CFD modeling of spontaneous heating in a large-scale coal chamber

Liming Yuan*,

*	 Corresponding author. Tel.: þ1 412 386 4961; fax: þ1 412 386 6595.
 

E-mail address: lcy6@cdc.gov (L. Yuan).
 

Alex C. Smith

Pittsburgh Research Laboratory, National Institute for Occupational Safety and Health, P.O. Box 18070, Cochrans Mill Road, Pittsburgh, PA 15236, USA

abstract

Three-dimensional computational fluid dynamics (CFD) modeling is conducted to simulate spontaneous

heating in a large-scale coal chamber with a forced ventilation system. Spontaneous heating is modeled

as the low-temperature oxidation of coal using kinetic data obtained from previous laboratory-scale

spontaneous heating studies. Heat generated from coal oxidation is dissipated by convection and

conduction, while oxygen and oxidation products are transported by convection and diffusion. The water

vapor transfer and the effect of heat of wetting are not modeled. The CFD model is validated by

comparing simulation results with test results from U.S. Bureau of Mines experiments conducted in the

coal chamber. The model predicts lower temperatures in the early stage but agrees well on the induction

time for spontaneous heating. The effects of airflow rate and order of reaction on the spontaneous

heating process are also examined. The calibrated CFD model is found to be useful for predicting the

induction time for spontaneous heating in underground coal mines.

1. Introduction

Spontaneous heating of coal occurs when sufficient oxygen is

available to sustain the low temperature reaction of coal with

oxygen but the heat produced by the coal oxidation is not

adequately dissipated by conduction or convection, resulting in

a net temperature increase in the coal mass. Coal oxidation is an

irreversible exothermic reaction and its reaction rate increases with

temperature. The increase in temperature also leads to a higher

oxidation rate. If not averted with appropriate action, this process

results in thermal runaway and a fire ensues.

Spontaneous heating has long been a problem in the mining,

storage, and transport of coal. From 1990 to 1999, approximately

17% of the 87 total reported fires for U.S. underground coal mines

were caused by spontaneous heating (DeRosa, 2004). A number of

methods have been proposed and used in attempting to predict

the spontaneous heating tendencies of coals in laboratory experiments, as reviewed by Carras and Young (1994). Some commonly

used methods are crossing point measurements, isothermal and

adiabatic calorimetry, oxygen sorption, and temperature differential. In the U.S., the Bureau of Mines developed the minimum

spontaneous heating temperature test method using an adiabatic

heating oven to predict the relative spontaneous heating tendency

to spontaneous heating for U.S. coals (Smith & Lazzara, 1987).

Although laboratory results from the above experiments are

valuable, their extrapolation to the large scale, especially the

underground mine environment, has not been completely

successful because of complicated scaling effects that cannot be

reproduced in small-scale experiments. It is both difficult and

expensive to conduct large-scale experiments to study spontaneous heating. Most large-scale experiments have attempted to

characterize the heat and mass transport properties occurring

during spontaneous heating in coal stockpiles. Only two largescale spontaneous heating tests are available in the literature

(Cliff, Clarkson, Davis, & Bennett, 2000; Smith, Miron, & Lazzara,

1991) that are designed to simulate spontaneous heating under

actual mine conditions.

Some numerical modeling studies have been done to understand the mechanisms of spontaneous heating (Arisoy & Akgun,

1994; Brooks & Glasser, 1986; Edwards, 1990; Monazam, Shadle, &

Shamsi, 1998; Nordon, 1979; Rosema, Guan, & Veld, 2001; Schmal,

Duyzer, & van Heuven, 1985; Zarrouk, O’Sullivan, & St. George,

2006). However, these studies are one- or two-dimensional models

that mainly focused on small-sized coal stockpiles. Little modeling

work has been done simulating actual underground mining

conditions. Saghafi and Carras (1997) did numerical modeling of

spontaneous heating in an underground coal mine with a ventilation system, but their work was also limited to two dimensions. In

this study, a three-dimensional CFD modeling of spontaneous

heating of coal, based on the U.S. Bureau of Mines (USBM) largescale coal chamber tests, was conducted. The coal chamber was

built by the USBM to study the spontaneous heating of a large coal

mass under conditions that simulate a mined-out area (gob) of

a mine (Smith et al., 1991).
2. USBM tests

The detailed experimental setup and results from three tests

conducted by the USBM in the coal chamber are available in literature (Smith et al., 1991). Here a brief description of the experimental setup is provided to facilitate understanding of the

development of the CFD model.

The coalbed chamber is 1.8 m high by 1.8 m wide by 4.5 m long

and is preceded and followed by two 1.8-m-high by 1.8-m-wide by

1.2-m-long plenum areas. The schematic of coalbed chamber and

plenum areas is shown in Fig. 1.

Fig. 1. Schematic of coalbed chamber and plenum areas (Smith, Miron, & Lazzara,

1991).

The sidewalls and floor of the structure are lined with ceramic

firebrick. The front and rear walls and the roof of the structure are

constructed of 0.16-cm-thick sheet steel. The interior surfaces of

the front and rear plenum walls and the plenum roofs are covered

with 10 cm of fiberglass blanket insulation. A 1.8-m-high by 1.8-mwide 0.6-cm-mesh wire screen, reinforced by a 10-cm-mesh wire

screen, separates the coalbed from the rear plenum area. The

coalbed and front plenum are separated by two 0.9-m-wide by 1.8­

m-long, 0.6-cm-mesh wire screens, reinforced by 10-cm-mesh wire

screen. The chamber holds up to 12,000 kg of coal and is provided

with a forced ventilation system. The ventilation air to the coalbed

is provided by two air compressors. The maximum airflow that can

be supplied to the coalbed is 200 L/min. Air enters the coal chamber

through a 1.3-cm-ID copper tube in the front plenum area, and exits

via a 25-cm-ID duct out of the rear plenum.

The temperature histories of the coalbed were recorded using

thermocouples arranged in 7 vertical arrays of 9 thermocouples,

0.3, 0.9, 1.5, 2.1, 2.7, 3.4, and 4.0 m from the front of the coalbed, and

3 horizontal arrays of 21 thermocouples, 0.45, 0.9, and 1.35 m above

the coalbed floor. Each array contained 9 thermocouples evenly

distributed over the surface along the coalbed width direction.

Across the width of the coalbed, the thermocouples were located

0.45, 0.9, and 1.35 m from the wall. A gas analysis system was used

to monitor the exit gas stream for CH4, CO, CO2 and O2 concentrations, via a 0.9-cm-ID stainless steel gas sampling tube located

0.9 m up into the rear plenum exhaust duct.

Three tests were conducted using different coals and different

ventilation conditions during the study. In the first two tests,

a sustained heating was not achieved. In the first test, Colorado D

seam coal was used with an initial airflow rate of 50 L/min. The

airflow rate was reduced to 30 L/min at 9 days, further reduced to

15 L/min at day 58 and lasted to 93 days with a maximum

temperature increase of 6 0C. In the second test, Colorado F seam

coal was used with an initial airflow rate of 30 L/min. The airflow

rate was increased to 50 L/min at 1.8 days, reduced to 25 L/min at

15.7 days, further reduced to 15 L/min at day 57 and lasted to 84.8

days with a maximum temperature increase of 9 0C. This paper

models the results of the third test with thermal runaway occurring

after 23 days. In the third test, hereafter referred to as the USBM

test, approximately 12,000 kg of the as-received Wyoming No. 80

coal was crushed to -2 cm. No. 80 coal exhibited a high spontaneous heating potential in laboratory-scale tests (Smith & Lazzara,

1987). 10% of coal was dried and placed from 1.7 to 2.8 m into the

coalbed with a height of 0.6–1.5 m above the floor of the coalbed.

The rest of the chamber was filled with the as-received coal. The

use of dried coal at the center was to expedite the spontaneous

heating process. The airflow was 50 L/min at the start, was

increased to 100 L/min at 0.8 days, 150 L/min at 7.6 days, and 200 L/

min at 21.7 days.

3. Modeling of low-temperature coal oxidation

The chemical reaction between coal and oxygen at low

temperatures is complex. Generally, three types of processes are

believed to occur (Carras & Young, 1994): (i) physical adsorption;

(ii) chemical adsorption, which leads to the formation of coaloxygen complexes and oxygenated carbon species; and (iii)

oxidation in which the coal and oxygen react with the release of

gaseous products, typically carbon monoxide (CO), carbon dioxide

(CO2), and water vapor (H2O). Of the above processes, oxidation is

by far the most exothermic. Physical adsorption can begin at

ambient temperature when coal is exposed to oxygen. Chemical

adsorption takes place from ambient temperature up to 70 0C.

Initial release of oxygenated reaction products starts from 70 to

150 0C, while production of more fully oxygenated reaction

produces occurs from 150 to 230 0C. The rapid combustion takes

place over 230 0C. The coal temperature rise from ambient

temperature to 230 0C is a slow process compared to the rapid

temperature increase after 230 0C. In practice, the occurrence of

rapid combustion represents a major fire hazard and needs to be

prevented if possible. The start of the rapid temperature rise is also

called thermal runaway. The time to reach a thermal runaway is

called induction time. The induction time can be used to indicate

the potential hazard of a spontaneous heating.

The moisture content of coal can play an important role in lowtemperature coal oxidation. The interaction between water vapor

and coal can be exothermic or endothermic depending on whether

the water condenses or evaporates. Sondreal and Ellman (1974)

reported that for dried lignite, the rate of temperature rise due to

the adsorption of water increased with the moisture content up to

a value of 20% water (by mass) and then decreased with further

increasing moisture content. Smith and Lazzara (1987) found that,

initially, the rate of temperature rise depends on the heat-ofwetting. Later the heating curves pass through an inflection point,

in which neither the heat-of-wetting mechanism nor the oxidation

mechanism dominates. In the final phase, the oxidation mechanism

dominates.

The effect of the moisture content of the air on the spontaneous

heating process was also dependent on coal rank and temperature.

Smith and Glasser (2005) concluded that adsorption of water vapor

does not in itself compete with the low-temperature oxidation in

terms of ‘heat generation,’ but appears to speed up the oxidation

rate, and possibly plays a catalytic role. The same conclusion was

reached by Smith and Lazzara (1987). In this study, the effect of

water vapor is not considered, and only the coal oxidation is

simulated.

The chemical reaction between coal and oxygen at low

temperature is very complicated and is not well understood. The

gaseous reaction products evolved during coal oxidation are

primarily CO, CO2 and H2O. A little quantity of oxalic acid and

mixture of aromatic acids and unsaturated hydrocarbons like C2H2,
C2H4 and C2H6 have also been reported. In this study, it is assumed

that CO2 and CO are the only reaction products from the coal

oxidation. The detailed chemical structure of coal varies with the

rank and origin of the coal. It is difficult to quantify the exact

relationship between the gaseous production rate and the amount

of oxygen consumed. According to experimental data (Smith et al.,

1991), one mole of coal reacting with one mole of oxygen generates

one mole carbon dioxide (CO2) and roughly 0.1 mole carbon

monoxide (CO) plus heat at the early stage of coal oxidation. So the

chemical reaction equation can be written as:

CoalDO2 /CO2 D0:1CODheat (1)

The dependence of the rate of oxidation, r, on temperature and

oxygen concentration can be expressed in the Arrhenius form:

r A O2 n 1⁄4 1⁄2 ] ð- Þ exp E=RT (2)

where the chemical reactionrate isdefinedas the rate of change inthe

concentrations of the reactants and products with a unit of kmol/

(m3 s), A is the pre-exponential factor with a unit of(kmol/m3

)

1-n s-1

,

E is the apparent activation energy with a unit of kJ/mol, R is gas

constant witha unitof kJ/(mol K), n is the apparentorder of reaction, T

is the absolute temperature inK, and [O2]is the oxygen concentration

with a unit of kmol/m3

. The value of the apparent order of the reaction, n, in low-temperature oxidation studies of coal and other

carbonaceous materials, has been shown to vary from w0.5 to 1.0

(Carras & Young,1994), and is about 0.61 for some U.S. coals (Schmidt

& Elder, 1940). Using this value, the reaction rate becomes

r 1⁄4 1⁄2O 0 2] :61A expð-E=RTÞ (3)

The value of apparent activation energy, E, of different coals can

vary between 12 and 95 kJ/mol. The pre-exponential factor, A,

depends more on coal rank and measurement method, and has

a typical value between 1 and 7 x 105

/s. The values of activation

energy and pre-exponential factor for No. 80 coal used in this study

were measured by Smith and Lazzara (1987) using an adiabatic

heating oven with a temperature range of 20–200 0C. In their study,

activation energy and pre-exponential factor were derived using

the simple Arrhenius equation

dT 1⁄4 A* expð-E=RTÞ (4) dt

By plotting the log of the rate of temperature rise, dT/dt, versus

1/T, the activation energy, E, was determined from the slope as

66.5 kJ/mol and the pre-exponential factor, A*, from the intercept as

1.9 x 106 K/s. This equation implies a zero order reaction rate. In

order to differentiate with the pre-exponential factor A in Eqs. (1)

and (3), here A* was used to denote the pre-exponential factor for

the zero order reaction; thus it has a unit of K/s. The relationship

between A and A* can be obtained by an applying the energy

balance equation to coal particles

dT

rsCps Q O 0:61A exp E=RT (5) dt 1⁄4 1⁄2 ] ð- Þ 2

where rs is the coal particle density in kg/m3

, Cps is the coal specific

heat in J/(kg K) and Q is the heat released during coal oxidation per

mole oxygen consumed in kJ/mol-O2. Substituting Eq. (4)into Eq. (5):

rsC * psA expð-E=RTÞ 1⁄4 Q1⁄2O2]

0:61A expð-E=RTÞ

Thus,

rsCps A 1⁄4 A* (6) Q1⁄2O2]

0:61

The heat generated from oxidation is dissipated by conduction

and convection while the oxygen and oxidation products are

transported by convection and diffusion. The early stage of spontaneous heating is a slow process, and the gas and coal particles are

assumed to be in thermal equilibrium. The detailed modeling of

heat transfer is provided in a previous study (Yuan & Smith, 2008).

4. Coal properties and coalbed permeability

The physical and kinetic properties of the coal used in the USBM

test and the model are shown in Table 1. The coalbed is treated as

a porous medium in the modeling, and the porosity and permeability of the coalbed are used as input in the model. The coalbed is

assumed to be evenly packed of coal particles with an average

diameter of 2 cm. The porosity of the coalbed was estimated using

the equation:

rb 3 1⁄4 1 - rp

where rb is the coal bulk density and rp is the coal particle density.

Using the coal bulk density and particle density of 870 and 1240 kg/

m3

, respectively, the estimated porosity is 0.3. Inside the coalbed

chamber, the permeability was assumed to be homogeneous and

isotropic; the permeability within the coalbed was approximated

by the Carmen–Kozeny equation for flow in packed beds (Bird,

Stewart, & Lightfoot, 1966):

33d2

k 1⁄4 150ð1 - Þ3 2

where d is the particle diameter. Using 3 1⁄4 0.3 and d 1⁄4 0.02 m,

k 1⁄4 1.13 x10-7 m2

. The porosity and permeability were assumed to

remain constant throughout the coal oxidation reaction.

5. Numerical modeling

A commercial CFD software program, FLUENT1

1 Reference to a specific product is for informational purposes and does not imply

endorsement by NIOSH.

from Fluent, Inc.,

was used in this study to simulate the gas flow and spontaneous

heating in the coalbed chamber as well as the gas flow in two

plenum areas. FLUENT is a general purpose CFD solver for a broad

spectrum of flow, heat transfer and chemical reaction modeling

applications. FLUENT can model the mixing and transport of

chemical species by solving conservation equations describing

convection, diffusion, and reaction sources for each component

species. Multiple simultaneous chemical reactions can be modeled,

with reactions occurring in the bulk phase and/or on wall or

particle surfaces, and in the porous region. In this study, the gas

flow in the chamber was treated as laminar flow in a porous

medium using Darcy’s law. The spontaneous heating of coal was

modeled as a surface chemical reaction, coal oxidation, occurring

on the coal surface in a porous medium. The heat generated from

coal oxidation is dissipated by convection and conduction, while

oxygen and oxidation products are transported by convection and

diffusion. The generic mass transfer equation solved by FLUENT is

reduced to

Y 2 2 2 v i vY vY v Y v Y v Y

ru þ i i i i rv y

þ rw 1⁄4 rD x z i Di v v x2 þ r v y2 v v þ i rDi þ Si (7) vz2

where Y is the gas component concentration, u, v and w are

velocities at x, y, z directions, respectively, m is gas kinetic viscosity;
k is the permeability of the coalbed, D is the gas diffusion coefficient, S is the rate of species production or consumption and can be

calculated based on the rate of reaction. The generic heat transport

equation is reduced to

 

 vT vT vT vT

3rgCpg þ ð1 - 3ÞrcCpc þ rgCpg u þ v þ w vt vx vy vz

! 2 2 2 v T v T v T 1⁄4 leff þ þ þ rQ (8) vx2 vy2 2 vz

where 3 is the porosity, rg, Cpg are the density and specific heat for

the gas, rc, Cpc are the density and specific heat for coal, Q is the heat

of reaction of coal oxidation and leff is the effective thermal

conductivity of the coal matrix. The rate of oxidation, r, is calculated

using Eq. (2). The effective thermal conductivity is calculated as:

leff 1⁄4 3lg þ ð1 - Þ3 lc

where lg and lc are the thermal conductivity for gas and coal.

Because of the limitation of the FLUENT program, the water vapor

transfer and the effect of heat of wetting are not modeled in this

study.

Table 1

The physical and kinetic properties of the coal.

Coal particle density 1240 kg/m3

Coal bulk density 870 kg/m3

Coal specific heat 1003.2 J/kg-K

Coal conductivity 0.1998 W/m-K

Heat of reaction 300 kJ/mol-O2

Activation energy 66.5 kJ/mol

Pre-exponential factor 1.9 x 106 K/s

Coal particle diameter 2 cm

Initial coal temperature 300 K

The physical model and mesh for the CFD simulation were

generated using the mesh generator software, GAMBIT, from

Fluent, Inc. Mesh used in the CFD modeling is shown in Fig. 2. The

cell size was 5 cm. The total cell number was about 180,000.

Fig. 2. Mesh used in the CFD modeling.

The

geometrical layout for the coalbed chamber and two plenums is

shown in Fig. 3.

Fig. 3. Geometrical layout for the coalbed chamber and two plenums.

The input data for the CFD modeling are the initial conditions

and boundary conditions. The initial conditions are that the coal

and air are all at 300 K. The boundary conditions used in the

simulations are the same as the ventilation flows for the USBM test

as described in Section 2.

A simulation was conducted first without coal oxidation to

obtain steady state flow field and gas distributions in the coalbed

chamber and plenum areas. Then, the unsteady simulations with

coal oxidation were conducted using the steady state solution as

the initial conditions. The initial time step was 1 h, and was reduced

to 1 min when significant temperature rise occurred.

6. Simulation results and discussion

Spontaneous heating can begin at ambient temperature when

coal is exposed to oxygen. As the spontaneous heating proceeds,

the coal temperature increases slowly. The temperature rise usually

consists of two periods. The first period is a slow temperature rise,

called the induction period, while the second one is a fast

temperature rise. When the coal temperature reaches about 500 K

(230 0C), the spontaneous heating mechanism changes to rapid

combustion (Babrauskas, 2003). In this study, with the goal of

understanding the mechanisms of spontaneous heating, the

simulations were focused on the spontaneous heating mechanism

at temperatures below 500 K. All simulation results were presented

in a vertical center-plane of coalbed chamber and plenums as

shown in Fig. 3.

6.1. Simulation results for the development of spontaneous

heating process

The simulation results are shown in Figs. 4–10. These results

indicate that the development of the heating process in the coalbed

can be divided into four stages. During the first stage of spontaneous heating, the temperature rises slowly. Fig. 4 shows the

temperature distribution at 8.3 days.

Fig. 4. Temperature distribution (K) in coalbed chamber and plenum areas at 8.3 days.

The maximum temperature

was 305 K, and temperature rise occurred over most of the coalbed.

Close to the front plenum, the temperature was slightly lower

because of higher air velocity. The oxygen concentration was still at

21% everywhere in the coalbed.

During the second stage, as the temperatures in the coalbed

increased, the heat dissipated by the airflow also increased. Because

of higher velocity close to the front of the coalbed, more heat was

dissipated by the airflow. Thus, the high temperature zone moved

back close to the rear plenum. Fig. 5 shows the temperature
distribution at 24.6 days. The maximum temperature was 391 K,

and the high temperature zone was close to the rear plenum. Fig. 6

shows the oxygen concentration distribution in the coalbed

chamber and plenums. Around the high temperature zone, the

oxygen concentration was about 2%.

Fig. 5. Temperature distribution (K) in coalbed chamber and plenum areas at 24.6

days.

Fig. 6. Oxygen concentration distribution (1 1⁄4100%) in coalbed chamber and plenum

areas at 24.6 days.

During the third stage, as the rate of temperature rise increased,

more oxygen was consumed, leading to insufficient oxygen for coal

oxidation close to the rear plenum. Therefore, the high temperature

zone started to move toward the front of the coalbed. Fig. 7 shows

the temperature distribution at 25.6 days.

Fig. 7. Temperature distribution (K) in coalbed chamber and plenum areas at 25.6

days.

The maximum temperature was 459 K, and the high temperature was close to the front of

the coalbed. Fig. 8 shows the oxygen concentration distribution at

25.6 days.

Fig. 8. Oxygen concentration distribution (1 1⁄4100%) in coalbed chamber and plenum

areas at 25.6 days.

As can be seen, there was nearly no oxygen available

downstream away from the high temperature zone.

During the fourth stage, the high temperature zone was limited

to a small area close to the center of the front mesh screen as shown

in Fig. 9. The maximum temperature was 491 K at 25.8 days. This is

because almost all oxygen was consumed in the coalbed as shown

in Fig. 10.

6.2. Comparison between simulation results and the

USBM test results

Similar phenomena were observed in the USBM test (Smith

et al., 1991). In the USBM test, the entire coalbed showed indications of heating immediately after the airflow was started. This

temperature increase was probably caused by the heating of

wetting and heat of adsorption. In the USBM test, the thermal

runaway occurred near the center of the coalbed after 23 days. The

thermal reaction zone then moved toward the front of the coalbed

due to oxygen depletion in the center of the coalbed. At 25.3 days,

thermal runaway occurred near the front of the coalbed. The

simulation results are consistent with these experimental

observations.

The simulation results were compared to the USBM test

results in Figs. 11–14. In the USBM test, the maximum temperature appeared at the thermocouple 0.3 m from the front of the

coalbed and 0.3 m from the floor. Fig. 11 compares the measured

temperature at this location with the calculated temperature

from the simulation. It can be found that during the induction

period, the measured temperature was always higher than that

calculated in the simulation. Since about 10% of the total volume

of coal was dried before the USBM test, the higher measured

temperatures are probably due to the effect of heat of wetting,

which is the heat generated by the adsorption of water vapor by

the coal surface and is not modeled in the simulation. By

comparing the adiabatic oven test results for the same kind of

coal, Smith et al. found that the heat of wetting was the dominant mechanism in the early part (first 20 days) in the USBM

test. Thermal runaway started roughly at the same time in the

USBM test and the simulation. In the simulation, the temperature rose very quickly to about 450 0C, then leveled off for more

than one day followed by continual rise again, while in the USBM

test, the temperature rose roughly at a constant rate, probably
because of the large logging intervals in the data acquisition

system, ranging from 30 min to 4 h.

Fig. 9. Temperature distribution (K) in coalbed chamber and plenum areas at 25.8

days.

Fig. 10. Oxygen concentration distribution (1 1⁄4100%) in coalbed chamber and plenum

areas at 25.8 days.

300 

350 

400 

450 

500 

550 

600 

15 20 25 30 

Temperature (K) 

test 

simulation 

0 5 10 

Time (day) 

Fig. 11. Comparison between simulation and test for temperature at 0.3 m from the

front of the coalbed.

Fig.12 compares the temperatures at the location 2.7 m from the

front of the coalbed and 0.3 m from the floor.

500 

Temperature (K) 

450 

400 

350 

300 

test 

simulation 

0 5 10 15 20 25

Time (day) 

Fig. 12. Comparison between simulation and test for temperature at 2.7 m from the

front of the coalbed.

30 

The calculated

temperature was also lower than the measured temperature during

the induction period at this location. After the start of the thermal

runaway, the rate of temperature rise became nearly the same for

both measured and calculated temperatures. As discussed by Smith

and Lazzara (1987) in their laboratory-scale studies, the heat of

wetting is the dominant mechanism at the early stage, but as the

temperature rises, the oxidation process becomes the dominant

mechanism. Although the adsorption of water vapor was not

modeled, the calculated temperatures were in good agreement

with the measured values once the coal oxidation process became

the dominant mechanism.

The oxygen concentration measured at exit of the 25-cm-ID

duct was compared to the calculated value from the simulation,

shown in Fig. 13. In the simulation, the oxygen concentration

changed minimally during the induction period, while in the

USBM test the oxygen concentration decreased to about 17% in

the first day. This is because a large amount of oxygen was

adsorbed by the coal surfaces at the beginning of the USBM test,

and this oxygen adsorption is not modeled in the simulation. As

reviewed by Wang, Dlugogorski, and Kennedy (2003), oxygen

adsorption includes physical adsorption and chemical adsorption.

Physical adsorption is non-specific and somewhat similar to the

process of condensation. Chemical adsorption, also called

chemisorption, is surface-specific and involves forces much

stronger than those operating in physical adsorption. Physical

adsorption results in single or multiple layers of adsorbed molecules, while chemisorption is limited to a monolayer of molecules

at the pore surfaces.

Initially, oxygen adsorption proceeds at a high rate but after

some hours drops off to a slower rate. The oxygen concentration

in the simulation decreased quickly to zero after thermal runaway

began, characterized by the Arrhenius equation. However, in the

USBM test, when the airflow was increased to 200 L/min at 21.7

days, the oxygen concentration first increased from 11% to 12.3%,

then slowly decreased to 10%, followed by a quick decrease again.

The reason why the increase of airflow to 200 L/min had no effect

in the simulation is that oxygen concentration in the simulation

was about 20.4% before the airflow rate was increased to 200 L/

min, while in the USBM test the oxygen concentration already

dropped to about 11% because of oxygen adsorption and coal

oxidation.

The CO concentrations from the USBM test and the simulation are compared in Fig. 14. In the USBM test, CO concentration

first increased quickly as thermal runaway occurred. When the

airflow was increased to 200 L/min, the CO concentration first

decreased, probably because of dilution, then increased slightly

and leveled off followed by a quick increase again to about 2%. In
80

the simulation, once the thermal runaway occurred, the CO

concentration increased quickly and leveled at 2.03% eventually,

because all the oxygen was consumed by the coal oxidation, and

the oxidation rate was completely dominated by the airflow

rate.

25 

20 

15 

10 

5 

test 

simulation 

0 

0 5 10 15 20 25 30 

Time (day) 

O2 (%) 

Fig. 13. Comparison between simulation and test for oxygen concentration at exit.

2.5 

test
 

simulation
 

2 

CO (%)

1.5 

0.5 

0 

0 5 10 15 20 25 0 

Time (day) 

Fig. 14. Comparison between simulation and test for carbon monoxide concentration

at exit.

1 

3

6.3. Effect of airflow rate

As described in Smith et al. (1991), two additional USBM tests

were also conducted in the coalbed chamber before the third one

which is simulated in this study. However, a sustained heating

was not achieved during the first and second USBM tests.

Compared to the third USBM test, the airflow rates were lower in

the first and second USBM tests. In the first USBM test, the airflow

rate was 50 L/min initially, was changed to 30 L/min at 9 days, and

was reduced to 15 L/min at 58 days; in the second USBM test, the

airflow rate was 30 L/min initially, was changed to 50 L/min at 1.8

days, was reduced to 25 L/min at 15.7 days, and was reduced to

15 L/min at 57 days. Simulations were conducted to examine the

effect of airflow rate on the spontaneous heating. With all

parameters kept the same, only the ventilation was changed to

the one used in the first and second USBM test, respectively.

Fig. 15 shows the temperature histories at 0.3 m from the front of

the coalbed for three ventilation conditions.

550 

500 

Temperature (K) 450 

400 

350 ventilation: test 1 

ventilation: test 2 

ventilation: test 3 

300

0 20 40 60

Time (day) 

Fig. 15. Temperature histories at 0.3 m from the front of the coalbed for three ventilation conditions.

For both ventilation

conditions used in the first and second USBM tests, a thermal

runaway was reached in the simulations. The induction time was

about 50 days for the first USBM test ventilation and about 45

days for the second USBM test ventilation. Although much longer

induction times were obtained for the first and second ventilation

flows than for the third USBM test ventilation flow, the simulation

results indicate that the ventilation was not the reason that

thermal runaway was not achieved in the first and second USBM

tests. The reason was probably due to the heat-of-wetting of dried

coal used in the third USBM test and the increased surface area

and weakening of the internal coal structure because of the

crushing of the coal just prior to the third experiment.

6.4. Effect of order of reaction

The value of the order of the reaction in low-temperature

oxidation studies of coal has been shown to vary from ~0.5 to 1.0

(Carras and Young, 1994). In most mathematical models, the order

of reaction is assumed to be equal to 1 in order to simplify the

mathematics. In this study, the value used for the order of reaction

was 0.61. The order of reaction affects the rate of heat generation, as

shown in shown in Eq. (2). Simulations were conducted to examine

the effect of the order of reaction on the spontaneous heating. With

all parameters kept the same, only the order of reaction was

changed to 1 and 0.5, respectively. Fig. 16 shows the temperature

histories at 0.3 m from the front of the coalbed for the different

orders of reaction. With the order of reaction of 1, after 30 days, the

temperature only increased by 2 degrees. With the order of reaction

of 0.5, the simulated thermal runaway occurred about 10 days

earlier than for the case with the order of reaction of 0.61, indicating

that lower order of reaction results in shorter induction time. This is

because that once the coal oxidation starts, some oxygen is

consumed quickly, leading to lower oxygen concentration locally.

With a lower value of order of reaction, the rate of reaction is less

dependent on oxygen concentration. Therefore, the rate of reaction

increases quickly, leading to an earlier rapid temperature rise, thus

a shorter induction time. When the order of the reaction is zero, the

rate of reaction is completely independent of the oxygen concentration. With a larger value of order of reaction, the rate of reaction

becomes more oxygen concentration controlled. The rate of reaction is reduced because of less oxygen available. Thus, the rate of

temperature rise is slowed down, leading to a longer induction

time.
300 

350 

400 

450 

500 

550 

0 5 10 15 20 25 30 

Temperature (K) 

n=0.61 

n=1.0 

n=0.5 

Time (day) 

Fig. 16. Temperature histories at 0.3 m from the front of the coalbed for the different

orders of reaction.

7. Conclusions

CFD simulations were conducted to model the spontaneous

heating of coal in a large-scale coalbed chamber. Simulation results

demonstrate that the CFD model reasonably reproduces the major

features of spontaneous heating, and the simulation results are in

good agreement with the USBM test results. However, the simulated temperatures in coalbed during the induction period were

lower than those in the USBM test. This discrepancy is caused by

not modeling the effect of water vapor on spontaneous heating. The

higher oxygen concentration during the induction period is

because of the effect of oxygen adsorption on the coal surfaces,

which is also not modeled in the simulations. Although the model

predicted lower temperatures and higher oxygen concentrations in

the induction stage, the predicted induction time from simulations

agrees well with the USBM test results. In real applications,

prediction of induction times is very important to prevent spontaneous heating fires, especially in underground coal mines.

Under conditions studied in this work, the higher airflow rate

results in a shorter induction time. Simulation results indicate

that the airflow rates used in the first and second USBM tests in

the coalbed chamber could support thermal runaway with longer

induction times if other conditions were the same as in the third

USBM test. The order of reaction has a major effect in predicting

the induction time. Lower values of order of reaction resulted

in the shorter induction times. Under conditions studied here,

the value of 0.61 gave a better result compared to values of 0.5

and 1.0.

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