A Process Model for Underground Coal Gasification- Part-I: Cavity Growth

Transcription

1 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

2 A Process Model for Underground Coal Gasification- Part-I: Cavity Growth Ganesh Samdani 1, Preeti Aghalayam 2, Anuradda Ganesh 3, R. K. Sapru 4, B. L. Lohar 4 and Sanjay Mahajani *,1 1 Department of Chemical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai Department of Chemical Engineering, Indian Institute of Technology Madras, Chennai Department of Energy Science and Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 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

3 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 linkage 1. 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/Nm 3.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 contamination 3. The process involves several phenomena, including complex flow patterns, multiple chemical reactions, water influx from the nearby aquifer, and heat and mass-transfer effects 4. 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 surface 5. 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 process 6. 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 elsewhere 2,7.Available models can be classified into packed bed models 8-10, channel models 11-14, coal block models and process models 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 Biezen 19 is limited by assumptions related to heat transfer including constant reactor temperature. CFD based process models 20,21 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 spalling 14. Perkins modeled spalling as a function of critical conversion of coal implying that 3

4 some amount of coal remains unreacted because of spalling 15.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

5 the production well. This paper focuses on modeling the initial vertical growth during phase- I. 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 patterns 20,23,24. The importance of the transport processes that occur 5

6 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 work 23,25. 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

7 distribution. Detailed procedures of CFD-based RTD studies can be found in our earlier work 23. 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 rubble void rubble zone 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

8 Heat loss to overburden Roof (Coal block) (drying + pyrolysis + reactions, endothermic) Mass transfer (Gas) Heat transfer (Radiation) Heat transfer (Convection) Spalling (Solids) Void (CSTR) (gas phase reactions only) Towards outflow channel From injection well Rubble (radial PFR) (pyrolysis +reactions, exothermic) Heat transfer (Convection) Bulk flow (Gas) 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 variables 10. 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

9 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

10 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. F gi n j=1 (1) V = a ijr j Boundary condition: at V = V 0, F gi = F gi,0 C gi C pi (A c u g ) T g i = h V T(T g T s ) j=1 H j R j (2) n Boundary condition: atv = V 0, T g = T g,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). (Q g T g ) V n j=1 = R P ( a ijr j i ) A cu g P PT g V (3) Boundary condition: at V = V 0, u g = u g,0 Here, Q g = A c u g andf gi = Q g C gi 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. ρ i n j=1 (4) t = M i a s,ij R j Initial condition: att = 0, ρ i = ρ i,0 T ρ i C s i ps,i t = k 2 V effa T s c + h V T(T g T s ) n j=1 H j R j (5) Initial condition: at t = 0, T s = T s,0 Boundary conditions: at V = V0, Ts = Ts,0 T at V = Vtr, k eff A s tr = σε r 4 (T V 2 ε s,tr T s,roof ) r 4 An equation of state is used to relate the gas-phase pressure, temperature, and concentrations. P RT = n i=1 C gi (6) 10

11 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 μ = 1 u V A c K g (7) per 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. C gi t = 1 (C ν n τ gi,in C gi ) + a ν ij R j + k y,cav (C gi,roof C gi ) A roof V cav in j=1 (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

12 n T g C gi C pi = 1 (C ν n i=1 t τ gi,inh i,in C gi H i ) ΔH ν j=1 j R j F w ΔH vap + h T,cav (T s,roof in T g ) A roof V cav + k y,cav (C gi,roof C gi )H i,roof A roof V cav (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 char 26. 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

13 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: ρ i n = M t i j=1 a s,ij R j (10) Initial condition: at t = 0, ρ i = ρ i,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. T ρ i C s i ps,i t = [k 2 V effa T s c ] V n j=1 ΔH jr j (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, Ts= Td T At V = V0, k eff A s roof = σε r 4 (T V 2 ε s,tr T 4 s ) + h T,cav (T void T s ) (12) r 13

14 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 [D effa c 2 C gi n ] + a V j=1 ijr j = 0 (13) at V = V roof, D eff A roof C gi V = k y,cav(c gi,void C gi ) at V = Vd, V = V d, D eff A d C gi V = 0; and D effa d C steam V = v df φ(ρ w,l ρ w,g )/M w 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. ρ s C ps T s t = V [ka c 2 T s V ] (14) Boundary conditions: at V = V T, T s = T T at V = V d, T s = T d 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

15 v df = 1 ( k T d [ x ] +k d+[ T d x ] d+ ) (15) φ(ρ w,l ρ w,g )/M w ΔH vap 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 coal 9,10. Tar undergoes fastreforming (Reaction 11) in presence of its char 26. 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

16 Table 1. Set of reaction, respective kinetic models and parameters for the reactions of coal of interset. no. Reaction Representation E k 0(sec -1 atm -N α,n Kinetic ref (J/mol) ORsec -1 ) model 1 Drying H 2 O (l) H 2 O (g) only in roof zone and controlled by heat transfer 2 Pyrolysis CH a O b 0.78C CH H 2 O CO H ,0 VRM CO C 9 H c 3 Char combustion C + O 2 CO E+7 0,1 RPM 28 4 Steam gasification C + H 2 O CO + H E+8 0,1 RPM 29 5 CO 2 gasification C + CO 2 2CO E+7 0,0.234 RPM+LH 30 6 Methanation C + 2H 2 CH E-6 1,NA volumetric 31 7 Water-gas-shift CO + H 2 O CO 2 + H E+7 0,1 volumetric 9 8 Tar cracking/reformin g 9 Gas phase oxidation C 9 H c + 9H 2 O 9CO + (9 + c 2 ) H 2 spontaneous tar cracking reaction in presence of its char 26 H O 2 H 2 O approximate rates as a function of gas 9 CO + 0.5O 2 CO 2 temperature and oxygen concentration CH 4 + 2O 2 CO 2 + 2H 2 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, R g = k 0 e ( E RT ) T α f(p N g )C Char,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: R = 1 (1 R c )+(1 R m ) (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

17 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

18 differential equation, which is converted into an ODE in the time domain using method of lines. START Inputs: Solid: temperature, density, Gas: conc, temperature, pressure t = 0 t = t + dt NO V= 0, y i = y i0 T g = T g0 END YES t= t end V = V + dv Increase the volume of rubble (PFR) if spalling condition is satisfied (Fig. A2) Calculate exit gas composition and temperature at current time Solve CSTR balance equations (Eq. 8,9) Increase the volume of drying zone, if velocity front has crossed volume of one node (Fig. A3) Solve PFR gas mass balance and energy balance using values at previous time (Eq. 1,2,3) Calculate gas densities and temperature at current time and volume in rubble Solve PFR solid mass balance and energy balance (Eq. 4,5) Calculate solid composition and temperature at current time and volume in rubble 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 YES V wet = V wet,end V= V end YES V dry = V dry,0, y i = y i0 T g = T g0 NO Calculate temperature profile Solve for the wet zone energy balance equations (Eq. 14) V dry = V dry + dv Solve for the dry zone energy and mass balance equations (Eq. 10,11,12,13) V wet = V wet + dv Calculate drying and pyrolysis gas release, gas and solid composition and temperature V wet = V wet,0, T g = T g0 YES V dry = V dry,end NO Figure 7. Procedure for solving different sets of equations of the process model. 18

19 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 Vc 2 ) 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 literature 9,10,33. 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 m 3 is discretized in finite nodes of volume 2 x 10-4 m 3. 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

20 Table 2. Input parameters for simulating the UCG process. Sr. No. Parameter Value 1 Initial volume of spalled char 0.02 m 3 2 Steam/O 2 ratio Initial ignition period 30 s 4 Feed gas and initial solid temperature in rubble 600 K 5 Coal type: Lignite Proximate Volatile matter % Ultimate Carbon % Analysis Fixed Carbon % analysis Hydrogen % 5.15 Ash % 2.01 Nitrogen % 0.53 Oxygen Initial spalled char density 200 kg m-3 7 Ash Content 5 % 8 Initial porosity Molar flow rate 3.2 x 10-3 kmol m -2 s Step size in time 2.5 s 11 Total simulation time 10 hrs 12 Size of a volume element 2e-4 m 3 13 Initial volume of dry zone 8e-3 m 3 14 Initial rubble permeability 100 Darcy 15 Initial particle diameter 5 mm 16 Initial density of coal 1000 kg/m 3 17 Pressure 4.8 atm. 18 Distance between the wells ~ 0.5 m 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

21 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 Temperature (K) Volume (m3) 1 hr 2 hr 3 hr 4 hr 6 hr 8 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

22 hr 0.5 hr hrs Char Density (kg/m3) char Density (kg/m3) Volume (m3) a) b) Volume (m3) 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

23 9 x 10-3 Char Oxidation 0.02 Steam Gasification Reaction Reaction rate (kmol/m3s) Reaction rate (kmol/m3s) Volume (m3) Volume (m3) 1.2 x 10-4 Boudard Reaction 1.2 x Methanation Reaction 1 1 Reaction rate (kmol/m3s) Reaction rate (kmol/m3s) Volume (m3) Volume (m3) 10 x 10-3 Water Gas Shift Reaction 5 x 10-6 H2 Oxidation Reaction rate (kmol/m3s) Reaction rate (kmol/m3s) Volume (m3) Volume (m3) 2 x 10-6 CO Oxidation 9 x CH4 Oxidation Reaction rate (kmol/m3s) Reaction rate (kmol/m3s) Volume (m3) Volume (m3) Figure 10. Plot of the rates of various reactions in the rubble zone after one hour. 23

24 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. Gas Mole fractions Oxygen Steam Hydrogen Methane CO CO Volume (m3) 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

25 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. Gas Mole fractions Oxygen Steam Hydrogen Methane CO CO 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

26 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 Calorific Value (kj/mol) 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

27 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. Char Density (kg/m3) Temperature (K) Time (hrs) a) b) time (hrs) 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 movement of drying front (m) 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

28 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. Gas Mole fractions Oxygen Steam Hydrogen Methane CO CO 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) Calorific value Energy output Time (hrs) 28

29 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 work 33. These experiments were performed by mimicking the actual UCG process for a coal block of approximately 30 x 25 x 20 cm 3 (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 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 elsewhere 33. 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 phase- II 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