through shaft SZ4 reduced the airflow in other downcast shafts. The greatest changes were observed in shaft SZ5, located in close vicinity of shaft SZ4. An increase in the pressure of the fan installed at shaft SZ4 may even change airflow direction in shaft SZ5. Figure 5 presents a closed canonical scheme of the network, where green was used to show the extent of overpressure in branches caused by an additional forcing fan. The change in the direction of airflow was also shown.

In each of the analysed variants, the fan pressure of the forcing fan compensates for the pressure drop and the natural ventilating pressure in the shaft and influences the branches adjacent to the shaft (19-25, 19-20, 20-24, 20-21 and 20-29). In the case of variant 3, we can observe a two-fold increase in the volume flow rate passing through the downcast shaft SZ4, but the total fan pressure reaches 3510 Pa and is distributed within the downcast shaft and the adjacent branches (19-25, 19-20, 20-24, 20-21 and 20-29). In branches 24-25 and 25-26, the direction of airflow is reversed. When three forcing fans are connected to the downcast shaft SZ4 (variant 4), their combined pressure is ca. 4200 Pa, while the airflow increases only slightly in comparison with the previous variant (by ca. 65.9 m3/s). The calculation results of the changes of fans’ operating point are presented in Table 2 and in Figure 6. The calculations provide evidence that the increase in airflow is limited, which results from the cooperation and mutual interference of fans with the specified characteristic curves. A significant increase in the airflow rate in the network would have to involve raising forcing fan pressure to very high levels. Figure 7 shows both the increases in airflow and air power of fans in the network. The diagram and the previous analyses lead to the conclusion that installing forcing fans in downcast shafts or in their vicinity would call for considerable investments. Besides, high operation costs must be reckoned with, connected with electricity consumption by the fan motors. The resulting increase in the total volumetric flow rate of air in the network (which turns out to be insignificant) would involve much greater electricity consumption by all fans in the network. The calculations show an increase in airflow in the area of the downcast shaft after installing a forcing fan. However, the airflow decreases in the remaining downcast shafts. Therefore there is no possibility of increasing total airflow in the network. Additionally, it results in extra investment and operating costs. Therefore, it appears reasonable to consider changing the function of one of the downcast shafts and equipping it with a station of exhaust fans. 5. Conclusions The development of mining districts in deep underground mines, which is a consequence of deposit depletion and opening new mining fields, calls for drilling new shafts, combined with extending the existing ventilation network. The results include changes in the extension and equivalent resistances of primary airflow routes in the main ventilation infrastructure. As a result, the ventilation network is becoming increasingly complex. 8

Changes in a ventilation network may be necessary in order to ensure the required ventilation flow rates in mining districts. In order to achieve this goal in non-gassy mines, there is a possibility of building in a subsurface station of the main forcing fans at the bottom of downcast shafts. A measurable effect of such an action should be an increase in the total airflow in a ventilation system. In case of ventilation networks with a single downcast shaft and a single upcast shaft, the selection of a forcing fan to be used in the network is relatively simple. In this situation, the same airflow will pass through both fans. The best option is to install a fan with the same characteristic curve as the fan at the upcast shaft. It must be remembered, however, that overpressure may develop in a part of the network, with resulting underpressure in the other parts. Depending on the resistance of its subsystem, the forcing fan may have a different pressure than the exhaust fan. Therefore, the characteristic curve of the forcing fan must be matched to the characteristic curve of the existing exhaust fan. In real extended ventilation networks, the task of selecting an appropriate forcing fan is much more complex. In order to estimate the impact of installing a forcing fan on the system, numerical methods of calculating airflow distribution must be employed, e.g. the Hardy Cross method. The calculations of airflow distribution made for the ventilation network of P-S mine have revealed that installing a forcing fan at one of the downcast shafts will cause only a limited increase in the total amount of air supplied to the mine. At the same time there is an increase in the air power output of the fan built in the network. Therefore, in addition to investing in the building fans, operating costs resulting from the consumption of electricity will be incurred. For the analysed network, building in subsurface main forcing fans to increase airflow in the ventilation network is not a good solution, both in terms of technology and economy. Despite the lack of a significant increase in the amount of total air in a ventilation network there is a positive result from an increase in the airflow in excavations located close to the downcast shaft with a forcing fan. However, the possible disturbances in airflow distribution in other branches of the ventilation network caused by the overpressure of the fan have to be taken into consideration. The further from the forcing fan it is built in, the smaller its impact is. To sum up, it must be remembered that an increase in the total amount of air flowing through the entire ventilation system depends on the complexity of the network and the characteristic curves of fans built in upcast shafts. The aim of installing forcing fans in the primary ventilation system of a multiple-fan mine is to step up the primary ventilation capacity. Forcing fans can be employed to intensify ventilation in a specific group of intake airways. Acknowledgements The authors would like to acknowledge the mining company for support and assistance in project implementation. The research work presented in the article is supported by the framework of statutory activities, AGH University of Science & Technology, No. 11.11.100.005.

9

References Acuna, E.I., Lowndes, I.S., 2014. A Review of Primary Mine Ventilation System Optimization. Interfaces. 44 (2), 163-175. Atkinson J.J., 1854. On the Theory of the Ventilation of Mines. Trans. North of England Inst. of Min. Engrs., 3 (1854-5), p.118. Bluhm S., Moreby R., Von Glehn F., Pascoe C., 2014. Life-of-mine ventilation and refrigeration planning for Resolution Copper Mine. J. S. Afr. I. Min. Metall. 114 (6), 497-503. Budryk W., 1961. Wentylacja kopalń - Cześć 1 - Przewietrzanie wyrobisk. Wydawnictwo Górniczo-Hutnicze, Katowice (Polish book). Burrows J., Hemp R., Holding W., Smith R.M., 1981. Environmental engineering in South African mines. The Mine Ventilation Society of South Africa, Johannesburg. Cross H., 1936. Analysis of flow in networks of conduits or conductors. Univ. Illinois Bull. 286, 1–32. Du Plessis J.J.L., Marx W.M., Nell C., 2014. Efficient use of energy in the ventilation and cooling of mines. J. S. Afr. I. Min. Metall. 114, 1033-1037. Dziurzyński W., Kruczkowski J., 2007. Validation of the mathematical model used in the VENTGRAPH programme on the example of the introduction of new headings to the ventilation network of mine” Arch. Min. Sci. 52, 155-169. El-Nagdy K.A., 2013. Stability of multiple fans in mine ventilation networks. Int. J. Min. Technol. 23, 569–571. Hardcastle S.G., 1995. 3D-canvent: An interactive mine ventilation simulator. Proc. 7th U.S. Mine Ventilation Sympos. (Society for Mining, Metallurgy & Exploration, Englewood, CO), pp. 467–472. Lilic N., Kuzmanovic D., 1994. Optimization of air distribution in mine ventilation networks. Yugosl. J. of Oper. Res. 4 (I), 105- 113. Luo W., Xie X., Xiao H., Cui Ch., Yin X., Su M., Wang T., Li J., Tan X., 2014. Reliability calculation of mine ventilation network. Procedia Eng. 84, 752 – 757. Maleki B., Mozaffari E., 2016. A comparative study of the iterative numerical methods used in mine ventilation networks. Int. J. Adv. Comput. Sci. Appl. 7(6), 356-362. Marx W, Belle B.K., 2002. Simulating airflow conditions in a South African coal mine, using the VUMA-network simulation software. http://www.vuma.co.za/pdf/VumaC.pdf (accessed 16.08.26). McPherson M.J., 1993. Subsurface ventilation and environmental engineering. Chapman & Hall, London. Mrozek K., Piechota S., Siewierski S., 1996. Part III Mining, in: KGHM Polska Miedz S.A. Monografia (Monograph). (Eds), Wyd. KGHM Cuprum CBR, Spolka z o.o., Wroclaw, Lubin, pp. 397-643 (Polish book). Patterson, R., Luxbacher, K., 2012. Tracer gas applications in mining and implications for improved ventilationcharacterisation. Int. J. Min. Reclam. Environ. 26,337–350. Pawiński J., Roszkowski J., Strzemiński J., 1995. Przewietrzanie kopalń. Ślaskie Wydawnictwo Techniczne, Katowice (Polish book) Scott D.R., Hinsley F.B., 1951. Ventilation network theory. Parts 1 to 4. Colliery Eng. 28, 67-71, 159-166, 229-235, 497-500. Szlązak N., Liu J., Borowski M., Obracaj D., 1998. Numerical determination of diagonal branches in mining ventilation networks. Arch. Min. Sci. 4, 549-561. Szlązak N., Obracaj D., Borowski M., 1999. Possibilities for taking advantage of main multi-fan station for optimization of ventilation network in the gassy mine. AGH J. Min. Geoeng. 4 (23), 263–273 (Polish text). Șuvar M.C., Lupu C., Arad V., Cioclea D., Păsculescu V.M., Mija N., 2014. Computerized simulation of mine ventilation networks for sustainable decision making process. Environ. Eng. Manage. J. 13 (6), 1445-1451. von Glehn F. H., Marx W. M., Bluhm S. J., 2008. Verification and calibration of ventilation network models. Proc of the 12th U.S. North American Mine Ventilation Symposium, pp. 275-279. Wala A.M., Altman T., 1987. Canonical diagram as a graph representation of a mine ventilation network. Min. Eng. 39 (38), 796-800.

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Wallace K.G. Jr., 2001. General operational characteristics and industry practices of mine ventilation systems. http://www.mvsengineering.com/files/Publications/07th_INT-1.pdf (accessed 16.08.26). Wang Y.J., 1984. A Non-linear Programming Formulation for Mine Ventilation Networks with Natural Splitting. Int. Jour. of Rock Mech. Min. Sci. and Geomech. 21, 43–45. Wang Y.J., 1992. Characteristic curves for multiple-fan ventilation systems. Trans SME. 292, 1829–36. Widiatmojo, A., Sasaki, K., Sugai, Y., Suzuki, Y., Tanaka, H.,Uchida, K., Matsumoto, H., 2015. Assessment of air dispersion characteristic in underground mine ventilation: Field measurement and numerical evaluation. Process Saf. Environ.Protect. 93, 173–181. Widzyk-Capehart E., Watson B., 2001. Agnew gold mine expansion, mine ventilation expansion evaluation using Ventsim., http://www.ventsim.com/wpcontent/uploads/2016/01/Agnew_Gold_Mine_Expansion_using_Ventsim.pdf (accessed 16.08.26). Xu G., Jong E.C., Kray D. Luxbacher K.D., McNair H.M., 2016. Effective utilization of tracer gas in characterizationof underground mine ventilation networks. Process Saf. Environ. Protect. 99, 1–10. Xu, G., Jong, E.C., Luxbacher, K.D., Ragab, S.A., Karmis, M.E., 2015.Remote characterization of ventilation systems using tracergas and CFD in an underground mine. Saf. Sci. 74, 140–149.

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Figure 1. Simple ventilation network, a) canonical diagram, b) simplification of the diagram

12

Figure 2. Characteristic curves for both exhaust (W1) and forcing (Wt2) fans in a simple ventilation network (Rz=R1+R2); a) R1 > R2, b) R2 > R1

13

Figure 3. Mining field of the P-S mine

14

Figure 4. Simplified layout of the ventilation network of the P-S mine

15

Figure 5. Closed canonical diagram with localisation of the forcing fan and range of its impact on the ventilation network and changes in airflow direction

16

Figure 6. Characteristic curves of fans with operating points for each of the analysed variants with an additional forcing fan a) for W1 Shaft, b) for W2 Shaft, c) for SZ4 Shaft

17

Figure 7. The calculated increases in airflows and air power of fans in the ventilation network of the P-S mine

18

Table 1. Structure of the ventilation network Branch No.

Inlet junction

Outlet junction

Branch resistance Ri (kg/m7)

Average air density, i (kg/m3)

Volumetric flow rate, 𝑉̇𝑖 (m3/s)

Diff. altitude Z2-Z1 (m)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52

1 8 8 10 1 2 9 2 3 2 3 3A 3 28 28A 4 5 5 6 1 26 25 26 27 1 19 25 19 20 20 21 22 24 22 22A 23 1 11 11 12 16 11 20 29 16 12 13 14 14 7 1 1A

8 10 15 7 2 9 10 3 4 4 3A 4 28 28A 4 5 9 6 7 26 25 27 27 28 19 25 24 20 24 21 22 23 23 22A 23 16 11 21 12 16 18 29 29 18 13 13 14 5 15 1A 1A 1

0.00514 0.01626 0.05262 0.00071 0.00105 0.05771 0.00530 0.00180 1.23960 0.57060 0.07629 0.06161 0.09065 0.01276 0.02076 0.00217 0.06800 0.00121 0.00051 0.00435 0.09745 0.67130 0.01934 0.00072 0.00130 0.29017 0.02168 0.00345 0.01365 0.30144 0.00312 0.03865 0.00938 0.00775 0.00782 0.00037 0.00016 0.00348 0.00139 0.46235 0.00042 0.20322 0.02699 0.00431 0.44141 0.02512 0.00424 0.01661 0.67748 0.00167 1.75567 0.00007

1.27 1.27 1.27 1.24 1.29 1.31 1.26 1.34 1.31 1.31 1.32 1.29 1.33 1.31 1.29 1.28 1.28 1.26 1.24 1.33 1.40 1.36 1.39 1.34 1.33 1.40 1.35 1.37 1.33 1.33 1.33 1.31 1.32 1.30 1.30 1.31 1.30 1.35 1.33 1.31 1.31 1.33 1.32 1.30 1.30 1.30 1.28 1.27 1.26 1.18 1.18 1.18

416.7 283.3 133.3 516.7 400.0 183.3 233.3 166.7 33.3 50.0 100.0 100.0 33.3 200.0 200.0 416.7 50.0 566.7 733.3 200.0 50.0 16.7 150.0 166.7 300.0 33.3 66.7 266.7 116.7 16.7 216.7 83.3 183.3 133.3 133.3 400.0 483.3 200.0 233.3 33.3 366.7 50.0 133.3 183.3 33.3 200.0 233.3 200.0 33.3 1250.0 50.0 1300.0

-820 90 -20 30 -960 140 90 0 30 30 15 15 -180 100 110 110 0 30 90 -1260 110 10 120 0 -1210 60 90 100 50 50 30 70 100 35 35 10 -1000 -60 35 15 -45 10 120 -5 90 105 10 30 10 690 -10 10

19

of

Natural ventilation pressure, NVP (J/m3) -608.36 105.44 -24.48 40.64 -531.4 119.6 108.39 0,00 27.34 26.51 12.84 16.25 -149.28 110.38 130.52 126.9 0.00 38.27 123.95 -425.82 43.63 6.47 55.13 0.00 -382.75 22.42 66.37 55.12 45.79 43.73 26.29 68.4 95.2 37.72 39,00 9.65 -512.15 -40.85 25.64 13.72 -43.81 8.06 119.86 -5.22 90.45 104.86 10.97 34.33 12.76 1057.79 -10.84 10.84

53 54 55 56 57

18 1 1B 15 16

1B 1B 1 6 4

0.00626 1.70153 0.00032 0.01118 0.91852

1.23 1.20 1.20 1.25 1.30

20

550.0 33.3 583.3 166.7 33.3

985 -10 10 50 20

1193.84 -9.41 9.41 70.43 20.58

3

Variant No.

Volumetric flow rate (m /s)

Primary intake air

Primary return air

Surface air leakage to the fan station (m 3/s)

Main fan station Volumetric flow rate (m3/s)

Fan pressure (Pa)

W1

W2

W1

W2

W1

W2

Wt3

Iteration steps

Table 2. The results of calculating airflows in downcast shafts and upcast shafts and fan pressure

SZ1

SZ2

SZ3

SZ4

SZ5

Total

W1

W2

Total

1

413.5

399.3

487.4

317.9

212.4

1830.5

1256.8

573.7

1830.5

43.3

33.6

1300.1

607.3

4336

1981

-

6

2

412.3

381.2

331.5

599.7

120.1

1844.8

1260.7

584.1

1844.8

43.1

31.5

1303.8

615.6

4313

1753

1775

10

3

411.2

362.2

195.9

795.9

83.8

1849.0

1260.3

588.7

1849.0

43.1

30.5

1303.4

619.2

4314

1651

3510

13

4

410.8

358.8

146.8

861.8

72.8

1851.0

1260.8

590.2

1851.0

43.1

30.2

1303.9

620.4

4312

1618

4195

13

21