A Process Model for Underground Coal Gasification- Part-I:
Cavity Growth
(Preprint version of an original research article to be submitted to Fuel Journal)
Indian Institute of Technology Bombay
1
A Process Model for Underground Coal Gasification- Part-I:
Cavity Growth
Ganesh Samdani1, Preeti Aghalayam2, Anuradda Ganesh3, R. K. Sapru4, B. L. Lohar4
and Sanjay Mahajani*,1
1
Department of Chemical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076
2
Department of Chemical Engineering, Indian Institute of Technology Madras, Chennai 600036
3
Department of Energy Science and Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076
4
Institute of Reservoir Studies, ONGC, Ahmedabad
Abstract
In underground coal gasification (UCG), a cavity is formed in the coal seam due to
consumption of coal. The irregular-shaped cavity consists of three distinct zones: a spalledrubble zone on the cavity floor, a cavity roof at the top and a void zone between the two.
During UCG, the coal seam between the injection and production wells undergoes two
distinct growth phases. In phase-I, coal/char near injection well gets consumed and cavity
grows in a vertical (radial) direction and hits the overburden. Phase-II starts thereafter, in
which the cavity grows in the horizontal direction towards the production well. The geometry
and flow patterns are distinctly different in these two phases and should be considered as two
separate events while modeling UCG process. This part of the paper presents an unsteadystate model for gas production during the initial vertical growth of the cavity in phase-I. A
computationally less expensive compartment modeling approach, based on computational
flow dynamics (CFD), is used to establish non-ideal flow patterns in the cavity. Furthermore,
the model also incorporates reaction kinetics, heat transfer, mass transfer, intra-particle
diffusional limitations and thermo-mechanical failure (spalling) of coal by using required
parameters for coal of interest. The simulations are performed for a typical Indian lignite and
the results are interpreted to demonstrate potential of the developed model. Simulations
results such as dynamics in rubble, void and roof zone are explained using different
parameters including reaction fronts, gas composition and exit gas calorific value. The
average calorific value of exit gas was observed to be relatively steady in spite of changes
occurring in each zone. Finally the simulation results are analyzed by comparing with the
results of the reported laboratory-scale experiments performed on the same coal under UCGlike conditions.
Keywords: Underground coal gasification, compartment model, spalling, syn-gas, lignite
2
Introduction
Underground coal gasification (UCG) is a process of in-situ conversion of coal into
combustible gases. The process involves vertical drilling of injection and production wells up
to the bottom of the coal seam and connecting them with a horizontal highly-permeable
linkage1. The reactants injected are air or oxygen, with or without steam. The products of the
process include CO, CO2, H2, CH4, H2O, and tars. Figure 1 describes the UCG process with
illustrations. A successful application of UCG provides a low-medium calorific value gas,
i.e.,3-12 MJ/Nm3.The merits of UCG include reduced environmental pollution, elimination of
transportation costs, ability to exploit deep and un-minable coal reserves, and possible carbon
capture and sequestration (CCS)2. On the other hand, the process runs the risk of problems
such as land subsidence and ground-water contamination3. The process involves several
phenomena, including complex flow patterns, multiple chemical reactions, water influx from
the nearby aquifer, and heat and mass-transfer effects4. Because of thermal shocks and the
inherent heterogeneity of the coal seam, small coal particles or blocks often break away and
fall from the roof surface5. This thermo-mechanical failure, called spalling, exposes more
surface area of the coal to the reactive environment. In addition to high temperatures, coal
type and geology also influence the spalling process6.
Because of the complexity of the UCG process and inability to visualize the underground
cavity, process model plays a very important role. The model should provide useful inputs at
the design stage for determining capacity of a pair of wells and should be able to predict the
effects of unforeseen events such as water intrusion or sudden spalling. Several modeling
efforts are reported in the literature and reviews are found elsewhere2,7.Available models can
be classified into packed bed models8-10, channel models11-14, coal block models15-18 and
process models19-21. However, first three classifications have idealized flow patterns, and
hence cannot adequately include effect of actual flow patterns on product gas composition.
On the other hand, most process models are based on assumptions which are difficult to
verify, or they neglect important features to save computational time. The process model
developed by Biezen19 is limited by assumptions related to heat transfer including constant
reactor temperature. CFD based process models20,21 are limited by huge computational loads
for simulating actual underground gasifier. In addition to actual flow patterns, inclusion of
spalling, as an essential cavity growth mechanism, for successful UCG process is very
important. Britten developed a one-dimensional model of the coal seam to account for
spalling14. Perkins modeled spalling as a function of critical conversion of coal implying that
3
some amount of coal remains unreacted because of spalling15.Similar to Britten and Perkins,
other attempts to include spalling were also limited by simplified definition of the
phenomena.
Injection and production wells and
connecting channel are availed.
Oxygen/air is injected
Cavity starts growing because of
combustion and spalling.
Sufficient cavity size &
temperature is obtained.
Injection of steam + oxygen/air
Cavity starts growing radially and
syngas is released (Phase-I)
Cavity hits the overburden
(completion of phase-I)
Forward growth towards
production well (phase-II)
Syngas is produced continuously
(phase-II)
Figure 1. Schematic of UCG process by linked vertical wells (LVW) technique showing different phases of
cavity growth (actual distance between two wells (50-60 m) is usually much larger than depicted).
We view the UCG process occurring in two distinct phases, characterized by the direction of
cavity growth and the state of the cavity (Figure 1). Actual distance between injection and
production wells is very large and figure 1 is not to the scale. In the first phase, cavity grows
vertically till it hits the overburden and in the second phase, it grows horizontally, towards
4
the production well. This paper focuses on modeling the initial vertical growth during phaseI. In this work, we predict the growth of the cavity through an unsteady-state model for the
three zones (rubble, void and roof) in the cavity. A model is developed and solved using the
experimental data on kinetics, spalling and physical parameters for an Indian lignite.
Model Development for UCG during Vertical Cavity Growth
Input information
Figure 2 shows the important inputs needed for development of UCG model. For
determination of reaction kinetics, it is necessary to generate laboratory data under UCG-like
conditions the mass-transfer and diffusion effects, if any. Similarly, correlations for heat and
mass-transfer coefficients and appropriate spalling (thermo-mechanical failure) parameters
have to be determined for flow and thermal conditions in the UCG geometry. Model inputs
associated with kinetics, heat/mass transfer and spalling have been determined for the coal of
interest and are briefly explained later. Unlike other parameters, spalling characteristics are
expected to be scale-dependent, and therefore these parameters might require tweaking for
simulation of field scale experiments. Another input required for modeling is actual flow field
in UCG cavity, which is dealt with in the next section.
Figure 2. Input and output information associated with the UCG-process model.
Flow characterization and the compartment model
A complex non-ideal flow pattern, which is strongly affected by cavity shape and size, exists
inside the UCG cavity. Studies using computational fluid dynamics (CFD) are essential for
understanding these flow patterns20,23,24. The importance of the transport processes that occur
5
in the UCG cavity is demonstrated in these studies and it can be concluded that the
oversimplification of the cavity geometry or flow patterns leads to unreliable results. On the
other hand, developing a complete reaction enabled CFD model for UCG geometries would
require enormous computational efforts. This suggests a need to simplify the modeling
approach to obtain relatively rapid but reliable predictions. Therefore, the model is reduced
by approximating the flow patterns inside the cavity using a compartment-modeling
technique. This technique involves representing the complex reactor geometry by a network
of ideal reactors, based on flow patterns inside the actual non-ideal reactor. Flow patterns
inside any reactor can be determined by residence-time distribution (RTD) studies. The RTD
studies reported in this paper are performed using ANSYS Fluent: a commercial CFD
software. Figure 3 shows a section of the UCG cavity and its geometry created in ANSYS.
Size of the cavity and size of the spalled particles are of the order of 2 m and5 mm,
respectively, and are based on our earlier work23,25. The geometry shows an inlet pipe, a
rubble zone around the inlet, and a void between roof and rubble. For flow simulations, the
rubble is considered as a porous medium with constant porosity. The rubble zone geometry is
divided into six subzones that allows us to specify different temperatures along the radial
direction, depending on the position of combustion and gasification fronts inside the spalled
char.
Figure 3. The geometry used for RTD studies.
For the RTD studies, continuity as well as momentum and energy balance equations are
solved to get a steady-state flow field. Boundary conditions used for these simulations are:
gases coming from inlet have constant temperature and flow rate, outlet is at constant
pressure, roof wall has an outward heat flux for drying inside the cavity roof, and bottom wall
transfers heat to the bottom rock. The flow field obtained after solving the balance equations
with appropriate boundary conditions is then frozen and a pulse of tracer is introduced
through the inlet. Solving the unsteady-state tracer-balance equation provides the exit-age
6
distribution. Detailed procedures of CFD-based RTD studies can be found in our earlier
work23.
Figure 4 shows the plot of velocity vectors on a vertical section of cavity geometry,
calculated from CFD studies. By examining these flow patterns inside the UCG cavity,
existence of distinct flow fields inside the rubble and the void space surrounding the rubble is
established. Therefore, we found it appropriate to consider a compartment model with a
hemispherical radial plug flow reactor (PFR) followed by a continuous-stirred tank reactor
(CSTR) for rubble and void zone, respectively (Figure 4). The proposed compartment model
is validated by comparing the CFD based exit-age distribution of the actual UCG cavity and
that of the proposed network of ideal reactors (not shown here).
roof
roof
void
rubble
zone
rubble
void
Figure 4. Velocity vectors showing flow patterns and proposed process model based on the CFD results
The interactions between different zones in UCG cavity are shown in figure 5. Gases enter
the rubble and flow radially in a plug-flow manner while reacting with char. Direction of
species transport between roof and void depends on driving force for individual species,
however the net flow mainly constitutes steam from roof to void. Because of net exothermic
effect, heat is generated in rubble whereas it is consumed inside roof, mainly due to drying.
Roof also loses part of the heat received from the rubble to the overburden. Gases, leaving the
void zone, flow towards the production well through the outflow channel.
7
Heat loss to
overburden
Roof (Coal block)
(drying + pyrolysis +
reactions, endothermic)
Mass transfer
(Gas)
Heat transfer
(Convection)
Heat transfer
(Radiation)
Spalling
(Solids)
Void (CSTR)
(gas phase
reactions only)
Heat transfer
(Convection)
From
injection well
Towards
outflow channel
Bulk flow
(Gas)
Rubble (radial PFR)
(pyrolysis +reactions,
exothermic)
Figure 5. Heat and mass transport between different zones in UCG cavity.
Models for different zones and equations/phenomena relating transport between these zones
are described in following section along with important assumptions and model features.
Plug-flow reactor model for char rubble
In this sub-model for rubble, the rubble is assumed to be hemispherical and the feed,
introduced at the center, distributes symmetrically in the radial direction in a plug-flow
manner. Thus, variations in the temperature and composition in both solid and gas phases are
only in a radial direction. The model is a set of spatial-temporal stiff partial differential
equations and is computationally intensive. To simplify the model, a pseudo steady-state
assumption is made for the gas species because of the large differences in the characteristic
times of the solid and gas variables10. This assumption allows dividing the system of
equations into two sets: 1) steady-state gas-phase mass and energy balances in the radial
direction and 2) a set of solid-balance equations in the time domain.
The assumptions and important features of this model are as follows:

The gas phase consists of seven species: N2, O2, H2O, H2, CH4, CO and CO2. The first
three are injected through the inlet and the others are products of the UCG process.
Nitrogen is not present, if pure oxygen with or without steam, is injected.

The solid phase consists of three species: coal, char and ash.
8

Darcy’s law accounts for the pressure-drop term in the momentum-balance equation.

Axial dispersion is not accounted for the gas-phase balance equations.

The porosity and permeability of the rubble are considered to be functions of the
extent of local solid conversion at a given time.

This sub-model considers a set of ten reactions, which are discussed later with details
of their kinetic models. Drying is not considered, as the coal is completely dried and
partly pyrolysed before it spalls on the rubble.

Solid and gas phase temperatures are related through a suitable correlation for the
convective heat-transfer coefficient; mass-transfer resistance is considered for all
heterogeneous reactions.

Provisions are made to simulate the initial ignition period when the coal bed is heated
to initiate the reactions.

The hemispherical-geometry is incorporated by accounting for the variation in crosssectional area at each radial position within the cavity.

An initial layer of ash with a thickness of the order of the discretized volume is
assumed to be present at the core of the hemispherical cavity.

Heat is transferred to the roof by radiation from top of the rubble.

All spalled particles are of uniform initial size and structure such that the intra-particle
diffusivities are same for all.

The rubble zone grows over time due to spalling of coal from the roof. At every
spalling instance, new layers of relatively cold spalled coal are formed on the top of
the rubble zone.

No volume contraction occurs during reaction i.e. there is no change in rubble zone
volume because of reactions.
The mathematical equations for the mass and energy balances for both gas and solid phases
are described by Eqs. 1-5.
9
Gas-phase balance: The gas-phase balance equations consist of a set of nine equations seven for gas-phase species, one for gas-phase temperature, and one for gas velocity.
𝜕𝐹𝑔𝑖
𝜕𝑉
= ∑𝑛𝑗=1 𝑎𝑖𝑗 𝑅𝑗
(1)
Boundary condition: at 𝑉 = 𝑉0 , 𝐹𝑔𝑖 = 𝐹𝑔𝑖,0
∑𝑖 𝐶𝑔𝑖 𝐶𝑝𝑖 (𝐴𝑐 𝑢𝑔 )
𝜕𝑇𝑔
𝜕𝑉
= − ℎ𝑇 (𝑇𝑔 − 𝑇𝑠 ) − ∑𝑛𝑗=1 ∆𝐻𝑗 𝑅𝑗
(2)
Boundary condition: at𝑉 = 𝑉0 , 𝑇𝑔 = 𝑇𝑔,0
The equation for the gas-phase velocity is obtained by summing Eq. 1 over all species and
replacing the term for total concentration by the equation of state (Eq. 6).
𝜕(𝑄𝑔⁄𝑇𝑔 )
𝜕𝑉
𝑅
= 𝑃 (∑𝑛𝑗=1 ∑𝑖 𝑎𝑖𝑗 𝑅𝑗 ) −
𝐴𝑐 𝑢𝑔 𝜕𝑃
(3)
𝑃𝑇𝑔 𝜕𝑉
Boundary condition: at 𝑉 = 𝑉0 , 𝑢𝑔 = 𝑢𝑔,0
Here, 𝑄𝑔 = 𝐴𝑐 𝑢𝑔 and𝐹𝑔𝑖 = 𝑄𝑔 𝐶𝑔𝑖
The Darcy flow equation is used for the pressure-drop term in this equation.
Solid-phase balance: The solid-phase ODEs include four equations - three for unsteady-state
material balance of solid species (coal, char, and ash) and one for energy balance.
𝜕𝜌𝑖
𝜕𝑡
= 𝑀𝑖 ∑𝑛𝑗=1 𝑎𝑠,𝑖𝑗 𝑅𝑗
(4)
Initial condition: at𝑡 = 0, 𝜌𝑖 = 𝜌𝑖,0
∑𝑖 𝜌𝑖 𝐶𝑝𝑠,𝑖
𝜕𝑇𝑠
𝜕𝑡
𝜕
𝜕𝑇
= 𝜕𝑉 ⌈𝑘𝑒𝑓𝑓 𝐴2𝑐 𝜕𝑉𝑠 ⌉ + ℎ𝑇 (𝑇𝑔 − 𝑇𝑠 ) − ∑𝑛𝑗=1 ∆𝐻𝑗 𝑅𝑗
(5)
Initial condition: at 𝑡 = 0, 𝑇𝑠 = 𝑇𝑠,0
Boundary conditions: at V = V0,
at V = Vtr, −𝑘𝑒𝑓𝑓 𝐴𝑡𝑟
𝜕𝑇𝑠
𝜕𝑉
Ts = Ts,0
𝜎𝜀
4
4
= 2−𝜖𝑟 (𝑇𝑠,𝑡𝑟
− 𝑇𝑠,𝑟𝑜𝑜𝑓
)
𝑟
An equation of state is used to relate the gas-phase pressure, temperature, and concentrations.
𝑃
𝑅𝑇
= ∑𝑛𝑖=1 𝐶𝑔𝑖
(6)
10
The model gives rise to a set of nine gas-phase balance equations, which are to be solved in
the radial direction. A set of four solid-balance equations (i.e., three solid densities and
temperature) are solved simultaneously in the time domain.
Darcy’s law (Eq. 7) relates velocities with pressure for porous medium.
𝜕𝑃
𝜕𝑉
= −
1
𝜇
𝐴𝑐 𝐾𝑝𝑒𝑟
𝑢𝑔
(7)
Back-mixed reactor model for the void space
As mentioned earlier, the void space has a back-mixed flow pattern, and therefore there are
no spatial variations in the temperature and gas-phase compositions.
The assumptions and important features of this model are as follows:

The gas phase consists of seven species (N2, O2, H2O, H2, CH4, CO, and CO2).

Drying and partial pyrolysis of coal occurs inside the cavity roof and the resulting
gases enter the void space.

Only water-gas shift reaction and three gas-phase oxidation reactions take place in the
void space.
The mathematical equations for the mass and energy balances are given by Eqs. 8 and 9. The
system of ODEs consists of a set of eight equations—seven for the gas species and one for
the temperature.
Gas-species balance: These are the unsteady-state, CSTR-balance equations. The inlet
composition and temperature for the CSTR are that of the exit gas from rubble zone.
𝜕𝐶𝑔𝑖
𝜕𝑡
1
𝜈
= 𝜏 (𝐶𝑔𝑖,𝑖𝑛 − 𝐶𝑔𝑖 𝜈 ) + ∑𝑛𝑗=1 𝑎𝑖𝑗 𝑅𝑗 + 𝑘𝑦,𝑐𝑎𝑣 (𝐶𝑔𝑖,𝑟𝑜𝑜𝑓 − 𝐶𝑔𝑖 ) 𝐴𝑟𝑜𝑜𝑓 ⁄𝑉𝑐𝑎𝑣
𝑖𝑛
(8)
Initial condition: at t = 0, Cgi = Cgi,0
Energy balance: It involves the terms for heat in-out due to bulk motion, heat of reaction,
heat required to evaporate water influx, if any, heat transferred between the roof and void,
and heat-in due to bulk motion of gases between the roof and cavity.
11
∑𝑛𝑖=1 𝐶𝑔𝑖 𝐶𝑝𝑖
𝜕𝑇𝑔
𝜕𝑡
1
𝜈
𝜏
𝜈𝑖𝑛
= (𝐶𝑔𝑖,𝑖𝑛 𝐻𝑖,𝑖𝑛 − 𝐶𝑔𝑖 𝐻𝑖
) − ∑𝑛𝑗=1 Δ𝐻𝑗 𝑅𝑗 − 𝐹𝑤 Δ𝐻𝑣𝑎𝑝 + ℎ𝑇,𝑐𝑎𝑣 (𝑇𝑠,𝑟𝑜𝑜𝑓 −
𝑇𝑔 ) 𝐴𝑟𝑜𝑜𝑓 ⁄𝑉𝑐𝑎𝑣 + 𝑘𝑦,𝑐𝑎𝑣 (𝐶𝑔𝑖,𝑟𝑜𝑜𝑓 − 𝐶𝑔𝑖 )𝐻𝑖,𝑟𝑜𝑜𝑓 𝐴𝑟𝑜𝑜𝑓 ⁄𝑉𝑐𝑎𝑣
(9)
Initial condition: at t = 0, Tg = Tg,0
Roof model
Figure 6 shows a typical UCG cavity and a simplified form of the actual spherical roof
geometry. There are three zones: wet zone, dry zone, and gas film next to the void. The dry
and wet zones are separated by the moving drying front.
The assumptions and important features of the model are as follows:

The mathematical equations describing the roof model are divided in two parts. For
the wet zone, only the heat-balance equation is solved with conduction as the only
mode of heat transfer. For the dry zone, the balance equations for temperature, mass
flux, gas species, and solid densities are solved with appropriate boundary conditions.

Coal undergoes pyrolysis and the resulting partly-charred material starts gasifying in
the dry zone itself. Tar, wherever formed, gets reformed spontaneously at higher
temperature in the presence of char26.

The net heat flux across the drying front, located at xd (Fig. 6), determines the mass
flux of steam that enters the dry zone.

Heat transfer to the roof is due to convection from the void inside the cavity and
radiation from the top of the rubble.

Generally, there is a net heat flux from the cavity and rubble to the roof, and a net
mass flux of gas species into the void.

Thermal equilibrium is assumed between gas and solids in dry zone.

It is also assumed that the ash separates instantaneously from the char surface.

The balance equations used to describe the system are the balance equations for seven
gas species (N2, O2, H2O, H2, CH4, CO, and CO2), two solid species (coal and char)
and energy.

Complete set of eleven reactions is included in roof model, however extents of
reactions, other than drying and pyrolysis, are very small because of relatively low
temperatures.
12
Figure 6. UCG cavity showing simplified schematic of different regions in the roof zone.
Dry zone- solid phase balance: The solid-phase can be described by a set of three ODEs i.e.
two for coal and char, and one energy balance. The pyrolysis reaction produces char, tar, and
pyrolysis gases, of which tar gets reformed and char can further gasify.
Solid species balance:
𝜕𝜌𝑖
𝜕𝑡
= 𝑀𝑖 ∑𝑛𝑗=1 𝑎𝑠,𝑖𝑗 𝑅𝑗
(10)
Initial condition: at t = 0, 𝜌𝑖 = 𝜌𝑖,0
Energy balance: The boundary conditions for the energy balance equation are constant
temperature at the drying front and a net heat flux due to radiation and convection at the
boundary open to the cavity.
∑𝑖 𝜌𝑖 𝐶𝑝𝑠,𝑖
𝜕𝑇𝑠
𝜕𝑡
𝜕
𝜕𝑇
= 𝜕𝑉 [𝑘𝑒𝑓𝑓 𝐴2𝑐 𝜕𝑉𝑠 ] − ∑𝑛𝑗=1 Δ𝐻𝑗 𝑅𝑗
(11)
Initial condition: at t =0, Ts in dry zone is defined as a linear interpolation between roof
temperature and Td.
Boundary conditions: at V = Vd,
At 𝑉 = 𝑉0, −𝑘𝑒𝑓𝑓 𝐴𝑟𝑜𝑜𝑓
𝜕𝑇𝑠
𝜕𝑉
Ts= Td
𝜎𝜀
4
= 2−𝜀𝑟 (𝑇𝑠,𝑡𝑟
− 𝑇𝑠4 ) + ℎ𝑇,𝑐𝑎𝑣 (𝑇𝑣𝑜𝑖𝑑 − 𝑇𝑠 )
𝑟
13
(12)
Gas-phase balance: The gas-phase species balance consists of a set of seven equations - one
for each component. Because of the large differences in the characteristic times of changes in
the solid and gas phases, the gas phase can be assumed to be in a pseudo steady state.
Another assumption, that diffusion is the only mode of gas-species transport, reduces the gasphase balance equations to a steady-state diffusion-reaction model.
The boundary conditions for the gas-species balance equations are convective mass flux at
the boundary open to the cavity and a zero-flux condition at the drying front for all species,
except steam. Steam is generated at the drying front and the flux depends on the drying front
velocity.
𝜕
𝜕𝑉
[𝐷𝑒𝑓𝑓 𝐴2𝑐
𝜕𝐶𝑔𝑖
𝜕𝑉
] + ∑𝑛𝑗=1 𝑎𝑖𝑗 𝑅𝑗 = 0
at V = Vroof , −𝐷𝑒𝑓𝑓 𝐴𝑟𝑜𝑜𝑓
𝜕𝐶𝑔𝑖
𝜕𝑉
at V = Vd, V = V𝑑 , −𝐷𝑒𝑓𝑓 𝐴𝑑
(13)
= 𝑘𝑦,𝑐𝑎𝑣 (𝐶𝑔𝑖,𝑣𝑜𝑖𝑑 − 𝐶𝑔𝑖 )
𝜕𝐶𝑔𝑖
𝜕𝑉
= 0; 𝑎𝑛𝑑 − 𝐷𝑒𝑓𝑓 𝐴𝑑
𝜕𝐶𝑠𝑡𝑒𝑎𝑚
𝜕𝑉
= 𝑣𝑑𝑓 𝜙(𝜌𝑤,𝑙 − 𝜌𝑤,𝑔 )/𝑀𝑤
where, vdf the velocity of the drying front, calculated later in this section, ρw,l and ρw,g are
density of water in liquid and gas phase at two sides of drying front. After discretizing the
diffusion term, the solid and gas phase balance equations give rise to a set of differential
algebraic equations (DAEs).
Wet zone energy balance: In the wet coal zone, moisture content and porosity are considered
to be uniform everywhere. Therefore, only transient conduction equations are solved with
appropriate boundary conditions.
𝜌𝑠 𝐶𝑝𝑠
𝜕𝑇𝑠
𝜕𝑡
𝜕
𝜕𝑇
= 𝜕𝑉 [𝑘𝐴2𝑐 𝜕𝑉𝑠 ]
(14)
Boundary conditions:
𝑎𝑡 𝑉 = 𝑉𝑇 , 𝑇𝑠 = 𝑇𝑇
𝑎𝑡 𝑉 = 𝑉𝑑 , 𝑇𝑠 = 𝑇𝑑
The drying front velocity can be calculated (Eq. 15), if the difference in the heat fluxes across
the drying front and the heat of vaporization at operating pressure are known.
14
𝑣𝑑𝑓 =
1
𝜙(𝜌𝑤,𝑙 −𝜌𝑤,𝑔 )/𝑀𝑤
−𝑘𝑑− [
(
𝜕𝑇
𝜕𝑇
] +𝑘𝑑+ [ ]
𝜕𝑥 𝑑−
𝜕𝑥 𝑑+
Δ𝐻𝑣𝑎𝑝
)
(15)
Once the drying front velocity is calculated, the corresponding increase in the size of the dry
zone can be determined. The values of different state variables corresponding to the nodes
added to the dry zone due to the movement of the drying front are:
1. The density of coal and char for all new nodes are the initial values in the coal seam.
2. The temperature and concentrations of gas species for the new last node on the
moving drying front are the values at the last node in the previous time step.
3. The temperature and concentrations of gas species for all intermediate nodes are
determined by linear interpolation. The two end points for interpolation are the new
last node and last-but-one node in the previous time step.
Reaction Kinetics
The set of 11 reactions used in the current model are reported in table 1. Chemical formula of
tar formed in pyrolysis is based on the similar studies on coal9,10. Tar undergoes fastreforming (Reaction 11) in presence of its char26. Reaction 7, the water-gas shift (WGS)
reaction, is a reversible reaction. WGS reaction kinetics given in table 1 is for forward
reaction; the backward reaction rate parameters are calculated based on reaction equilibrium.
Methane-steam reforming equilibrium reaction is not considered because of very small
fraction of methane in exit gas was observed during the laboratory-scale UCG experiments.
Intrinsic kinetic parameters for CO2 gasification, steam gasification, and char combustion for
the coal of interest are determined by our group. The kinetics of methanation, water-gas shift
(WGS) reaction, and gas-phase oxidation reactions are taken from literature. All these
reactions, except drying, occur in rubble zone and only homogeneous reactions are
considered in void zone. In roof zone model, all the reactions are included, however rates of
drying and pyrolysis are the only significant ones. Coal composition (ultimate and proximate
analysis) for the coal of interest is required for pyrolysis rate, which is given in table 2.
Stoichiometric coefficients for pyrolysis products are calculated by solving equations for
balances of elements, volatile matter and fixed carbon.
15
Table 1. Set of reaction, respective kinetic models and parameters for the reactions of coal of interset.
no.
Reaction
Representation
E
(J/mol)
1
Drying
2
Pyrolysis
𝐻2 𝑂(𝑙) → 𝐻2 𝑂(𝑔)
k0(sec-1 atm-N
α,N
-1
ORsec )
Kinetic
ref
model
only in roof zone and controlled by heat transfer
𝐶𝐻𝑎 𝑂𝑏 → 0.78𝐶 +
73670
1403
0,0
VRM
27
0.017𝐶𝐻4 + 0.28𝐻2 𝑂 +
0.016𝐶𝑂 + 0.07𝐻2 +
0.018𝐶𝑂2 + 0.019𝐶9 𝐻𝑐
3
Char combustion
𝐶 + 𝑂2 → 𝐶𝑂2
140000
1.69E+7
0,1
RPM
28
4
Steam gasification
𝐶 + 𝐻2 𝑂 → 𝐶𝑂 + 𝐻2
207013
1.261E+8
0,1
RPM
29
5
CO2 gasification
𝐶 + 𝐶𝑂2 → 2𝐶𝑂
237020
4.71E+7
0,0.234
RPM+LH
30
6
Methanation
𝐶 + 2𝐻2 → 𝐶𝐻4
150000
2.337E-6
1,NA
volumetric
31
7
Water-gas-shift
𝐶𝑂 + 𝐻2 𝑂 → 𝐶𝑂2 + 𝐻2
60272
3E+7
0,1
volumetric
9
8
Tar
𝐶9 𝐻𝑐 + 9𝐻2 𝑂
spontaneous tar cracking reaction in presence of
cracking/reformin
𝑐
→ 9𝐶𝑂 + (9 + ) 𝐻2
2
its char
26
g
9
Gas phase
𝐻2 + 0.5𝑂2 → 𝐻2 𝑂
approximate rates as a function of gas
oxidation
𝐶𝑂 + 0.5𝑂2 → 𝐶𝑂2
temperature and oxygen concentration
9
𝐶𝐻4 + 2𝑂2 → 𝐶𝑂2 + 2𝐻2 𝑂
RPM: Random Pore Model (Ψ=3.74), LH: Langmuir–Hinshelwood
The RPM (random pore model)32 rate expressions used in this study is given by,
𝑅𝑔 = − 𝑘0 𝑒 (
−𝐸⁄ ) 𝛼
𝑅𝑇 𝑇 𝑓(𝑝𝑔 𝑁 )𝐶𝐶ℎ𝑎𝑟,0 (1
− 𝑋)√1 − 𝜓 ∗ 𝑙𝑜𝑔(1 − 𝑋)
(16)
The rates of heterogeneous reactions can be influenced by mass-transport limitations from the
bulk gas to the solid surface, diffusion through particles or the ash layer, and kinetic
limitations at the solid surface. The internal transport and surface kinetics can be lumped
together by introducing effectiveness factors for heterogeneous reactions on spherical
particles which quantifies and includes the diffusion/internal-mass-transfer effects in reaction
model. The calculation of the effectiveness factor for RPM based kinetics for gasification
reactions is explained in supporting information. Coupling this with the external mass
transfer effects leads to the following expression for the overall rate, RT:
1
)+(1
⁄𝑅𝑚 )
𝑐
𝑅 = (1⁄𝑅
(17)
where, RC is the effective chemical rate, evaluated by multiplying the intrinsic rates of the
heterogeneous reactions (Rg) at surface conditions by their effectiveness factors and Rm is the
external mass-transfer rate of a limiting reactant. This approximation is not necessary for
16
reactions taking place in the roof because the roof model, itself, is a diffusion-reaction model
for gases.
Physical Properties
The physical properties required as inputs to the model include porosity, permeability, heat
and mass-transport parameters for solid-gas interactions inside rubble and between cavity and
its roof. The correlations used in the simulation are given in the supporting information.
Spalling
The rate of spalling is expressed in terms of the mass of spalled rubble in one spalling
instance. For the coal of interest, this rate is deduced from the results of spalling experiments
performed in our laboratory25. Experimental results showed a variation in spalling rate from
2-20 kg/m2/hr. Spalling, being a thermo-mechanical and thermo-chemical phenomena,
depends on coal seam temperature. Coal seam temperature has a one-to-one relation with
rubble temperature and therefore, this model incorporates spalling as a function of rubble-top
temperature. This methodology is further substantiated by performing simulations for the
range of spalling rates and it was observed that for any given spalling rates, spalling occurs at
an almost constant corresponding rubble surface temperature. Therefore, a condition for
spalling is defined such that spalling occurs if the temperature of the top of the rubble (Trt)
crosses a certain limit and this increases the volume of the rubble. This limiting temperature
is higher for low spalling rates. For a typical spalling rate observed during experiments on the
lignite of interest, the limit for spalling (Trt) is 900 K. An increase in the volume of rubble
means addition of volume elements in PFR model. The temperature and solid densities of
partly pyrolyzed spalled coal are averaged over the number of volume elements spalled in
that particular spalling instance.
Solution Procedure
A MATLAB solver for stiff ODE’s solution procedures is used to solve the balance
equations. Figure 7 gives a detailed procedure for solving model equations from different
zones in the UCG cavity. The equations are divided into six sets. The first set consists of
first-order ODEs that describe the gas-phase temperature, velocity, and concentrations in the
spalled rubble (PFR). The second set is equations describing the solid temperature and
densities in the rubble (PFR). Here, the solid-phase heat-balance equation is a partial-
17
differential equation, which is converted into an ODE in the time domain using method of
lines.
Inputs:
Solid: temperature, density,
Gas: conc, temperature, pressure
START
t=0
t = t + dt
NO
V= 0, yi = yi0 Tg = Tg0
END
YES
t= tend
V = V + dV
Solve PFR gas mass balance and energy balance
using values at previous time (Eq. 1,2,3)
Increase the volume of rubble (PFR) if
spalling condition is satisfied (Fig. A2)
Calculate gas densities and temperature at
current time and volume in rubble
Calculate exit gas composition and
temperature at current time
Solve PFR solid mass balance and energy
balance (Eq. 4,5)
Solve CSTR balance equations (Eq. 8,9)
Calculate solid composition and temperature at
current time and volume in rubble
Increase the volume of drying zone, if velocity
front has crossed volume of one node (Fig. A3)
Solve Darcy’s law for calculation of pressure
profile in rubble (Eq. 7)
Calculate the velocity of drying front based on
difference in heat fluxes at drying front (Eq. 15)
NO
V= Vend
YES
NO
YES
Vwet= Vwet,end
Vdry= Vdry,0, yi = yi0 Tg = Tg0
Vdry = Vdry + dV
Calculate temperature profile
Solve for the dry zone energy and mass
balance equations (Eq. 10,11,12,13)
Solve for the wet zone energy balance
equations (Eq. 14)
Calculate drying and pyrolysis gas release, gas and
solid composition and temperature
Vwet = Vwet + dV
YES
Vwet= Vwet,0, Tg = Tg0
Vdry= Vdry,end
Figure 7. Procedure for solving different sets of equations of the process model.
18
NO
The third equation is the momentum balance for the spalled-char zone, which, for the current
system, reduces to Darcy’s law relating gas-phase pressure to gas-phase velocity. The system
of equations is solved on a uniform volume-grid system. The solution begins by initializing
the system of balance equations i.e. specifying the initial and boundary conditions. The
equations are solved in the order of solid-phase, gas-phase, and momentum balance. The
solution of the momentum-balance equation provides a pressure profile, starting from the last
node (at the exit), where the pressure is known, to the inlet, making use of the previouslydetermined velocities. The hemispherical geometry is accounted for by relating the cross
section area with the volume, as Ac = (18π Vc2)1/3. Once the rubble zone equations are solved
for the complete rubble volume, we solve the fourth set of equations, which is the gas-species
balance in the void. This is a set of first-order ODEs in the time domain. The fifth set of
equations is for the dry zone inside the cavity roof, which consists of balance equations for
gas species, solid densities, temperatures, and the molar flux of steam from the drying front.
This system of equations is solved on a volume grid similar to the one for spalled-char
volume. The set of DAEs describing the dry zone is solved simultaneously at a given time,
starting from grid next to the cavity-roof wall and going to the grid at the drying front. Once
the procedure is performed till the last node, we solve the sixth set of equations. These are the
energy-balance equations for wet zone and they are solved on a similar volume grid. After
solving for both the dry and wet zones in the roof, the drying front velocity and the steam
molar flux from the drying front are calculated. Once this solution procedure is followed for a
time step, the time is increased to the next level. Estimates for the solution at any time level
are made based on the solutions at the previous time level and serve as initial guesses. While
solving the equations, checks are performed for spalling and changes in the dry zone volume
caused by movement of the drying front. Detailed algorithm for inclusion of effects of
spalling and movement of the drying front are presented in supporting information.
Results and Discussion
Table 2 shows the important input parameters used to simulate the process modelError!
Reference source not found..
These are based on experiment and simulation data reported in
literature9,10,33. The total simulation time is 10 hours with a step size of 2.5 seconds for
simulation, and the initial spalled char volume of 0.02 m3 is discretized in finite nodes of
volume 2 x 10-4 m3. This volume corresponds to laboratory-scale UCG experiments; results
from these experiments are used for validation of the model. The representative results are
illustrated in this section.
19
Table 2. Input parameters for simulating the UCG process.
Sr. No.
Parameter
Value
1
Initial volume of spalled char
0.02 m3
2
Steam/O2 ratio
3.57
3
Initial ignition period
30 s
4
Feed gas and initial solid temperature in rubble
600 K
5
Coal type:
Proximate
Analysis
Lignite
Volatile matter %
Fixed Carbon %
Ash %
47.72
50.26
2.01
Ultimate
analysis
6
Initial spalled char density
Carbon %
Hydrogen %
Nitrogen %
Oxygen
200 kg m-3
7
Ash Content
5%
8
Initial porosity
0.25
9
Molar flow rate
3.2 x 10-3 kmol m-2 s-1
10
Step size in time
2.5 s
11
Total simulation time
10 hrs
12
Size of a volume element
2e-4 m3
13
Initial volume of dry zone
8e-3 m3
14
Initial rubble permeability
100 Darcy
15
Initial particle diameter
5 mm
16
Initial density of coal
1000 kg/m3
17
Pressure
4.8 atm.
18
Distance between the wells
~ 0.5 m
65.78
5.15
0.53
18.97
Rubble model
Figure 8 shows the temperature profiles along the rubble volume at different times. Solid and
dotted lines represent the gas and solid temperatures, respectively. The vertical lines indicate
the volume of the rubble on the floor of the cavity at the corresponding time. The change in
the volume of rubble is due to spalling of partly pyrolyzed coal from roof of the cavity.
Ignition applied in the initial 30 sec. for 10% of the rubble volume raises the solid
temperature sufficiently (≈ 900 K) to trigger the reactions of char. Being exothermic, char
combustion results in rise in the solid temperature. The solid then heats the gas through
convection. Thus, as the temperature within the cavity increases, various other reactions take
place simultaneously, including steam gasification, Boudard reaction, methanation, and
water-gas shift reaction. The net heat effect of these reactions is exothermic, which increases
20
solid and gas temperatures. The position in the rubble at which a sudden sharp rise in
temperature occurs is the reaction front. The temperature profiles at intervals of an hour or
two clearly depict the movement of the reaction front with time.
1300
1200
Temperature (K)
1100
1000
900
800
700
600
500
0
0.01
0.02
0.03
0.04
0.05
6 hr
8 hr
0.06
Volume (m3)
1 hr
2 hr
3 hr
4 hr
10 hr
Figure 8. Temperature profiles along the rubble volume at different times (solid and dotted curve: gas
and solid temperature, vertical lines are drawn to show the volume of spalled char at the specified time).
Oxidation and gasification reactions take place as the gasifying agents (steam and carbon
dioxide) come into contact with the char. Rubble temperature rises steeply at the start of the
reaction zone due to the highly-exothermic oxidation reaction and then drops towards the top
of the rubble zone, which is exposed to the void. The heat conducted from the reaction front
increases the temperature of the external surface of the char rubble, which radiates a certain
fraction of that heat to roof of the cavity. Moving away from the reaction front, towards the
external surface of the char rubble, the temperature of the gas is higher than the solid. This is
attributed to the heat provided by the gas phase reactions; no significant heterogeneous
reactions take place near the external surface of the char rubble due to relatively lower solid
temperatures.
Figure 9 shows the char density profiles along the reactor volume as time progresses. Char is
continuously consumed to produce ash and gaseous products via heterogeneous reactions
next to the reaction front. Figure 9a shows the profile of char densities before spalling occurs,
and Figure9b shows the char density profile after few spalling instances.
21
200
160
400
140
350
120
100
80
60
a)
300
250
200
150
40
100
20
50
0
0
0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
Volume (m3)
10 hrs
450
char Density (kg/m3)
Char Density (kg/m3)
180
500
1 hr
0.5 hr
0
0
b)
0.01
0.02
0.03
Volume (m3)
0.04
0.05 0.056
Figure 9. Char densities along the rubble volume at different times.
Figure 10 plots the reaction rates at the end of an hour. Since the temperature increases
steeply at the reaction front, there is a sharp rise in the reaction rates. The oxidation,
gasification, and water-gas reaction rates are higher than those of other reactions. The reason
for high rates of steam gasification, compared to combustion, is the higher composition of
steam entering the reactor (>3.5 times that of the amount of oxygen). The Boudard and
methanation reactions are slower than steam gasification under the conditions of interest. The
rate of the water-gas shift reaction is significantly higher than that of the other gas-phase
reactions. Methanation and water-gas shift reactions take place over almost the entire
temperature zone but their rates are lower after crossing the reaction front. The peak of the
Boudard reaction is slightly shifted toward the right compared to the peaks for oxidation and
steam gasification due to the higher concentration of CO2 formed after oxidation reaction.
22
Steam Gasification Reaction
Char Oxidation
-3
9
x 10
0.02
0.018
8
0.016
Reaction rate (kmol/m3s)
Reaction rate (kmol/m3s)
7
6
5
4
3
2
0.012
0.01
0.008
0.006
0.004
1
0.002
0
0
0.005
0.01
0.015
Volume (m3)
0.02
0
0
0.025
Boudard Reaction
-4
1.2
0.014
x 10
0.02
0.025
x 10
0.02
0.025
0.02
0.025
0.02
0.025
1
Reaction rate (kmol/m3s)
Reaction rate (kmol/m3s)
0.01
0.015
Volume (m3)
Methanation Reaction
-15
1.2
1
0.8
0.6
0.4
0.2
0.8
0.6
0.4
0.2
0
0
0.005
0.01
0.015
Volume (m3)
0.02
0
0
0.025
Water Gas Shift Reaction
-3
10
0.005
x 10
0.005
H2 Oxidation
-6
5
0.01
0.015
Volume (m3)
x 10
4.5
8
Reaction rate (kmol/m3s)
Reaction rate (kmol/m3s)
4
6
4
2
0
3.5
3
2.5
2
1.5
1
-2
0.5
-4
0
0.005
0.02
0
0
0.025
CO Oxidation
-6
2
0.01
0.015
Volume (m3)
x 10
x 10
8
1.6
7
Reaction rate (kmol/m3s)
Reaction rate (kmol/m3s)
0.01
0.015
Volume (m3)
CH4 Oxidation
-14
9
1.8
1.4
1.2
1
0.8
0.6
6
5
4
3
2
0.4
1
0.2
0
0
0.005
0.005
0.01
0.015
Volume (m3)
0.02
0
0
0.025
0.005
0.01
0.015
Volume (m3)
Figure 10. Plot of the rates of various reactions in the rubble zone after one hour.
23
The water-gas shift reaction reverses direction soon after the reaction front and further down,
its direction changes again. This could be attributed to the transition point where the
concentration of hydrogen exceeds that of steam.
Figure 11 shows the plot of mole fractions of the gas-phase species along the length of the
reactor after 1 hour. Oxygen and steam remain unreacted until the reaction front, indicating
that the entire char is consumed till this rubble volume in an hour. Once the reactants enter
the reaction zone, oxygen starts reacting exothermically with char to produce carbon dioxide.
Due to the high temperatures at the reaction front, steam gasification simultaneously
produces hydrogen and carbon monoxide. As the water-gas shift reaction takes place across
the entire char rubble, we observe a continuous increase in hydrogen and carbon dioxide
mole fractions while carbon monoxide and steam compositions decrease.
0.8
Oxygen
Steam
Hydrogen
Methane
CO
CO2
0.7
Gas Mole fractions
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.005
0.01
Volume (m3)
0.015
0.02
Figure 11. Plot of gas-mole fractions along the rubble volume after1 hour.
Figure 12 plots the mole fractions of gases leaving the rubble and entering the void against
time. Due to combustion reaction, oxygen gets consumed rapidly, whereas a significant
proportion of steam is always present, despite being a reactant for gasification. This is due to
reversible water-gas shift reaction. The average product gas-mole fraction is in an almost
cyclic steady state with respect to time; and the variation is at the spalling instances which
occurs if its criteria are satisfied. The variation in the exit-gas mole fraction between two
spalling events (shown in Figure 12) can be explained as follows: When the reaction starts in
the rubble, the rubble temperature increases due to the net exothermicity. This increase in
24
temperature reverses the direction of the equilibrium of the water-gas shift reaction, resulting
an increase in mole fraction of carbon monoxide and a decrease in fraction of hydrogen. As
the calorific value of hydrogen and carbon monoxide are similar, the calorific value
approaches steady state before the first spalling instant. At the spalling event, partlypyrolyzed coal from the roof of the cavity falls on the rubble. The temperature of the spalled
coal is much less than that of the rubble on the floor. This shifts the equilibrium of WGS in
the forward direction. Apart from the changes in equilibrium, another reason for the increase
in hydrogen at the instant of spalling is, the increased rates of pyrolysis of coal after it spalls
on the hot rubble. Pyrolysis produces volatile gases, such as CO2, CO, H2, and CH4, and
generates char and tar. CO release by pyrolysis is minimal. Therefore, the CO mole fraction
decreases significantly after spalling. The methane fraction before spalling is negligible in the
exit gas, however, spalling gradually results in an increase in the methane fraction.
0.8
Oxygen
Steam
Hydrogen
Methane
CO
CO2
0.7
Gas Mole fractions
0.6
0.5
0.4
0.3
0.2
0.1
0
0
2
4
6
8
10
Time(hrs)
Figure 12. Plot of mole fraction of gas leaving the rubble zone versus time.
Figure 13 illustrates the variation in the calorific value of the rubble-exit-gas, on a dry basis.
The gross calorific value is calculated as:
Calorific value (kJ/mol) = HCO yCO + HH2 yH2 + HCH4 yCH4
(18)
The calorific value of the exit gas is almost steady before the first spalling instance. This is
because sufficient coal is present beyond the reaction front resulting in same length of
reaction zone even while coal is consumed. If the reaction zone reaches the external surface
of the rubble, or if spalling occurs, the calorific value changes. As shown in Figure 13, the
25
changes in the calorific value at the spalling instance are evident. As spalling occurs, the solid
temperature at the external surface of the rubble decreases because the partly-pyrolysed and
relatively-cold coal falls on the external surface of the rubble, reducing the gas temperature as
well as the reaction rates. These reduced reaction rates cause a dip in the calorific value.
However, as the coal falling on the rubble is partially pyrolyzed, it starts releasing volatile
matter in the form of combustible gases, thereby regaining the calorific value. Therefore, the
exit gas composition gets affected by both reduction in rates of heterogeneous char reactions
and by increased rates of pyrolysis, resulting in a dynamics in its calorific value, as shown in
Figure 13.
The recurring behavior in the calorific value of the product gas also depends on factors such
as volume of the rubble, volume of coal spalled and position of reaction front. When the
reaction front is close to the external surface of the rubble, its temperature is high enough to
increase radiation flux to the roof, leading to spalling. After spalling takes place the external
surface of the rubble gets cooled again. This cycle continues until the roof of the coal seam
hits the overburden.
200
180
Calorific Value (kJ/mol)
160
140
120
100
80
60
40
20
0
0
2
4
6
8
10
Time(hrs)
Figure 13. The calorific value of the rubble exit gas with time.
Roof model
Heat transfer from the cavity to the roof causes pyrolysis of coal resulting in an increase in
char density with respect to time, as shown in Figure14a. This increase in char density
corresponds to a proportional decrease in coal density. Because of spalling, partly-pyrolyzed
coal from roof falls onto the rubble surface. Therefore, the roof interior which is at a
26
relatively lower temperature gets exposed to the cavity leading to the pyrolysis of interior of
roof. This dynamics is evident through a sudden fall in temperature and char density at
spalling instance and gradual increase thereafter as shown in Figure 14a and b.
Heat transfer from the void to the roof forms separate dry and wet zones inside the roof. The
movement of the drying front, separating the two zones, is tracked and shown in Figure 15.
10
450
9
445
7
Temperature (K)
Char Density (kg/m3)
8
6
5
4
3
2
440
435
430
425
1
0
0
1
a)
2
3
4
5
6
Time (hrs)
7
8
9
420
0
10
1
2
3
4
b)
5
6
time (hrs)
7
8
9
10
Figure 14.(a) Char-density and (b) temperature profiles for first 10 nodes inside the UCG cavity roof,
starting from the volume element exposed to the void.
0.06
movement of drying front (m)
0.05
0.04
0.03
0.02
0.01
0
0
1
2
3
4
5
6
7
8
9
10
time (hrs)
Figure 15. Tracking the movement of the drying front inside the cavity roof.
Void model
Gases leaving the rubble and the roof enter the void between them. Only gas-phase reactions
take place in the void; in the absence of oxygen, WGS reaction is the only significant gas-
27
phase reaction. Figure 16 shows the profiles of exit gas from the cavity. The variations in the
mole fractions are qualitatively similar to the variations in the composition of the gas leaving
the rubble. The main difference is in the steam fraction, which increases significantly due to
the addition of steam from the roof.
0.8
Oxygen
Steam
Hydrogen
Methane
CO
CO2
0.7
Gas Mole fractions
0.6
0.5
0.4
0.3
0.2
0.1
0
0
2
4
6
8
10
Time (hrs)
Figure 16. The cavity exit-gas mole fractions versus time.
Trends of the exit-gas calorific values (Figure 17) are similar to those for the calorific value
of gases leaving the rubble. The difference can be explained on the basis of spalling, the
WGS reaction, and the addition of pyrolysis gases from the roof.
Calorific value (kJ/mol) & Energy output (kJ/hr)
250
Calorific value
Energy output
200
150
100
50
0
0
2
4
6
Time (hrs)
28
8
10
Figure 17. Variation of exit gas calorific value and energy output; vertical lines indicate spalling instance.
At spalling instance, the extent of increase in calorific value depends on loss of heat due to
drying inside roof and relative amounts of gases in exit gas flow. However, energy output
starts increasing just after every spalling instances, which indicates a positive effect of faster
pyrolysis of coal after it spalls on relatively hot rubble. Energy output is the function of exit
gas calorific value and its flow rate. Peak in energy outlet profile is observed much before the
next spalling instance, indicating decline in pyrolysis rate of the spalled coal, which reduces
the exit gas molar flow rate. It has been shown in our model for phase-II that in a real UCG
process, these effects get dampened because of the presence of a series of spalling events
happening all along the outflow channel.
Comparison with laboratory experiments
In this section, process-model results are compared with the performance of laboratory-scale
UCG experiments reported in our earlier work33. These experiments were performed by
mimicking the actual UCG process for a coal block of approximately 30 x 25 x 20 cm3 (L x
H x W). Two vertical holes were drilled and connected at bottom of the coal block. The inlet
oxygen-flow rates applied were 800-1250 ml/min (4 x 10-5 kmol/min) and the steam-flow
rate was set as per the selected steam-to-oxygen ratio. During experiments, oxygen is
introduced continuously and steam is introduced in a cyclic manner. The cyclic addition is
adopted mainly because of the fact that a continuous flow of a mixture of steam and oxygen
prevented sustainable gasification during experiments. More details of these experiments can
be found elsewhere33. These experiments were performed on a small coal block whereas the
actual UCG process is applied for very long coal seams, i.e., those with a high ratio of the
distance between the wells to the coal-seam thickness. Therefore, although both phase-I and
phase-II of growth are relevant in an actual UCG operation, the small L/H ratios make phaseII irrelevant in laboratory experiments. For this reason, the phase-I model results are
compared with the laboratory experiments.
Figure 18 compares the average gas fractions predicted by the model and those observed
during laboratory UCG experiments under similar conditions. Though the model overpredicts the hydrogen composition and under-predicts the CO2 composition, match between
experimental and model results is satisfactory. Temperature and water content of exit gas
may affect the relative yields of H2, CO and CO2 because of equilibrium of WGS reaction,
however this comparison is not possible because of un-availability of this experimental data.
29
Apart from gas composition, gas calorific value, cavity size and cavity growth rate (volume
consumed per mole of the gas fed) are also calculated and compared in Table 3. These results
show that the process model predicts the results reasonably well.
0.5
0.45
expt
Mole fractions
0.4
Phase I
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
CO2
H2
CO
O2
CH4
Figure 18. Comparison of the predicted calorific value and gas-mole fractions (on dry basis) with microUCG experiments under similar conditions.
Table 3. Comparison of the predicted cavity-growth and the laboratory scale-UCG performance under
similar conditions for the operation time of 11.5 hrs.
Parameter
Laboratory Experiments
Process Model
Calorific value (kJ/mol)
~160 (average)
157 (average)
For O2 flow rate (kmole/min)
3.2 x 10-5
3 x 10-5
Total volume consumed (cc)
~1000
1120
Growth rate (cc/mole gas fed)
45
54
Conclusion
A simplified process model is developed using the compartment-modeling approach for
underground coal gasification. The model incorporates spalling characteristics, heat- and
mass-transfer effects, particle diffusion effects, roof dynamics, and all important chemical
reactions, including drying and pyrolysis. The model successfully predicted outlet-gas
compositions and temperatures along the reactor volume with respect to time. It may be noted
that, despite several changes occurring within the reactor, the exit concentrations remain
within a specific range between two spalling instances and after an initial stabilization period.
This is due to the presence of large amount of coal on the floor of the cavity beyond the
30
reaction zone for a long time. The amount of coal/char present in the rubble depends on
spalling, which makes it critical to determine the spalling characteristics of the given coal for
reliable predictions. The UCG performance predicted by the model is in agreement with that
observed during laboratory experiments.This model can also be used for UCG of any coal
after obtaining pertinent input data on kinetics and spalling.
Notations
Acronyms
CCS
CFD
CRIP
CSTR
DAE
LVW
PFR
RPM
RTD
UCG
WGS
Carbon Capture and Sequestration
Computational Fluid Dynamics
Controlled Retracting Ignition Point
Continuous Stirred Tank Reactor
Differential-Algebraic Equation
Linked vertical Wells
Plug Flow Reactor
Random Pore Model
Residence Time Distribution
Underground Coal Gasification
Water Gas Shift
Symbols
Ac
Aroof
Cg
Cp
Deff
E
ΔH
Fg
Fw
H
Kper
M
N
V
P
Qg
R
RC
Rj
RM
RT
T
Vc
Vcav
Cross sectional area (m2)
Area of roof surface (m2) changes with time
Gas concentration (kmol/m3)
Specific heat (kJ/kmol/K for gas and kJ/kg/K for solids)
Effective Diffusivity (m2/sec)
Activation energy (J/mol)
Heat of reaction (kJ/kmol)
Gas flow rate (kmol/sec)
Rate of water influx (kmol/sec)
Enthalpy (kJ/kmole)
Permeability of rubble (m2)
Molecular weight (kg/kmol)
Order of reaction
Volume (m3)
Pressure (kPa)
Gas flow rate in rubble (m3/sec)
Gas constant (kJ/kmol/K)
Lumped rate based on chemical reaction and internal resistance (kmol/m3/sec)
jth reaction (kmol/m3/sec)
Rate of mass transfer of limiting reactant (kmol/m3/sec)
Total rate (kmol/m3/sec)
Temperature (K)
Volume of PFR (m3)
Volume of cavity = volume of (rubble + void) (m3)
31
X
aij
as,ij
ug
hT
hTcav
keff
ky,cav
k0
t
vdf
Solid conversion
Stoichiometric coefficient of ith gas species in jth reaction
Stoichiometric coefficient of ith solid species in jth reaction
Gas velocity (m/sec)
Heat transfer coefficient in between gas and bed of particles (kW/m3/K)
Heat transfer coefficient from void to wall transfer (kW/m2/K)
Effective conductivity (kW/m/K)
Mass transfer coefficient from void to wall transfer (m/sec)
Specific rate constant(sec-1 (kmole/m3)-NK-α)
Time (sec)
Velocity of drying front (m/sec)
α
εr
ρ
σ
𝜇
τ
υ
Φ
Ψ
Temperature exponent in reaction kinetics
Radiation emissivity
Solid density (kg/m3)
Stefan Boltzmann constant (kW/m2/K4)
Viscosity of gas mixture (Pa sec)
Residence time in CSTR (sec)
Flow rate in CSTR (m3/sec)
Porosity
Structural Parameter for RPM
Subscripts
g
s
0
c
r
w
d
i
j
tr
in
cav
roof
vap
df
T
l
dry
wet
Gas phase
Solid phase
Inlet to the cavity
Cross-section
Values at roof
Water influx or water
Drying
Species index
Reaction index
Top of rubble
Inlet of CSTR
Cavity
Cavity roof
Vaporization
Drying front
Volume of total coal seam (at the end of wet zone)
Liquid phase
dry zone
wet zone
References
1. Gregg, D.; Edgar, T. F. Underground coal gasification. AIChE J1978, 24, 753.
2. Aghalayam, P. Underground Coal Gasification: A Clean Coal Technology. In
Handbook on Combustion; Wiley-VCH books, 2010; pp 257–275.
32
3. Zeirzer, R. Review and Critical Analysis of Underground Coal Gasification.
Undergraduate Thesis, University of Queensland Technology, 2004.
4. Burton, E.; Friedmann, J.; Upadhye, R.Best
Practices
in
Underground
Coal
Gasification. Contract No. W-7405-Eng-48: U.S. DOE, Lawrence Livermore
National Laboratory, Livermore, CA, 2006.
5. Britten, J.A. Recession of a coal face exposed to a high temperature. Int. J. Heat Mass
Transfer 1986, 29, 965.
6. Upadhye, R.S.; Field, J.E.; Fields, D.B.; Britten, J.A.; Thorsness, C.B. Experimental
Investigation of Coal Spalling. Report UCRL- 94418, Lawrence Livermore National
Laboratory, Livermore, CA, 1986.
7. Shafirovich, E.; Varma, A. Underground Coal Gasification: A Brief Review of
Current Status. Ind. Eng. Chem. Res.2009, 48, 7865.
8. Winslow, A. M. Numerical model of coal gasification in packed bed. Report UCRP77627, Lawrence Livermore National Laboratory. Livermore, CA, 1976.
9. Thorsness, C.B.; Greens, E.A.; Sherwood, A. A One Dimensional Model for in situ
Coal Gasification. Lawrence Livermore National Laboratory Report, UCRL- 52523,
1978.
10. Khadse, A.; Qayyumi, M.; Mahajani, S. M.; Aghalayam, P. Reactor Model for the
Underground Coal Gasification (UCG) channel. Int. J. Chem. React. Eng.2006, 4,
A37.
11. Dinsmoor, B.; Galland, J.M.; Edgar, T.F. Modeling of cavity formation during
underground coal gasification. J. Petro. Tech. 1978, 30, 695.
12. Coeme, A.; Pirard, J.P.; Mostade, M. Modeling of the chemical processes in a
longwall face underground gasifier at great depth. In Situ, 1993, 17, 83.
13. Kuyper, R.A.; Van Der Meer, Th.H.; Hoogendoorn, C.J. Turbulent natural convection
flow due to combined buoyancy forces during underground gasification of thin coal
layers. Chem. Engg. Sci.1994, 49, 851.
14. Britten, J.A.; Thorsness, C.B. Model for Cavity Growth and Resource Recovery
during Underground Coal Gasification. In Situ1989, 13, 1.
15. Perkins, G.; Sahajwalla, V. Steady-State Model for Estimating Gas Production from
Underground Coal Gasification. Energy Fuels, 2008, 22, 3902.
16. Tsang, T. H. T. Modeling of Heat and Mass Transfer during Coal Block Gasification.
Ph.D. Dissertation, University of Texas at Austin, Austin, TX, 1980.
33
17. Park, K.Y.; Edgar, T.F. Modeling of Early Cavity Growth for Underground Coal
Gasification. Ind. Eng. Chem. Res.1987, 26, 237.
18. Perkins, G.; Sahajwalla, V. A Mathematical Model for the Chemical Reaction of a
Semi-infinite Block of Coal in Underground Coal Gasification. Energy Fuels2005, 19
(4), 1679.
19. Biezen, E. N. G. Modeling of underground Coal Gasification. PhD thesis, Delft
University of Technology, The Netherland, 1996.
20. Nourozieh, H.; Kariznovi, M.; Chen, Z.; Abedi, J. Simulation study of underground
coal gasification in Alberta Reservoirs: geological structure and process modeling.
Energy Fuels. 2010, 24, 3540.
21. Nitao, J.J.; Camp, D.W.; Buscheck, T.A.; White, J.A.; Burton, G.C.; Wagoner, J.L.
Progress on a new integrated 3-D UCG simulator and its initial application.
Proceedings of 28th Annual International Pittsburgh Coal Conference, Pittsburgh,
2011.
22. Luo, Y.; Coertzen, M.; Dumble, S. Comparison of UCG cavity growth with CFD
model predictions. Seventh International Conference on CFD in the Minerals and
Process Industries. CSIRO, Melbourne, Australia, 2009.
23. Daggupati, S.; Mandapati, R. N.; Mahajani, S. M.; Ganesh, A.; Pal, A. K.; Sharma, R.
K; Aghalayam, P. Compartment modeling for flow characterization of underground
coal gasification cavity. Ind. Eng. Chem. Res.2011, 50, 277.
24. Perkins, G.; Sahajwalla, V. Modelling of heat and mass transport phenomena and
chemical reaction in underground coal gasification. Chem. Eng. Res. Des.2007, 85,
329.
25. Bhaskaran, S.; Mahajani, S. M.; Ganesh, A.; Sapru, R. K.; Mathur, D. K.; Pal, A. K.;
Sharma, R. K. An apparatus and process to analyze and characterize spalling due to
thermo-mechanical failure of coal during underground coal gasification. Indian Patent
Application No. 3620/MUM/2013.
26. Matsuhara, T.; Hosokai, S.; Norinaga, K.; Matsuoka, K. Li, C. Z.; Hayashi, J. In-Situ
Reforming of Tar from the Rapid Pyrolysis of a Brown Coal over Char. Energy
Fuels2010, 24, 76.
34
27. Mandapati, R. N. PhD pre-synopsis report. Department of Chemical Engineering,
Indian Institute of Technology Bombay, Mumbai. April-2014.
28. Samdani, G.; De, S.; Mahajani, S.M.; Ganesh, A. Effect of bed diffusion and
operating parameters on char combustion in the context of underground coal
gasification. In Proceedings of 2011 COMSOL Conference, Bangalore, India. Nov2011.
29. Samdani, G.; Ganesh, A.; Aghalayam, P.; Sapru, R. K.; Lohar, B. L.; Mahajani, S. M.
Kinetics of heterogeneous reactions with coal in context of underground coal
gasification. Communicated to CEJ.
30. Mandapati, R.N.; Daggupati, S.; Mahajani, S.M.; Ganesh, A.; Aghalayam, P.
Experiments and kinetic modeling for CO2 gasification of Indian coal chars in the
context of underground coal gasification. Ind. Eng. Chem. Res.2012, 51, 15041.
31. Tomita, A.; Mahajan, O. P.; Jr, P. L. W. Reactivity of heat treated coals in hydrogen.
Fuel1977, 56, 144.
32. Bhatia, S. K.; Perlmutter, D. D. A random pore model for fluid−solid reactions: I.
Isothermal and kinetic control. AIChE J. 26 (1980) 379-386.
33. Daggupati, S.; Mandapati, R.; Mahajani, S.; Ganesh, A.; Sapru, R.K.; Sharma, R.K.;
Aghalayam, P. Laboratory studies on cavity growth and product gas composition in
the context of underground coal gasification. Energy2011, 36, 1776.
35
1. Reaction diffusion on particle level
For a gas-solid non-catalytic reaction in a particle involving solid reactant (e.g., char-gas
reactions), the mass balance equation for the gas and the solid can be written as follows:
𝜕𝐶𝑔
𝜕𝑡
+ ∇ ∙ (−𝐷𝑒𝑓𝑓 ∇𝐶𝑔 ) = 𝑅𝑔
(A1)
Where 𝐶𝑔 is gas concentration, Deff is effective diffusivity of the reactant gas through char
and 𝑅𝑔 is the rate of consumption of gas. Similarly, char consumption can be related to the
rate as,
𝜕𝐶𝑐ℎ𝑎𝑟
𝜕𝑡
= 𝑏 ∗ 𝑅𝑔
(A2)
Where, 𝐶𝑐ℎ𝑎𝑟 is concentration of char and b is the stoichiometric coefficient of char in its
reaction with the particular gas.
Here, 𝑅𝑔 , the rate of reaction, is a function of gas concentration and solid concentration,
which is given by,
𝑅𝑔 = − 𝑘 ∗ 𝐶𝑔 ∗ 𝐶𝐶ℎ𝑎𝑟,0 ∗ 𝑆(𝐶𝐶ℎ𝑎𝑟 )
= − 𝑘 ′ ∗ 𝐶𝑔 ∗ 𝐶𝐶ℎ𝑎𝑟,0 ∗ (1 − 𝑋) ∗ √1 − 𝜓 ∗ 𝑙𝑜𝑔(1 − 𝑋)
(𝐴3)
Where,
𝑆(𝐶𝐶ℎ𝑎𝑟 )= internal surface area per unit volume of the particle = f(concentration of char)
𝜓= structural parameter in random pore model
X = local char conversion
𝐶𝐶ℎ𝑎𝑟,0 = initial char concentration
k' = k*S0 where, k is rate constant and S0 is initial surface area.
The above equations are solved simultaneously by an appropriate numerical method to obtain
the overall rate of consumption of char. Solving these equations for all the particles in the
UCG reactor will be computationally very expensive. Hence, we simplify the rate model by
introducing effectiveness factor. Effectiveness factoris the measure of reduction in rate of a
solid-gas reaction because of the pore diffusion resistance experienced by the reactant or
36
product gases through the porous solid reactant. The theory of effectiveness factor for the
first order reaction is well documented in literature1. Extension of this theory for few other
forms of reactions rates, like Petersen model, Dispersed solid model, is also available in
literature2. However, calculation procedure for effectiveness factor for RPM based kinetics is
not available.
For calculating effectiveness factor in the case of RPM type rate expression, we first assumed
that the time scales for diffusion inside the particle and the change in surface area and
effective diffusivity are much different, and can be treated as independent processes for
modeling purpose. This allows us to solve the gas phase balance and obtain an expression for
the Thiele modulus. With the above stated assumption, we can use the Thiele modulus (𝑀𝑇 )
for a spherical particle, which is given by:
𝑑
𝑀𝑇 = 6 ∗ √
𝑘∗𝐶𝐶ℎ𝑎𝑟,0
(A4)
𝐷
And the effectiveness factor (𝜂) is given by,
𝜂=
1
(
1
𝑀𝑇 tanh(3𝑀𝑇 )
−
1
3 𝑀𝑇
)
(A5)
Once this relationship is obtained, the gas balance equation will be solved, taking the surface
area and effective diffusivity as a function of solid concentration. As shown later, there is a
reasonable agreement between the predictions by the numerically solved reaction-diffusion
model and the approximate effectiveness factor enabled rate expression.
Rate of the reaction after applying effectiveness factor is,
𝑟𝑎𝑡𝑒 = 𝜂 ∗ 𝑘 ∗ 𝐶𝑔𝑎𝑠,𝑆 ∗ 𝐶𝐶ℎ𝑎𝑟,0 ∗ (1 − 𝑋) ∗ √1 − 𝜓 ∗ log(1 − 𝑋)
(A6)
Where, 𝐶𝑔𝑎𝑠,𝑆 is the concentration of gas species on the surface of spherical char particle.
To verify the applicability of this procedure to our system of reactions viz. steam and CO2
gasification, we performed simulations which are discussed below.
The main assumptions of the reaction-diffusion model for a spherical particle are:
1. The variations in gas concentration and solid density are only in radial direction.
37
2. The char particle is composed of char and ash, and char is the only reacting species. It
is also assumed that the amount of ash and its bulk density remain constant during the
conversion of the char particle.
3. A perfect gas behavior is assumed for the gasifying agent and product gas as well.
4. The gasifying agent is assumed to flow over the particle at a high flow rate such that
its partial pressure at the outer surface of the particle can be assumed to be constant.
5. Diffusivity through char monolith is a function of conversion and is maximum (1.1e-5
m2/sec) for complete conversion.
6. Continuum description of the porous solid bed is assumed.
With these assumptions, the governing equations are solved with appropriate boundary
conditions using COMSOL Multiphysics software. The results for CO2 gasification thus
calculated by this reaction-diffusion model and the effectiveness factor enabled model are
compared in Figure A1 for different values of structural parameters (ψ) used in random pore
model. The values of structural parameters used for comparisons are based on a study on coal
of interest3.
a)
b)
c)
d)
Figure A1. Comparison of conversion of char by RPM with and without use of effectiveness factor with a)
ψ = 3, b) ψ = 4, c) ψ = 5 and d) ψ = 6
38
This study demonstrates that the procedure of determination of effectiveness factor can be
reliably used for RPM kinetics, over the range of structural parameter used in this work.
References:
1. Levenspiel, O. Chemical Reaction Engineering; Third Eds, John Wiley & Sons: New
York, 1999.
2. Calvelo, A.; Cunningham, R. E. Overall effectiveness factor for gas-solid reactions. J
Cat. 1970, 16, 397.
3. Mandapati, R.N.; Daggupati, S.; Mahajani, S.M.; Ganesh, A.; Aghalayam, P.
Experiments and kinetic modeling for CO2 gasification of Indian coal chars in the
context of underground coal gasification. Ind. Eng. Chem. Res.2012, 51, 15041.
2. Physical Properties
The physical properties required as input to the model include porosity, permeability, and
heat and mass transport parameters.
Permeability
It has been reported that the logarithmic plot of permeability (K) versus porosity (𝜙) is a
linear function for the range of porosity studied for Wyodak coal1. An empirical relation
relates permeability with porosity by Eq. A7:
𝐾
𝐾0
= 𝑒𝑥𝑝[𝛼(𝜙 − 𝜙0 )]
(A7)
Where 𝐾0 𝑎𝑛𝑑𝜙0 are initial permeability and porosity, respectively. It is reported that α is
approximately equal to 12 and depends on porosity.
This relation is then used in combination with the Carmen-Kozeny equation to establish a
characteristic particle size for the use in other correlations. A relation developed for the
change in particle size is given byEq. A8.
𝑑
𝑑0
3
=
𝜙 2 (1−𝜙 )
𝛼
( 𝜙0 ) (1−𝜙)0 𝑒𝑥𝑝 ( 2 (𝜙
− 𝜙0 ))
(A8)
Thermal conductivity
A correlation to relate effective thermal conductivity that accounts for conduction in
solid,conduction through fluid adjacent to the solid and radiant transfer, is available in
39
literature2. The simplified form of the equation for the solid thermal conductivity is given by
Eq. A9,
𝑘𝑒𝑓𝑓 =
1−𝜙
1
( )+1⁄(25𝑘𝑔 +𝑑𝐿𝑠 )
𝑘𝑠
+ 𝜙𝑑𝐿𝑣
(A9)
Where, 𝑘𝑠 is the conductivity of the solid matrix and 𝑘𝑔 is the conductivity of the gas, d is
5.4×10−12 𝑇 3
𝑠
particle size, 𝜙 is porosity, 𝐿𝑠 = 3.16 × 10−12 𝑇𝑠 3 and 𝐿𝑣 = 1−0.125𝜙⁄(1−𝜙)
.
Specific heats
Similar to thermal conductivity, both temperature and composition have a role in determining
the specific heat. The effective specific heat is calculated using Eq. A10.
𝐶𝑝.𝑒𝑓𝑓 = 𝜙𝑔 𝐶𝑝,𝑔 + 𝜙𝑠 𝐶𝑝,𝑠
(A10)
Where, the solid specific heat is given by equation A11.
𝐶𝑝,𝑠 = {
𝑤𝑒𝑡
𝐶𝑝,𝑠
(𝑖𝑛𝑤𝑒𝑡𝑧𝑜𝑛𝑒, 𝑓𝑜𝑟𝑇 ≤ 𝑇𝑑 )
(A11)
𝑑𝑟𝑦
𝐶𝑝,𝑠 (𝑖𝑛𝑤𝑒𝑡𝑧𝑜𝑛𝑒, 𝑓𝑜𝑟𝑇 ≤ 𝑇𝑑 )
The specific heat of wet coal is taken from literature, as a constant value3, whereas in dry
coal, specific heat is a function of ash and ash-free-coal fractions and temperature (Eq. A12).
𝑑𝑟𝑦
𝑎𝑠ℎ−𝑓𝑟𝑒𝑒
𝑎𝑠ℎ
𝐶𝑝,𝑠 = 𝑌𝑠𝑎𝑠ℎ 𝐶𝑝,𝑠
+ (1 − 𝑌𝑠𝑎𝑠ℎ )𝐶𝑝,𝑠
(A12)
Where,
𝑎𝑠ℎ
𝐶𝑝,𝑠
= (754 + 0.586 𝑇)//4.184
𝑎𝑠ℎ−𝑓𝑟𝑒𝑒
𝐶𝑝,𝑠
= 2.673 + 0.002617 𝑇 − 116900/𝑇^2
Expressions for thermal properties are similar for the roof and the spalled char, difference
being the use of local roof porosity in roof model instead of bed porosity in the spalled char.
Gas phase specific heat and enthalpies are also expressed as functions of gas temperature, and
used for defining different physical properties.
Interphase Transport Coefficients
40
For interphase transfer inside the spalled rubble, a correlation for the heat transfer coefficient
(hT) in packed bed, given by Eq. A13, is used4.
ℎ𝑇 = ℎ𝐴 =
0.91𝐶𝑔 𝑣𝑔 0.49 𝜗0.51 6𝑠(1−𝜙) 1.51
𝑃𝑟 2⁄3
[
𝑑
]
(A13)
Where A is surface area per unit volume of bed, 𝑣 is kinematic viscosity, Pr is Prandtl
number.
In case of transfer between void and roof the correlation proposed in our earlier studies is
used5.
Nu = 114.0 x Re0.4138
(A14)
h = 139.6 x 𝑉𝐻0.35
(A15)
An effective mass transfer coefficient is essential to determine the net reaction rates. Mass
and heat transfer coefficientsare related by using analogies and the expression is given byEq.
A16.
𝑘𝑦
ℎ𝑇
𝑃𝑟 2⁄3 1
= ( 𝑆𝑐 )
(A16)
𝐶𝑇
The mass transfer coefficient specified above is based on a mole fraction driving force.
References:
1. Thorsness, C.B.; Greens, E.A.; Sherwood, A. A One Dimensional Model for in situ
Coal Gasification. LLNL Report, UCRL 52523, 1978.
2. Yagi, S.; Kunii, D. Studies on effective thermal conductivities in packed beds. AIChE
J.1957, 3, 373.
3. Tsang, T. H. T. Modeling of Heat and Mass Transfer during Coal Block Gasification.
Ph.D. Dissertation, University of Texas at Austin, Austin, TX, 1980.
4. Bird, R.B.; Stewart, W.E.; Lightfoot, E.N. Transport Phenomena; Second Eds, Wiley
India (P) Ltd: New Delhi, 2002.
5. Daggupati, S.; Mandapati, R.N.; Mahajani S.M.; Ganesh, A.; Aghalayam, P. A Study
on the Temperature Profile and Heat Transfer Coefficients in UCG Cavities.
Proceedings of 27th International Pittsburg Coal Conference. Istanbul, Turkey, 2010.
41
3. Procedure for defining dynamics due to spalling:
From solution procedure
Spalling count<N
T_tr > 900K
Nodes.dry >10
NO
YES
Add Nodeinc*dV in the rubble zone module
Reduce ‘Nodeinc’ Nodes from dry zone
Specify properties in new nodes
To solution procedure
Figure A2. Algorithm for checking spalling conditions and defining properties after the spalling instance
(Spalling count = maximum number of instances of spalling, defined for given thickness of the coal seam;
Nodes.dry = no. of nodes in the dry zone, T_tr = temperature of top surface of rubble, Nodeinc = no. of
nodes to be increased in rubble zone).
42
4. Procedure for defining dynamics due to drying front movement:
From solution procedure
delVd = vdf*dt*Across + remainingVd
NO
delVd > delV
YES
Nodedrynew = floor (delVd/delV)
remainingVd = (delVd/delV - Nodedrynew/delV)
Nodesdry = Nodesdry + Nodedrynew
remainingVd = delVd
Specify properties in newly added
nodes, if added
To solution procedure
Figure A3. The algorithm for increase in the dry-zone volume due to drying front movement; delV = one
finite volume in the dry zone; Nodesdry = number of grid points in the dry zone; delVd = increase in dryzone volume due to drying-front velocity; Nodedrynew = the increase in the number of volume elements
of the dry zone).
43