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A Multi-scale model for CO2 capture: A Nickel-based oxygen carrier in Chemical-looping Combustion
Proceedings, 10th IFAC International Symposium on Proceedings, 10th of IFAC International Symposium on Advanced Control Chemical Processes Proceedings, 10th IFAC International Symposium on Proceedings, 10th of IFAC International Symposium on at www.sciencedirect.com Advanced Control Chemical Processes Available Shenyang, Liaoning, China, July 25-27, 2018 online Advanced Control of Chemical Processes Proceedings, 10th IFAC International Symposium on Advanced Control of Chemical Processes Shenyang, Liaoning, China, July 25-27, 2018 Shenyang, Liaoning, July 25-27, 2018 Advanced Control of China, Chemical Processes Shenyang, Liaoning, China, July 25-27, 2018 Shenyang, Liaoning, China, July 25-27, 2018
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IFAC PapersOnLine 51-18 (2018) 97–102
Multi-scale model for CO A 2 capture: Multi-scale model for CO A 22 capture: Multi-scale model for CO capture: A Multi-scale model for CO capture: A 2 Nickel-based oxygen carrier in Multi-scale model for CO capture: A Nickel-based oxygen carrier in 2 Nickel-based carrier Nickel-based oxygen oxygen carrier in in Chemical-looping Combustion Nickel-based oxygen carrier in Chemical-looping Combustion Chemical-looping Chemical-looping Combustion Combustion Combustion Huabei Chemical-looping You, Yue Yuan, Jingde Li, Luis Ricardez Sandoval
Huabei You, Yue Yuan, Jingde Li, Luis Ricardez Sandoval Huabei Huabei You, You, Yue Yue Yuan, Yuan, Jingde Jingde Li, Li, Luis Luis Ricardez Ricardez Sandoval Sandoval Huabei You, of Yue Yuan, Engineering, Jingde Li, Luis Ricardez Sandoval Department Chemical University of Waterloo, Department of Chemical Engineering, University of Waterloo, Department of Chemical Engineering, University of Waterloo, Waterloo, Canada (e-mail: [email protected]) Department of Chemical Engineering, University of Waterloo, Waterloo, Canada (e-mail: [email protected]) Waterloo, Canada [email protected]) Department of Chemical Engineering, University of Waterloo, Waterloo, Canada (e-mail: (e-mail: [email protected]) Waterloo, Canada (e-mail: [email protected]) Abstract: In this work, we present a multi-scale modelling framework for the Ni-based oxygen Abstract: In this work, we present aa multi-scale modelling framework for the Ni-based oxygen Abstract: this we present framework for Ni-based carrier (OC)In that explicitly accountmodelling for the complex reaction mechanism taking Abstract: Inparticle this work, work, wecan present a multi-scale multi-scale modelling framework for the the Ni-based oxygen oxygen carrier (OC) particle that can explicitly account for the complex reaction mechanism taking carrier (OC) particle that can explicitly account for the complex reaction mechanism taking place on(OC) theIn contacting surface between gasaccount and solid reactants in Chemical Looping Combustion Abstract: this work, we present a multi-scale modelling framework for the Ni-based oxygen carrier particle that can explicitly for the complex reaction mechanism taking place on the contacting surface between gas and solid reactants in Chemical Looping Combustion place on the contacting surface between gas and solid reactants in Chemical Looping Combustion (CLC). This multi-scale framework consists of a gas diffusion model and a surface reaction carrier (OC) particle that can explicitly account for the complex reaction mechanism taking place on the contacting surface between gas and solid reactants in Chemical Looping Combustion (CLC). This multi-scale framework consists of aa gas diffusion model and aa surface reaction (CLC). This multi-scale framework gas diffusion model surface reaction model. equations are usedconsists togas describe gas diffusion insideand OC whereas place onContinuum the contacting surface between andof reactants in Chemical Looping Combustion (CLC). This multi-scale framework consists ofsolid athe gas diffusion model and aparticles, surface reaction model. Continuum equations are used to describe the gas diffusion inside OC particles, whereas model. Continuum equations are used to describe the gas diffusion inside OC particles, whereas Mean-field approximation method is adopted to simulate the micro-scale events, such as molecule (CLC). This multi-scale framework consists of a gas diffusion model and a surface reaction model. Continuum equations are used to describe the gasthe diffusion insideevents, OC particles, whereas Mean-field approximation method is adopted to simulate micro-scale such as molecule Mean-field approximation method is adopted to simulate the micro-scale events, such as stream molecule adsorption and elementary reaction, occurring on the gas contacting surface. A pure CO is model. Continuum equations are used to describe the diffusion inside OC particles, whereas Mean-field approximation method is adopted to simulate the micro-scale events, such as molecule adsorption and elementary reaction, occurring on the contacting surface. A pure CO stream is adsorption and reaction, occurring on the surface. A pure stream is employed as theelementary fuel gas whereas the NiO istoused as contacting the metal oxide because it CO isasone of the Mean-field approximation method is adopted simulate the micro-scale events, such molecule adsorption and elementary reaction, occurring on the contacting surface. A pure CO stream is employed as the fuel gas whereas it is one of the the NiO is used as the metal oxide because employed as the fuel gas whereas the NiO is used as the metal oxide because it is one of the mostly used material in laboratory and pilot-scale plants. Rate constants for the micro-scale adsorption and elementary reaction, occurring on the contacting surface. A pure CO stream is employed as material the fuel gas whereas the NiO is used as the metal oxide because it ismicro-scale one of the mostly used in laboratory and pilot-scale plants. Rate constants for the mostly used in and pilot-scale plants. Rate constants for events in gas the present work were from a systematic Density Functional employed as material the fuel whereas the NiO is obtained used as the metal oxide because it ismicro-scale one of the mostly considered used material in laboratory laboratory and pilot-scale plants. Rate constants for the the micro-scale events considered in the present work were obtained from aa systematic Density Functional events considered in the present work were obtained from systematic Density Functional Theory (DFT) analysis, which provides a reasonable elementary reaction kinetics and lays a mostly used material in laboratory and pilot-scale plants. Rate constants for the micro-scale events considered in the present work were obtained from a systematic Density Functional Theory (DFT) analysis, which provides aa reasonable elementary reaction kinetics and lays aa Theory (DFT) analysis, which provides reasonable elementary reaction kinetics and solid foundation for multi-scale calculations. A sensitivity analysis on the size of intra-particle events considered in the present work were obtained from a systematic Density Functional Theory (DFT) analysis, which provides a reasonable elementary reaction kinetics and lays lays a solid foundation for multi-scale calculations. A sensitivity analysis on the size of intra-particle solid foundation for calculations. A analysis on size of intra-particle pore the adsoprtion rate constant wasaconducted toelementary assess the mass transport Theory (DFT) analysis, which provides reasonable reaction kinetics and on laysthe a solid and foundation for multi-scale multi-scale calculations. A sensitivity sensitivity analysis on the the size of effects intra-particle pore and the adsoprtion rate constant was conducted to assess the mass transport effects on the pore and the adsoprtion rate constant was conducted to assess the mass transport effects on the porous particle. The proposed multi-scale model shows reasonable tendencies and responses to solid foundation for multi-scale calculations. A sensitivity analysis on the size of intra-particle pore and the adsoprtion rate constant was model conducted to reasonable assess the mass transport effects on the porous particle. The proposed multi-scale shows tendencies and responses to porous particle. The multi-scale shows tendencies and responses to changes inthe key modelling parameters. pore and adsoprtion rate constant was model conducted to reasonable assess the mass transport on the porous particle. The proposed proposed multi-scale model shows reasonable tendencies andeffects responses to changes in key modelling parameters. changes in key modelling parameters. porous particle. The proposed multi-scale model shows reasonable tendencies and responses to changes in key modelling parameters. © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. changes in Multi-scale key modelling parameters. Keywords: model, Heterogeneous modelling, CO2 capture, Chemical-looping Keywords: Multi-scale model, Heterogeneous modelling, CO 2 capture, Chemical-looping Keywords: Multi-scale model, Heterogeneous combustion, Oxygen carrier. capture, Chemical-looping Chemical-looping Keywords: Multi-scale model, Heterogeneous modelling, modelling, CO CO22 capture, combustion, Oxygen carrier. combustion, Oxygen carrier. Keywords: Multi-scale model, Heterogeneous modelling, CO 2 capture, Chemical-looping combustion, Oxygen carrier. combustion, Oxygen carrier. 1. INTRODUCTION most of the common OC particles have is that reaction 1. INTRODUCTION most of the common OC particles have is that reaction 1. INTRODUCTION most of OC particles have that and conversion rates often (or reaction several) 1. INTRODUCTION most of the the common common OC decrease particles after haveaais isfew that reaction and conversion rates often decrease after few (or several) and conversion rates often decrease after a few (or CLC cycles. Thus, having access to an OC model that 1. INTRODUCTION most of the common OC particles have is that reaction and conversion rateshaving often decrease after aOC few model (or several) several) cycles. Thus, access to an that Chemical-looping combustion (CLC) is one of the most CLC CLC cycles. Thus, having access to an OC model that can evaluate the impact of the reaction kinetics on the and conversion rates often decrease after a few (or several) Chemical-looping combustion (CLC) is one of the most CLC cycles. Thus, havingofaccess to an OC model that can evaluate the impact the reaction kinetics on the Chemical-looping combustion (CLC) is one of the most promising greenhouse gas emission control technologies. can evaluate the impact of the reaction kinetics on the overall performance of theofaccess OC particle will greatly help Chemical-looping combustion (CLC)control is one technologies. of the most can CLC cycles. Thus, having to an OC model that promising greenhouse gas emission evaluate the impact the reaction kinetics on the overall performance of the OC particle will greatly help promising greenhouse gas emission control technologies. The concept of chemical looping involves the use of a Chemical-looping combustion (CLC) is one of the most overall performance of the OC particle will greatly help the modelling of CLC process which can demonstrate the promising greenhouse gas looping emissioninvolves control the technologies. can evaluate the impact of the reaction kinetics on The concept of chemical use of a overall performance of the OC particle will greatly help modelling of CLC process which can demonstrate the The concept looping involves the use of of aa the metal oxidegreenhouse asof thechemical oxygen carrier (OC) whichthe continuously promising gas emission control technologies. the modelling of CLC process which can demonstrate the technical viability of this emerging technology for CO The concept of chemical looping involves use overall performance of the OC particle will greatly help metal oxide as the oxygen carrier (OC) which continuously the modelling of CLC process which can demonstrate the22 technical viability of this emerging technology for CO metal oxide as the oxygen carrier (OC) which continuously circulates between a fuel-reactor, where the OC provides The concept of chemical looping involves the use of a technical viability of this emerging technology for CO capture and clean power generation. metal oxide as the oxygen carrier (OC) which continuously the modelling of CLC process which can demonstrate the22 circulates the OC provides between aa fuel-reactor, where technical viability of thisgeneration. emerging technology for CO capture and clean power circulates between fuel-reactor, where the OC provides oxygen to between burn theoxygen fuel, and an air-reactor, where the OC technical metal oxide as the carrier (OC) which continuously capture and clean power circulates afuel, fuel-reactor, where thewhere OC provides viability of thisgeneration. emerging technology for CO2 oxygen to burn the and an air-reactor, the OC capture and clean power generation. The most common OC models available in the literature oxygen to burn and the OC is oxidized with the air.afuel, Compared toair-reactor, the traditional fuel comcirculates fuel-reactor, where thewhere OC fuel provides oxygen to between burn the fuel, and an anto air-reactor, where thecomOC capture The most common OC models available in the literature and clean power generation. is oxidized with air. Compared the traditional The most common OC in literature Shrinking Unreacted Coreavailable Model(Ryu et al., 2001), is oxidized with air. Compared to the traditional fuel combustion process, CLC does not require extra separation oxygen to burn fuel, and not antoair-reactor, where thecomOC are Thethe most common OC models models available in the the literature is oxidized with the air. Compared the traditional fuel are the Shrinking Unreacted Core Model(Ryu et al., 2001), bustion process, CLC does require extra separation are the Shrinking Unreacted Core Model(Ryu et al., 2001), the Changing Grain Size Model (Garc´ ıa-Labiano et al., The most common OC models available in the literature bustion process, CLC does not require extra separation units to obtain a pure CO stream, thus minimizing the is oxidized with air. Compared to the traditional fuel comare the Shrinking Unreacted Core Model(Ryu et al., 2001), 2 not require extra separation bustion process, CLC does the Changing Grain Size Model (Garc´ ıa-Labiano et al., units to a pure CO obtain stream, thus minimizing the 2 the Changing Grain Size Model (Garc´ ıa-Labiano et al., 2005), and the Nucleation and Nuclei Growth Model (Hosare the Shrinking Unreacted Core Model(Ryu et al., 2001), units to obtain a pure CO stream, thus minimizing the energy penalty associated with CO capture process. 2 bustion process, CLC does not require extra separation the Changing Grain Size Model (Garc´ ıa-Labiano et al., 2 units topenalty obtain associated a pure COwith thus minimizing the 2005), and the Nucleation and Nuclei Growth Model (Hos2 stream, energy CO capture process. 2 capture process. 2005), and the Nucleation and Nuclei Growth Model (Hossain and de Lasa, 2010). The Shrinking Unreacted Core the Changing Grain Size Model (Garc´ ıa-Labiano et al., energy penalty associated with CO 2 capture units topenalty obtain associated a pure COwith thus minimizing the 2005), and the Nucleation and Nuclei Growth Model (Hos2 stream, energy CO process. sain and de Lasa, 2010). The Shrinking Unreacted Core 2 In order to design, optimize, and eventually scale-up the 2005), sain and de Lasa, 2010). The Shrinking Unreacted Core Model depicts the oxygen carrier particle as a spherical and the Nucleation and Nuclei Growth Model (HosIn orderpenalty to design, optimize, scale-up the energy associated withand COeventually sain and de Lasa, 2010). The Shrinking Unreacted Core 2 capture process. Model depicts the oxygen carrier particle as a spherical In to optimize, and eventually scale-up the CLC process, a variety of the fuelair-reactors models depicts the oxygen carrier particle as spherical grainand made the reactant (metal oxide). In order order to design, design, optimize, and and eventually scale-up the Model sain de of Lasa, 2010). The Shrinking Unreacted Core CLC process, a variety of the fueland air-reactors models Model depicts the solid oxygen carrier particle as aa Reactions spherical grain made of the solid reactant (metal oxide). Reactions CLC process, a variety of the fueland air-reactors models have beentodeveloped. The three parameters for the Model In order design, optimize, andmain eventually scale-up grain made the solid reactant (metal oxide). Reactions initially takeof place at the outer surface of as theaunreacted CLC process, a variety of the fueland air-reactors models depicts the oxygen carrier particle spherical have been developed. The three main parameters for the grain made of the solid reactant (metal oxide). Reactions take place at the outer surface of the unreacted have been developed. The three parameters for design of reactors in CLC process are: the total models loadthe of initially CLC process, a variety of the fuel-main and (1) air-reactors initially take at outer of solid which inward as the reaction proceeds. have been developed. The three main parameters for the grain made ofplace themoving solid reactant (metal oxide). Reactions design of reactors in CLC process are: (1) the total load of initially takekeeps place at the the outer surface surface of the the unreacted unreacted solid which keeps moving inward as the reaction proceeds. design of reactors in CLC process are: (1) the total load of bed material; (2) the circulation rate of the bed material; have been developed. The three main parameters for the solid which keeps moving inward as the reaction proceeds. The Changing Grain Size Model assumes that the oxygen design of reactors in CLC processrate are: of (1)the thebed total load of initially take place at the outer surface of the unreacted bed material; (2) the circulation material; solid which keeps moving inward as the reaction proceeds. The Changing Grain Size Model assumes that the oxygen bed material; (2) the circulation rate of the bed material; and (3) the gas leakage between two reactors (Lyngfelt design of reactors in CLC process are: (1) the total load of The Changing Grain Size Model assumes that the oxygen carrier particle is a mixture of metal oxide grains and inert bed material; (2) leakage the circulation rate ofreactors the bed (Lyngfelt material; The solid which keeps moving inward as the reaction proceeds. and (3) the gas between two Changing Grain Size Model assumes that the oxygen carrier particle is a mixture of metal oxide grains and inert and (3) the gas leakage between two reactors (Lyngfelt et al., 2001). The firstcirculation twobetween parameters directly depend on The bed material; (2) the rate of the bed material; carrier particle is a mixture of metal oxide grains and support grains; the fuel gas diffuses through the interstices and (3) the gas leakage two reactors (Lyngfelt Changing Grain Size Model assumes that the oxygen et al., 2001). The first two parameters directly depend on carrier particle is a mixture of metalthrough oxide grains and inert inert support grains; the fuel gas diffuses the interstices et al., 2001). The first two parameters directly depend on the performance of the selected oxygen carrier. and (3) the gas leakage between two reactors (Lyngfelt support grains; the fuel diffuses through the interstices between grains,is i.e. thegas particle’s reacts with et al., 2001). Theoffirst two parameters directly depend on carrier particle a mixture of metalpore, oxideand grains and inert the performance the selected oxygen carrier. support grains; the fuel gas diffuses through the interstices between grains, i.e. the particle’s pore, and reacts with the performance the selected oxygen carrier. et al., 2001). Theof first two parameters directly depend on between grains, i.e. the particle’s pore, and reacts with the metal oxide grains representing by the Shrinking Unrethe performance of the selected oxygen carrier. support grains; the fuel gas diffuses through the interstices between grains, i.e. the particle’s by pore, and reactsUnrewith The ideal oxygen carrier should have the following proper- the metal oxide grains representing the Shrinking The ideal oxygen carrier should have the following properthe performance of the selected oxygen carrier. the metal oxide grains representing by the Shrinking Unreacted Core Model. Furthermore, the Nucleation and Nuclei between grains, i.e. the particle’s pore, reacts with The ideal oxygen carrier should have the following properthe metal oxide grains representing by the and Shrinking Unreties: high reactivity; resistance against carbon deposition; acted Core Model. Furthermore, the Nucleation and Nuclei The ideal oxygen carrier should have the following properties: high reactivity; resistance against carbon deposition; acted Core Model. Furthermore, the Nucleation and Nuclei Growth Model assumes that all reactions inside the oxygen the metal oxide grains representing by the Shrinking Unreties: high reactivity; resistance against carbon deposition; acted Core Model. Furthermore, the Nucleation and Nuclei high mechanical strength; and sufficient stability in sucThe ideal oxygen carrier should have the following properGrowth Model assumes that all reactions inside the oxygen ties: high reactivity; resistance against carbon deposition; high mechanical strength; and sufficient stability in sucGrowth Model assumes that inside the oxygen carrier particle areFurthermore, initiated by reactions the Nucleation formation nuclei in acted Core Model. and Nuclei high mechanical strength; and sufficient stability in sucModel assumes that all all reactions insideof the oxygen cessive cycle reactions. Particles made ofcarbon pure metal ties: high reactivity; resistance deposition; carrier particle are initiated by the formation of nuclei in high mechanical strength; and against sufficient stability inoxide suc- Growth cessive cycle reactions. Particles made of pure metal oxide carrier particle are initiated by the formation of nuclei in the solid phase and then continue with subsequent growth Growth Model assumes that all reactions inside the oxygen cessive cycle reactions. Particles made of pure metal oxide carrier particle are initiated by the formation of nuclei in do not have enough mechenical strength and also tend high mechanical strength; and sufficient stability in sucthe solid phase and then continue with subsequent growth cessive cycle reactions. Particles made of pure metal oxide do not have enough mechenical strength and also tend the solid phase and then continue with subsequent growth of the formed nuclei. The reaction rate is calculated using carrier particle are initiated by the formation of nuclei in do not have enough mechenical strength and also tend the solid phase and then continue with subsequent growth to form agglomerations. However, this problem can be cessive cycle reactions. Particles made of pure metal oxide of the formed nuclei. The reaction rate is calculated using do not have enough mechenical strength and also tend to form agglomerations. However, this problem can be the formed nuclei. The reaction rate is calculated using aof function that contains parameters estimated by growth fitting the solid phase and then continue with subsequent to form agglomerations. However, this problem can be of the formed nuclei. The reaction rate is calculated using avoided by combining the metal oxide with another inert do not have enough mechenical strength and also tend that contains parameters estimated by fitting to form by agglomerations. However, thiswith problem caninert be athe avoided combining the metal oxide another aa function function that contains by model with experimental data.rateestimated the formed nuclei. The parameters reaction is calculated using avoided combining the metal oxide with another function that contains parameters estimated by fitting fitting support material. On the the main issue that to form by agglomerations. However, this problem caninert be of the model with experimental data. avoided by combining theother metalhand, oxide with another inert support material. On the other hand, the main issue that the model with experimental data. a function that contains parameters estimated by fitting support material. On the other hand, the main issue that the model with experimental data. avoided combining theother metalhand, oxidethe with another support by material. On the main issue inert that support material. On the other hand, the main issue that the model with experimental data.
2405-8963 © 2018, IFAC (International Federation of Automatic Control) Copyright 2018 IFAC 97 Hosting by Elsevier Ltd. All rights reserved. Copyright 2018 responsibility IFAC 97 Control. Peer review© of International Federation of Automatic Copyright ©under 2018 IFAC 97 Copyright © 2018 IFAC 97 10.1016/j.ifacol.2018.09.264 Copyright © 2018 IFAC 97
2018 IFAC ADCHEM 98 Shenyang, Liaoning, China, July 25-27, 2018Huabei You et al. / IFAC PapersOnLine 51-18 (2018) 97–102
The OC particle models described above have been used to simulate the temperature and conversion profiles inside some common oxygen carriers during the CLC process. The simulation results were found to be in reasonable agreement with experimental data. These models have assumed that the concentration of gas reactant only varies in one direction that is normal to the particle surface. These models have also considered that the chemical reactions can be simplified as first order reactions with respect to the concentration of gas species. In a real setting, concentration profiles in both axial and radial directions exist when the gas (i.e. the fuel) diffuses through the particle’s pore. Moreover, reactions are actually taking place on the solid surface, and the mechanism is generally more complex than first order reactions. Therefore, these models are not able to describe the impact of radial concentration gradients across the pore and the complexity of reaction kinetics which, as suggested by experimental results, plays an important role and should be taken into account when developing oxygen carrier particle models (Dueso et al., 2012). The difficulty in modelling the impact of reaction kinetics lies in the discrepancies between the evolution of the chemical reactions on the particle’s surface and the continuum mechanics that describes the transport of molecules in the gas phase. Specifically, the gas diffusion in the pore occurs at the micrometer length scale whereas the surface events are usually taking place in atomic dimensions. In addition, the corresponding time scale for the chemical reactions is also orders of magnitude smaller than that for gas diffusion. As a result, simulating gas diffusion and surface reaction simultaneously throughout the entire spacial domain is computationally intensive. To tackle this problem, Vlachos (1997) assessed the numerical feasibility of multi-scale integration hybrid (MIH) algorithms that links a unimolecular surface reaction model to a macroscopic species transportation model by decomposing the system into two partially overlapping subdomains. To the authors’ knowledge, multi-scale models that predict events taking place inside the OC in CLC has not been proposed in the literature.
Fig. 1. Schematic of the present multi-scale model. adsorbed molecules will react with the solid reactant on the surface and release the product into the gas phase. The gas concentration profile in radial and axial directions within the pore is calculated using mass conservation equations (i.e. gas phase model). The surface reactions are simulated by a surface model using the Mean-field approximation method (Kevrekidis et al., 1984). The gas phase model and the surface model are coupled through a mass flux boundary condition located at the top of the surface, i.e. above the pore’s inner walls.
The present work presents a multi-scale framework for oxygen carrier particle in Chemical-looping combustion. Nickel oxide is selected to be the solid reactant in oxygen carrier because it is a common oxygen carrier used for laboratory and pilot-scale demonstration plants and exhibits high reactivity and stability (Mattisson et al., 2006). For simplicity, the fuel gas in this work only contains carbon oxide. The proposed multi-scale model for Ni-based oxygen carrier used in CLC process is presented in the next section.
The following assumptions are adopted in the model: (1) Structure of the OC particles does not change during the reaction. (2) OC particles are considered isothermal. (3) Mass transport through the particle only occurs by diffusion. (4) OC particles are surrounded by fuel gas and the gas concentration remain constant during the CLC process.
2. MODEL DEVELOPMENT 2.1 Gas Diffusion Model The overall configuration of the multi-scale model is illustrated in Figure 1. The oxygen carrier is considered to be a spherical particle with numerous cylindrical pores. Fuel gas enters the particle through the inlet of the pore and diffuses in both axial (z) and radial (r) directions.
The two dimensional unsteady-state mass transport of molecules in the gas phase is described by the continuum equation: ∂Ci ∂Ci 1 ∂ ∂ 2 Ci = De,i r + De,i . (1) ∂t r ∂r ∂r ∂z 2
When a gas molecule reaches the inner wall of the pore (i.e., boundary in the r-direction), it will either stay in the gas phase or get adsorbed onto the wall surface. The
with the following initial and boundary conditions: 98
2018 IFAC ADCHEM Shenyang, Liaoning, China, July 25-27, 2018Huabei You et al. / IFAC PapersOnLine 51-18 (2018) 97–102
Ci (t, z, r) t=0 ∂Ci (t, z, r) ∂z z=0 ∂Ci (t, z, r) ∂r r=0 ∂Ci (t, z, r) −De,i ∂z z=L
∂Ci (t, z, r) −De,i ∂r
r=R
=0
(2)
=0
(3)
=0
(4)
Kinetics parameters are obtained from density functional theory (DFT) simulations (see Kinetic Parameters section). Table 1 shows the parameters used in this study. The surface site density CT was published by Okazawa et al. (2007) whereas the operating conditions were taken from Ad´anez et al. (2012). These conditions are representative of pilot-scale CLC plants.
= kg,i Ci (t, z, r) z=L − Cibulk = −ka,i Ci (t, z, r) +
CT kr,i θi (t) NA
r=R
99
(5) θempty (t)
Table 1. Model Parameters Parameters (Unit) Temperature, T (K) Pressure, P (atm) Particle radius (Pore length), L (m) Pore radius, R (m) Porosity, ε Effective Diffusivity of CO, De,CO (m2 · s−1 ) Effective Diffusivity of CO2 , De,CO2 (m2 · s−1 ) Density of sites, CT (sites · m−2 ) bulk (mol · m−3 ) Bulk gas concentration, CCO bulk (mol · m−3 ) Bulk gas concentration, CCO 2 Sherwood number, Sh
z
(6)
where Ci is concentration of gas i in the pore; r and z are the radial and axial domains representing; R and L are the pore radius and pore length, respectively; De,i is the effective diffusivity of gas i in the pore; kg,i is the external mass transfer coefficient of gas species i; Cibulk is the bulk concentration of gas i; θempty is the surface coverage of empty sites on the surface; θi is the surface coverage of surface species i; ka,i is the adsorption rate constant of surface species i; kr,i is the reaction rate constant of surface species i; CT is the density of surface sites; NA is the Avogadro’s number.
Values 1173 1 1.0 × 10−4 1.0 × 10−8 0.4 9.775 × 10−7 7.796 × 10−7 1.33 × 1019 10.0 0.0 7
2.2 Surface Model
The effective diffusivity of gas i was calculated as a function of gas diffusivity and particle porosity: De,i = Dg,i ε2 (7) where ε is the pore porosity.
As shown in Figure 1, The pore surface is considered to be a finite square lattice. Each lattice site can be occupied by at most one molecule through adsorption. According to the results from DFT simulations, CO molecules tend to attach to the oxygen atoms on the exposed NiO surface and form a NiO − CO micro-structure. After formation of NiO − CO, CO captures the oxygen atom in NiO and becomes CO2 . The desorption of CO2 is considered to be much faster than the proceding reactions; thus, this step is not considered explicitly in the present model. Therefore, the reaction mechanisms used in the present work involves two steps: A CO molecule in gas phase adsorbs onto an empty site on the surface (i.e. an available oxygen atom); and the adsorbed CO reacts with NiO and produces CO2 :
When gas diffuses through the pore, molecular diffusion and Knudsen diffusion are both present. Therefore, gas diffusivity was calculated as follows: −1 1 1 + (8) Dg,i = Dm,i DK,i where the molecular diffusivity Dm,i and the Knudsen diffusivity DK,i are calculated using the following correlations (Fuller et al., 1966): 0.5 1.0 × 10−7 T 1.75 Mi−1 + MS−1 (9) Dm,i = 2 P ( i νi )1/3 + ( S νi )1/3 2 8RT (10) DK,i = r 3 πMi
k
a → NiO − CO∗ CO(g) + NiO∗ −−−
kr
NiO − CO∗ −−−→ Ni∗ + CO2 (g)
(12) (13)
where ∗ denotes an empty site on the surface.
The present mechanism assumes that the oxygen on the surface is in excess during the time period in the simulation and the CO2 molecule leaves the surface instantly after it was formed. Hence, CO molecules always have access to oxygen atoms and no CO2 molecule will stay on the surface (the surface coverage of CO2 is zero).
where T is the temperature in Kelvin; Mi is the molecular weight of gas i; MS is the molecular weight of the solvent S; P is the pressure in atm; νi is the diffusion parameters of the diffusing species. The external mass transfer coefficient kg was calculated using Sherwood number: Dm,i Sh (11) kg,i = dpar where Sh is the Sherwood number; dpar is the particle diameter.
Mean Field Approximation Mean-field approximation assumes that the adsorbed molecules are distributed homogeneously on the surface. The effect of the surface configuration on a single adsorbate is approximated by the average occupancy of lattice sites by any of the adsorbed molecules. The rate of change of the surface concentration of species i (Cisurf ) can be described as the rate of adsorption minus the rate of consumption:
The surface coverage fractions of empty sites and surface species i at each point in time across the axial domain is determined from the surface model (see Section 2.2 ). 99
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dCisurf (t) dt
n = ka,i Ci r=R 1 − θj (t) −
j=1
kr,i Cisurf (t)
(14)
k
Equation 14 can also be expressed in terms of the surface coverage fraction as follows: n dθi (t) NA = θj (t) ka,i Ci r=R 1 − dt CT j=1 − kr,i θi (t) (15)
i where Ci r=R is concentration of gas i above the surface and is estimated from the gas phase model; n is the number of surface species (n = 1 in this framework).
The sum of the coverage fraction of all surface species and empty sites will always be equal to one; therefore, the following equation is also valid in the Mean-field approximation: n θi (t) (16) 1 = θempty (t) + i=1
For the proposed reaction mechanisms, the following equations are considered in the present surface model: dθCO (t) NA = ka CCO r=R θempty − kr θCO (t) (17) dt CT 1 = θempty (t) + θCO (t)
(18)
Kinetic Parameters. Density functional theory (DFT) is carried out to calculate the kinetic parameters used in this work using Vienna Ab Initio Simulation Package (VASP). The projector-augmented wave (PAW) method (Bl¨ochl, 1994) with the generalized gradient approximation of Perdew-Burke-Ernzerhof (Perdew et al., 1996) is chosen to describe the system. To simulate the reactions, a 6layer nickel oxide slab model is constructed while the 2 bottom layers are fixed. Through structural relaxation and nudged-elastic-band method (Henkelman et al., 2000), we have established the 2-step carbon monoxide oxidation mechanism discussed in the previous section. 2.3 Model Coupling In the present work, the gap-tooth method (Gear et al., 2003) is adopted to compute the concentration gradients across the pore’s axial domain. As shown in Fig. 1, the tooth represents the surface model placed at equallyspaced discrete points in the axial domain of the multiscale model whereas the gap is the length between two subsequent teeth (i.e. surface models). The implicit backward Euler discretization has been employed to solve for the gas diffusion model. The number of teeth (surface models) considered in this system matches with the discretized nodes in the z -direction of the gas phase model. At time t = t , the surface coverage of molecule i on a tooth patch located at the specific node (z , R) is determined using the surface model (Eq. 17 to 18). Note that the concentration of gas species i at that same 100
node point Ci (t , z , R) represents the input to the surface model. The calculated coverage θi t=t at node (z , R) is needed to evaluate the gas phase boundary condition (Eq. 6) and provides the mass flux at node (z , R). The later is required to solve for the gas diffusion model (Eq. 1) for the next time interval. The number of teeth points required to solve the model is problem-specific. The present work used ten teeth to obtain a trade-off between numerical accuracy and computational cost. This coupling scheme is based on the interaction between the gas diffusion model and the surface model - the concentration of gas species i above the surface affects the surface configuration through the adsorption term in Eq. 15, which in turn determines the adsorption rates that enter into the boundary condition of the gas diffusion model (Eq. 6). 3. RESULTS AND ANALYSIS The multi-scale model presented in the previous section was implemented in Python 3.6; Each simulation requires approximately 574 CPU seconds (3.4GHz Intel i7-3770 processor). Because of the scarcity of similar OC particle models and comparable experimental data, model validation cannot be performed at this time. Therefore, we carried out a sensitivity analysis on the key modelling parameters to evaluate their effects on the system’s behavior. Table 2 shows the kinetic parameters obtained from DFT simulations. To obtain the reaction rate constants for this process, we screened multiple configurations and found the most stable structures from DFT analysis for reactants and products in the surface reaction system (not discussed here for brevity). Transition states of this 2-step-reaction are searched as saddle points, which are confirmed by frequency calculations. The rate constants are calculated using the same temperature used in the gas diffusion model (1173K); The parameters presented in Table 1 and 2 are considered to be the reference condition. The rate of reactions taking place inside the OC particle depends on several factors such as the physical properties of the particles (particle size, porosity, composition, etc.) and chemical kinetics of the reactions. The effects of the pore size and the adsorption rate constant on the CO conversion rate and the surface reaction rates were assessed using the concentration profile at the center point in the outlet (z = 0, r = 0) (see Fig. 1). As shown in Fig. 2 and 4 (red line), the CO concentration at that center point reached steady state within one second, whereas 30 seconds are needed for the CO2 concentration to reach steady state (see the red line in Fig. 3 and 5). These results suggest that the rate of gas diffusion is not controlling the rates of surface reactions that consume CO and produce CO2 . Table 2. Kinetic Parameters Parameters (Unit) CO adsorption rate constant, ka (m · s−1 ) CO2 formation rate constant, kr (s−1 )
Values 2.90 × 10−6 3.13
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Fig. 2. Effect of the varying pore radius on the evolution of CO concentration at the center of the particle.
Fig. 4. Effect of ka on the evolution of CO concentration at the center of the particle.
Fig. 3. Effect of the varying pore radius on the evolution of CO2 concentration at the center of the particle.
Fig. 5. Effect of ka on the evolution of CO2 concentration at the center of the particle.
3.1 Effect of the pore size
in the radial direction causes the CO2 concentration at the center of a larger pore to be lower than that of a smaller pore.
Figure 2 shows the impact of pore radius on the consumption rate of CO. The evolution of CO concentration at the center of the end of the pore (i.e. the center of the OC particle) was simulated using a +/- 10% change in the pore radius on each simulation; steady state was achieved within one second in all three cases (see Fig. 2). The result shows that CO concentration at steady state within a larger pore is higher than that obtained for a smaller pore. This behavior is expected because increasing pore size also promotes mass transport, thus enhancing the diffusion process. On the other hand, concentration of CO2 reached steady state after 120 seconds in all three simulations using a +/- 10% change in the pore radius. Compared to Fig. 2, increasing the CO concentration did not lead to an increase in the steady state CO2 concentration. However, note that the concentration at the center point will also be affected by the radial gas diffusion. That is, a larger pore radius leads to a longer distance between the inner wall of the pore (i.e. pore surface) to that center point. Hence, a longer period of time is required for the product generated on the pore surface to reach the center of the pore. Therefore, it is reasonable to consider that the gas diffusion taking place 101
3.2 Effect of the adsorption rate constant The limiting step for reactions in the present model is CO adsorption as the adsorption rate constant ka is 106 magnitude smaller than the CO2 formation rate constant kr . To analyze the effect of this variable on the extent of reaction inside the particle, several simulations were carried out using different adsorption rate constants ranging from -10% to +10%. The results show that the concentration of CO reached steady state within one second. The steady state concentration of the reactant gas CO increased by 13% when the adsorption rate constant decreased by 10% (see Fig. 4). Correspondingly, when ka decreased, the concentration of gas product CO2 at steady state also decreased, as a smaller ka means CO molecules in the gas phase are less likely to adsorb onto the surface; and the decrease in available adsorbed CO molecules will slow down the CO2 formation reaction.
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and H2 ) will be used to replace the pure CO stream considered in this work; also more reaction details will be considered; Kinetic Monte Carlo (KMC) method will be employed to simulate the many-body interactions taking place in the pore’s surface. REFERENCES
Fig. 6. Effect of the adsorption rate constant ka on the CO surface coverage in the axial direction. Furthermore, the surface coverage of CO at equally-spaced teeth points in the axial direction was evaluated after the concentration of CO and CO2 both reached steady state (see Fig. 6). As expected, the surface coverage of CO at the inlet of the pore (Pore length = 1.0 × 10−4 ) was higher than that at the end of the pore due to the higher inlet concentration. Moreover, increasing the adsorption rate constant increased the surface coverage at each tooth point, which agrees with the decrease in the steady state concentration of CO (Fig. 4) as more CO molecules will diffuse from the gas phase and adsorb onto the pore surface. Note that the CO surface coverage did not reach the steady state after 120 seconds, whereas the CO concentration reached the steady state within 1 second. That is, the increasing amount of available CO molecules on the surface did not increase its consumption rate substantially. This indicates that, although the adsorption rate constant is significantly smaller than the reaction rate constant, the latter may be the rate controlling parameter in the initial stages of this process. 4. CONCLUSION A multi-scale particle model framework consisting of a gas diffusion model and a surface reaction model has been developed for oxygen carrier particles used in a typical CLC system. Chemical reaction kinetics is explicitly considered in the surface model using reaction rate constants obtained from DFT analysis. NiO was selected to be the solid reactant that provides oxygen, and a pure CO stream was assumed to be the gas reactant (fuel gas). This model was then used to predict the influence of pore size and adsorption rate constant on the steady state concentration profile of the gas species inside the particle. Currently, due to the lack of similar OC particle models or experimental data for the simulated NiO system, model validation will be considered in the future work. The sensitivity analysis showed reasonable tendencies and responses to changes in key modelling parameters, which indicates the feasibility of this model. The present multi-scale particle model framework will be further developed in the following aspects: Syngas (CO 102
Ad´anez, J., Abad, A., Garc´ıa-Labiano, F., Gay´ an, P., and de Diego, L.F. (2012). Progress in chemical-looping combustion and reforming technologies. Progress in Energy and Combustion Science, 38(2), 215–282. Bl¨ochl, P.E. (1994). Projector augmented-wave method. Physical Review B, 50(24), 17953–17979. Dueso, C., Ortiz, M., Abad, A., Garc´ıa-Labiano, F., de Diego, L.F., Gay´an, P., and Ad´anez, J. (2012). Reduction and oxidation kinetics of nickel-based oxygencarriers for chemical-looping combustion and chemicallooping reforming. Chemical Engineering Journal, 188, 142–154. Fuller, E.N., Schettler, P.D., and Giddings, J.C. (1966). New Method for Prediction of Binary Gas-phase Diffusion Coefficients. Industrial & Engineering Chemistry, 58(5), 18–27. Garc´ıa-Labiano, F., de Diego, L.F., Ad´anez, J., Abad, A., and Gay´ an, P. (2005). Temperature variations in the oxygen carrier particles during their reduction and oxidation in a chemical-looping combustion system. Chemical Engineering Science, 60(3), 851–862. Gear, C., Li, J., and Kevrekidis, I.G. (2003). The gaptooth method in particle simulations. Physics Letters A, 316(3), 190–195. Henkelman, G., Uberuaga, B.P., and J´onsson, H. (2000). A climbing image nudged elastic band method for finding saddle points and minimum energy paths. The Journal of Chemical Physics, 113(22), 9901–9904. Hossain, M.M. and de Lasa, H.I. (2010). Reduction and oxidation kinetics of Co-Ni/Al2 O3 oxygen carrier involved in a chemical-looping combustion cycles. Chemical Engineering Science, 65(1), 98–106. Kevrekidis, I., Schmidt, L., and Aris, R. (1984). Rate multiplicity and oscillations in single species surface reactions. Surface Science, 137(1), 151 – 166. Lyngfelt, A., Leckner, B., and Mattisson, T. (2001). A fluidized-bed combustion process with inherent CO2 separation; application of chemical-looping combustion. Chemical Engineering Science, 56(10), 3101 – 3113. Mattisson, T., Johansson, M., and Lyngfelt, A. (2006). The use of NiO as an oxygen carrier in chemical-looping combustion. Fuel, 85(5-6), 736–747. Okazawa, T., Nishizawa, T., Nishimura, T., and Kido, Y. (2007). Oxidation kinetics for Ni(111) and the structure of the oxide layers. Phys. Rev. B, 75, 033413. Perdew, J.P., Burke, K., and Ernzerhof, M. (1996). Generalized Gradient Approximation Made Simple. Physical Review Letters, 77(18), 3865–3868. Ryu, H.J., Bae, D.H., Han, K.H., Lee, S.Y., Jin, G.T., and Choi, J.H. (2001). Oxidation and reduction characteristics of oxygen carrier particles and reaction kinetics by unreacted core model. Korean Journal of Chemical Engineering, 18(6), 831–837. Vlachos, D.G. (1997). Multiscale integration hybrid algorithms for homogeneous–heterogeneous reactors. AIChE Journal, 43(11), 3031–3041.
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Multi-scale model for CO A 2 capture: Multi-scale model for CO A 22 capture: Multi-scale model for CO capture: A Multi-scale model for CO capture: A 2 Nickel-based oxygen carrier in Multi-scale model for CO capture: A Nickel-based oxygen carrier in 2 Nickel-based carrier Nickel-based oxygen oxygen carrier in in Chemical-looping Combustion Nickel-based oxygen carrier in Chemical-looping Combustion Chemical-looping Chemical-looping Combustion Combustion Combustion Huabei Chemical-looping You, Yue Yuan, Jingde Li, Luis Ricardez Sandoval
Huabei You, Yue Yuan, Jingde Li, Luis Ricardez Sandoval Huabei Huabei You, You, Yue Yue Yuan, Yuan, Jingde Jingde Li, Li, Luis Luis Ricardez Ricardez Sandoval Sandoval Huabei You, of Yue Yuan, Engineering, Jingde Li, Luis Ricardez Sandoval Department Chemical University of Waterloo, Department of Chemical Engineering, University of Waterloo, Department of Chemical Engineering, University of Waterloo, Waterloo, Canada (e-mail: [email protected]) Department of Chemical Engineering, University of Waterloo, Waterloo, Canada (e-mail: [email protected]) Waterloo, Canada [email protected]) Department of Chemical Engineering, University of Waterloo, Waterloo, Canada (e-mail: (e-mail: [email protected]) Waterloo, Canada (e-mail: [email protected]) Abstract: In this work, we present a multi-scale modelling framework for the Ni-based oxygen Abstract: In this work, we present aa multi-scale modelling framework for the Ni-based oxygen Abstract: this we present framework for Ni-based carrier (OC)In that explicitly accountmodelling for the complex reaction mechanism taking Abstract: Inparticle this work, work, wecan present a multi-scale multi-scale modelling framework for the the Ni-based oxygen oxygen carrier (OC) particle that can explicitly account for the complex reaction mechanism taking carrier (OC) particle that can explicitly account for the complex reaction mechanism taking place on(OC) theIn contacting surface between gasaccount and solid reactants in Chemical Looping Combustion Abstract: this work, we present a multi-scale modelling framework for the Ni-based oxygen carrier particle that can explicitly for the complex reaction mechanism taking place on the contacting surface between gas and solid reactants in Chemical Looping Combustion place on the contacting surface between gas and solid reactants in Chemical Looping Combustion (CLC). This multi-scale framework consists of a gas diffusion model and a surface reaction carrier (OC) particle that can explicitly account for the complex reaction mechanism taking place on the contacting surface between gas and solid reactants in Chemical Looping Combustion (CLC). This multi-scale framework consists of aa gas diffusion model and aa surface reaction (CLC). This multi-scale framework gas diffusion model surface reaction model. equations are usedconsists togas describe gas diffusion insideand OC whereas place onContinuum the contacting surface between andof reactants in Chemical Looping Combustion (CLC). This multi-scale framework consists ofsolid athe gas diffusion model and aparticles, surface reaction model. Continuum equations are used to describe the gas diffusion inside OC particles, whereas model. Continuum equations are used to describe the gas diffusion inside OC particles, whereas Mean-field approximation method is adopted to simulate the micro-scale events, such as molecule (CLC). This multi-scale framework consists of a gas diffusion model and a surface reaction model. Continuum equations are used to describe the gasthe diffusion insideevents, OC particles, whereas Mean-field approximation method is adopted to simulate micro-scale such as molecule Mean-field approximation method is adopted to simulate the micro-scale events, such as stream molecule adsorption and elementary reaction, occurring on the gas contacting surface. A pure CO is model. Continuum equations are used to describe the diffusion inside OC particles, whereas Mean-field approximation method is adopted to simulate the micro-scale events, such as molecule adsorption and elementary reaction, occurring on the contacting surface. A pure CO stream is adsorption and reaction, occurring on the surface. A pure stream is employed as theelementary fuel gas whereas the NiO istoused as contacting the metal oxide because it CO isasone of the Mean-field approximation method is adopted simulate the micro-scale events, such molecule adsorption and elementary reaction, occurring on the contacting surface. A pure CO stream is employed as the fuel gas whereas it is one of the the NiO is used as the metal oxide because employed as the fuel gas whereas the NiO is used as the metal oxide because it is one of the mostly used material in laboratory and pilot-scale plants. Rate constants for the micro-scale adsorption and elementary reaction, occurring on the contacting surface. A pure CO stream is employed as material the fuel gas whereas the NiO is used as the metal oxide because it ismicro-scale one of the mostly used in laboratory and pilot-scale plants. Rate constants for the mostly used in and pilot-scale plants. Rate constants for events in gas the present work were from a systematic Density Functional employed as material the fuel whereas the NiO is obtained used as the metal oxide because it ismicro-scale one of the mostly considered used material in laboratory laboratory and pilot-scale plants. Rate constants for the the micro-scale events considered in the present work were obtained from aa systematic Density Functional events considered in the present work were obtained from systematic Density Functional Theory (DFT) analysis, which provides a reasonable elementary reaction kinetics and lays a mostly used material in laboratory and pilot-scale plants. Rate constants for the micro-scale events considered in the present work were obtained from a systematic Density Functional Theory (DFT) analysis, which provides aa reasonable elementary reaction kinetics and lays aa Theory (DFT) analysis, which provides reasonable elementary reaction kinetics and solid foundation for multi-scale calculations. A sensitivity analysis on the size of intra-particle events considered in the present work were obtained from a systematic Density Functional Theory (DFT) analysis, which provides a reasonable elementary reaction kinetics and lays lays a solid foundation for multi-scale calculations. A sensitivity analysis on the size of intra-particle solid foundation for calculations. A analysis on size of intra-particle pore the adsoprtion rate constant wasaconducted toelementary assess the mass transport Theory (DFT) analysis, which provides reasonable reaction kinetics and on laysthe a solid and foundation for multi-scale multi-scale calculations. A sensitivity sensitivity analysis on the the size of effects intra-particle pore and the adsoprtion rate constant was conducted to assess the mass transport effects on the pore and the adsoprtion rate constant was conducted to assess the mass transport effects on the porous particle. The proposed multi-scale model shows reasonable tendencies and responses to solid foundation for multi-scale calculations. A sensitivity analysis on the size of intra-particle pore and the adsoprtion rate constant was model conducted to reasonable assess the mass transport effects on the porous particle. The proposed multi-scale shows tendencies and responses to porous particle. The multi-scale shows tendencies and responses to changes inthe key modelling parameters. pore and adsoprtion rate constant was model conducted to reasonable assess the mass transport on the porous particle. The proposed proposed multi-scale model shows reasonable tendencies andeffects responses to changes in key modelling parameters. changes in key modelling parameters. porous particle. The proposed multi-scale model shows reasonable tendencies and responses to changes in key modelling parameters. © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. changes in Multi-scale key modelling parameters. Keywords: model, Heterogeneous modelling, CO2 capture, Chemical-looping Keywords: Multi-scale model, Heterogeneous modelling, CO 2 capture, Chemical-looping Keywords: Multi-scale model, Heterogeneous combustion, Oxygen carrier. capture, Chemical-looping Chemical-looping Keywords: Multi-scale model, Heterogeneous modelling, modelling, CO CO22 capture, combustion, Oxygen carrier. combustion, Oxygen carrier. Keywords: Multi-scale model, Heterogeneous modelling, CO 2 capture, Chemical-looping combustion, Oxygen carrier. combustion, Oxygen carrier. 1. INTRODUCTION most of the common OC particles have is that reaction 1. INTRODUCTION most of the common OC particles have is that reaction 1. INTRODUCTION most of OC particles have that and conversion rates often (or reaction several) 1. INTRODUCTION most of the the common common OC decrease particles after haveaais isfew that reaction and conversion rates often decrease after few (or several) and conversion rates often decrease after a few (or CLC cycles. Thus, having access to an OC model that 1. INTRODUCTION most of the common OC particles have is that reaction and conversion rateshaving often decrease after aOC few model (or several) several) cycles. Thus, access to an that Chemical-looping combustion (CLC) is one of the most CLC CLC cycles. Thus, having access to an OC model that can evaluate the impact of the reaction kinetics on the and conversion rates often decrease after a few (or several) Chemical-looping combustion (CLC) is one of the most CLC cycles. Thus, havingofaccess to an OC model that can evaluate the impact the reaction kinetics on the Chemical-looping combustion (CLC) is one of the most promising greenhouse gas emission control technologies. can evaluate the impact of the reaction kinetics on the overall performance of theofaccess OC particle will greatly help Chemical-looping combustion (CLC)control is one technologies. of the most can CLC cycles. Thus, having to an OC model that promising greenhouse gas emission evaluate the impact the reaction kinetics on the overall performance of the OC particle will greatly help promising greenhouse gas emission control technologies. The concept of chemical looping involves the use of a Chemical-looping combustion (CLC) is one of the most overall performance of the OC particle will greatly help the modelling of CLC process which can demonstrate the promising greenhouse gas looping emissioninvolves control the technologies. can evaluate the impact of the reaction kinetics on The concept of chemical use of a overall performance of the OC particle will greatly help modelling of CLC process which can demonstrate the The concept looping involves the use of of aa the metal oxidegreenhouse asof thechemical oxygen carrier (OC) whichthe continuously promising gas emission control technologies. the modelling of CLC process which can demonstrate the technical viability of this emerging technology for CO The concept of chemical looping involves use overall performance of the OC particle will greatly help metal oxide as the oxygen carrier (OC) which continuously the modelling of CLC process which can demonstrate the22 technical viability of this emerging technology for CO metal oxide as the oxygen carrier (OC) which continuously circulates between a fuel-reactor, where the OC provides The concept of chemical looping involves the use of a technical viability of this emerging technology for CO capture and clean power generation. metal oxide as the oxygen carrier (OC) which continuously the modelling of CLC process which can demonstrate the22 circulates the OC provides between aa fuel-reactor, where technical viability of thisgeneration. emerging technology for CO capture and clean power circulates between fuel-reactor, where the OC provides oxygen to between burn theoxygen fuel, and an air-reactor, where the OC technical metal oxide as the carrier (OC) which continuously capture and clean power circulates afuel, fuel-reactor, where thewhere OC provides viability of thisgeneration. emerging technology for CO2 oxygen to burn the and an air-reactor, the OC capture and clean power generation. The most common OC models available in the literature oxygen to burn and the OC is oxidized with the air.afuel, Compared toair-reactor, the traditional fuel comcirculates fuel-reactor, where thewhere OC fuel provides oxygen to between burn the fuel, and an anto air-reactor, where thecomOC capture The most common OC models available in the literature and clean power generation. is oxidized with air. Compared the traditional The most common OC in literature Shrinking Unreacted Coreavailable Model(Ryu et al., 2001), is oxidized with air. Compared to the traditional fuel combustion process, CLC does not require extra separation oxygen to burn fuel, and not antoair-reactor, where thecomOC are Thethe most common OC models models available in the the literature is oxidized with the air. Compared the traditional fuel are the Shrinking Unreacted Core Model(Ryu et al., 2001), bustion process, CLC does require extra separation are the Shrinking Unreacted Core Model(Ryu et al., 2001), the Changing Grain Size Model (Garc´ ıa-Labiano et al., The most common OC models available in the literature bustion process, CLC does not require extra separation units to obtain a pure CO stream, thus minimizing the is oxidized with air. Compared to the traditional fuel comare the Shrinking Unreacted Core Model(Ryu et al., 2001), 2 not require extra separation bustion process, CLC does the Changing Grain Size Model (Garc´ ıa-Labiano et al., units to a pure CO obtain stream, thus minimizing the 2 the Changing Grain Size Model (Garc´ ıa-Labiano et al., 2005), and the Nucleation and Nuclei Growth Model (Hosare the Shrinking Unreacted Core Model(Ryu et al., 2001), units to obtain a pure CO stream, thus minimizing the energy penalty associated with CO capture process. 2 bustion process, CLC does not require extra separation the Changing Grain Size Model (Garc´ ıa-Labiano et al., 2 units topenalty obtain associated a pure COwith thus minimizing the 2005), and the Nucleation and Nuclei Growth Model (Hos2 stream, energy CO capture process. 2 capture process. 2005), and the Nucleation and Nuclei Growth Model (Hossain and de Lasa, 2010). The Shrinking Unreacted Core the Changing Grain Size Model (Garc´ ıa-Labiano et al., energy penalty associated with CO 2 capture units topenalty obtain associated a pure COwith thus minimizing the 2005), and the Nucleation and Nuclei Growth Model (Hos2 stream, energy CO process. sain and de Lasa, 2010). The Shrinking Unreacted Core 2 In order to design, optimize, and eventually scale-up the 2005), sain and de Lasa, 2010). The Shrinking Unreacted Core Model depicts the oxygen carrier particle as a spherical and the Nucleation and Nuclei Growth Model (HosIn orderpenalty to design, optimize, scale-up the energy associated withand COeventually sain and de Lasa, 2010). The Shrinking Unreacted Core 2 capture process. Model depicts the oxygen carrier particle as a spherical In to optimize, and eventually scale-up the CLC process, a variety of the fuelair-reactors models depicts the oxygen carrier particle as spherical grainand made the reactant (metal oxide). In order order to design, design, optimize, and and eventually scale-up the Model sain de of Lasa, 2010). The Shrinking Unreacted Core CLC process, a variety of the fueland air-reactors models Model depicts the solid oxygen carrier particle as aa Reactions spherical grain made of the solid reactant (metal oxide). Reactions CLC process, a variety of the fueland air-reactors models have beentodeveloped. The three parameters for the Model In order design, optimize, andmain eventually scale-up grain made the solid reactant (metal oxide). Reactions initially takeof place at the outer surface of as theaunreacted CLC process, a variety of the fueland air-reactors models depicts the oxygen carrier particle spherical have been developed. The three main parameters for the grain made of the solid reactant (metal oxide). Reactions take place at the outer surface of the unreacted have been developed. The three parameters for design of reactors in CLC process are: the total models loadthe of initially CLC process, a variety of the fuel-main and (1) air-reactors initially take at outer of solid which inward as the reaction proceeds. have been developed. The three main parameters for the grain made ofplace themoving solid reactant (metal oxide). Reactions design of reactors in CLC process are: (1) the total load of initially takekeeps place at the the outer surface surface of the the unreacted unreacted solid which keeps moving inward as the reaction proceeds. design of reactors in CLC process are: (1) the total load of bed material; (2) the circulation rate of the bed material; have been developed. The three main parameters for the solid which keeps moving inward as the reaction proceeds. The Changing Grain Size Model assumes that the oxygen design of reactors in CLC processrate are: of (1)the thebed total load of initially take place at the outer surface of the unreacted bed material; (2) the circulation material; solid which keeps moving inward as the reaction proceeds. The Changing Grain Size Model assumes that the oxygen bed material; (2) the circulation rate of the bed material; and (3) the gas leakage between two reactors (Lyngfelt design of reactors in CLC process are: (1) the total load of The Changing Grain Size Model assumes that the oxygen carrier particle is a mixture of metal oxide grains and inert bed material; (2) leakage the circulation rate ofreactors the bed (Lyngfelt material; The solid which keeps moving inward as the reaction proceeds. and (3) the gas between two Changing Grain Size Model assumes that the oxygen carrier particle is a mixture of metal oxide grains and inert and (3) the gas leakage between two reactors (Lyngfelt et al., 2001). The firstcirculation twobetween parameters directly depend on The bed material; (2) the rate of the bed material; carrier particle is a mixture of metal oxide grains and support grains; the fuel gas diffuses through the interstices and (3) the gas leakage two reactors (Lyngfelt Changing Grain Size Model assumes that the oxygen et al., 2001). The first two parameters directly depend on carrier particle is a mixture of metalthrough oxide grains and inert inert support grains; the fuel gas diffuses the interstices et al., 2001). The first two parameters directly depend on the performance of the selected oxygen carrier. and (3) the gas leakage between two reactors (Lyngfelt support grains; the fuel diffuses through the interstices between grains,is i.e. thegas particle’s reacts with et al., 2001). Theoffirst two parameters directly depend on carrier particle a mixture of metalpore, oxideand grains and inert the performance the selected oxygen carrier. support grains; the fuel gas diffuses through the interstices between grains, i.e. the particle’s pore, and reacts with the performance the selected oxygen carrier. et al., 2001). Theof first two parameters directly depend on between grains, i.e. the particle’s pore, and reacts with the metal oxide grains representing by the Shrinking Unrethe performance of the selected oxygen carrier. support grains; the fuel gas diffuses through the interstices between grains, i.e. the particle’s by pore, and reactsUnrewith The ideal oxygen carrier should have the following proper- the metal oxide grains representing the Shrinking The ideal oxygen carrier should have the following properthe performance of the selected oxygen carrier. the metal oxide grains representing by the Shrinking Unreacted Core Model. Furthermore, the Nucleation and Nuclei between grains, i.e. the particle’s pore, reacts with The ideal oxygen carrier should have the following properthe metal oxide grains representing by the and Shrinking Unreties: high reactivity; resistance against carbon deposition; acted Core Model. Furthermore, the Nucleation and Nuclei The ideal oxygen carrier should have the following properties: high reactivity; resistance against carbon deposition; acted Core Model. Furthermore, the Nucleation and Nuclei Growth Model assumes that all reactions inside the oxygen the metal oxide grains representing by the Shrinking Unreties: high reactivity; resistance against carbon deposition; acted Core Model. Furthermore, the Nucleation and Nuclei high mechanical strength; and sufficient stability in sucThe ideal oxygen carrier should have the following properGrowth Model assumes that all reactions inside the oxygen ties: high reactivity; resistance against carbon deposition; high mechanical strength; and sufficient stability in sucGrowth Model assumes that inside the oxygen carrier particle areFurthermore, initiated by reactions the Nucleation formation nuclei in acted Core Model. and Nuclei high mechanical strength; and sufficient stability in sucModel assumes that all all reactions insideof the oxygen cessive cycle reactions. Particles made ofcarbon pure metal ties: high reactivity; resistance deposition; carrier particle are initiated by the formation of nuclei in high mechanical strength; and against sufficient stability inoxide suc- Growth cessive cycle reactions. Particles made of pure metal oxide carrier particle are initiated by the formation of nuclei in the solid phase and then continue with subsequent growth Growth Model assumes that all reactions inside the oxygen cessive cycle reactions. Particles made of pure metal oxide carrier particle are initiated by the formation of nuclei in do not have enough mechenical strength and also tend high mechanical strength; and sufficient stability in sucthe solid phase and then continue with subsequent growth cessive cycle reactions. Particles made of pure metal oxide do not have enough mechenical strength and also tend the solid phase and then continue with subsequent growth of the formed nuclei. The reaction rate is calculated using carrier particle are initiated by the formation of nuclei in do not have enough mechenical strength and also tend the solid phase and then continue with subsequent growth to form agglomerations. However, this problem can be cessive cycle reactions. Particles made of pure metal oxide of the formed nuclei. The reaction rate is calculated using do not have enough mechenical strength and also tend to form agglomerations. However, this problem can be the formed nuclei. The reaction rate is calculated using aof function that contains parameters estimated by growth fitting the solid phase and then continue with subsequent to form agglomerations. However, this problem can be of the formed nuclei. The reaction rate is calculated using avoided by combining the metal oxide with another inert do not have enough mechenical strength and also tend that contains parameters estimated by fitting to form by agglomerations. However, thiswith problem caninert be athe avoided combining the metal oxide another aa function function that contains by model with experimental data.rateestimated the formed nuclei. The parameters reaction is calculated using avoided combining the metal oxide with another function that contains parameters estimated by fitting fitting support material. On the the main issue that to form by agglomerations. However, this problem caninert be of the model with experimental data. avoided by combining theother metalhand, oxide with another inert support material. On the other hand, the main issue that the model with experimental data. a function that contains parameters estimated by fitting support material. On the other hand, the main issue that the model with experimental data. avoided combining theother metalhand, oxidethe with another support by material. On the main issue inert that support material. On the other hand, the main issue that the model with experimental data.
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2018 IFAC ADCHEM 98 Shenyang, Liaoning, China, July 25-27, 2018Huabei You et al. / IFAC PapersOnLine 51-18 (2018) 97–102
The OC particle models described above have been used to simulate the temperature and conversion profiles inside some common oxygen carriers during the CLC process. The simulation results were found to be in reasonable agreement with experimental data. These models have assumed that the concentration of gas reactant only varies in one direction that is normal to the particle surface. These models have also considered that the chemical reactions can be simplified as first order reactions with respect to the concentration of gas species. In a real setting, concentration profiles in both axial and radial directions exist when the gas (i.e. the fuel) diffuses through the particle’s pore. Moreover, reactions are actually taking place on the solid surface, and the mechanism is generally more complex than first order reactions. Therefore, these models are not able to describe the impact of radial concentration gradients across the pore and the complexity of reaction kinetics which, as suggested by experimental results, plays an important role and should be taken into account when developing oxygen carrier particle models (Dueso et al., 2012). The difficulty in modelling the impact of reaction kinetics lies in the discrepancies between the evolution of the chemical reactions on the particle’s surface and the continuum mechanics that describes the transport of molecules in the gas phase. Specifically, the gas diffusion in the pore occurs at the micrometer length scale whereas the surface events are usually taking place in atomic dimensions. In addition, the corresponding time scale for the chemical reactions is also orders of magnitude smaller than that for gas diffusion. As a result, simulating gas diffusion and surface reaction simultaneously throughout the entire spacial domain is computationally intensive. To tackle this problem, Vlachos (1997) assessed the numerical feasibility of multi-scale integration hybrid (MIH) algorithms that links a unimolecular surface reaction model to a macroscopic species transportation model by decomposing the system into two partially overlapping subdomains. To the authors’ knowledge, multi-scale models that predict events taking place inside the OC in CLC has not been proposed in the literature.
Fig. 1. Schematic of the present multi-scale model. adsorbed molecules will react with the solid reactant on the surface and release the product into the gas phase. The gas concentration profile in radial and axial directions within the pore is calculated using mass conservation equations (i.e. gas phase model). The surface reactions are simulated by a surface model using the Mean-field approximation method (Kevrekidis et al., 1984). The gas phase model and the surface model are coupled through a mass flux boundary condition located at the top of the surface, i.e. above the pore’s inner walls.
The present work presents a multi-scale framework for oxygen carrier particle in Chemical-looping combustion. Nickel oxide is selected to be the solid reactant in oxygen carrier because it is a common oxygen carrier used for laboratory and pilot-scale demonstration plants and exhibits high reactivity and stability (Mattisson et al., 2006). For simplicity, the fuel gas in this work only contains carbon oxide. The proposed multi-scale model for Ni-based oxygen carrier used in CLC process is presented in the next section.
The following assumptions are adopted in the model: (1) Structure of the OC particles does not change during the reaction. (2) OC particles are considered isothermal. (3) Mass transport through the particle only occurs by diffusion. (4) OC particles are surrounded by fuel gas and the gas concentration remain constant during the CLC process.
2. MODEL DEVELOPMENT 2.1 Gas Diffusion Model The overall configuration of the multi-scale model is illustrated in Figure 1. The oxygen carrier is considered to be a spherical particle with numerous cylindrical pores. Fuel gas enters the particle through the inlet of the pore and diffuses in both axial (z) and radial (r) directions.
The two dimensional unsteady-state mass transport of molecules in the gas phase is described by the continuum equation: ∂Ci ∂Ci 1 ∂ ∂ 2 Ci = De,i r + De,i . (1) ∂t r ∂r ∂r ∂z 2
When a gas molecule reaches the inner wall of the pore (i.e., boundary in the r-direction), it will either stay in the gas phase or get adsorbed onto the wall surface. The
with the following initial and boundary conditions: 98
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Ci (t, z, r) t=0 ∂Ci (t, z, r) ∂z z=0 ∂Ci (t, z, r) ∂r r=0 ∂Ci (t, z, r) −De,i ∂z z=L
∂Ci (t, z, r) −De,i ∂r
r=R
=0
(2)
=0
(3)
=0
(4)
Kinetics parameters are obtained from density functional theory (DFT) simulations (see Kinetic Parameters section). Table 1 shows the parameters used in this study. The surface site density CT was published by Okazawa et al. (2007) whereas the operating conditions were taken from Ad´anez et al. (2012). These conditions are representative of pilot-scale CLC plants.
= kg,i Ci (t, z, r) z=L − Cibulk = −ka,i Ci (t, z, r) +
CT kr,i θi (t) NA
r=R
99
(5) θempty (t)
Table 1. Model Parameters Parameters (Unit) Temperature, T (K) Pressure, P (atm) Particle radius (Pore length), L (m) Pore radius, R (m) Porosity, ε Effective Diffusivity of CO, De,CO (m2 · s−1 ) Effective Diffusivity of CO2 , De,CO2 (m2 · s−1 ) Density of sites, CT (sites · m−2 ) bulk (mol · m−3 ) Bulk gas concentration, CCO bulk (mol · m−3 ) Bulk gas concentration, CCO 2 Sherwood number, Sh
z
(6)
where Ci is concentration of gas i in the pore; r and z are the radial and axial domains representing; R and L are the pore radius and pore length, respectively; De,i is the effective diffusivity of gas i in the pore; kg,i is the external mass transfer coefficient of gas species i; Cibulk is the bulk concentration of gas i; θempty is the surface coverage of empty sites on the surface; θi is the surface coverage of surface species i; ka,i is the adsorption rate constant of surface species i; kr,i is the reaction rate constant of surface species i; CT is the density of surface sites; NA is the Avogadro’s number.
Values 1173 1 1.0 × 10−4 1.0 × 10−8 0.4 9.775 × 10−7 7.796 × 10−7 1.33 × 1019 10.0 0.0 7
2.2 Surface Model
The effective diffusivity of gas i was calculated as a function of gas diffusivity and particle porosity: De,i = Dg,i ε2 (7) where ε is the pore porosity.
As shown in Figure 1, The pore surface is considered to be a finite square lattice. Each lattice site can be occupied by at most one molecule through adsorption. According to the results from DFT simulations, CO molecules tend to attach to the oxygen atoms on the exposed NiO surface and form a NiO − CO micro-structure. After formation of NiO − CO, CO captures the oxygen atom in NiO and becomes CO2 . The desorption of CO2 is considered to be much faster than the proceding reactions; thus, this step is not considered explicitly in the present model. Therefore, the reaction mechanisms used in the present work involves two steps: A CO molecule in gas phase adsorbs onto an empty site on the surface (i.e. an available oxygen atom); and the adsorbed CO reacts with NiO and produces CO2 :
When gas diffuses through the pore, molecular diffusion and Knudsen diffusion are both present. Therefore, gas diffusivity was calculated as follows: −1 1 1 + (8) Dg,i = Dm,i DK,i where the molecular diffusivity Dm,i and the Knudsen diffusivity DK,i are calculated using the following correlations (Fuller et al., 1966): 0.5 1.0 × 10−7 T 1.75 Mi−1 + MS−1 (9) Dm,i = 2 P ( i νi )1/3 + ( S νi )1/3 2 8RT (10) DK,i = r 3 πMi
k
a → NiO − CO∗ CO(g) + NiO∗ −−−
kr
NiO − CO∗ −−−→ Ni∗ + CO2 (g)
(12) (13)
where ∗ denotes an empty site on the surface.
The present mechanism assumes that the oxygen on the surface is in excess during the time period in the simulation and the CO2 molecule leaves the surface instantly after it was formed. Hence, CO molecules always have access to oxygen atoms and no CO2 molecule will stay on the surface (the surface coverage of CO2 is zero).
where T is the temperature in Kelvin; Mi is the molecular weight of gas i; MS is the molecular weight of the solvent S; P is the pressure in atm; νi is the diffusion parameters of the diffusing species. The external mass transfer coefficient kg was calculated using Sherwood number: Dm,i Sh (11) kg,i = dpar where Sh is the Sherwood number; dpar is the particle diameter.
Mean Field Approximation Mean-field approximation assumes that the adsorbed molecules are distributed homogeneously on the surface. The effect of the surface configuration on a single adsorbate is approximated by the average occupancy of lattice sites by any of the adsorbed molecules. The rate of change of the surface concentration of species i (Cisurf ) can be described as the rate of adsorption minus the rate of consumption:
The surface coverage fractions of empty sites and surface species i at each point in time across the axial domain is determined from the surface model (see Section 2.2 ). 99
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dCisurf (t) dt
n = ka,i Ci r=R 1 − θj (t) −
j=1
kr,i Cisurf (t)
(14)
k
Equation 14 can also be expressed in terms of the surface coverage fraction as follows: n dθi (t) NA = θj (t) ka,i Ci r=R 1 − dt CT j=1 − kr,i θi (t) (15)
i where Ci r=R is concentration of gas i above the surface and is estimated from the gas phase model; n is the number of surface species (n = 1 in this framework).
The sum of the coverage fraction of all surface species and empty sites will always be equal to one; therefore, the following equation is also valid in the Mean-field approximation: n θi (t) (16) 1 = θempty (t) + i=1
For the proposed reaction mechanisms, the following equations are considered in the present surface model: dθCO (t) NA = ka CCO r=R θempty − kr θCO (t) (17) dt CT 1 = θempty (t) + θCO (t)
(18)
Kinetic Parameters. Density functional theory (DFT) is carried out to calculate the kinetic parameters used in this work using Vienna Ab Initio Simulation Package (VASP). The projector-augmented wave (PAW) method (Bl¨ochl, 1994) with the generalized gradient approximation of Perdew-Burke-Ernzerhof (Perdew et al., 1996) is chosen to describe the system. To simulate the reactions, a 6layer nickel oxide slab model is constructed while the 2 bottom layers are fixed. Through structural relaxation and nudged-elastic-band method (Henkelman et al., 2000), we have established the 2-step carbon monoxide oxidation mechanism discussed in the previous section. 2.3 Model Coupling In the present work, the gap-tooth method (Gear et al., 2003) is adopted to compute the concentration gradients across the pore’s axial domain. As shown in Fig. 1, the tooth represents the surface model placed at equallyspaced discrete points in the axial domain of the multiscale model whereas the gap is the length between two subsequent teeth (i.e. surface models). The implicit backward Euler discretization has been employed to solve for the gas diffusion model. The number of teeth (surface models) considered in this system matches with the discretized nodes in the z -direction of the gas phase model. At time t = t , the surface coverage of molecule i on a tooth patch located at the specific node (z , R) is determined using the surface model (Eq. 17 to 18). Note that the concentration of gas species i at that same 100
node point Ci (t , z , R) represents the input to the surface model. The calculated coverage θi t=t at node (z , R) is needed to evaluate the gas phase boundary condition (Eq. 6) and provides the mass flux at node (z , R). The later is required to solve for the gas diffusion model (Eq. 1) for the next time interval. The number of teeth points required to solve the model is problem-specific. The present work used ten teeth to obtain a trade-off between numerical accuracy and computational cost. This coupling scheme is based on the interaction between the gas diffusion model and the surface model - the concentration of gas species i above the surface affects the surface configuration through the adsorption term in Eq. 15, which in turn determines the adsorption rates that enter into the boundary condition of the gas diffusion model (Eq. 6). 3. RESULTS AND ANALYSIS The multi-scale model presented in the previous section was implemented in Python 3.6; Each simulation requires approximately 574 CPU seconds (3.4GHz Intel i7-3770 processor). Because of the scarcity of similar OC particle models and comparable experimental data, model validation cannot be performed at this time. Therefore, we carried out a sensitivity analysis on the key modelling parameters to evaluate their effects on the system’s behavior. Table 2 shows the kinetic parameters obtained from DFT simulations. To obtain the reaction rate constants for this process, we screened multiple configurations and found the most stable structures from DFT analysis for reactants and products in the surface reaction system (not discussed here for brevity). Transition states of this 2-step-reaction are searched as saddle points, which are confirmed by frequency calculations. The rate constants are calculated using the same temperature used in the gas diffusion model (1173K); The parameters presented in Table 1 and 2 are considered to be the reference condition. The rate of reactions taking place inside the OC particle depends on several factors such as the physical properties of the particles (particle size, porosity, composition, etc.) and chemical kinetics of the reactions. The effects of the pore size and the adsorption rate constant on the CO conversion rate and the surface reaction rates were assessed using the concentration profile at the center point in the outlet (z = 0, r = 0) (see Fig. 1). As shown in Fig. 2 and 4 (red line), the CO concentration at that center point reached steady state within one second, whereas 30 seconds are needed for the CO2 concentration to reach steady state (see the red line in Fig. 3 and 5). These results suggest that the rate of gas diffusion is not controlling the rates of surface reactions that consume CO and produce CO2 . Table 2. Kinetic Parameters Parameters (Unit) CO adsorption rate constant, ka (m · s−1 ) CO2 formation rate constant, kr (s−1 )
Values 2.90 × 10−6 3.13
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Fig. 2. Effect of the varying pore radius on the evolution of CO concentration at the center of the particle.
Fig. 4. Effect of ka on the evolution of CO concentration at the center of the particle.
Fig. 3. Effect of the varying pore radius on the evolution of CO2 concentration at the center of the particle.
Fig. 5. Effect of ka on the evolution of CO2 concentration at the center of the particle.
3.1 Effect of the pore size
in the radial direction causes the CO2 concentration at the center of a larger pore to be lower than that of a smaller pore.
Figure 2 shows the impact of pore radius on the consumption rate of CO. The evolution of CO concentration at the center of the end of the pore (i.e. the center of the OC particle) was simulated using a +/- 10% change in the pore radius on each simulation; steady state was achieved within one second in all three cases (see Fig. 2). The result shows that CO concentration at steady state within a larger pore is higher than that obtained for a smaller pore. This behavior is expected because increasing pore size also promotes mass transport, thus enhancing the diffusion process. On the other hand, concentration of CO2 reached steady state after 120 seconds in all three simulations using a +/- 10% change in the pore radius. Compared to Fig. 2, increasing the CO concentration did not lead to an increase in the steady state CO2 concentration. However, note that the concentration at the center point will also be affected by the radial gas diffusion. That is, a larger pore radius leads to a longer distance between the inner wall of the pore (i.e. pore surface) to that center point. Hence, a longer period of time is required for the product generated on the pore surface to reach the center of the pore. Therefore, it is reasonable to consider that the gas diffusion taking place 101
3.2 Effect of the adsorption rate constant The limiting step for reactions in the present model is CO adsorption as the adsorption rate constant ka is 106 magnitude smaller than the CO2 formation rate constant kr . To analyze the effect of this variable on the extent of reaction inside the particle, several simulations were carried out using different adsorption rate constants ranging from -10% to +10%. The results show that the concentration of CO reached steady state within one second. The steady state concentration of the reactant gas CO increased by 13% when the adsorption rate constant decreased by 10% (see Fig. 4). Correspondingly, when ka decreased, the concentration of gas product CO2 at steady state also decreased, as a smaller ka means CO molecules in the gas phase are less likely to adsorb onto the surface; and the decrease in available adsorbed CO molecules will slow down the CO2 formation reaction.
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and H2 ) will be used to replace the pure CO stream considered in this work; also more reaction details will be considered; Kinetic Monte Carlo (KMC) method will be employed to simulate the many-body interactions taking place in the pore’s surface. REFERENCES
Fig. 6. Effect of the adsorption rate constant ka on the CO surface coverage in the axial direction. Furthermore, the surface coverage of CO at equally-spaced teeth points in the axial direction was evaluated after the concentration of CO and CO2 both reached steady state (see Fig. 6). As expected, the surface coverage of CO at the inlet of the pore (Pore length = 1.0 × 10−4 ) was higher than that at the end of the pore due to the higher inlet concentration. Moreover, increasing the adsorption rate constant increased the surface coverage at each tooth point, which agrees with the decrease in the steady state concentration of CO (Fig. 4) as more CO molecules will diffuse from the gas phase and adsorb onto the pore surface. Note that the CO surface coverage did not reach the steady state after 120 seconds, whereas the CO concentration reached the steady state within 1 second. That is, the increasing amount of available CO molecules on the surface did not increase its consumption rate substantially. This indicates that, although the adsorption rate constant is significantly smaller than the reaction rate constant, the latter may be the rate controlling parameter in the initial stages of this process. 4. CONCLUSION A multi-scale particle model framework consisting of a gas diffusion model and a surface reaction model has been developed for oxygen carrier particles used in a typical CLC system. Chemical reaction kinetics is explicitly considered in the surface model using reaction rate constants obtained from DFT analysis. NiO was selected to be the solid reactant that provides oxygen, and a pure CO stream was assumed to be the gas reactant (fuel gas). This model was then used to predict the influence of pore size and adsorption rate constant on the steady state concentration profile of the gas species inside the particle. Currently, due to the lack of similar OC particle models or experimental data for the simulated NiO system, model validation will be considered in the future work. The sensitivity analysis showed reasonable tendencies and responses to changes in key modelling parameters, which indicates the feasibility of this model. The present multi-scale particle model framework will be further developed in the following aspects: Syngas (CO 102
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