Chapter 1

AN APPROACH TO MINE VENTILATION BASED ON THE AERODYNAMIC POTENTIAL OF VENTILATING AIR TREATED AS A MIXTURE OF DRY AIR, WATER VAPOUR AND LIQUID WATER DROPLETS

H. Bystroń
Central Mining Institute, Katowice, Poland

ABSTRACT

The purpose of the paper was to verify an approach to mine ventilation based on the aerodynamic potential when adopting the thermodynamic approach by Barenbrug (Barenbrug, 1974) as a criterion of truth. The conformity of energy and power balances in both approaches has been ascertained. Nevertheless, there considerable differences occurred between energies and powers lost to remove water vapour. The cause of these differences is explained.

KEYWORDS

Aerodynamic potential, local and main natural ventilating energies, lost energies and powers, energy and power balances for ventilation system

INTRODUCTION

The purpose of the paper was the verification of an approach to mine ventilation based on the aerodynamic potential when adopting a thermodynamic approach (Barenbrug, 1974) as a criterion of truth. On this way it is possible to verify the formula, by the use of which the mechanical energy expended to achieve the removal of water vapour has been determined. This is motivated by the need of economical yet safe mine ventilation.

AERODYNAMIC POTENTIAL OF VENTILATING AIR TREATED AS A MIXTURE

The aerodynamic potential, , J/(kg dry air), is determined by the formula (Bystroń, 2000 b, c):

(1)

where: p, Pa, * corrected pressure; p_s, Pa, and v_as, m³/(kg dry air) - pressure and apparent specific volume in the isentropic flow, determined respectively by use of the following formulae:

,
(2), (3)

(4)

where: subscript )₁ indicates, that the given quantity concerns the cross-section 1 of the top of the downcast shaft;  = 1.4 - the isentropic exponent; g, m/s² - local gravitational acceleration; z, m, - elevation above sea level; w, m/s - average velocity; v_a, m³/(kg dry air) and X, kg/(kg dry air) - apparent specific volume in the polytropic flow and moisture content respectively - determined by the following formulae (Hemp, 1989; Mc. Pherson, 1993):

,
(5), (6)

(7)

In accordance with the defined aims of the paper, we start from the measured parameters: elevation, z, m, corrected pressure, p, Pa, and the dry-bulb and wet-bulb temperatures of ventilating air, t, t', ⁰C - respectively (Table 1) with reference to 20 measuring stations (Figure 1) and gravitational acceleration, g = 9.79 m/s² - taken from the thermodynamic approach (Barenbrug, 1974).

Using the appropriate data from the Table 1, we calculate by use of the formulae (1) to (7) respectively the aerodynamic potential,  , and the parameters: p_p, X, v_a, W, p_s, v_as and , (Table 1) concerning the measuring stations from 1 to 20 in the ventilation system (Figure 1).

Figure 1. Line diagram of the mine ventilation system

DROP OF THE AERODYNAMIC POTENTIAL, MASS OF LIQUID WATER DROPLETS AND TECHNICAL WORKS IN THE POLYTROPIC AND ISENTROPIC FLOWS

The drop of the aerodynamic potential, δ, J/(kg dry air), in the branch d-w of the ventilation system is determined by the formula:

δ = _d * _w (8)

where the subscripts )_d and )_w indicate, that the given quantity (parameter) concerns the inflow cross-section d and outflow cross-section w respectively of the branch d-w.

The mass of liquid water droplets, m_W, kg/(kg dry air), is determined by use of the formula (Ochęduszko, 1974):

m_W = X_d * X_w (9)

in which the condition X_d > X_w is sustained.

Table 1. Parameters of ventilating air at measuring stations (Figure 1)

Sta-tion	Corrected	Temperatures		Elevation above sea level	Partial water vapour pressure	Moisture content	Apparent specific volume	Numerical quantity	Pres-sure	Apparent specific volume	Aero-dynamic potential
		pressure	Dry-bulb				Wet-bulb						in the polytropic flow		in isentropic flow
	p	t	t'	z	pp	X	va	W	ps	vas	
No.	Pa	^0C	^0C	m	Pa	kg/kg d. air	m^3/kg d. air	-	Pa	m^3/kg d.air	J/kg d. air
1	84,193	25.8	14.7	1,575.8	1,070	0.008006	1.032333	1.000000	84,193	1.032333	0
2	99,254	22.6	21.0	112.8	2,384	0.015303	0.876346	1.047460	99,028	0.919341	208
3	100,426	22.5	21.5	9.6	2,498	0.015869	0.866594	1.050808	100,140	0.912036	261
4	98,831	25.9	25.5	116.3	3,236	0.021056	0.897950	1.047346	98,990	0.919590	-146
5	98,831	22.6	21.8	116.3	2,560	0.016537	0.881800	1.047346	98,990	0.919590	-146
6	98,831	24.2	23.7	116.3	2,897	0.018784	0.889691	1.047346	98,990	0.919590	-146
7	95,519	26.7	26.0	360.0	3,317	0.022373	0.933480	1.039441	96,400	0.937175	-825
8	93,724	27.8	27.2	365.2	3,569	0.024625	0.958184	1.039272	96,345	0.937555	-2,457
9	84,000	25.6	14.7	1,595.9	1,082	0.008118	1.034196	0.999348	84,001	1.034018	-1
10	98,763	21.0	20.8	126.2	2,443	0.015773	0.876584	1.047025	98,884	0.920295	-111
11	99,941	21.5	21.3	22.0	2,519	0.016082	0.868145	1.050405	100,006	0.912909	-59
12	98,146	26.6	26.4	128.9	3,427	0.022506	0.908378	1.046938	98,855	0.920488	-653
13	98,146	21.4	21.3	128.9	2,526	0.016428	0.884201	1.046938	98,855	0.920488	-653
14	98,146	24.0	23.9	128.9	2,958	0.019330	0.896060	1.046938	98,855	0.920488	-653
15	95,034	26.6	25.4	361.2	3,169	0.021455	0.936594	1.039402	96,387	0.937263	-1,268
16	93,724	27.4	26.3	365.2	3,353	0.023080	0.954624	1.039272	96,345	0.937555	-2,457
17	93,724	27.6	26.8	365.2	3,474	0.023939	0.956532	1.039272	96,345	0.937555	-2,457
18	81,362	22.2	22.2	1,576.7	2,675	0.021144	1.077399	0.999971	84,184	1.032409	-2,914
19	84,184	23.4	23.4	1576.7	2,877	0.022006	1.046914	0.999971	84,184	1.032409	0
20	84,184	25.7	14.7	1576.7	1,076	0.008049	1.032168	0.999971	84,184	1.032409	0

Table 2. Parameters of ventilating air in branches and meshes: 1, 2 , 3 and 4 of ventilation system (Figure 1)

Branch	Aerody-namic	Mass of liquid	Polytropic	Technical work in flow		Local na-tural ven-	Energy lost to remove:		Usable energy	Frictional	Mass flow	Aerody-namic
	potential drop	water droplets	exponent	polytro- pic	isentro- pic	tilating energy	water vapour	liquid water droplets	of fan station	energy loss	of dry air	resistance
-	δ	mW	n	lt	lts	en	lP	lW	eu	qf		R
d * w	J/kg d. air	kg/kg d. air	-	J/kg d. air	J/kg d. air	J/kg d. air	J/kg d. air	J/kg d. air	J/kg d. air	J/kg d. air	kg d. air/s	m^2/kg^2 d. air
1-2	-208	0	1.004608	-14,309	-14,645	336	-52	0	0	180	241	0.003099
2-3	-53	0	1.048977	-1,021	-1,071	50	-8	0	0	5	120	0.000347
2-5	354	0	0.688371	372	389	-17	0	0	0	343	121	0.023427
3-4	407	0	0.450415	1,407	1,460	-53	11	0	0	340	120	0.023611
6-7	679	0	0.709469	3,018	3,086	-68	30	0	0	581	241	0.010003
7-8	1,632	0	0.726281	1,698	1,704	-6	1	0	0	1,625	241	0.027978
9-10	110	0	0.979191	-14,041	-14,393	352	-57	0	0	519	195	0.013649
10-11	-52	0	1.225708	-1,027	-1,080	53	-8	0	0	9	94	0.001019
10-13	542	0	0.724296	543	570	-27	0	0	0	515	101	0.050485
11-12	594	0	0.400072	1,594	1,650	-56	12	0	0	526	94	0.059529
14-15	615	0	0.728289	2,851	2,912	-61	28	0	0	526	195	0.013833
15-16	1,189	0	0.727989	1,239	1,246	-7	1	0	0	1,181	195	0.031059
17-18	457	0.002795	1.188712	12,539	12,424	115	156	17	0	399	436	0.002099
18-19	-2,914	0	1.187903	-2,997	-2,949	-48	0	0	2,997	35	436	0.000184
20-1	0	0	-0.666995	-9	-9	0	0	0	0	0	0	0
20-9	1	0.000069	1.114825	190	190	0	0	0	0	1	0	0
Mesh 1 (1,2,5,6,7,8,17,18,19,20,1): 0				312	0	312	135	17	2,997	3,157	436	0.017407
Mesh 2 (1,2,3,4,6,7,8,17,18,19,20,1): 0				326	0	326	138	17	2,997	3,168	436	0.017481
Mesh 3 (9,10,13,14,15,16,17,18,19,20,9): 0				324	0	324	128	17	2,997	3,176	436	0.017470
Mesh 4 (9,10,11,12,14,15,16,17,18,19,20,9): 0				348	0	348	132	17	2,997	3,196	436	0.017596

Both technical works in the polytropic flow, l_t, and in the isentropic flow, l_ts, J/(kg dry air), are determined respectively by the formulae (Bystroń, 2000 c):

(10)

(11)

where n - polytropic exponent:

(12)

Using the data from the Table 1, respectively, we have calculated by the use of the formulae (8) to (12) the parameters δ , m_W , n, l_t and l_ts (Table 2) concerning the branches d-w of the ventilation system (Figure 1).

MECHANICAL ENERGY LOSSES, USABLE ENERGY OF the FAN STATION

The local natural ventilating energy, e_n, J/(kg dry air ), generated in the branch d-w, is determined by:

e_n = l_t * l_ts (13)

Both mechanical energies, l_W , l_P, J/(kg dry air), lost to remove liquid water droplets and water vapour are determined by use of the following formulae (Bystroń, 2000 b, c):

− in case of a downcast shaft or dip-heading (
)

(14)

(15)

− in case of a up-cast shaft or incline (
)

   (16)

(17)

The usable energy, e_u, J/(kg dry air ), of the fan station d-w is determined by the formula:

(18)

The frictional mechanical energy loss,
, J/(kg dry air), in the branch d-w with (e_u > 0) or without the fan station (e_u = 0), is given by the formula:

= δ + e_n * l_P * l_W + e_u (19)

Using the appropriate data from Tables 1 and 2, we have calculated the parameters e_n, l_W, l_P, e_u and q_f respectively, by use of the formulae (13) to (19)
(Table 2).

The aerodynamic resistance, R, m²/(kg² dry air), of the branch d-w of the ventilation system is determined by:

(20)

where
, (kg dry air)/s, - mass flow along the branch. The aerodynamic resistance, R, m²/(kg² dry air), of the mesh enclosing the surface atmosphere is determined by equivalent formulae:

(21), (22)

where , (kg dry air)/s - mass flow through the main fan station.

In Table 2 are specified mass flows,
, (kg dry air)/s, (Barenbrug, 1974) as well as aerodynamic resistances, R, of branches or meshes - calculated respectively by use of the formulae (20) and (21) or (20) and (22).

MAIN NATURAL VENTILATING ENERGY, RESULTANT CHARACTERISTICS OF THE VENTILATION SYSTEM

The natural ventilating energy, , J/(kg dry air), generated in the mesh j containing the surface atmosphere is determined by the expression:

= , i = 1,2,...,N_j

where: i - number of the branch d-w, N_j - amount of all branches in the mesh j.

The main natural ventilating energy, , J/(kg dry air), in a mine ventilation subsystem or a system with one fan station is determined by the expression (Bystroń, 2000 a):

= , j = 1,2,...,M (23)

where: M -the number of all meshes j. On the basis of Table 2 and expression (23) we record for the ventilation system (Figure 1):

= (312, 326, 324, 348) =

= 312 J/(kg dry air ) (24)

Figure 2. Resultant characteristics of network and characteristics of main natural ventilating energy,
=
= idem = 312 in the ventilation system (Figure 1)

The mesh, in which the main natural ventilating energy is generated, is termed the main mesh of the ventilation system. The aerodynamic resistance of the main mesh, R, m²/(kg² dry air), is determined by the expression:

, j = 1, 2,..., M (25)

On the basis of Table 2 and expression (25) we record for the ventilation system (Figure 1):

(0.017407, 0.017481, 0.017470, 0.017596) =

= 0.017407 m²/(kg² dry air) (26)

The aerodynamic resistance of the main mesh is the resistance of the ventilation system.

The equation of the resultant characteristics of the ventilation network as the element of the ventilation system (Figure 1) has the form (Bystroń, 2000 b):

(27)

where: , (kg dry air)/s - mass flow of dry air, R, m²/(kg² dry air), - aerodynamic resistance determined by (26).

In Figure 2 are plotted the characteristics of the main natural ventilating energy as described by the equation:

= idem = 312 J/(kg dry air) (28)

and the resultant characteristics of the ventilation network by the equation (27), where the point R (Figure 2) of the equilibrium of the ventilation system (Figure 1) is determined by the co-ordinates: : = 436 (kg dry air)/s , e_uR = e_u = 2,997 J/(kg dry air).

In Figure 3 are plotted: isentrope 1-2_s described by the equation
, where p₁ = 84,193 Pa,
= 1.032333 m³/(kg dry air) (Table 1) and the natural ventilating energy: local = 336 and main = 312 J/(kg dry air) (Table 2).

ENERGY BALANCE

The energy balances both for the ventilation system and for the main mesh 1 (1,2,5,6,7,8,17,18,19,20,1) (Figure 1) are exactly the same. In the fourth line down from the top of Table 2 the elements of these balances expressed in J/(kg dry air) are given; namely:

• ­usable energy both of the fan station, e_u = 2,997, and of the main natural ventilating energy, = =
  = 312,

• frictional mechanical energy loss, = 3,157, mechanical energy lost to remove water vapour, = 135, and liquid water droplets, = 17.

The sum of available energies, e_u + = 3,309, is equal to the sum of lost mechanical energies, = 3,309. Thus the energy balance: e_{u +} =

is exactly satisfied.

Figure 3. Local natural ventilating energy,
= 336, in the branch 1-2 and main natural ventilating energy,
= 312, in the ventilation system (Figure 1)

Table 3. Comparison of energy balances for the ventilation system (Figure 1)

Approach to mine ventilation:	Barenbrug	Author	Differ-rence, per cent
Usable energy of fan station, eu	2,998	2,997	- 0.03
Main natural ventilating energy,	311	312	0.32
Sum of usable energies, eu +	3,309	3,309	0.00
Frictional loss of mechanical energy,	3,141	3,157	0.51
Mechanical energies lost to remove: - water vapour,	(151)	135	-10.60
- liquid water droplets,	(17)	17	0.00
Sum of these energies,	168	152	- 9.52
Sum of lost mechanical energies,	3,309	3,309	0.00

In Table 3 the energy balances determined in the thermodynamic approach (Barenbrug, 1974) and the author's approach based on the above-mentioned aerodynamic potential are presented. These balances are identic. Nevertheless, there occur the considerable differences between the following elements of these balances, i. e. between:

• sums of mechanical energy lost to remove water vapour: (135 - 151) = -16; (-10.60%),

• sums of mechanical energies lost to remove water vapour and liquid water droplets (152 +
  - 168) = - 16; (-9.52%).

We underline, that the energies = (151) and = (17) (Table 3) have not been given in the above-mentioned Barenbrug's work, but they have been presented in the work (Hemp, 1986).

POWER BALANCE

The usable power, N_n, of the local natural ventilating energy and the usable power, N_u, of the main fan station, the frictional power loss, N_f, the powers, N_P and N_W, lost to remove water vapour and liquid water droplets - expressed in W - are determined respectively by use of the formulae (Barenbrug, 1974):

,
,

which concern the branches d-w of the ventilation system (Figure 1) with adequate parameters: e_n, l_P, l_W, q_f and e_u as well as with the mass flow , (kg dry air)/s.

Using the Figure 1, the appropriate data from the Table 2 and the above-mentioned formulae we have calculated the powers specified in Table 4. In the lines from 2 to 5 from below of this table the following sums of powers are specified concerning the meshes from 1 to 4 of the ventilation system (Figure 1).

In the last line of Table 4 the elements of the power balance for this ventilation system, expressed in kW, are given; namely:

• available power of the main fan station, N_u = 1,306.692, and the sum of power of local natural ventilating energies,

• the sum of frictional power losses, = 1,383.162, the sum of powers to remove: water vapour, =58.231 and liquid water droplets, = 7.412.

The sum of usable power, N_u + = 1,448.805 is equal to the sum of lost powers
N_W ) =
= 1,448.805. Thus the power balance:

N_u + =

is exactly in equilibrium.

Table 4. Power balance for the ventilation system (Figure 1)

Branch	Power of local nat.		Power lost to remove:				Frictional		Usable power
	ventilating energy		Water vapour		Liquid water droplets		power loss		of fan station
d-w		Nn		NP		NW		Nf		Nu
1-2	80.976		-12.532		0		43.380		0
2-3	6.000		-0.960		0		0.600		0
2-5	-2.057		0		0		40.777		0
3-4	-6.360		1.320		0		41.160		0
6-7	-16.388		7.230		0		140.021		0
7-8	-1.446		0.241		0		391.625		0
9-10	68.640		-11.115		0		101.205		0
10-11	4.982		-0.752		0		0.846		0
10-13	-2.727		0		0		52.015		0
11-12	-5.264		1.128		0		49.444		0
14-15	-12.090		5.460		0		102.570		0
15-16	-1.365		0.195		0		230.295		0
17-18	50.140		68.016		7.412		173.964		0
18-19	-20.928		0		0		15.260		1306.692
20-1	0		0		0		0		0
20-9	0		0		0		0.195		0
Mesh 1:	90.297		62.955		7.412		805.027		1,306.692
Mesh 2:	91.994		56.085		7.412		806.010		1,306.692
Mesh 3:	81.670		62.556		7.412		675.504		1,306.692
Mesh 4:	84.115		62.932		7.412		673.779		1,306.692
System:	142.113		58.231		7.412		1,383.162		1,306.692

In Table 5 the power balances and their component elements as determined by the thermodynamic approach (Barenbrug, 1974) and the author's approach based on the aerodynamic potential are given. These balances are identical in practice.

Nevertheless, considerable differences occur between the following elements of these balances, i. e. between:

• sums of power expended to remove water vapour: (58.231+ - 65.088) = - 6.857; (- 10.53%),

• sums of powers used to remove water vapour and water droplets: (65.643 * 72.5) = * 6.857; (* 9.46%).

We stress, that the powers = (65.088) and = (7.412) (Table 5) have not been given in the work (Barenbrug, 1974). Based on Tables 3, 4 and 5 we have: = (7.412) and =
+
+ N_W) - = 72.5 - (7.412) = (65.088).

Table 5. Comparison of power balances for the ventilation system (Figure 1)

Approach to mine ventilation:	Baren-brug	Author	Differ-rence, per cent
Usable power of fan station, Nu	1,307.1	1,306.692	0.03
Power of main natural ventilating energy, Nn	141.8	142.113	0.22
Sum of usable powers, Nu + Nn	1,448.9	1,448.805	- 0.01
Sum of frictional power losses,	1,376.4	1,383.162	0.49
Sum of power lost to remove: - water vapour,	(65.088)	58.231	-10.53
- liquid water droplets,	(7.412)	7.412	0.00
Sum of both lost powers,	72.5	65.643	- 9.46
Sum of all lost powers,	1,448.9	1,448.805	- 0.01

ADDITIONAL QUESTIONS AND CONCLUSIONS

In order to recognise the reason for the appearance of the considerable above-mentioned differences we present the following consideration:

In case of the approach based on the aerodynamic potential - acting in accordance with the work (Bystroń, 2000 b) - we proceed from the relationship:

(Ochęduszko, 1974). When performing the necessary transformations we obtain:

(29), (30)

From matching both relations (29) and (30), the expression
(where
, J/kg,) and the equation of motion
results the following form of the last equation:

(31)

Dividing both sides by the following form of Poisson's equation:

, we derive the expression
. Comparison of the right side of this expression and relationship (30) results in:

From this relationship and the equation of energy for the isentropic flow:
, we obtain:

(32)

As a result of subtraction by sides of the following equation of local natural ventilating energy: de_n +
+ v_a dp * v_as dp = 0 from the equation of motion (31) we have:

(33)

Subtracting equation (32) from equation (33) and matching of the expression obtained with the equation: d = v_as (dp * dp_s ), we obtain (Bystroń 2000 b):

The first element of the right side of this equation we equate to the sum (dl_P + dl_W). This results in:

dl_P + dl_W
(34)

In case of a downcast shaft or dip-heading (z_d z_w) - where, in accordance with the classical theory (Ochęduszko, 1974), water vapour condensation does not take place - one obtains l_W = 0, dl_W = 0 (Barenbrug, 1974, Hemp, 1989). From the integration of the equation (34) assuming that dl_W = 0 formula (15) results.

In case of a upcast shaft or incline (z_d < z_w) we rearrange the first factor of the right side of equation (34) as follows:

On the basis of this expression, formula (9) and equation (34), as well as on the basis of the above-mentioned theory, we can write:

,

The integrals of these equations are formulae (16) and (17) respectively.

In case of the thermodynamic approach (Barenbrug, 1974) on the basis of the work (Hemp, 1989) and relation: a =
(X_d * X_w ) and r = X , we obtain:

(35)

(36)

If we assume, that the ventilating air velocities are negligibly low, w_d = 0, w_w = 0, then from formula (16) will result (36). This does not influence formulae (15), (17) and (35).

According to the above consideration we conclude, that expression (35) is the reason for the above-
-mentioned considerable differences between energies and powers expended to remove water vapour as well as water vapour and liquid water droplets.

This work was sponsored by the Committee
of Scientific Research, Warsaw

REFERENCES

Barenbrug, A. W. T.,1974, ”The Thermodynamic Approach to Mine Ventilation,” Chapter 12. The Ventilation of South African Gold Mines. Mine Vent. Soc. of South Africa. Cape Town, pp. 244-265

Bystroń, H., 2000 a, ”The Main and Booster Natural Ventilating Energies in the Mine Ventilation Network,” (in Polish), Archives of Mining Sciences, Vol. 45, No 2, pp. 171-198

Bystroń, H., 2000 b, “ Aerodynamic Potential of Ventilating Air in Difficult Thermic Condition Mine,” (in Polish), Przegląd Górniczy, No 10, pp. 1-11

Bystroń, H., 2000 c, “Basic Parameters of Ventilation Subsystem in the Light of Aerodynamic Potential and Assumptions Concerning Ventilating Air,” (in Polish), Mechanizacja i Automatyzacja Górnictwa, No 11, pp. 5-17

Hemp, R., 1989, “The Thermodynamic Aspects of Mine Airflow,” Chapter 2. Environmental Engineering in South African Mines. The Mine Vent. Soc. of South Africa, pp. 29-48

McPherson, M. J., 1993, “Mine Ventilation Thermodynamics,” Chapter 8. Subsurface Ventilation and Environmental Engineering. Chapman & Hall, London, pp. 241-281

Ochęduszko, S., 1974, “Moist Gases,” Chapter 29. Applied Thermodynamics (in Polish). Wydaw. Nauk. Techn., Warsaw, pp. 266-278

2

I SZKOŁA AEROLOGII GÓRNICZEJ 1999

5

8

PROCEEDINGS OF THE 7^TH INTERNATIONAL MINE VENTILATION CONGRESS

7

AN APPROACH TO MINE VENTILATION BASED ON THE AERODYNAMIC

---