Composition Change Model for Sealed Atmosphere in Coal 

Mines 

R. K. Zipf, Jr. 

NIOSH – OMSHR, Pittsburgh, PA, USA 

K. M. Mohamed 

NIOSH – OMSHR, Pittsburgh, PA, USA 

ABSTRACT: A sealed atmosphere in a mined-out area of an underground coal mine is simply a volume with 

homogeneous composition governed by boundary conditions. This paper presents a mathematical model based 

upon the conservation of mass principle that describes the flow of air (nitrogen and oxygen), methane and carbon 

dioxide into and out of a sealed atmosphere and the time-dependent changes in gas concentration within the 

sealed atmosphere. As boundary conditions, the model includes the inflow of methane and carbon dioxide from 

the surrounding strata, the inflow of nitrogen as an inert gas, the production of carbon dioxide from coal oxidation 

and the related depletion of oxygen. The model also considers the barometric pressure which can either cause air 

to flow into the sealed atmosphere or gas to flow out of that volume, depending on the pressure differential with 

the sealed atmosphere. The mathematical model is implemented into a MATLAB® program for calculation and 

data display. Using a range of realistic input parameters, the model shows that the atmosphere within sealed 

atmospheres tends to become fuel-rich inert and the pressure tends to increase due to the inflow of methane gas 

from the surrounding strata. Sealed atmospheres may therefore have a natural tendency to outgas, i.e. to release 

gas into the mine atmosphere as leakage around and through the seals. The pressure within the sealed atmosphere 

will depend on the leakage gas flow resistance of the mine seal and the surrounding rock between the sealed 

atmosphere and the active mine. If this resistance is high enough, it appears possible to maintain the sealed 

atmosphere in a fuel-rich inert condition and outgassing at all times despite changes in the barometric pressure. 

Designing the seal and the sealed area to control leakage such that the sealed atmosphere remains inert could 

result in safer sealed areas with minimal explosion hazard. 

1 Introduction 

1.1 Need for a Composition Change Model 

The Sago Mine disaster of 2006 and the ensuing changes 

to mine sealing regulations caused the U.S. coal industry to 

become more aware of the atmospheric composition within 

sealed atmospheres and how that composition can change 

over time. The composition of the atmosphere behind seals 

determines the design explosion pressure that those seals 

must resist. Under certain conditions, the sealed 

atmosphere may become self-inert, and the time required 

for self-inertization to occur may receive consideration 

prior to conducting a sealing operation. During the 

construction and cure time for seals, the sealed atmosphere 

must remain inert (non-explosive), until the seal achieves 

its design strength. Sealed atmospheres may “breathe” and 

exchange gases with the mine atmosphere, causing the 

sealed atmosphere composition to change. 

The sealed atmosphere behavior and the factors 

controlling it have not received extensive scientific study. 

Actual measurements of the sealed atmosphere 

composition are not available because sealed areas may 

not be readily accessible for direct measurements. 

However, evidence suggests that many sealed atmospheres 

tend to become and remain inert by themselves. 

1.2 Objectives 

This paper presents a mathematical model describing the 

condition and composition changes of sealed atmospheres 

in coal mines. The model considers the following factors 

affecting the sealed atmosphere composition: 

 Methane inflow from remnant coal or methane 

reservoirs in the roof and floor strata 

 Addition of the inert gases nitrogen or carbon 

dioxide 

 Carbon dioxide production from coal oxidation 

 Oxygen depletion from coal oxidation 

 Seal leakage resistance 

 Barometric pressure changes 

Presenting this mathematical composition change model 

may facilitate the understanding and interpretation of

actual measurements of the sealed atmosphere composition 
should they become available. With this theoretical model, 

it is demonstrated that sealed atmospheres will become 

inert and will remain inert if the air leakage into the sealed 

atmosphere is controlled. Maintaining the sealed 

atmosphere inert by minimizing leakage may result in 

safer sealed area with minimal explosion hazard. 

1.3 Related Prior Work 

Mining engineers have considered the atmosphere 

behind seals and how barometric pressure changes will 

affect that atmosphere. Dawson (1955) noted the practical 

difficulty in building air-tight seals that prevent gas from 

entering or exiting sealed atmospheres. Stevenson (1968) 

found a correlation between decreasing barometric 

pressure and increased methane concentration in a bleeder 

system. Fauconnier and Beukes (1978) correlated 

measured barometric and sealed atmosphere pressure 

changes, and noted the time lag between the two. 

Neethling (1989) described how methane could migrate 

closer to the active face during periods of falling 

barometric pressure and migrate away during rising 

pressure. Fauconnier (1992) conducted statistical analyses 

of explosions in South African coal mines and found that 

barometric pressure drops longer than 1 day were a 

contributing factor to gas explosions. Timko et al. (1987) 

measured gas velocity through longwall gob and sealed 

atmospheres that ranged from 0.0051 to 0.0150 m/s. At 

this rate, gas might take about 8 hours to cross a 300-mwide longwall panel. The measured gas leakage through 

each 140 kPa seal ranged from 0.12 to 0.24 m3

/s. 

However, the magnitude of the pressure differential 

causing that gas flow is not known. While the changes to 

the sealed atmosphere are known qualitatively and some 

measurements of those changes are available, researchers 

have not explored the composition of the sealed 

atmosphere with any quantitative models to better 

understand the processes and the interrelationships 

between important parameters affecting the processes. 

The “Gob Assistant Program” (Foster-Miller, 1988) 

may have been the first effort to understand the sealed 

atmosphere quantitatively and to calculate leakage quantity 

in and out. The intent of the Gob Assistant Program was to 

aid mine ventilation planning in order to 1) reduce the 

methane in return airways from outgassing seals, 2) reduce 

spontaneous combustion potential and 3) reduce explosion 

potential within sealed atmospheres behind ingassing seals. 

The Gob Assistant Program solved the differential 

form of a conservation of mass equation for a sealed 

atmosphere as it “breathes” in and out due to atmospheric 

pressure fluctuations. As input, the program required the 

volume of the sealed atmosphere, the mine ventilation 

pressure (barometric pressure), the seal leakage constant 

and the methane inflow rate into the sealed atmosphere. As 

output, the program calculated the pressure within the 

sealed atmosphere, and then determined the leakage rate 

either in or out. The program appeared to compute the 

methane concentration within the sealed atmosphere, but it 

did not consider other important gases such as oxygen, 

nitrogen or carbon dioxide. Unfortunately, the Gob 

Assistant Program is no longer available. 

The work described in this paper attempts to extend the 

concepts behind the Gob Assistant Program and provide a 

practical tool to understand the composition of the sealed 

atmosphere and the factors affecting it. 

2 Derivation of the Composition Change Model 

2.1 Volume of Sealed Atmosphere 

Figure 1 shows the assumed volume for the Composition 

Change Model (CCM).

 

 

 

 

Sealed Vo lume V 

M = total mass of gas 

M = Mm + Mn + Mo + Mc 

Pt = Pm + Pn + Po +Pc 

Methane 

inflowQm 

Air 

leakage in 

or 

gas 

leakage 

out 

Figure 1 Volume V of sealed atmosphere containing total 

mass of gas M with constant methane inflow 

rate and leakage in or out depending on 

barometric pressure. 

 This volume, V, contains 4 gas 

species, namely, methane, oxygen, nitrogen and carbon 

dioxide, denoted by subscripts m, n, o and c. Total mass, 

M, is the sum of the masses of each gas species. The total 

pressure Pt, inside the volume is the sum of the partial 

pressures of each species, Pm, Pn, Po and Pc. The mass, 

concentration and partial pressure for each species varies 

in time. This model treats the partial pressures for each 

species as the four unknown quantities. 

2.2 Boundary Conditions 

Figure 1 also indicates the two primary boundary 

conditions on the volume, namely, methane inflow rate 

and leakage either in or out. The methane inflow rate, Qm, 

is the methane volume liberated within the sealed 

atmosphere per unit time, and it has units of m3

/s. In 

addition to the methane inflow rate, the model includes 

nitrogen inflow rate, Qn, and carbon dioxide inflow rate, 

Qc, to simulate inert gas addition to the sealed atmosphere. 

The model also considers coal oxidation and the related 

carbon dioxide production and oxygen depletion. These 

quantities depend upon the oxygen partial pressure and the 

rate constants ro and rc, which have units mass (oxygen or 

carbon dioxide) per unit time per unit of oxygen partial 

pressure. This simple approximation of coal combustion is 

not intended to simulate spontaneous combustion. Full 

discussion of these additional model capabilities for inert 
gas addition and coal oxidation will appear in related 

papers. 

The other boundary condition on the sealed atmosphere 

is leakage. Outside the sealed atmosphere, the barometric 

pressure denoted by Pv(t) changes as a function of time. 

The gas quantity, QL, leaking through seals is defined as 

QL  Lc Pt (t)  Pv (t) (1)

where: Lc = leakage coefficient 

Pt(t) = total pressure of the sealed atmosphere, 

and 

Pv(t) = barometric pressure outside sealed 

atmosphere. 

When Pt (t)  Pv (t) the seal is ingassing, i.e. air is 

flowing into the sealed atmosphere. Conversely, when 

P t(t)  P v (t) the seal is outgassing, i.e. gases are flowing out 

of the sealed atmosphere. During an ingassing condition, 

the leakage quantity is air with composition 79% nitrogen 

and 21% oxygen. Methane and carbon dioxide, which are 

present in the mine atmosphere in small quantities, are 

neglected. During an outgassing condition, the leakage 

quantity has the composition of the sealed atmosphere. 

This leakage quantity relationship is identical in form 

to the typical air flow relation: 

H = RQ2

 (2)

where: H = head loss

 R = resistance and 

Q = flow quantity. 

Therefore, this leakage quantity relationship implies 

turbulent airflow. Stokes (1985) measured the air flow 

velocity and flow resistance through a longwall gob and 

concluded that turbulent flow relations applied. Depending 

on the magnitude of the leakage quantity, laminar flow 

may exist, and a linear leakage quantity relationship may 

apply; however, leakage quantity data measured by Weiss 

et al. [1993, 1996] tends to support the non-linear 

relationship used. 

2.3 Assumptions 

The Composition Change Model (CCM) shown in Figure 

1 makes numerous critical assumptions: 

1.	 Composition throughout the sealed atmosphere is 

homogeneous. 

2.	 Mixing of any added gases, such as methane, 

inert gas or air from leakage, occurs 

instantaneously and completely so that 

homogeneity of the sealed atmosphere is 

maintained at all times. 

3.	 Temperature (T) is constant throughout the sealed 

atmosphere. 

4. The volume (V) is constant. 

5.	 Total pressure (P(t)) varies with time but is 

independent of location within the sealed 

atmosphere. 

6. Leakage in and out of the sealed atmosphere is 

the sum of leakage through all seals, around all 

seals and through the rock surrounding seals. 

7.	 The composition of leakage inflow is that of air. 

The methane concentration in the active mine 

atmosphere is neglected and assumed zero. 

8. The composition of leakage outflow is identical to 

that of the sealed atmosphere. 

The model does not consider any spatial dimensions or the 

geometry of the sealed atmosphere. Composition gradients 

into the sealed atmosphere due to leakage or point sources 

of gas are neglected. The sealed atmosphere is simply a 

volume with homogeneous composition governed by 

boundary conditions. This simple model, however, appears 

to be the first model of its kind for examining the 

composition of the sealed atmosphere and considering the 

main factors controlling that atmosphere. It may provide 

useful guidance for later, more complex models that 

properly consider spatial variations in composition. 

2.4 Equations for the Composition Change Model 

Based on the conservation of mass principle, and the ideal 

gas law, P = ρRT the following system of ordinary 

differential equations was developed to describe the 

composition of a sealed atmosphere. 

For the ingassing condition where Pt  t  Pv (t) 

dP m (t)  m R T  m Q dt V	 m

 (3)

dP n (t) N p nRn T A  p nRnT 

QIG  Lc P(t)  Pv (t) dt V V (4) 

dP o (t) 1 N   p oRo T r Q  oRoT P (t) dt V IG V o 

1 A p  R T  o o L c P(t)  Pv (t) (5)

V

dPc (t) cR  c T r R T 

Q  c c

c P (t) dt V V o 

 (6)

For the outgassing condition where P t t  P v (t)

dP m (t)  m Rm T L Q P (t) c

m  m P(t)  P ( V V v t) dt (7) 

dP 	  n	 (t) N R T L  p n n Q ( V IG  P t) c P(t)  P t) dt n ( V v 

 (8) 

dP (t) (1 N p ) o R  o o T r Q  oRoT P (t) dt V IG V o 

 L   Po (t) c  P(t)  P (9) v (t)  V 

dPc (t)  cRcT r

Q  c RcT Pc (t) P (t)  L P(t)  P (t) dt V c V o V c v (10) 

The variables and constants in these equations are defined 

as follows: 

Pm, Pn, Po and Pc are the partial pressures for methane, 

nitrogen, oxygen and carbon dioxide, respectively, as a 

function of time. 
P is the total pressure or the sum of the partial pressures 

for each gas species and is a function of time.
 

Pv is the barometric pressure and is a function of time. 

Qm is the methane inflow rate. 

QIG is the nitrogen inert gas inflow rate at purity Np. 

Qc is the carbon dioxide inert gas inflow rate that is 

assumed to be 100% pure.
 
 

Np is the purity of the nitrogen inert gas, which is usually 

in the range of 90 to 95%. The balance of the nitrogen inert 

gas is assumed to be oxygen.
 
 

Ap is the nitrogen fraction in air leaking into a sealed
 
 

volume and is assumed to be 79%. The balance is 21%
 
 

oxygen. All other gases in the mine air such as carbon
 
 

dioxide, water vapor, argon and other gases are neglected
 
 

as insignificant. 

Rm, Rn, Ro and Rc are the specific gas constants for 

methane, nitrogen, oxygen and carbon dioxide,
 
 

respectively. 

ρm, ρn, ρo and ρc are the gas densities at standard pressure 

and temperature for methane, nitrogen, oxygen and carbon 

dioxide, respectively. 

LC is the leakage coefficient for the sealed volume. 

T is the temperature and is assumed constant. 

V is the sealed volume and is assumed constant.
 
 

ro and rc are the rate of oxygen depletion and the rate of
 
 

carbon dioxide production as a function of oxygen partial 

pressure.
 
 

3 MATLAB® Implementation of CCM 

3.1 Computational Scheme 

The system of ordinary differential equations for ingassing 

conditions (equations 3 through 6) or outgassing 

conditions (equations 7 through 10 have the following 

form: 

dPS (t) 

 f t, P (t), P (t), P (t), P (t), P (t) dt S m n o c v (11) 

To integrate the ingassing and outgassing systems of 

differential equations, the fourth- and fifth-order-accurate 

Runge-Kutta method in MATLAB® was used. By this 

method, the next values in time for Pm, Pn, Po and Pc are 

computed as: 

Pm (ti 1 )  Pm (ti )  t f1 ti , Pm ti , Pn ti , Po ti , Pc ti , Pv ti  (12) 

P n (t i1 )  P n (t i )  t f 2 t i , P m t i , 	 Pn   t i , Po   t i , Pc t i , P v t i  (13) 

P o (t i1 )  P o (t i )  t f 3 t i , P m t i , P n t i , P o t i , P c t i , P v t i  (14) 

P c (t i1 )  P c (t i )  t f 4 t i , P m t i , P n t i , P o t i , P c t i , P v t i  (15) 

where ∆t is the time step, ti is the current time step and ti+1 

is the next time step. A typical time step ranges from 50 to 

500 seconds, depending on the problem. 

Given the physical constants, input parameters, 

barometric pressure and initial conditions for partial 

pressures of methane, nitrogen, oxygen and carbon 

dioxide, the model calculates new values for the partial 

pressure of each gas species at future times, using both the 

ingassing and the outgassing sets of ordinary differential 

equations. The total pressure in the sealed atmosphere is 

then calculated as: 

Pt (t 1 )  Pm (ti1 i )  Pn (ti1 )  Po (ti1 )  Pc (ti1 ) (16) 

Depending on whether the ingassing condition 

P tt  P v (t) or the outgassing condition P t t  P v (t) applies, 

the updated values for partial and total pressure are 

selected from the appropriate computation. Finally, the 

leakage volume in or out is computed with equation 1. 

3.2 Data Input for CCM 

Figure 2 shows the data input interface in the CCM 

program. 

Figure 2 input screen for Composition Change Model 

(CCM). 

All units used by CCM are SI, i.e., kilogram, 

meter, second, Pascal for pressure and Kelvin for 

temperature. Major input parameters are the time step, the 

volume of the sealed atmosphere, leakage coefficient, 

methane inflow rate and the initial volumetric 

concentration of the gas species. Other parameters include 

the gas constants, gas densities and initial temperature, 

which are not normally changed by the user. 

CCM uses a sine function to describe barometric pressure 

changes. Key parameters for this model include the 

average pressure, the maximum pressure change 

(amplitude), period and time offset for the sine wave. With 

this sine function, it is possible to consider longer-term 

barometric pressure changes from or low and high pressure 

weather systems as well as cyclic changes due to diurnal 

variations. A constant pressure case can be defined by 

setting the amplitude equal to zero. Constantly increasing 

or decreasing barometric pressure can be specified by 

setting the period very long and adjusting the time offset. It 

is also possible to input measured barometric pressure 

change data directly, and this option will be explored by 

further research. 

3.3 Data Display from CCM 

CCM creates three different plots of calculated data: 

1. Gas species volumetric concentration versus time 

as shown in Figure 3. 
 

 

2. Leakage rate (QL), barometric pressure and sealed 

atmosphere pressure versus time as shown in 

Figures 4 and 5. 

3. Leakage rate and pressure difference between 

sealed atmosphere pressure and barometric 

pressure versus time (not shown). 

 

Figure 3 Methane, nitrogen and oxygen concentration 

versus time for sealed atmosphere with 0.25 

m3

/s methane inflow rate, 1,000,000 m3 volume 

and 0.00625 m3

/s/Pa1/2 leakage coefficient. 

Carbon dioxide concentration remains zero. 

This example considers a non-reactive coal 

which does not consume oxygen or produce 

carbon dioxide. 

Figure 4 Leakage from and pressure within sealed 

atmosphere versus time with constant

barometric pressure. 

Figure 5 Leakage from and pressure within sealed 

atmosphere versus time with cyclic barometric 

pressure. 

The user can manipulate the scales as the data dictates. 

3.4 A Note on Rounding Errors and Time Step 

CCM employs an explicit method for numerical 

integration of the system of ordinary differential equations. 

Depending on the time step set by the user, rounding errors 

can occur, leading to apparent numerical instabilities. 

These errors may arise when the system transitions from 

an ingassing to an outgassing condition or vice versa. To 

eliminate such errors, the MATLAB® code sets the leakage 

flow to zero when the absolute difference between the total 

seal pressure and the barometric pressure is less than 5 Pa. 

4 Estimating Input Parameters for CCM 

Tables 1, 2 and 3 provide bounds for the major input 

parameters for CCM, namely, the volume V of the sealed 

atmosphere, the methane inflow rate Qm, and the leakage 

coefficient LC. 

Table 1 Order of magnitude estimates for typical volumes 

in a coal mine. 

Mined-out component Volume range – m3 

Single entry – 1 to 5 km 10,000 to 50,000 

3 entry gate road – 1 to 5 km 50,000 to 200,000 

7 entry mains – 1 to 5 km 100,000 to 500,000 

Room-and-pillar panel 50,000 to 1,000,000 

Longwall panel 500,000 to 1,500,000 

Approximate range 10,000 to 10,000,000 

Table 2 Approximate ranges for methane inflow rate Qm. 

Volume, m3 

10,000 

Low influx 

rate, m3

/s 

(50 days to 

> 20% 

CH4) 

0.0005 

Medium 

influx rate, 

m3

/s 

(10 days to > 

20% CH4) 

0.0025 

High influx 

rate, m3

/s 

(2 days to > 

20% CH4) 

0.01 

100,000 0.005 0.025 0.1 

1,000,000 0.05 0.25 1 

10,000,000 0.5 2.5 10 
Table 3 Values for leakage coefficient into sealed 

atmosphere (Weiss et al., 1993, 1996). 

Leakage 

quantity 

(m3

/s) 

Pressure 

differential 

(Pa) 

Leakage 

coefficient 

(m3/s/Pa1/2) 

Lowest values 0.019 1000 0.0006 

measured at NIOSH 

Old MSHA guideline 

for 140 kPa seals 

0.047 250 0.0030 

Estimating the volume is a critical first step, and 

knowing the volume mined-out provides an upper bound 

for this parameter. Subsidence and flooding of mined-out 

areas can only decrease the volume from this upper bound 

estimate. The user should calculate the volume from a 

mine map, taking into account the mining history and mine 

subsidence. The volumes presented in table 1 are based on 

typical coal mine dimensions and show that the volume 

may range from about 104

 to 107 m3. 

Immediately prior to sealing a volume, the methane 

inflow rate is determined by measuring the methane 

concentration difference between the concentration in the 

return and that in the intake air and the volume flow rate of 

the ventilating air. The methane inflow rate used by CCM 

depends on the size of the sealed area and the methane 

influx rate. Three methane influx rates are defined, low, 

medium and high. At low, medium or high methane influx 

rate a sealed atmosphere will reach a fuel-rich inert 

condition defined as 20% methane by volume in 50, 10 or 

2 days, respectively. Kingery and Dornenberg (1957) 

provided measurements of the methane influx rate into 

mined-out areas. Depending on the coal seam and the age 

of the mined-out volume, the methane influx ranged from 

0.018 to 3.76 m3

 /s /106 m2. 

From an estimate of the methane inflow rate obtained 

prior to sealing, measuring the time required to achieve a 

certain methane concentration provides an approximate 

check on the volume estimate for the sealed atmosphere. 

The volume is estimated as: 

t (17) V  c Qm	 

Cm 

where: Qm = methane inflow rate 

Cm = methane concentration at time tc 

tc = time to achieve methane concentration 

Cm. 

This relation assumes that leakage in or out of the 

sealed atmosphere is negligible during the initial selfinertization phase immediately after seal construction and 

that the methane concentration is uniform throughout the 

volume. 

The leakage coefficient is used in equation 1 to 

determine the gas quantity flowing in or out of a sealed 

area given the pressure differential across the seals. Weiss 

et al. (1993, 1996) used a method to estimate LC from 

direct measurements of the leakage quantity through a test 

seal. In conducting the quantity measurements, researchers 

erected an airtight brattice curtain in front of the test seal 

that had a 0.30-m-square hole cut into it to concentrate the 

flow. Using a vane anemometer to detect flow, researchers 

could measure flow quantities as low as 0.019 m3

/s at 

differential pressure of up to 1,000 Pa. With this 

experimental setup, the smallest detectable value for the 

leakage coefficient is about 0.0006 m3

/s/Pa1/2. 

Another method to measure the leakage coefficient for 

a sealed area uses indirect measurements of the leakage 

quantity developed from measurements of methane 

concentration in the ventilating air upstream and 

downstream of a seals. For an outgassing set of seals, the 

leakage quantity flowing from the sealed atmosphere is 

(C mD C QL  mU )

QV (CmSV CmD )	 (18)

where: QV = ventilation airflow past a set of seals 

CmU = methane concentration upstream of the 

set of seals

 CmD = methane concentration downstream of 

the set of seals 

CmSV = methane concentration within the sealed 

atmosphere. 

Application of this method requires precision 

measurements of the methane concentration using a gas 

chromatograph on air samples. Simple measurements with 

handheld methanometers may not have sufficient precision 

for reliable determination of QL. 

Whether a direct or indirect measurement of leakage 

quantity from a sealed atmosphere is made, the leakage 

coefficient is calculated as: 

Q LC  L

P (19)

where ∆P is the measured pressure differential between the 

sealed atmosphere and the mine atmosphere. 

Prior to 2006, MSHA had guidelines for the allowable 

leakage through 140 kPa seals as constructed and 

evaluated within the NIOSH Lake Lynn Experimental 

Mine (Weiss et al., 1993, 1996). With a 250 Pa pressure 

differential, the leakage through a single seal could not 

exceed 0.047 m3

/s. These obsolete guidelines implied a 

leakage coefficient less than 0.0030 m3

/s/Pa1/2. For 

multiple seals, the leakage coefficients of each seal are 

added to determine the total leakage coefficient. 

5	 General Behavior of Sealed Atmospheres as 

Computed with CCM 

Based on the input parameters shown in Figure 2, CCM 

calculated the concentration and partial pressure for each 

gas species as a function of time. The volume is 1,000,000 

m3

 which is typical of several open room-and-pillar panels. 

The methane inflow rate is 0.25 m3

/s which is considered a 

medium influx rate for this sealed atmosphere. At this 

inflow rate, the sealed atmosphere should reach a methane 

concentration of 20% in about 9.3 days, as long as the 

leakage in or out of the sealed atmosphere is small. The 

assumed total leakage coefficient is 0.00625 m 3 /s/Pa 1/2 ,

which implies a tight set of seals. 
Figure 3 shows the calculated concentration for each 

gas species versus time. As expected, the methane 

concentration reaches 20% in about 240 hours (10 days). 

After 70 days, the concentration has reached 80% and the 

rise rate has decreased. Nitrogen and oxygen 

concentrations fall steadily and maintain a constant ratio of 

about 4-to-1, the same as the initial conditions. CCM 

calculations with a low or high methane influx rate 

produce calculated concentration behavior similar to that 

shown in Figure 3, except the time to reach 20% methane 

is longer or shorter, respectively. Note that carbon dioxide 

concentration remains zero, because the rate constants ro 

and rc are zero. This example does not consider a reactive 

coal. 

Figure 4 shows the calculated leakage from the sealed 

atmosphere and the calculated pressure within. Also shown 

is the specified barometric pressure, which is assumed 

constant at 100,765 Pa. With the constant methane inflow 

rate of 0.25 m3

/s, the pressure within must rise within the 

sealed atmosphere by some amount to drive an equivalent 

leakage volume. As expected, the leakage out from the 

sealed atmosphere reaches a constant value of slightly 

more than 0.25 m3

/s in about 120 hours (5 days), and the 

sealed atmosphere pressure stabilizes at 102,365 Pa. The 

small difference between methane inflow rate and leakage 

out of the sealed atmosphere arises due to density 

difference between methane and the general sealed 

atmosphere. 

6 Barometric Pressure Change Effects with CCM 

In the previous calculations with CCM, barometric 

pressure remained constant at one standard atmosphere. 

Changes in the barometric pressure can cause a sealed 

atmosphere to outgas when the barometric pressure falls or 

to ingas when it rises. This section briefly examines how 

barometric pressure changes affect the sealed atmosphere. 

Table 4 summarizes the range of barometric pressure 

variations for a variety of causes and the approximate time 

period or duration for each change. 

Table 4 Range for variations in barometric pressure. 

Cause of 

barometric 

pressure 

change 

Period Pressure change 

mbars In. Hg In. 

H2O 

Pa 

Diurnal 

variation 

1 day 3–4 0.09– 

0.12 

1.2–1.6 300– 

400 

Weather 

systems 

2–5 days 17–34 0.5 – 

1.0 

7–13 1,700– 

3,400 

Severe storms 2–10 hours 34–68 1.0– 13–27 3,400– 

2.0 6,800 

Severe 

hurricane 

2–5 days 166 5 68 16,600 

Low and high pressure 

weather systems can change the barometric pressure up to 

about 3,400 Pa (1 inch Hg) over a few days, while severe 

stormsor passing weather fronts can induce pressure 

changes up to about 6,800 Pa (2 inch Hg) in a few hours. 

The worst case is that of a hurricane, which could depress 

the barometric pressure by up to 16,600 Pa (5 inch Hg). To 

examine these pressure change effects, researchers input 

the cyclic barometric pressure function defined in Figure 2. 

Over a period of 10 days, pressure rises by 6,000 Pa and 

then falls by the same amount, simulating a series of 

severe storm systems. 

Figure 5 shows the calculated leakage, calculated 

sealed atmosphere pressure and the prescribed barometric 

pressure versus time. The calculated methane 

concentration versus time within the sealed atmosphere 

with the cyclic barometric pressure change did not differ 

substantially from that shown in Figure 3 where the 

barometric pressure remained constant. As shown in 

Figure 5, the peak sealed atmosphere pressure lags the 

peak barometric pressure by about 24 hours. The sealed 

atmosphere pressure remains greater than the barometric 

pressure at all times in this case, so the sealed atmosphere 

outgases continuously. The outgassing leakage rate ranges 

from about 0.06 to 0.39 m3

/s, and as expected, averages 

about 0.25 m3

/s. 

This calculation demonstrates that if the leakage 

coefficient for a sealed atmosphere is less than a certain 

threshold, the sealed atmosphere can tolerate a substantial 

barometric pressure change and still outgas continuously. 

7 Tentative Design Principles 

The Composition Change Model (CCM) shows how the 

sealed atmosphere changes in composition upon sealing 

from air to a self-inert state given sufficient time, a 

nominal methane inflow rate and a reasonable leakage 

coefficient. On average, the methane volume flowing into 

a sealed atmosphere must equal the leakage volume 

flowing out. CCM shows that because of the methane 

inflow, the sealed atmosphere not only tends to become 

self-inert, but it also tends to re-pressurize slightly in order 

to drive the natural outgassing. Therefore, by designing 

seals and sealed atmospheres to minimize the leakage rate, 

it appears possible to create sealed atmospheres that 

become self-inert and remain inert by design. An 

atmosphere that is inert by design would minimize the 

explosion hazard from sealed areas. 

The suggested steps necessary to design a sealed 

atmosphere to become inert and remain inert are as 

follows. A design example based on prior calculations in 

this paper is also provided. 

1.	 Estimate the volume V and the methane inflow 

rate Qm prior to sealing. For this design example, 

V = 1,000,000 m3

 and Q 3 m = 0.25 m /s. 

2.	 	 Estimate the time required to become fuel-rich 

inert with a methane concentration greater than 

20%. In this case that time is 10 days. 

3.	 	 Determine a design barometric pressure change 

and time period based on typical conditions at the 

site. This decision dictates how much barometric 

pressure change that the sealed atmosphere must 

withstand and still continue to outgas. In this 

example, the design pressure change is 6,000 Pa 
decrease over 5 days, as was used in the prior 

calculations. 

4.	 Estimate the design leakage coefficient as 

L Q / ΔP c L where QL ≈ Qm. In this example, 

maximum LC is estimated as 0.0032 m3

/s/Pa1/2, 

based on leakage coefficients presented in table 3. 

5.	 Calculate the actual design leakage coefficient. 

Using CCM to calculate the response of the 

sealed atmosphere to changes in barometric 

pressure, the maximum allowable leakage 

coefficient L is calculated as 0.01 m3 C /s/Pa1/2. 

With this maximum value for LC, the sealed 

atmosphere always remains in an outgassing 

condition even under a barometric pressure 

decrease of 6,000 Pa over a 5 day period. Figure 5 

shows leakage calculations for an LC of 0.00625 

m3

/s/Pa1/2, and the sealed atmosphere always 

remains in an outgassing condition. 

6.	 Design seals to meet the maximum allowable 

leakage coefficient L 3 1/2 C = 0.01 m /s/Pa . This 

leakage coefficient represents the total leakage 

quantity emanating from a sealed atmosphere. If 

multiple seals are used to create a sealed 

atmosphere, the sum of the leakage coefficients 

for each seal must be less than the maximum 

allowable LC. The earlier MSHA guidelines for 

evaluating 140 kPa seals at the NIOSH Lake 

Lynn Experimental Mine implied a leakage 

coefficient of 0.0030 m3

/s/Pa1/2. In this design 

example, up to 3 such seals could be used to 

create the sealed atmosphere. New seals designed 

to withstand higher explosion pressure should 

have even lower leakage coefficients; however, 

no data is available at this time. 

7.	 If by design, the sealed atmosphere is inert, the 

345 kPa standard may apply. The sealed 

atmosphere will require monitoring of the 

composition until it becomes inert and the seal 

reaches its design strength. After the sealed 

atmosphere becomes self-inert, periodic

monitoring is required to demonstrate that it 

remains inert and outgases continuously as 

designed. A differential pressure gage installed 

through a seal can show that the sealed 

atmosphere is outgassing and therefore remains 

inert. 

8 Conclusions 

Using the conservation of mass principle, researchers 

present a theoretical mathematic model called CCM that 

describes how methane, nitrogen, oxygen and carbon 

dioxide concentrations change within a sealed atmosphere 

in response to gas inflow rates, leakage in or out and 

barometric pressure changes. Application of the model 

shows that because of the methane inflow, sealed 

atmospheres tend to become fuel-rich and inert naturally if 

leakage in or out of the sealed atmosphere is controlled. A 

sealed atmosphere that is inert by design would minimize 

the explosion hazard in sealed areas. CCM may help 

interpret and understand measurements of the atmospheric 

composition within sealed atmospheres. Engineering 

sealed atmospheres to become inert and remain inert 

through leakage-control-based design may lead to greater 

safety by preventing potentially explosive mixtures from 

ever developing within sealed atmospheres. 

9 Disclaimers 

The findings and conclusions in this report are those of the 

authors and do not necessarily represent the views of the 

National Institute for Occupational Safety and Health. 

Mention of any company or product does not imply 

endorsement by NIOSH. 

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