USBM Contract No. SO241032 

STUDY OF MINE FIRES AND MINI VENTILATION 

Part I 

Computer Simulation of Ventilation Systems Under 

the Influence of Mine Fires 

Rudolf E. Greuer 

Principal Investigator 

Michigan Technological University 

College of Engineering 

~epartment of Mining Engineering 

USBM CONTRACT REPORT NO. SO241032 

DEPARTMENT OF THE INTERIOR 

BUREAU OF MIYES 

WASHINGTON, D. C. 
FOREWORD 

This report was prepared by Michigan Technological University, 

College of Engineering, Department of Mining Engineering, Houghton, 

Michigan, under USBM Contract No. S0241032. The contract was initiated 

under the Coal Mine Health and Safety Program. It was administered under 

the technical direction of PMSRC with Dr. R. F. Chaiken acting as the 

technical project officer. Mr. D. J. Askin was the contract administrator 

for the Bureau of Mines. 

This report is a summary of the work recently completed as part 

of this contract during the period June 4, 1974 to October 14, 1977. 

This report was submitted by the author on September 14, 1977. This 

technical report has been reviewed and approved. 

It is hereby certified that no inventions have been made on this 

project. 

The views and conclusions contained in this document are those of the 

author and should not be interpreted as necessarily representing the 

official policies of the Interior Department's Bureau of Mines or of the 

U.S. Government. 
SUMMARY 

The existing computer programs for the simulation of ventilation 

systems under normal ventilation conditions are reviewed and a suitable 

program for including the influence of mine fires is selected. New program parts are written for the consideration of methane productions in 

coal mines, heat and gas productions of mine fires, temperature and air 

composition changes in ventilation systems, and the ventilation forces 

resulting from the latter. Other program parts are provided for the 

detection of danger zones and reversed air currents and for the inclusion 

of recirculated air currents in the network analysis. Existing program 

and new program parts are combined, 

The resulting new program can be used for a multitude of assignments. It is designed for the practical ventilation engineer and should 

be applicable to all types of ventilation emergency plans, in particular 

mine fire plans. 

The organization of the program and its mathematical basis are 

described. A FORTRAN IV listing and several flow diagrams are included. 

Eight executed examples are discussed, input and output for these examples 

explained. Storage requirements and execution times are estimated. 
TABLE OF CONTENTS 

Page 

Introduction ................ 4 

Review of Existing Programs for Ventilation Network 

Calculations ................ 8 

Mathematical Description of Ventilation Networks for 

Airflow and Pressure Distribution Calculations . 11 

4 . Program Description ............. 15 

4.1 Network Part of Program ............ 15 

4.1.1 Section"ReadInputDataW ........... 2 Complete Input Data. Output of Input ....... 3 Arrange Airways to Size and Magnitude R*O ..... 4 Set Up Base System ............. 5 FormMeshes ............... 6 Satisfy Junction Equations .......... 7 Calculate Natural Ventilation Pressure ...... 8 Iteration ................ 9 Fan Characteristic ............. 10 Continue in Appropriate Program Part ....... 11 Calculate Resistance of Regulators ....... 12 Output of Results ............. 

4.2 Concentration Part of Program .......... 

4.2.1 Read and Complete Input Data ........ 2 Set Up JNO List ........... 3 Calculate Methane Evolution ........ 4 Output of Input ............ 5 Flowscheme ............. 6 Relate JNO- and JNOL-Lists ........ 7 Indices of Starting Junction ((Atmosphere) ... 8 Conditions at Roadway Ends ........ 8.1 General Remarks ........... . 2 Concentration Changes and Added Heat in Airways 

. 3 Temperature Changes in Airways ...... 9 Conditions in Junctions ......... 10 Recirculation. First Approximation ..... 11 Recirculation. Preparation for Iteration ... 12 Calculation of Natural Ventilation Pressure . . 13 Reroute to Appropriate Program Section .... 14 Output of Results ........... 

4.3 Cooperation of Program Sections ......... 
Page 

4.4 Examples for Program Use ........... 49 

4.4.1 General Remarks .............. 49 

4.4.2.1 Example 1: 

2 2 : 

3 3 : 

4 4 : 

5 5: 

6 6: 

simulation of a Normal Ventilation state . Changed Surface Temperature ...... Main Fan Failure ......... Fire in a Horizontal Airway ...... Oxygen Rich Fire at Bottom of Timbered Raise 

Fuel Rich Fire in Descensionally Ventilated 

Raise ............. Oxygen Rich Fire in an Intake Shaft ... Layout of Fire Warning System ..... 

4.5 Organization of Input ............ 118 

4.5.2 Control and Contamination Cards ........ 120 

4.6 Storage Requirements ............. 122 

4.7 Execution Time ............... 123 

5 . Table of Text Nomenclature ........... 124 

6 . Bibliography ........... 127 

7 . Program Listing ............... 129 

~ist of Computer Symbols Which Are Explained in Text . . 152 

List of Additional Computer Symbols Not Quoted in Text . . 160 
INTRODUCTION 

Most of the major mine disasters have throughout the history of 

mining been caused by explosions and fires and both causes remain among 

the greatest potential hazards in mining. The greatest hazard of mine 

fires is the poisonous and sometimes explosive combustion products which 

are carried through the mines by their ventilation. 

To combat this hazard, the paths which the combustion products 

take, must be known for the proper designation of escape routes and the 

safe and economical performance of fire fighting activities. To predict 

these paths is complicated by the fact that the fires themselves can 

cause considerable ventilation disturbances. The volume expansion of the 

air as it passes through the fire has a constriction or throttle effect. 

Density differences in non-horizontal communicating airways create buoyancy effects similar to chimney drafts. The intensity of the fires, on 

the other hand, depends on their oxygen supply, i.e. the airflow rates 

and oxygen concentration which are provided by the ventilation system. 

The conventional analog computers and digital computer programs 

for ventilation network (airflow distribution) calculations are not 

capable of taking this mutual interaction between fires and ventilation 

systems into account. They cannot distinguish between air of different 

qualities (concentrations, temperatures) either. The preferred compromise has been until now to use these conventional analog computers or 

digital computer programs and to support them with manual calculations. 

This approach can be satisfying when no recirculation of air 

occurs and the fire generated ventilation forces are relatively small. 

Concentration of methane and combustion products can, in these cases be 

determined by a sequence of simple mixing processes in the network nodes 

once the airflow distribution is known. The fire generated ventilation 

forces, which depend on the air temperature downstream of the fire, can 

be calculated for an estimated airflow rate through the fire and then 

inserted in the network calculation. Unchanged temperatures and natural 

ventilation pressures are assumed for all other air currents. If the 

airflow rate through the fire, which is then obtained in the network 

calculation, is too far off the estimate, the process is repeated with 
a new, better estimate. The amount of manual work involved in this procedure may be cumbersome but is manageable, if, as in the preparation of 

emergency plans, sufficient time is available. 

With recirculation, temperatures and concentration of several 

of the air currents, which enter network nodes, are not known and the 

calculation of the state of the mixture leaving the nodes is therefore 

not possible. To overcome this difficulty some method of describing the 

network configuration mathematically or of applying an iterative approximation method has to be used. Recirculation is common in hardrock mines 

and can be caused by the fire itself in coal mines even though it is not 

permitted under normal ventilation conditions. With large fire generated 

ventilation forces the ventilation disturbances become such that the 

assumption of unchanged temperatures and natural ventilation pressures 

in all airways except for those immediately downstream of the fire does 

no longer hold either. In such cases the amount of manual work becomes 

excessive, or so many simplifying assumptions have to be made that the 

results of the calculations have only a limited value. 

Due to its great importance for escape and fire fighting plans, 

mining engineers have studied the interaction between ventilation systems 

and fires for several decades. The large amount of conducted theoretical 

and experimental work was recently reviewed (7), the still existing gap 

for coal mine fires is in the process of being closed (3,5) . Ventilation 

network calculations with digital computers are becoming more and more 

common and with them the availability of reliable data on ventilation 

systems. In the same way as suitable computer programs for ventilation 

network calculations have led to considerable improvements in the ordinary 

ventilation planning work, it can be expected that suitable programs for 

fire emergencies will lead to improvements in this field also. This 

report describes such a program and demonstrates its application with a 

number of examples. 

The here introduced program can fulfill the following functions : 

a) it starts with a conventional network calculation for the state of the 

mine before the emergency; 

b) next, it simulates the production of heat and contaminants in designated locations; 
C) next, it calculates the resulting temperature and concentration 

aistribution based on the airflow obtained in step a, if recirculation occurs it makes use of an iterative approximation method; 

d) next, it calculates the fire generated ventilation forces; 

e) next, it inserts these forces into the network and repeats the network calculation to determine the changed airflow distribution; 

£1 next, it repeats steps b through e until an equilibrium is reached; 

g) finally, it analyzes the results for danger zones caused by instable 

airways, airflow reversals, high temperatures, high concentrations 

of methane or combustion products. 

As this sequence indicates, it was attempted to determine an 

equilibrium under steady state conditions. The crucial heat exchange 

between rock and air is, however, calculated under non-steady state conditions, taking the changing rock temperature into account. If the 

change of the ventilation system with time shall be investigated, it is 

necessary to execute a series of calculations for different time intervals since the beginning of the emergency event. 

The program has the options to execute network, temperature, 

and concentration calculations combined or separately. It has been made 

as flexible as possible to make it useful for a multitude of assignments. 

Methane concentrations are, however, always determined when a change in 

the airflow distribution takes place, since this is indispensable for 

coal mines. In its organization the program has been divided into two 

parts, labeled "network part" (for functions a and e) and "concentration 

part" (for all the other functions). The network part contains basically 

an earlier existing program for conventional network calculations. It 

was attempted to change this existing program and its input data as little 

as possible in order to make the use of the new program, for users of the 

conventional network program, as simple as possible. 

It has been attempted to keep the amount of input data in the 

new program small and to extract as much information as possible from 

these data. Input data are furthermore analyzed for completeness and 

for such mistakes that occur most frequently. When possible, incomplete 

data are amended by average values and inccrrect data are corrected. 
The formulation of heat and combustion products as a function 

of the oxygen supply to the fire has intentionally been kept very simple. 

There is no difficulty in amending the program with fire characteristics 

of any desired properties. But to introduce these, in a form that they 

are applicable to all types of mines and fuels, would require so many 

additional explanations and input data that at this stage the introduction of the new program for practical emergency planning would be impeded. 

On the whole, this program has been drafted with routine application by practical ventilation engineers in mind. It is, as far as the 

author knows, the first program of its kind and the necessity of some 

changes will certainly be felt after it has been exposed to some practical 

use. 
REVIEW OF EXISTING PROGRAMS FOR VENTILATION 

NETWORK CALCULATIONS 

Ventilation network calculations, whose goal is the determination 

of airflow and pressure distributions in mine ventilation systems, have 

been performed routinely and at a large scale with computers for approximately two and a half decades. Throughout the fifties and the first half 

of the sixties, analog computers were mainly used for this purpose. They 

were almost completely replaced by digital computers, after the latter 

became more and more available, larger, cheaper, and faster. Digital 

computers, being all purpose computers, can usually perform network calculations more economically than the single purpose analog computers. The 

first reported ventilation network calculations with digital computers were 

performed in 1958 and since 1960 they have become routine in West Germany, 

where large ventilation problems necessitated the wide use of analog computers before. From the mid-sixties on, digital computers were in all 

major mining countries, either routinely used for network calculations or 

their use was being investigated. To date such calculations have become 

a self-understanding part of all ventilation planning. A review of the 

history of ventilation network calculations with computers and the different programs in use has been given by the author in an earlier report 

(7) 

Normal environmental factors, like concentrations of contaminants or temperatures, are heavily influenced by the airflow distribution. 

On the other hand, it is quite possible that the airflow distribution is 

influenced by these environmental factors. There exists an increasing 

number of attempts to combine ventilation network calculations in digital 

computer programs with the precalculation of environmental conditions 

(1,6,,10,16,19). None of these efforts have, however, progressed far 

enough to be useful for the simulation of fire emergency situations. 

All programs for ventilation network calculations which are 

presently used employ the CROSS iteration method of balancing pressures 

around loops. Its principles are described in a large number of earlier 

papers on network calculations (e.g. 6,20). Experience has shown that 

this method allows working with the most simple program and organization 
of the input data and does not pose any difficulties, time or storagewise, 

for average sized modern computers. Previous limitations in computer 

capacity, which led to other programs with lower storage requirements or 

higher execution speeds, do practically no longer exist. It was, therefore, decided to use for this contract the CROSS method of balancing 

pressures. It was furthermore decided to utilize and modify a program 

which already had a large number of users in the U.S. This would make 

the understanding of the new program, at least for some people,' easier. 

It would, furthermore, allow them to use existing network calculation 

data for the new program, 

There seem to be two different programs for ventilation network 

calculations in wide use in the U.S. (6); the so-called Pennsylvania 

State University program (6,20), and the so-called Michigan Technological 

University program (7). The last published version of the Penn State 

program (20) was written before 1970. It was described in great detail 

in 1972 (6). The Michigan Tech program originated in West Germany around 

1965 as a new, more compact, version of older existing programs and is 

widely used by German ventilation engineers. It is very similar to the 

standard program of the British National Coal Board, which was issued in 

1967, since both programs have the same source. Since this program was 

not a genuine novelty and a large number of copies together with manuals 

are in circulation, no detailed description of this program was published. 

The Penn State and Michigan Tech programs are not very different. 

They use the same mathematical description of ventilation networks and 

use essentially the same solution method. Judgment of the quality of a 

computer program is to a large part based on how familiar one is with 

the program and the way in which input and output are organized. As long 

as programs give correct results with the same amount of computer and 

user effort, they must be considered as being equally useful. 

The author, having participated in writing the Michigan Tech 

program and having carefully studied the Penn State program feels, however, that the former program is simpler to use and it seems to have a 

better convergence also. The reason is, perhaps, that it was written by 

practical ventilation engineers who had to perform large numbers of network calculations for their planning purposes. The features which the 
author thinks should be changed in the P~M State program are the following : 

Airways (branches) should obtain identification numbers, not just 

sequence numbers; if input cards are placed in a different sequence or if 

the network changes, these sequence numbers will change also, which is a 

great inconvenience. 

The use of a junction marker array in the "tree building process" 

limits the junction numbers to a few places or causes a lot of storage 

waste. 

The natural ventilation pressure has to be calculated and 

inserted manually, 

The approximation of the fan characteristic requires 90 statements. The feared undulations of polynomials which led to this occurs, 

however, only at both ends of the fan characteristic curve. 

To use only the airflow rates of fixed quantity airways and the 

highest flow rates from indicated fan characteristics, or to use for all 

airways of the first mesh a rate of 100,000 cfm for the calculation of the 

initial airflow distribution, gives a poor start, 

The output comprises a lot of actually unneeded information. 

Since the distribution of the Penn State and Michigan Tech programs seem to be of the same order of magnitude, it was decided to use 

the Michigan Tech network program for the new program. 
MATHEMATICAL DESCRIPTION OF VENTILATION NETWORKS FOR 

AIRFLOW AND PRESSURE DISTRIBUTION CALCULATIONS 

The mathematical description of ventilation networks is not 

uniform and considerable confusion exists among practical ventilation 

engineers in this respect. It seems, therefore, advantageous to explain 

the principles which have been used in this report. 

The networks are considered to be in a steady state. The forces 

acting on the ventilation system do not change very rapidly so that 

inertia forces of the air can be neglected. The response of the ventilation system to changing forces is considered as a sequence of equilibrium 

states to which the steady state mathematical description of network 

applies. 

The mathematical description of ventilation networks can be 

based on mass flow rates or volume flow rates of air. Ventilation engineers prefer to work with volume flow rates because these flow rates, 

being the product of cross sectional area and measured airflow speed, are 

3 

easy to visualize. Moreover, energies (ft-lb) per unit volume ( ft ) have 

2 the dimensions of pressures (ft-lb/ft3 = lb/ft ) and can, like fan pressures or the pressure losses in airways, be directly read from manometers 

or barometers. Problems arise from the fact that due to density changes 

of the air the volume flow rates change also, even when the mass flow 

rates remain constant. This makes it, in ventilation surveys, difficult 

to detect genuine air leakage currents. In network calculations, suitable allowances have to be made for the fact that the volume flow rates 

entering airways are not necessarily equal to the volume flow rates 

leaving them. Energy balances are distorted by the fact that equal 

energy quantities (ft-lb/lb) can be expressed by different pressures 

3 (ft-lb/ft ), which in ventilation pressure surveys usually leads to an 

overestimate of natural ventilation pressures and requires, in network 

calculations, suitable adjustments. 

The network calculations in this report will, therefore, be 

based on mass flow rates, but since these and the pertinent energy quantities per unit mass (ft-lb/lb = ft, heads) are unfamiliar to many 

ventilation engineers, they are with the help of reference densities dr 
converted into quantities with the dimensions of volume flow rates and 

pressures. The reference densities are nothing more than constant factors which are carried through the calculations with the sole aim of 

obtaining results in familiar units. For their magnitude a value close 

to the average density in that part of the mine, for which the results of 

the network calculation are most important, is chosen. They are stated 

at the beginning of the program together with a reference temperature 

which corresponds to this density. 

This approach requires preparing the input data of the network 

calculation in the following way. The measured actual flow rates Q, 

having an average density of d, are converted to the reference volume 

flow rate Qr according to 

The pressure loss H which has been obtained from an altimeter survey L 

(15) or read from the manometer of a trailing hose (9) is converted to 

the reference pressure loss 

If pressure losses have been calculated from the formula 

where K = friction factor 

L = airway length 

0 = airway perimeter 

A = airway cross sectional area 

and if the Bureau of Mines schedule of friction factors has been used 

(11) , the conversion is 

Measured fan pressure H are converted to 

F 
Fan pressures obtained from fan characteristics based on a density of 

3 0.075 lb/ft are converted to 

Natural ventilation heads h which as heat energy converted into mechaniN' 

cal work are represented by the area enclosed in a pressure-volume (p-v) 

diagram (hN = - $ v dp = - $ dp/d) , are expressed as natural ventilation 

pressure 

If resistance factors R have been determined from measured pressure losses 

H and airflow rates Q according to L 

they have to be converted to 

in order to make the equation H = Rr (Q~/~o~) fit. Lr 

If they have been calculated from Bureau of Mines friction factors (11) 

3 with the help of the formula R = K L 0/(5.2 A ) , they have for the same 

purpose to be converted to 

It is, in this report, from now on assumed that volume flow rates Q, 

pressures H and resistance factors R are based on a constant reference 

density and the subscripts r are, therefore, from now on omitted. 

With this agreement and the assumption of steady state flow 

conditions, ventilation networks can be described by three different 

sets of equations: resistance equations or equivalents, junction equations, and mesh equations. 
Every airway with a flow resistance obeys the resistance equation 

2 

H = Ti Q . If the airway has no flow resistance but contains a pressure L 

source H an equation H = f(Q) is substituted. If the resistance is F' F 

made variable in order to keep the airflow rate Q constant (fixed quantity 

airway) an equation 

Q = constant 

takes the place of the resistance equation. 

The law of mass conservation applies to every junction. 

The airflow rate entering a junction must be equal to the airflow rate 

leaving it, These are the junction equations of networks. 

The first law of thermodynamics applies to every mesh, which can be 

written as 

The sum of all pressure losses in the airways of a mesh is equal to the 

sum of all pressures generated by pressure sources plus the natural 

ventilation pressure in this mesh. 

If the number of airways in a network is nb, the number of junctions n , and the number of meshes is n , there are 

j m 

n resistance or equivalent equations, b 

n - 1 junction equations, and 

j 

= % - nj 

+ 1 mesh equations. 
PROGRAM DESCRIPTION 

4.1 NETWORK PART OF PROGRAM 

4.1.1 Section "Read Input Data" 

The input data for this program part comprise: one network control card; airway cards; junction cards; fan characteristic cards; and 

additional airway cards. 

Junction and fan characteristic cards may be omitted if the 

information contained in them is not considered essential to the expected 

result of the calculation. The option of additional airway cards has been 

introduced to be capable of using already existing decks or files of airway cards from conventional ventilation network calculations, which do not 

contain all the information needed for the use of this program. 

The network control card has to state: 

NB 

NJ 

NFNUM 

NADBC 

NVPN 

NEW ) 

NCONC ) 

NTEMP 

MAD J 

ITN 

number of airways 

number of junctions 

number of fan characteristics to be read in 

number of additional airway cards 

marker; NVPN > 0 indicates that NJ junction cards shall be read 

in and that natural ventilation pressures shall be calculated 

from junction card data 

(values larger than 0 indicate that network, concentration, 

marker (and temperature calculations shall be performed; these 

(can be executed independently of each other 

maximal number of times a network calculation shall be performed 

in one program run 

maximal number of iterations permitted within network and concentration parts of program 

reference density 

reference temperature 

The two numbers MADJ and ITN are safety switches against endless 

computer runs with meaningless data. 

NB airway cards are needed which can be arranged in any arbitrary 

sequence. There are three types of airway cards: regular airway cards, 

marked by WTYP = 0; fixed quantity airway cards, marked by NWTYP = -1; 

fan cards, marked by NWTYP = 1. 

All airway cards have to state: 
airway number 

junction number of airway beginning 

junction number of airway end 

Regular airway cards have to state: 

resistance factor of airway when computer is not expected to 

calculate this figure 

Fan cards have to state (in the R-column) the fan pressure. his 

will be the acting fan pressure, when no fan characteristics are given. 

Fixed quantity cards have to state: 

Q desired constant airflow rate 

In regular airway and fan cards the statement of an estimated Q 

is optional. When it is in the right order of magnitude it is helpful for 

obtaining a fast solution. 

The airway properties: 

KF friction factor 

LA airway length 

A cross sectional area 

0 perimeter 

may be stated at this place in the airway cards. They may be stated later 

in the NADBC additional airway cards, or average properties, read into the 

computer at the beginning of the concentration part, may be used, 

For NVPN > 0, NJ junction cards have to be provided. Each one 

has to state: 

JNO junction number 

T temperature of junction 

Z elevation of junction 

Since this information is used for the calculation of the natural ventilation pressure only, the data do not have to be very accurate, The statement of: 

CH4C methane concentration in junction 

is optional. It is used in the concentration part to estimate the methane 

evolution ofairways if no better information has been given. It can be 

stated later with the input data of the concentration part, if so desired. 

The possibility to state it here was introduced because the junction cards 

provide ample space. 
NFNUM sets of fan characteristic cards have to be provided. Every 

set comprises one fan identity card, stating: 

NOF airway number of fan 

MPTS number of points which shall be used to define the fan characteristic 

and as many curve point cards as are needed to state: 

QF airflow rate at point of fan characteristic 

PF fan pressure at point of fan characteristic 

for all of the MPTS points. Ten points contained in two cards will usually 

be sufficient. 

4.1.2 Complete Input Data, Output of Input 

In this section the NADBC additional network airway cards are 

read in. They contain: 

NOX airway number 

KX friction factor K 

LX airway length 

AX cross sectional area 

OX perimeter 

A check is made to see if all the additional cards refer to airways which are part of the network. If not, their content is disregarded 

and a message printed. It is then checked to see if the resistance factor 

R for every regular airway has been stated. If not, it is checked to see 

if R can be calculated from the stated airway dimensions, but a stated R 

always overrides a calculated value. If R has not been stated and cannot 

be calculated, a network calculation is impossible. The computer shows 

where data are lacking, prints out the received input data together with 

the message that no network calculation has been performed and moves on 

to the concentration part of the program. It does the same if no network 

calculation is desired (NETW 0). As a preparation for the network calculation the counters MADJC and ITCT as well as the markers NSW, NSNVP, NNVP, 

and MARKN are set to zero. 

4.1.3 Arrange Airways to Size and Magnitude R*Q 

Numerical values of resistance factors are small and are tradi10 tionally stated as R*10 . In order to make the resistance equation 
H~ = R Q2 fit, Q is, in this formula, expressed in units of 10' cfm. This 

conversion is done in the first pass through this program part when NSW 5 - 

0. 

Theoretical investigations have shown that the convergence of the 

CROSS iteration method is improved when airways with high resistance factors are made so-called "primary1' airways, which occur in one mesh only 

(18). It has been shown by earlier experiences with digital computers 

that when meshes are formed in this way, an acceptable rate of convergence 

can be achieved altogether (7) and many existing programs follow this 

route. Additional practical experience has shown that an even better convergence can be reached when airways with high products R*Q appear in as 

few meshes as possible, i.e. are made primary airways. This makes the 

denominator of the CROSS correction formula small and the corrections consequently large. 

In preparation for the selection of primary airways, an INU-list 

is formed. This contains, in its lowest places, the fans for which no fan 

characteristic has been given (constant pressure fans). The regular airways follow in the order of their increased magnitude R*Q. Tihe list is 

completed with the fixed quantity airways and the fans, for which a fan 

characteristic has been given (variable pressure fans) . The positions of 

these fans in the airway list is at this time put into a special NFREGlist in order to be able to locate them later on when fan pressures have 

to be determined. 

The reason for this arrangement is that, in the next program section, primary airways are selected from the top of the INU-list. Fixed 

quantity airways can, according to their definition, have no airflow rate 

corrections. They should, therefore, occur in as few meshes as possible. 

Variable pressure fans have to adjust their pressures after every airflow 

rate correction. To make them primary airways, which are corrected only 

once in every iteration, keeps the computing effort low. It prevents, 

furthermore, oscillations of the system, which can occur when a large 

number of variable pressure fans are cooperating. 

4.1.4 SetUpBaseSystem 

As with all computer sorting processes, the principles employed 

in this section are not complicated but are hard to explain. The best 
way to understand the procedures, if one desires, is to go through a 

numerical example. Since the procedures are not new or unique they shall 

not be discussed detail here. 

Starting out with the airway in the lowest place of the INU-list, 

the base system or a tree of N - 1 "secondary" airways is assembled in 

j 

such a way that all junctions of the network are connected, but no meshes 

are formed. The number of remaining primary airways is (N - N. + 1 = b 3 Nm' 

equal to the number of meshes. Everyone of the remaining branches will, 

therefore, when added to the base system, close a mesh. All airways which 

become part of the base system are entered into a list of secondary airways, the KNO-list. The remaining primary airways are marked by giving 

their finishing junctions JF a negative sign. 

In assembling the base system the airways are scrutinized in 

ascending order of their places in the INU-list. This means that the KNOlist of secondary airways contains the fixed pressure fans and the airways 

with the lowest possible products R*Q. If a fixed quantity airway has to 

be entered into the KNO-list, which usually means that all airways entering 

and leaving a junction are fixed quantity airways, a message is printed 

and this airway is treated like a regular airway. If an airway, like a 

dead-end working, is only connected to the network at one end, a message 

is printed out also. 

4.1.5 Form Meshes 

Every primary airway, which is either a fixed quantity airway, 

variable pressure fan, or a regular airway with a high product R*Q, will. 

form a mesh with secondary airways. As one can visualize from connecting 

two branches of a tree (secondary airways), there is only one possibility 

to form a mesh. The meshes are found by adding to both ends of a primary 

airway a sequence of secondary airways from the KNO-list until the ends 

meet. Two lists are used to describe the meshes. The MSL-list contains 

the whole sequence of primary and secondary airways which forms all the 

meshes in the network. The MEND-list contains the places of the secondary 

airways in the MSL-list, which closed a mesh when it was formed. Thus, if 

the first two meshes would comprise 6 and 10 airways, one would have: 

 MEND(^) = 6, MEND(2) = 16. The primary airways in these meshes would have 
the places MSL(1) and E~(6+1), the two meshes would occupy the places 1 

through 6, and 7 through 16 in the MSL-list. 

4.1.6 Satisfv Junction Emations 

The CROSS approximation method does not interfere with the junction equations, but these have to be satisfied originally to make the 

method work. This can be done by placing the airflow rates of every primary airway into all the airways which belong to the mesh of this primary 

airway. With N airflow rates Q existing in the N airways and N - 1 b b j 

junction equations, Nb - (Nj - 1) = N airflow rates can be arbitrarily m 

chosen. N is equal to the number of primary airways. m 

This can be visualized in the following way. If we assume that 

in every mesh a certain airflow rate is circulated, the junction equations 

must be satisfied. Whatever flows into the junctions, through which this 

mesh passes, must flow out of them again. The primary airways, being part 

of one mesh only, carry this specific airflow rate. The secondary airways 

carry the airflow rates of all the meshes of which they are a part. 

The program accomplishes this by setting the airflow rates of all 

secondary airways, found from the MSL and MEND-lists, initially to zero. 

It then takes the airflow rates, which have been indicated for the primary 

airways in the airway cards, and puts.them into the airways of the pertinent meshes. The directions, in which the airflow rates circulating in 

the meshes pass through the airways, have to be noted. All airflow rates 

are then for every individual airway summed up, and the result is an 

airflow distribution which satisfies the junction equations. 

Calculate Natural Ventilation Pressure 

This section of the program is executed in the first network 

calculation (NSNVP I_ 0) only where junction cards with temperature and 

elevation data were read in (NVPN > 0). If it has to be assumed that heat 

sources or changed surface temperatures have altered the temperature distribution in the mine, the pertinent natural ventilation pressures are 

calculated in a different way in another section of the program. 
Natural ventilation pressures are caused by the conversion of 

heat into mechanical energy, which is then available to propel the air 

and to overcome friction losses. Under steady-state conditions cyclic 

processes which are provided by every mesh of the ventilation system are 

necessary for such a conversion. The amount of heat converted into work 

per unit weight of air h is indicated by the area enclosed by the mesh in 

N 

a pressure (p) .volume (v) diagram (h = - f v dp) . Data on specific N 

volumes and pressures are usually not available at mines and are tedious 

to determine. Data on temperatures and elevations can, however, be 

easily obtained. The author suggested, therefore, in the early sixties, 

determining the natural ventilation from: 

where: T = absolute temperature 

Z = elevation 

Tm = average absolute temperature 

in the mesh under consideration 

and to let the computer calculate h and incorporate it in the network 

N 

calculation from information on temperatures and elevations of the network 

junctions. The error which is caused by substituting l/Tm f T dZ for 

- $ v dp has been investigated (7) and is comparatively small. This method 

of considering natural ventilation network calculations is a very convenient one, is part of the Michigan Tech program, and has found its way 

into many other programs also. 

For lack of other information, a linear temperature change between 

junctions is assumed, which is accurate enough for the normal state of 

mines. The natural ventilation pressure H based on a reference density N 

DR can then be calculated from: 

where: n = number of airways in mesh 

Ts,Zs = temperatures and elevations of starting junctions 

of airways in mesh 

Tf,Zf = temperatures and elevations of finishing junctions 

of airways in mesh 

The computer performs this calculation and stores the natural ventilation 

pressure, which has been obtained for the meshes of the network in a FNVPlist. 
4.1.8 Iteration 

The CROSS correction, which is used in this program is: 

where: Ri,Qi = resistance and airflow rate of regular airways 

contained in the mesh 

*Fi = pressure of fans contained in the mesh 

HN = natural ventilation pressure of the mesh 

dI$Ji/dQi = gradient of the fan pressure characteristic 

at airflow rate Q 

This correction is applied to every mesh in the network except for those 

which have a fixed quantity airway as primary airway, and this process is 

reiterated until either a specified number of iterations has been performed 

or a specified threshold is no longer exceeded, 

For variable pressure fans, the estimated fan pressure contained 

in the airway card and a gradient RGRAD = dHF/dQ = 0 is assumed in the 

first iteration. In the following iterations, values determined in the 

next program section are used. Calculated at first is the numerator of 

the CROSS correction DPSUM - FNVP, then the denominator RQSUM, then the 

correction DQ, then the corrected flow rates Q of the airways in the mesh, 

finally the sum of all corrections in one iteration DQSUM = 2 ABS(DQ). 

4.1.9 Fan Characteristic 

The fan characteristics were read into the computer with the fan 

characteristic cards, in which, for every fan with the airway number NOF 

for MPTS points, the airflow rates QF and fan pressures PF had been stated, 

Intermediate fan pressure values FANP, at the airflow rate FANQ, are 

determined with the help of LAGRANGE'S interpolation formula: 

(FANQ-QF2) (FANQ-QF3) . . . . (FANQ-QFn) 

FANP = (QF~-QF~) (QF~-QF~) . . . (QF~-QF~) 
This formula permits very simple programming and gives a smooth fit of 

the fan curves. Exceptions are the boundary regions where undulations 

can occur. Beyond the last stated point of the characteristic one can 

have steep extensions. To avoid difficulties in the boundary region, 

into which the fan might enter during the iteration process, the fan 

pressure is, for the region to the left of the second point and to the 

right of the second last point, made equal to the pressures in these 

points. Fans, which in the last iteration before the output of a result 

are still in these regions, are entered into a NFCW-list which is later 

used for printing a warning. 

For the gradient of the characteristic RGRAD = dH /dQ, the slope f 

of a straight connection between the two stated points to the left and the 

right of the operating point FANQ, FANP is used. This approach is good 

enough since the justification of RGRAD in CROSS' correction formula is 

questioned anyway (14) . 

The calculated fan pressures FANP replace the estimated pressures 

in the R-list of the input data. The counter of iterations, which have 

been performed with a particular assembly of meshes (IT), and the counter 

of the total number of iterations performed in the network calculation 

(ITCT), are raised by one. 

4.1.10 Continue in Appropriate Program Section 

At least two iterations (IT = 2) have to be performed, otherwise 

the fan characteristics would remain unconsidered. After the second 

iteration, a check is made to see if the sum of all corrections DQSUM is 

5 smaller than 0.002*10 . If it is, and for NSNVP 5 - 0, control passes to 

the next program section. NSNVP is a marker which indicates with NSNVP 2 

0, that this is the first network calculation of the program run, and that 

the sections "calculate natural ventilation pressure" and "calculate 

5 resistance of regulators" have to be executed. For DQSUM 1_ - 0.002*10 , a 

check is made to see if ITCT does not exceed the limit ITN set in the 

control card. If it does in the last network calculation of the program 
run, the marker MARKN will cause the printing of a warning. For ITCT 2 

ITN, a check is made to see if the number of iterations with the present 

mesh assembly approaches twenty. This indicates a poor convergence and 

a new mesh assembly is made by giving control to the section "arrange 

airways to size and magnitude R*Q1'. The marker NSW, which prevents a 

5 renewed division of Q by 10 , is made positive; the marker NSFLOW is set 

to zero. NSFLOW - 0 indicates that a new mesh selection has been made in 

the network part of the program and that a new flow scheme in the concentration part of the program is therefore necessary. 

If this was not the first network calculation of the computer 

run (NSNVP > 01, the next two program sections would be omitted. In 

preparation for the concentration part of the program, the airflow rates 

5 

are multiplied by 10 . A check is made to determine if, during the last 

network calculation which the computer was assigned to make (MADJC - 

MADJ), an airflow reversal has taken place. If it has, it is an indication that an airway changes its airflow direction in every network calculation. This means that the airway is so unstable that the minute 

adjustments of temperature and airflow distribution, which are made in 

consecutive steps, did let the airflow in the airway oscillate. Since 

the magnitude of the adjustments is well below the perennial changes 

which occur in real mines, it seemed important to detect these airways 

rather than to suppress the oscillations by finer adjustment procedures. 

4.1.11 Calculate Resistance of Reuulators 

The concept of fixed quantity airways is a valuable planning aid 

for the simulation of such airways through which, in the realitv of a 

mine, a certain fixed quantity is allowed to flow irrespective of the 

state of the rest of the ventilation system. This concept is as old as 

the use of computers for network calculations and was already part of the 

first digital computer programs. The adjustment of regulators by mine 

personnel, with which the airflow rate is kept constant, will not happen 

in the case of an emergency. The fixed quantity airways have, therefore, 

to be converted into regular airways to obtain a realistic simulation of 

their behavior. This can cause problems with fixed quantity airways 
which are used to simulate the outflow of compressed air. They should be 

put in series with a pressure source in the same way as, in reality, the . 

compressed air lines are connected to a compressor. 

Fixed quantity airways are, therefore, in this program only 

treated as fixed quantity airways in the first network calculation of 

the computer run. After its completion, their resistance is calculated 

and they are converted into regular airways. This section the program 

is consequently executed only once (NSNVP = 0). If the changes in the 

ventilation system are such that new network calculations become necessary 

(NSNVP # 01, this section is omitted. 

The determination of the resistance of fixed quantity airways 

proceeds in the that meshes containing them are sorted out with the 

help of the MSL and MEND-lists, The pressures H acting on the fixed 

L' 

quantity airways, are determined by summing up the pressures in all other 

2 airways of these meshes. The resistance is calculated from R = HL/Q . 

Subsequently NWTYP of the fixed quantity airways is changed from -1 to 0, 

which means they are converted into regular airways. 

4.1.12 Output of Results 

This output contains the results of the first netwark calculation. 

If temperature and concentration calculations are subsequently desired 

(NCONC > 0, NTEMP > O), the output will show on which initial network data 

they were based. If they are not desired (NCONC 0 NTEMP - 0 this 

will be the only output and the computer will print information to that 

effect. Printed are, for the regular and fixed quantity airways, the 

airway numbers NO, their junction numbers JS, JF, calculated airflow rates 

Q, and pressure losses P, resistance factors R, and the stated airway 

dimension lengths LA, cross sectional areas A, friction factors KF', and 

perimeters 0. A separate table is provided for fans with numbers NO, 

junctions JS, JF, airflow rates Q, and fan pressures I?. Since ventilation 

planning comprises, frequently, the selection of suitable fans, the characteristics, which were used in the network calculation, are indicated 

also. Finally, the number of airways and the number of junctions is 

printed because they may be needed in future plannings, and experience 

shows that, in their statement, errors occur frequently. 
In preparation for the next network part, the markers NSFLOW and 

ITCT are set to zero, 

4.2 CONCENTRATION PART OF PROGRAM 

4.2.1 Read and Complete Input Data 

The input data for this program part comprise: one concentration 

control card; one average value card; additional airway cards; additional 

junction cards; and contamination cards. All cards except for the control 

card are optional. The computer must, however, receive the input data, 

which it needs for the assigned calculations somehow, either as average 

data or as detailed airway data, The concentration control card has to 

state: 

NDIM 

NCH4C 

NAV 

MAXJ 

INFLOW 

JSTART 

TSTART 

TIME 

CRITSM 

CRITGS 

CRITHT 

WRNPR 

WRNSM 

WRNGS 

WRNHT 

additional number of concentration airway cards to follow 

additional number of concentration junction cards to follow 

marker for presence of average value card (> 0 yes) 

highest junction number used in network 

number of cards specifying contamination 

number of junctions from which concentration calculations shall 

start; normally this will be the atmosphere 

temperature in JSTART 

time which has elapsed since beginning of contamination; this is 

necessary for the temperature calculation where non-steady 

state conditions have to be assumed, only 

accuracy with which the results for smoke, methane, and temperature are expected; when recirculation occurs, an iteration 

method has to be used and these are the threshold values at 

which iterations stop 

pressure losses, smoke concentrations, methane concentrations, 

and temperatures which shall be considered to be critical, so 

special attention should be drawn to them in output 

The average value card contains average values for: 

TAVR rock temperature 

HAAVR rock diffusivity 

HKAVR rock thermal conductivity 

KFAVR friction factorof airways 

LAAVR airway length 

AAVR airway cross sectional area 

OAVR airway perimeter 

This card is optional. It was introduced to keep the amount of input data 

as small as possible. Rock temperatures, diffusivities, conductivities, 
and airway friction factors can in many cases be assumed to be the same 

for many airways of the mine. Many airways exist in hardrock mines, like 

raises between levels, which have, essentially, all the same dimensions. 

If detailed, accurate information is needed, it can always be entered with 

the airway cards and override the average values. Another reason for the 

introduction of average values was to prevent the termination of a computer 

run due to lack of, perhaps, rather insignificant airway properties. 

If additional concentration airway cards are wanted, NDIM in the 

concentration control card has stated how many of them. They contain: 

NOX airway number 

CH4VX methane volume production rate in airway 

CH4PAX methane volume production rate per unit surface area in airway 

TROCKX average rock temperature in airway 

HAX thermal diffusivity of rock in airway 

HKX thermal conductivity of rock in airway 

DZRDX elevation change in airway 

Except for NOX, all of this information is optional. DZRDX must, however, 

be unequal to zero if it shall override elevation changes calculated from 

junction elevations, because the computer cannot decide if it is equal to 

zero or if it has been forgotten. If it is equal to zero, it should be 

given a small positive or negative value close to zero. . 

If additional concentration junction cards are wanted, NCH4C in 

the concentration control card has stated how many of them. They contain 

only : 

JNOX junction number 

CH4CX methane concentration in junction 

and are used if one wants to determine the methane evolution from concentrations in junctions and this was not entered into the junction cards in 

the network part of the program. 

If contamination enters the ventilation system, INFLOW contamination cards have to be used. Besides the airway number they contain three 

sections: the first one with a specified contamination which can be anything; the second one applying to oxygen rich fires; the third one applying 

to fuel rich fires or any type of fire. As discussed in the introduction, 

this is a preliminary stage which can be improved once the necessity 

exists. The contamination cards contain: 
NCENT number of airways into which the contaminants enter 

CONT 

CONC 

HEAT 

Section 1 

volume flow rate of contaminated inflow 

concentration of contaminant in inflow 

heat entering airway 

Section 2 

02MIN oxygen concentration with which fumes leave fire zone 

Section 3 

SMP02 smoke production per ft3 of oxygen delivery 

HTPO2 heat production per ft3 of oxygen delivery 

Section 2 overrides section 1, section 3 overrides section 1 and 2. 

Control card, optional average value card, and optional additional 

airway cards are read in. Methane evolution rate per airway CH4VX and per 

unit area of airway CH4PAX, rock temperature TROCKX, thermal diffusivity 

HAX and conductivity HKX, and elevation change DZRDX, are placed in the 

airway files CH4V, CH4PA, TROCK, HA, HK, and DZRD. A check is made to see 

if the number of airway cards in the input was equal to the stated number 

of cards NDIM. If not, a message is printed and the calculation terminated. 

The airway files are then completed. For every airway a check is 

made to see if data for thermal diffusivity HA and conductivity HK from the 

just received additional airway cards, and if data for the friction factor 

KF, the airway length LA, the cross sectional area A, and the perimeter 0 

from the network part of the program exist. If they don't, average values 

from the average value card are substituted. If this card does not exist, 

a message is printed and the calculation terminated. The elevation change 

DZRD cannot be checked because it may in reality be equal to zero. Before 

an average value is substituted for the rock temperature TROCK, it is 

first checked to see if junction cards exist in the network part (NVPN > 

0). If yes, the airway is marked by giving its airway number NO a different sign than the rest of the airways. Temperatures T and elevations 

Z of starting and finishing junctions of these airways are then retrieved I. 

from the junction files of the network part of the program. Rock temperatures are calculated from these in the following way. When the assumption 

is made that the increase of rock temperature with depth has, due to the 
heat exchange between rock and air, become the same as the increase of 

rock temperature with depth, the air temperature change can, for steady 

state heat transfer, be described by (7): 

t = trO - ga LAsin 6 + (tl - tro) exp (-a 0 LA/G CP) 

where: t = rock temperature at beginning of airway rO 

tl = air temperature at beginning of airway 

'a = autocompression gradient 

B = slope angle (positive for ascending, negative for 

descending ventilation) 

a = convection coefficient 

G = weight flow rate 

CP = specific heat of air 

If, for the convection coefficient, the approximation: 

2 (7) where: a = convection coefficient (Btu/ft -hr-O~) 

V = air speed (ft/sec) 

is used, the exponent can be converted to: 

With DZRD = LA sin f3 and the definition of an average rock temperature 

'a TROCK = t - -DZRD rO 2 

one obtains for the rock temperature 

t2 - tl * exp(-X*LA) + DZRD*ga 

TROCK = 'a 

- - DZRD (1 - exp (-X*LA) 2 

Elevation changes DZRD are calculated as the difference between the two 

elevations if DZRD, in the files, is equal to zero. It is for this reason 

that DZRDX in the input data should not be made exactly equal to zero, 

even for a horizontal airway, which it usually isn't anyway in so-called 

level airways. 

4.2.2 SetUpJNOList 

If no junction number cards were, in the network part of the program, read into the computer, no junction number list (JNO-list) yet exists. 
It is set up in this program section together with a check, if the stated 

number of junctions is equal to the actual number, and, when necessary, 

with a correction. This is a frequent source of error when concentration 

calculations are performed only. The reason is that the number of junctions must be obtained by marking them in a check-list, whereas the 

number of airways can simply be obtained by counting the airway cards. It 

can be disputed whether junction cards and information on junctions serve 

a useful purpose. The calculation of the natural ventilation pressure in 

this way is, however, so widespread that in this program junction cards 

were retained. The occasionally made comment of storage waste is not 

true. Since the number of junctions is, with at least three airways 

entering or leaving a junction, equal to or smaller than 2/3 of the airway number, it takes, at the most, the same space to store temperature and 

elevation data junction-wise with a special junction number list than to 

do it airway-wise. 

4.2.3 Calculate Methane Evolution 

With a junction number list established, potential additional 

NCH4C junction cards can be read in. They contain, besides the junction 

number, only methane concentrations CH4C in junctions, which are placed 

into the pertinent list. A check is made again to see if all cards refer 

to junctions of the network. When not, a message is printed but no termination of calculations takes place since information on methane evolution 

is provided from several sides. 

For all ventilation planning in coal mines, it is very important 

to assess the methane evolution since changes in the airflow distribution 

will cause changes in the methane concentration distribution also. Airflow 

reductions can lead to dangerous concentrations, the main concern in all 

fire fighting operations. It is justified to consider the rate of methane 

release from coal faces, ribs, and pillars as roughly constant over short 

time periods. Even the increased methane production caused by mining 

operations will, when the operations stop, only gradually taper off (2,121. 

The rate of methane evolution per airway CH4V is introduced into 

this program in three different ways. ~t is in the additional airway cards 
either stated directly (CH4VX) or stated per unit surface area (CH4PAX) 

and then multi-plied by the surface area LA*O. If both statements have not 

been given, it is calculated from the methane concentrations in junctions 

by assuming that the concentration change between starting and finishing 

junction of an airway multiplied by its airflow rate is equal to its 

methane production. 

This last approach is a convenient one since methane concentrations in junctions, like temperatures, are, by most ventilation engineers, 

known by heart for their mine. It is, however, a crude approach since it 

is accurate only when merging air currents have the same concentrations. 

If the printout of the input data for concentrations and temperature calculations shows that the methane production obtained in this way is 

unrealistic for some airways, it has to be stated directly. Methane 

evolutions CH4V obtained from direct statements CH4VX override all other 

values; those indirectly obtained from CH4PAX override the ones derived 

from junction concentrations. 

At the end of this section, the contamination cards are read in. 

4.2.4 Output of Input 

To allow a critical assessment of the quality of results obtained 

with the help of this program, all important input data, which are not 

contained in the network output, are printed out. These data comprise a 

table with airway numbers NO, starting and finishing junctions JS, JF, 

elevation differences DZRD, rock temperatures TROCK, methane evolution 

CHIV, thermal conductivity HK, and thermal diffusivity HA. The time after 

the beginning of the contamination TIME, number JSTART and temperature 

TSTART of that junction, from which the calculation starts, are given also. 

Finally, the contamination with NCENT, CONT, CONC, HEAT, OIMIN, SMPO2, and 

HTPO2 is listed, or, if no contamination occurs, a relevant message is 

printed. 

4.2.5 Flowscheme 

All airways are checked for negative airflow rates. If any are 

detected, the flow is made positive by exchanging starting and finishing 
junctions. This makes a new mesh selection necessary in following network 

calculations and the marker NSFLOW is, therefore, set equal to zero. With 

the exchange of junctions, the sign of the elevation change DZRD has to be 

changed also. 

For the purpose of identifying airways with airflow reversals in 

the output, they are placed into a NREV file and their total number is 

counted by NRCT. Since the possibility exists that in the iteration process between the network and concentrations parts of the program, an airway experiences airflow reversal repeatedly, it is checked to see if this 

airway is not already in the NREV file. If it is, this means that an even 

number of reversals has taken place and that the airflow in this airway 

has its original direction again. It is therefore removed from the NREV 

file. After all airways have been checked, the NREV file is compacted and 

NRCT set to its proper value. 

For the purpose of calculating temperatures and concentrations, 

one has to know which air currents go into the same junction and are mixed 

there and which air currents leave from the same junction and have consequently the same properties. Since the number of airways connected to a 

junction can change in wide limits, it is not advisable to compile this 

information in a multidimensional array in which many places could remain 

empty. Instead a series of one-dimensional arrays is used, which was, for 

the same reasons, the approach with the mesh-lists in the network part of 

the program also. The procedures chosen for assembling these arrays are 

similar to the ones used by GEIGER (6). The following 5 arrays are set 

JNOL list of all junction numbers arranged according to magnitude of 

numbers 

NGOUT list of all airways going away from junctions 

LOUT list of last place occupied in NGOUT-list by a series of airways 

leaving a particular junction 

NGIN list of all airways entering junctions 

MIN list of last places occupied in NGIN-list by a series of airways 

entering a particular junction 

The example given in Fig. 1 may make this procedure clearer. The first 

junction number considered is JNOL(1) = 3. LOUT(^) = 2 indicates that 

airways NGOUT (1) = 3 and NGOUT (2) = 5 leave this junction. MIN (1) = 1 

indicates that airway NGIN(1) = 1 enters it. The second junction number 
Fig. 1: Flowscheme of a simple network described with the help 

of onedimens ional arrays 

JNOL NGOUT LOUT NGIN MIN 

I I I I 0 

JNOL JNO JLR 
is JNOL (2) = 5. Airways leaving this junction occupy the places LOUT (1) 

+ I = 3 through LOUT(2) = 3 in the NGOUT-list, consequently NGOUT(3) = 6 

is the only airway leaving this junction. Airways entering this junction 

occupy the places MIN(1) + 1 = 2 through MIN(2) = 3 in the NGIN-list, consequently NGIN(2) = 3 and NGIN(3) = 4 are entering this junction. The 

procedures for all other junctions are the same. 

In the JNOL-list the junction numbers are arranged according to 

their magnitude. If a JNO-list has been created by (NVPN >O) reading 

junction cards in the network part of the program into the computer, the 

junction numbers in this list can be in any arbitrary sequence which is 

convenient for input and output. Both lists are correlated by the JLRlist which indicates in which place a junction from the.J'NOL-list is contained in the JNO-list. Fig. 1 shows, for instance, that the junction 

JNOL (1) = 3 can from JLR(1) = 4 be located as JNO(4) = 3. 

In this section the contaminant concentrations in junctions PROP 

and PRCH4 are set equal to zero also. 

4.2.7 Indices of Starting Junction (Atmosphere) 

The indices of the junction at which one wants the temperature 

and concentration calculation to begin are determined, They are MSTART 

for the JNOL-list and ISTART for the JNO-list. The temperature of this 

junction is set to TSTART, which had been stated in the control card. The 

counter MRC and the marker MARKC are set to zero. 

4.2.8 Conditions at Roadway Ends 

4.2.8.1 General Remarks 

Determined with the help of this program are: contaminant concentrations; methane concentrations; and temperatures, 

Changes of concentrations and temperatures can occur in roadways 

due to contaminants, methane, and heat entering or leaving the air. They 

can occur in junctions due to mixing of air currents with different 
concentrations and temperatures. Since the processes in roadways and 

junctions are completely different, two different program sections have 

been provided. 

Contaminant concentrations in roadways have received the name 

RDPROP, in junctions PROP, at roadway beginnings PROPJS. Methane concentrations have received the names RDCH4, PRCH4, and CH4JS. Temperatures 

have received the names TRD, T, and TJS. 

Temperature calculations are performed only when demanded (NTEMP 

> 0). Concentration calculations are performed when demanded (NCONC > O), 

but also when only temperature calculations were desired, since varying 

temperatures can cause varying airflow distributions and, therefore, 

varying methane concentrations. 

The concentration calculations have, at this stage, been kept 

quite simple since the program requires that entering or leaving contaminants be specified. The temperature calculations have, however, become 

relatively comprehensive and complicated. On the one hand, the techniques 

for precalculating mine temperatures are more advanced than those for precalculating contaminant production~. On the other hand, the author attached 

more importance to these temperature precalculations since ventilation 

disturbances are mainly caused by thermal forces, not by concentration 

changes. 

Roadway calculations start out with setting the properties PROPJS, 

CH4JS, TJS at the beginning of roadways, leaving a junction equal to the 

equivalent properties PROP, PRCH4, T in this junction when the properties 

are known. For the first calculations this junction will be the starting 

junction JSTART, later on every junction, for which the calculations of 

the program section "conditions in junctions", could be completed. The 

roadways coming out of the junctions are found from the LOUT- and NGOUTlists and identical calculations are performed for all of them. At the 

start of every calculation the counter ICFTM is set to zero. 

4.2.8.2 Concentration Changes and Added Heat in Airways 

A check is made to see if contaminants or heat enter the airway 

(NO = NCENT). If not, the volume flow rate of the pure (100% concentration) contaminant CONTAM, the volume flow rate of the gas current carrying 
the contaminant CONTQ, and the heat addition HEATAD are set equal to zero. 

If a contaminant or heat enters the mine air, it can be specified in the 

contamination cards in several ways. In section 1 the volume flow rate of 

the gas current carrying the contaminant CONT, its concentration CONC (%) , 

and the heat HEAT are specified. CONTAM, CONTQ and HEATAD are determined 

from : 

CONTAM = CONT*CONC/100 

CONTQ = CONT 

HEATAD = HEAT 

CONT and HEAT can have negative signs for gas absorptions and heat sinks. 

If the inflow CONT is so large that it influences the airflow distribution, 

which will very rarely be the case, a fixed quantity airway similar to 

compressed air discharges should be provided for it. 

Section 2 of the contamination card applies to oxygen rich fires 

and states the oxygen concentration 02MIN with which the fumes leave the 

fire zone. The assumption is made that all consumed oxygen is converted 

into C02. The oxygen concentration entering the fire zone is 0.21 - 

PROPJS, the oxygen consumption is 0.21 - PROPJS - 02MIN/100f the volume 

flow rate of CO consequently: . 2 

CONTAM = (0.21 - PROPJS - 02MIN/100) * Q 

No additional gas enters the mine: 

CONTQ = 0 

3 The rate of heat generation is, with 437 Btu/ft of consumed oxygen: 

HEATAD = CONTAM * 437 

Section 3 applies to fuel rich fires and contaminant and heat 

3 production, SMP02 and HTP02 per ft of oxygen delivery, have to be stated. 

One obtains: 

CONTAM = (0.21 - PROPJS) *Q*SMP02 

HEATAD = (0.21 - PROPJS) *Q*HTPO2 

CONTQ = 0 
At this place, a suitable function relating contaminant and heat production 

with the oxygen supply can easily be introduced, if so desired and such a 

function is available. 

Contamination and methane concentration at the end of the roadway 

can then be calculated from: 

If a temperature calculation is desired (NTEMP > O), the heat addition 

HEATAD finds use; if it is not desired TRD is set equal to zero, JF' made 

negative to mark the completed roadway calculation, and the rest of this 

program section is omitted. 

4-2.8.3 Temperature Changes in Airways # 

The air temperature is increased by heat addition and subsequently reduced again by heat transfer to the airway walls. The temperature increase: 

where : tl = temperature before heat addition 

DR = reference density 

CP = specific heat of air 

If for CP a temperature function CP = a + b*t is assumed, one obtains: 

and with a = 0,2376 ~tu/l.bO~, b = 0.000024 ~tu/lb'~O~, 

This equation is based on pure air. One might dispute if the assumption of 

temperature variable specific heats is necessary, since the influence of 

the air composition is neglected, but the introduction of variable specific 

heats causes no great difficulties. 
Heat transfer to the airway walls lets the air temperature drop 

from an initial value of t to t, which for horizontal airways can be 1 

calculated from (7) : 

t = tr + (tl - tr) exp (-HK*LA*O*K(a) / (Q*DR*cP*R~) ) 

where: tr = rock temperature 

Ro = 2 A/O = hydraulic radius 

K(a), the so-called "coefficient of age", is a dimensionless scale for the 

thickness of the insulating rock layer surrounding airways which increases 

with age. Its use allows treating non-steady state heat transfer like a 

steady state process and has, therefore, in mine ventilation become common 

practice. 

In non-horizontal airways, the change of rock temperature with 

depth and the so-called "autocompression heat", the increase of air temperature with air pressure, have to be included. If one makes the justified assumption that the rock immediately surrounding an airway has, with 

some age of the airway, assumed the same temperature as the air ordinarily 

passing through it, geothermal and autocompression gradients become the 

same and the temperature can be calculated from (7): 

= tr~ - ga LA sin 6 + (t - tro) exp (-HK*LA*O*K(a) / (Q*DR*CP*RO) ) 1 

where: ga = autocompression gradient 

6 = slope angle (positive for ascending, negative for 

descending ventilation) 

trO = rock temperature at airway beginning 

If an average rock temperature TROCK = tr~ - 'a *DZRD/2 is defined, one 

obtains with DZRD = LA*sin 8: 

t = TROCK + (tl - TROCK) exp (-HK*LA*O*K(a)/(Q*DR*CP*RO)) 

The autocompression gradient g can be calculated from the mechanical heat 

a 

equivalent 778.26 ft-lb/Btu and CP as: 
The coefficient of age K(a) is a function of the dimensionless Fourier 

(FO) and Biot (BI) numbers. They are defined as: 

where HA and HK are the previously introduced thermal diffusivity and 

conductivity and HC is the convection coefficient. 

K(a) has been calculated by several researchers whose results are 

in good agreement (7). A solution for short periods of heat exchange has 

been provided by SCERBAN and Kremnev (17) which reads: 

K(a) = BI - BI~ *f(x)/(0.375 + BI) 

2 X 

where f (x) = [l - exp(x ) * (I - - 

2 1 exp(-x)dx)] 

J;; 0 

and x = (0.375 + BI) 

For the calculation of the error function 

in this computer program, the author introduced the power series: 

2 (-lln x 2n+1 9 (XI = - 1 -*- for x 5 2.5 

n 2n+l - J;; n=o 

JT .. exp (-x') [l - - 

1*3 

- [l - $(XI 1 - - 1*3*5 + . . . .I 

2 2x 2x 2 (2X2l2 (2x 2 3 

for x > 2.5 

Development.of the series is stopped when the terms in the brackets become 

smaller than 

The convection coefficient HC is a function of air thermal conductivity HKA, Reynolds number RN, Prandtl number PR, and airway dimensions. A formula proposed by KREITH (13) for the turbulent flow in smooth 

ducts seems to be an average among the many suggestions found in the 

literature (7) . It reads: 
With the Prandtl number being essentially independent of the air temperature, and having a value of 0.70 between 0 and 1600'~ and with R = 2A/O, 0 

this becomes: 

A correction for rough walls can be made by introducing the correction 

factor (7) : 

f (lOO/RN) 0.125 

COR = (y) 

where: f = friction coefficient of rough wall 

fo = friction coefficient of hydraulically smooth wall 

The friction coefficient f is proportional to the friction factor KF. For LI 3 

a density of 0.075 Ib/ft the relationship is f = KF/809, for a reference 

density DR it is f = KF*0. 075/(809*DR) . 

f (FRO in the program) can be obtained from: 0 

The thermal conductivity of air can be approximated by: 

HKA = 0.015 (T/492) Btu/ft h OF 

where: T = absolute air temperature (OR) 

The temperature dependence of air viscosity VISC and weight WT, both of 

which are needed for the Reynolds number, can be expressed by: 

-4 T 1.75 

VISC = 10 * 1.43 (-1 2 

492 ft /sec 

WT = DR * (TR + 460)/T 

where: TR = reference temperature 

and the Reynolds number: 

RN = V ~~/Visc 
where : Do = hydraulic diameter = 4 A/O 

V = air velocity 

with V = Q*DR/(60*AWWT) 

The program starts the temperature calculation by setting the temperature 

at the beginning of the airway TJS equal to the pertinent junction temperature To If a heat addition takes place (HEATAD = O), the temperature 

behind the heat source is determined and made equal to TJS, It is stored 

in the TFSI file also because it is needed in later program sections. 

For the calculation of WT, VISC, CP, and HKA, the average temperature in the roadway is needed, It is tentatively (ICE'TM = 0) assumed 

to be the arithmetic mean between starting and rock temperature (TM = (TJS 

+ TROCK)/2). If after the completion of the temperature calculation the 

result shows that the temperature at the end of the roadway TRD is more 

than 50'~ different from TROCK, a new TM is assumed (ICFTM = 1) . Since the 

temperature along an airway follows an exponential curve of the type: 

TRD = TROCK + (TJS - TROCK) exp(-X*LA) 

the factor X can be calculated from the last calculated TRD value as: 

1 

X = - [ln (TJS - TROCK) / (TRD - TROCK) 1 

LA 

and TM can be determined as the integral mean 1/LA TRD*dLA as: 

TROCK (TJS - TROCK) 

LA*X exp (-X*LA) ) 

This procedure of assuming a new TM is repeated until the calculated 

values for TRD vary less than 50'~. Since TM is, at this place, only 

needed to take the changes of the air properties WT, VISC, CP, and HKA 

with temperature into account, this threshold of 50'~ seems to be stringent 

enough. After these properties have been determined, Reynolds number RN, 

convection coefficient HC, Fourier number FO, Biot number BI, and coefficient of COAGE are calculated. The exponent in the temperature formula: 

becomes with R = 2 A/O and the factor 60 min/hr, when HK is, as customary, 0 

expressed per hour but Q is stated per minute: 
2 XNEW = HK*LA*O *COAGE/(~~O*DR*Q*CP*A) 

and TRD can be calculated. XNEW is placed in a file for future use. 

After the calculation has been completed, the roadway is marked by making 

its finishing junction JF negative. 

Conditions in Junctions 

Junctions, for which the junction calculations have been completed, receive a negative number JNO. They are disregarded in this program section. For the other junctions with a positive JNO, the airways 

going into a junction are located from the MIN- and NGIN-lists. In order 

to be able to perform a junction calculation the roadway calculations for 

these airways must have been completed, which means that they must all 

have negative finishing junctions. If they don't, the junction is disregarded. For the rest, the air quantities Q flowing into the junction 

(SUMAIR), the contaminant quantities RDPROP * Q (SUMPR), the methane 

quantities RDCH4 * Q, and the enthalpies TRD * Q * CP (SUMHT) are all 

summed up. Contaminant and methane concentrations in the junction are 

calculated' from: 

PROP = SWR/SUMAIR 

the temperatures from: 

which with CP = 0.2376 + 0.000024 * T results in: 

The program returns to the section "conditions at roadway ends" where the 

number JNO of the junctions, with completed junction calculations, is made 

negative. 

4.2.10 Recirculation, First Approximation 

If, in the previous section, no junctions with a positive JNO can 

be found for which all entering airways have negative finishing junctions 
JF, recirculation occurs in the network. The alternating roadway and 

junction calculations cannot be continued since concentrations and temperature of recirculated air entering a junction are not known. This 

difficulty is overcome by introducing estimated concentrations and temperatures for all recirculated airflows, with which the junction and 

roadway calculations are completed. The results obtained for the recirculated airflows are then taken as new, better estimates and the concentration and temperature calculations for the network are repeated. 

This process is continued until the differences between results and 

estimates are smaller than the thresholds CRITSM, CRITGS, CRITHT stated 

in the control card. 

A variety of methods was tried to overcome the recirculation 

problem. With the complexity of most ventilation networks, only iteration methods seem to be practical. The herein described procedure, which 

is similar to the adjustment of trigonometric height measurements, showed 

the best convergence. 

The program section starts by setting NREC = I. NREC helps in 

searching for junctions where the ratio of recirculated air QREC to not 

< recirculated air QIN is QREC/QIN = NREC/2. If no such junction can be 

found, NREC is stepwise increased. 

All junction numbers JNO are then checked for their signs. Negative junction numbers are counted by L and then disregarded because the 

junction calculations have been completed for them. Positive junction 

numbers JNO are one after the other compared with the finishing junctions 

JE' of airways. Junctions JNO, for which no negative JF can be found 

C (JNO + JF + 0, N = 01, are disregarded because no airway with a complete 

roadway calculation exists for them. The remaining junctions JNO are the 

ones where recirculated air enters the intake air. 

To find reasonable first estimates for the recirculated air, 

concentrations RDPROP, RDCH4, and temperatures TRD for the airways with 

completed roadway calculations (JNO + JF = 0) as we11 as their airflow 

rates Q are summed up (SRPR, SRCH4, STRD, QIN) and average values AVRPR, 

AvRCH~, AVTRD are calculated. The airways with recirculated air are 

entered into a temporary file (MEMREC) first and their airflow rates are 

summed up also (QREC). If a comparison shows that the recirculated airflow 
rate QREC for an airway is smaller than one half of the not recirculated 

air QIN (QREC*2/QIN - NREC 01, the airway and the first estimates for 

its concentrations and temperature are entered into the permanent recirculation files. If QREC is larger than 1/2 QIN, the next positive junction JNO is tried. If no junction with QREC 5 1/2 QIN could be found, 

NREC is increased by 1 which changes the criterion to QREC 5 QIN. If 

again no junction can be found, NREC is increased to 3 and so on, 

The recirculation files have been introduced to avoid the repetition of this search procedure in every step of the iteration process, in 

which concentrations and temperatures of recirculated airflows are determined. Airways with recirculation are counted with MRC, their place in 

the airway list is transcribed from the temporary file MEMREC into NOREC, 

and the first estimates for their concentrations and temperatures are 

entered into ESTPR, ESTCH4, ESTTR. After this, they receive these estimated values as their roadway end properties RDPROP, RDCH4, TRD, and their 

finishing junctions are made negative as if the roadway calculation had 

been completed. The place of the pertinent junction in the JNOL-list is 

located and the junction calculation for this junction completed. The 

program statements for doing this are essentially the same as in the program section "conditions in junctions". The program returns to the 

section "conditions at roadway ends". 

4.2.11 Recirculation, Preparation for Iteration 

If in the previous program section it has been found that all 

junction numbers JNO are negative (L LNJ), the calculation of concentrations and temperatures is complete. All finishing junctions JF and junction numbers JNO are made positive again. If the counter MRC for the 

recirculation files indicates that no recirculation exists (MRC = 01, the 

rest of this program section is omitted. For MRC > 0 the differences 

DIFPR, DIFCH4, DIFTRD between last estimated values ESTPR, ESTCH4, ESTTR 

and last calculated results RDPROP, RDCH4, TRD are determined for every 

airway with recirculation, If these differences are larger than the 

thresholds CRITSM, CRITGS, CRITHT, a marker L is made > 0. The last 

calculated properties RDPROP, RDCH4, TRD are made the new estimates ESTPR, 

ESTCH4, ESTTR, and the finishing junctions JF' are made negative. If this 
was the last iteration, these junctions will be the only negative ones in 

the JF-list and can be used to identify recirculation paths. The iteration counter ITCT is raised by one. If a positive marker L indicates that 

more iterations are necessary, it is checked to see if the maximum number 

ITN, which had been stated in the control card, is not exceeded. If not, 

the computer goes back to the beginning of the section "conditions at roadway ends" to start another iteration. If ITN would be exceeded, the marker 

.MARKC is made positive for an appropriate message. If temperature and network calculations were demanded, the next program section is entered, if 

not, this section is omitted and a message printed. 

4.2.12 Calculation of Natural Ventilation Pressure 

This section determines the thermal forces which are caused by 

changed temperature distributions and introduces them into the ventilation 

system. 

The energy per unit mass, which is required to overcome the flow 

resistance of an airway, is proportional to the velocity of the air in the 

airway. The same applies to the pressure loss when the latter is based on 

a constant reference density. If the density of the air changes, energy 

or pressure losses will change inversely proportional to the square of the 

density ratios. If the density change is caused by temperature changes, 

energy or pressure losses will change proportional to the square of the 

absolute temperature ratios. This change can,.in a mass flow rate based 

network calculation, be accounted for by multiplying the resistance factor ? 

R by a factor (T2/T1) where the subscripts 1 and 2 denote the old and 

new temperatures. 

Since temperatures along the length LA of an airway vary, it is 

2 

necessary to use a mean square temperature Tm , which for accurate calculations should be: 

With the previously quoted formula (section "conditions at roadway ends") : 

gaDZRD 

t = tr + (tl - tr) exp (-X*LA) - 2 (1 + exp (-X*LA) ) 
one obtains with the abbreviations: 

E = ga*DZRD/2, B = (tl - track , XNEW = X*LA 

2 +- 

XNEW (Track - E)*(B - E)*(l - exp(-XNEW)) 

The natural ventilation pressure can be calculated from: / 

f T dZ ccn be replaced by Z t *DZRD when one assumes airways with constant 

m 

slopes. This requires knowing the mean temperature t = LA I t dLA in 

m 

the airways. It can be calculated from the above formula for t as: 

The program starts this section by setting the temperature at the beginnings 

of airways T1 equal to the temperature T of the starting junction JS. If 

contamination in an airway occurs (NCENT = NO), T1 is set equal to the 

calculated temperature TFSI behind the contamination source. The mean temperature TMRD (i.e. t ) and mean square absolute temperature TMSQR (i. e. 

2 m 

T ) are calculated next for every airway. To account for the pressure m 

loss changes with temperature, the resistance Eactor R is set to new 

adjusted values which are the product of RSTD and the ratio rmSQR/(TR + 

2 460) . RSTD is the resistance factor of the airways based on the reference 

temperature TR. 

If the marker NSFLOW z.0 indicates that an airflow reversal has 

taken place, a new mesh selection is necessary before the natural ventilation pressure can be calculated. The rest of this program section is, 

therefore, omitted. With NSFLOW > 0, the natural ventilation pressures 

are calculated for all meshes of the network. 

Since it is the thermal forces (i.e. the changed flow resistances 

and natural ventilation pressures and among these mainly the latter) which 

can alter the temperature distribution and with it the thermal forces 

again, the changes of natural ventilation pressures from one iteration to 
the next one are made the threshold for the decision whether more iterations should be performed. The natural ventilation pressure FNVP of the 

last iteration is therefore preserved as ONVP before a new value FNVP is 

calculated. § T dZ = C t *DZRD is calculated by summing up in HSU the 

m 

products FRNVP = TMRD*DZRD for all airways of a mesh. The direction in 

which the computer progressed in forming the mesh is accounted for by 

FACT (+1 for direction JS to JF, -1 for direction JF to JS). The average 

temperature in the mesh is calculated as the weighed arithmetic mean by 

summing up in TSU all absolute values of FRNVP and dividing them by two 

times the total elevation change in the mesh. 

Errors in the statement of DZRD can make the sum of all elevation 

changes around a mesh unequal to zero. This means that the temperatureelevation plot of the mesh is not closed which can, even for small errors 

in DZRD, cause very large errors for the natural ventilation pressure. 

The sum of all positive elevation changes ZUP and all negative changes 

ZDOWN in traversing around the mesh is, therefore, determined. For ZUP # 

ZDOWN the mesh is closed by substituting the reference temperature for the 

gap - 

The differences between old and new natural ventilation pressures 

are calculated and their absolute values summed up in DNVP. 

4.2.13 Reroute to Appropriate Program Section 

Calculations of the natural ventilation pressure are necessary at 

two places in the program: within the network calculation; at the completion of the temperature calculation in order to find out if such significant changes have taken place that a new network calculation is required. 

If the former is the case and the natural ventilation pressures 

are wanted for a network calculation, this is indicated by the marker 

NNVP > 0 and the program returns to the section "iteration" of the network 

part. The marker NNVP and the counter ITCT are set to zero. If the 

latter is the case, it is checked to see if the average change in the 

natural ventilation pressure between the last two iterations was larger 

than 0.001 inches watergage per mesh. If it was smaller, the calculation 

is considered to be canpleted and the section "output of results" is 

entered. If it was larger, it is checked to see if the maximum number of 
iterations MADJ between network and concentration part, which had been 

stated in the control card, has been reached (MADJC - MADJ 2 0). In this 

case a message is printed before the output section is entered also. For 

(MADJC - MADJ < 0, the counter MADJC is raised by one, the counter ITCT 

and the marker MARKN are reset to zero, the marker NSNVP is set to one, 

all finishing junctions JF are made positive and the airflow rates Q are 

5 divided by 10 again. If NSFLOW LO indicates that a new mesh selection 

is necessary, NSW is made equal to one and the section "arrange airways to 

size and magnitude R*Qn is entered. For NSFLOW > 0, the calculation is 

continued in the section "iteration". 

4.2.14 Output of Results 

The pressure losses for the regular airways are calculated and 

the fan pressure extracted from the R-file. If the stated maximum number 

of iterations ITN was exceeded in the network part (MARKN > 0) or in the 

concentration part (MARKC > O), warnings are printed. 

A table with the results of the calculations for the states of the 

airway ends comes next. It lists airway numbers NO, junctions JS and JF, 

calculated airflow rates Q, temperatures TRD, smoke concentrations RDPROP, 

methane concentrations RDCX4, and pressure losses P. The term "smoke" 

stands for "contaminant" because it is shorter and this program will 

mainly be used for fire emergency plans. Airflow rates and pressures are 

based on reference densities. 

Another table with the results of the calculations for the junctions follows. It contains junction numbers JNO, temperatures T, smoke 

concentrations PROP, and methane concentrations PRCH4. The number of 

iterations MADJC between network and concentration parts of the program 

is printed next. 

The list of all finishing junctions JF is then scrutinized for 

negative values which indicate recirculation. The pertinent airways and 

their junctions are printed out together with an explanation that a 

recirculation path is closed at this place. 

Next, it is checked to see if any threshold limits for critical 

states (WRNPR, WRNGS, WRNSM, WRNHT) were specified. If not, a message is 
printed. If yes, all airways are checked for critical states and if any 

are detected they are placed in a printed list of airways together with 

the critical conditions. The same is done for junctions. 

With the help of the counter NRCT and the NREV-list, which were 

both established at the beginning of the section "flowscheme", airways 

with airflow reversal are finally printed out. To make the airways in the 

printed list appear in the same sequence as in all other airway lists, they 

have to be extracted in this sequence from the NREV-list. With this last 

list, the output is complete. 

4.3 COOPERATION OF PROGRAM SECTIONS 

The cooperation of the different program sections is shown in 

Figs. 2a - 2e. The computer nomenclature, which has been used in these 

figures, is listed in Table 1. 

Fig. 2a shows all existing major connections between program sections. Fig. 2b indicates which connections are used when only a network 

calculation is desired. Fig. 2c does the same for a concentration or temperature calculation without a network calculation. Fig. 2d refers to a 

combined network, concentration, and temperature calculation (NETW=l, 

NCONC=l, NTEMP=l), where the stated number of iterations is sufficient 

(ITCT < ITN, MADJC < MADJ), where no airflow reversals occur in the 

iteration process (which would make new mesh selections necessary), and 

where no recirculation occurs. Fig. 2e shows the same for the case of 

airflow reversals during the iteration process. 

Figs. 2d and 2e are simplifications. Normally airflow reversals 

will happen at some stages of the iteration process and not happen at 

others. The reversals, in turn, can cause or remove recirculation. An 

insufficient number of iterations will be the rule at the start of the 

calculations also. The usual flowchart will, therefore, resemble Fig. 2a 

more than Figs. 2d or 2e. 

4.4. EXAMPLES FOR PROGRAM USE 

4.4.1 General Remarks 

The program has been designed in such a way that it can be used 

for all mine ventilation systems, coal mines and hardrock mines alike. It 
NETWORK PART CONCENTRATION PART 

i - MARK0 - 

Read&Compl. =I Output of Start Network Input Netw. Input 

1 , I-. rr CJTPHPt) 
NETWORK PART CONCENTRATION PART 

: Read&Compl. Start Network Input 

I 

Base System 

Meshes D 

Junc t. E quat. 

I 

Output of 

1 \ * i 

Natevent. Ps. dfPbl= 0 

I 

btT:B--p ~teratton 

t7fl $ I7'U Its# Fancharacter. ' 

ITCT >ITN DQsuM 4 0.002 

Regulators B 

Output Netw. 

a\. 

1 ~onc. ~nput I 

Methane ~vol7 

Output of i 

Flowchar

Recisculat. 

1st Approx. Preparation 
NETWORK PART CONCENTRATION PART 

-1Base System I 

b 4 

I Meshes I 

Read&Compl. Output of 

Network Input Netw. Input 

1Junct. Equat. 1 

, Read&Compl. 

Conc. Input 

I Iteration 1 

I 

I Fancharacter. I - - pp 

Continue 1 

Instabilities 

1 

Methane Evol. 

GI' I Concentr. Inp. I 

I JNO - JNOL ] 

Roadway Cond. Junct. Cond

Output . 
NETWORK PART CONCENTRATION PART 

(Netw. Input 

* 

Read&Compl. Read&Compl. 

Network Input Conc. Input 

I 

JNO List NJPM., 

R*Q 

Base System I 

, Methane Evol. , 

Meshes . / Output of 

Concentr. Inp. 

I 4 

Flowscheme 

I JNO - JNOL 

,20 

AI 

111 

Indic. Start 

I Nat-vent. Pr. 

I 

I 

Iteration 

a~suM?o.oo~ IT=l Fancharacter. 

/ 

4 Regulators 

i UQ~UN < 0.802 t 

Output Netw. . i 

'\d---i( Instabilities 
NETWORK PART CONCENTRATION PART 

madm ! e-w. .- 

% JNO List 

Arrange R*Q 

/"' , : 

Base System 

", 

Methane Evol. 

I 

I Output of 

Meshes 

Concentr. Inp. 

Junct. Equat. DUVP/MNO 

>o.w / 1 

IT )20 I 

rFI 

\ J 

Flowscheme 

\ JNO - JNOL 

\ - t * I;\ / Indic. Start 

I \ 

- 

I Nate~ent. Pr. v 

Roadway Cond. Junct. Co

/ 

Instabilities 17

Output - - - 
Table 1: Computer Nomenclature for Cooperation of Program Sections 

CRITGS thresholds for corrections in iterations of concentration part 

CRITHT of program 

CRITSM 

DIFCH4 change in properties between last two iterations of concentraDIFPR tion part of program 

DIFTRD 

average change of natural ventilation pressure per mesh 

0.001 threshold for adjustment of natural ventilation pressure to 

changed temperature distribution (0.001 inches watergage) 

CQSUM sum of all corrections in one network iteration 

threshold for corrections in network iterations (200 cfm) 

IT counter of iterations in network part for every given mesh 

assmebly 

ITCT counter of iterations in network and concentration parts of 

program 

ITN maximal allowed number of iterations 

- J'S? finishing junction of airway; a negative sign of JF is used as 

marker for completed roadway calculations 

ZJF<O roadway calculations for all airways going into one particular 

junction have been completed 

JNO junction number; a negative sign of JNO is used as marker for 

completed junction calculations 

all junction calculations have been completed 

MADJ maximal allowed number of exchanges between network and concentration parts of program 

MAD JC counter of exchanges between network and concentration parts 

MARKD>O no resistance nor dimensions were stated for an airway 

MRC counter of airways closing recirculation paths 

NCONC>O a concentration calculation shall beperformed 
Table 1 (continued) 

NETW>O a network calculation shall be performed 

NNVP>O this is a natural ventilation pressure calculation within the 

network part of the program 

junction cards were used and read into the computer 

NTEMP>O a temperature calculation shall be performed 
can perform network (flow distribution), concentration, and temperature 

calculations separately as well as combined. Concentration calculations 

can be performed for methane and other contaminants, separately or combined. The quantities of contaminants entering the ventilation system can 

be stated directly as flow rates and concentrations or, as for fires, as a 

function of the oxygen supply. 

Rather than demonstrating all possible combinations, a number of 

examples shall be given which are all different from each other but still 

relatively close to mine ventilation realities. The examples have been 

selected for an easy understanding of how to use the program rather than 

for a demonstration of the program capabilities. All examples are based 

on the same comparatively small ventilation network to make the understanding simple and not to burden this report with too much input and output 

information. The program has been used so far for mines with up to 180 

airways. 

The selected ventilation system is that of a small multilevel 

coal mine with single entries and longwall faces. This type of mine was 

chosen because it represents something like a blend of hardrock and coal 

ventilation systems. Sufficient nonhorizontal airways, like in many 

hardrock mines, exist for the development of large thermal drafts and at 

the same time methane evolution is taking place. Fig. 3 shows the ventilation plan this system. Those input data, which were used in all 

examples, are compiled in Tables 2 through 6. 

The data from Tables 2 through 4 are fead into the computer in 

the network part of the program. Table 2 lists the contents of the airway 

and additional airway cards, table 3 the contents of the junction cards. 

Information on temperatures and elevations of junctions is required only 

when a network calculation with natural ventilation pressures, based on 

actually observed temperatures, is desired. If not, elevation differences can be stated and temperatures can be calculated in the concentration part of the program and can be entered here or later via additional 

junction cards. Table 4 lists the points of the fan characteristic which 

are entered with the fan characteristic cards. Fig. 4 shows a plot of 

these fan characteristics. 

The input, which during the concentration part of the program is 

read into the computer has been kept to a minimum. Table 5 lists methane 



Table 3: List of Junction Cards Containing Junction Numbers JNO, Temperatures T, elevations Z, and methane concentrations CH4C 

JNO 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

JNO 
5 

'd 0000 

e... 8 oooo 

p, CVCVcJLn 

mrl (U 

a, 

E: 

cd 

5 

2 

0 U) 

m 0 

. d'm 
8 

G 

t 

u: 

0 

O~dQO00OOOOOOOOOdOdOOOOO&,OOOOOOdOO~0Or3OC>OOOOr3OOOO~~ 

Z e..... e.o...~C.*.b*..oe..ew.eeem.o..o*..o*.....~ 

3 6UlP=CN-4 J3rf-WlNN NNC MMMNc(,~~W~~~~Mbb+M~3~drd+c3 a~m+m-G3Q t+ WrUOcbQ Nab I f I I .W#.r, 1 .NmdP m-fi 1 -).MO.,I I 1-NO 8'~

I- L?~L~VI LCI V" LC\ M r~ I rbtm mm J NN NN ot 

4aCttm i I I &i 

>t ma 

W 

Lu 
productions for the active longwall faces, Table 6 some additional methane 

concentrations in junctions. Methane productions in other airways, elevation differences, and rock temperatures have not been stated. They are 

calculated from methane concentrations, elevations, and temperatures in 

junctions, which are contained in the junction cards. Thermal conductivities and diffusivities have not been stated for individual airways either, 

instead average values from the average value card are used. Table 7 gives 

a summary of the input which was used in this way for the concentration 

part of the program. 

The output has, in all examples, been organized in the same way. 

It starts (Table -a) with the results of a conventional network calculation executed with the Michigan Tech program. This network calculation is 

always performed as a check if the input data for the network description 

are correct and complete. In many cases these data will already exist 

from previous network calculations. A list of fan operating points in the 

network calculations comes next (Table b . Additionally used input is 

listed in Table -c. The results of the concentration and temperature calculations and of the new network calculation, which takes the thermal 

forces developed by the new temperature distribution into account, are 

shown in Tables -d and -e. Table -d list temperatures, smoke (contaminant) 

concentrations, methane concentrations, air flow rates and pressure losses 

for airway ends. The two last quantities are based on reference densities. 

Pressure losses in airways were added.because their magnitude is a criterion for the stability of airways. Table -e contains temperatures, 

smoke and methane concentrations for junctions. Table -f lists airways 

and junctions with critical conditions and airways with airflow reversals 

to draw the attention of the program user to these. The number of iterative adjustments between network and concentration parts of the program 

is stated in Table -e. If this number has been too small for completion 

of the calculation, a message is printed out in Table -b. 

4.4.2 Executed Examples 

4.4.2.1 Example 1: Simulation of a Normal Ventilation State 

Tlhis example brings a simulation of the normal ventilation system 

without any contamination. The results are contained in Tables 8 a - f. 






so 

-0 

0' *' 

=rm 

'or 

00 

00 

00 

00 

3m d 

00 

em0 * 

an 

I 

00 

.a 0 

a0 

0 :a 

mo M 

0-0 

M 0. 

m 

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A comparison of the junction temperatures and junction methane concentrations from Table 8e with the input data from Table 3 shows good agreement. 

A comparison between airflow rates in Table 8a and Table 8d shows an 

acceptable but not complete agreement. The reason is that the Michigan 

Tech program assumes, for the temperatures on which the calculation of 

natural ventilation pressures are based, linear changes along the airways 

whereas the change in reality is exponential. 

4.4.2.2 Example 2: Changed Surface Temperature 

This example investigates how a change in the surface temperature 

from 50°F.to 90°F has after 6 hours effected the airflow distribution. 

The results are contained in Tables 9 a - f. A comparison of calculated 

temperatures with those from example 1 shows that the temperatures increase mainly in the intake airways whereas in the return airways they 

remain virtually unchanged. This reduces the natural ventilation in the 

meshes going through the intake shafts and subsequently the airflow 

entering the mine. The result is a slight increase in methane concentrations which at several places rise to above 1%. 

Junction temperatures based on 50'~ and 90'~ (lower placed 

figures) from Tables 8 and 9 have been plotted into Fig. 5. In some 

places the calculated temperatures for 90'~ surface temperature are lower 

than those for 50'~. The explanation is that for the 90'~ an elapsed time 

period of 6 hrs instead of 2 hrs was assumed. This allows the buildup of 

a thicker layer of insulating rock around the airways. 

For airway 50 (the leakage from the surface into the fan drift), 

a temperature of 107'~ has been calculated. The reason is that the rock 

temperature for this airway was determined from the temperature difference 

between junctions 1 and 32. The genuine temperature rise in airway 50, 

which has no practical importance, would have been obtained by stating the 

genuine rock temperature of this airway in the input data. 

4.4.2.3 Example 3: Main Fan Failure 

It is assumed that the surface fan fails (airway 51) but that the 

underground booster fan continues to work. The surface temperature is 50°F, 

the time after the event 15 minutes. 

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A problem of this type, where a large part of the mine is ventilated by small natural ventilation pressures only, can give problems to 

the program in its herein presented form. These pressures are smaller than 

the tolerances which have been allowed in the CROSS approximation method 

in order to keep the number of iterations low. This means that the CROSS 

method can, for the same input data, come up with different answers for 

the airflow directions. This has no practical importance. Airways with 

pressure losses lower than the chosen tolerances are so unstable that a 

precalculation of their airflow rates or directions makes little practical 

sense. 

In this program, every time that an airflow reversal takes place 

in a computer run, a new flowscheme and mesh assembly has to be set up, 

followed by a new network calculation with the help of the CROSS method. 

The result can be a continuous oscillation of airflow directions in the 

unstable airways. The obvious remedy, to make the tolerances smaller, 

offers little advantage. One does no longer get convergence problems, but 

the results are no more.convincing. 

A better way for problems of this type is to assume that the temperature distribution remains constant and to perform only one network 

calculation followed by a concentration calculation but not by a temperature calculation. Tables 10 a - f show the results. In judging these, 

one should keep in mind that the aixways with low pressure losses must be 

considered unstable. The output draws special attention to recirculation 

and the airways with airflow reversals also. Fig. 6 shows the methane 

concentration of junctions before (Table 8) and after (lower placed 

figures) (Table 10) the main fan failure. Arrows mark airways with airflow reversal. 

4.4.2.4 Example 4: Fire In a Horizontal Airway 

A fire is assumed at the beginning of airway 5 (NCENT). It is 

estimated that 30,000 cfm of air (CONT) travels through the fire zone, 

leaves a smoke (carbon dioxide) concentration of 1.00% (CONC) , and pro4 duces a heat of 15*10 Btu/min (HEAT). The results of the calculations 

are shown in Tables 11 a - f. One sees that the fumes coming from the 

fire have cooled down to almost normal temperatures before they leave 

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airway 5. Consequently, there is no substantial change in the air flow or 

temperature distribution. Since airway 5 is an intake airway, almost the 

whole mine is filled with smoke except for the part ventilated from intake 

shaft 4. 

4.4.2.5 Example 5: Oxygen Rich Fire at Bottom of Timbered Raise 

A fully developed fire burns at the bottom of raise airway 18. 

This raise is timbered and it is assumed that the fumes leave the fire zone 

with an oxygen concentration of 16% (02MIN). The results of the calculation are shown in Tables 12 a - f. The natural ventilation of the fire 

will increase the air flow in airway 18 from approximately 24,000 cfm to 

40,000 cfm (based on the reference density). Raise 20, which is an 

unstable descensionally ventilated airway, will experience a stable air 

flow reversal and transport approximately 10,000 cfm of fumes up to the 

next higher level, where an additional contamination of airway 11 takes 

place. 

4.4.2.6 Example 6: Fuel Rich Fire in a Descensionally Ventilated Raise 

A smoldering fire is assumed in raise airway 20. Since the raise 

is poorly ventilated, the possibility of considerable preheating shall be 

considered, leading to a fuel rich fire. In this, all of the oxygen in the 

3 air supply is consumed. The smoke production (SMP02) per ft of oxygen is 

3 estimated to be I ft , the heat production (HTP02) 300 Btu. The results 

are shown in Tables 13 a - f. Raise 20 develops a very powerful natural 

draft, transporting approximately 31,000 cfm of smoke up into airway 11. 

Since 11 is the return for airways 8, 9, and 10, these airways will experience air flow reduction and methane concentration increases to above 1%. 

In the design of the program it has been assumed that the location 

of a fire is at the beginning of the airway in which the fire occurs. If 

an air flow reversal in an airway with fire occurs, the program will move 

the fire zone from one end of the airway to the other end. This feature 

had been introduced to assume, for the detection of instabilities, the 

worst possible conditions. If this approach becomes unrealistic, one has 

to consider the fire zone as a separate airway whose location is fixed. 

This shall be demonstrated with the next example. 

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4.4.2.7 Example 7: Oxygen Rich Fire in an Intake Shaft 

It shall be investigated if a fire in the timbered shaft airway 

3 is capable of reversing the air flow in this shaft. For this purpose 

the shaft simulation is divided into three parts: an upper section airway 53; a lower section airway 52; and the fire zone airway 3. A length 

of 27 ft is assumed for the fire zone, the remaining shaft length is 2550 

ft (Fig, 7). Tentatively different locations are selected for the fire 

zone until an air flow reversal occurs. With the section below the fire 

zone being 50, 75, or 100 ft long, not sufficient natural ventilation 

pressure is developed for a reversal, although the air flow rate through 

the shaft drops from approximately 103,000 cfm normal to 43,000, 27,000, 

and 17,000 cfm (Table 14 a - c). With the section below the fire zone 

being 125 ft long, the reversal in the shaft has taken place (Tables 15 a - 

f) and a large air flow rate of 207,000 cfm is exhausting. This in turn 

causes reversals and high methane concentrations in a number of other airways. Fig. 7 shows a plot of original air flow rates (Table 15a) and 

final air flow rates (Table 15d) with the lower placed figures indicating 

the latter state. 

Should the fire start at the top of the shaft, one will have a 

somehow different phenomenon. Air flow reversal will occur fast but will 

be maintained only when the fire zone is more than 100 ft below the surface. 

Otherwise the natural ventilation pressure will, after the reversal, be too 

weak to maintain this flow direction and a very unstable state with fluctuations of the air flow will develop, 

4.4.2.8 Example 8: Layout of Fire Warning System 

It shall be investigated if a fire warning system installed at 

the upcast shaft airway 49 can detect spontaneous combustion in the gob 

area of longwall face airway 17. For this purpose one releases 100 cfm 

of contaminant (CONT) with a concentration (CONC) of 100.00% into airway 

17. Table 1.6 shows that this results in a concentration of 0.0347% in 

upcast shaft 49 and of 0.1218% in return airway 48. If a detection of 5 

ppm CO can be accomplished, the spontaneous combustion source must release 

at least 100*5/347 = 1.44 cfm of CO for an instrument installation at the 

surface and 100*5/1218 = 0.41 cfm for an installation in airway 48. 
ORGANIZATION OF INPUT 

4.5.1 Common Input Cards 

The sequence of input data is: 1 network control card; NB airway 

cards; NJ junction cards (optional); NFNUM sets of fan characteristic cards 

(optional) , each set comprising 1 fan identity card, 1 or more curve point 

cards; NADBC additional network airway cards (optional), 

If a concentration or temperature calculation is desired, these 

cards are followed by: 1 concentration control card; 1 average value card 

(optional); NDIM additional concentration airway cards; NCH4C additional 

concentration junction cards (optional) ; INFLOW contamination cards 

(optional) . 

The term "optional" does not mean that all of the optional cards 

can be omitted. There must be sufficient input information for the given 

assignm.ent. Otherwise a message will state what is lacking and the calculation will be terminated. 

The network control card contains: 

NB NJ NFNUM NADBC NVPN NETW NCONC NTEMP MADJ ITN DR TR 

FORMAT ( 1015,2F10.5) 

These symbols have been explained in the program description, In example 

1 this control card reads: 

51 32 2 3 11 11 10 30 .075 70.0 

The NB airway cards contain: 

NO JS JF NWTYP R Q KF LA A 0 

FORMAT (415,F10.3,F10.0,2110,2F10,1) 

For instance, airway card 1, which remained unchanged in all examples, 

reads : 

1 1 2 0 0.156 200000 250 2597 200.0 50.0 

The NJ junction cards contain: 

JNO T Z CH4C (optional) 

FORMAT (15,Tll,F5.1,~20 ,F6 .O ,F5.2) 

For instance, junction card 1 read in all described examples: 

1 50.0 114 

The NFNUM sets of fan characteristic cards contain the fan identity card with: 

NOF MPTS 
FORMAT (215) 

and the curve point cards with: 

QF PF QF PF QF PF QF PF QF PF 

FORMAT (5(F8.O,F6.2)) 

For instance, the set for fan No. 6, which was used throughout all examples, reads: 

The NADBC additional airway cards contain: 

NOX KX LX AX OX 

FORMAT (15,~41,2110,2~10.1) 

For instance, card 45 reads in all described examples: 

45 100 300 80.0 35.0 

The concentration control card contains: 

NDIM NCH4C NAV MAXJ INFLOW JSTART TSTART TIME CRITSM CRITGS 

CITHT WRNPR WRNSM WRNGS WRNHT 

FORMAT (615,F5.1,F8.2,F7.5,F5.3,F6.3,F4.2,F6.4,F4.1,F5.0) 

In example 1 this control card reads: 

5 2 1 32 0 1 50.0 2.0 0.005 0.10 0.20 0.01 0.05 

1.0 95.0 

The magnitude of the iteration thresholds CRITSM, CRITGS, CRITHT 

is a matter of personal preference. Low values will require more iterations but give more accurate results and vice versa. The selection of the 

warning thresholds depends on what one considers to be a state requiring 

special attention. 

The average value card contains: 

TAVR HMVR HKAVR KFAVR LAAVR AAVR OAVR 

FORMAT (3F10.5,2110,2F10.2) 

It reads in the calculations of this report: 

70.0 0.10 3.0 100 1000 100.0 100.0 

Only HAAVR and HKAVR were used in the calculations. 

The NDIM additional concentration cards contain: 

NOX CH4VX CH4PAX TROCKX HAX HKX DZRDX 

FORMAT (15,F10.2,4F10.5,F10.1) 
In the described examples, 5 such cards were used stating the 

methane production CH4VX of the longwall faces only. Card 1 reads, for 

instance : 

9 320.0 

The NCH4C additional concentration junction cards contain: 

JNOX a34cx 

FORMAT (I5 ,T26 ,F5.2) 

These calculations used two such cards for the input of two additional 

junction concentrations. The first of the cards reads, for instance: 

27 0.60 

The INFLOW contamination cards contain: 

NCENT CONT CONC HEAT 02MIN SMF'02 HTP02 

FORMAT (15,F10.O,F10.5,F10.2,3F10.5) 

Patterns for these cards will be given later. 

In all of the described examples all input cards, except for the 

network and concentration control cards, and the contamination cards, did 

not change, since the network did not change either. Two new airway and 

two new junction cards were added, only in example 7. 

4.5.2 Control and Contamination Cards 

In example 1 a simulation of the normal ventilation system without any contamination was demanded. This requires a network, concentration, and temperature calculation. It was assumed that the surface temperature is 50.0'~. The time after the ventilation change (which in this 

case did not take place) was arbitrarily set to 2 hrs. 

The network control card states in this case: 

and the concentration control card states: 

5 2 1 32 0 1 50.0 2.0 0.005 0.10 0.20 0.01 0.05 

There are no contamination cards since INFLOW = 0. 

In exampie 2 the normal ventilation system, without contamination 

but with a surface temperature of 90.0'~ 6 hrs after the temperature change, 

was simulated. This requires a network, concentration, and temperature 

calculation. 
The network control card remains the same as in example 1, the 

concentration control card changes to: 

5 2 1 '32 0 1 90.0 6.0 0.005 0.10 0.20 0.01 0.05 

1.0 95 

No contamination cards are needed. 

In example 3 a failure of the surface fan 51 was assumed. The 

surface temperature is ~o'F, the time after the fan failure 0.25 hrs. 

Only a network and concentration calculation, but no temperature calculation, was performed. To indicate the fan failure the network airway card 

51 has to be changed from NWTYP = 1 to NWTYP = 0. Into the R column, which 

for the airway cards of NWTYP = 1 states the fan pressure, the flow resistance of the idling fan has to be inserted. The set of fan characteristic 

cards for fan 51 has to be removed. 

The network control card reads consequently: 

51 32 13 11 10 10 30 0.075 70.0 

the concentration control card reads: 

5 2 1 32 0 1 50.0 0.25 0.005 0.10 0.20 0.01 0.05 

1.0 95 

No contamination cards are needed. 

In example 4 a fire was assumed at the beginning of airway 5, 

producing 30,000 cfm of contaminated air (CONT) with a smoke concentration 

4 of 1.0% (CONC) and 15*10 Btu/min heat production (HEAT). Of interest is 

a time period 1 hour after the event. The network control card remains 

the same as in examples 1 and 2, the concentration control card reads: 

5 2 1 32 1 1 50.0 1.0 0.005 0-10 0.20 0.01 0.05 

1.0 95 

The contamination card reads: 

5 30000. .1.0 150000.00 0. 0. 0. 

In example 5 an oxygen rich timber fire was assumed at the bottom 

of raise 18 which reduces the oxygen concentration of the air traveling 

through the fire zone to 16.0% (02MIN). Network and concentration control 

cards remain the same as in example 4, but the contamination card changes 

to: 

18 0. 0. 0. 16.0 0. 0. 
In example 6 a fuel rich fire in raise 20 is assumed which produces 1 cfm of smoke with 100% concentration and 300 Btu of heat per cfm 

of oxygen. The network and concentration control cards remain the same as 

in the previous example, the contamination card changes to: 

20 0. 0. 0. 0. 1.00 300,OO 

In example 7, o -rich timber fires are assumed at different loca- 2 

tions in shaft 3. Two new airways, 52, 53, and two new junctions, 33, 34, 

are introduced. Their network airway and junction cards have to be added. 

The number of airways NB, and the number of junctions NJ, and the highest 

junction number MAXJ, change. The network control card reads, therefore: 

53 34 2 3 11 11 10 30 0.075 70.0 

the concentration control card reads: 

5 2 1 34 1 1 50.0 0.5 0.005 0.10 0.20 0.01 0.05 

1.0 95 

and the contamination card reads: 

3 0. 0. 0. 16.0 0. 0. 

In example 8 a contaminant volume of 100.00 cfm (CONT) with a 

concentration of 100.0% (CONC) is released into airway 17. No heat is 

added. The network control card reads: 

51 32 2 3 11 11 10 30 0.075 70.0 

the concentration control card reads: 

5 2 132 11 50.0 0.1 0.005 0.10 0.20 0.01 0.05 

1.0 95 

and the contamination card reads: 

17 100. 100.00 0. 0. 0. 0. 

STORAGE REQUIREMENTS 

The storage requirements for the execution of this program are 

not small, but not excessive either. NB (number of airways) places are 

needed for the arrays: 

NO, JS, JF, Q, NGOUT, NGIN, RDPROP, TRD, LA, A, 0, KF, CH4V, CH4PA, TROCK, 

HA, HK, DZRD, RDCH4, XNEW, R, RST, FRNVP, NWTYP, P, RQ, INU, KJS, KJF, KNO. 

These are 30 arrays which, with the EQUIVALENCE (P,RQ) , (CH4PA,RDCH4) , 

(NGOUT, INU) , (NGIN ,KJF) , (MIN,KN0) , can be reduced to 26. 
NJ (number of junctions) places are needed for the arrays: 

LOUT, MIN, JNOL, JNO, JLR, PROP, CH4C, T, 2, PRCH4 

These are 10 arrays which with EQUIVALENCE (CH4C, PRCH4) , (2, PROP) , (LOUT, 

KJS) can be reduced to 6. 

NFNUM (number of fans) places are needed for the arrays: 

NOF, MPTS, NFREG, NFCW, RGRA 

MPTS (number of curve points) * NFNUM places are needed for the 

arrays : 

QF, PF 

NB - NJ + 1 places are needed for the arrays: 

FNVP, MEND 

How large the array MSL has to be is hard to predict, since the 

number of airways in meshes depends very much on the network configuration. 

A figure of 5 to 10 times the number of airways NB will usually be sufficient. 

As many places as recirculation paths exist, are needed for the 

arrays : 

MEMREC, NOREC, ESTPR, ESTCH4, ESTTR 

A number of 1/5*NB should be sufficient even for bad cases. 

As many places as airways with inflow of contaminants exist are 

needed for the arrays: 

HEAT, MCENT, CONT, CONC, 02MIN, SMP02, HTP02, TFSI 

How many places the array NREV requires depends on the type of 

calculations. This array registers the airways with airflow reversal. In 

the worst case this can be all NB airways, but normally a smaller number 

of 1/3*NB should be sufficient. 

With the assumption of NJ = 2/3*NB, NFNM = 1/30*NB and MPTS = 10 

this adds up to approximately 40*NB. Few network calculations use more 

than NB = 200 airway simulations. 

4.7 EXECUTION TIME 

This depends on the number of iterations, which have to be performed, In the described examples it never exceeded 10 seconds with a 

UNIVAC 1110. As a safeguard against excessive time consumptions, which 

can happen in unstable networks with oscillating air currents, the thresholds ITN and MADJ are stated in the network control card. 
5. TABLE OF TEXT NOMENCLATURE 

Text Computer Text 

Symbol Symbol Page Dimension Definition 

2 

A A 12 ft airway cross sectional area 

29 Btu 

a HC 2 convection coefficient 

ft hr OF 

COR 

BI 

COR 

CP 

FRO 

FANP 

29 slope angle 

in. wg. 

in. wg. 

in. wg. 

in. wg. 

in. wg. 

Biot Number 

correction of convection coefficient for r

specific heat of air 

hydraulic diameter of airway 

actual average air density in airway 

reference air density 

Fourier Number 

friction coefficient for rough walls 

friction coefficient for hydraulically sm

weight flow rate of air 

auto compression gradient 

actual fan pressure 

reference fan pressure 

actual pressure loss 

reference pressure loss 

natural ventilation head 

natural ventilation pressure 
Table of Text Nomenclature (continued) 

Text Computer Text 

Symbol Symbol Page 

Dimension 

FNVP 13 in. wg. 

COAGE 38 

LA 12 

NB 14 

NJ 14 

14 

0 12 

13 

12 

Q 

R 

RSTD 

TRD 

TM 

TM 

TMRD 

TMSQR 

TROCK 

lolo in. wg. 

3 (ft /mid 2 

reference natural ventilation pressure 

friction factor 

coefficient of age 

airway length 

number of' airways in network 

number of junctions in network 

number of meshes in network 

airway perimeter 

static air pressure 

actual volume flow rate 

reference volume flow rate 

resistance factor 

reference resistance factor 

hydraulic radius 

absolute air temperature 

temperature of air in airway 

estimated average air temperature in airw

average absolute air temperature in airwa

mean air temperature in airway 

mean square absolute air temperature in a

rock temperature 
Table of Text Nomenclature (continued) 

Text Computer Text 

Symbol Symbol Page Dimension Definition 

TR TR 40 OF reference temperature 

T JS 29 OF 

TRS 29 OF 

TO, T1 21 OR 

air temperature at beginning sf airway 

rock temperature at beginning of airway 

absolute temperatures of starting and fin

of airway 

v 13 ft3/lb specific volume of air 

V 29 ft/sec air velocity 

VISC 40 2 VISC ft /sec kinematic viscosity of air 

WT WT 40 specific weight of air 

quantity ~O/(G*CP) 

. quantity (0.375 + BI) 6 

XNEW XNEW 42 exponent in formula for air temperature in 

Z Z 21 ft elevation 

zsrzf ZO, Zl 21 ft elevations of starting and finishing junc
6. BIBLIOGRAPHY 

1. Amano, K. and Shigeno, S., An underground ventilation network analysis 

and estimation of temperature of air current. A Decade of Digital 

Computing in the Mining Industry. AIME, New York, 1969 

2. Cervik, J., An investigation of the behavior and control of methane 

gas. Min. Congr. Journ. 53 (19671, No. 7, pp. 52/57 

3. Chaiken, R. F. and.Singer, J. M., Experimental coal mine fire research. 

IV International Symposium on Combustion Processes 1975, 

Czestochowa, Poland 

4. Duerr, H. G., The calculation of ventilation and compressed air networks based on energy principles under consideration of thermal 

energies with the help of electronic digital computers. Bergbau 

Wissenschaften 10 (1963) , pp. 73/84 

5. Edwards, J. C., Perlee, H. E., and Chaiken, R. F., Flame spread in a 

duct fire. ASME-AICHE Heat Transfer Conference 1976, St. Louis 

6. Geiger, G. E., Development of an Air quality simulator for coal mines. 

NTIS Pb-213 833, 1972 

7. Greuer, R., Influence of mine fires on the ventilation of underground 

mines. NTIS Pb-225 834, 1973 

8. Hall, C. J., Wang, F. D., and Wang, Y. J., Athermodynamic basedventilation network digital computer program. International Mine 

Ventilation Congress Johannesburg, 1975 

9. Haxtman, H. L., Mine ventilation and air conditioning. The Ronald 

Press Company, New York, 1960 

10. Hitchcock, W. W. and Hoover, T. E., Computer analysis of mine ventilation and environmental control. International Mine Ventilation 

Congress Johannesburg, 1975 

11. Kingery, D. S., Introduction to mine ventilation principles and 

practice. USBM Bulletin 589, 1960 

12. Kissell, F. N., Methane migration characteristics of the Pocahontas 

No. 3 coal bed. USBM Rep. Inv. 7649, 1972 

13. Kreith, F., Principles of heat transfer. International Textbook 

Company, 1965 

14. Maassen, F., Ventilation calculation by digital computer. Bergbau 

Wissenschaften 9 (1962), pp. 179/190 
15. McElroy, G. E. and Kingery, D. S., Making ventilation pressure surveys 

with altimeters. USBM Inform. Circ. 7809, 1957 

16. McPherson, M. J., The simulation of airflow and temperature in the 

stopes of South African gold mines. International Mine Ventilation Congress Johannesburg, 1975 

17. Scerban, A. N. and Kremnev, 0. A,, The scientific basis of calculations and control of climatic conditions in deep mines. A. N. 

Ukrain. RSR, Kiev, 1959 

18. Scott, D. R. and Hinsley, F. B., Ventilation network theory. Colliery 

Engrg. 28 (1951), pp. 67/71, 159/166, 229/235, 497/500 

19. Stefanko, R. and Ramani, R. V., Computerized planning for mine atmospheric environment. International Mine Ventilation Congress 

Johannesburg, 1975 

20. Wang, Y. J. and Saperstein, L. W., A computer-aided solution of 

complex ventilation networks. Transact. Soc . Min . Engrs . AIME 

247 (1970), pp. 238/250 
PROGRAM LISTING 

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8. LIST OF COMPUTER SYMBOLS WHICH ARE EXPLAINED IN TEXT 

Computer Text 

Synbol Page Definition 

A 

AAVR 

AVRCH 4 

AVRPR 

AVTRD 

AX 

CH4C 

CH4CX 

CH4 JS 

CH4PA 

CH4PAX 

CH4V 

CH4VX 

COAGE 

CONC 

CONT 

CONTAM 

CONTQ 

COR 

CRITGS 

CRITHT 

CRITSM 

airway cross sectional area 

average airway cross sectional area 

average methane concentration of unrecirculated air currents enteri

average contaminant concentration of unrecirculated air currents en

average temperature of unrecirculated air currents entering junctio

airway cross sectional area 

methane concentration in junction 

methane concentration in junction 

methane concentration at roadway beginning 

methane volume production rate per ft2 of surface area in airway 

2 methane production rate per ft surface area in airway 

methane volume production rate in airway 

methane production rate in airway 

coefficient of age 

concentration of contaminant in gas inflow 

volume flow rate of contaminated gas inflow 

volume flow rate of contaminant 

volume flow rate of gas inflow carrying the contaminant 

correction of HC for rough walls 

accuracy of methane concentration calculation when recirculation oc

accuracy of temperature calculation when recirculation occurs 

accuracy of contamination calculation when recirculation occurs 
List of Computer Symbols Which Are Explained in Text (continued) 

Computer Text 

Symbol Page Definition 

DNVP 

DPSUM 

DQ 

DQSUM 

DR 

DZRD 

DZRDX 

ESTCH4 

ESTPR 

ESTTR 

FACT 

FANP 

FANQ 

FNVP 

FRNVP 

HA 

HAAVR 

HAX 

HC 

HEAT 

HEATAD 

HK 

HKA 

- - 

difference between natural ventilation pressures in last two iterat

sum of pressure losses around mesh 

CROSS correction per mesh 

sum of DQ for all meshes of network 

reference density 

elevation change in airway 

elevation change in airway 

estimated methane concentration for recirculated air 

estimated contaminant concentration for'recirculated air 

estimated temperature for recirculated air 

factor indicating direction of elevation change 

fan pressure at airflow rate FANQ 

airflow rate passing through fan 

list of natural ventilation pressures in meshes 

product TMRD*DZRD 

thermal diffusivity of rock in airway 

average rock diffusivity 

thermal diffusivity of rock in airway 

convection coefficient 

heat entering airway 

heat addition to air 

thermal conductivity of rock in airway 

thermal conductivity of air 
List of Computer Symbols Which Are Explained in Text (continued) 

Computer Text 

Symbol Page 

Definition 

HKAVR 26 average rock thermal conductivity 

HKX 27 thermal conductivity of rock in airway 

HSU 47 sum of quantities FRMVP 

HTP02 

ICFTM 

INFLOW 

INU 

ISTART 

IT 

ITCT 

ITN 

JF 

JLR 

JS 

JSTART 

JNO 

JNOL 

JNOX 

KF 

KFAVR 

KNO 

KX 

3 heat production per ft of oxygen delivery 

marker 

number of contamination cards 

auxiliary list for forming base system 

index of JSTART in JNO-list 

iteration counter 

iteration counter 

maximal number of iterations in network and concentration calculatio

junction number of airway end 

list relating JNO- and JNOL-lists 

junction number of airway beginning 

number of junction from where concentration calculation shall start 

junction number 

list of junction numbers in increasing order 

junction number 

friction factor 

average friction number 

list of airways in base system 

friction factor 
List of Computer Symbols Which Are Explained in Text (continued) 

Computer Text 

Symbol Page Definition 

LA 

LAAVR 

LOUT 

LX 

MADJ 

MAD JC 

MARKC 

MARKN 

MAX J 

MEMREC 

MEND 

MIN 

MPTS 

MSL 

MSTART 

NADBC 

NAV 

NB 

NCENT 

NCH4C 

NCONC 

NDIM 

NETW 

- - - - - - - - -- - - -- 

airway length 

average airway length 

list of last airway per junction in NGOUT-list 

airway length 

maximal number of network calculations in one program run 

iteration counter 

marker 

marker 

highest junction number 

temporary list of airways carrying recirculated air 

list of mesh ends in MSL-list 

list of last airway per junction in NGIN-list 

number of points used to define fan characteristics 

list of all independent meshes 

index of JSTART in JNOL-list 

number of additional airway cards 

marker for presence of average value card 

number of airways in network 

number of airways into which contaminants enter 

additional number of concentration junction cards 

marker for desired concentration calculation 

additional number of concentration airway cards 

marker for desired network calculation 
List of Computer Symbols Which Are Explained in Text (continued) 

Computer Text 

Symbol Page Definition 

NFNUM 

NFREG 

NGIN 

NGOUT 

NJ 

NO 

NOF 

NOREC 

NOX 

NOX 

NNVP 

NRCT 

NREC 

NREV 

NSFLOW 

NSNVP 

NSW 

NTEMP 

NVPN 

NWTYP 

0 

OAVR 

ONVP 

number of fan characteristics to be read into computer 

list of fans with characteristic 

list of airways entering junction 

list of airways leaving junction 

number of junctions in network 

airway number 

airway number of fan 

permanent list of airways carrying recirculated air 

airway number 

airway number 

marker 

number of airways with airflow reversal 

marker 

list of airways with airflow reversal 

marker 

marker 

marker 

marker for desired temperature calculation 

marker for presence of junction cards 

airway type 

airway perimeter 

average airway perimeter 

natural ventilation pressure in last iteration 
List of Computer Symbols Which Are Explained in Text (continued) 

Computer Text 

Symbol Page Definition 

02MIN 

OX 

P 

PF 

PR 

PRCH4 

PROP 

PROP JS 

Q 

QF 

QIN 

QREC 

R 

RDCH4 

RDPROP 

RGRAD 

RN 

RSTD 

SMPO2 

SRCH4 

SRPR 

STRD 

SUMAIR 

oxygen concentration of fumes leaving fire zone 

airway perimeter 

calculated pressure losses and fan pressures 

fan pressure at given point of fan characteristic 

Prandtl number 

methane concentration in junction 

contaminant concentration in junction 

contaminant concentration at roadway beginning 

airflow rate 

airflow rate at given point of fan characteristic 

suna of unrecirculated airflow rates entering junction 

recirculated air entering junction 

resistance factor of airway 

methane concentration at roadway ends 

contaminant concentration at roadway ends 

slope of fan characteristic 

Reynolds number 

resistance factor based on reference temperature TR 

contaminant production per f t3 of oxygen delivery 

sum of methane concentrations of unrecirculated airflows entering ju

sum of unrecirculated contaminant flow rates entering junction 

sum of temperatures of unrecirculated airflows entering junction 

total airflow rate entering junction 
~ist of Computer Symbols Which Are Explained in Text (continued) 

Computer Text 

Symbol Page Definition 

total methane flow rate entering junction 

SUMHT total enthalpy/reference density entering junction 

total contaminant flow rate entering junction 

temperature of air in junction 

SUMPR 

T 

TFSI 

TIME ' 

T JS 

TM 

TMRD 

air temperature behind heat source 

time since beginning of contamination 

temperature at roadway beginning 

estimated average air temperature 

mean temperature of air in airway 

TMSQR 

T1 

TR 

TRD 

TROCK 

mean square absolute temperature 

air temperature at beginning of airway 

reference temperature 

temperature at roadway end 

average rock temperature in airway 

TROCKX average rock temperature in airway 

temperature in JSTART TSTART 

TSU 

WRNGS 

WRNHT 

sum of absolute quantities FRNVP (in concentration part of program) 

threshold value for critical methane concentration 

threshold value for critical temperature 

threshold value for critical pressure loss 

threshold value for critical contamination 

exponent in formula for calculation of temperatures in roadways 

WRNPR 

WRNSM 

XNEW 

9. LIST OF ADDITIONAL COMPUTER SYMBOLS NOT QUOTED IN TEXT 

(This list does not contain some temporary used indices and counters whose mea

and function, when reading the program, can be easily recognized) 

Computer Symbol Definition 

ADDT intermediate quantity for calculation of COAGE 

BI Biot number 

CH4S, CH4F methane concentrations in starting and finishing junctions of airw

CP 

DIFCH4 

DIFTRD 

ES ,EF 

FO 

FRO 

FX 

KJF 

KJS 

MARKD 

MBEGW 

specific heat of air 

difference in last two iterations for methane concentration 

difference in last two iterations for air temperatures 

elevations of starting and finishing junctions of airway 

Fourier number 

coefficient of friction for hydraulically smooth walls 

intermediate quantity for calculation of COAGE 

temporary list for assembling base system 

temporary list for assembling base system 

marker 

first airway in mesh 

MENDW last airway in mesh 

MESC mesh counter 

MNO number of meshes in network 

NBL counter 
List of Additional Computer Symbols Not Quoted in Text (continued) 

Computer Symbol Definition 

NBU 

NFCW 

NRETU 

POT 

OLADDT 

QBL 

QBR 

RQ 

RQSUM 

SUMT 

TO, T1 

TOLD 

TRS , TRF 

TSU 

VART 

VISC 

WT 

X 

counter 

list of fans whose characteristic is exceeded 

marker 

exponent for COR 

intermediate quantity for calculation of COAGE 

lowest airflow rate used of fan characteristic 

highest airflow rate used of fan characteristic 

product R*Q 

sum of all products 2*R*Q 

intermediate quantity for calculation of COAGE 

absolute temperatures of starting and finishing junctions of airway 

part of program) 

last calculated temperature at airway end 

temperatures of starting and finishing junctions of airways 

sum of absolute temperatures of all junctions in mesh (used in netw

progrm) 

content of square root for calculating temperature behind a heat so

kinematic viscosity of air 

specific weight of air 

quantity aO/ (G*cP)