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A Fluidized Bed Process Model of a Chemical Looping Combustion Fuel Reactor
Mario R. Eden, Marianthi Ierapetritou and Gavin P. Towler (Editors) Proceedings of the 13th International Symposium on Process Systems Engineering – PSE 2018 July 1-5, 2018, San Diego, California, USA © 2018 Elsevier B.V. All rights reserved. https://doi.org/10.1016/B978-0-444-64241-7.50038-0
A Fluidized Bed Process Model of a Chemical Looping Combustion Fuel Reactor Chinedu O. Okoli, Andrew Lee*, Anthony P. Burgard and David C. Miller National Energy Technology Laboratory, 626 Cochrans Mill Road, Pittsburgh, PA, 15236, USA [email protected]
Abstract The development of a bubbling fluidized bed chemical looping combustion (CLC) fuel reactor model to support process synthesis and large-scale optimization is presented in this work. The model is built using the Institute for the Design of Advanced Energy Systems (IDAES) PSE framework and is implemented in Pyomo. It is equation-oriented and consists of a set of differential algebraic equations, which describe the gas and solid phase reactions between the fuel gas and oxygen carrier (OC), as well as the mass and heat transfer phenomena occurring in the different regions of the fluidized bed. In addition, the model provides axial profiles of the hydrodynamic and state variables. The capabilities of the model are demonstrated for the simulation of an industrial scale CLC fuel reactor which uses a hematite-based solid as the OC for natural gas combustion. The impact of select design variables on the performance of the model is evaluated, and the results show that methane conversion is more sensitive to changes in bed diameter than to the OC/fuel ratio. In addition, negligible performance differences are seen between the co-current and counter-current configurations indicating that good mixing between the gas and solid phases occurs within the bed. Keywords: chemical looping combustion, fluidized bed, fuel reactor, process model.
1. Introduction Chemical looping combustion (CLC) is a promising approach to provide cost effective, low carbon energy from fossil fuels. It creates a CO 2 rich flue gas with less equipment than other technologies such as oxy-combustion, which requires an air separation unit, or post-combustion carbon capture in conjunction with a conventional fossil-based power plant (Adanez et al., 2012). CLC is an active area of research and development in the areas of materials, process design, optimization, and scale up. The CLC process consists of two interconnected reactors, a fuel reactor and an air reactor, with a metallic oxygen carrier (OC) circulating between them. In the fuel reactor, the OC is reduced, oxidizing the fuel to produce nitrogen free flue gas consisting mainly of CO2 and H2O. In the air reactor, the reduced OC is oxidized with air. Fluidized bed reactors have been investigated as reaction vessels for CLC because of their excellent gas/solid contacting. The overall performance of the CLC process is dependent on efficient and effective gas and solid contacting in the fuel reactor. Computational models used in conjunction with an experimental development program can help to accelerate the development of new energy technologies. The models provide a representation of complex physical phenomena that might be difficult or expensive to measure in physical prototypes. In addition, the models can be used to optimize a
C. Okoli et al.
260 Table 1. Feed Conditions and fluidization properties Gas Feed Conditions Flow rate (mol/s) 298.11 Temperature (K) 800 Composition (%): CH4 45.82 CO2 47.72 H2O 6.46
OC Feed Conditions Flow rate (kg/s) 1,235 Temperature (K) 1186 Composition (%): Fe2O3 45 Fe3O4 0 Al2O3 55
OC Fluidization properties Min Fluid. Vel. (m/s) 0.04 Min. Fluid. Void. (-) 0.45 Particle Diam. (mm) 0.28 Solid Density (kg/m3) 3,252
complete, integrated process to identify the design and operating conditions that should be studied during bench and pilot scale testing. Finally, the models can be used in conjunction with statistical design of experiments to maximize the learning from expensive pilot scale testing. A particular research need when developing a new technology such as CLC is to consider systems integration and optimization. A systems level CLC process will comprise of phenomena ranging from the micro-scale, such as mass transfer associated with gas diffusion into the OC particle, to the macro-scale, such as the interaction of different unit operations in the flowsheet. Understanding and balancing these interactions can be best accomplished by employing large-scale optimization models of the complete system. Because such systems typically have nonlinear interactions, rigorous optimization approaches are able to identify important trade-offs and process synergies, which cannot be readily observed from simple sensitivity experiments. To effectively employ these large-scale optimization methods requires the development of suitable models that are sufficiently rigorous to capture all the important underlying physics of the process, from micro to macro scale, while also formulated in a way that is computationally efficient. Models built using an equation-oriented framework are particularly suitable for large-scale optimization since they provide first and second derivative information which is required by advanced optimization solvers capable of exploiting large, sparse matrices. To address these challenges, the Institute for the Design of Advanced Energy Systems (IDAES) is developing an open-source PSE framework to enable the rapid development and optimization of next generation advanced energy systems. The framework is based on the Pyomo algebraic modeling language (Hart et al. 2017). This paper describes the development of a bubbling fluidized bed (BFB) CLC fuel reactor within the IDAES framework. The model is developed in a modular fashion from two standalone models – a reaction kinetics and physical properties model and a fluidized bed hydrodynamic model. The capabilities of the overall model are demonstrated for the simulation of an industrial scale CLC fuel reactor in which natural gas is combusted using a hematitebased OC.
2. Methodology 2.1. Bed hydrodynamic model The fundamentals of the hydrodynamic model developed in this work are based on the three-region BFB model described by Kunii and Levenspiel (1968). The three-regions are the bubble, emulsion, and cloud-wake regions. In this model gas bubbles formed at the distributor plate rise through a dense emulsion phase carrying along a cloud of gas with suspended solids. The rest of the gas is in the emulsion phase, which also contains most of the solids. The Kunii and Levenspiel model assumes that the solids are
Fluidized Bed Process Model of a Chemical Looping Combustion Fuel Reactor
261
isothermal and well-mixed, thus neglecting the impact of axial variations in the solid phase. Furthermore, they assume an average bubble diameter to estimate the bed hydrodynamic properties. Lee and Miller (2013) utilized the Kunii and Levenspiel approach in their modeling of a BFB for CO2 adsorption from flue gas, extending the approach by considering axial variations in both the gas and solid phases, because adsorption processes are strongly impacted by temperature and pressure variations. They also use a bubble growth equation to model the bubble diameter as a function of height. The resulting model is a steady-state one-dimensional system of differential algebraic equations (DAEs). This model has been extended for the hydrodynamic model of the CLC fuel reactor with changes made to the relevant model equations to account for the different reaction kinetics. 2.2. Reaction kinetics and physical property model It is assumed that natural gas contains only methane, with the higher hydrocarbons treated as methane equivalents. In the fuel reactor, the Fe2O3 based OC is reduced to Fe3O4 by reaction with CH4. It is assumed that methane reforming within the reducer is negligible; thus, the overall reaction considered here is given by Eq.(1): ܪܥସ ͳʹ݁ܨଶ ܱଷ ՜ ͺ݁ܨଷ ܱସ ʹܪଶ ܱ ܱܥଶ
(1)
The reaction kinetics used in this model for the reaction of a hematite based OC with methane are as reported by Abad et al. (2007) and shown in Eq.(2): ௗ ௗ௧
ൌ
ଷ
(2)
మ
ఘ ሺଵିሻయ
where X is the fraction conversion of the metal oxide in the OC, C (mol/m3) is the reaction gas concentration (CH4 in this case), b is the reaction stoichiometric coefficient (12 moles of Fe2O3 converted per mole of CH4), k (m1.9mol-0.3s-1) is the kinetic rate constant, ρm is the molar density of the carrier particle (32,811 mol/m3), and rg is the particle grain radius (2.6e-7 m) within the OC particle. The value of n is 1.3. The kinetic constant k follows an Arrhenius type relationship with temperature, T (K). ݇ ൌ ͲǤͲͲͲͺቀ
ିସଽ ோ்
ቁ
(3)
Since the system operates at high temperature and low pressure, the ideal gas law was used for the state variables in the gas phase. The heat capacity of both the gas and solid phases are calculated using the standard Shomate correlations (Chase, 2008). Gas phase diffusivity (Wilke method), thermal conductivity (Wassilijewa equation) and viscosity (Wilke method) correlations are obtained from Poling et al., 2001. 2.3. Model implementation The CLC fuel reactor model is built by integrating two standalone models: the bed hydrodynamic model, and the reaction kinetics and physical property model. This approach allows the fuel reactor model to be adapted to study other OCs by changing the reaction and physical property model. It also allows the CLC fuel reactor model to be integrated into large scale flowsheets for systems optimization. The resulting system of DAEs is discretized using Pyomo’s automatic discretization tool, pyomo.dae (Nicholson et al., 2017), with orthogonal collocation on finite elements using the Lagrange-Radau method. 16 finite elements with 3 collocation points per element were used. The resulting discretized model consists of 12,710 variables and
C. Okoli et al.
262
12,710 equations. The model is solved using IPOPT on an Intel Xeon CPU with 31 GB RAM. The solution times (including initialization) are 15.52 s for the co-current configuration and 15.70 s for the counter-current configuration.
3. Results The primary application for this model is the development and optimization of advanced CLC systems. Feed conditions and fluidization properties used for this simulation case study (see Table 1) are obtained from a techno-economic study (Keairns et al., 2014) for a commercial scale industrial, natural gas-fueled, steam generation plant. It is assumed that the natural gas contains only methane and that the combined natural gas and fluidization gas (steam and CO2) streams are pressurized to 400 kPa and preheated to 800 K before entering the fuel reactor. The fuel reactor is assumed to have a diameter of 5.57 m, which is comparable to the industrial scale values used in Keairns et al. 2014, and the bed height (22.14 m) is selected such that the gas outlet pressure is close to atmospheric conditions. The profiles of select variables of a simulated co-current configuration are shown in Figure 1. In the co-current configuration both the gaseous fuel and solid OC are fed at the bottom of the bed (x = 0) and exit at the top of the bed (x = 1). From Figure 1(a), it can be seen that the reaction is very fast in the first 10 % of the bed since most of the methane conversion takes place in the lower regions. There is also a noticeable variation between the mole fraction and temperature profiles (Figure 1(b)) in the bubble and emulsion regions of the bed suggesting that there are mass transfer limitations and inefficient mixing of gases between those regions. This can be partly explained by an increase in gas bubble size from 0.02 m at the bottom of the bed to 3.05 m at the top of the bed as shown in Figure 1(c). As bubble size increases mass transfer resistances (c)
0.4 0.3
4
Bubble diameter (m)
Methane Mole Fraction (-)
(a) 0.5
Bubble Emulsion
0.2 0.1
3
2
1
0
0
0
0.2
0.4 0.6 Normalized bed height
0.8
(b) 1200
0.2
0.4
0.6
1
0.8
Normalized bed height (d) 1190
Solid Temperature (K)
Gas Temperature (K)
0
1
1120 1040
Bubble Emulsion
960 880 800 0
0.2
0.4
0.6
Normalized bed length
0.8
1
1185 Cloud-Wake Emulsion
1180 1175 1170 1165
1160 0
0.2
0.4
0.6
0.8
Normalized bed length
Figure 1. Profile data of selected variables vs. bed height (a) Methane mole fraction (b) Gas velocities (c) Gas Temperatures (d) Solid Temperatures
1
Fluidized Bed Process Model of a Chemical Looping Combustion Fuel Reactor
263
between the bubble and the cloud-wake and emulsion regions increase; thus gas mixing between regions becomes poorer. The temperature profile of the solid phase (Figure 1(d)) shows that the temperature drops from 1186 K at the inlet to 1166 K at the outlet because the reaction is endothermic. Note also that the temperature profiles of the cloud-wake and emulsion regions are virtually identical, suggesting that good mixing occurs between these two regions of the solid phase. The sensitivity of the co-current configuration’s methane conversion to some design parameters was also evaluated. It was found that increasing the bed diameter by 9 % leads to a 2.1 percentage point increase in methane conversion while reducing the bed diameter by 9 % leads to a 2.7 percentage point decrease in methane conversion. Furthermore, a 24 % increase in OC flow rate results in a 1.1 percentage point increase in methane conversion, while a 24 % decrease in OC flow rate results in a 2.3 percentage point decrease in methane conversion. These results suggest that the methane conversion is more sensitive to changes in bed diameter than in OC flow rate, indicating that residence time is more important than the OC/fuel ratio for improving fuel conversion. Table 2 summarizes the model results for co-current and counter-current configurations. In the counter-current configuration, the solid OC is fed at the top of the bed (x = 1) and exits at the bottom of the bed (x = 0), thus both configurations will have different solid temperature and composition profiles. For the given design conditions, 91.4 % methane conversion is achieved, with 43 % of the OC converted for the co-current configuration while 93.28 % methane conversion and 44 % OC conversion is achieved for the counter-current configuration. The close similarity between the values for both configurations suggest that they have similar gas/solid residence times, and that the impact of good mixing within the bed as a result of fluidization dominates compared to the impact of the solid feed/exit locations. Thus, other design considerations such as controllability or ancillary unit setup need to be evaluated before any configuration selection decisions can be made. The kinetic model has been validated at small scales (Abad et al. 2007), and the hydrodynamic trends of the model such as the bubble diameter profile are similar to those available in literature (Lee and Miller 2013). On-going future work is focusing on using pilot scale data to validate the model’s hydrodynamic parameters and the kinetic parameters of oxygen carriers of interest for a wide range of operating conditions. The resulting robust, validated model will be used in the IDAES PSE framework to optimize the design and performance of a complete CLC system consisting of the fuel and air reactors, as well as ancillary equipment such as turbines and heat exchangers. Table 2. Comparison between co-current and counter-current configurations
CH4 Conversion (%) OC Conversion (%) Exit Gas Pressure (kPa) Exit Gas Flowrate (mol/s) Exit Solid Flowrate (kg/s) Exit Gas Temperature (K) Exit Solid Temperature (K)
Co-current configuration 91.38 43.03 107.58 547.75 1,227.17 1,153.33 1,166.29
Counter-current configuration 93.28 43.93 108.41 552.93 1,227 1,165.77 1,165.72
264
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4. Conclusions This work discusses the development of a fluidized bed CLC fuel reactor model suitable for use in the large scale optimization of CLC systems using the IDAES PSE framework. The model was applied to the simulation of a CLC fuel reactor and shows that in a co-current configuration most of the fuel conversion occurs in the lower regions of the bed due to very fast reaction rates. Furthermore, methane conversion is more sensitive to changes in bed diameter than to the OC/fuel ratio. Another important finding was that good gas/solid mixing within the bed from the fluidization leads to negligible performance differences between co-current and counter-current configurations.
Acknowledgements and Disclaimer This research was supported in part by an appointment to the National Energy Technology Laboratory Research Participation Program, sponsored by the U.S. Department of Energy and administered by the Oak Ridge Institute for Science and Education. KeyLogic Systems, Inc.’s contributions to this work were funded by the National Energy Technology Laboratory under the Mission Execution and Strategic Analysis contract (DE-FE0025912) for support services. This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.
References A. Abad, J. Adanez, F. Garcia-Labiano, L. F. de Diego, P. Gayan, and J. Celeya, 2007, Mapping of the range of operational conditions for Cu-Fe-, and Ni-based oxygen carriers in chemicallooping combustion, Chemical Engineering Science, 62, 533 – 549. J. Adanez, A. Abad, F. Garcia-Labiano, P. Gayan, and L. F. deDiego, 2012, Progress in Chemical-Looping Combustion and Reforming Technologies. Progress in Energy and Combustion Science, 38, 2, 215 – 282. W. E. Hart, C. D. Laird, J. P. Watson, D. L. Woodruff, G. A. Hackebeil, B. L. Nicholson and J. D. Siirola, 2017, Pyomo – Optimization Modeling in Python, 2nd ed., Springer, Vol. 67. M. W. Chase, 1998. NIST – JANAF Thermochemical Tables. Journal of Physical and Chemical Reference Data, Monograph 9, 1 – 1951, 4th ed. D. Keairns, R. Newby, V. Shah, M. Turner, M. Woods, A. Zoelle, S. Ostheim, S. Carpenter, G. Richards, D. Straub, and R. Breault, 2014, Industrial Carbon Management Initiative: Chemical Looping Combustion Techno-Economic Study, U.S. National Energy Technology Laboratory. URS-RES-1100564/002. D. Kunii and O. Levenspiel, 1968. Bubbling Bed Model: Model for the Flow of Gases through a Fluidized Bed, Industrial & Engineering Chemistry Fundamentals, 7, 3, 446 – 452. A. Lee, and D. C. Miller, 2013, A One-Dimensional (1-D) Three-Region Model for a Bubbling Fluidized-Bed Absorber. Industrial & Engineering Chemistry Research, 52, 469 – 484. B. L. Nicholson, J. D. Siirola, J. P. Watson, V. M. Zavala, L. T. Biegler (2017). Pyomo.DAE: A modeling and automatic discretization framework for optimization with differential and algebraic equations. Mathematical Programming Computation, 10.1007/s12532-017-0127-0 B. M. Poling, J. M. Prausnitz, J. P. O’Connell (2001). The properties of gases and liquids. McGraw Hill, 5th ed.
A Fluidized Bed Process Model of a Chemical Looping Combustion Fuel Reactor Chinedu O. Okoli, Andrew Lee*, Anthony P. Burgard and David C. Miller National Energy Technology Laboratory, 626 Cochrans Mill Road, Pittsburgh, PA, 15236, USA [email protected]
Abstract The development of a bubbling fluidized bed chemical looping combustion (CLC) fuel reactor model to support process synthesis and large-scale optimization is presented in this work. The model is built using the Institute for the Design of Advanced Energy Systems (IDAES) PSE framework and is implemented in Pyomo. It is equation-oriented and consists of a set of differential algebraic equations, which describe the gas and solid phase reactions between the fuel gas and oxygen carrier (OC), as well as the mass and heat transfer phenomena occurring in the different regions of the fluidized bed. In addition, the model provides axial profiles of the hydrodynamic and state variables. The capabilities of the model are demonstrated for the simulation of an industrial scale CLC fuel reactor which uses a hematite-based solid as the OC for natural gas combustion. The impact of select design variables on the performance of the model is evaluated, and the results show that methane conversion is more sensitive to changes in bed diameter than to the OC/fuel ratio. In addition, negligible performance differences are seen between the co-current and counter-current configurations indicating that good mixing between the gas and solid phases occurs within the bed. Keywords: chemical looping combustion, fluidized bed, fuel reactor, process model.
1. Introduction Chemical looping combustion (CLC) is a promising approach to provide cost effective, low carbon energy from fossil fuels. It creates a CO 2 rich flue gas with less equipment than other technologies such as oxy-combustion, which requires an air separation unit, or post-combustion carbon capture in conjunction with a conventional fossil-based power plant (Adanez et al., 2012). CLC is an active area of research and development in the areas of materials, process design, optimization, and scale up. The CLC process consists of two interconnected reactors, a fuel reactor and an air reactor, with a metallic oxygen carrier (OC) circulating between them. In the fuel reactor, the OC is reduced, oxidizing the fuel to produce nitrogen free flue gas consisting mainly of CO2 and H2O. In the air reactor, the reduced OC is oxidized with air. Fluidized bed reactors have been investigated as reaction vessels for CLC because of their excellent gas/solid contacting. The overall performance of the CLC process is dependent on efficient and effective gas and solid contacting in the fuel reactor. Computational models used in conjunction with an experimental development program can help to accelerate the development of new energy technologies. The models provide a representation of complex physical phenomena that might be difficult or expensive to measure in physical prototypes. In addition, the models can be used to optimize a
C. Okoli et al.
260 Table 1. Feed Conditions and fluidization properties Gas Feed Conditions Flow rate (mol/s) 298.11 Temperature (K) 800 Composition (%): CH4 45.82 CO2 47.72 H2O 6.46
OC Feed Conditions Flow rate (kg/s) 1,235 Temperature (K) 1186 Composition (%): Fe2O3 45 Fe3O4 0 Al2O3 55
OC Fluidization properties Min Fluid. Vel. (m/s) 0.04 Min. Fluid. Void. (-) 0.45 Particle Diam. (mm) 0.28 Solid Density (kg/m3) 3,252
complete, integrated process to identify the design and operating conditions that should be studied during bench and pilot scale testing. Finally, the models can be used in conjunction with statistical design of experiments to maximize the learning from expensive pilot scale testing. A particular research need when developing a new technology such as CLC is to consider systems integration and optimization. A systems level CLC process will comprise of phenomena ranging from the micro-scale, such as mass transfer associated with gas diffusion into the OC particle, to the macro-scale, such as the interaction of different unit operations in the flowsheet. Understanding and balancing these interactions can be best accomplished by employing large-scale optimization models of the complete system. Because such systems typically have nonlinear interactions, rigorous optimization approaches are able to identify important trade-offs and process synergies, which cannot be readily observed from simple sensitivity experiments. To effectively employ these large-scale optimization methods requires the development of suitable models that are sufficiently rigorous to capture all the important underlying physics of the process, from micro to macro scale, while also formulated in a way that is computationally efficient. Models built using an equation-oriented framework are particularly suitable for large-scale optimization since they provide first and second derivative information which is required by advanced optimization solvers capable of exploiting large, sparse matrices. To address these challenges, the Institute for the Design of Advanced Energy Systems (IDAES) is developing an open-source PSE framework to enable the rapid development and optimization of next generation advanced energy systems. The framework is based on the Pyomo algebraic modeling language (Hart et al. 2017). This paper describes the development of a bubbling fluidized bed (BFB) CLC fuel reactor within the IDAES framework. The model is developed in a modular fashion from two standalone models – a reaction kinetics and physical properties model and a fluidized bed hydrodynamic model. The capabilities of the overall model are demonstrated for the simulation of an industrial scale CLC fuel reactor in which natural gas is combusted using a hematitebased OC.
2. Methodology 2.1. Bed hydrodynamic model The fundamentals of the hydrodynamic model developed in this work are based on the three-region BFB model described by Kunii and Levenspiel (1968). The three-regions are the bubble, emulsion, and cloud-wake regions. In this model gas bubbles formed at the distributor plate rise through a dense emulsion phase carrying along a cloud of gas with suspended solids. The rest of the gas is in the emulsion phase, which also contains most of the solids. The Kunii and Levenspiel model assumes that the solids are
Fluidized Bed Process Model of a Chemical Looping Combustion Fuel Reactor
261
isothermal and well-mixed, thus neglecting the impact of axial variations in the solid phase. Furthermore, they assume an average bubble diameter to estimate the bed hydrodynamic properties. Lee and Miller (2013) utilized the Kunii and Levenspiel approach in their modeling of a BFB for CO2 adsorption from flue gas, extending the approach by considering axial variations in both the gas and solid phases, because adsorption processes are strongly impacted by temperature and pressure variations. They also use a bubble growth equation to model the bubble diameter as a function of height. The resulting model is a steady-state one-dimensional system of differential algebraic equations (DAEs). This model has been extended for the hydrodynamic model of the CLC fuel reactor with changes made to the relevant model equations to account for the different reaction kinetics. 2.2. Reaction kinetics and physical property model It is assumed that natural gas contains only methane, with the higher hydrocarbons treated as methane equivalents. In the fuel reactor, the Fe2O3 based OC is reduced to Fe3O4 by reaction with CH4. It is assumed that methane reforming within the reducer is negligible; thus, the overall reaction considered here is given by Eq.(1): ܪܥସ ͳʹ݁ܨଶ ܱଷ ՜ ͺ݁ܨଷ ܱସ ʹܪଶ ܱ ܱܥଶ
(1)
The reaction kinetics used in this model for the reaction of a hematite based OC with methane are as reported by Abad et al. (2007) and shown in Eq.(2): ௗ ௗ௧
ൌ
ଷ
(2)
మ
ఘ ሺଵିሻయ
where X is the fraction conversion of the metal oxide in the OC, C (mol/m3) is the reaction gas concentration (CH4 in this case), b is the reaction stoichiometric coefficient (12 moles of Fe2O3 converted per mole of CH4), k (m1.9mol-0.3s-1) is the kinetic rate constant, ρm is the molar density of the carrier particle (32,811 mol/m3), and rg is the particle grain radius (2.6e-7 m) within the OC particle. The value of n is 1.3. The kinetic constant k follows an Arrhenius type relationship with temperature, T (K). ݇ ൌ ͲǤͲͲͲͺቀ
ିସଽ ோ்
ቁ
(3)
Since the system operates at high temperature and low pressure, the ideal gas law was used for the state variables in the gas phase. The heat capacity of both the gas and solid phases are calculated using the standard Shomate correlations (Chase, 2008). Gas phase diffusivity (Wilke method), thermal conductivity (Wassilijewa equation) and viscosity (Wilke method) correlations are obtained from Poling et al., 2001. 2.3. Model implementation The CLC fuel reactor model is built by integrating two standalone models: the bed hydrodynamic model, and the reaction kinetics and physical property model. This approach allows the fuel reactor model to be adapted to study other OCs by changing the reaction and physical property model. It also allows the CLC fuel reactor model to be integrated into large scale flowsheets for systems optimization. The resulting system of DAEs is discretized using Pyomo’s automatic discretization tool, pyomo.dae (Nicholson et al., 2017), with orthogonal collocation on finite elements using the Lagrange-Radau method. 16 finite elements with 3 collocation points per element were used. The resulting discretized model consists of 12,710 variables and
C. Okoli et al.
262
12,710 equations. The model is solved using IPOPT on an Intel Xeon CPU with 31 GB RAM. The solution times (including initialization) are 15.52 s for the co-current configuration and 15.70 s for the counter-current configuration.
3. Results The primary application for this model is the development and optimization of advanced CLC systems. Feed conditions and fluidization properties used for this simulation case study (see Table 1) are obtained from a techno-economic study (Keairns et al., 2014) for a commercial scale industrial, natural gas-fueled, steam generation plant. It is assumed that the natural gas contains only methane and that the combined natural gas and fluidization gas (steam and CO2) streams are pressurized to 400 kPa and preheated to 800 K before entering the fuel reactor. The fuel reactor is assumed to have a diameter of 5.57 m, which is comparable to the industrial scale values used in Keairns et al. 2014, and the bed height (22.14 m) is selected such that the gas outlet pressure is close to atmospheric conditions. The profiles of select variables of a simulated co-current configuration are shown in Figure 1. In the co-current configuration both the gaseous fuel and solid OC are fed at the bottom of the bed (x = 0) and exit at the top of the bed (x = 1). From Figure 1(a), it can be seen that the reaction is very fast in the first 10 % of the bed since most of the methane conversion takes place in the lower regions. There is also a noticeable variation between the mole fraction and temperature profiles (Figure 1(b)) in the bubble and emulsion regions of the bed suggesting that there are mass transfer limitations and inefficient mixing of gases between those regions. This can be partly explained by an increase in gas bubble size from 0.02 m at the bottom of the bed to 3.05 m at the top of the bed as shown in Figure 1(c). As bubble size increases mass transfer resistances (c)
0.4 0.3
4
Bubble diameter (m)
Methane Mole Fraction (-)
(a) 0.5
Bubble Emulsion
0.2 0.1
3
2
1
0
0
0
0.2
0.4 0.6 Normalized bed height
0.8
(b) 1200
0.2
0.4
0.6
1
0.8
Normalized bed height (d) 1190
Solid Temperature (K)
Gas Temperature (K)
0
1
1120 1040
Bubble Emulsion
960 880 800 0
0.2
0.4
0.6
Normalized bed length
0.8
1
1185 Cloud-Wake Emulsion
1180 1175 1170 1165
1160 0
0.2
0.4
0.6
0.8
Normalized bed length
Figure 1. Profile data of selected variables vs. bed height (a) Methane mole fraction (b) Gas velocities (c) Gas Temperatures (d) Solid Temperatures
1
Fluidized Bed Process Model of a Chemical Looping Combustion Fuel Reactor
263
between the bubble and the cloud-wake and emulsion regions increase; thus gas mixing between regions becomes poorer. The temperature profile of the solid phase (Figure 1(d)) shows that the temperature drops from 1186 K at the inlet to 1166 K at the outlet because the reaction is endothermic. Note also that the temperature profiles of the cloud-wake and emulsion regions are virtually identical, suggesting that good mixing occurs between these two regions of the solid phase. The sensitivity of the co-current configuration’s methane conversion to some design parameters was also evaluated. It was found that increasing the bed diameter by 9 % leads to a 2.1 percentage point increase in methane conversion while reducing the bed diameter by 9 % leads to a 2.7 percentage point decrease in methane conversion. Furthermore, a 24 % increase in OC flow rate results in a 1.1 percentage point increase in methane conversion, while a 24 % decrease in OC flow rate results in a 2.3 percentage point decrease in methane conversion. These results suggest that the methane conversion is more sensitive to changes in bed diameter than in OC flow rate, indicating that residence time is more important than the OC/fuel ratio for improving fuel conversion. Table 2 summarizes the model results for co-current and counter-current configurations. In the counter-current configuration, the solid OC is fed at the top of the bed (x = 1) and exits at the bottom of the bed (x = 0), thus both configurations will have different solid temperature and composition profiles. For the given design conditions, 91.4 % methane conversion is achieved, with 43 % of the OC converted for the co-current configuration while 93.28 % methane conversion and 44 % OC conversion is achieved for the counter-current configuration. The close similarity between the values for both configurations suggest that they have similar gas/solid residence times, and that the impact of good mixing within the bed as a result of fluidization dominates compared to the impact of the solid feed/exit locations. Thus, other design considerations such as controllability or ancillary unit setup need to be evaluated before any configuration selection decisions can be made. The kinetic model has been validated at small scales (Abad et al. 2007), and the hydrodynamic trends of the model such as the bubble diameter profile are similar to those available in literature (Lee and Miller 2013). On-going future work is focusing on using pilot scale data to validate the model’s hydrodynamic parameters and the kinetic parameters of oxygen carriers of interest for a wide range of operating conditions. The resulting robust, validated model will be used in the IDAES PSE framework to optimize the design and performance of a complete CLC system consisting of the fuel and air reactors, as well as ancillary equipment such as turbines and heat exchangers. Table 2. Comparison between co-current and counter-current configurations
CH4 Conversion (%) OC Conversion (%) Exit Gas Pressure (kPa) Exit Gas Flowrate (mol/s) Exit Solid Flowrate (kg/s) Exit Gas Temperature (K) Exit Solid Temperature (K)
Co-current configuration 91.38 43.03 107.58 547.75 1,227.17 1,153.33 1,166.29
Counter-current configuration 93.28 43.93 108.41 552.93 1,227 1,165.77 1,165.72
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4. Conclusions This work discusses the development of a fluidized bed CLC fuel reactor model suitable for use in the large scale optimization of CLC systems using the IDAES PSE framework. The model was applied to the simulation of a CLC fuel reactor and shows that in a co-current configuration most of the fuel conversion occurs in the lower regions of the bed due to very fast reaction rates. Furthermore, methane conversion is more sensitive to changes in bed diameter than to the OC/fuel ratio. Another important finding was that good gas/solid mixing within the bed from the fluidization leads to negligible performance differences between co-current and counter-current configurations.
Acknowledgements and Disclaimer This research was supported in part by an appointment to the National Energy Technology Laboratory Research Participation Program, sponsored by the U.S. Department of Energy and administered by the Oak Ridge Institute for Science and Education. KeyLogic Systems, Inc.’s contributions to this work were funded by the National Energy Technology Laboratory under the Mission Execution and Strategic Analysis contract (DE-FE0025912) for support services. This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.
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