U.S. BUREAU OF MINES 

TRAINING WORKSHOP 

ON THE 

"MFIRE" MINE FIRE AND VENTILATION SIMULATOR 

MFIRE USERS MANUAL 

VERSION 2.20 

AUGUST 1995

U. S. Bureau of Mines 

Twin Cities Research Center 

Minneapolis, MN
U.S. BUREAU OF MINES TRAINING WORKSHOP 

ON THE 

"MFIRE" MINE FIRE AND VENTILATION SIMULATOR 

MFIRE USERS MANUAL 

VERSION 2.20 

AUGUST 1995 

By Linneas W. Laage1, Rudolf E. Greuer2, and William H. Pomroy3

1

Mining Engineer, Twin Cities Research Center, Bureau of Mines, 

Minneapolis, MN. 

2

Mining Engineer, Twin Cities Research Center, Bureau of Mines, 

Minneapolis, MN; and Professor of Mining Engineering, Michigan 

Technological Univ., Houghton, MI. 

3

Group Supervisor, Twin Cities Research Center, Bureau of Mines, 

Minneapolis, MN. 

 ACKNOWLEDGEMENT 

The technical assistance of Dr. Xintan Chang in the development 

of the MFIRE code and the preparation of this manual is 

greatfully acknowledged. Dr. Chang is currently Professor of 

Mining Engineering, Xian Mining Institute, Xian, Shaanxi, The 

Peoples Republic of China. 
 DISCLAIMER 

The Bureau of Mines expressly declares that there are no 

warranties express or implied which apply to the software 

contained herein. By acceptance and use of said software which is 

conveyed to the user without consideration by the Bureau of 

Mines, the user hereof expressly waives any and all claims for 

damage and/or suits for or by reason of personal injury, or 

property damage, including special, consequential or other 

similar damages arising out of or in any way connected with the 

use of the software contained herein. 
MFIRE USERS MANUAL 

 VERSION 2.20 

 CONTENTS 

1.0 INTRODUCTION................................................6 

2.0 DEVELOPMENT OF MFIRE........................................7 

2.1 HISTORY OF MINE VENTILATION MODELING...................8 

2.2 DESIGN OF MFIRE ......................................12 

2.3 MASS BASED FLOW RATES.................................13 

2.4 TRANSIENT STATE CONCENTRATION SIMULATION..............13 

2.5 STEADY STATE FIRE DISTURBANCE SIMULATION..............15 

2.6 TRANSIENT STATE SIMULATION OF FIRES AND VENTILATION 

SYSTEMS..............................................18 

2.7 CONSIDERATION OF WATER VAPOR..........................20 

2.8 MFIRE PERFORMANCE.....................................23 

3.0 USER SELECTED REFERENCE DENSITY AND TEMPERATURES...........25 

3.1 THEORY OF REFERENCE DENSITY...........................25 

3.11 AIRFLOW IN MINE PASSAGES........................27 

3.12 Pressure PRODUCTION OF FANS.....................29 

3.2 MFIRE INPUT...........................................33 

3.21 MFIRE CONVERSION RULES..........................34 

4.0 PROGRAM INSTALLATION AND OPERATION.........................35 

4.1 CHANGES IN MFIRE 2.20 FROM PREVIOUS VERSIONS..........36 

5.0 INPUT DATA FILES...........................................37 

5.1 GENERAL STRUCTURE OF DATA FILE........................37 

5.2 DATA FORMAT...........................................38 

5.3 CHANGES IN MFIRE 2.20 DATA FILE FROM PREVIOUS VERSIONS38 

5.4 DETAILED DESCRIPTION OF DATA INPUT REQUIREMENTS.......39 

6.0 OUTPUT FILES...............................................51 

6.1 CONTENTS OF THE OUTPUT FILE...........................51 

7.0 MFIRE ERRORS..............................................52 

7.1 DATA FILE ERRORS......................................52 

7.2 PROGRAM ERROR DETECTION...............................52 

7.3 LOCATING ERRORS.......................................53 

8.0 MODELING FIRES.............................................54 

8.1 General Information and Basic Assumptions.............54 

8.2 Fixed Heat Input Fire.................................55 

8.3 Oxygen Rich and Fuel Rich Fires.......................55 

8.4 Oxygen Rich Fire......................................55 

8.5 Fuel Rich Fire........................................56 

8.6 Estimating Fire Parameters............................57 

8.7 Heat Release Rate and Burning Rate....................58 

8.8 Complex Assemblies and Multiple Fuels.................58 

8.9 Ventilation Velocity Effects..........................59 

8.10 Heating Values of Fuels..............................60 

8.11 Fume Production......................................60 
8.12 Fire Modeling Examples...............................61 

Example 1............................................62 

Example 2............................................63 

Example 3............................................64 

Example 4............................................65 

Example 5............................................66 

Example 6............................................67 

Example 7............................................68 

9.0 MFIRE APPLICATION EXAMPLES.................................70 

9.1 Multi-Level Mine Example .............................70 

9.2 Single-Level Mine Examples............................77 

REFERENCES.....................................................92 

APPENDIX 1 INPUT PARAMETER TABLES...........................94 

TABLE 1 - HEATING VALUES OF MINE COMBUSTIBLES.............95 

TABLE 2 - CO2 AND CO PRODUCTION CONSTANTS (ß VALUES) ......96 

TABLE 3 - RELATIONSHIPS OF BASIC FIRE PARAMETERS..........97 

TABLE 4 - ßCO2 AND ßCO PRODUCTION CONSTANT UNIT CONVERSIONS .98 

TABLE 5 FRICTION FACTORS................................99 

TABLE 6 THERMAL PROPERTIES OF ROCK.....................100 

APPENDIX 2 INPUT DATA FILE TEMPLATE.........................101 

APPENDIX 3 PROGRAM LISTING OF MFIRE VARIABLES................106 

APPENDIX 4 ADDITIONAL INFORMATION SOURCES...................110 

7 

 1.0 INTRODUCTION 

MFIRE is a computer simulation program that performs normal 

ventilation network planning calculations, and dynamic transient 

state simulation of ventilation networks under a variety of 

conditions. The program is useful for the analysis of ventilation 

networks under thermal and mechanical influence. MFIRE simulates a 

mine's ventilation system and its response to altered ventilation 

parameters, external influences such as temperatures, and internal 

influences such as fires. Extensive output enables detailed 

quantitative analysis of the effects of the proposed alteration to 

the ventilation system 

Network simulation using digital computers has become widespread 

throughout the mining industry in recent years. However, as the 

sophistication of the simulator increases (MFIRE, for example), the 

complexity of input data requirements and interpretations of 

results requires more skill and knowledge from the users. Perhaps 

the most difficult part of using MFIRE is to construct the data set 

describing the mine's physical layout and its ventilation 

properties. The initial attempts to get the data set running often 

reveal unknown or ignored aspects of the mine's ventilation. 

MFIRE was written in Fortran 77 and compiled with Microway1

 Fortran 

for the Intel 80386 based computers with a 80387 math co-processor. 

The source code is portable and available for users who wish to 

modify the source code to operate on other computers. 

This user manual describes the development of MFIRE, the input 

format and requirements, the output, common errors, fire 

parameters, and examples MFIRE application. Valuable reference 

material is included in the appendices. Knowledgeable users may 

skip directly to the PROGRAM INSTALLATION AND OPERATION section to 

begin using MFIRE immediately. 

----------------------------------------------------------------- 

1

Reference to specific products does not imply endorsement by the 

Bureau of Mines. 

----------------------------------------------------------------- 
8 

2.0 DEVELOPMENT OF MFIRE 

Mine ventilation control and mine fire detection and fighting are 

inseparable. Mine fires produce gases and heat, which the 

ventilation systems transport through the mines. These gases can 

be poisonous and/or explosive. The heat can cause ventilation 

disturbances, which take the gases along unexpected routes or 

affect the formation of explosive methane mixtures. 

The calculation of the airflow distribution in mine ventilation 

systems as a result of fans, thermal forces, and flow resistances 

is a formidable mathematical problem. It comprises the solution of 

twice as many equations as there are airways; half of these 

equations are quadratic equations. This sort of problem led to the 

design of special analog computers in the 1950's and 60's and, from 

the early 1960's on, to the increasing use of electronic digital 

computers. With the rapidly increasing availability and capacity 

of digital computers, airflow rate and pressure loss distribution 

calculations, commonly called ventilation network calculations, 

have become routine, and a great number of computer programs exist 

for this purpose. Practically all the programs are capable of 

performing the required calculations, although differences exist in 

how the square equations are linearized, the mass conservation law 

is introduced and observed, the fan characteristics are simulated, 

and the thermal drafts are considered. All of the programs were 

based on steady-state conditions. 

Of greatest concern in the past were the fire-generated ventilation 

disturbances. Ventilation engineers developed a large number of 

methods, by manual calculation, to detect potentially unstable 

airways with airflow reversals in case of a fire. When the analog 

and digital computers became available for ventilation planning, 

they were almost immediately applied to this problem. The expected 

fire-generated ventilating pressures were manually inserted into 

the network simulations, with their values usually obtained from 

experience or from rough calculations. The mutual influence of 

fire intensities and ventilation conditions were not taken into 

account. If gas concentrations were calculated at all, they were 

only calculated for the cases where no recirculation existed. All 

calculations were, as in conventional network calculations, based 

on steady-state conditions or based on the assumption that no 

changes with time occur. 

The U.S. Bureau of Mines and Michigan Technological University 

first solved this problem with steady-state analysis, and the 

resulting program became known as the MTU/BOM code. Because the 

mine fire process is dynamic in nature, work on the transient-state 

modeling problem continued with the resulting program, MFIRE, which 

accommodates dynamic state modeling of the fire. 
9 

MFIRE version 2.20 includes: calculations based on mass flow 

rates, natural ventilation, spline or least squares fan curve 

fitting and boundry fixing, air reversal and recirculation 

calculations. Condensation and evaporation in the mass flow and 

heat exchange calculations was removed from MFIRE 2.20 but will be 

incorporated in a later version. The program is useful for the 

analysis of ventilation networks under the influence of natural 

ventilation, fans, fires, or any combination of these. MFIRE 

simulates a mine's ventilation system and its response to altered 

ventilation parameters such as the development of new mine workings 

or changes in ventilation control structures, external influences, 

and internal influences. Extensive output enables detailed, 

quantitative analysis which the alteration will cause in the 

ventilation system. 

This chapter reviews the evolution of the MFIRE program from its 

infancy as a simple digital network simulator that replaced analog 

computers to the present version. Landmark features and modeling 

improvements are discussed. 

2.1 HISTORY OF MINE VENTILATION MODELING 

Ventilation network calculations have been performed for several 

centuries. Due to mathematical difficulties caused by diagonal 

airways, the preferred method of practitioners was a trial and 

error approach in which junction and mesh equations were made 

compatible. Since the beginning of this century, airflow and 

pressure loss distributions in a large number of more frequently 

occurring subnetworks were analytically and graphically determined. 

 These were the subjects of numerous publications and were of 

considerable help to practitioners. 

Trial and error methods, which can be surprisingly efficient in one 

case, can become frustratingly inefficient in another. A large 

number of methods of successive approximation were consequently 

developed. Atkinson's solution in 1854 for a single diagonal 

airway and Cross's method because of its general applicability and 

simplicity became the widest known examples. Some of these methods 

were based on the linearization of the quadratic resistance 

equation and used in electric analog computers. Practically all of 

the methods were tested for their utility with digital computers 

when these became available. 

The forerunners of analog computers were fluid flow models. They 

were used in several countries but never found wide application. 

The similarity between node and mesh equations in ventilation 

networks with Kirchoff's laws of electrical networks made the 

electrical models persuasive. The first patent for an electric 

analog computer for water and gas networks was awarded in 1941 in 

Germany. This computer used filament bulb resistance to model the 

second power resistance function in the network calculations. 
10 

The idea was taken up or independently discovered in several 

countries, but the limited working range of commercially-available 

filament bulbs made them inflexible and the number installed 

remained small. Development of a specially- constructed low 

voltage lamp in the United States overcame this obstacle and in 

1954 a "network analyzer" was installed at the U.S. Bureau of 

Mines, after six earlier installations had shown their usefulness 

with waterworks (McElroy, 1954). 

In 1951-52, the University of Nottingham (UK) pioneered the idea to 

combine an electrical network simulation of the nodes and mesh 

equations of ventilation networks with a manual approximation 

method for the resistance equation. This led to the design of the 

commercially available "National Coal Board Network Analyzer", 

which found a wide distribution. Home-built models and 

modifications, using different approximation methods for the 

resistance equation, were used in almost all mining countries. At 

some places ancillaries for adjustment steps without calculations 

were introduced. 

An electromechanical analog computer, in which the approximation of 

the resistance equation was automatically performed, was first 

developed in 1950 at a German coal mine. It became commercially 

available in 1952. Thirteen of these computers were installed in 

German coal mines and a larger number were installed abroad and for 

gas and water companies. In 1959, electronic function generators 

for the simulation of the resistance equation were introduced in 

Japan; in 1960 the German manufacturer adopted this principle, 

also. In 1964, a British model became commercially available and 

may be the only one still on the market. In 1962, the French coal 

mines built an electronic model which has been used for several 

decades. 

Fully-automatic analog computers for ventilation network 

calculations are excellent planning tools. Their handicap is that 

they are single purpose machines. All-purpose digital computers 

became commercially available in the late 1950's and predictably 

replaced the majority of the analog computers. 

The literature reports that the first network calculations with 

digital computers were performed for waterworks in the United 

States in 1957. The first digital ventilation network calculations 

were reported in Belgium in 1958 and in Germany in 1959. Following 

the lead of gas and water companies, efforts to replace the 

expensive analog computers with digital computers began in Germany 

in 1958. The replacement progressed quite rapidly since many of 

the analog computer users were cooperating with this effort. The 

literature reports that the same coal company which had pioneered 

the use of electromechanical analog computers performed almost all 

of their network calculations on digital computers by the end of 

1959. 
11 

By the end of 1969 the majority of analog computer users, 

representing 80 pct of the German coal production, had switched to 

digital computers. 

Since the first attempts with the Cross method of balancing 

pressure losses gave poor convergence most other known 

approximation methods were initially attempted. These were dropped 

when it was found that assembling meshes in such a way that airways 

with high resistance factors or, even better, with high products of 

airflow rates and resistance factors, occurred in as few meshes as 

possible overcame the convergence problem. The mesh assembly was 

done in a systematic way by arranging a tree in a sequence from 

tree tip to root, which allows the computer to elect correct 

movements when assembling the meshes. 

From 1961 on, it became customary to include natural ventilation 

obtained from information on temperatures and elevations in every 

mesh. Fixed quantity airways had always been a feature of analog 

computers and were included in the earliest applications of digital 

computers. Fan characteristics were treated in different ways as 

storage allowed. A FORTRAN version of a type of standard program 

became a part of the IBM program library in 1966; in 1967 it was 

adopted by the British National Coal Board for ventilation planning 

purposes at its divisional computer centers. It has been used for 

instructional purposes at Michigan Technological University (MTU) 

since 1967. Although many enhancements and attempts at 

improvements were made, it is basically still in its original form 

and is the core of the MFIRE program. 

As the availability of digital computers increased, the number of 

users doing creative work in ventilation planning increased 

tremendously. Due to personal, societal, or company restraints, 

much work went unreported. However, by analyzing available 

published literature, it is clear that continental European 

ventilation engineers cooperated closely. An advanced program 

capable of performing high speed calculations for large networks 

was in use in France in 1961. A storage saving program based on 

the Cross method of flow rate balancing was introduced in 1967. In 

Japan network calculations with digital computers started in 1961. 

 Convergence-improving mesh assemblies were reported in 1969. In 

Russia, first attempts with digital computers were made in 1963. 

In 1965 and 1967, reports on different approximation methods were 

published. In Great Britain, the first network calculations with 

the meshes assembled manually were reported in 1964. A program 

with automatic mesh assembly was described in 1965. In the United 

States, the first program to prove the usefulness of digital 

computers was described in 1963; an improved version allowing the 

inclusion of fan characteristics was reported in 1964. Both 

programs still required the manual assembly of meshes. 
12 

In 1967, a much more sophisticated program with mesh assembly and 

assignment of initial airflow rates performed by the computer was 

reported and in 1970 a new version of the program which 

accommodated fixed quantity airways was described. 

Over the past two decades efforts focussed on: (1) replacing the 

Cross method with more efficient approximation methods, (2) 

combining network calculation for optimization purposes with 

operations research approaches, (3) making the programs more user 

friendly in particular by using interactive graphics, (4) combining 

network calculations with temperature and concentration 

calculations, and (5) extending network calculations to transient 

state conditions. 

The first objective has been a continual goal since the first days 

of digital computer use. So far, all results seem to confirm that 

the Cross method for networks of ordinary size and complexity is as 

good or better than other methods. The second objective is a very 

valid one since network calculations are only a means to an end. 

The third objective is probably the most important one. 

The non-steady-state behavior of ventilation systems has attracted 

research in connection with control problems since the 1950's. 

Studies concentrated upon the effects of explosions, gas outbursts, 

and other mechanical disturbances. A publication describing the 

use of digital computers for this purpose originated in Poland in 

1972 and another one using analog computers was published in 

Yugoslavia in 1984. 

Efforts to combine ventilation network calculations with the 

precalculation of temperatures and humidities started in Japan in 

1969. An early program which included temperatures, humidity, 

methane and dust concentrations, plus a transient state methane 

simulator originated at the University of Pittsburgh in 1972. In 

1975, at the First International Mine Ventilation Congress, reports 

on four programs from the United States and Great Britain for 

combined network, temperatures and humidity calculations were 

given. At the Third Congress in 1984, a program for temperature, 

humidity, and radon concentrations was introduced from Australia. 

Litigation connected with the Sunshine mine fire in the mid-1970's 

showed that existing programs could only partially simulate the 

interaction of mine fires and ventilation systems. Although manual 

non-steady-state temperature precalculations had become a common 

feature and steady-state fume concentrations were easy to add as 

long as no recirculation occurred, manual insertions of thermal 

draft, and throttling effects proved to be cumbersome and the 

handling of recirculation to be impossible. 
13 

This led to the development of a new program at MTU in 1975 and 

1976. The goals of this program were to determine the equilibrium 

between fires and ventilation systems in steady- state conditions 

at any given time. The crucial heat exchange between rock and air 

were calculated under non-steady-state conditions. The program was 

based on mass flow rates and considered natural ventilation in all 

meshes and throttling effects in all airways. Airflow reversal and 

fume recirculation were also calculated. This program, sometimes 

referred to as the MTU/BOM code, was the first building block of 

MFIRE. 

2.2 DESIGN OF MFIRE 

The potential for ventilation disturbances caused by fires has 

always been a great concern in fire emergency planning. Where mine 

workings extend over large elevation differences and where the 

ventilation is weak, such disturbances have been the cause of large 

mine disasters. The 1928 mine fire at Roch-la-Moliere (France), 

which killed 48 miners, is a classic and often-quoted example. The 

first computer simulator (Greuer, 1977) for the interaction of mine 

fires and mine ventilation systems focused, therefore, on the 

assessment of these disturbances. 

This MTU/BOM code made use of the existing programs for ventilation 

network calculations. Steady-state conditions for the ventilation 

as well as for the fire were assumed. The resulting program 

featured mass-based flow rates and transient state temperature 

simulation. The program was useful and became popular because of 

its simplicity. These features became part of the more advanced 

transient-state computer model, MFIRE. 

The program was written for routine applications by practical 

ventilation engineers but without violating physical laws or 

simplifying facts of practical importance. The amount of necessary 

input data has been kept small and checks are performed for their 

completeness and for such errors as occur most frequently. Where 

they do not influence the results significantly, user-stated 

average values can be used to reduce the input. 

The output provides a listing of airflow rates and pressure losses 

in airways, methane and contaminant concentrations, and 

temperatures at airway ends. Concentrations and temperatures are 

also listed for junctions. Recirculation paths and airways with 

airflow reversals, as well as airways and junctions with critical 

conditions, are additionally listed to alert the user to potential 

danger zones. 
14 

2.3 MASS BASED FLOW RATES 

Performing network calculations based on actual volume flow rates 

makes difficult the consideration of the law of conservation of 

mass. Thus, to minimize computational effort, most computer 

programs simplify the problem by assuming a "law of volume 

conservation" instead. Although this assumption normally does not 

lead to gross inaccuracies, serious errors are introduced when 

larger density changes occur, such as in a mine fire. 

The user is allowed to specify a reference air density and 

corresponding temperature. These serve as a scale against which 

other densities, expressed by their temperatures, are measured. 

All input and output are converted to the reference state defined 

by the reference density and temperature. In order to avoid output 

conversion and to obtain values which come close to the actual, 

density dependent, pressure losses, fan pressures, and volume flow 

rates, a reference density which is close to the prevailing actual 

density should be used. 

2.4 TRANSIENT STATE CONCENTRATION SIMULATION 

The assumption of steady-state conditions may be good enough for 

the determination of airflow rate and temperature distributions, 

because airflow rate changes are caused by temperature changes, and 

temperature changes are observed in the immediate vicinity of the 

fire only. Investigations showed that ventilation disturbances 

caused by thermal forces create negligible inertia forces. The 

airflow assumes steady-state conditions in a very short time as 

pressure differences propagate at the speed of sound. Changed 

airflow rate and temperature distributions are, therefore, reached 

almost instantaneously and time is a minor factor. 

Time is definitely an important factor with concentration 

distributions. Gases travel with the ventilation currents, which 

normally means speeds of less than 3 to 4 km/h. Many airways 

downwind of a fire can, for a considerable time after the start of 

the fire, remain clear of gases. In many cases, the increase of 

airway gas concentration happens only gradually before steady-state 

conditions are reached. Assuming steady-state concentration 

distributions in fire emergency planning frequently means 

needlessly excluding airways as escapeways, although they are 

perfectly safe for a long time. 

The simulation of concentration distributions does not involve 

physical principles other than the law of mass conservation. 

Additionally, the assumptions are made that perfect mixing of air 

currents occurs in nodes, no longitudinal diffusion in airways 

exists, and flow velocities in planes perpendicular to flow 

directions are equal. 
15 

In the resulting programs (Bastow, 1979 and Greuer, 1981), mine 

atmosphere is divided into control volumes of homogeneous 

concentrations, which advance with the flow through the ventilation 

system. When control volumes meet at airway junctions, they are 

combined to form new control volumes. Because many junctions can 

be reached via different paths with different amounts of dilution 

having occurred, the number of control volumes can become quite 

large, depending on the type of ventilation system. When 

recirculation occurs, the number can virtually become infinite with 

smaller and smaller concentration differences between the newlyformed control volumes. 

The problem of this simulation is not one of mathematics but of 

sorting. All control volumes that arrive at a junction have to be 

detected, and the sequence of their arrival has to be determined. 

The new control volumes, which are generated in the junctions, have 

to be advanced into the outgoing airways together with checks to 

see if they affect any other junctions. If they do, part of the 

computations have to be repeated. 

The main difficulty in writing this program was, therefore, not one 

of mathematics but one of keeping the computing time within 

tolerable limits. Experience showed that the choice of the time 

increment in which the control volumes are advanced is of great 

importance. If the increment is too large, control volumes may 

have to be passed through more than one junction, which lengthens 

and complicates calculations. If the increment is too short, a 

large number of advancements has to be performed. The solution was 

to let the program select the optimal length of the time interval 

as a function of the network type. 

Variations of the program accommodated the exposure simulation of 

escaping miners in 1983 (Greuer, 1983), the simulation of escape 

movements of miners, based on warning times and travel speeds in 

1983, (Greuer, 1983), and simulation of mobile contaminant sources 

in 1984 (Sheng, 1984). 

This program is based on the assumption of constant airflow rates. 

 These can be the airflow rates prevailing in the early stages of a 

fire or the airflow rates resulting from the equilibrium of firegenerated (thermal) and other (fan, airway resistances) ventilating 

forces. In the first case, very little input data and expertise on 

the part of the program user are required. The only ventilation 

information needed is data on the network configuration (airway and 

node identification numbers), airflow rates, and airway lengths and 

cross-sectional areas. The program was useful where fire-generated 

ventilation disturbances had not yet occurred, in particular for 

the layout of fire detection systems. It would also be helpful for 

the design of fire escape plans if an early fire warning system 

allowed for the evacuation of the mine before the fire progressed 

beyond its initial stage. 
16 

In the second case, considering fire disturbances, the 

determination of the airflow rates has to precede the concentration 

calculations. This requires detailed information on the 

ventilation system and some ventilation expertise by the program 

user. 

2.5 STEADY STATE FIRE DISTURBANCE SIMULATION 

If the terminology of ventilation engineers is used, one can say 

that fires have two effects on ventilation systems: a throttling 

effect caused by the volume increase of the air passing through the 

fire zone, and a natural draft effect caused by the conversion of 

heat into mechanical energy. 

The throttling effect is easy to assess. The energy requirement 

per unit mass to overcome friction losses is proportional to the 

square of the flow velocity. The latter is in turn proportional to 

the specific volume or the absolute temperature. The energy 

requirements to transport air through an airway are, therefore, 

proportional to the square of the absolute temperature. If a fire 

causes the temperature increase, the same amount of energy will 

transport less air. 

Natural draft effects, or the conversion of heat into mechanical 

energy, can occur where the air changes its pressure and its 

specific volume when it goes through a cyclic process. Every loop 

of the ventilation system can be considered a cyclic process and 

can, therefore, develop natural draft effects. The amount of heat 

converted into mechanical energy is, according to the first law of 

thermodynamics, equal to the integral of the product of specific 

volume times pressure change. 

The determination of numerical values of this integral is 

cumbersome because of the continual pressure changes in ventilation 

systems and owing to the fact that the specific volume cannot be 

directly measured. A good approximation is possible in most cases 

by establishing a functional relationship between this integral and 

an analogous integral of the product of temperature times elevation 

change, which is easier to determine. 

Precalculations of the throttling and natural draft effect require, 

therefore, the precalculation of temperatures. These are functions 

of the airflow distribution, which determines the oxygen supply to 

the fire, the heat transfer to the airway walls, and the mixing of 

air currents in junctions. The airflow distribution, on the other 

hand, is a function of the temperature-induced throttling and 

natural draft effects. It was this interaction between fires and 

ventilation systems, together with the occurrence of recirculation, 

which for many years was considered to be too complicated for 

computer simulations. 
17 

The MTU/BOM code combines conventional network (airflow rate, 

pressure loss) calculations with concentration and temperature 

calculations and automatically accounts for the throttling and 

natural draft effects. It converges to establish the equilibrium 

at which fire-generated thermal forces (throttling and natural 

draft) are balanced by the other ventilation forces (fans and 

resistances). 

The beginning of the code is a network calculation for the pre-fire 

state, to ascertain that the input data are correct. Based on the 

type of fuel, fuel loading, and air supply, the heat and 

contaminant production is calculated next. This is followed by a 

calculation of the temperature and concentration distribution, 

based on the original airflow rates. The fire-generated thermal 

forces (throttling and natural draft effects) are then determined 

and inserted into a new network calculation. This sequence of 

calculations is repeated until the calculated thermal forces remain 

constant. This means that equilibrium has been found and, 

temporarily, steady-state conditions for the airflow rate, pressure 

loss, and temperature distribution have been established. 

This approach can be justified because changes of the temperature 

distribution are observed only in the vicinity of the fire and 

short distances downwind from it. Fire-caused thermal forces are, 

therefore, generated almost instantaneously, and changed airflow 

rate and temperature distributions also establish themselves almost 

instantaneously. This does not apply to the concentration 

distributions, however, and, only in rare cases, to fire 

intensities. Even if the fire intensity does not change, the 

temperature distribution will change with time, since the airway 

walls will be heated and provide less cooling. This is taken into 

account by considering the transient-state nature of the heat 

transfer, although with the simplifying assumption that the 

equilibrium airflow did prevail from the very beginning of the 

fire. 

The MTU/BOM code was divided into two main parts: network and 

concentration/temperature. To make the program as flexible as 

possible, network, temperature, and concentration calculations can 

be performed separately or combined. Methane concentrations are, 

however, always determined when a change in the airflow 

distribution takes place, since this is indispensable for coal 

mines. 

The network part basically contains the previous network simulator 

and performs airflow rate and pressure-loss calculations. The 

program uses the Hardy Cross method, since studies, which were 

recently updated by a variety of investigators, showed that for 

networks of the size of mine ventilation systems, this method still 

gives the shortest calculating times when accompanied by a 

convergency promoting method of mesh selection. 
18 

This can be done by letting airways with large products of airway 

resistances and airflow rates appear in as few meshes as possible. 

 The pertinent mesh assembly process occupies a large portion of 

the program but its computer execution is superior to most other 

mesh-assembly programs. 

So-called fixed quantity airways or regulators, which maintain a 

constant airflow rate and which are a valuable planning aid, have 

to be converted into regular airways if more than a conventional 

network calculation is demanded. In case of an emergency, there 

will be no time to pay attention to the adjustment of regulators 

that keep the airflow rate constant. 

Concentration and temperature calculations are performed jointly in 

the second program part because they have many common features. 

One can think of heat as being a contaminant, also, and temperature 

changes caused by heat influx or by mixing airflows are calculated 

in the same way as concentration changes. 

Concentration and temperature changes in roadways can be caused by 

entering methane, by fire-produced contaminants and heat, and by 

heat entering or leaving the airway. In junctions, they can occur 

because of mixing of air currents with different concentrations and 

temperatures. Both processes are fundamentally different, and two 

separate program sections have been provided. 

The calculations start at a node with known temperatures and 

concentrations. Normally this will be the surface or someplace in 

the intake airways. With the conditions at their beginnings thus 

known, roadway calculations are conducted for all airways leaving 

this node. Next, a check for junctions where the conditions of all 

entering airways are known is performed. If found, the entering 

air currents are mixed and roadway calculations are performed for 

all airways leaving this junction. 

This process is interrupted when recirculated air enters a 

junction. In this case, the alternating airway and junction 

calculations cannot be continued since concentrations and 

temperatures of the recirculated entering air are not known. The 

difficulty is overcome by using an iteration method. Starting out 

with estimated values for the properties of the recirculated air, 

the roadway and junction calculations are continued as if they were 

known. With this assumption, the values, which are then obtained 

for the recirculated air by the successive roadway and junction 

calculations, are next used as new, better estimates. The process 

is repeated until estimated and calculated values agree. Airways 

with recirculation are placed in a special list in the output to 

draw attention to the fact that they carry potentially contaminated 

air into intake airways. It is surprising to note how much 

recirculation can exist in many mines without being recognized. 
19 

Heat and combustion products developed by fires can either be 

estimated by the user or can be determined by the program as 

functions of the oxygen supply of the fire. The heat exchange with 

the airway walls is calculated with the help of Fourier's equation 

of thermal conduction, for which solutions have been built into the 

program. 

A crucial role in these calculations is played by the rock 

temperature, which is a function of virgin rock temperature and the 

airway history. It is possible, in principle, to determine the 

temperature distribution in the rock and to provide an accurate 

solution to Fourier's equation, if the airway history is known. 

Normally, this will not be the case. 

Because fire emergency plans deal with short time spans, as 

compared to the age of the airway at least, and since only thin 

layers of rock surrounding the airways are affected by the 

temperature changes, it seems to be accurate enough to work with 

effective rock temperatures for this layer. These are close to the 

normal air temperatures, modified by the temperature difference 

caused by convection, and are determined by the program. If better 

information exists, it can, of course, be fed into the computer and 

used. The fire-generated thermal forces are the throttling and 

natural draft effects. They are determined by making use of the 

calculated temperature distributions. 

Because of its capabilities to calculate concentrations and 

temperatures and to take thermal forces into account, the program 

is not only used for fire emergencies but also for ordinary 

ventilation planning purposes. Several versions exist, developed 

by program users. The program has found substantial use for fire 

simulations in high-rise buildings during the last few years. 

 2.6 TRANSIENT STATE SIMULATION OF FIRES AND VENTILATION SYSTEMS 

The transient concentration distribution programs are useful in 

many ways. The assumption of time-constant airflow rates is 

justified for the early stages of a fire when a weak fire does not 

influence the airflow distribution. When, at a later stage, more 

intense fires may interact noticeably with the ventilation system, 

with the fire intensity controlled by the air supply to the fire, 

and with the airflow distribution affected by the fire intensity, 

this interaction should be taken into account. Correspondingly, 

initially, a program was written for this condition in which, for 

the sake of simplicity, steady-state conditions were assumed. 

The shortcoming of this program was that it determined the state of 

a ventilation system at the end of a specified time interval only, 

with the assumption that the airflow distribution at the end of 

this interval prevailed from the beginning of the fire throughout 

the time interval. 
20 

This could be true, but it might be a simplification of reality. 

There are several different approaches for a complete transientstate simulation of ventilation systems. The first method 

investigated was a finite-difference method based on Newton's 

second law. It starts with the momentum balance of small elements 

of air masses to set up the governing equations, and ends up with a 

set of simultaneous equations that have to be solved for the whole 

system in each time increment. This method was discarded after a 

lengthy trial for the following two reasons: 

 1. With the involvement of simultaneous equations, the 

calculation load increases rapidly when a ventilation network 

becomes large. 

 2. For most cases in mine ventilation, the airflow can assume 

steady-state in a time period short enough to justify the 

application of steady-state theories. 

The chosen approach was then to consider the transient process as a 

sequence of short-time steady-state processes during each of which 

an equilibrium between ventilating pressures (fan and thermal 

pressures) and airflow-rate-produced pressure losses exists. If 

the temperature distribution changes, the equilibrium will be 

disturbed and a new airflow distribution will result. The new 

equilibrium for the end of the time interval is found by a sequence 

of alternating temperature, thermal pressure, and network 

calculations. The results of the last calculation serve as the 

input for the succeeding calculation. 

Neither the airflow rates at the beginning of the time interval nor 

at its end are representative of the whole time interval. With the 

assumption that changes in the airflow rate during the time 

interval follow a linear pattern, the arithmetic average of the two 

values is used to represent the average airflow rate. 

An interval-oriented simulation technique, which updates its data 

base in every prefixed time interval, was adopted (Chang, 1987). 

An event-oriented simulation would be more efficient, but with a 

transient-state simulation, ventilation system conditions change 

constantly, which makes events undistinguishable. The control 

volume approach, with control volumes being blocks of air of 

uniform composition, was retained. In other words, the time is 

divided into a series of time intervals; the airflow into air 

segments. 

If data records were set up for every airway in a system, a 

majority of the efforts would be unnecessary because the variation 

of ventilation parameters in most airways that were not directly 

affected by the hot fumes are at most of a secondary significance 

in shaping the airflow distribution in the system. It is assumed 

that the mean air temperature and airflow resistance of an airway 
21 

will remain unchanged if no significant changes in ventilation 

conditions occur. The criteria to judge a significant change 

include whether fumes ever got into the airway and whether drastic 

condition changes (air temperature change larger than 2 deg C, or 

fume concentration change larger than 0.1 pct) happened in the 

beginning junction of the airway. When no significant change 

happens in an airway, its original resistance and mean air 

temperature are taken as the values in the present time interval. 

This program was ported to the personal computer world and was 

released as MFIRE in 1988. With the aid of user reports, bug fixes 

were made and maintenance versions were released. 

2.7 CONSIDERATION OF WATER VAPOR 

The early releases of MFIRE did not consider water vapor. MFIRE 

2.0 and 2.1 were derived from older code which did incorporate the 

following method for water vapor consideration. The older code 

lacked robustness and users found small but significant problems 

under certain circumstances. MFIRE 2.20 returned to the framework 

of version 1.29 and added the fan features described later. This 

section is intentionally left in the manual for reference as water 

vapor consideration will be incorporated in future releases. 

Air temperature precalculation is necessary for simulation of 

thermal disturbances such as mine fires. It is recognized that 

even seemingly dry airways are to a considerable extent influenced 

by water migration, evaporation, or condensation. Small water 

quantities can, due to the large latent heat of water, have great 

effects. Due to the existence of water evaporation and 

condensation in a system, mass and heat transfer must be considered 

concurrently. 

Past attempts to describe the effects of water on mine air 

temperatures fall roughly into two categories. One of them uses 

statistical tools to systematically interpret field-measured data 

for empirical relationships among temperature, humidity, and other 

ventilation parameters. It does not attempt to explain the nature 

of their dependence or to draw generally valid conclusions. Rather 

it offers useful equations of localized significance. 

The other is a semi-empirical technique that tries to derive 

functional relationships between temperature and other ventilation 

parameters. A number of loosely defined factors, coefficients, and 

more or less justified relations are introduced for this purpose to 

provide for general applicability. There exist, however, so many 

assumptions, which are neither theoretically sound nor universally 

tenable, that the usefulness of this approach has to be limited in 

range or a lack in accuracy must be expected. There exist by now a 

large number of approaches to predict the combined dry heat 

transfer by conduction within the rock and by convection from the 
22 

rock to the air. None of these approaches take the parallel mass 

transfer of water and its temperature effect satisfactorily into 

account. 

The model developed for MFIRE follows a rigorous analytical 

approach and a rigorous analytical solution can be obtained (Chang 

and Greuer, 1985). Since the calculation of numerical solutions 

turns out to be a very time-consuming task, approximations for 

short time periods, with which one is concerned in emergency 

planning, were developed also. 

Additional difficulties arise from boundary conditions. Water can 

evaporate or condense on airway walls with pertinent changes in 

wall temperatures. It can condense as fog in the bulk flow of the 

air with a concomitant change in the temperature gradient between 

airway walls and air. To be properly considered, these wall 

temperature changes have to be recorded. To keep the amount of 

record-keeping small, so-called stations in intervals of a few 

hundred feet are established, for which the correct data are 

recorded. For the space between stations, interpolations are used. 

The governing equation was set up as: 

subject to: Tr=Trv at t=0 for all R 

 Tr=Trv when t>0 and R → ∞

and the boundary condition equation: 

where: Dt = mass transfer coefficient, 

 h = heat transfer coefficient, 

 Lw = latent heat of water at wall temperature, 

 R = coordinate in the radial direction, 

 Ro = hydraulic radius of airway, 

 t = time, 

 Tr = rock temperature, 

 Trv = initial rock temperature, 

 Ta = air temperature, 

 Xw = absolute humidity of air, 

 Xww = absolute humidity in the wall layer, 

 α = thermal diffusivity, 

 λ = thermal conductivity of rock, and 

 φ = wetness of airway wall 

⎟

⎟

⎠

⎞ ⎜

⎜

⎝

⎛

∂

∂

∂

∂

∂

∂

RRx

T +

R

T

 =

t

T r

2

r 2 r α

hx(= T -T +) L x D xx( X - X =atR ) R R

T twar www o

r λ φ ∂

∂
23 

The governing equation of energy conservation describes the heat 

transfer in two superimposing processes: the heat transfer between 

airflow and its surroundings, and the enthalpy flux accompanying 

the mass transfer of water vapor. Assumptions for this model 

include: an airway of infinite length, homogeneity and isotropy of 

rock, negligible heat transfer in the axial direction of the 

airway, and constant thermal and heat transfer parameters. 

In the boundary condition equation, the wetness of the wall is 

defined as the ratio of wet area to the total surface area. It is 

assumed that the wet portion and dry portion of a wall share a 

common humidity ratio and temperature in the wall film, a thin 

layer close to the wall. When the wall wetness equals the ratio of 

absolute humidity of air in the main air flow to that in the wall 

layer film, the vapor content in the wall film is in equilibrium 

with that of the main flow. The boundary conditions also imply that 

the mass transfer, or water evaporation and condensation from the 

wall, occurs in the vicinity of the wall, and the heat absorbed or 

liberated is either from or towards the wall. 

A one-dimensional differential equation can then be set up for an 

infinitesimal control volume of air based on the energy 

conservation law. Its solution describes the air temperature 

variation along an airway on the basis of a known solution to the 

governing equation of heat transfer. 

A non-dimensional wall temperature, frequently called the 

coefficient of age, is used to relate the governing equation of 

air-rock heat transfer and air temperature variation. Due to the 

fact that the initial condition of air temperature at the beginning 

junction of an airway is needed in computing the air temperature 

variation in the airway, the air temperature distribution in the 

ventilation system can only be calculated through an 

airway-by-airway process. 

The air temperature in an airway is calculated as a temperature 

superposition of two processes. One process is the heat transfer 

between the airflow and its surroundings. The other is the mass 

transfer due to water evaporation and/or condensation. The 

solution is quite complicated and lengthy and is not included here 

for space and time reasons. (Chang and Greuer, 1985) 

The key to solving the governing equation lies in the interpretation of the boundary condition in which the absolute humidity is 

a complicated function of temperature. The relationship between 

the saturated water vapor pressure and temperature is replaced by a 

series of linear segments. Then, the governing equation is 

separated into two sets of superimposing differential equations 

with boundary/initial conditions, which can be regarded as a dry 

air temperature model and a wet-case temperature correction model, 

respectively. 
24 

The superimposition of their solutions gives the air temperature 

variation for the process of simultaneous heat/mass transfer in the 

airways. 

Though this model works well under normal mining conditions, in 

some cases, it may not be a good approximation to assume that 

humidity ratios of airflows into a common junction from different 

airways are equal to that in the junction. This situation can be 

corrected by measuring the humidity for each airway separately, if 

necessary. Another characteristic of the model is that the average 

wall temperature is used to evaluate the saturated vapor pressure 

in the wall layer of an airway. Because of this, a specified 

humidity ratio that conflicts with the model is physically 

possible. When the humidity ratio of air along an airway is 

decreasing due to vapor condensation on a wall, the wall wetness 

loses its meaning and can not be determined. To avoid this 

problem, the wetness of an airway under condensation must be 

explicitly specified. 

The additional input requirements are simply the wetness of airway 

walls as a percentage of total surface area in each airway and the 

relative humidity in junctions. 

2.8 MFIRE PERFORMANCE 

Research was conducted to validate MFIRE's calculation of 

temperature distribution in an airway due to a mine fire, as 

temperatures are the most significant source of ventilation 

disturbances. Three fire tests were conducted at the Waldo Mine 

near Magdalena NM. The Waldo Mine is operated by New Mexico 

Institute of Mining and Technology for experimental and research 

purposes. Three experiments were conducted; two with wood and one 

with diesel fuel. A complete description of the mine and tests can 

be found in the Bureau Open File Report 80-93 "Waldo Mine Fire 

Experiments of March 1990" by Laage and Carigiet. 

The fire site was instrumented in the Waldo Tunnel on the 9th 

level. Arrays of thermocouples and temperature sensing devices 

were placed downwind of the fire and into boreholes over the fire. 

 The variation of heat flow rate to the rock was back calculated 

based on varying temperatures in the rock. The enthalpy changes in 

the airflow were obtained from the temperature sensing arrays. 

Then MFIRE and its functions were used to model fires of constant 

heat influx for the duration of the experimental fires. The total 

modeled heat influx for each fire was equal to the fuel loading. 

Energy curves as functions of time were produced from the measured 

real fire temperatures and the temperatures predicted by MFIRE. 

These energy curves were integrated and then compared with the fuel 

loading from the fires. 
The total heat transfer to rock and air were also calculated. The 

ability of MFIRE is illustrated in the following two tables. 

In Table 1, the total measured and total modeled heat transfer 

deviation from the actual fuel loading is shown as a percentage of 

total fuel loading. These deviations are quite small for fullscale fire tests and are near the experimental limits. 

 TABLE 1 

HEAT TRANSFER DEVIATIONS, PERCENT 

Experiment Measured heat Modeled heat 

number transfer deviation transfer deviation 

1 - 2.5% + 2.3% 

2 + 4.1% - 2.6% 

3 - 6.0% + 2.8% 

 Table 2 compares the percentage of heat transferred to the 

airflow based on the actual fuel loading. This is an important 

comparison as the heat transfer to the air is the cause of the 

ventilation disturbances. 

 Table 2 

HEAT TRANSFERRED TO AIRFLOW, PERCENT 

Experiment Heat transfer, measured Heat transfer, modeled 

 1 92% 98% 

 2 96% 93% 

 3 88% 99% 

There are, of course, many sources for experimental error and back 

calculation assumptions, however, a discussion of these is beyond 

the scope of this paper. These tables show a very close agreement 

between the measured and modeled heat transfer to the air as well 

as to the total fuel loading and these experiments illustrate the 

overall performance of MFIRE. 

25 
26 

 3.0 USER SELECTED REFERENCE DENSITY AND TEMPERATURES 

3.1 THEORY OF REFERENCE DENSITY 

Performing network calculations based on actual volume flow rates 

makes the consideration of the law of conservation of mass 

difficult. Most computer programs substitute a "law of volume 

conservation" instead. Although this may normally not lead to 

serious errors, it is definitely a serious error when, like in the 

heated air behind a fire, larger density changes occur. MFIRE is 

based on mass flow rates. 

Three states of ventilation air are discussed in this chapter; the 

standard air with a density of 0.075 pounds per cubic foot and 

denoted with a subscript “s”, the reference air at a user selected 

state of density “w*” and corresponding temperature “T*” denoted 

with a superscript “*”, and an actual in place state where only the 

variable is used. The reference density and temperature correspond 

to MFIRE input variables DR and TR respectivly. 

Mass flow rates are calculated with the aid of a reference density, 

w* and a corresponding reference temperature, T*. To obtain output 

which comes close to the actual, density dependent, pressure 

losses, fan pressures, and volume flow rates, a constant reference 

density w* which is close to the prevailing actual density w is 

used. If one prefers, one can select the standard density 

ws = 0.075 lb/ft3 as reference density w*. 

The "reference temperature" is the temperature pertinent to the 

"reference density" at the prevailing pressures in the ventilation 

system. It is not used for temperature calculations. Its sole 

purpose is to express the "reference density". Since it serves 

only as a scale against which other densities, expressed by their 

temperatures, are measured, its choice is not very crucial. 

Summarized with the use of a "reference density" the principle of 

basing pressure losses, fan pressures, and resistance factors on a 

standard density is extended to volume flow rates also. 

Ventilation network calculations are based on the law of mass 

conservation and on the law of energy conservation. Unfortunately, 

we have become accustomed to express mass flow rates by volume flow 

rates, which are not conserved. And to express energies as 

ventilation pressures (ft-lb/ft3 = lb/ft2α "wg) or work per unit 

volume, which leads for the same work due to changing volumes to 

different numbers for the energy. Many ventilation engineers 

convert pressure losses HL, fan pressures HF and resistance factors 

R to a standard density of ws = 0.075 lb/ft3. This gives a correct 

energy balance and leads in the calculation of pressure losses with 
27 

the formula HL = R * Q2

 to correct values, when the actual flowing 

volume flow rate Q is used. 

It has become customary in mining to express flow rates as volume 

flow rates (cfm = ft3/min) and energies per unit volume. 

ft-lb/ft3 = lb/ft2= 1/5.2 "wg 

Air densities change. Equal mass flow rates result therefore in 

different volume flow rates and equal energy amounts in different 

energy amounts per unit volume. Since two of the basic laws used 

in mine ventilation are the law of mass conservation and the law of 

energy conservation, the above approach is not practical. It has 

nevertheless been retained by ventilation engineers, because they 

find it difficult to visualize mass flow rates in lb/min or 

energies in ft-lb/lb. 

To provide correct energy balances, the U.S. Bureau of Mines has 

recommended the use of the constant standard density of 0.075 lb/ft3 

when expressing energies per unit volumes. This means essentially 

to express them as energies per unit mass. If, for instance, an 

airway has a pressure loss of 

HL = 0.5 "wg at the average air density w = 0.078 lb/ft3 in the 

airway, 

this would mean an energy of 

0.5*5.2 = 2.6 ft-lb/ft3 (lb/ft2) or 2.6/0.078 = 33.33 ft-lb/lb (ft). 

This is the figure which should be used, but since it is too 

abstract, it is multiplied by the standard density 

ws = 0.075 lb/ft3. 

HLs = 33.33 ft * 0.075 lb/ft3

 = 2.5 lb/ft2 or 2.5/5.2 = 0.481 "wg. 

 ws 0.075 

Or: HLs = HL ---- = 0.5 ------- = 0.481 "wg. 

 w 0.078 

The same process is employed with all energies, fan pressures as 

well as pressure losses and natural ventilation pressures, which 

means that all energies are expressed per unit mass but are 

multiplied by a constant conversion factor of ws = 0.075 lb/ft3. If 

pressure losses are calculated using the familiar formulas: 

HL = R*Q2

 K*L*P*Q2

or HL = ---------- , the actual densities w which are contained in 

 5.2 A3
28 

m&

m&

&

m&

R and K are replaced by ws. This is done by multiplying 

 ws R or K by ----- : 

 w 

 

Rs = R * ws/w or Ks = K * ws/w 

which converts HL into Hls. The airflow rates Q are in all cases the 

actual volume flow rates, which vary for constant mass flow rates 

 inversely proportional to the density: 

Q = /w. 

This poses difficulties in ventilation calculations since the law 

of mass conservation but not a law of volume conservation has to be 

satisfied. 

3.11 AIRFLOW IN MINE PASSAGES 

MFIRE input and output is in terms of volume flow rates Q*

 at a 

reference state, which are actually mass flow rates m divided by 

a reference density w*, irrespective of the magnitude of the actual 

density w: 

 

Q* = Q * w/w* = /w*. 

The choice of the reference density is left to the program user. 

The closer it is to the actual densities w, the less confusion is 

generated. The term w*

 plays the same role as the standard density 

ws and if deemed practical, w* can be selected to be equal to ws. Mass based energies are then expressed by 

HL

*

 = HL * w*/w or HL

*

 = HLs * w*/ws

and the pertinent resistance factors by 

K* = K * w*/w or K* = Ks * w*/ws 

R*

 = R * w*/w or R* = Rs * w*/ws

Pressure loss HL and volume flow rates Q are related by the familiar 

resistance equation HL = R*Q2. If a similar expression in terms of 

HL

*

, Q* and R* shall be used, one obtains from 

HL

*

 =HL * w*/w and Q* =Q*w/w* and R* =R * w*/w or R* =Rs * w*/ws : 

HL

*

 = R*(w*/w)2Q*2

If in the equations HL = R*Q2 or HLs = Rs*Q2, the term HL

*

 takes the 

place of HL or HLs and Q* the place of Q, then R and Rs have to be 

replaced by the term 
29 

R*

(w*/w)2. 

If density changes are caused by temperature changes, w*/w can be 

replaced by 

T/T*, 

where T* is a reference temperature leading to the reference density 

w*. 

Example

An airway has the following dimensions: L = 1,000 ft; A = 64 ft2; P 

= 32 ft; 

At State 1, a density of w = 0.078 lb/ft3, a volume flow rate of Q = 

50,000 ft3

/min and a pressure loss of HL = 0.610 "wg were measured. 

 The mass flow rate is: 

 = Q*w = 3,900 lb/min. m&

The resistance of the airway is 

 R = HL/Q2 = 0.610/(0.5*105)2 = 2.44*10-10 "wg/cfm2. 

Its K-factor is 

 K = R*5.2*A3/(L*P) = 103.94*10-10lb*min2/ft4. 

With a standard density of ws = 0.075 lb/ft3, this gives 

Rs = 2.44*10-10*0.075/0.078 = 2.346*10-10 "wg/cfm2 and 

Ks = 103.94*10-10*0.075/0.078 = 99.942*10-10lb*min2ft4. 

With a reference density of w* = 0.074 lb/ft3 this gives 

 R* = R*w*/w = 2.44*10-10*0.074/0.078 = 2.315*10-10 "wg/cfm2 or 

 R* = Rs*w*/ws = 2.346*10-10*0.074/0.075 = 2.315*10-10 "wg/cfm2. 

The conversion of K-factors is equivalent. The energy losses are: 

HL = R*Q2

 = 2.44(0.5)2 = 0.610 "wg 

HLs = Rs*Q2 = 2.346(0.5)2 = 0.587 "wg 

HL

*

 = R*(w*/w)2Q2* = 2.315(0.074/0.078)2(0.52703)2 = 0.579 "wg 

All three energy terms express the same energy per unit mass: 

HL/w = 0.610*5.2/0.078 = 40.7 ft-lb/lb 

HLs/ws = 0.587*5.2/0.075 = 40.7 ft-lb/lb 
30 

m&

HL

*

/w* = 0.579*5.2/0.074 = 40.7 ft-lb/lb 

In State 2, the mass flowrate remains constant but the density 

changes from: 

 w = 0.078 to 

 w = 0.070 lb/ft3, which results in a volume flowrate of 

Q = 50,000*0.078/0.070 = 55,714 cfm and Q* = /w* = 52,703 cfm. 

Then: 

HL = R*Q2

 = 2.44 (0.070/0.078) 0.557142 = 0.680 "wg 

HLs = Rs*Q2 = 2.346 * 0.557142 = 0.728 "wg 

HL

*

 = R*(w*/w)2Q2 = 2.315 (0.074/0.070)2 0.527032 = 0.719 "wg 

Again, all three terms express the same energy. 

HL/w = 0.680*5.2/0.070 = 50.5 ft-lb/lb 

HLs/ws = 0.728*5.2/0.075 = 50.5 ft-lb/lb 

HL

*

/w* = 0.719*5.2/0.074 = 50.5 ft-lb/lb 

 State 1 State 2 

 w = 0.078 lb/ft3 w = 0.070lb/ft3 w1/w2 = 1.11 

HL 0.610 0.680 HL1/HL2 = 1/1.11 HL α 1/w 

Hls 0.587 0.728 HLs1/HLs2 = 1/1.24 HLs α 1/w2

HL

*

 0.579 0.719 HL

*

1/HL

*

2 = 1/1.24 HL

* α 1/w2

3.12 Pressure PRODUCTION OF FANS 

When energy exchanges between fans and air are expressed per mass 

unit of air (hF, fanheads), they are functions of air and impeller 

velocities only. Fan airflow rates QF are not influenced by air 

densities. When energies are expressed per unit volume (HF, fan 

pressures), they are proportional to the air density, since the 

correlation between masses and volumes is the density w. 

Consequently, if a fan characteristic HF1 = f(QF,w1) is based on a 

certain air density w1, the fan and airspeeds (and therefore the 

volume flow rate QF) are kept constant, and the fan is made to work 

with a different density w2, the new characteristic 

 w2 
31 

m&

HF2 = f(QF,w2) can be obtained from HF2 = --- * f(QF,w1) 

 w1 

If the characteristic has been given for a standard air density ws = 

0.075 lb/ft3 (when fan characteristics are quoted by manufacturers) 

the pertinent fan would at a density of w have the characteristic: 

 w 

HF = ---- * f(QF,ws). 

 ws

The airflow rate QF is in all cases the actual volume flow rate of 

the air passing through the fan. When standardized volume flow 

rates Q* are used, one has to remember that they are actually mass 

flow rates divided by a constant reference density w*: 

 QF = / w*

. 

The actual volume flowrate QF of the air through the fan, which 

controls the energy exchange, is therefore 

 QF = QF

*

(w*/w). 

The fan pressure HF

*

, based on a reference density w*, is 

 

 HF

*

 = HFS (w*/ws) or HF

*

 = HF (w*/w). 

The consequence for basing ventilation network calculations on 

reference densities is that if fan characteristics have been given: 

for actual densities w as HF = f(QF,w) 

or for standardized densities ws as HFs = f(QF,ws) 

they have to be transformed to 

 w*

HF

*

 = ---- * f(QF

*

 (w*/w)) or to 

 w 

 w*

HF

*

 = ---- * f(QF

*

 (w*/w)). 

 ws

Example

The pressure HF1 of a fan has at a density of w1 = 0.078 lb/ft3 and 

at several airflow rates QF been determined as 

HF1 = 1.0 - 2.0 (QF * 10-5 - 0.4) "wg 
32 

If the density of the air passing through the fan changes to 

w2 = 0.070 lb/ft3

, one will observe a fan characteristic of 

HF2 = (w2/w1) (1.0 - 2.0 (QF*10-5 - 0.3)) "wg 

If the density changes to ws = 0.075 lb/ft3, one will observe 

HFs = (ws/w1) (1.0 - 2.0 (QF*10-5 - 0.3)) "wg 

It is assumed that this fan works in series with the above 

described tunnel of 1,000 ft length and 64 ft2 cross sectional area. 

 The resistance factor of this tunnel had been determined as 

R1 = 2.44*10-10 "wg/cfm2 at a density of w1 = 0.078 lb/ft3 R2 = (w2/w1) R1 "wg/cfm2

 at a density of w2 = 0.070 lb/ft3 Rs = (ws/w1) R1 "wg/cfm2

 at a density of ws = 0.075 lb/ft3 

Pressure loss in the tunnel HL and fan pressure HF balance each 

other. Air flow rates in the tunnel Q and through the fan QF must 

be equal. One obtains for all three air densities. 

R1 * Q2 = 1 - 2.0 (QF *10-5 - 0.3) 

Q = QF = 49,770 cfm. 

This phenomenon of constant flow rates of air through an airway in 

series with a fan irrespective of varying densities is to be 

expected. Pressure losses as well as fan pressures are directly 

proportional to the density and rise and fall therefore 

simultaneously. 

The use of reference units w*, Q*, QF

*

, HL

*

, and HF

*

 should naturally 

give the same answers as obtained above. One has however to bear 

in mind that all of these reference units are mass units used at 

different densities. If, for instance, the volume flow rate Q 

remains constant but the density w changes, the reference density 

volume flow rate Q*

, which expresses actually the mass flow rate, 

will have to change also. 

With HL

*

 = R*(w*/w)2Q*2, w* = 0.074 lb/ft3, w1 = 0.078 lb/ft3 and 

ws = 0.075 lb/ft3

and R1

*

 = R1 (w*/w1) 

 R2

*

 = R2 (w*/w2) = R1 (w2/w1) (w*/w2) = R1

*

 R3

*

 = R3 (w*/w3) = R1 (w3/w1) (w*/w3) = R1

*

one obtains for the pressure losses in the above described tunnel: 

HL1

*

 = R1 (w*/w1) (w*/w1)2 Q1

*2 = R1*

 (w*/w1)2 Q1

*2
 = 2.315*10-10 (0.074/0.078)2

 Q1

*2 = 2.084*10-10 * Q1*2 

HL2

*

 = R1

*

 (0.074/0.070)2 Q2

*2 = 2.587*10-10 * Q2*2

HLs

*

 = R1

*

 (0.074/0.075)2 Qs

*2 = 2.254*10-10 * Qs*2

The above described fan characteristic of 

HF1 = 1.0 - 2.0 (QF * 10-5 - 0.3) 

for w1 = 0.078 lb/ft3 has to be transformed to 

HF1

*

 = (0.074/0.078) (1.0 - 2.0 (Q1

*

 (w*/w1) * 10-5 - 0.3)) 

HF2

*

 = (0.074/0.078) (1.0 - 2.0 (Q2

*

 (w*/w2) * 10-5 - 0.3)) 

HFs

*

 = (0.074/0.078) (1.0 - 2.0 (Qs

*

 (w*/ws) * 10-5 - 0.3)) 

The following table compiles some of the data from these formulas. 

 w Q*

 Q*(w*/w) HL

*

 HF

*

 HL

*

(w/w*) R* 

 (lb/ft3) cfm cfm "wg "wg "wg "wg/cfm2 

 

w1 = 0.078 52,460 49,770 0.5735 0.5735 0.6044 2.315*10-10

w2 = 0.070 47,080 49,770 0.5735 0.5735 0.5424 2.315*10-10

ws = 0.075 50,443 49,770 0.5735 0.5735 0.5812 2.315*10-10

The hypothetical volume flow rates Q*, which stand for mass flow 

rates, vary. Multiplied by (w*/w) one obtains from them the 

actual flowing volume flow rates Q = Q* (w*/w), and they remain 

constant. The hypothetical pressure losses HL

*

 and fan pressures 

HF

*

, which stand for energies per unit mass or for heads, remain 

constant. The pressure losses HL = HL

*

 (w*/w), which stand for 

energies per unit volume, change with the air density. The 

resistance factor R*

 remains constant, which is a pleasant 

feature of the use of reference densities. After all, the 

resistance is a property of the airway and is not changed by 

ventilation conditions. 

3.2 MFIRE INPUT 

MFIRE works with masses and reference densities. All input and 

output energy and airflows are at the reference state. That 

means that the input data for airway resistances are R* , for air 

flow rates in fixed quantity airways Q*, and for pressures in 

constant pressure sources HN

*

 and HF

*

. The friction factor K is at 

the standard state of 0.075 lb/ft3

 as this is most commonly 

reported in tables and only used when actual measurements for R 

33 
are not available. Resistances calculated with the K factor are 

adjusted to the reference state as: 

 K*L*P w*

 R*

 = ---------- ----- 

 5.2 A3 0.075 

Most data on fan characteristics are transformed to the standard 

density of ws = 0.075 lb/ft3, before communicated by the 

manufacturers or filed by the users. These fan characteristic 

must be transformed to the reference state. 

When density changes are caused by temperatures, the ratio of 

absolute temperatures are used to convert to the reference state. 

 The ratio T/T* is: 

 in place Temperature + 460 

------------------------------- 

 reference temperature + 460 

and usually offers only small changes to the ventilation data if 

a representative reference state is selected. 

34 
3.21 MFIRE CONVERSION RULES 

Variable To convert to reference state 

resistance R R* = R * w*/w or 

measured R* = R * T/T*

resistance R R* = R * w*/w or 

user calculated R* = R * T/T*

resistance R input standard K, length, area, perimeter 

MFIRE calculated 

Airflow Q Q* = Q * w/w* or 

measured Q* = Q * T*/T 

Airflow Q estimate Q 

to be calculated 

friction factor K Input at standard density of 0.075 

fan curve data Remains unchanged 

QF airflow 

fan curve data Hfa

*

 = Hfan * w*

n /w or 

PF or Hfan pressure Hfan

*

 = Hfan * T/T*

Fixed pressure fan Hfan

*

 = Hfan * w*/w or 

 Hfan

*

 = Hfan * T/T*

Fixed airflow Q Q* = Q * w/w* or 

 Q* = Q * T*/T 

35 
4.0 PROGRAM INSTALLATION AND OPERATION 

The program MFIRE 2.20 consists of three executables: MFIRE0.EXE, 

MFIRE1.EXE and MFIRE2.EXE. The execution, control and 

intermediate file handling is handled by a batch file, 

MFIRE 2.20 was compiled with Microway FORTRAN and the royalty 

free ERGO DOS memory extender was bound into the executable. The 

ERGO DOS memory extender is not compatible with some memory 

managers. If difficulties are encountered, temporarily disable 

your memory manager. Networks of up to 500 airways and 350 

junctions can be modeled. Input for MFIRE is in the form of a 

data file. The data file contains lines of numerical data 

describing the physical mine, the ventilation parameters present, 

the fans, and the proposed thermal or mechanical disturbances. 

Output from MFIRE is sent to the file MFIRE.OUT which is created 

in the directory where the MFIRE program resides. The output can 

have up to four levels of increasing detail. Subsequent 

executions of MFIRE will overwrite the old MFIRE.OUT file with 

the new MFIRE.OUT file. If archiving of MFIRE.OUT files is 

desired, they can be renamed with the DOS RENAME command to 

prevent overwriting. The WFOUT file can be reviewed and/or 

printed with text editing software. 

The equipment and additional software necessary to use MFIRE 

includes: 

1. IBM1

 PC or compatible computer with MS or PC DOS 3.3 or later 

version; 

2. hard disk drive with at least 2 megabytes of disk space; 

3. Intel 80386 CPU and 80387 or compatible math-coprocessor; 

4. at least 1 Megabytes RAM; and 

5. a text editor or suitable word processor. To install the 

program, the user should make a directory on the hard disk drive. 

The contents of the program disk are then copied into that 

directory. 

36 
37 

To start MFIRE 2.20, the user types "MFIRE" and follows the 

instructions for user responses and the location of the data 

file. Two screens of information about the program are presented 

followed by a prompt for the user to identify the location of the 

data file. The user responds with a standard DOS path and 

filename for the input data file. After a data file name is 

entered, depending upon the user defined selection of program 

features, MFIRE will sequentially perform: 

1) General network balancing of volumetric air flow rates. 

2) Network balancing considering temperatures, heat exchange with 

rock, and natural ventilation. This network balancing involves 

balancing the pressure losses and gains in the network meshes to 

accommodate mass based flow rates. 

3) Dynamic, transient state modeling with user selected dynamic 

fire growth and user selected time increments for updating the 

ventilation changes and spread of contaminants. 

4) Calculation of new ventilation equilibrium due to contaminant 

(fire) presence, and distribution of the contaminants (POC, 

methane, etc) under the altered steady state conditions. 

 4.1 CHANGES IN MFIRE 2.20 FROM PREVIOUS VERSIONS 

Bug type fixes are described in detail in the file “README.220" 

on the distribution disk. 

MFIRE 2.20 removed the humidity calculations available in 

versions 2.0/2.1. 

For the slection of fan curve fitting, the cubic spline and least 

squares methods are available. For the handling of the boundary 

region of the fan curve, there are three choices: 1) the slopes 

of the both right and left boundary region of fan curve are same 

as that at the most right and left data points of input fan 

characteristic curve or 2) the slope of the right boundary region 

of fan curve is sent to zero or 3) the slopes of right and left 

boundary region of fan curve are sent to zero. The flexible 

choices for fan curve fitting method and the handling of boundary 

region of fan curve improve the common suitability and 

calculation convergence of program MFIRE for various input data 

sets. 
38 

5.0 INPUT DATA FILES 

Numerical data or input files are used to describe the mine's 

ventilation system and physical characteristics necessary for 

ventilation calculations as well as the physical or mechanical 

disturbance to be modeled and simulated. Data lines are read by 

the program and the data items are used to provide information to 

the program variables. The data file is in ASCII format, 

sometimes called a DOS text format. Creation or modification of a 

data file is accomplished with text editor software. Most word 

processors are also capable of making the required ASCII type 

files. Sample data files are included on the program disk. 

When selecting software for editing the data files, the user 

should be aware that the software will also be used for viewing 

the output of the simulation. An editor or word processor capable 

of unlimited file size is necessary. The output file can be 

quite large (several megabytes) if a lengthy simulation is 

performed. The output can be sent to a printer for a hardcopy 

listing however, the user should also be aware that most printers 

currently used with PCs print at rates of 100 to 300 characters 

per second and large output files may take several hours to 

print. Viewing the output with a text editor can save much time 

and paper. 

5.1 GENERAL STRUCTURE OF DATA FILE 

MFIRE 2.20 allows the comment lines utilized by version 1.29. Any 

line with a dollar sign “$” in the first column is ignored. 

These lines may be used to easily remove or change data such as 

fan curves or fire events and to annotate the data file. 

Altogether, data lines comprise the following 

data groups. 

Control line number 1 

Airway lines 

Junction lines (optional) 

Fan lines (optional) 

Fire source lines (optional) 

Control line number 2 (optional) 

Average-value lines (optional) 

Time table lines defining condition changes (optional) 

A data file must be set up according to the input requirements. 

Because errors tend to occur in the preparation of data file, a 

template file, INPUT.FMT was created (Appendix 2 of this User 

manual). This file consists of instruction lines detailing the 

data line groups in the required order and the location of each 
39 

data item on each line as well as the meaning of each data item 

required. This file serves to remind and prompt the user for data 

lines and items at the proper locations. 

To use the template, simply copy the file INPUTW.FMT to the data 

disk space, and add data into the data file by adding lines at 

proper places and following the instructions given in the 

INPUT.FMT file. The user can then use the DOS RENAME command to 

uniquely identify the new data file. 

5.2 DATA FORMAT 

1. Distinction between an integer and a real number is not 

required. Integer 5 can be 5, or 5.0 in the data file. Real 

number 3.0 can be 3 or 3.0 in the data file. 

2. A comma and a blank space can be used interchangeably as 

delimiters to separate input values. Two or more blank spaces 

adjacent to one another act as one blank in separating input 

values. Blank spaces adjacent to a comma have no effect in 

separating input values. 

3. Zero values can be omitted, but the related delimiters 

(commas) must be present. 

For example, if input is needed for the following data items: 

N,R,S,I,T,L,P,M 

where: N=5; R=10; S=7.52; I=0; T=-4; L=0; P=0; and M=0 

then the following input lines would have the same effect. 

5,10.0,7.52,0,-4.0,0,0.0,0 

5 10 7.52 0 -4 0 0 0 

5 10 7.52 , , -4,,,, 

 5.3 CHANGES IN MFIRE 2.20 DATA FILE FROM PREVIOUS VERSIONS 

1. In Control Line 1, TOUT and CONCT have returned 

2. The Surface Data Junction group have returned. 

3. The time table of vbersion 1.29 has returned. 

4. Comment and Instruction lines are accepted. 

5. The variable “NSWT” was added as the the third variable on fan 

line number 1 to select the fan curve fitting method. 

6. The variable “NPLOT” was added as the third fan line to select 
40 

the treatment of curve boundry conditions. 

 5.4 DETAILED DESCRIPTION OF DATA INPUT REQUIREMENTS 

1. Control Line number 1 consists of the following variables: 

NB,NFNUM,INFLOW,NVPN,NETW,TR,MADJ,ITN,NTEMP,TINC,SPAN,IOUT,TOUT,CONCT,DR

where: 

NB is the number of airways in the network. Maximum NB is 500. 

NFNUM is the number of fans which have characteristic curve input 

data. Maximum NFNUM is 10. 

INFLOW is the number of contamination sources in the system. 

Maximum INFLOW is 10. 

NVPN is a flag. If there are junction cards to be read in, NVPN 

must be equal to or less than zero. The junction lines must be 

omitted if NVPN is greater than zero. When the junction cards 

are omitted, only the network simulation will be performed. 

NETW is a flag. When NETW equals 1, only the network simulation 

will be performed. The output will consist of conventional 

network calculations without consideration of contaminant 

sources. 

TR is the reference or air average temperature in the mine in 

degrees F. If the input value of TR is less than 10 F or higher 

than 110 F., the default value of 75 F. will be used. 

MADJ is the maximum number of iterations in the temperature 

section. If its input is less than 10 or larger than 80, the 

default value of 15 will be used. 

ITN is the maximum number of iterations in the dynamic simulation 

section. If its input is less than 10 or larger than 80, the 

default value of 15 will be used. 
41 

NTEMP is a flag. When NTEMP equals 1, only network balancing with 

consideration of temperature effects are performed. Set NTEMP 

equal to 0 for the simulation to proceed to transient state and 

fire modeling. 

 

TINC is the time increment for the dynamic simulation section in 

sec. If the input value is 0 or less, default value of 15 sec. 

will be used. 

SPAN is the time span for the dynamic simulation of the proposed 

event in min. The default value is 5 minutes. 

IOUT is a marker to define the level of detail of the output file 

where: 0=brief; 1=normal; -1=detailed; and -2 = most detailed. 

TOUT is the time interval for output in minutes. If events are 

changing significantly, it is not followed. 

CONCT is a flag used during development. Set to 0. 

DR is the reference density in pounds per cubic foot of air 

corresponding to the reference temperature, TR. 

2. Airway lines. Each line describes a single branch in the 

network to be modeled. Each line consists of the following 

variables: 

NO,JS,JF,NWTYP,R,Q,KF,LA,A,O,HA,HK,CH4V,CH4PA,TROCK

Where: 

NO is the airway identification number (ID). NO must be between 1 

and 9980. 

JS is the starting junction ID number of the airway. JS must be 

between 1 and 999. 

JF is the ending junction ID number of the airway. JF must be 

between 1 and 999. 

NWTYP is the marker for airway type. Values of NWTYP can be: 1 = 

fan branch (with zero airflow resistance); 0 = normal airway; 

and -1 = fixed quantity airway (regulator). A regulator will be 

converted to a normal airway or fan branch after the network 

balancing is performed depending upon the method by which the 

user-specified airflow requirement can be satisfied. During the 

simulation, a fire source branch will automatically be given 

NWTYP value of 1. 

R is the resistance of a normal airway in 1.0*E-10 in. w.g./(cfm)2

. 

When the input value of R is equal to or less than 0, R will be 
42 

 calculated from KF, LA, A and O. If these input data items are 

not complete, an error message will be issued. 
43 

When the input value of R is larger than zero, it will override 

the value calculated from KF, LA, A and O. 

For a fan branch (NWTYP=1), R is the fan pressure in in. w.g. A 

fan without input for its characteristic curve will be regarded 

as a fixed-pressure fan and the value of R will be used to define 

the fan pressure. 

Q is the volume airflow rate in the branch in CFM. 

KF is the friction factor in 1.0*E-10 lbm*min2

/ft4. The default 

value is 100. (Typical Friction Factor values are shown in Table 

5 in Appendix 1 of this manual.) 

LA is the length of the airway in ft. The default value is 500. 

A is the cross-sectional area of airway in ft2

. The default value 

is 100.0. 

O is the perimeter of airway in ft. The default value is 40.0. 

HA is the thermal diffusivity of rock in ft2/hr. The default 

value is 0.1. 

HK is the thermal conductivity of rock in BTU/hr*ft*F The default 

value is 3.0. (Typical values for HA and HK for various rock 

types are shown in Table 6 in Appendix 3 of this manual.) 

CH4V is the methane emission rate for the whole airway in ft3/min 

under the reference conditions (1 atmosphere and TR). If CH4V is 

zero or less, the methane emission rate in the airway will be 

calculated from CH4PA. 

CH4PA is the methane emission rate per unit surface area of the 

airway in ft3

/min*ft2 under the reference conditions. If CH4PA is 

 input as zero or less, the methane emission rate will be 

calculated from the methane concentration in junctions (CH4C). If 

both CH4V and CH4PA are 0, methane emissions are not considered. 

TROCK is the rock temperature in deg. F. of the airway (quasiequilibrium wall surface temperature before the fire started). It 

is normally calculated in the program run and does not require 

input from the user. If the user has better data available, it 

may be input here to override the calculated value. The 

acceptable range of user specified rock temperature is from 0 F 

to 150 F. 
44 

3. Junction Lines section 1 are used to describe conditions and 

locations of the junctions. When NVPN is negative or zero, each 

junction referenced in the airway data section must have a one 

line input. Otherwise, the junction lines must be omitted. 

Junction Lines section 1 consist of four variables: 

JNO,T,Z,CH4C 

where, 

JNO is the junction ID number. It must be between 1 and 999. 

T is the junction temperature in degrees F. 

Z is the junction elevation in ft. above a datum level. 

CH4C is the methane concentration in pct in the junction. 

(optional) 

Junction lines section 2 identifies atmospheric junctions. These 

are used when the ventilation system has multiple atmospheric 

junctions with different elevations. The junctions should be 

connected with very low resistance and hoigh airflow branches 

wich represent the surface connection between the junctions. 

Junction lines section 2 consists of three variables: JAN, JA, 

JATP where: 

JAN is the number of atmospheric junctions. JAN is on the first 

line of the data group. If only one junction is in the 

atmosphere, JAN is 1 and JA and JATP are not used. 

The rest of the data group consists oflines; each line describing 

an atmospheric junction with : JA and JATP where: 

 

JA is the ID number of the atmoispheric junction 

JATP is a marker for the type of the atmospheric junction. 0 is 

the value for the starting junction for the simulation and 1 is 

th value for all other atmospheric junctions. 

4. Fan description consists of three lines. Fan line number 1 

consists of three variables: 

NOF, MPTS, and NSWT 

where, 

NOF is the ID number of the airway in which the fan is located. 

MPTS is the number of data pairs describing the fan 

characteristics. Maximum MPTS is 10. 
45 

NSWT is a marker to select the type of curve fitting. 1 selects 

least squares; 2 selects the spline method; 3 allows the computer 

to auto select and 4 is a combination of manual and automatic. 
46 

5. Fan line number 2 consists of data pairs describing the fan 

characteristic curve in the form: 

QF,PF, QF,PF, QF,PF, QF,PF, QF,PF 

Where QF is the airflow through the fan in cfm and PF is the fan 

pressure in in. w.g. corresponding to QF. For each data point, a 

pair of QF and PF data must be specified. Up to 5 pairs of QF and 

PF data points may be on a line. A maximum of 10 data points or 

two lines may be used to describe the fan characteristics. The 

line order of the input points of the fan curve must be in 

ascending numerical order from small QF to large QF. 

Fan lines numbers 1 and 2 describe one fan. Additional fans are 

described by adding another set of fan lines numbers 1 and 2. The 

number of fans described here must equal NFNUM on control line 

number 1. If NFNUM is zero or less, fan lines 1 and 2 must be 

omitted. 

Fan line nimber thee consists of one variable NPLOT. NPLOT 

selects the treatment of the fan curve in regions undefined by 

the fan data set. If NPLOT=1, the curve is extended following 

it’s gradient at both ends. If NPLOT=2, the left boundry is 

extended following it’s gradient and the right boundry is sent to 

zero. If NPLOT=3, both boundries are sent to zero. 

6. Contamination (fire source) lines consist of up to nine 

variables. Data item INFLOW in control line number 1 indicates 

the number of contamination sources that are present in the 

ventilation system. Each of the contamination sources requires a 

one line data input. If the input value of INFLOW in control line 

number 1 is zero or less, contamination lines must be omitted. 

Contamination lines may include the following data items: 

NCENT,CONT,CONC,HEAT,O2MIN,SMPO2,HTPO2,QCENT,TPR 

where, 

NCENT is the ID number of the airway with a fire source located 

at the entrance of the incoming airflow. 

CONT is the contaminated gas inflow from the contamination source 

in cfm. 

CONC is the concentration of fumes in the contaminated gas, CONT, 

in pct. 

HEAT is the heat influx at the fire source in Btu/min. 

O2MIN is the oxygen concentration leaving the fire source in pct. 
47 

SMPO2 is the fume production in ft3

 for each ft3 of oxygen 

reaching the fire source. 

HTPO2 is the heat generation in BTU for each ft3 of oxygen 

reaching the fire source. 
48 

CONT, CONC and HEAT define a fixed heat input fire source. O2MIN 

defines an oxygen rich fire. SMPO2 and HTPO2 define a fuel rich 

fire. When they all have non zero input values, the oxygen rich 

model overrides fixed heat input fire model, while the fuel rich 

fire model overrides the oxygen rich model. The oxygen rich and 

fuel rich fires are primarily research tools. While the oxygen 

rich and fuel rich fire models were retained in MFIRE 2.0, the 

fixed heat output model will be suitable for most mining uses. 

QCENT is the reference airflow in ft3

 at which the above 

parameters are defined. When the airflow is less than or greater 

than QCENT, the heat generation from the fire source will 

decrease or increase accordingly but in a damped fashion. If 

QCENT is less than 10 cfm, the damping is not performed. 

TPR is the leading time period in min. for an oxygen rich fire to 

reach full strength. Heat generation is calculated from available 

oxygen. Increasing the airflow to a fire will increase heat 

output, however the heat output will lag the increased airflow. 

The quantity of lag will vary with the fuel type and is user 

defined with TPR. The effect is linear over the time TPR. 

9. Control Line number 2 consists of the following variables: 

NAV,JSTART,TSTART,TIME,CRITSM,CRITGS,CRITHT,WRNPR,WRNSM,WRNGS, 

WRNHT 

where: 

NAV is a marker. If NAV is 1 or larger an average value card is 

present in the data file to supply required values which may have 

been omitted in the data file. 

JSTART is the ID number of starting junction in the ventilation 

system. At the junction of JSTART (usually the atmosphere), 

conditions never change . 

TSTART is the air temperature at the starting junction in deg. F. 

TIME: time span to assume quasi-equilibrium in hrs. Default 5. 

CRITSM is the accuracy criterion for fume calculation in pct. The 

default value is 0.005. 
49 

CRITGS is the accuracy criterion for methane calculation in pct. 

The default value is 0.01. 

CRITHT is the accuracy criterion for temperature calculation in 

deg. F. The default value is 0.1. 

WRNPR is the pressure drop criterion in in. w.g. for issuing a 

warning message. The default value is 0.01. 

WRNSM is the fume concentration criterion in pct. for issuing a 

warning message. The default value is 0.05. 

WRNGS is the methane concentration criterion in pct. for issuing 

a warning message. The default value is 1.0. 

WRNHT is the high temperature criterion in deg. F for issuing a 

warning message. The default value is 100.0 degrees F. 

The last seven data items serve as calculation accuracy criteria 

or warning message issuing criteria. In most cases, the available 

default values will be suitable. To activate the respective 

default values, place a zero at that location in the data file. 

10. The average value line consists of a set of average values 

for data items which are required for the program to run. The 

average value line supplies these data items if they can not be 

obtained from the data file or default values. These items are 

used to supply unknown or omitted data. The presence of an 

average value line is indicated by a value of 1 or greater for 

the variable NAV in control line number 2. These items include: 

HAAVR,HKAVR,KFAVR,LAAVR,AAVR,OAVR 

where, 

HAAVR is the average thermal diffusivity of rock in ft2

/hr. The 

default value is 0.1. 

HKAVR is the average thermal conductivity of rock in Btu/hr*ft*F. 

The default value is 3.0. 

KFAVR is the average friction factor in 

1.0*E-10 lbm*min2

/ft4. The default value is 100. 

LAAVR is the average length of an airway in ft. The default value 

is 500. 
50 

AAVR is the average cross sectional area of an airway in ft2

. The 

default value is 100.0. 

OAVR is the average perimeter of an airway in ft. The default 

value 40.0 

To select a default value, use zero for the respective data item. 

If the entire set of default values are to be used, set NAV=0 on 

control line number 2 and omit the average value line. 

Time table lines for describing condition changes during the 

dynamic simulation can consist of seven types of condition 

changes related to the variable ICODE. Each event is described by 

one line of data variables. The general input scheme for the 

line is: TS, ICODE and related data. TS indicates the starting 

time of the condition change, and ICODE defines the nature of the 

condition change. NBR identifies the airway where the event 

occurs. There is no limit for the number of events. The order of 

events must be from small TS to large TS. Time table lines, 

ICODEs and the parameters are defined as: 

 TS,1,NBR,R 

The ICODE 1 changes branch "NBR" to an ordinary airway with 

airflow resistance equal to "R" at "TS" minutes after time=0. 

"R" is expressed in 1.E-10 inches W.G./(CFM)2

. 

 

 TS,2,NBR,INDEX 

 QF1,PF1,QF2,PF2,QF3,PF3,QF4,PF4,QF5,PF5 

The ICODE 2 changes branch "NBR" to a fan branch. The fan is 

described by "INDEX" number of points on its fan curve. A 

maximum of 5 points is allowed. Each point on the fan curve is 

defined by an airflow quantity (QF) and corresponding pressure 

(PF) value. Quantity is expressed in ft3

/min and pressure is 

expressed in inches W.G. The points must be listed in ascending 

order of QF. 
51 

 TS,3 NBR,CONT,CONC,HEAT,02MIN,SMPO2,HTPO2,QCENT,TPR 

The ICODE 3 changes branch "NBR" to a fire source branch at "TS" 

minutes after time=0. The remaining variables CONT, CONC, HEAT, 

O2MIN, SMPO2, HTPO2, QCENT, TPR retain the same meanings and are 

expressed in the same units as in the contamination source line. 

 TS,4,NBR 

The ICODE 4 changes fire source branch "NBR" to an ordinary 

airway at time "TS" minutes after time=0. 

 TS,5,TINC 

This input changes the time increment of the dynamic simulation 

to a new value "TINC" at "TS" minutes after time=0. "TINC" is 

expressed in seconds. 

 TS,6,TOUT 

The time interval for output is changed to TOUT at TS minutes 

after time zero. 

 TS,7,JDPP 

At time TS detgailed output results will be shown for airways on 

the immediate down stream side of the junction JDPP. 
52 

6.0 OUTPUT FILES 

All output is saved in the file MFIRE.OUT in the directory and/or 

disk containing the program. The file name MFIRE.OUT is hard-coded 

into the program. Subsequent MFIRE runs will over write the old 

file. Simply rename the old MFIRER.OUT file if archiving is 

desired. The file can be inspected with a text processor and sent 

to a printer, if needed. 

6.1 CONTENTS OF THE OUTPUT FILE 

The comment lines, reference temperature, air density, a table of 

the units of measure for the results and the average values are 

shown at the start of MFIRE.OUT. 

All input data will be shown in the output file if IOUT on Control 

line number 1 is -1 or less. For each contamination source, a new 

branch will automatically be set up. The new airway and junction ID 

numbers will not interfere with the original numbering scheme of 

the data file. 

Next are the results of the selected simulation(s) in the following 

order: network balancing, network balancing considering 

temperatures, transient state modeling, and altered equilibrium due 

to fire and distribution of the contaminants. 

Depending upon the contents of the data file and the simulation 

selected, attention, warning, and error message will be shown at 

locations where calculations resulted in unusual conditions. 
53 

7.0 MFIRE ERRORS 

The usual run time errors will occur when illegal mathematical 

operations are attempted by MFIRE. A variety of memory management 

errors are possible as well. MFIRE will run best on a "plain" DOS 

machine. Disabling non compatible memory managers will usually 

allow MFIRE to execute. 

7.1 DATA FILE ERRORS 

Two types of data file errors can occur. 

1. An error may occur because the input data file itself is 

invalid. This may be caused by: 

The data file can not be found due to incorrect spelling, drive or 

path specification. Check the spelling and path at the prompt for 

location of the data file. 

The data file contains non-ASCII symbols. Check the operation of 

the text processor to insure that only ASCII characters are 

produced. Delete all non ASCII and/or all out of place characters. 

2. Data are accepted by the program, but are incorrect for the data 

types or ranges or the combination causes a data inconsistency. 

This may be due to: 

An invalid character is located where a numerical value is 

required. 

The input data value is outside the reasonable range. 

The input data is insufficient to build the model for simulation. 

The input data exceeds the capacity of the program. 

7.2 PROGRAM ERROR DETECTION 

When the program is running, tracing messages are given on the 

screen indicating the group and lines of data that have been read 

and the section of the program that is executing. Program 

termination indicates that problems are caused by the subsequent 

(not read) data file section. 

For each detected error, a descriptive message starting with: 

 * ERR * 

is issued and the program terminates. 
54 

When a possibly wrong value and/or its calculated intermediate 

result is detected, a descriptive message starting with: 

 * WRN * 

is issued and the program continues. 

If a modification of input value or calculated intermediate result 

is automatically made by the program, a descriptive message 

starting with: 

 * ATTN * 

is issued and the program continues. 

7.3 LOCATING ERRORS 

If a message indicates that the error condition occurred due to the 

data input file, locate the line and the value of input data item 

which caused the error with the screen message, output file message 

and the lists of input data. 

If no error message is issued but the simulation results are not as 

expected, carefully check the list of input data shown in the 

output file. 

WARNING messages and ATTENTION messages may reveal an error in the 

input data even though the program continues to operate. Insure 

that the default values or modifications adopted by the program run 

are acceptable. 

Anomalistic data, though not necessarily incorrect or impossible, 

may lead to an anomalous simulation. For example, making a fan 

unusually powerful may prevent a normal strength fire from 

affecting the airflow distribution in the system. Much care must be 

employed before considering an extreme case. If a message 

indicates that the accuracy criterion in the temperature section of 

the program was not satisfied, a table detailing the current 

parameters of airways which have large fluctuation in the average 

air temperature from iteration to iteration is produced. If the 

pattern of the parameters is clearly cyclical while the variation 

of natural ventilation pressure is stable or cyclical from 

iteration to iteration, then, most likely there is no single 

equilibrium stage for the event. If the variation of natural 

ventilation pressure decreases steadily though slowly, increasing 

the value of data item variables MADJ or ITN (on control line 

number 1) may allow convergence. 
55 

8.0 MODELING FIRES 

This section outlines procedures for using MFIRE to model fire 

events in a mine. The following subsections describe the three 

types of fires MFIRE can model, criteria for choosing the most 

suitable fire type for a given situation, specifying the numerical 

parameters which define a given fire, and interpreting MFIRE output 

resulting from a fire simulation. A variety of case examples are 

provided which illustrate the methods discussed. Various data 

tables are included in the Appendix which can be used to help 

specify fire parameters. 

MFIRE was originally developed as a research tool to aid in 

analyzing the complex interactions between fires and mine 

ventilation systems. The primary emphasis was on ventilation 

aspects, however the method of modeling fires is also quite 

involved. A thorough understanding of MFIRE's fire models is 

therefore required if meaningful fire simulation results are to be 

achieved. 

8.1 General Information and Basic Assumptions 

MFIRE users can choose from among three types of fires to 

appropriately model a given fire situation. The three types are: 

 Fixed Heat Input Fire 

 Oxygen Rich Fire 

 Fuel Rich Fire 

The characteristics of each fire type, and the selection criteria 

for determining the fire type which most appropriately suits a 

given situation are provided below. 

For oxygen rich and fuel rich fires, MFIRE assumes complete 

combustion of a hydrocarbon fuel to produce carbon dioxide (CO2) and 

water. Accordingly, throughout MFIRE and its accompanying 

documentation, the term "fumes" refers to CO2, and the calculation 

of fume concentration is based on an idealized ratio multiplier 

relating oxygen consumed by the fire and CO2 produced by the fire. 

However "real world" fires produce a variety of combustion 

products, and many MFIRE users are concerned with products other 

than CO2, such as carbon monoxide (CO). MFIRE allows the user to 

model the production of other combustion products by specifying a 

fume production rate corresponding to the combustion product of 

interest and the fire scenario simulated. 

 

Another basic assumption incorporated in MFIRE concerns the amount 

of heat generated by combustion. 
56 

MFIRE assumes 437 BTU of heat are produced for each cubic foot (ft3

) 

of oxygen (O2) consumed by a fire. Since not all fires necessarily 

conform to this relationship, some MFIRE users may wish to model 

fires producing heat at a rate other than 437 BTU/ft3 of oxygen. 

This option is available within the program, and the procedure for 

doing so is described later in this section. 

8.2 Fixed Heat Input Fire 

The fixed heat input fire refers to a fire which is defined by a 

specified heat influx and a specified fume production rate. Three 

MFIRE variables are used to specify a fixed heat input fire are: 

HEAT - heat influx at the fire source, 

 expressed in BTU/min 

CONT - fume production rate, expressed 

 in ft3

/min 

CONC - concentration of fumes produced, 

 expressed in percent 

Most MFIRE users will find the fixed heat input fire to be the most 

generally applicable fire type for routine fire modeling purposes. 

 

Methods for selecting appropriate values for the fixed heat input 

fire variables to realistically represent a desired fire are 

discussed in Sections 8.6 through 8.11. Section 8.12 contains 

examples of these calculations. 

8.3 Oxygen Rich and Fuel Rich Fires 

Oxygen rich and fuel rich fires are special case fires which 

describe combustion behaviors somewhat unique to mine situations, 

and they are distinguished by the mode of pyrolysis. Combustion 

occurs whenever sufficient pyrolyzed fuel and oxygen are present at 

or above the ignition temperature. The mode of pyrolysis, or the 

heating of a fuel surface to generate gaseous fuel necessary for 

combustion, affects the characteristics of the fire and the extent 

to which the limited amount of oxygen available is consumed by the 

fire. 

8.4 Oxygen Rich Fire 

In the oxygen rich case, heat produced by the fire is transferred 

to unburned fuel surfaces through convection and radiation, causing 

pyrolysis in a largely localized process near the flame. 
57 

Much of the air passing through the fire zone is not involved in 

pyrolysis or combustion, resulting in moderate to high oxygen 

concentrations downstream from the fire. 

An oxygen rich fire is defined by the concentration of oxygen 

contained in the ventilation stream downstream from the fire. 

MFIRE calculates a corresponding heat influx due to the fire by 

multiplying the number of cubic feet per minute of oxygen lost 

through combustion by the standard combustion ratio multiplier (437 

BTU per cubic feet of oxygen consumed). 

The MFIRE variable which is used to specify an oxygen rich fire is: 

O2MIN - O2 concentration downstream from 

 fire, expressed as percent O2

MFIRE assumes a nominal ambient oxygen concentration of 21 pct. in 

an uncontaminated air flow. 

8.5 Fuel Rich Fire 

In the fuel rich case, the fire zone is so large and so hot that 

the entire quantity of air passing through the fire zone is heated 

to a temperature sufficient to cause pyrolysis of fuel. The heated 

air passing though the fire zone pyrolyzes any fuel it contacts. 

The pyrolyzed fuel burns intensely until all available oxygen in 

the air stream is depleted. Fuel continues to pyrolyze, but cannot 

burn due to lack of oxygen. Pyrolyzed but unburned fuel remains in 

the downstream ventilation, giving rise to the term fuel rich fire. 

The heat release rate from a fuel rich fire is defined by the 

ventilation rate through the fire zone and a user-defined heat 

release per cubic foot of oxygen delivered to the fire. MFIRE 

calculates a corresponding heat influx due to the fire by 

multiplying the number of cubic feet per minute of oxygen lost 

through combustion (which is simply 21 pct. of the total air flow) 

by the user-defined heat release per cubic feet of oxygen consumed. 

 Fume production is also defined by the user. The MFIRE variables 

which are used to specify a fuel rich fire are: 

SMPO2 - fume production, expressed in ft3

 of 

 fumes per ft3 of O2 consumed 

HTPO2 - heat generated, expressed in BTU's 

 per ft3

 of O2 consumed 

For a given fuel loading and ventilation rate, a fuel rich fire 

burns more intensely than an oxygen rich fire. Fuel rich fires 

propagate faster, produce higher temperatures and higher 

concentrations of combustion products (possibly in the explosive 

range), and consume more oxygen. 
58 

For these reasons, fuel rich fires represent a far greater hazard 

than oxygen rich fires. Depending on the fuel loading, ventilation 

rate, and intensity of the ignition source, a fire may start as 

oxygen rich, only to "jump state" to become fuel rich. 

Fortunately, fuel rich fires are extremely rare events. It is 

estimated that less than 0.1 pct. of mine fires reach the fuel rich 

state. 

When only CONT, CONC, and HEAT have non-zero values in an input 

data file, a fixed heat input fire is modeled. If these variables 

 have non-zero values, but O2MIN also has a non-zero value, the 

oxygen rich case overrides the fixed heat input fire, and an oxygen 

rich fire is modeled. Likewise, if the foregoing variables have 

non-zero values, but SMPO2 or HTPO2 also have non-zero values, the 

fuel rich case overrides the fixed heat input and oxygen rich 

cases, and a fuel rich fire is modeled. 

8.6 Estimating Fire Parameters 

Although the MFIRE program will accurately model any of the three 

fire types described above, the user must properly specify 

numerical values for the fire variables if the results are to be 

meaningful. 

The two critical parameters which define the intensity of the fire 

and its effects on a mine's ventilation system are heat release 

rate and fume production rate. The heat release rate determines 

the thermal energy released into the mine. This thermal energy 

creates throttling and buoyancy effects, which in turn, cause 

changes in air flow rates, changes in methane concentrations due to 

dilution effects, reversals, recirculation, etc. The fume 

production rate determines the amount of combustion fumes produced 

by the fire and therefore, the concentration of fumes throughout 

the network. 

For fixed heat input fires, the heat release rate and fume 

production rate are inserted directly into the MFIRE input data 

file by the user. Normally, the user finds it necessary to 

calculate values for these parameters using fundamental combustion 

data for the fuel or fuels involved in the simulated fire. These 

calculations are performed separate from the MFIRE program, and the 

results are the direct determination of values for the variables 

HEAT and CONT. 

For oxygen rich and fuel rich fires, heat release rate and fume 

production rate are specified indirectly by the user when values 

are assigned to the variables O2MIN, HTPO2, and SMPO2. However, 

for meaningful oxygen rich and fuel rich fires to be simulated, the 

user may need to perform similar calculations as are required when 

specifying parameters for a fixed heat input fire. 
59 

These calculations are performed separately from the MFIRE program 

to determine heat release rate and fume production rate using 

fundamental combustion data for the fuel or fuels involved in the 

simulated fire. Once the heat release and fume production rates 

are known, values for O2MIN, HTPO2, and SMPO2 can be easily 

derived. 

8.7 Heat Release Rate and Burning Rate 

Heat release rate is determined by the following formula: 

Hr = Br x Hv

 where: 

Hr is heat release rate, expressed in BTU/min 

Br is burning rate, expressed in lbs/min; and 

Hv is heating value of the fuel, expressed in BTU/lb 

Burning rates are estimated or measured. For example, if a 100- 

pound stack of wood burns in 40 minutes, the average burning rate 

is 2.5 lbs/min. 

8.8 Complex Assemblies and Multiple Fuels 

 

Although simple in theory, specifying burning rates for many mine 

fire scenarios can be quite tricky. For example, an MFIRE user may 

wish to model a fire involving multiple fuel sources combined into 

a highly complex assembly - for example, a load-haul-dump or a 

conveyor drive. 

This problem has been addressed for residential and commercial 

occupancies. Full scale fire tests have been conducted, and 

burning rate, heat release rate, and fume production rate data have 

been experimentally obtained for common residential and office 

furnishings such as upholstered chairs, sofas, carpeting, computer 

work stations, etc. However, actual experimental data on burning 

rates and heat release rates for "real world" mine fire hazards are 

not available. This forces the MFIRE user to estimate these 

critical parameters. 

The recommended method for estimating burning rates, heat release 

rates, and fume production rates for a complex assembly presenting 

multiple fuels involves 4 steps: 

1. conceptualize a specific fire scenario and subdivide the 

 fire into discrete phases; 
60 

 2. for each phase, individually determine heat release rate 

 and fume production rate for each fuel material; 

 3. sum the heat release rates and fume production rates for 

 each phase; 

 4. use the Time Table feature of MFIRE to specify a "new" 

 fire corresponding to the time sequence and fire 

 parameters of each phase. 

Normally, a complex fire scenario can be subdivided into a sequence 

of phases, with each phase defined by its duration and fuels 

involved. Each phase should represent a different stage in the 

growth and development of the fire. Ideally, each phase would 

involve steady-state burning of a specific combination of fuel 

materials. As a fire grows in intensity or a different fuel 

material becomes involved, a new phase would start. When all the 

phases are combined into a continuous sequence, they approximate 

the total fire, only in a step-wise fashion. Case example 7 at the 

end of this chapter illustrates the application of this 

methodology. 

Clearly, this process is imprecise at best. The conceptualized 

fire scenario may or may not be realistic. The estimated burning 

rates of the individual fuels may or may not be reasonable. The 

step-wise approximation of the total fire may be a significant 

departure from reality. Therefore, MFIRE users are urged to 

perform multiple simulations using input data which spans a range 

of possible values, and analyze the results to assess overall 

effects. 

For example, a user might be concerned about the potential for the 

air flow in a certain escapeway to be contaminated by combustion 

products from a fire occurring at a distant location in the mine. 

To minimize unnecessary calculations, this user might wish to 

initially perform a simulation of a fire which is significantly 

larger than could be realistically expected at that location. Very 

little effort would be required to "guess" at these unrealistically 

high values for the fire parameters. If this size fire produces a 

level of contamination in the escapeway or other ventilation 

disturbances which are considered to be acceptable (ie: such that 

escape would not be impaired), no further analysis may be 

necessary. If this size fire produces an unacceptable level of 

contamination, the extra time and effort required to "fine tune" 

the estimates of fire parameters might then be justified. 

8.9 Ventilation Velocity Effects 

Another complicating factor is the effect of ventilation velocity 

on burning rates and resulting heat release rates. 
61 

Within practical ranges of ventilation velocity, burning rates tend 

to increase with increased ventilation velocity and decrease with 

decreased ventilation velocity. Thus, if a fire causes an increase 

or decrease in ventilation, it should cause a corresponding 

increase or decrease in burning rate. 

This complication is automatically accommodated within MFIRE when 

an optional reference airflow rate variable is used. As 

ventilation flows change due to a fire, heat release rates for the 

fire are automatically adjusted upward or downward accordingly. A 

damping factor maintains heat release rates within reasonable 

limits, preventing upward adjustments from exceeding double, and 

downward adjustments from falling lower than one-half, the initial 

heat release rate of the fire. 

8.10 Heating Values of Fuels 

Heating values of fuels are determined experimentally and published 

in the engineering literature. Heating values of standard fuels 

such as wood (various species and moisture content), coal (various 

seams and sources), coke, petroleum oil products, etc. are 

published in handbooks of mechanical engineering, fire protection 

engineering, combustion engineering, and chemistry and physics. 

Heating values of some specialized mining materials (conveyor belt, 

brattice, etc.) have been experimentally determined by the Bureau 

of Mines and published in various Bureau reports. Heating values 

for a representative sample of mine combustibles are provided in 

Table 1 of the Appendix. 

8.11 Fume Production 

Fume production rates are determined by the following formula: 

Fr(CP) = Hr x ß 

 where: 

Fr(CP) is the fume production rate for the combustion 

 product of interest, expressed in ft3/min; 

Hr is heat release rate, expressed in BTU/min; and 

ß is the production rate constant for the 

 combustion product of interest 

Values of ß for the two most common combustion products, CO2 and CO, 

have been experimentally derived for a variety of mine combustibles 

during both flaming and smoldering combustion. These ß values are 

contained in Table 2 in the Appendix. 
62 

The basic relationships between the various fire parameters are 

summarized in Table 3 in Appendix 3. Table 4 in Appendix 1 shows 

conversion factors to perform unit conversions for ß values (ß 

values often appear in the literature in SI units, however MFIRE 

requires ß values to be expressed in English units). 

Fume production rates are expressed in ft3

/min in an MFIRE input 

data file, while "fumes" in an MFIRE output, are expressed in 

percent. Expressing fumes in percent form in the output file can 

be somewhat confusing and cumbersome, particularly for simulations 

of small to moderate sized fires where fume concentrations may be 

orders of magnitude less than 1%. This is especially true for 

simulations of CO production, since CO concentrations are usually 

expressed in parts per million (ppm). To aid in interpreting 

output, users are reminded that the conversion factor between 

percent and ppm is "x 10,000." For example: 

 0.001% = 10 ppm 

 0.01% = 100 ppm 

 0.1% = 1,000 ppm 

 1% = 10,000 ppm 

8.12 Fire Modeling Examples 

Several examples are provided to illustrate the methods for 

determining appropriate numerical values for the critical fire 

parameters required for MFIRE fire simulations. 
63 

 Example 1 

Determine heat release rate and CO and CO2 production from a 

transformer oil spill fire. The fire is contained in a 12 by 15 ft 

area (180 ft2), and the spill occurred in a mine entry having a 

ventilation rate of 120,000 CFM. The fuel has a heating value of 

20,000 BTU/lb, a specific gravity of 0.72 (density of 45 lb/ft3), 

and a known burning rate, which is expressed as depth of fuel 

burned per unit time, of 8 in/hr (0.011 ft/min). 

1a. For heat release rate: 

 Hr = Br x Hv

 = 180 ft2 x 0.011 ft/min x 45 lb/ft3 x 20,000 BTU/lb 

 = 1,782,000 BTU/min 

1b. For CO2 production rate: 

 Fr(CP) = Hr x ß 

 = 1,782,000 BTU/min x 0.0015 ft3/BTU 

 = 2673 ft3/min of CO2

1c. For CO production rate: 

 Fr(CP) = Hr x ß 

 = 1,782,000 BTU/min x 0.00009 ft3/BTU 

 = 160.4 ft3/min of CO 

For this example, if a fixed heat input fire were to be modeled, 

values for the fire variables would be as follows: 

HEAT = 1782000 (1,782,000 BTU/min) 

CONT = 2673 (for CO2, 2673 ft3

/min) 

CONT = 160 (for CO, 160 ft3/min) 

CONC = 100 (contaminate assumed at 100 pct.) 
64 

 Example 2 

Determine heat release rate and CO and CO2 production from a fire in 

a pile of Pittsburgh seam coal. The cone-shaped pile is 15 ft in 

dia and 6 ft high (360 ft3), and the bulk density of the broken coal 

is 50 lb/ft3. The pile burns with visible flames, and is 

completely consumed over a 48 hr period. 

2a. For heat release rate: 

 Hr = Br x Hv

 = 6.25 lb/min x 14,000 BTU/lb 

 = 87,500 BTU/min 

2b. For CO2 production rate: 

 Fr(CP) = Hr x ß 

 = 87,500 BTU/min x 0.0017 ft3/BTU 

 = 149 ft3/min 

2c. For CO production rate: 

 Fr(CP) = Hr x ß 

 = 87,500 BTU/min x 0.00014 ft3/BTU 

 = 12.3 ft3/min of CO 
65 

Example 3 

Determine heat release rate and CO and CO2 production from a wood 

crib fire. The 8 ft high crib is constructed from 4 ft long 

Douglas fir (density of 35 lbs/ft3) 6x6's, solid stacked. The crib 

is completely consumed in 3 hrs, resulting in an average burning 

rate of 25 lbs/min. 

3a. For heat release rate: 

 Hr = Br x Hv

 = 25 lb/min x 8,000 BTU/lb 

 = 200,000 BTU/min 

3b. For CO2 production rate: 

 Fr(CP) = Hr x ß 

 = 200,000 BTU/min x 0.0020 ft3/BTU 

 = 400 ft3/min of CO2

3c. For CO production rate: 

 Fr(CP) = Hr x ß 

 = 200,000 BTU/min x 0.00005 ft3/BTU 

 = 10 ft3/min of CO 
66 

 Example 4 

Estimate the downstream oxygen concentration from a coal pile fire 

for modeling an O2 rich type fire. (Use the coal pile fire from Case 

Example 2, and assume 50,000 CFM ventilation.) 

87,500 BTU/min ÷ 437 BTU/ft3 O2 = 200 ft3/min O2 consumed 

O2 inflow = 0.21 x 50,000 = 10,500 ft3/min O2

10,500 ft3/min O2 - 200 ft3/min O2 = 10,300 ft3/min O2

10,300 ft3/min O2 ÷ 50,000 ft3/min = 0.206 

downstream O2 = 20.6% 
67 

 Example 5 

How large a fire is required to reduce the downstream O2 content of 

the ventilation stream to 16%? (Assume 50,000 CFM) 

O2 depletion = 21% - 16% = 5% 

5% O2 x 50,000 ft3/min = 2,500 ft3/min O2

 2,500 ft3/min O2 x 437 BTU/ft3 O2 = 1,092,500 BTU/min 

A fire generating 1,092,500 BTU/min would consume 10 barrels of 

diesel oil/hour, 4 tons of wood/hour, or 2.7 tons of coal/hour. 
68 

 Example 6 

How large a fire is required to produce a "fuel rich" fire state? 

(assume 50,000 CFM ventilation, and recall that a "fuel rich" fire 

consumes all O2 inflow) 

 50,000 ft3/min x 0.21 = 10,500 ft3/min O2

 10,500 ft3/min O2 x 437 BTU/ft3 O2 = 4,588,500 BTU/min 

A fire generating 4,588,500 BTU/min would consume over 40 barrels 

of diesel oil/hour, 17 tons of wood/hour, or 11 tons of coal/hour. 
69 

 Example 7 

Estimate heat release rate and CO production from a fire on a 

diesel-powered load-haul-dump vehicle. The fire starts when a pinhole leak occurs in a 4,000 PSI hydraulic line which sprays fuel 

onto a hot exhaust manifold. After 1 minute, various hoses and 

electrical wiring begin to burn. Two minutes later, the hoses burn 

through, providing additional liquid hydrocarbon fuel (HC). Eight 

minutes later, pressure in the hydraulic system has decayed, 

stopping the original pin-hole leak and greatly reducing the 

hydrocarbon fire, however both rear tires begin to burn. 

At T = 0 minute, oil begins to leak and the fire ignites almost 

immediately (assume 0.5 mm orifice): 

Hr(pin hole) = 20,000 BTU/lb x 4 lb/Min = 80,000 BTU/Min 

CO(pin hole) = 0.00009 ft3

/BTU x 80,000 BTU/Min = 7.2 ft3/Min 

At T = 1 minute, pin hole leak continues; hoses and wiring begin 

burning: 

Hr(pin hole) = 20,000 BTU/lb x 4 lb/Min = 80,000 BTU/Min 

Hr(hoses) = 14,000 BTU/lb x 2 lb/Min = 28,000 BTU/Min 

Hr(wiring) = 15,500 BTU/lb x 1 lb/Min = 15,500 BTU/Min 

Hr(total) = Hr(pin hole) + Hr(hoses) + Hr(wiring)

= 80,000 + 28,000 + 15,500 = 123,500 BTU/Min 

 CO(pin hole) = 0.00009 ft3/BTU x 80,000 BTU/min = 7.2 ft3/min 

 CO(hoses) = 0.00012 ft3

/BTU x 28,000 BTU/min = 3.4 ft3/min 

 CO(wiring) = 0.00012 ft3

/BTU x 15,500 BTU/min = 1.9 ft3/min 

 CO(total) = CO(pin hole) + CO(hoses) + CO(wiring)

= 7.2 + 3.4 + 1.9 

 

= 12.5 ft3/BTU 
70 

At T = 3 minutes, hoses burn through, releasing additional liquid 

hydrocarbons (estimate 10 Gal/Min): 

Hr(HC's) = 20,000 BTU/lb x 60 lb/Min = 1,200,000 BTU/min 

Hr(total) = Hr(pin hole) + Hr(hoses) + Hr(wiring) + Hr(HC's)

= 80,000 + 28,000 + 15,500 + 1,200,000 

= 1,323,500 BTU/min 

CO(HC's) = 0.00009 ft3/BTU x 1,200,000 BTU/min = 108 ft3/min 

CO(total) = CO(pin hole) + CO(hoses) + CO(wiring) + CO(HC's)

= 7.2 + 3.4 + 1.9 + 108 

= 120.5 ft3

/BTU 

At T = 11 minutes, hydraulic system pressure decay has reduced HC 

fuel flow from original pin hole leak and subsequent hose burnthrough, however hoses and wiring continues to burn and rear tires 

are burning: 

Hr(HC's) = 20,000 BTU/Min x 2 lb/Min = 40,000 BTU/Min 

Hr(tires) = 14,100 BTU/Min x 8 lb/Min = 112,800 BTU/Min 

Hr(total) = Hr(hoses) + Hr(wiring) + Hr(HC's) + Hr(tires)

= 28,000 + 15,500 + 40,000 + 112,800 

= 196,300 BTU/Min 

CO(HC's) = 0.00009 ft3

/BTU x 40,000 BTU = 3.6 ft3/min 

CO(tires) = 0.00012 ft3

/BTU x 112,800 BTU = 13.5 ft3/min 

CO(total) = CO(hoses) + CO(wiring) + CO(HC's) + CO(tires)

= 3.4 + 1.9 + 3.6 + 13.5 

= 22.4 ft3/BTU 
71 

9.0 MFIRE APPLICATION EXAMPLES 

The following examples illustrate various MFIRE fire modeling 

capabilities. They are intended as tutorial aids to help acquaint 

new MFIRE users with techniques for modeling fires and for 

interpreting results of fire simulations. 

The simulations are based on two mine networks; one a multi-level 

mine, the other a single-level mine. 

9.1 Multi-Level Mine Example 

The multi-level mine ventilation network is depicted in Figure 1. 

A main fan, in a blowing mode, is used to course ventilation air 

into the mine on the bottom level. Air flows upward through 

drifts, raises, and old stopes, and exits the mine's upper levels 

through two portals. 

For this example, a fire is simulated in branch 9, which is a 110 

foot long inclined drift connecting two mine levels having an 

elevation difference of 76 feet. Ventilation disturbances and CO 

levels will be noted every 15 seconds over a 15 minute period. 

The simulation involves a transformer oil fire, and the fixed heat 

input fire type (dry conditions) is modeled. Properties of the oil 

are the same as in Example 1 in the previous section (20,000 

BTU/lb, 8 in/hr burning rate, 45 lb/ft3

 density, ß for CO of 0.00009 

ft3/BTU). Flame spread across the spilled fuel is quite rapid, so 

the fire achieves steady-state burning without a prolonged 

incipient or smoldering stage. The spill covers an area of 4 ft by 

8 ft. 

The heat release rate for this fire is: 

4 ft x 8 ft x 0.011 ft/min x 45 lb/ft3

 x 20,000 BTU/lb = 316,800 

BTU/min 

and the CO production rate is: 

316,800 BTU/min x 0.00009 ft3

/BTU = 28.5 ft3/min 

The appropriate values for the fixed heat input fire variables are: 

 CONT = 28.5 

 CONC = 100 

 HEAT = 316800 
72 
73 

Therefore, the Time Table Lines list as follows: 

 0,3, 9 , 28.5, 100,316800, 0 , 0 , 0 , .75 , 0 

corresponding to the variables: 

TS,ICODE,NBR,CONT,CONC,HEAT,O2MIN,SMPO2,HTPO2,QCENT,TPR 

Figure 2 shows the network at the start of the simulation (T = 0), 

and highlights the location of branch 9, the network branch 

containing the fire. Figure 3 shows the network 30 seconds after 

the start of the simulation. Note the extent of ventilation 

disturbances caused by the fire in less than 1 minute. These 

disturbances include fume contamination of 8 network branches, 7 

reversals, and 1 recirculation path. Also note branch 14, which 

initially became contaminated, and then reversed, drawing fumeladen air back through junction 12. 

Figure 4 shows the network after 2-1/2 minutes. Branch 14 has 

reversed again, coursing air in its original direction. All other 

reversed branches have maintained their altered flow direction, and 

branch 28 has also reversed. Fume-laden air has reached the 

surface through branch 40. 

Figure 5 shows the network after 6 minutes. Fume-laden air has now 

reached the surface through branches 32, 39, 47, and 40. Note also 

that the fume front has nearly closed the recirculation path. 

Figure 6 shows the network after 15 minutes. Fumes have nearly 

filled the upper portions of the mine, including the recirculation 

path. Flow in branch 14 has again reversed direction, and is 

coursing air and fumes from junction 11 to junction 12. This 

reversal, if it is sustained, will eventually cause branches 14 and 

19 to purge themselves of fumes. 
74 
75 
76 
77 
78 

9.2 Single-Level Mine Examples 

The single-level mine is depicted in Figure 7, a simple 3 section 

coal mine. Fresh air enters the mine through branch 1 and splits 

at junction 2. Branch 2 supplies air to junction 8, a working 

section. Methane is liberated in this working section at the rate 

of 230 ft3

/min, which divides equally between branches 3 and 4. 

Branch 5 splits at junction 3 to form branches 16 and 9, which 

supply air to working sections at junctions 5 and 4 respectively. 

These working sections also liberate 230 ft3/min of methane, which 

is equally distributed between branches 15, 7, 8, and 10. 

Placement of appropriately sized regulators in branches 21, 22, 23, 

24, and 25 results in methane concentration of 0.68 pct in section 

returns and the main return. 

Two example simulations are provided. In the first example, a fire 

occurs in branch 26, followed by the unfurling of parachute 

stoppings in the intake to pressurize the intake and reduce air 

flow to the fire. In the other example, a fire also occurs in 

branch 26, but in this case, a roof fall occurs in branch 3 due to 

the fire. 

Simulated Fire

The simulated fire, which is the same in both examples, occurs on a 

diesel-powered utility vehicle. The primary combustibles are 

diesel fuel, hydraulic oil, lubricating oil, rubber, and grease. 

The fire's heat release rate is estimated at 80,000 BTU/min and CO 

production is estimated at 11.5 ft3/min. The fire is initiated at 

time = 0 for both examples. The appropriate values for the fixed 

heat input fire variables are: 

 CONT = 11.5 

 CONC = 100 

 HEAT = 80000 

Therefore, the Time Table Lines for the fire list as follows: 

0,3,26 , 11.5, 100, 80000, 0 , 0 , 0 , .75 , 0 

corresponding to the variables: 

TS,ICODE,NBR,CONT,CONC,HEAT,O2MIN,SMPO2,HTPO2,QCENT,TPR 
79 
80 

Example of the Effect of a Parachute Stopping

Parachute stoppings are unfurled in the intake, which is branch 2, 

at time = 15 minutes. Resistance of the stoppings is estimated at 

500. Therefore, the Time Table Lines for the new resistance list as 

follows: 

15,1,2,500 

corresponding to the variables: 

TS,ICODE,NBR,R 

Figure 8 shows the fire located in branch 26 at time = 0 minutes. 

At time = 3 minutes, shown in Figure 9, fumes have advanced into 

branches 3 and 4. At time = 9 minutes, shown in Figure 10, fumes 

have advanced into branch 21 and continue to fill branch 4. At 

time = 15 minutes, shown in Figure 11, the resistance of branch 2 

has been increased to R = 500 by unfurling parachute stoppings. 

Fumes have advanced to branch 11 and continue to fill branch 4. 

At time = 18 minutes, shown in Figure 12, branches 21 and 3 have 

reversed due to the increase in flow through branches 5, 16, 7, and 

25 resulting from the increased resistance in branch 2. Air from 

branch 25 now splits at junction 9, with flow toward both junction 

10 and junction 14. The reversal of branches 21 and 3 has caused 

the fumes in that system of returns to be divided. Uncontaminated 

air from branch 25 is pushing fume-laden air outby through branches 

11 and 12, but inby through branches 21 and 3. The increase in 

flow through branch 5 also reduces the methane concentration in the 

returns from both junction 5 and junction 4. 

At time = 24 minutes, shown in Figure 13, Fumes continue to be 

pushed inby through branch 3 and outby through branches 19, 20, and 

4. At time = 30 minutes, shown in Figure 14 and corresponding to 

the end of the simulation, fumes continue to be pushed inby through 

branch 3, and outby through branches 4 and 22. All fumes which had 

contaminated branches 14, 11, 12, 19, and 20 have been exhausted. 

In addition, due to the low flow through branch 3, the methane 

concentration has risen above 1.0 pct in that branch. 
81 
82 
83 
84 
85 
86 
87 
It should be noted that when fumes enter a branch but have not yet 

reached the end of the branch, the table labeled "TEMPERATURE AND 

CONCENTRATION AT AIRWAY ENDS, PRESSURE IN AIRWAYS" will list the 

fume concentration for that branch as 0.00. This table will not 

display a fume concentration for a given branch until the fume 

front has reached the end of that branch. When fumes have entered, 

but not completely filled a branch, the position of the fume front, 

expressed as the distance from the beginning of the branch, is 

displayed in the table labeled "DATA FOR THE FUME FRONT IN 

AIRWAYS." 

When a fume front is retreating rather than advancing, as occurs in 

this example at time = 30 minutes in branch 3, the "TEMPERATURE AND 

CONCENTRATION AT AIRWAY ENDS" table will continue to indicate a 

fume concentration until the branch is completely purged. 

88 
Example of the Effect of a Roof Fall

The initial ventilation conditions and the first few minutes of the 

fire are same as in the first example (Figures 7-10). Thus, the 

Time Table Lines which define the fire are the same as the previous 

example: 

0,3,26 , 11.5, 100, 80000, 0 , 0 , 0 , .75 , 0 

corresponding to the variables: 

TS,ICODE,NBR,CONT,CONC,HEAT,O2MIN,SMPO2,HTPO2,QCENT,TPR 

However at time = 15 minutes, shown in Figure 15, a roof fall 

occurs in branch 3. The resistance in this branch is immediately 

increased to R = 500. 

Therefore, the Time Table Lines for the new resistance list as 

follows: 

15,1,3,500 

corresponding to the variables: 

TS,ICODE,NBR,R 

At time = 24 minutes, shown in Figure 16, fumes have nearly filled 

branch 4 and have been exhausted from the mine through branch 20. 

In branch 3, the methane concentration has exceeded 1 pct due to 

inadequate dilution resulting from restricted air flow caused by 

the roof fall. At time = 30 minutes, shown in Figure 17, fumes 

continue to be exhausted, and have advanced into branch 13. Also, 

the methane concentration continues to exceed 1 pct in branch 3. 

89 
90 
91 
92 
REFERENCES 

Bastow, K.R., 1979, "Real-Time Simulation of Contaminant Flow 

Through Mine Ventilation Networks Under the Influence of Mine 

Fires," M.S. Thesis, MI Technol. Univ., Houghton, MI, 306 pp. 

Chang, X., 1987, "Digital Simulation of Transient Mine 

Ventilation," Ph.D. Thesis, MI Technol. Univ., Houghton, MI, 

162 pp. 

Chang, X., and Greuer, R.E., 1985, "Simplified Method To 

Calculate the Heat Transfer Between Mine Air and Mine Rock," 

Paper in Proceedings of the 2d U.S. Mine Ventilation Symposium, 

ed. by P. Moussett-Jones, A.A. Balkema, pp. 429-438. 

Chang, X., and Greuer R.E., 1987, "A Mathematical Model for Mine 

Fires," Ch. in Proceedings of the 3d U.S. Mine Ventilation 

Symposium. Soc. Min. Eng., AIME, Littleton, CO, pp. 453-462. 

Greuer, R.E., 1977, "Study of Mine Fires and Mine Ventilation; 

Part I. Computer Simulation of Ventilation Systems Under the 

Influence of Mine Fires," (contract SO241032, MI Technol. Univ.) 

BuMines OFR 115(1)-78, 165 pp.; NTIS PB 288 231. 

Greuer, R.E., 1981, "Real-Time Precalculation of the Distribution 

of Combustion Products and Other Contaminants in the Ventilation 

System of Mines," (Contract JO285002, MI Technol. Univ.). BuMines 

OFR 22-82, 263 pp.; NTIS PB 82-183104. 

Greuer, R.E., 1983, "A Study of Precalculation of Effect of Fires 

on Ventilation System of Mines," (contract JO285002, MI Technol. 

Univ.) BuMines OFR 19-84, 293 pp.; NTIS PB 84-159979. 

Greuer, R.E., 1979, "A New Computer Program for the Design of 

Ventilation Emergency Plans," Ch. in Proceedings of 2d. 

International Mine Ventilation Congress, Reno, NV, pp. 129-134. 

McElroy, G.E., 1954, "A Network Analyzer for Solving MineVentilation-Distribution Problems," BuMines IC 7704, 13 pp. 

Sheng, J., 1984, "Determination of the Cumulative Exhaust Effects 

of Diesel Powered Equipment Underground,". M.S. Thesis, MI 

Technol. Univ., Houghton, MI, 159 pp. 

93 
94 
95 

APPENDIX 1 INPUT PARAMETER TABLES 

TABLE 1 HEATING VALUES OF MINE COMBUSTIBLES 

TABLE 2 CO2 AND CO PRODUCTION CONSTANTS (ß VALUES) 

TABLE 3 RELATIONSHIPS OF BASIC FIRE PARAMETERS 

TABLE 4 CO2 AND CO PRODUCTION CONSTANT (ß VALUES) UNIT 

 CONVERSIONS 

TABLE 5 FRICTION FACTORS 

TABLE 6 ROCK THERMAL PROPERTIES 
96 

TABLE 1 - HEATING VALUES OF MINE COMBUSTIBLES 

 Fuel Type or Source Heating Value (BTU/lb)

 Coal WV; Pocahontas No. 3 14,4001,2

 PA; Pittsburgh 14,0001,2

 IL; No.5 10,8001,2

 WY; No. 3 10,7001,2

 CO; Fox Hill 8,6001,2

 Wood White Pine 8,0001

 Douglas Fir 8,0001

 Red Oak 7,7001

 Elm 7,7001 

 

 Petroleum Oil Gasoline 20,8001

 Diesel 20,0001

 Kerosene 19,8001

 Texas Crude 19,4001

 Transformer Fluid 18,2001,3

 Conveyor Belt Styrene Butadiene Rubber 13,3003

 Polyvinyl Chloride 10,5003

 Neoprene 10,0003

 Brattice Cloth Polyvinyl Chloride 10,1003

 Jute 5,8003

 Vent Duct Rigid Fiberglass Reinforced 

 Polyester Resin 3,9004

 

1

 Baumeister, T. and L.S. Marks, Standard Handbook for Mechanical 

 Engineers, McGraw-Hill, New York, NY, 1967. 

2

 as received 

3

 Egan, M.R., Summary of Combustion Products From Mine Materials: 

 Their Relevance to Mine Fire Detection, U.S. Bureau of Mines 

 Information Circular 9272, 1990. 
TABLE 2 - CO2 AND CO PRODUCTION CONSTANTS (ß VALUES)1

Fuel; Type and Source Fire State ßCO2(ft3/BTU) ßCO(ft3/BTU) 

 Wood; Douglas Fir Flaming 0.0020 0.00005 

 Coal; Pittsburgh Seam Flaming 0.0017 0.00014 

 Coal; Pittsburgh Seam Smoldering 0.0017 0.00021 

 Oil; Transformer Flaming 0.0015 0.00009 

 Belt; Styrene Butadiene Flaming 0.0015 0.00010 

 Belt; Neoprene Flaming 0.0015 0.00020 

 Rubber Flaming 0.0015 0.00012 

 Brattice; PVC Flaming 0.0009 0.00011 

 Brattice; PVC Smoldering 0.0010 0.00009 

 Brattice; Jute Flaming 0.0016 0.00003 

 Brattice; Jute Smoldering 0.0016 0.00002 

 Vent Duct; Rigid Flaming 0.0017 0.00013 

1 Egan, M.R., Summary of Combustion Products From Mine Materials: 

 Their Relevance to Mine Fire Detection, U.S. Bureau of Mines 

 Information Circular 9272, 1990. 

97 
 TABLE 3 - RELATIONSHIPS OF BASIC FIRE PARAMETERS 

 * Burning Rate x Heating Value = Heat Release Rate 

 * Heat Release Rate ÷ 437 = O2 Consumption Rate 

 * Heat Release Rate x ßCO2 = CO2 Production Rate 

 * Heat Release Rate x ßCO = CO Production Rate 

DATA SOURCES FOR FIRE PARAMETERS 

 Burning Rate......Measure or Estimate 

 Heating Value.....Varies by Fuel.......Published Literature 

 ßCO2.............. Varies by Fuel.......Published Literature 

 ßCO............... Varies by Fuel.......Published Literature 

98 
 TABLE 4 - ßCO2 AND ßCO PRODUCTION CONSTANT UNIT CONVERSIONS 

Published ß values are often expressed in SI units, usually as 

g/kj, however, MFIRE utilizes English System units. The above 

unit conversions can be used to convert ß values from SI to 

English units. 

A. To convert ßCO2 value from g/kJ to ft3/BTU... 

 g/kJ (ßCO2) x 0.0022 lb/g ÷ 44 lb/lb-mol x 359 ft3/lb-mol ÷ 0.948 

BTU/kJ 

 or 

 g/kJ (ßCO2) x 1.89 x 10-2 = ft3/BTU 

 

B. To convert ßCO value from g/kJ to ft3/BTU... 

 g/kJ (ßCO) x 0.0022 lb/g ÷ 28 lb/lb-mol x 359 ft3

/lb-mol ÷ 0.948 

BTU/kJ 

 or 

 g/kJ (ßCO) x 2.98 x 10-2 = ft3/BTU 

99 
100 

TABLE 5 FRICTION FACTORS1

Airway Type Degree of Straight | Sinuous or Curved 

 Surface | | Slightly | Moderately |  Irregularity | Amount of Obstruction - C=Clean, S=Slight, M | C S M | C S M | C S M | 

 | | |  Minimum | 10 15 25 | 20 25 35 | 25 30 40 | 3Smooth/Lined Average | 15 20 30 | 25 30 40 | 30 35 45 | 4 Maximum | 20 25 35 | 30 35 45 | 35 40 50 | 4 | | | | Sedimentary Minimum | 30 35 45 | 40 45 55 | 45 50 60 | 5Rock or Average | 55 60 70 | 65 70 80 | 70 75 85 | 8Coal Maximum | 70 75 85 | 80 85 95 | 85 95 100 | 9 | | | | Timbered Minimum | 80 85 95 | 90 95 105 | 95 100 110 | 10(5-ft Average | 95 100 110 | 105 110 120 | 110 115 125 | 12centers) Maximum | 105 110 120 | 115 120 130 | 120 125 135 | 13 | | | |  Minimum | 90 95 105 | 100 105 115 | 105 110 120 | 11Igneous Rock Average | 145 150 160 | 155 160 165 | 160 165 175 | 17 Maximum | 195 200 210 | 205 210 220 | 210 215 225 | 22Friction Factor Units are 1.0*E-10 lbm*min2/ft4

1 McElroy, G.E., Engineering Factors in the Ventilation of Metal Mine

 U.S. Bureau of Mines, Bulletin 385, 1932 
101 

TABLE 6 THERMAL PROPERTIES OF ROCK 

The thermal properties of rock required for MFIRE input are 

thermal conductivity, k, and thermal diffusivity, α. A third 

thermal property, constant pressure specific heat, Cp, may be 

used along with density, ρ, to relate k and α as, 

 

 k = α * ρ * Cp

MFIRE uses thermal conductivity in units of BTU/hr*ft*oF and 

 thermal diffusivity in units of ft2/hr. Multiply SI thermal 

conductivity in units of W/m*oK by 0.5782 to obtain thermal 

conductivity in units of BTU/hr*ft*oF. Likewise, multiply SI 

thermal diffusivity units of m2/s by 38,750 to obtain thermal 

diffusivity units of ft2/hr. 

The data in this appendix were assembled or calculated or 

extrapolated from various sources and is intended to provide a 

starting point for MFIRE users. Published data from other 

sources may range ± 100 pct or more from these values due to 

measurement methods and rock variations. In situ conditions, 

especially porosity and pore fluid greatly influence data values. 

In most cases the exact value is not critical as most of the 

thermal energy from a mine fire is carried away from the fire by 

the airflow and transferred to the rock at low rates over 

comparatively long distances and consequently a large surface 

area. If parametric simulations with MFIRE show that these 

values are critical to the outcome of a particular simulation, 

the user should thoroughly investigate the thermal properties of 

the rock in question. 

ROCK/MATERIAL Thermal conductivity, k Thermal Diffusivity, 

α

 BTU/hr*ft*oF ft2/hr 

brick 0.4 0.02 

basalt 0.6 - 1.4 0.02 - 0.04 

calcite 0.2 0.006 

clay 0.8 0.004 

anthracite coal 0.2 0.006 

concrete 0.5 - 0.8 0.02 - 0.03 

diabase 1.1 - 1.3 0.03 - 0.04 

dolo-stone 0.8 - 3.6 0.02 

granite 1.0 - 3.4 0.03 - 0.09 

limestone 0.7 - 3.6 0.02 - 0.1 

marble 1.2 - 3.2 0.03 - 0.08 

sandstone 0.9 - 2.2 0.03 - 0.06 
102 

APPENDIX 2 INPUT DATA FILE TEMPLATE 

$----------------------------------------------------------------------$ 

$ $ 

$ *** INPUT FORMAT INSTRUCTION FILE FOR PROGRAM MFIRE *** $ 

$ $ 

$ GENERAL RULES FOR DATA INPUT: $ 

$ $ 

$ * NO NEED TO DISTINGUISH INTERGER AND REAL NUMBERS. SYMBOLS USED $ 

$ IN NUMERICAL INPUT COMPRISE THE FOLLOWING LIST: $ 

$ 1 2 3 4 5 6 7 8 9 0 . , - + BLANK $ 

$ * FREE FORMAT ALLOWED. COMMA AND BLANK SPACE CAN BOTH BE DELIMINA- $ 

$ TORS. SEQUENTIALLY DISTRIBUTED BLANK SPACES ACT AS ONE DELIMINATOR.$ 

$ BLANKS ADJACENT TO A COMMA HAS NO EFFECT IN SEPARATING INPUT TERMS.$ 

$ * ZERO INPUT CAN BE OMITTED BUT ITS DELIMINATOR CAN'T EXCEPT BEING $ 

$ THE LAST ONE IN A LINE. $ 

$ * A LINE WHOSE FIRST NON-BLANK SYMBOL IS "$" IS AN INSTRUCTION $ 

$ LINE WHICH WILL BE IGNORED IN A PROGRAM RUN. $ 

$ * A LINE WHOSE FIRST NON-BLANK SYMBOL IS NEITHER ONE USED IN THE $ 

$ ABOVE LIST FOR NUMERICAL INPUT NOR "$", OR WHICH CONTAINS MORE $ 

$ THAN 3 SYMBOLS OUTSIDE OF THE LIST, IS A COMMENT LINE WHICH WILL $ 

$ BE SHOWN IN THE OUTPUT FILE. $ 

$----------------------------------------------------------------------$ 

$----------------------------------------------------------------------$ 

$ (1) COMMENTS (OPTIONAL) $ 

$ $ 

$ YOU MAY PUT NOTES HERE TO REMIND YOU IN THE FUTURE. THEY WILL BE $ 

$ SHOWN IN THE OUTPUT FILE. THE NUMBER OF TOTAL ACTIVE COMMENT LINES $ 

$ IS 50. THE ACTIVE WIDTH OF A LINE IS 72 COLUMNS. $ 

$----------------- INPUT YOUR COMMENTS HERE ----------------------$ 

$----------------------------------------------------------------------$ 

$ (2) CONTROL CARD I: $ 

$ NB,NFNUM,INFLOW,NVPN,NETW,TR,MADJ,ITN,NTEMP,TINC,SPAN,IOUT,TOUT $ 

$ CONCT,DR $ 

$ $ 

$ NB: NUMBER OF AIRWAYS IN NETWORK, MAX. 500 $ 

$ NFNUM: NUMBER OF FAN CHARACTERISTICS, MAX. 10. $ 

$ INFLOW: NUMBER OF CONTAMINATION SOURCES, MAX. 10. $ 

$ NVPN: MARKER FOR PRESENCE OF JUNCTION CARDS, 0: PRESENT. $ 

$ NETW: MARKER, 1: ONLY THE NETWORK PART WILL BE PERFORMED. $ 

$ TR: REFERENCE TEMPERATURE OF AIR, DEG. F. DEFAULT VALUE 75. $ 

$ MADJ: MAX. NO. OF ITERATION IN TEMP. PART. DEFAULT 20. $ 

$ ITN: MAX. NO. OF ITERATION IN DYNAMIC PART, DEFAULT 20. $ 

$ NTEMP: MARKER. 1: SIMULATION GOES ONLY UP TO TEMPERATURE PART. $ 

$ TINC: TIME INCREMENT IN DYNAMIC SIMULATION PART, SEC. $ 

$ SPAN: TIME SPAN OF DYNAMIC SIMULATION, MIN. $ 

$ IOUT: OUTPUT, 0: BRIEF; 1: NORMAL; -1: DETAIL; -2; MORE DETAILED.$ 

$ TOUT: TIME INTERVAL FOR OUTPUT, IN MIN. $ 
103 

$ CONCT: MARKER. 1: SIMULATION GO TO TRANSIENT CONCENTRATION ONLY $ 

$ 0: SIMULATION GO TO ALL TRANSIENT STATE $ 

$ DR: REFERENCE DENSITY IN LBM/FT3, DEFAULT BASED ON TR AND 1 ATM. $ 

$ $ 

$ *** INPUT DATA FOR CONTROL CARD I HERE *** $ 

$NB,NFNUM,INFLOW,NVPN,NETW,TR,MADJ,ITN,NTEMP,TINC,SPAN,IOUT,TOUT,CONCT,DR 

$ AIRWAY LINES HERE 

$ NO,JS,JF,NWTYP,R,Q,KF,LA,A,O,HA,HK,CH4V,CH4PA,TROCK $ 

$ $ 

$ * IF NB IS 2 OR LARGER, THE NUMBER OF AIRWAY CARDS (LINES) MUST BE $ 

$ NB. IF NB IS 1 OR LESS, THE AIRWAY CARDS MUST END WITH 9999. $ 

$ * KF,LA,A,O,HA,HK HAVE THEIR AVERAGE OR DEFAULT VALUES WHICH ARE $ 

$ ACTIVATED BY INPUTING ZERO FOR THE RESPECTIVE TERMS. $ 

$ * TROCK DOES NOT NEED TO INPUT EXCEPT WHEN YOU WANT TO OVERRIDE THE$ 

$ PROGRAM CALCULATED VALUE. $ 

$ * COMMENT LINES ARE ACTIVE IN THIS DATA PARAGRAPH. $ 

$ $ 

$ NO: AIRWAY ID NUMBER (1 TO 9980). $ 

$ JS: JUNCTION ID NUMBER OF AIRWAY BEGINNING (1 TO 999). $ 

$ JF: JUNCTION ID NUMBER OF AIRWAY END (1 TO 999). $ 

$ NWTYP: AIRWAY TYPE, 1: FAN; 0: ORDINARY; -1: FIXED-Q. $ 

$ R: RESISTANCE OF AIRWAY 1.E-10 IN. W.G./(CFM)2. $ 

$ Q: AIRFLOW RATE IN CFM. $ 

$ KF: FRICTION FACTOR IN 1.E-10 LBM*MIN2/FT4. $ 

$ LA: AIRWAY LENGTH IN FT. $ 

$ A: AIRWAY CROSS SECTIONAL AREA IN FT**2. $ 

$ O: AIRWAY PERIMETER IN FT. $ 

$ HA: THERMAL DIFFUSIVITY OF ROCK, FT2/HR. $ 

$ HK: THERMAL CONDUCTIVITY OF ROCK, BTU/HR*FT*F. $ 

$ CH4V: METHANE EMISION RATE IN AIRWAYS FT3/MIN. $ 

$ CH4PA: METHANE EMISION RATE PER UNIT SURFACE AREA, FT/MIN. $ 

$ TROCK: AVERAGE ROCK TEMPERATURE IN AIRWAY, DEGREE F. $ 

$ $ 

$ *** INPUT DATA FOR AIRWAY CARDS HERE *** $ 

$-------- NO,JS,JF,NWTYP,R,Q,KF,LA,A,O,HA,HK,CH4V,CH4PA,TROCK ---------$ 

$----------------------------------------------------------------------$ 

$ (4) JUNCTION CARDS: $ 

$ JNO,T,Z,CH4C $ 

$ $ 

$ * IF NVPN IS 0 OR LESS, EACH JUNCTION SPECIFIED IN JS AND JF MUST $ 

$ HAVE A ONE-LINE INPUT HERE. OTHERWISE JUNCTION CARDS MUST BE $ 

$ OMITTED. $ 

$ $ 

$ JNO: JUNCTION ID NUMBER (1 TO 999) $ 

$ T: TEMPERATURE OF AIR IN JUNCTIONS, DEGREE F. $ 

$ Z: ELEVATION OF JUNCTIONS, FT. $ 

$ CH4C: METHANE CONCENTRATION IN JUNCTIONS, PERCENTAGE. $ 

$ $ 

$ *** INPUT JUNCTION CARDS HERE *** $ 

$------------------------- JNO,T,Z,CH4C -------------------------------$ 
104 

$----------------------------------------------------------------------$ 

$ (5) JUNCTION CARDS II (JUNCTIONS IN THE ATMOSPHERE) $ 

$ A STARTING JUNCTION IS THE JUNCTION WHERE ATMOSPHERE CONDITIONS $ 

$ ARE DEFINED. ALL OTHER JUNCTIONS ON THE SURFACE ARE JUNCTIONS IN $ 

$ THE ATMOSPHERE. $ 

$ IF THERE ARE MORE THAN ONE JUNCTION IN THE ATMOSPHERE, JUNCTION $ 

$ CARD II IS EMPLOYED. OTHERWISE, ONLY NUMBER "1" IS READ IN. $ 

$ $ 

$ JAN: THE NUMBER OF THE JUNCTIONS IN THE ATMOSPHERE $ 

$ JA: JUNCTION ID NUMBER $ 

$ JATP: JUNCTION TYPE: $ 

$ 0: STARTING JUNCTION $ 

$ 1: OTHER ATMOSPHERE JUNCTIONS EXCEPT STARTING JUNCTION $ 

$ $ 

$   INPUT DATA FOR JUNCTION CARD II HERE ** ** $ 

 $ 

$--------------------------- JAN --------------------------------------$ 

$------------------------- JA,JATP ------------------------------------$ 

$----------------------------------------------------------------------$ 

$ FAN CARDS I AND II COMPRISE A DATA GROUP WHICH MUST REPEAT NFNUM $ 

$ TIMES FOR NFNUM FAN CURVES. IF NFNUM IS 0 OR LESS, FAN CARDS I AND $ 

$ II MUST BE OMITTED. $ 

$ $ 

$ (5) FAN CARD I: $ 

$ NOF,MPTS,NSWT $ 

$ NOF: ID NUMBER OF FAN BRANCH. $ 

$ MPTS: NUMBER OF POINTS DEFINING FAN CHAR, MAXIMUM 10. $ 

$ NSWT: SELECTION OF FAN CURVE FITTING, 1: LEAST SQUARES $ 

$ 2: SPLINE 3. AUTO 4.AUTO+MANUAL $ 

$ (6) FAN CARD II: (IF MPTS IS LARGER THAN 5, CONTINUE IN 2ND LINE.)$ 

$ QF,PF,QF,PF,QF,PF,QF,PF,QF,PF $ 

$ QF: AIRFLOW AT GIVEN POINT OF FAN CHAR, CFM. $ 

$ PF: PRESSURE AT GIVEN POINT OF FAN CHAR, IN.W.G. $ 

$ (7) FAN CARD III: NPLOT $ 

$ NPLOT: TREATMENT OF THE BOUNDARY RANGE OF FAN CURVE $ 

$ 1: EXTEND FAN CURVE BY FOLLOWING GRADIENTS OF TWO ENDS. $ 

$ 2: EXTEND FAN CURVE AS ABOVE AT LEFT BOUNDARY REGION AND $ 

$ SEND GRADIENT OF RIGHT BOUNDARY REGION TO ZERO. $ 

$ 3. SEND GRADIENT OF BOTH SIDES OF BOUNDARY REGION TO ZERO.$ 

$ *** INPUT FAN CARDS I,II, AND III HERE *** $ 

$--------------------------- NOF,MPTS,NSWT ----------------------------$ 

$------------------ QF,PF,QF,PF,QF,PF,QF,PF,QF,PF ---------------------$ 

$-------------------------------NPLOT----------------------------------$ 

$----------------------------------------------------------------------$ 

$ (7) CONTAMINATION (HEAT SOURCE) CARDS: $ 

$ NCENT,CONT,CONC,HEAT,O2MIN,SMPO2,HTPO2,QCENT,TPR $ 

$ $ 
105 

$ * EACH HEAT SOURCE MUST HAVE A ONE-LINE INPUT HERE. THE NUMBER OF $ 

$ TOTAL FIRE SOURCES WAS SPECIFIED BY "INFLOW" IN CONTROL CARD I. $ 

$ $ 

$ NCENT: ID NUMBER OF AIRWAYS WHERE HEAT SOURCES LOCATE. $ 

$ CONT: VOLUME FLOW RATE OF CONTAMINATED GAS INFLOW IN CFM. $ 

$ CONC: CONCENTRATION OF CONTAMINANT IN GAS INFLOW, %. $ 

$ HEAT: HEAT ENTERING OR LEAVING AIRWAY IN BTU/MIN. $ 

$ O2MIN: OXYGEN CONCENTRATION OF AIR CURRECT LEAVING FIRE ZONE, %. $ 

$ SMPO2: CONTAMINANT PRODUCTION PER FT**3 OF OXYGEN DELIVERY. $ 

$ HTPO2: HEAT PRODUCTION (BTU) PER FT**3 OF OXYGEN DELIVERY. $ 

$ QCENT: REF. Q DEFINING FIRE CHARACTERISTICS, CFM. $ 

$ TPR: LEADING TIME PERIOD IN MIN. FOR FIRE TO REACH FULL STRENGTH.$ 

$ $ 

$ *** INPUT DATA FOR FIRE SOURCES HERE *** $ 

$---------- NCENT,CONT,CONC,HEAT,O2MIN,SMPO2,HTPO2,QCENT,TPR ----------$ 

$----------------------------------------------------------------------$ 

$ (8) CONTROL CARD II $ 

$ NAV,JSTART,TSTART,TIME,CRITSM,CRITGS,CRITHT,WRNPR,WRNSM,WRNGS,WRNHT$ 

$ $ 

$ * A SET OF DEFAULT VALUES ARE AVAILABLE. THEY CAN BE ACTIVATED BY $ 

$ INPUTING ZERO FOR THE RESPECTIVE TERMS. $ 

$ $ 

$ NAV: MARKER. 1 OR LARGER: AVERAGE-VALUE CARD IS PRESENT. $ 

$ JSTART: STARTING JUNCTION (ATMOSPHERE). $ 

$ TSTART: TEMPERATURE AT THE START JUNCTION, DEGREE F. $ 

$ TIME: TIME SPAN TO ASSUME QUASI-EQUILIBRIUM, HOUR. DEFAULT 10. $ 

$ CRITSM: ACCURACY IN FUME CALCULATION, %. DEFAULT 0.005. $ 

$ CRITGS: ACCURACY IN METHAME CALCULATION, %, DEFAULT .01. $ 

$ CRITHT: ACCURACY IN TEMPERATURE CALCULATION, F. DEFAULT 0.1. $ 

$ WRNPR: PRESSURE DROP WARNING CRITERIA, IN.W.G. DEFAULT 0.01. $ 

$ WRNSM: FUME CONCENTRATION WARNING CRITERIA, %. DEFAULT 0.05. $ 

$ WRNGS: METHANE CONCENTRATION WARNING CRITERIA, %. DEFAULT 1.0. $ 

$ WRNHT: HIGH TEMPERATURE WARNING CRITERIA, F. DEFAULT 100.0. $ 

$ $ 

$ *** INPUT DATA FOR CONTROL CARD II HERE *** $ 

$- NAV,JSTART,TSTART,TIME,CRITSM,CRITGS,CRITHT,WRNPR,WRNSM,WRNGS,WRNHT-$ 

$----------------------------------------------------------------------$ 

$ (9) AVERAGE-VALUE CARD: $ 

$ HAAVR,HKAVR,KFAVR,LAAVR,AAVR,OAVR $ 

$ $ 

$ IT MUST EXIST IF NAV IN CONTROL CARD II IS 1 OR LARGER. A DEFAULT$ 

$ VALUE CAN BE ACTIVATED BY INPUTING ZERO FOR THE RESPECTIVE TERM. $ 

$ WHEN NAV IS ZERO OR LESS, THE WHOLE SET OF DEFAULT VALUES WILL BE $ 

$ TAKEN. $ 

$ $ 

$ HAAVR: AVERAGE THERMAL DIFFUSIVITY OF ROCK, FT2/HR. DEFAULT 0.1. $ 

$ HKAVR: AVERAGE THERMAL CONDUCTIVITY OF ROCK, BTU/HR*FT*F. $ 

$ DEFAULT 3.0. $ 
106 

$ KFAVR: FRICTION FACTOR, 1.E-10 LBM*MIN2/FT4. DEFAULT 100. $ 

$ LAAVR: AVERAGE LENGTH OF AIRWAY, FT. DEFAULT 500. $ 

$ AAVR: AVERAGE SECTIONAL AREA OF AIRWAY, FT2. DEFAULT 100. $ 

$ OAVR: AVERAGE PERIMETER, FT. DEFAULT 40. $ 

$ $ 

$ *** INPUT AVERAGE-VALUE CARD HERE IF NEEDED *** $ 

$----------------- HAAVR,HKAVR,KFAVR,LAAVR,AAVR,OAVR ------------------$ 

$----------------------------------------------------------------------$ 

$ (10) TIME TABLE FOR CONDITION CHANGES: $ 

$ $ 

$ THIS TIME TABLE CAN CONTAIN THE FOLLOWING CONDITION CHANGES. IT $ 

$ MUST END WITH A ONE-LINE INPUT OF A VALUE LARGER THAN "SPAN" IN $ 

$ CONTROL CARD I. THIS TIME TABLE MUST EXIST, BUT MAY CONTAIN ONLY $ 

$ THE ENDING LINE. THE ORDER OF CHANGING CONDITIONS MUST BE ARRANGED$ 

$ ACCORDING TO THE RESPECTIVE OCCURING TIME. $ 

$ $ 

$ 1) TS,1,NBR,R $ 

$ THIS INPUT CHANGES BRANCH "NBR" TO AN ORDINARY AIRWAY WITH $ 

$ AIRFLOW RESISTANCE EQUAL TO "R" AT "TS" MIN. AFTER TIME ZERO. $ 

$ TS: OCCURING TIME OF THE CHANGE CONDITION, MIN. $ 

$ NBR: AIRWAY ID NUMBER. $ 

$ R: RESISTANCE OF AIRWAY 1.E-10 IN. W.G./(CFM)2. $ 

$ 2) TS,2,NBR,INDEX,QF1,PF1,QF2,PF2,QF3,PF3,QF4,PF4,QF5,PF5 $ 

$ THIS INPUT CHANGES BRANCH "NBR" TO A FAN BRANCH WITH ITS $ 

$ CHARACTERISTICS SPECIFIED BY "QF1" TO "PF5". $ 

$ INDEX: NUMBER OF DATA POINTS TO DEFINE FAN CHAR. MAX. 5. $ 

$ QF: AIRFLOW RATE IN FT**3/MIN. $ 

$ PF: CORRESPONDING FAN PRESSURE IN IN. W.G. $ 

$ 3) TS,3,NBR,CONT,CONC,HEAT,02MIN,SMPO2,HTPO2,QCENT,TPR $ 

$ THIS INPUT CHANGES BRANCH "NBR" TO A FIRE SOURCE BRANCH WITH $ 

$ FIRE CHAR. SPECIFIED BY "CONT" TO "TPR", WHICH RETAIN THE SAME $ 

$ MEANING AS IN FIRE SOURCE CARD (7). REFER BACK TO (7) FOR DETAIL $ 

$ 4) TS,4,NBR $ 

$ THIS INPUT CHANGES FIRE BRANCH "NBR" TO AN ORDINARY AIRWAY AT $ 

$ TIME "TS". $ 

$ 5) TS,5,TINC $ 

$ THIS INPUT CHANGES TIME INCREMENT IN SYNAMIC SIMULATION TO A $ 

$ NEW VALUE "TINC" IN SEC. $ 

$ 6) TS,6,TOUT $ 

$ THIS INPUT CHANGES OUTPUT INTERVAL TO A NEW VALUE OF "TOUT" $ 

$ MIN. $ 

$ 7) TS,7,JDPP $ 

$ THIS INPUT FORCES DETAILED RECORDS TO BE SET UP FOR AIRWAYS $ 

$ WHICH ARE ON THE IMMEDIATE DOWN-STREAM SIDE OF JUNCTION "JDPP" $ 

$ AT "TS" MIN. AFTER TIME ZERO. $ 

$ $ 

$ *** INPUT CONDITION CHANGE TIME TABLE HERE *** $ 

$-- (IT MUST END WITH A ONE-LINE VALUE LARGER THAN "SPAN" IN CARD I) --$ 
107 

 APPENDIX 3 PROGRAM LISTING OF MFIRE VARIABLES 

C NB: NUMBER OF AIRWAYS IN NETWORK. 

C NJ: NUMBER OF JUNCTIONS IN NETWORK. 

C NFNUM: NUMBER OF FAN CHARACTERISTICS. 

C NVPN: MARKER FOR PRESENCE OF JUNCTION CARDS, 0: PRESENT. 

C NETW: MARKER, 1: ONLY THE NETWORK PART WILL BE PERFORMED. 

C NTEMP: MARKER, 1: ONLY UP TO THE TEMP. PART WILL BE PERFORMED. 

C MADJ: MAX. NO. OF ITERATION IN TEMP. PART. 

C ITN: MAX. NO. OF ITERATION IN NON-STEADY STATE SIMULATION. 

C DR: REFERENCE DENSITY OF AIR, LBM/FT3. 

C TR: REFERENCE TEMPERATURE OF AIR, DEG. F. 

C TINC: TIME INCREMENT IN SIMULATION, SEC.. 

C SPAN: TIME SPAN OF SIMULATION, MIN.. 

C IOUT: OUTPUT. 0: BRIEF; 1: NORMAL; -1: DETAIL; -2: MORE DETAILED. 

C TOUT: TIME INTERVAL FOR OUTPUT, MIN. 

C CONCT: MARKER. 1: SIMULATION FOR TRANSITE CONCENTRATION SIMULAC TION ONLY 

C NAV: MARKER FOR PRESENCE OF AVE. VALUE CARDS. 

C MAXJ: HIGHEST JUNCTION NUMBER. 

C INFLOW: NUMBER OF CONTAMINATION CARDS. 

C CRITSM: ACCURACY OF FUME CALCULATION. 

C CRITGS: ACCURACY OF METHAME CALCULATION. 

C CRITHT: ACCURACY OF TEMPERATURE CALCULATION. 

C NO(NMX): AIRWAY NUMBER. 

C JS(NMX): JUNCTION NUMBER OF AIRWAY BEGINNING. 

C JF(NMX): JUNCTION NUMBER OF AIRWAY END. 

C NWTYP(NMX): AIRWAY TYPE. 

C R(NMX): RESISTANCE OF AIRWAY 1.E-10 IN. W.G./(CFM)**2. 

C Q(NMX): BALANCED AIRFLOW RATE, ASSUMING EQUILIBRIA, CFM 

C P(NMX): CALCULATED PRESSURE LOSS IN IN. W.G.. 

C KF(NMX): FRICTION FACTOR. 

C LA(NMX): AIRWAY LENGTH IN FT. 

C A(NMX): AIRWAY CROSS SECTIONAL AREA IN FT**2. 

C O(NMX): AIRWAY PERIMETER IN FT. 

C RSTD(NMX): RESISTANCE FACTOR BASED ON TR. 

C DZRD(NMX): ELEVATION CHANGE IN AIRWAY IN FT. 

C FRNVP(NMX): PRODUCT TMRD*DZRD. 

C NREV(NMX): NUMBER OF AIRFLOW REVERSALS IN AN INTERVAL. 

C RDCH4(NMX): METHANE CONCENTRATION AT ROADWAY ENDS. 

C RDPROP(NMX): CONTAMINANT CONCENTRATION AT ROADWAY ENDS. 

C TRD(NMX): TEMPERATURE AT ROADWAY ENDS. 

C TJS(NMX): TEMPERATURE AT ROADWAY BEGINNING. 

C RDOP(NMX): BACKUP ARRAY FOR RDPROP. 

C RCH4(NMX): BACKUP ARRAY FOR RDCH4. 

C FFRNVP(NMX): DZRD/TMRD. 

C RA(NMX): BACKUP ARRAY FOR R. 

C NNREV(NMX): NUMBER OF AIRFLOW REVERSALS SINCE TIME ZERO.. 

C NOF(IMX): AIRWAY NUMBER OF FAN. 

C NFREG(IMX): LIST OF FANS WITH CHARACTERISTICS. 

C RGRAD(IMX): SLOPE OF FAN CHARACTERISTIC. 

C NFCW(IMX): LIST OF FANS WHOSE CHAR. EXCEEDED. 

C MPTS(IMX): NUMBER OF POINTS DEFINING FAN CHAR. 

C QF(IMX,IMY): AIRFLOW AT GIVEN POINT OF FAN CHAR. 

C PF(IMX,IMY): PRESSURE AT GIVEN POINT OF FAN CHAR. 

C NSKP(IMX): MARKER INDICATING PERFORMANCE OF SPLINE. 

C NEGQ(IMX): MARKER INDICATING AIRFLOW REVERSAL IN FAN BRANCH. 

C JSB(NMX): BACKUP ARRAY FOR JS. 

C NSWT(NMX): SWTCH TO SELECTED FAN CURVE FITTING METHOD 

C 1 LEAST SQUARE 2.SPLINE 3.AUTOMATIC 4.AUTO+MANUAL 

C MNO: NUMBER OF MESHES IN NETWORK. 
108 

C MEND(NMY): LIST OF MESH ENDS IN MSL-LIST. 

C MSL(LMX): LIST OF ALL INDEPENDENT MESHES. 

C FNVP(NMY): LIST OF NVP IN MESHES. 

C RQ(NMX): AUXILIARY LIST OF R*Q. 

C INU(NMX): AUXILIARY LIST FOR FORMING BASE SYST. 

C KNO(NXX): LIST OF AIRWAYS IN BASE SYSTEM. 

C KJS(NXX): LIST OF JUNCTIONS IN BASE SYSTEM. 

C KJF(NXX): LIST OF JUNCTIONS IN BASE SYSTEM. 

C JNO(NMY): JUNCTION NUMBER. 

C T(NMY): TEMPERATURE OF AIR IN JUNCTIONS. 

C Z(NMY): ELEVATION OF JUNCTIONS. 

C CH4C(NMY): METHANE CONCENTRATION IN JUNCTION. 

C JNOL(NMY): LIST OF JUNCTION NUMBERS IN INCREASING ORDER. 

C PROP(NMY): CONTAMINANT CONCENTRATION IN JUNCTION. 

C PRCH4(NMY): METHANE CONCENTRATION IN JUNCTION. 

C JLR(NMY): LIST RELATING JNO- AND JNOL-LISTS. 

C TROCK(NMX): AVERAGE ROCK TEMPERATURE IN AIRWAY. 

C TMRD(NMX): MEAN TEMPERATURE OF AIR IN AIRWAY. 

C HA(NMX): THERMAL DIFFUSIVITY OF ROCK. 

C HK(NMX): THERMAL CONDUCTIVITY OF ROCK. 

C NCENT(NMX): NUMBER OF AIRWAYS INTO WHICH FUME ENTERS. 

C CH4V(NMX): METHANE EMISION RATE IN AIRWAYS. 

C CH4PA(NMX): METHANE EMISION RATE PER UNIT SURFACE AREA. 

C CONT(IMX): VOLUME FLOW RATE OF CONTAMINATED GAS INFLOW. 

C CONC(IMX): CONCENTRATION OF CONTAMINANT IN GAS INFLOW. 

C HEAT(IMX): HEAT ENTERING AIRWAY. 

C O2MIN(IMX): OXYGEN CONCENTRATION OF FUMES LEAVING FIRE ZONE 

C SMPO2(IMX): CONTAMINANT PRODUCTION PER CUBIC FT OF OXYGEN. 

C HTPO2(IMX): HEAT PRODUCTION PER CUBIC FT OF OXYGEN DELIVERY 

C TFSI(IMX): AIR TEMPERATURE BEHIND HEAT SOURCE. 

C O2BEH(IMX): OXYGEN CONTENT BEHIND FIRE SOURCES. 

C TPR(IMX): TRANSITION TIME OF FIRE IN MIN. 

C HTAD(IMX): REDUCED HEAT INPUT DUE TO HIGH AIR TEMPERATURE. 

C QCENT(IMX): "STD. Q' AT WHCIH FIRE TAKES THE INPUT PARAMETERS. 

C NGIN(NMX): LIST OF AIRWAYS ENTERING JUNCTION. 

C MMIN(NMX): LIST OF LAST AIRWAY PER JUNCTION IN NGIN-LIST. 

C NGOUT(NMX): LIST OF AIRWAYS LEAVING JUNCTION. 

C LOUT(NMX): LIST OF LAST AIRWAY PER JUNCTION IN NGOUT-LIST. 

C MEMREC(NMX): TEMPORARY LIST OF AIRWAYS CARRYING RECIRC. AIR. 

C NOREC(NMX): PERMANENT LIST OF AIRWAYS. 

C ESTPR(NMX): ESTIMATED CONCENTRATION FOR RECIRCULATED AIR. 

C ESTCH4(NMX): ESTIMATED METHANE CONCENTRATION. 

C ESTTR(NMX): ESTIMATED TEMPERATURE. 

C 

C XNEW(NMX): EXPONENT FOR TEMPERATURE CALCULATION. 

C DCOAGE(NMX): COEFFICIENT OF AGE. 

C TIME: TIME ASSUMING QUASI-EQUILIBRIA. 

C TSTART: TEMPERATURE AT THE START JUNCTION. 

C JSTART: START JUNCTION (ATMOSPHERE). 

C TLEFT(NMX): TIME INCREMENT FOR MAKING UP A NORMAL INTERVAL. 

C SUMQ(NMY): TOTAL AIRFLOW RATES ENTERING JUNCTION. 

C SUMC(NMY): TOTAL CONTAMINANT FLOW RATES ENTERING JUNCTION. 

C SUMM(NMY): TOTAL METHANE FLOW RATES ENTERING JUNCTION. 

C SMHEAT(NMY): TOTAL ENTHALPY/REFRENCE DENSITY ENTERING JUNCTI 

C PROPS(NMX): BACKUP ARRAY FOR PROP. 

C PRCH4S(NMX): BACKUP ARRAY FOR PRCH4. 

C QQ(NMX): DAMPED AND TIME-AVERAGED AIRFLOW RATE. 

C QTP(NMX): BACKUP ARRAY FOR Q, FIXED IN EACH INTERVAL. 

C TTJS(NMX): BACKUP ARRAY FOR TJS. 

C TTRD(NMX): BACKUP ARRAY FOR TRD. 

C TAS(NMX): BACKUP ARRAY OF T. 

C BI(NMX): BIOT NUMBER. 
109 

C WRNPR: PRESSURE DROP WARNING CRITERIA. 

C WRNGS: METHANE CONCENTRATION WARNING CRITERIA. 

C WRNSM: FUME CONCENTRATION WARNING CRITERIA. 

C WRNHT: HIGH TEMPERATURE WARNING CRITERIA. 

C IOMIT(IMX): AIRWAYS FOR WHICH DETAILED DATA RECORDS WERE OMITTED. 

C ROMIT(IMX,3): DATA AT STARTING J OF DATA-OMITTED AIRWAY. 

C IAC: COUNTER OF IOMIT AND ROMIT. 

C DELTAT: SPAN OF TIME INCREMENT. 

C TACC: CUMULATED TIME AFTER EVENT IN SEC. 

C SUMFNV: SUM OF NVP CORRECTION IN SYSTEM. 

C IBTN(NMX): ARRAY HOLDING ADDRESS OF RECORD FOR AIRWAY (N 

C DPPA(NMZ,10,5): MASTER DATA STORAGE ARRAY IN DYNAMIC SIMULATI 

C NSAC(NMX,2): DATA RECORD STATUS OF AIRWAY (NMX). 

C TMRDA(NMX): BACKUP ARRAY FOR TMRD. 

C DELTAQ(NMX): VARIATION OF AIRFLOW IN AIRWAYS. 

C DPPB(NMZ,10,5): BACKUP ARRAY FOR DPPA. 

C NSACB(NMX,2): BACKUP ARRAY FOR NSAC. 

C GBTN(10,5): AUXILIARY ARRAY FOR DATA TRANSFER. 

C JCH(NMY): MARKER INDICATING JUNCTION COND. CHANGE. 

C TAUXA(NMZ,10): AIR TEMP. AT REAR ENDING OF SEGMENTS. 

C TAUXB(NMZ,10): BACKUP ARRAY FOR TAUXA. 

C TAUXC(NMZ): AIR TEMP. BEYOND THE FIRST SEGMENT. 

C TAUXD(NMZ): BACKUP ARRAY OF TAUXC. 

C FMASS(NMZ): MASS OF AIR BEYOND THE FIRST SEGMENT. 

C JDP: NUMBER OF JUNCTIONS INITIATING DATA RECORDS. 

C JDPP(IMX): JUNCTIONS WHICH INITIATE DATA RECORDS. 

C QRCD(NMX,10): AIRFLOW RATES DURING ITERATIONS. 

C TMRCD(NMX,10): MEAN AIR TEMP. IN AIRWAYS DURING ITERATION. 

C HRM(IMX): VARIATION OF NVP PER MESH DURING ITERATION. 

C JAN: TOTAL NUMBER OF ATMOSPHERE JUNCTIONS 

C JAJ: NUMBER OF ATMOSPHERE JUNCTIONS EXCEPT STARTING JUNCTION 

C JA1(10): JUNCTION ID NUMBER (IN ATMOSPHERE) 

C JATP(10): JUNCTION TYPE (IN ATMOSPHERE) 

C JSTAR(10): JUNCTIONC CONNECTED WITH ENTRY AIRWAYS EXCEPT STARING 

C JUNCTION 

C TSTAR(10): TEMPERATURE IN THE JUNCTION AT ARRAY (JSTAR) 

C MSTAR(10): JUNCTION NUMBER CORRESPONDING TO ARRAY (JNOL) 

C ISTAR(10): JUNCTION NUMBER CORRESPONDING TO ARRAY (JNO) 

C TTT: INTERMEDIATE ARRAY FOR TEMPERATURE WHEN SIMULATE FOR TRANSIENT 

C CONCENTRATION SIMULATION ONLY (CONCT=1). 

C TJSS:INTERMEDIATE ARRAY OFR TTJS WHEN CONCT=1. 

C TRDD: INTERMEDIATE ARRAY FOR TTRD WHEN CONCT=1. 

C QQQ: INTERMEDIATE ARRAY FOR QQQ WHEN CONCT=1. 

C COF: THE COEFFIENT OF FAN EQUATION FITTED BY LEAST SQUARES. 

C ND: THE DEGREE OF FAN EQUATION FITTED BY LEAST SQUARES. 

C N1A: THE NUMBER OF COEFFICIENTS OF FAN EQUATION. 

C NSWT: TO SELECT FAN CURVE FITTING METHOD 

C 1 LEAST SQUARE 2.SPLINE 3.AUTOMATIC 4.AUTO+MANUAL 

C NCOF: ARRAY FOR THE NUMBER OF COEFFICIENTS OF FAN EQUATION 

C INIFAN: THE FLAG SHOWS THE LARGE STATE CHANGE IN SYSTEM AND THE 

C MESHES REFORM DESIRED. 

C NPLOT: TREATMENT OF THE BOUNDARY RANGE OF FAN CURVE 

C 1: EXTEND FAN CURVE BY FOLLOWING GRADIENTS OF TWO ENDS. 

C 2: EXTEND FAN CURVE AS ABOVE AT LEFT BOUNDARY REGION AND 

C SEND GRADIENT OF RIGHT BOUNDARY REGION TO ZERO. 

C 3. SEND GRADIENT OF BOTH SIDES OF BOUNDARY RANGE TO ZERO. 
110 

APPENDIX 4 ADDITIONAL INFORMATION SOURCES 

DiNenno, P.J., ed., SFPE Handbook of Fire Protection Engineering, 

First Edition, National Fire Protection Association, 1 

Batterymarch Park, Quincy, MA, 1988. 

Mitchell, D.W., Mine Fires, Maclean Hunter Publishing Co., 29 

North Wacker Dr., Chicago, IL, 1990. 

Hartman, H.L., ed., Mine Ventilation and Air Conditioning, Second 

Edition, John Wiley and Sons, New York, NY, 1982. 

Ho, C. Y., series editor, Y. S. Touloukian, W. R. Judd and R. F. 

Roy, editors, CINDAS DATA SERIES on MATERIAL PROPERTIES, Volume 

II-2 Physical Properties of Rocks and Minerals