Chapter 2

ESTABLISHING MINE VENTILATION POTENTIALS

R. E. Greuer

Department of Mining Engineering Michigan Technological University Houghton, MI 49931

ABSTRACT

In hydraulic networks it is common to call the sum of absolute pressure and the product of density and elevation of a point its potential. This is a point function which can be used to predict flow directions and flow rates between points. Potential differences can be obtained by summing up pump pressures and deducting pressure losses.

The results of summing up fan pressures and deducting pressure losses in mine ventilation networks depend, due to varying air densities, on the selected paths. The thus obtained potentials are path functions and can only to a limited degree be used to predict flow directions and flow rates. Since thermodynamic properties are point functions, they offer themselves as potentials. But none of the known thermodynamic properties meet the desired characteristics of potentials. In the form of approximations potentials are nevertheless widely used. The author describes the different methods of establishing potentials, about which he has learned, and characterizes them with executed examples.

KEYWORDS

Mine ventilation potentials, ventilation planning, network stability, flow directions, natural ventilation pressure, pressure losses, and thermodynamic availability

INTRODUCTION

A potential in fluid mechanics is the sum of the absolute pressure plus the product of density and elevation.

Potentials are handy and popular quantities because they allow one to predict flow directions and to calculate flow rates when two points with known potentials are connected. When, as in hydraulics, the density of the fluid remains constant, it is easy to determine potentials. The sum of the pressure losses minus the pump pressures gives the potential difference between two points. Potentials are therefore widely used in hydraulics.

There has always been a great demand that potentials should be specified in ventilation systems for the purpose of indicating the direction of leakage flow and of flow rates between two points, in case the two points should be connected by an airway.

Contrary to hydraulic networks, the densities in ventilation systems vary. The results of summing up pressure losses and subtracting fan pressures depend on the path chosen for this operation. Moving along two different paths between points can result in two different potential differences, the divergence being the natural ventilation pressure in the mesh formed by the two paths. If the natural ventilation pressure is large, as can be the case when larger elevation and temperature changes occur along the traversed paths, the divergence can be large and it is no longer possible to predict air flow directions and flow rates from potential differences.

The desired potential can therefore not be a path function, it has to be a point function. All thermodynamic properties are point functions. There are many different properties but none of the more commonly used properties have been found useful to predict air flow directions and flow rates.

Some promise is seen in the thermodynamic availability. This is frequently called a potential for the usefulness of energy contents. The thermodynamic availability can be defined in terms of other thermodynamic properties and functions, which are needed in ventilation network calculations anyway. This makes its use attractive and, since availability analysis is a powerful tool in thermodynamic design, hope was placed on making it a useful tool in ventilation planning also.

The executed examples, which are presented in this report, show unfortunately that the usefulness of the availability as a ventilation potential is very limited. Like another point function, the pressure, it is too much influenced by the elevation to be of practical value.

Due to their popularity in hydraulics potentials are nevertheless widely used in mine ventilation. How they are obtained varies. There is little literature on this subject. This report describes the different methods to establish potentials of which the author has learned through the literature or communication with colleagues and characterizes them with executed examples. The method developed and favored by the author is to distribute the natural ventilation of a mesh to its airways proportional to their pressure losses and inversely proportional to the sum of the absolute of all pressure losses of the airways of the mesh.

THERMODYNAMICS OF VENTILATION NETWORKS

Ventilation network calculations can be based on volume flow rates (m³/s) and energies per unit volume (J/m³ = Pa = ventilation pressures) or on mass flow rates (kg/s) and energies per unit mass (J/kg). The so-called mesh equations in network calculations make use of what is called in thermodynamics the energy equation. It reads per unit mass

v dp + g dZ + dV²/2 + dh_l - dh_f = 0

or per unit volume with ρ = 1/v and dp_l = ρ dh_l and dp_f = ρ dh_f

dp + ρ g dZ + ρ /2 dV² + dp_l - dp_f = 0

with v = specific volume (m³/kg)

 = 1/v = density (kg/m³)

p = pressure (Pa)

g = gravitational acceleration = 9.81 m/s²

Z = elevation (m)

V = velocity (m/s)

h_l = head loss (J/kg)

h_f = fan head (J/kg)

p_l = pressure loss (Pa)

p_f = fan pressure (Pa)

Integration around a mesh results in

∑ h_l - ∑ h_f = -
v dp = h_n

∑ p_l - ∑ p_f = -
ρg dZ = p_n

where h_n = natural ventilation head (J/kg)

p_n = natural ventilation pressure (Pa)

In this report both, network calculations based on volumes and based on masses are used.

It is in the US more popular to base flow rates and energies on volumes than to use masses. On the other hand, using masses is the simplest way to satisfy the law of mass conservation. The author uses normally a compromise. The network calculations are based on masses. But the results are then with the help of a constant conversion factor, the reference density, expressed per unit "reference volume".

THERMODYNAMIC PROPERTIES AS POTENTIALS

A potential has to be a point function. All thermodynamic properties are point functions. The more commonly used properties in ventilation network calculations are elevation Z and temperature T. They are normally known or easy to obtain. Three other properties, pressure p, entropy s, and availability Ψ might be useful as potentials. Since they are less used in ventilation network calculations they are normally not known.

If elevations and temperatures of nodes and head losses of airways are known, it is not difficult to calculate the pressure of nodes. Assuming polytropic processes the relation

p₂ = p₁ (T₂/T₁)**A with A = (-g dZ - h_l)/(R (T₂ -T₁))

can be applied, which for isothermal processes has to be changed to

p₂ = (p₁)**B with B = (-g dZ - h_l)/(R T₁).

Starting from a reference point, normally the surface, all node pressures can be calculated. What one obtains is a standard pressure distribution, based on a constant reference point pressure.

If the reference point is also used for entropies and availabilities, it is possible to to calculate entropy s and availability Ψ of nodes from pressure p, elevation Z, and temperature T with

s = Cp ln(T/T₀) - R ln (p/p₀)

Ψ = Cp (T - T₀) - T₀ (s - s₀) + g (Z - Z₀)

where To, so, Zo are arbitrarily chosen reference levels for temperature, entropy, and elevation. In this report s₀= 0 J/kg, Z₀ = 0 m, and T₀ = 283.2 K apply to the surface state of the air.

With this one can calculate densities dns (ρ) of nodes and average densities adns, entropy changes ds and availability changes dpsi (dΨ) for airways.

If pressure losses p_l = h_l ρ are known, it is not difficult to calculate pressures p and the other properties ρ, s, and .

The pressure change in an airway from p₁ to p₂ is

p₂ = (p₁ (1 - g dZ/(2 R T₁)) - p_l)/(1 + g dZ/(2 R T₂)

if the approximation ∫ v dp = 2 (p₂ + p₁)/(ρ ₁ + ρ ₂) is accepted.

Table 1. Air Properties in an Adiabatic Mine

Airway Data

no	js	jf	dZ	dT	hl	Pl	dpsi	ds	adns
1	1	2	-500.0	4.9	150.0	188.4	-148.57	0.5848	1.2560
2	2	3	-500.0	4.9	150.0	196.2	-145.78	0.5749	1.3079
3	3	4	.0	.0	1000.0	1326.4	-966.55	3.4130	1.3263
4	2	5	.0	.0	1132.1	1441.2	-1112.76	3.9292	1.2729
5	4	5	500.0	4.9	.0	.0	-.43	-.0587	1.2913
6	4	6	.0	.0	1000.0	1310.7	-966.55	3.4130	1.3106
7	6	7	500.0	-4.9	150.0	191.3	-146.73	.4579	1.2749
8	5	7	.0	.0	1132.1	1421.6	1112.85	3.9295	1.2556
9	7	8	500.0	-4.9	150.0	183.6	-148.87	.4655	1.2199
10	8	9	.0	2.5	-2534.4	3056.8	2534.30	-.0814	1.2062
11	9	1	.0	-2.5	.0	.0	-11.26	-8.8277	1.2250

Node Data

jno	T	Z	dns	p	psi	s
1	283.2	.0	1.2303	100000.0	.0	.0000
2	288.1	-500.0	1.2816	105971.7	-148.57	.5848
3	293.0	-1000.0	1.3342	112190.3	-294.35	1.1597
4	293.0	-1000.0	1.3184	110864.0	-1260.90	4.5727
5	288.1	-500.0	1.2642	104530.8	-1261.33	4.5140
6	293.0	-1000.0	1.3028	109553.5	-2227.45	7.9857
7	288.1	-500.0	1.2470	103109.3	-2374.18	8.4436
8	283.2	.0	1.1927	96943.5	-2523.05	8.9091
9	285.7	.0	1.2196	100000.3	11.25	8.8277

Figure 1.

Table 1 shows as an example the network of Fig. 1 with input data for head losses h_l, pressure losses p_l, elevation changes dZ and temperature changes dT of airways and absolute temperatures T and elevation Z of nodes. Assumed is an adiabatic mine without any heat exchanges between air and airway walls. This assumption allows a manual check of the performed calculations. The head losses were arbitrarily chosen in such a way that airflow standstill in the diagonal airway 5 results.

Pressures p can be used to determine the available pressure loss in a connection between two nodes.

p_l = (p₁ - p₂) + (ρ₁ + ρ₂) g (Z₁ - Z₂)/2

Availabilities can be used to determine available head losses in a connection between two nodes.

h_l = T_av/T₀ (Ψ₁ - Ψ₂) +

(T_av/T₀ - 1) (Cp(T₂-T₁) + g (Z₂ - Z₁))

Differences of pressure p all by themselves are of little use to predict air flow directions and rates in potential connections between nodes. The pressure is too much influenced by the elevation and an elevation change of less than 0.1 m affects a pressure change of 1 Pa.

Something similar applies to availabilities. The change of availability with pressure losses is approximately equal to 1 J/kg per Pa. The change with elevation and temperature depends on the temperature of the airway. Is the average temperature of the air 5^o higher than the reference temperature T₀, a temperature increase of 1° affects an availability increase of approximately 17 J/kg. For an elevation increase of 1 m one obtains 0.17 J/kg.

An important role plays the reference temperature. If the reference temperatures are 10° or 20° higher than the airway temperatures, the availability increases are approximately 34 J/kg and 66 J/kg per degree temperature increase and 0.33 J/kg and 0.65 J/kg per Meter elevation increase.

For adiabatic airways, where elevation and temperature changes balance each other, the availability change is close to the pressure loss. For other airways it is difficult to make a fast estimate of available pressure losses from availability figures.

POTENTIALS DERIVED FROM PRESSURE LOSSES OR HEAD LOSSES OR AVAILABILITY CHANGES

For the following demonstrations the network of Fig. 1 with the data of Table 2 were used. The same symmetrical setup as in Table 1 was employed, but the network is no longer adiabatic and the fan pressure was increased. The airflow rates Q are stated as standard m³. The results of property calculations are contained in Table 3.

Table 2. Example of a Non-Adiabatic Mine

Airway Data Node Data

No	js	jf	R	Q	pl	jno	T	Z
1	1	2	12.5	178.6	398.7	1	283.2	.0
2	2	3	15.0	105.3	166.4	2	288.1	-500.0
3	3	4	200.0	105.3	2219.2	3	293.0	-1000.0
4	2	5	400.0	73.3	2146.7	4	298.0	-1000.0
5	4	5	000.0	.0	.0	5	293.1	-500.0
6	4	6	200.0	105.3	2219.3	6	303.0	-1000.0
7	6	7	15.0	105.3	166.5	7	298.1	-500.0
8	5	7	400.0	73.3	2146.4	8	293.2	.0
9	7	8	12.5	178.6	398.7	9	295.7	.0
10	8	9	.0	178.6	-4623.6
11	9	1	.0	178.6	.0

It is sometimes suggested to project ventilation networks, which are based on pressures, into a horizontal plane. This is done by connecting all nodes of the network with a joint node in the plane through hypothetical airways with such high resistances, that the air flow distribution is not upset. If the joint node gets the potential zero the pressure loss of the hypothetical airway is then considered to be the potential of the point, with which the hypothetical airway connects.

It is easy to see that the potential difference between two points is not equal to the pressure loss in the airway between these points, if the two points have different densities. The hypothetical connections form a mesh with the airway and the mesh generates natural ventilation pressure. Table 4 gives the network of Fig. 1 with 6 hypothetical connections 12 through 17. One sees that the potential difference between nodes 4 and 5, which is obtained as the difference of pressure losses of the hypothetical airways 12 and 16, amounts to 107.93 Pa, although air flow standstill prevails in airway 5 between these points.

An equivalent approach is to drop the terms for temperature and elevation change when calculating availabilities. Availability changes are then obtained from Δ Ψ = T₀/T_av h_l. Table 5 shows an example for the network of Table 2. Slight differences of the pressure

Table 3. Air Properties in Non-Adiabatic Mine

Airway Data

no	js	jf	dZ	dT	pl	dpsi	ds	adns
1	1	2	-500.0	4.9	398.0	-314.07	1.1692	1.2547
2	2	3	-500.0	4.9	166.1	-123.20	.4952	1.3054
3	3	4	0	5.0	2214.2	-1414.16	22.7283	1.3077
4	2	5	.0	5.0	2144.9	-1538.48	23.1673	1.2554
5	4	5	500.0	-4.9	.0	-1.11	-.0563	1.2576
6	4	6	.0	5.0	2211.3	-1364.89	22.5543	1.2603
7	6	7	500.0	-4.9	165.8	-129.24	.3962	1.2114
8	5	7	.0	5.0	2149.1	-1493.02	23.0068	1.2088
9	7	8	500.0	-4.9	398.0	-330.06	1.1053	1.1597
10	8	9	.0	2.5	-4623.6	3943.63	-5.0578	1.1559
11	9	1	.0	-12.5	.0	-268.01	-43.3907	1.2043

  Node Data

jno	T	Z	dns	p	psi	s
1	283.2	.0	1.2303	100000.0	.000	.0000
2	288.1	-500.0	1.2790	105756.2	-314.071	1.1692
3	293.0	-1000.0	1.3318	111993.2	-437.270	1.1644
4	298.0	-1000.0	1.2836	109778.9	-1851.433	24.3927
5	293.1	-500.0	1.2317	103610.2	-1852.546	24.3365
6	303.0	-1000.0	1.2370	107567.6	-3216.325	46.9471
7	298.1	-500.0	1.1859	101461.1	-3345.564	47.3432
8	293.2	.0	1.1334	95374.9	-3675.625	48.4485
9	295.7	.0	1.1783	99998.5	268.007	43.3907

Table 4. Node Connection With Surface

Airway Data from Network Calculation

no	js	jf	R	Q	pl
1	1	2	12.5	177.6	394.3
2	2	3	15.0	104.7	164.3
3	3	4	200.0	104.9	2200.5
4	2	5	400.0	73.0	2129.0
5	4	5	1000.0	.0	.0
6	4	6	200.0	105.4	2220.5
7	6	7	15.0	106.0	168.7
8	5	7	400.0	73.5	2160.7
9	7	8	12.5	180.2	406.1
10	8	9	. 0	180.9	-4623.6
11	9	1	.0	180.9	.0
12	1	5	*10^6	.5	2639.5
13	1	7	*10^6	.7	4912.6
14	1	8	*10^6	.7	4623.6
15	1	3	*10^6	.2	567.5
16	1	4	*10^6	.5	2531.6
17	1	6	*10^6	.7	4523.6

Table 5. Reduced Availability Change Red.Av.

no	pl	adns	hl	Tav	dpsi	Red.Av.
1	394.3	1.2547	314.8	285.65	-314.07	311.58
2	164.3	1.3054	125.9	290.55	-123.20	122.67
3	2200.5	1.3077	1682.7	295.50	-1414.16	1612.69
4	2129.0	1.2554	1695.9	290.60	-1538.48	1652.67
5	.0	1.2576	.0	295.55	-1.11	.00
6	2220.5	1.2603	1761.9	300.50	- 1364.89	1660.45
7	168.7	1.2114	139.2	300.55	-129.24	131.20
8	2160.7	1.2088	1787.5	295.60	-1493.02	1712.49
9	406.1	1.1597	350.2	295.65	-330.06	335.41
10	-4623.6	1.1559	-4000.0	294.45	3943.63	-3847.17

losses in the two tables are caused by the iteration method of the network calculation. The quantity ΔΨ has in this Table been called the reduced availability Red. Av. In the same way as summing up head losses does not generate a point function, summing up reduced availabilities does not generate a point function either, although T₀/T_av h_l is smaller than h_l. There is some justification in this approach. The term h_l/T_av is equal to the entropy change caused by head losses.

A popular practice to establish potentials is to distribute natural ventilation heads or pressures on the airways of the meshes, in which they are generated. In the case of natural ventilation pressure it is argued, that

p_n= -
ρ g dZ

contributions to p_n are made by non-horizontal airways only and that they should be corrected. The distribution of natural ventilation pressure is done in some arbitrary fashion, as is in the insertion of natural ventilation pressure sources also.

To consider natural ventilation pressure in a systematic way one should for every non-horizontal airway determine the quantity ρ g Δ Z and insert it into the network calculation. To make these terms manageable it is advantageous to use (ρ - ρ _r) g Δ Z where ρ_r is an arbitrarily chosen average density. The natural ventilation pressure in a mesh is then

p_n = - ∑(ρ - ρ_r) g Δ Z = - ∑ ρg Δ Z.

For the distribution of p_n one calculates for every non-horizontal airway

Δ p_n = -g Δ Z (ρ - ρ_r)

Subtracting this term from the pressure loss p _l one obtains then a point function or potential p₀ = p_l - Δ p_n.

The problem with this potential is that it is as little illuminating concerning air flow rates and directions as are pressures and availabilities. To obtain information on possible pressure losses in a hypothetical connection between points one has to calculate Δpn for the connection and then to use pl = Δp₀ + Δp_n.

With the network of Table 2 an example for potentials obtained with different values ρ _r is given in Table 6. One sees that potential values depend heavily on the chosen ρ _r and that the potential differences and air flow directions are frequently unrelated.

Table 6. Pressure Loss Potentials Obtained With a Reference Density

Node	ρr= 1.23 kg/m^3	ρr= 1.25 kg/m^3	ρr= 1.27 kg/m^3
1	.0	.0	.0
2	-273.2	-371.3	-469.4
3	-67.6	-263.8	-460.0
4	-2268.1	-2464.3	-2660.5
5	-2403.5	-2501.6	-2599.7
6	-4488.6	-4684.8	-4881.0
7	-4564.2	-4662.3	-4760.4
8	-4625.5	-4625.5	-4625.5
9	-1.9	-1.9	-1.9

Table 7. Subtraction of NVP From Airways

Airways Nodes

no	js	jf	pl	modif. pl	jno	potential
1	1	2	398.0		1	.0
2	2	3	166.1		2	-398.0
3	3	4	2200.5		3	-564.1
4	2	5	2144.3	2366.6	4	-2764.6
5	4	5	.0		5	-2764.6
6	4	6	2214.5	1295.1	6	-4059.7
7	6	7	165.8		7	-4225.6
8	5	7	2149.1	1460.9	8	-4623.6
9	7	8	398.0		9	.0
10	8	9	-4623.6
11	9	1	.0

Mesh 1 comprises airways 4,-5,-3,-2. Natural ventilation

of -222.3 Pa was applied to airway 4

Mesh 2 comprises airways 6,3,7,9,2,1,11,10 Natural ventilation

of 919.4 Pa was applied to airway 6.

Mesh 3 comprises airways 8,5,3,9,2,1,11,10. Natural ventilation

of 688.1 Pa was applied to airway 8.

Another possibility to obtain potentials (or point functions for the pressure loss) is to subtract the natural ventilation pressure developed in a mesh from the pressure losses of the airways comprising this mesh. Table 7 shows an example where the natural ventilation pressure has been subtracted in each mesh from one airway only, the airway with the highest pressure loss. Once this has been done it is possible to calculate new substitute resistance factors for the airways with the subtracted natural ventilation pressure.

This does not cause any differences between a network calculation with the natural ventilation pressure considered or a network calculation with modified resistances since the mathematical description of the existing network is not changed.

If the network were changed by adding or deleting airways or changing resistances, one would have to expect a divergence. Tests showed that this divergence is in many cases not too large and may for practical purposes be ignored.

A systematic way to form point functions from head losses or pressure losses is to use the mesh forming procedures employed by programs for network calculations. The one that the author has used since the early sixties and which is part of the MFIRE programs of NIOSH works in the following way. If the network has nb branches and nj nodes it has nb - nj + 1 independent meshes. This is the number of the so-called primary airways, which comprise fans with characteristics, fixed quantity airways and airways with large products of resistance R and airflow rate Q. They have to be selected in such a way that the remaining airways, the so called secondary airways, form a tree, which means that they should reach every node but should not form meshes. Every primary airway will then form a mesh (and only one mesh) with secondary airways. The natural ventilation generated in this mesh is specific for this mesh.

Using secondary airways only, every node can be reached along one path only. If the pressure losses or head losses along this path are summed up, one obtains a point function. This may be quite useful, because the potential differences in the tree represent genuine head or pressure losses. The potential differences of the primary airways represent however the pressure or head losses of the primary airway minus the natural ventilation developed in the mesh of which the primary airway is a part. Table 7 brings an example based on the network of Table 3

POTENTIALS OBTAINED THROUGH ELIMINATING NATURAL VENTILATION BY DISTRIBUTING IT ON AIRWAYS

A method to obtain potentials sometimes used by ventilation engineers is to distribute the natural ventilation generated by a mesh on the pressure losses of the airways of this mesh. If the natural ventilation is small, like in coal mines, this method can be fully adequate. It shows promise for cases of larger natural ventilation energies also.

Since most airways are part of several meshes, the distribution has to be done in an iterative process. Convergency can be a problem.

The task is similar to the error adjustment calculations performed in surveying, when elevations of nodes of a network are to be determined and contradictions exist. Almost ten different approaches were tried by the author, with varying success. The best convergency was obtained with an adjustment process in which the natural ventilation p_n = ∑p_l is distributed to the airways of a mesh proportional to their pressure losses p_l and inversely proportional to the sum of the absolutes of all pressure losses ∑ p_l in the mesh.

Summarized, the pressure losses p_l(i) of the airways of a mesh are with the equation

Δp_l(i) =(∑ p_l(i)/∑ p_l(i)) p_l(i)

meshwise reduced to a new p_l and this process is continued through all meshes until the reduction term Δp_l disappears

Table 8. Distribution of NVP on All Airways

Input Output 1 Output 2

no	js	jf	pl	modif.pl	res.Q	modif.pl	res.Q
1	1	2	394.4	359.6	95.5%	360.9	95.2%
2	2	3	164.3	148.5	95.1%	148.7	95.1%
3	3	4	2200.5	1989.4	95.1%	1991.1	95.1%
4	2	5	2129.0	2137.9	100.2%	2139.8	100.3%
5	4	5	.0	.0	100.0%	.0	100.0%
6	4	6	2220.5	2016.4	95.3%	2014.0	95.2%
7	8	7	168.7	153.2	95.3%	153.0	95.25
8	5	7	2160.7	2169.6	100.2%	2162.0	100.0%
9	7	8	406.1	370.3	95.5%	370.8	95.6%
10	8	9	-4623.6	-5073.3	104.4%	-5037.8	104.4%
11	9	1	.0	.0	100.0%	.0	100.0%

Input is based on Table 3, Output 1 on mesh selection in

Table 7, Output2 on another, different mesh selection.

Table 8 gives an example. The pressure losses of Table 5 and the mesh selection of Table 7 (Output 1) and another mesh selection (Output 2) were used. Approximately 10 iterations were necessary in both cases.

One sees that the reduced pressure losses (modif. p_l) are not too dissimilar to the actual pressure losses, especially in view of the large natural ventilation pressures of the examples. The effect that the use of the reduced pressure losses instead of the actual pressure losses would have in a network calculation on the airflow rates is indicated in the column res.Q. One sees that the effects are not too large, barely measureable under mining conditions.

This method of distributing the natural ventilation pressure was also applied to the larger networks of existing mines. The convergency was with up to 10 iterations in all cases quite good.

VENTILATION POTENTIALS IN POPULAR USE

Uncontrolled air flow can have many serious consequences. Leakage currents can transport contaminants from inactive mine parts into active workings. Or they can transport oxygen from active to inactive parts and cause spontaneous combustion. Or they can make the sealing of mine fires ineffective.

The most effective way to prevent uncontrolled air flow is pressure balancing, in which pressure gradients propelling the air are eliminated.

The conditions for air flow are given by the energy equation, which was quoted at the beginning of this report. Without fans it reads

v dp + g dZ + dV²/2 + dh_l = 0 (J/kg)

dp + ρg dZ + ρ/2 dV²+ dp_l = 0 (J/m3 = Pa)

The terms dh_l or dp_l indicate if an air flow is possible, which in turn would then generate head and pressure losses. Integrating between two points 1 and 2 one obtains

h_l = - ∫ v dp + g (Z₁ - Z₂) + (V₁² - V₂²)/2 or

p_l = p₁ - p₂ + ρg dZ + ρ/2(V₁²- V₂²)

These are straight forward relationships. As stated above, things become difficult if there is more than one possible flow path between points 1 and 2 and one wants to characterize the possibility of air flow between these points, applicable to all connections, with a point function of the two points. This point function is the potential of the points.

Some remarks on the problem with assigning potentials and suggestions on how to proceed can be found in the literature of practically all mining countries. There is no uniform approach. The existing possibilities have been discussed in the earlier parts of this report.

Systematic studies on the use of potentials have been done since more than half a century in Poland. This country also pioneered methods to predict instabilities caused by fires without the use of computers, the so-called Budryk Plans.

A summary of the insights gained on potentials in more than 3 decades of work was given by Bystron (1979) at the Second International Mine Ventilation Congress. There may be newer work of which the author is not aware.

The potential introduced by Bystron is

p

Φ =(∫ v dp)_isentr. + g(Z - Z₀) + 1/2 (V² - V₀²)

p₀,v₀

It is equal to the minimum amount of work to transfer air from a reference state p₀,v₀,Z₀,V₀ to the state p,v, Z, V. Since a reversible process is assumed this amount of work could be retrieved in changing the state back from p, v, Z, V to the reference state. The concept used is in some respects similar to the availability concept, which expresses the maximum amount of work between a given state and a reference state. There are however the important differences that the availability difference of two states expresses the maximum amount of work output possible between two states. Bystron's aerodynamic potential difference expresses the maximum amount of work possible between two states with the pressures p₁ and p₂ when the process is a reversible adiabatic one which is defined by p₀ v_o^k= const. Should one encounter such a process, one would obtain h_l = φ₁ - φ₂.

A problem is that the numerical value of

          p

( ∫ v dp)_isentr.

       p₀,v₀

depends on the choice of p₀ and v₀. As

p

( ∫v dp)_isentr. = Cp T₀((p/p₀)^(k-1)/k -1)

p₀,v₀

indicates, the larger T₀ and the smaller p₀, the larger the value of the integral. Predicting airflow directions in airways which connect mine sections with greatly different pressures and temperatures must with Bystron's method require a great deal of experience

CONCLUSION

There does not seem to be a simple way to use potentials in mine ventilation.

Potentials are point functions. Properties are point functions also. None of the known properties seem to meet the desired characteristics of indicating air flow directions and air flow rates between points of different potentials.

If one decides to use potentials anyway for the purpose of indicating potential air flow direction and rates between points, some approximation is needed. It seems that using adjusted pressure losses, where natural ventilation has been distributed on the airways of the mesh, generating the natural ventilation, proportional to the pressure losses of the airways, is the best way to go.

REFERENCES

Bystron, Henryk: Aerodynamic Potential Used for the Control of Fire Areas in Mines. Second International Mine Ventilation Congress, Reno, NV, 1979, pp 460-69

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I SZKOŁA AEROLOGII GÓRNICZEJ 1999

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12

PROCEEDINGS OF THE 7^TH INTERNATIONAL MINE VENTILATION CONGRESS

11

ESTABLISHING MINE VENTILATION POTENTIALS

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