Compartment Modeling for Flow Characterization of Underground

Ind. Eng. Chem. Res. 2011, 50, 277–290

277

Compartment Modeling for Flow Characterization of Underground Coal Gasification Cavity Sateesh Daggupati,† Ramesh N. Mandapati,† Sanjay M. Mahajani,† Anuradda Ganesh,‡ A. K. Pal,§ R. K. Sharma,§ and Preeti Aghalayam*,† Department of Chemical Engineering and Energy Science and Engineering, IIT Bombay, Powai, Mumbai-400076, India, and UCG Group, IRS, ONGC, Chandkheda, Ahmedabad-380005, Gujarat, India

During underground coal gasification (UCG), a cavity is formed in the coal seam when coal is converted to gaseous products. This cavity grows three dimensionally in a nonlinear fashion as gasification proceeds. The cavity shape is determined by the flow field, which is a strong function of various parameters such as the position and orientation of the inlet nozzle and the temperature distribution and coal properties such as thermal conductivity. In addition to the complex flow patterns in the UCG cavity, several phenomena occur simultaneously. They include chemical reactions (both homogeneous and heterogeneous), water influx, thermomechanical failure of the coal, heat and mass transfer, and so on. Thus, enormous computational efforts are required to simulate the performance of UCG through a mathematical model. It is therefore necessary to simplify the modeling approach for relatively quick but reliable predictions for application in process design and optimization. The primary objective of this work is to understand the velocity distribution and quantify the nonideal flow patterns in a UCG cavity by performing residence time distribution (RTD) studies using computational fluid dynamics (CFD). The methodology of obtaining RTD by CFD is validated by means of of representative laboratory-scale tracer experiments. Based on the RTD studies, the actual UCG cavity at different times is modeled as a simplified network of ideal reactors, called compartments. The compartment model thus obtained could offer a computationally less expensive and easier option for determining UCG process performance at any given time, when used in a reactor-scale model including reactions. The network of ideal reactors can be easily simulated using a flowsheet simulator (e.g., Aspen Plus). We illustrate the proposed modeling approach by presenting selected simulation results for a single gas-phase second-order water-gas shift reaction. 1. Introduction Fossil fuels are the main energy sources in today’s world, currently accounting for over 85% of the world energy consumption. Coal generates 41.5% of the world’s electricity and provides 26.5% of global primary energy needs. Unlike the situations for oil and gas, it is estimated that there is enough coal to last over 100 years at the current rates of production in the world.1 Gasification of coal is considered to be more effective than combustion because it leads to lower emissions per unit of energy produced. Underground coal gasification (UCG) is a technique that permits access to coal that either lies too deep underground or is otherwise too costly to be exploited using conventional mining techniques. It also minimizes many of the safety, health, and environmental problems of deep mining of coal. The product gas can serve different purposes such as being used as fuel gas or as feedstocks for liquid fuels and chemicals.2 UCG is potentially a clean method of converting coal into a high-energy fuel gas and could be employed to replace small coal-fired power plants. Additionally, the product gas can be processed to remove its CO2 content before it is passed to the end users; the captured CO2 can then be stored in the underground cavity, thereby contributing to climate change mitigation.3 In the UCG process, initially, two wells, namely, injection and production, are drilled vertically from the surface to the * To whom correspondence should be addressed. Tel.: (022) 2576 7295. Fax: (022) 2572 6895. E-mail: [email protected]. † Department of Chemical Engineering, IIT Bombay. ‡ Energy Science and Engineering, IIT Bombay. § UCG Group.

coal seam at a certain distance, and a permeable channel link is created between them. Figure 1 shows a schematic diagram of the UCG process at any given time. To gasify the coal, a mixture of air/oxygen and steam is introduced into the coal seam through the injection well. The product gas travels through the cavity and elutes from the production well through the cavity. The generated product gas is collected at the surface and sent for end use after being cleaned.4 The quality of the product gas is influenced by several parameters such as the pressure inside the coal seam, coal properties, feed conditions, kinetics, and heat and mass transport within the coal seam. As gasification proceeds, an underground cavity is formed. The volume of the cavity increases progressively with coal consumption and thermomechanical spalling, if any, from the roof. As the cavity growth is irregular in three dimensions, the flow pattern inside the UCG cavity is highly nonideal. The complexity increases further because of several other processes occurring simultaneously, such as heat transfer due to convection and radiation, spalling, water intrusion from surrounding aquifers, several chemical reactions, and other geological aspects.5 Several mathematical models have been developed considering the UCG cavity as either a packed bed or a free channel.6-18 Aghalayam19 provided a comprehensive review of the current state-of-the-art in mathematical modeling of the UCG process. Most of the existing models consider the UCG cavity as a rectangular or cylindrical channel. They typically examine growth rates in one or two directions only. The actual UCG cavity is expected to be irregular in all three dimensions, and its growth rate might well be different in different directions.20 Furthermore, a complex nonideal flow pattern of the reactant gas prevails in the cavity and is strongly governed by the cavity

10.1021/ie101307k  2011 American Chemical Society Published on Web 11/30/2010

278

Ind. Eng. Chem. Res., Vol. 50, No. 1, 2011

Figure 1. Schematic diagram of the UCG process.

Figure 2. Phenomenological modeling of the underground coal gasification process for a nonspalling case.

shape. The characterization of the nonideal flow patterns in UCG is an important aspect, as it is likely to significantly influence the process performance. Computational fluid dynamics (CFD) studies are essential to understand these complex flow patterns within the cavity. Perkins and Sahajwalla21 developed a twodimensional axisymmetric CFD model of the UCG cavity that can be used to simulate the combined effects of heat and mass transport and chemical reaction during the gasification process. Although a number of assumptions and simplifications were made to make the simulations tractable, the results reveal the importance of transport and reaction processes occurring in the UCG cavity. Development of a complete process model for UCG has long been a major goal, as it will enable visualization of the underground phenomena and also permit prediction of the product gas quality at various conditions. However, it is also important to ensure that the UCG mathematical model is computationally tractable. A broad objective of our work is to develop a phenomenological model of UCG that would enable the prediction of UCG performance in relatively less computational time. Furthermore, the model should also provide better insight into the interactions between the various phenomena occurring during UCG operation. The phenomenological model we envisage at this stage is shown in Figure 2. Currently, our focus is on the UCG cavity and flow patterns. The cavity is subdivided into various compartments based on the flow patterns. These compartments exchange heat and mass with the cavity roof and the noncar-

bonaceous rocky floor. The heat transfer can be either convective or radiative. Steam and oxygen diffuse from the bulk of the cavity to the reacting roof, and product (i.e., CO, H2, etc.) mass transport takes place from the roof to the bulk. The transport of the evaporated water from the rocky floor can also be considered. In addition, there are several reactions that are occurring in the cavity and in the coal seam. In this work, the focus is on developing an understanding of the flow patterns. The compartment model approach provides significant computational savings in predictive modeling for UCG cavity flow patterns. Extensions to a validated compartment model to incorporate other interesting phenomena of UCG are possible, and one such example is provided in this article for a homogeneous reaction that is relevant for UCG. Thermo-mechanical spalling (see Figure 1) is an important cavity phenomenon, and if present, its effect on the reactant gas flow patterns in the cavity is important to analyze. Furthermore, the influence of nozzle orientations (vertical or horizontal, for example) and radiation on the reactant gas flow can be critical to the analysis as well. As a first step, in this study, we focus on reactant gas flow patterns in the absence of spalling using CFD. CFD results are further used to conduct numerical (virtual) tracer experiments and to determine the residence time distribution (RTD) or exit age distribution. Based on the flow patterns from the CFD simulations and the RTD studies, the cavity is modeled as a simplified network of ideal reactors. This technique is called compartment modeling and


279

Figure 3. Block diagram of the methodology of compartment modeling.

is used to characterize reactors of irregular geometries with complex flow patterns. Such geometries are viewed as a network

Figure 4. Geometries of UCG cavities of different sizes at different times.

of ideal reactors connected to each other through various streams including recycle, bypass, and so on.22 Among the previous

280


Table 1. Dimensions of the UCG Cavities at Different Times cavity size 0 (0 days)

1 (1 day)

2 (3 days)

3 (7 days)

4 (14 days)

9.1 0.01 0 0.2 0.2 0.2 0.2 0.2 0.1 800 119 78 422 386 398

9.1 1 2.5 1.32 0.9 0.3 0.25 0.2 0.1 1 919 925 174 135 983 334

9.1 2 4 2.2 1.5 0.42 0.3 0.25 0.1 3 009 937 267 232 17 854 211

9.1 2.5 6 3.2 2.2 0.52 0.4 0.3 0.1 4 697 616 411 344 2 825 016

9.1 3 7.8 4.7 3.3 0.7 0.6 0.4 0.1 7 846 400 8 321 528 4 682 295

distance between the injection and production wells (m) length of the cavity behind the inlet (backward direction) (m) length of the cavity dome from the inlet (forward direction) (m) height of the cavity (m) width of the cavity (m) at the injection well width of the cavity (m) at the outflow channel width of the cavity (m) at the back side of the injection well width of the cavity (m) at the outlet inlet and outlet diameter (m) no. of grid faces no. of grid nodes no. of grid cells (tetrahedral and hexagonal)

studies to consider the flow patterns in UCG, the most notable is by that Pirard et al.,23 who performed helium tracer tests during an underground coal gasification field trial at Alcorisa, Spain. Based on the tracer experimental data, they approximated the flow in the cavity as that given by stirred tanks in series with a dead zone interacting with the main reactor through diffusion. A similar work was reported by Debelle et al.24 for the same UCG field test in which tracer studies were carried out in a series of underground reverse combustion tests. Thorsness25 also performed tracer experiments in a UCG field test at the Hoe Creek trial (No. 3). The primary objective of those experiments was to identify whether steam injection from the surface is necessary or underground water is sufficient for gasification. In these experiments, deuterium was used as a tracer and was mixed with the feed. The D/H ratio was measured at the outlet. The major findings from these experiments were the source and location of water entering the cavity and the amount of water available underground. The deuterium response curve was fitted with a model of mixed tanks in two parallel paths. They suggested a need for a more rigorous compartment model to explain the observed results. These studies clearly demonstrate the importance of understanding the reactant gas flow patterns at various conditions relevant to UCG. To the best of our knowledge, no CFD-based compartment modeling approach for the UCG cavity has been reported in the open literature. In this study, we aim to perform detailed investigations on reactant gas flow patterns in the UCG cavity. The following methodology (see also Figure 3) was used to characterize the flow patterns: • CFD simulations were performed on a cavity of chosen size and shape, to determine the steady-state flow patterns of the reactant gases. • The velocity field obtained in the first step was frozen, and the tracer was introduced as a pulse. The unsteady-state model for the tracer balance was solved to obtain the exit age distribution. • To validate the methodology of obtaining the RTD from CFD simulations, a laboratory-scale glass UCG cavity setup was built, and tracer experiments were performed. The RTD obtained by performing CFD simulations for this laboratoryscale UCG cavity model at experimental conditions was compared with experimental RTD data to validate the approach. • A compartment model was developed such that the RTD of the compartment model was in agreement with that obtained by CFD under similar conditions. • The developed compartment model was further validated by comparing the homogeneous reaction-enabled steady-state CFD simulation results with those obtained from a steady-state flowsheet simulator (i.e., Aspen Plus) using the compartment

model parameters. A single gas-phase second-order water-gas shift reaction was chosen for this study. It should be noted that the present work characterizes only the flow patterns inside the cavity and is not a complete UCG model. Nevertheless, it will provide valuable flow-related inputs to a complete UCG process model that incorporates all of the reactions and is capable of predicting product composition. 2. CFD Simulations The general features of the UCG cavity are the presence of a thin char layer on the periphery of the cavity; a porous bed of mainly ash, char, and coal overlying the injection point if spalling is predominant; and a void space between the porous bed and cavity roof (see Figure 1). In the absence of spalling, the cavity is expected to be mostly void space with a small amount of ash fallen on the floor. The dimensions of the cavity in the vicinity of the injection point are of great interest. Because the fluid is injected low in the seam, it has a tendency to flow upward and outward from the injection point. Because of the high permeability of the void space relative to that of the ash, char, and coal beds, the majority of the flow between the injection and production wells is expected to occur in the void space. The advantage of CFD studies is that the flow pattern in the cavity can be effectively analyzed by using plots of the contours, velocity vectors, and path lines, which is otherwise not possible, particularly in laboratory-scale UCG experiments. Back-mixing and/or plug-flow regions within the cavity can be identified by using these plots. We present a total of 10 CFD simulation results on the flow pattern inside the cavity for two different nozzle orientations and five different cavity sizes. Geometry. Based on the data available in the literature,13,20 five different cavity sizes were chosen. The front, top, and crosssectional views of the geometries of cavities of size 0 (cavity at a time of 0 days, i.e., straight horizontal channel), size 1 (cavity at a time of 1 day), size 2 (cavity at a time of 3 days), size 3 (cavity at a time of 7 days), and size 4 (cavity at a time of 14 days) are shown in Figure 4. Geometries were created for all of these cavities and meshed using the commercial CFD software GAMBIT. The mesh used was unstructured, with tetrahedral grid cells in the whole volume of the reactor. Finer meshing was used in the regions near the inlet and outlet because the velocity gradients were stiff in these regions due to expansion and contraction. The number of grid cells increased with cavity size. The dimensions of different cavities used for the simulations are given in Table 1, which also includes the total numbers of grid faces, nodes, and cells of the meshed geometries. Separate geometries were created for vertical, inclined, and horizontal injections for all cavity sizes.


281

Table 2. Boundary Conditions and Other Specifications Used for CFD Studies parameter

value

inlet velocity carrier fluid (all properties at 1273 K) cavity temperature (isothermal) outlet pressure viscous model

4 m/s oxygen 1273 K 5 atm realizable κ-ε

Input Specifications. The inlet was given a velocity-inlet boundary condition of 4 m/s, such that the oxygen entering had a mass flow rate of around 35.07 kg/h (volumetric flow rate ) 113.14 m3/h) in the injection well. The outlet was given a pressure-outlet boundary condition. The entire cavity, unless specified otherwise, was assumed to be under isothermal conditions at 1273 K. The realizable κ-ε model with standard wall functions was used to model the turbulence in the cavity. In the first step, steady-state CFD simulations under nonreactive conditions were performed to predict the flow patterns inside the cavity. In this step, continuity and momentum balance equations for these meshed geometries were solved using FLUENT v6.3.26 computational fluid dynamics software to obtain the velocity distribution. FLUENT uses a control-volume formulation and the segregated solution method.26 The boundary conditions used are given in Table 2. The numerical solution was obtained for the following governing equations to obtain the flow patterns under the specified boundary conditions. Continuity equation ∂F + ∇ · (∂ b V) ) 0 ∂t Momentum equation ∂ (FV b) + ∇ · (FV bb V ) ) -∇p + ∇ · (τc) + Fg b+b F ∂t

(1)

(2)

A steady-state second-order upwind accurate discretization model was used to solve the above equations, and the SIMPLE (semi-implicit method for pressure-linked equations) algorithm was used to resolve the pressure-velocity coupling. Convergence Criteria and Grid Independence. To ensure that well-defined steady-state solutions were obtained from CFD simulations, convergence criteria that minimized the normalized errors of velocity and scalar equations were selected to be when the scalar residuals of each transport equation decreased to less than 1 × 10-7. It was also verified that the mass flow difference between entering and exiting streams was on the order of 10-8 kg/h, at the maximum. In the time-dependent (unsteady-state) solution, temporal accuracy for the species balance equation was solved until the scalar residue of this equation decreased to less than 1 × 10-7. A grid independence test for convergence was performed by varying the internal size/spacing. The spacing of cavity size 1 was changed from 0.06 to 0.02. Figure 5 shows the details of the grid independence test in which the volumeweighted average of the velocity magnitude was compared for different internal sizes. We can conclude that an internal spacing of 0.03 within the entire cavity was sufficiently small for obtaining an accurate flow field for cavity size 1, because it was found that refinement after a cell size of 0.03 did not affect the solution (i.e., there were no significant changes in the velocity magnitude and mean residence time at smaller sizes). RTD Simulations. After steady state in the cavity reactor had been determined, the velocity profile was frozen, and the response to tracer (which was considered to have properties similar to those of oxygen) injection was simulated to perform virtual tracer experiments. The effects of diffusion were

Figure 5. Grid independence test for cavity size 1.

minimized by considering the diffusivity of the tracer as 1 × 10-15 m2/s. The tracer was injected as a pulse into the feed at a mass fraction of 1.0. In this step, the following species transport equation was solved by utilizing the flow field frozen in the first step Species balance equation ∂ (FY ) + ∇ · (FV bYi) ) -∇ · b Ji ∂t i

(3)

The unsteady-state model was solved to obtain the concentration of the tracer in the form of the area-weighted average at the outlet, and the result was plotted against time. This plot represents the residence time distribution (RTD) under the conditions of interest. RTD profiles were thus obtained for horizontal and vertical injections and for cavities of different sizes. Results and Discussion. Figures 6-9 show the velocity fields in the cavities with vertical and horizontal injections. The contours of velocity magnitudes on a vertical plane (width ) 0) at the cavity center for cavities of sizes 0, 1, and 4 are shown in Figure 6. By virtue of vertical injection, the flow distributes around the inlet, whereas horizontal injection facilitates a significant parallel side-stream bypass toward the outlet. As anticipated, the overall average magnitude of the velocity decreased with increasing cavity size. Furthermore, from Figure 7, which shows the velocity field on a vertical plane at the inlet (x ) 0), two maximum velocity zones were observed: one at the mouth of the inlet and the other near the roof in the horizontal injection case. This is due to the fraction of the stream recycled from the entrance of the outflow channel. On the other hand, in the case of vertical injection, the maximum velocity zones were observed only at the bottom nearer the inlet. This trend was observed for all cavity sizes and for both injection orientations, as can be seen in Figure 7. Figure 8 shows the velocity vector in a representative cavity of size 1. It can be clearly seen that significant backmixing occurred on the different vertical planes along the axial direction in the cavity volume and that these zones disappeared at the entrance of the outflow channel, as can be seen on the x ) 2 cm plane of Figure 8. Path lines for chosen cavities of size 0 and 1 for different time steps for both vertical and horizontal injections are shown in Figure 9, which clearly demonstrates the path of an injected pulse from the inlet. Horizontal injection is associated with a relatively large fraction of a parallel side stream that

282


Figure 6. Contours of the magnitude of the velocity (m/s) on a center plane (width ) 0) for cavity sizes of 0, 1, and 4.

Figure 7. Contours of the magnitude of the velocity (m/s) on a vertical plane at the inlet (x ) 0) for cavity sizes of 0, 1, and 4.


283

Figure 8. Velocity vectors colored by velocity magnitude (m/s) for different vertical planes along the axial direction for cavity size 1 with vertical injection.

Figure 9. Path lines colored by velocity magnitude (m/s) for a chosen time steps of cavity size 0 (i.e., 50 and 200) and cavity size 1 (i.e. 300, 700, 1500, and 5000).

284


Figure 10. Comparison of E curves of all cavities for vertical injection with compartment model.

separately enters the outflow channel. The same qualitative behavior was also realized for other cavities with different sizes. Differences in the flow patterns for the two injections, such as bypassing, were also evident. In addition to these plots, the corresponding residence time distribution (E) curves are presented in Figure 10. The E curves were obtained from transient simulations in FLUENT as detailed earlier. In general, the following conclusions can be drawn from the E curves of all of the cavities:

(1) The initial delay in the response of the tracer concentration at the outlet for all geometries indicates that the cavity was not perfectly back-mixed and that zones of less back-mixing and of plug-flow-reactor- (PFR-) like behavior existed. It is expected that the PFR-like zone was close to the mouth of the outflow channel. (2) The gradual rise toward the peak in each case indicates a behavior similar to that of multiple continuous stirred-tank reactors (CSTRs) in series.

Ind. Eng. Chem. Res., Vol. 50, No. 1, 2011 Table 3. Percentages of Dead Volumes for Different Cavity Sizes and Both Nozzle Orientations volumea (m3)

percentage of dead volume

cavity size

actual volume, m3

vertical injection

horizontal injection

vertical injection


0 1 2 3 4

1.146 4.12 15.86 46.48 124.55

1.1458 4.11 15.8 46.2 115.61

1.1456 4.02 15.36 44.7 110.8

0.13 0.24 0.38 0.61 7.7

1.02 2.48 3.25 3.98 12.41

a

Volume ) volumetric flow rate × mean residence time.

Figure 11. Schematic diagram of cavity dimensions.

(3) Sharp initial peaks for all cavity sizes indicate that a fraction of the tracer bypassed the cavity and flowed through the outflow channel. This behavior, as anticipated, was more prominent in the case of horizontal injection. Sometimes, especially for large cavity sizes, we observed multiple peaks due to bypass. The value of the residence time (τ) was calculated for each cavity as the ratio of the volume of the cavity to the volumetric flow rate, giving 36, 132, 508, 1489, and 3990 s for sizes of 0, 1, 2, 3, and 4, respectively. In addition, the mean residence time (τm) was calculated for each cavity as the area under the E curve, giving 36, 131, 506, 1480, and 3704 s for vertical injection for cavity sizes of 0, 1, 2, 3, and 4, respectively. Table 3 lists the details of the variation of dead volume with cavity size. The percentage of dead volume was approximately 1-8% for the various cavity sizes for vertical injection. A similar trend was observed for horizontal injection as well, for which the mean residence times were 36, 129, 492, 1432, and 3549 s for cavity sizes of 0, 1, 2, 3, and 4 respectively. The percentage of dead volume increased with cavity size and was as high as 13% for the largest cavity for horizontal injection. As expected, the dead volume was greater in the case of horizontal injection. 3. Validation with Laboratory-Scale Tracer Experiments Tracer Experiments on Laboratory-Scale Cavity Reactor Setup. To validate the methodology of obtaining the RTD from CFD, a laboratory-scale UCG cavity size was chosen on the basis of data available in the literature.13,20 To perform the tracer experiments on the cavity reactor under laboratory conditions, a glass reactor of the prescribed cavity shape was fabricated. Figure 11 shows a schematic diagram of the cavity dimensions. Figure 12 shows a schematic diagram of the glass cavity setup used for this tracer study. The total volume of this laboratory-scale cavity reactor was around 5923 cm3. Cold, inert flow tracer experiments were carried out in this setup by choosing three different nozzle orientations (i.e., vertical, inclined, and horizontal injections) and three different nozzle positions (i.e., 1, 1.7, and 2.4 cm from the floor of the cavity). Nitrogen was chosen as the carrier gas and helium as the tracer for these experiments. At the start of each experiment, nitrogen gas was passed through the cavity at a constant flow rate of 1000 mL/min. The flow rate was controlled by an automated mass flow controller. Once a steady state had been attained,

285

helium gas (tracer) was introduced into the cavity as a step input. The volume fraction of helium in the outlet stream was measured continuously with time using a binary gas analyzer (Nucon, 4235-P). The tracer concentration was recorded with the help of a data acquisition system connected to the computer (i.e., the tracer concentration at the outlet was obtained every 1 s). F curves were generated from the tracer volume fraction data, which were obtained from the cavity at different nozzle positions and orientations. Virtual Tracer Experiments by CFD. The aim of this part of the study was to validate the methodology of obtaining the RTD from CFD simulations. To that end, the geometry corresponding to the experimental glass cavity described above was created in GAMBIT. Provisions for different nozzle orientations and nozzle positions were included. The procedure mentioned in section 2 was employed to obtain the steady-state flow patterns, providing the experimental conditions described above as inputs. Tracer concentration profiles were obtained for all cavities for various nozzle orientations and positions using transient simulations in CFD. The F curve was generated from the tracer concentration data for all of the above cases. Figure 13 shows a comparison of the experimental and simulated F curves for the cavity, for horizontal injection with a nozzle position of 1 cm from the floor. The agreement between experiments and simulations is reasonably good. A parity plot comparing the experimental values of F(t) with the simulation predictions is shown in Figure 14, which indicates that more than 99% of the data points lie within (10% of the ideal case. We propose that, in light of the negligible differences in the F curves obtained from experiments and CFD simulations, the proposed methodology of characterizing the nonideal flows in UCG cavities using numerical RTD curves obtained from CFD simulations is valid. 4. Compartment Modeling In addition to the CFD simulations, this work explored the use of the traditional compartment modeling technique to maintain computational simplicity. In general, compartment models are used to capture nonideal flow behavior. The results obtained from the tracer studies are used to model the real equipment as a series and/or parallel combination of ideal flow reactors. These ideal reactors are typically chosen to be perfectly mixed tanks or plug-flow reactors. In our case, the cavity was expected to behave like a combination of ideal flow reactors. The extent of deviation from the ideal behavior depends on the cavity geometry as well as the UCG process parameters. Based on the observations from velocity vectors, path lines, and E curves for cavities of all sizes, a compartment model was proposed as shown in Figure 15. The path line plots for both vertical and horizontal injections for all cavity sizes indicate that a fraction of inlet stream bypassed the main portion of the cavity volume (see Figure 9). Because the bypass was not exactly like an ideal PFR, we modeled it to be a series of backmixed reactors of equal volume. FLUENT has the ability to provide animation for tracer particles introduced at the inlet. This animation of particles for a given pulse showed that there were a number of recirculation zones (see also Figures 8 and 9). These animations also suggested that the main stream could be considered as a large mixed reactor followed by a series of small mixed reactors of equal volumes. Hence, the proposed compartment model was a combination of two parallel streams as shown in Figure 15. Back-mixing in each of these streams can be explained using a number of CSTRs in series. The number of CSTRs and the residence time of each reactor are

286


Figure 12. Laboratory-scale glass cavity setup for RTD studies.

Figure 15. Proposed compartment model for UCG cavity.

Figure 13. Comparison of F curves for both experiment and simulation.

vectors, path lines, and E curve suggested that its behavior was close to plug flow. This can be very well represented by the above-proposed structure. As the cavity size increased, the backmixing increased, which led to a decrease in plug-flow behavior and a reduction in the number of CSTRs in series. Formulation of the Compartment Model. In formulating the compartment model, unsteady-state tracer balance equations for each reactor in the proposed combination of reactors can be written as follows Main stream

(Cmj-1,i-1 - Cmj,i-1) τmj

(5)

Cmj,i ) Cmj,i-1 + [h × d(Cmj)]

(6)

d(Cmj,i) )

Bypass stream

Cbk-1,i-1 - Cbk,i-1 τbk

(7)

Cbj,i ) Cbj,i-1 + [h × d(Cbj)]

(8)

d(Cbk) )

Figure 14. Parity plot for F(t).

the model parameters that can be evaluated by comparing the E curves of the compartment model with that obtained by CFD. As mentioned before, the time lag in the RTD curve represents PFR-like behavior, and this zone was believed to be close to the outflow channel. For a special case of initial cavity size (straight horizontal channel), the compartment model was considered as a series of 10 equal volumes of small CSTRs in both the main and side streams. Because of the geometry of this cavity, which was a straight horizontal channel, the velocity

These unsteady-state equations were solved using Matlab to obtain the exit age distribution. The values of the model parameters, namely, the bypass ratio and residence time of each individual reactor, were obtained such that the E curve of the compartment model agreed well with that obtained by the CFD simulations. The model parameters thus obtained are given in Table 4. As expected, for both horizontal and vertical injections, the volumes of the CSTRs in both the main stream and the side stream increased with increasing cavity size as time proceeded. For horizontal injection, the bypass ratio decreased dramatically as the cavity size increased, whereas for vertical injection, low bypass ratios were observed because, in this case, the flow was distributed in all directions (see Figure 9). The volume of the

Ind. Eng. Chem. Res., Vol. 50, No. 1, 2011 Table 4. Model Parameters of All Cavities for Both Horizontal and Vertical Injection

Table 6. Boundary Conditions Used for the Reaction-Enabled CFD Simulation

cavity size model parameter

0

1

B VM1 (m3) VM2-VM5 (m3) VB1 (m3) VB2-VB5 (m3) VP (m3)

0.575 0.0392 0.0392 0.05 0.05 0.28

2

parameter 3

4

0.15 2.35 0.21 0.2 0.1 0.5

0.1 12.5 0.22 0.8 0.12 1.45

0.09 37 0.9 1.2 0.5 2.8

0.0502 113 2.45 0.12 0.05 4.3

0.13 42.5 0.72 0.0238 0.017 0.5

0.086 118 1.3 0.02 0.009 0.6

horizontal injection B VM1 (m3) VM2-VM5 (m3) VB1 (m3) VB2-VB5 (m3) VP (m3)

0.551 0.0372 0.0372 0.048 0.048 0.24

0.23 3 0.14 0.04 0.0029 0.28

0.17 14.5 0.32 0.026 0.022 0.4

Table 5. Goodness of Fit for Different Cavity Sizes error, e (%) cavity size

vertical injection


0 1 2 3 4

5.12 8.79 6.48 6.09 5.17

4.67 8.77 5.81 5.12 4.51

PFR near the exit increased with cavity size, which was consistently observed for both injection orientations. The goodness of fit was measured in terms of the average percentage error (e), defined as27 e (%) )

1 n

n

∑ i)1

|Emodel - ECFD | × 100 ECFD

value 3

vertical injection

287

volumetric flow rate (m /h) cavity temperature, K feed mixture (at 1173 K) at inlet feed composition at inlet Af, frequency factor for the forward reaction [m3/(mol s)] Ab, frequency factor for the backward reaction [m3/(mol s)] Ef, activation energy for the forward reaction [kJ/(kg mol)] Eb, activation energy for the backward reaction [kJ/(kg mol)]

112.372 1173 CO + H2O equal mole fractions 2.78 104.91 12600 78400

parallel side stream consisting of a series combination of five small perfectly mixed reactors followed by a plug-flow reactor; Figure 15) was incorporated in an Aspen Plus steady-state flowsheet simulator. Model parameters (i.e., residence times of all of the reactors in the compartment model, bypass ratios, etc.) were assigned to the blocks in the flowsheet (see Table 4). Steady-state simulations were performed to obtain the product gas compositions from this network of ideal flow reactors (i.e., the compartment model). The homogeneous water-gas shift reaction (eq 10), described by finite-rate kinetics,17 was considered. The rate expression for the water-gas shift reaction is given by eqs 11-13. The relevant kinetic parameters are provided in Table 6. R ) (kfCCOCH2O) - (kbCCO2CH2) (11) Water-gas shift reaction kf

CO + H2O 798 CO2 + H2

(10)

kb

(9)

The errors obtained for each cavity size in the case of both vertical and horizontal injections are given in Table 5. The percentage error was less than 10% in all cases. Thus, the proposed compartment model was suitable for all of the cavity sizes with different nozzle orientations. 5. Compartment Model Validation To validate the compartment model used to represent the mixing pattern, we considered a single homogeneous secondorder reversible water-gas shift reaction, which is one of the important reactions taking place under UCG conditions. It strongly influences the quality of the product gas in terms of the CO/H2 ratio. It is known that the first-order reaction is not affected by the mixing patterns and that the RTD alone is sufficient to predict the reaction conversion. In contrast, for reliable predictions in the case of non-first-order reactions (e.g., water-gas shift reaction), one has to use an appropriate compartment model along with the information on the RTD. The reactor-scale simulations for the compartment model were performed using a steady-state flow simulator (i.e., Aspen Plus) with the model parameters. Further, reaction-enabled CFD simulations were carried out independently (see Figure 3) to determine the composition of the product gas arising from the specified cavity under otherwise similar operating conditions. The two sets of results were compared to validate the developed compartment model. Steady-State Flowsheet Simulations for the Compartment Model in Aspen Plus. The compartment model (i.e., a series combination of five perfectly mixed reactors and also a

where

( ) ( )

kf ) Af exp

-Ef RT

(12)

kb ) Ab exp

-Eb RT

(13)

Ten independent simulations were performed to obtain the steady-state product gas composition for the five cavity sizes with two different nozzle orientations. The time required to obtain the results from the Aspen simulator was only less than 5 min using the above-mentioned computational source. Hence, this demonstrates that the compartment model-Aspen route reduces the computational burden on process simulations aimed at obtaining the product gas composition in the UCG cavity. It therefore offers a simpler way to determine UCG process performance at a particular time over the entire span. The mole fractions of H2 or CO2 obtained from the compartment model based on Aspen simulations are given in Table 7. Aspen simulations were performed for a single ideal CSTR and a PFR as well, with volumes equal to the total cavity volumes for all sizes. Further, Table 7 also reports the conversions predicted using the maximum mixedness model and the complete segregation model based on the respective E curves. The equations relevant for these models are well-established and can be found in standard textbooks.28 These simple models provide bounds on expected conversions, for a given RTD.28 The compartment model predictions lie between the ideal CSTR and PFR predictions, as can be seen in Figure 16. This clearly demonstrates that the whole cavity cannot be considered as either a single PFR or a single CSTR and indicates the importance of

288


Table 7. Comparison of Mole Fractions of H2 Predicted by CFD and Aspen vertical injection cavity size

CSTR

0 1 2 3 4

0.064 0.245 0.34 0.371 0.395

PFR

segregation model

maximum mixedness model

0.121 0.305 0.401 0.451 0.494

0.162 0.346 0.406 0.443 0.471

0.082 0.149 0.279 0.341 0.382

horizontal injection CFD

compartment model

segregation model

maximum mixedness model

CFD

compartment model

0.104 0.291 0.37 0.412 0.424

0.099 0.285 0.362 0.398 0.413

0.148 0.336 0.392 0.435 0.462

0.078 0.116 0.254 0.313 0.362

0.115 0.285 0.361 0.401 0.41

0.109 0.278 0.354 0.39 0.403

the characterization and quantification of nonideal behavior that exists within the cavity. It can also be noted that, as the size increased, the behavior of the cavity shifted from PFR to CSTR. In general, in cavities of sizes 1, 2, 3, and 4, it was observed that the conversion in the case of vertical injection was slightly higher than that for horizontal injection. This is because, in the latter case, a relatively large fraction of the feed bypassed the main volume of the cavity and spendt relatively less time in the cavity. Further, the PFR-like portion near the outflow channel in the case of vertical injection was relatively larger than that for horizontal injection. Reaction-Enabled CFD Simulations. The five cavities and different injection types studied in the preceding section were chosen for further CFD studies. The boundary conditions were the same as those used in the RTD studies. In addition to the continuity and momentum balance equations, the species balance was also invoked to obtain the product gas composition for the water-gas shift reaction. The feed mixture contained equal mole fractions of CO and H2O, at 1273 K, at the inlet. The entire cavity was considered to be isothermal at a temperature of 1273 K. The boundary conditions used for this study are given in Table 6. The reaction kinetics given by eqs 11-13 was incorporated. The mass, momentum, energy, and species balance equations (see eqs 1, 2, and 14) for the above-specified cases of meshed geometries were solved. Species balance equation ∂ (FY ) + ∇ · (FV bYi) ) -∇ · b J i + Ri ∂t i

400-500 CPU h of calculation on a Pentium Core 2 Duo 2.67 GHz workstation, which is much higher than that required for Aspen simulations using the compartment model. Results and Discussion. After steady state in the cavity reactor had been determined, the area-weighted average of the mole fractions of product species at the outlet were calculated for all cases. The mole fraction contours for H2 on a vertical plane created at the center line (i.e., width, y ) 0) for all cavity sizes are shown in Figure 17. Figure 17 shows that the H2 concentration was zero at the inlet and reached a maximum at the outlet. As expected, for the special case of a cavity of zero size, horizontal injection gave a higher conversion than vertical injection, which was also realized in both the CFD and Aspen simulation results. By virtue of the straight channel geometry, plug-flow behavior resulted in an increase in the conversion for horizontal injection, as can be seen in Table 7. The reactant and product concentrations from the inlet to the outlet show the expected trends. Table 7 also indicates that the mole percentage of H2 in the product gas increased with the cavity size, as a result of an increase in the residence time. Hence, it can be concluded that the water-gas shift reaction is kinetically controlled under these operating conditions. The parity plot comparing the mole fraction of H2 predicted from CFD with that from the Aspen simulation predictions is shown in Figure 18, and a very good agreement between the two can be observed. 6. Conclusions

(14)

A steady-state second-order discretization model was used to solve the above equations, and the solution was judged to be converged when the scalar residuals of each transport equations fell below 1 × 10-7. These simulations were expensive because of the incorporation of the nonlinear reaction rate terms during the solution of the flow equations. This procedure required

Figure 16. Comparison of mole fractions of H2 predicted from actual cavities with a single CSTR and a PFR of equal cavity volumes.

The residence time distribution (RTD) was obtained for cavities of different sizes, representing the UCG cavity at different times, using computational fluid dynamics simulations performed with the commercial software FLUENT. The E curves obtained for the cavity reactors matched well (within 10%) with that obtained from the proposed compartment model, consisting of a main stream of five CSTRs in series and a side stream of a series of five small CSTRs, followed by a PFR. When the cavity size was increased, the bypass ratio was found to decrease. It was found that recirculation zones existed in the cavity. The structure of the proposed model was found to be suitable for all cavity sizes with different nozzle orientations, albeit with different values for the volumes of the various reactors. To support the methodology of obtaining the RTD through CFD, the F curve was experimentally determined for a laboratory-scale UCG cavity reactor, which showed good agreement with that obtained by the CFD simulation. In the next step, the product gas composition for the water-gas shift reaction was obtained for cavities of different sizes at different times in the underground coal gasification process using both Aspen (with the compartment model) and CFD (with the original cavity) simulations. When the cavity size was increased, the mole fractions of H2 and CO2 were found to increase in both cases. The water-gas shift reaction was kinetically controlled under the operating conditions employed. The product gas compositions obtained from CFD and Aspen were comparable. All in all, we can conclude that, as the cavity size increases,


289

Figure 17. Contours of the mole fraction of H2 on a vertical plane at the center line (width, y ) 0) for a cavity size of 4 with vertical injection.

Nomenclature

Figure 18. Parity plot for mole fractions of H2 predicted by CFD and Aspen.

the behavior changes from PFR to CSTR. It can be seen that the time required to obtain the product gas composition through the reaction-enabled CFD simulations was much greater than that obtained through the compartment model-Aspen route. The proposed procedure of compartment modeling is a promising one, leading to a simple process model. These tools can serve as a good base for further work on global UCG process modeling and provides a less computationally intensive and reliable phenomenological model for UCG, capable of predicting the UCG process performance at a particular time. Future work will be aimed at examining the effects of temperature gradients in the cavity and the impact of thermomechanical spalling on the cavity flow patterns.

A ) frequency factor B ) bypass ratio BL ) backward length (i.e., cavity growth in the backward direction), cm Cbj,i ) tracer concentration in the jth CSTR in the bypass stream for the ith iteration Ci ) concentration of species i Cmj,i ) tracer concentration in the jth CSTR in the main stream for the ith iteration d(Cbji) ) derivative of the tracer concentration of the jth CSTR in the bypass stream for the ith iteration d(Cmj,i) ) derivative of the tracer concentration of the jth CSTR in the main stream for the ith iteration e ) average percentage error Eb ) activation energy for the backward reaction Ef ) activation energy for the forward reaction b F ) external body force FL ) forward length (i.e., cavity growth in the forward direction), cm h ) time step size H ) height of the cavity (i.e., cavity growth in the vertical direction), cm HI ) horizontal injection II ) inclined injection Jj ) diffusion flux of species j kb ) backward reaction rate constant keff ) effective thermal conductivity kf ) forward reaction rate constant p ) static pressure Ri ) rate of reaction of species i

290


t ) time, s b V ) velocity tensor V0 ) volumetric flow rate, m3/s VBj ) volume of the jth CSTR in the side stream of the compartment model, m3 VI ) vertical injection VMj ) volume of the jth CSTR in the main stream of the compartment model, m3 VP ) volume of the plug-flow reactor in the compartment model, m3 W ) width of the cavity (i.e., cavity growth in the transverse direction), cm Yi ) mole fraction of species i F ) density, kg/m3 Fg b ) gravitational body force cτ ) stress tensor τbj ) residence time of the jth CSTR in the bypass stream, s τe ) residence time of the plug-flow reactor at the exit, s τmj ) residence time of the jth CSTR in the main stream, s

Literature Cited (1) Coal Statistics. World Coal Institute. http://www.worldcoal.org/ resources/coal-statistics/. (2) Shafirovich, E.; Varma, A. Underground Coal Gasification: A Brief Review of Current Status. Ind. Eng. Chem. Res. 2009, 48, 7865–7875. (3) Khadse, A.; Qayyumi, M.; Mahajani, S. M.; Aghalayam, P. Underground Coal Gasification: A New Clean Coal Utilization Technique for India. Energy 2007, 32, 2061–2071. (4) Gregg, D. W.; Edgar, T. F. Underground Coal Gasification. AIChE J. 1978, 24, 753–781. (5) Burton, E.; Friedmann, J.; Upadhye, R. Best Practices in Underground Coal Gasification; Contract W-7405-Eng-48; Lawrence Livermore National Laboratory: Livermore, CA, 2006. (6) 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. (7) Yang, L. Study on the Model Experiment and Numerical Simulation for Underground Coal Gasification. Fuel 2004, 83, 573–584. (8) Thorsness, C. B.; Kang, S. W. Further DeVelopment of GeneralPurpose, Packed-Bed Model for Analysis of Underground Coal Gasification Processes; Report UCRL-92489; Lawrence Livermore National Laboratory: Livermore, CA, 1985. (9) Thorsness, C. B.; Greens, E. A.; Sherwood, A. A. One Dimensional Model for In-Situ Coal Gasification; Report UCRL-52523; Lawrence Livermore National Laboratory: Livermore, CA, 1978. (10) Magnani, C. F.; Farouq, A. S. M. Mathematical Modeling of the Stream Method of Underground Coal Gasification. Soc. Pet. Eng. J. 1975, 15, 425.

(11) Dinsmoor, B.; Galland, J. M.; Edgar, T. F. The Mechanism of Channel Growth During Underground Coal Gasification. J. Petrochem. Technol. 1978, 695, 698–704. (12) Harloff, G. J. Underground Coal Gasification Cavity Growth Model. J. Energy 1983, 7, 410–415. (13) Park, K. Y.; Edgar, T. F. Modeling of Early Cavity Growth for Underground Coal Gasification. Ind. Eng. Chem. Res. 1987, 26, 237–327. (14) Yang, L.; Liu, S. Numerical Simulation on Heat and Mass Transfer in Process of Underground Coal Gasification. Numer. Heat Transfer A 2003, 44, 537–557. (15) Perkins, G.; Sahajwalla, V. A Mathematical Model for the Chemical Reaction of a Semi-Infinite Block of Coal in Underground Coal Gasification. Energy Fuels 2005, 19, 1679–1692. (16) Perkins, G.; Sahajwalla, V. Steady-State Model for Estimating Gas Production from Underground Coal Gasification. Energy Fuels 2008, 22, 3902–3914. (17) Britten, J. A.; Thorsness, C. B. A Model for Cavity Growth and Resource Recovery During Underground Coal Gasification. In Situ 1989, 13, 1–53. (18) Perkins, G.; Sahajwalla, V. A Numerical Study of the Effects of Operating Conditions and Coal Properties on Cavity Growth in Underground Coal Gasification. Energy Fuels 2006, 20, 596–608. (19) Aghalayam, P. Underground Coal Gasification: A Clean Coal Technology, Handbook of Combustion; Wiley-VCH: New York, 2010; Vol. 5, pp 257-275. (20) Daggupati, S.; Mandapati, R. N.; Mahajani, S. M.; Ganesh, A.; Mathur, D. K.; Sharma, R. K.; Aghalayam, P. Laboratory Studies on Combustion Cavity Growth in Lignite Coal Blocks in the Context of Underground Coal Gasification. Energy 2010, 35, 2374–2386. (21) Perkins, G.; Sahajwalla, V. Modeling of Heat and Mass Transport Phenomena and Chemical Reaction in Underground Coal Gasification. Chem. Eng. Res. Des. 2007, 85, 329–343. (22) Levenspiel, O. Chemical Reaction Engineering; Wiley: New York, 1999. (23) Pirard, J. P.; Brasseur, A.; Coe¨me, A.; Mostade, M.; Pirlot, P. Results of the Tracer Tests during the El Tremedal Underground Coal Gasification at Great Depth. Fuel 2000, 79, 471–478. (24) Debelle, B.; Malmendier, M.; Mostade, M.; Pirard, J. P. Modelling of Flow at Thulin Underground Coal Gasification Experiments. Fuel 1992, 71, 95–104. (25) Thorsness, C. B. Steam Tracer Experiment at the Hoe Creek No. 3 Underground Coal Gasification Field Test; Report UCRL-53082; Lawrence Livermore National Laboratory: Livermore, CA, 1980. (26) FLUENT 6.3. Users Guide; Fluent Inc.: Lebanon, NH, 2005. (27) Singh, K. K.; Mahajani, S. M.; Shenoy, K. T.; Ghosh, S. K. Computational Fluid Dynamics Modeling of a Bench Scale Pump-Mixer: Head, Power and Residence Time Distribution. Ind. Eng. Chem. Res. 2007, 46, 2180–2190. (28) Fogler, H. S. Elements of Chemical Reaction Engineering; Prentice Hall: Upper Saddle River, NJ, 1999.

ReceiVed for reView June 18, 2010 ReVised manuscript receiVed October 8, 2010 Accepted November 8, 2010 IE101307K

Compartment Modeling for Flow Characterization of Underground

Recommend Documents