Dynamic Optimization Applied for Modelling and Optimal Control of a Packed Bed Reactor for Chemical-Looping Combustion

Dynamic Optimization Applied for Modelling and Optimal Control of a Packed Bed Reactor for Chemical-Looping Combustion

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12th IFAC Symposium on Dynamics and Control of Process including Biosystems 12th IFACSystems, Symposium on Dynamics and Control of Process Systems, including Biosystems 12th IFAC Symposium on Dynamics and Control of Florianópolis SC, Brazil, April 23-26, 2019 Process Systems, including Biosystems 12th IFAC Symposium on Dynamics Controlonline of Available at www.sciencedirect.com Florianópolis - SC,including Brazil, April 23-26,and 2019 12th IFACSystems, Symposium on Dynamics Control of Process Systems, Biosystems Florianópolis - SC,including Brazil, April 23-26,and 2019 Process Biosystems Process Systems, Biosystems Florianópolis -- SC, Brazil, 23-26, Florianópolis SC,including Brazil, April April 23-26, 2019 2019 Florianópolis - SC, Brazil, April 23-26, 2019

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IFAC PapersOnLine 52-1 (2019) 850–855 Dynamic Optimization Applied for Modelling and Optimal Control of aa Packed Dynamic Optimization Applied for Modelling and Optimal Control of Dynamic Optimization Applied for Modelling and Optimal Control of a Packed Packed Bed Reactor for Chemical-Looping Combustion Dynamic Optimization Applied for Modelling and Optimal Control of a Packed Bed Reactor for Chemical-Looping Combustion Bed Reactor for for Chemical-Looping Combustion Dynamic Optimization Applied Modelling and Optimal Control of a Packed Bed Reactor forLucio*, Chemical-Looping Combustion Marco Luis Ricardez-Sandoval ** Bed Reactor for Chemical-Looping Combustion Marco Lucio*, Luis Ricardez-Sandoval Marco Lucio*, Luis Ricardez-Sandoval ** **

Marco Lucio*, Lucio*, Luis Luis Ricardez-Sandoval Ricardez-Sandoval ** ** Marco Marco Lucio*, Luis Ricardez-Sandoval ** Waterloo *Chemical Engineering Department, University of Waterloo, *Chemical Engineering Department, University of Waterloo, Waterloo *Chemical Engineering Department, University of Waterloo, Waterloo Canada (Tel: +1 5198884567; e-mail: [email protected]). Canada (Tel: +1 5198884567; e-mail: [email protected]). *Chemical Engineering Department, University of Waterloo, Waterloo *Chemical Engineering Department, University of Waterloo, Canada (Tel: +1 5198884567; e-mail: [email protected]). ** Chemical Engineering Department, University of Waterloo,Waterloo Waterloo *Chemical Engineering Department, University ofof Waterloo, Waterloo ** Chemical Engineering Department, University Waterloo, Waterloo Canada (Tel: +1 5198884567; e-mail: [email protected]). Canada (Tel: +1 5198884567; e-mail: [email protected]). ** Chemical Engineering Department, University of Waterloo, Waterloo Canada (Tel: +1 5198884567x38667; e-mail: [email protected]). Canada (Tel: +1 5198884567; e-mail: [email protected]). Canada (Tel: +1 e-mail: [email protected]). ** Chemical Department, University of ** Chemical Engineering Department, University of Waterloo, Waterloo, Waterloo Waterloo Canada (Tel:Engineering +1 5198884567x38667; 5198884567x38667; e-mail: [email protected]). ** Chemical Department, e-mail: University of Waterloo, Waterloo Canada (Tel: +1 [email protected]). Canada (Tel:Engineering +1 5198884567x38667; 5198884567x38667; e-mail: [email protected]). Abstract: Chemical-looping Combustion (CLC) has recently emerged as a promising technology to curb Canada (Tel: +1 5198884567x38667; e-mail: [email protected]). Abstract: Chemical-looping Combustion (CLC) has recently emerged as promising technology to Abstract: Chemical-looping Combustion (CLC) recently emerged as aadirect promising technology to curb curb CO The novelty of CLC resides on itshas inherent ability of avoid contact between the fuel 2 emissions. CO emissions. The novelty of CLC resides on its inherent ability of avoid direct contact between the fuel 2 Abstract: Chemical-looping Combustion (CLC) has recently emerged as a promising technology to curb Abstract: Chemical-looping Combustion (CLC) recently emerged as a promising technology to curb CO emissions. The novelty of CLC resides on itshas inherent ability of avoid direct contact between the fuel stream. This study presents a dynamic modelling and2the air, while producing a highly concentrated CO 2 Abstract: Chemical-looping Combustion (CLC) has recently emerged as a promising technology to curb and the air, while producing a highly concentrated CO stream. This study presents a dynamic modelling 2 CO emissions. The novelty of CLC resides on its inherent ability of avoid direct contact between the 2 CO2controllability emissions. The novelty CLC resides on technical its inherent abilityThis ofofavoid direct between the fuel fuel the air, while producing ademonstrates highly concentrated CO2 stream. study presents a dynamic modelling and study thatof the feasibility a fixed bedcontact CLC reactor to produce CO emissions. The novelty CLC resides on technical its inherent abilityThis ofof direct between the fuel and study that the feasibility aa fixed bed CLC reactor to produce 2controllability the air, while producing aademonstrates highly concentrated study presents aa dynamic modelling 2 and the air, high while producing highly concentrated COoxidation stream. This study presents dynamic modelling controllability study thatof demonstrates the technical feasibility ofavoid fixed bedcontact CLC reactor to produce 2 stream. a constant temperature air stream during theCO stage. The heterogeneous model, which and the air, high whiletemperature producing highly concentrated This study presents a dynamic modelling aand constant air stream during the oxidation stage. heterogeneous model, which 2 stream. and controllability study that ademonstrates demonstrates theintechnical technical feasibility of fixed bedthe CLC reactor to produce controllability study that the feasibility of aaThe fixed bed CLC to produce aconsiders constant high temperature air stream during theCO oxidation stage. The heterogeneous model, which mass and heat transport resistances the oxygen carrier particle and bulkreactor fluid phase, was and controllability study that demonstrates the technical feasibility of a fixed bed CLC reactor to produce considers mass and heat transport resistances in the oxygen carrier particle and the bulk fluid phase, was constantusing highdata temperature airthestream stream during theaoxygen oxidation stage. The heterogeneous model, which aaconsiders constant high temperature during the oxidation stage. The heterogeneous model, which mass and heat transport resistances in the carrier particle the bulktofluid phase, was validated reported inair literature. Also, sensitivity analysis wasand conducted gain insight on avalidated constantusing highdata temperature during theaaoxygen oxidation stage. The heterogeneous model, which reported in literature. Also, sensitivity analysis was conducted gain insight on considers mass and heat transport resistances in the the oxygen carrier particle and the bulkto fluid phase, was considers mass and heat transport resistances in carrier particle bulk phase, was validated using data reported inairthe thestream literature. sensitivity analysis wasand conducted tofluid gain insight on system’s behaviour. Furthermore, an optimal Also, control problem was formulated tothe identify optimal control considers mass data and heat transport resistances in theaaoxygen carrier particle bulkto was system’s behaviour. Furthermore, optimal control problem was formulated to identify optimal control validated using reported in the thean literature. Also, sensitivity analysis wasand conducted tofluid gainphase, insight on validated using reported in literature. sensitivity analysis was conducted gain insight on system’s behaviour. Furthermore, an optimal control problem was formulated tothe identify optimal control profiles that candata improve the efficiency of thisAlso, process. validated using data reported in the literature. Also, a sensitivity analysis was conducted to gain insight on profiles that can improve the efficiency of this process. system’s behaviour. Furthermore, an optimal control problem was formulated to identify optimal control system’s behaviour. Furthermore, an optimal profiles that can improve the efficiency of thiscontrol process.problem was formulated to identify optimal control Keywords: CO capture, Dynamic modelling, Chemical-looping Combustion, Clean coal technology, 2 improve system’s behaviour. Furthermore, an optimal control problem was formulated to identify optimal control © 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. profiles that can the efficiency of this process. Keywords: capture, Dynamic modelling, Chemical-looping profiles thatCO can2 improve efficiency of this process. Keywords: CO capture, the Dynamic modelling, Chemical-looping Combustion, Combustion, Clean Clean coal coal technology, technology, Climate change profiles that can2mitigation. improve the efficiency of this process. Climate change mitigation. Keywords: CO capture, Dynamic modelling, Chemical-looping Combustion, Clean coal technology, technology, 2 Keywords: CO2mitigation. capture, Dynamic modelling, Chemical-looping Combustion, Clean coal Climate change Keywords: CO capture, Dynamic modelling, Chemical-looping Combustion, Clean coal technology, 2mitigation. Climate change Climate change mitigation. Climate change mitigation. oxidized OC with fuel (e.g. methane or syngas) regenerates the oxidized OC (e.g. or regenerates the 1. INTRODUCTION. oxidized OC with with afuel fuel (e.g. methane methane or syngas) syngas) regenerates OC and delivers highly concentrated CO2 stream, freethe of 1. INTRODUCTION. 1. INTRODUCTION. OC and delivers a highly concentrated CO stream, free of 2 oxidized OC with with afuel fuel (e.g. methane methane or syngas) syngas) regenerates the oxidized OC (e.g. or regenerates freethe of OC and delivers highly concentrated CO2 stream, nitrogen. The continuous rising of greenhouse gases (GHG) emissions 1. INTRODUCTION. 1. INTRODUCTION. oxidized OC with fuel (e.g. methane or syngas) regenerates the nitrogen. The continuous rising of greenhouse gases (GHG) emissions OC and delivers a highly concentrated CO stream, free 2 stream, free of OC and delivers a highly concentrated CO of nitrogen. The continuous rising of greenhouse gases (GHG) emissions 2 1. INTRODUCTION. due fossil fuel combustion is alarming. Carbon dioxide (CO 2) OC and delivers a highly concentrated CO stream, free of CLC process can be carried out using 2fluidized bed or due fossil fuel is Carbon dioxide (CO 2)) The nitrogen. The continuous rising of gases emissions nitrogen. The continuous risingand of greenhouse greenhouse gases (GHG) emissions dueone fossil fuel combustion combustion is alarming. alarming. Carbon dioxide 2 The CLC process can be out using bed is of many GHG has the property of(GHG) absorb and(CO emit The CLC canPacked be carried carried using fluidized fluidized bed or or nitrogen. The continuous rising of greenhouse gases (GHG) emissions fixed bed process reactors. bed out reactors avoid solid-gas is one of many GHG and has the property of absorb and emit due fossil fuel combustion is alarming. Carbon dioxide (CO ) 2) due fossil fuel combustion is alarming. Carbon dioxide (CO is one ofradiation many GHG andwavelength has the property ofemitted absorb andEarth; emit 2 fixed bed reactors. Packed bed reactors avoid solid-gas infrared in the range by The CLC process can be carried out using fluidized bed or The CLC process can be carried out using fluidized bed or fixed bed reactors. Packed bed reactors avoid solid-gas due fossil fuel combustion is alarming. Carbon dioxide (CO separation and allow the specification of a more compact infrared in wavelength range by Earth; 2) is one of many GHG and has the property of absorb and emit is one ofradiation many GHG and has the property ofemitted absorb andin emit infrared radiation inofthe the wavelength range emitted by Earth; CLC process canPacked be carried using bed or separation and allow the specification of aafluidized more compact thus, the increase carbon dioxide concentration the The fixed bed reactors. Packed bed out reactors avoid solid-gas fixed bed reactors. bed reactors avoid separation and allow the more solid-gas compact is one of many GHG and has the property of absorb and emit design due to anspecification increase in ofoperating pressure thus, the increase of carbon dioxide concentration in the infrared radiation in the wavelength range emitted by Earth; infrared inofthe wavelength emitted era by in Earth; thus, theradiation increase carbon dioxide concentration the reactor fixed bed reactors. Packed bed reactors avoid solid-gas reactor design due to an increase in operating pressure atmosphere, from 280 ppm during the range pre-industrial to 406 separation and allow the specification of a more compact separation andal.,allow ofoperating a implementing more compact reactor design due tothean increase pressurea infrared radiation inof wavelength emitted era by in Earth; (Noorman et 2007). Onspecification the other in hand, atmosphere, from 280 280 ppm during the range pre-industrial era to 406 thus, the2017 increase ofthe carbon dioxide concentration in the thus, the increase carbon dioxide concentration the atmosphere, from ppm during the pre-industrial to 406 andal., allow thean specification ofoperating a implementing more compact (Noorman et 2007). On the other hand, a ppm in has been directly associated with the rise in separation reactor design due to increase in pressure reactor design due to an increase in operating pressure (Noorman et al., 2007). On the other hand, implementing thus, the increase of carbon dioxide concentration in the packed bed reactor requires multibed configuration to providea ppm in 2017 has been directly associated with the rise in atmosphere, from 280 ppm duringassociated theStudies pre-industrial erarise to that 406 atmosphere, 280 ppm during the pre-industrial era to 406 ppm in average 2017from has been directly with in (Noorman reactor design due to an increase in operating pressure packed bed reactor requires multibed configuration to provide Earth’s surface temperature. have the shown et al., 2007). On the other hand, implementing (Noorman etreactor al., 2007). Onmultibed thethe other hand, implementing requires configuration to turbine; provideaa atmosphere, from 280 ppm duringassociated theStudies pre-industrial erarise to that 406 apacked high bed temperature stream to downstream gas Earth’s average surface temperature. Studies have shown shown that ppm in average 2017 has been directly associated with the rise in ppm in 2017 been directly the in Earth’s surface temperature. have et al., 2007). On the other hand, implementing a apacked high temperature stream to the downstream gas turbine; current fossil has fuel consumption for powerwith generation is (Noorman bed reactor requires multibed configuration to provide packed reactor multibed configuration to turbine; provide a high bed temperature stream to theprocess downstream ppm in average 2017 been directly associated the risethat in duringrequires the reduction fuel slipgas may occur current fossil has fuel consumption forStudies powerwith generation is additionally, Earth’s average surface temperature. Studies have shown that Earth’s surface temperature. have shown current fossil fuel consumption for power generation is packed bed reactor requires multibed configuration to provide additionally, during the reduction process fuel slip may occur responsible for almost 30% of all anthropogenic CO2 aaadditionally, high temperature stream to the theprocess downstream gas turbine; high temperature stream to downstream gas turbine; the may occur Earth’s average surface temperature. Studies have shown CO that should beduring avoided toreduction accomplish high fuel CO2 slip efficiency. responsible forfuel almost 30% of of for all anthropogenic CO current consumption power generation is current fossil fuel consumption for power generation is22 and responsible for almost all anthropogenic aand high temperature stream to theprocess downstream gas turbine; should be avoided to accomplish high CO efficiency. emissionsfossil (Halmann and 30% Steinberg, 2000; Mattisson et al., 2 slip additionally, during the reduction process fuel slip may occur additionally, during the reduction fuel may occur efficiency. and should be avoided to accomplish high CO 2 current fossil fuel consumption for power generation is emissions (Halmann and Steinberg, 2000; Mattisson et al., responsible for almost 30% of all anthropogenic CO responsible for almost of all anthropogenic emissions (Halmann and 30% Steinberg, 2000; Mattisson etCO al.,22 additionally, process fuel slip may occur Studies on CLC has the been mostly focused development 2008). and should should beduring avoided toreduction accomplish highon COthe efficiency. 2 efficiency. and be avoided to accomplish high CO 2 responsible for almost of all anthropogenic on has mostly focused on the development 2008). emissions and Steinberg, 2000; Mattisson al., emissions (Halmann (Halmann and 30% Steinberg, 2000; Mattisson et etCO al.,2 Studies Studies on CLC CLC has been been mostly focused on development 2008). and should be avoided to accomplish high COthe of suitable OC materials; on the other hand, very few studies 2 efficiency. emissions (Halmann and Steinberg, 2000; Mattisson et al., of OC materials; on the hand, very few studies studies One promising alternative to curb CO emissions is carbon Studies on has mostly focused on the 2008). Studies on CLC CLC has been been mostly focused onCLC the development 2008). of suitable suitable OC materials; the other other hand, verydevelopment few on dynamic modelling andon performance for packed beds One promising promising alternative alternative to to curb curb CO CO22 emissions is carbon emissions is carbon One on CLC has been mostly focused onCLC the development 2 2008). on dynamic modelling andon performance for CLC packed beds capture and sequestration (CCS). This concept entails the Studies of suitable OC materials; on the other hand, very few studies of suitable OC materials; the other hand, very few studies on dynamic modelling and performance for packed beds have been reported (Noorman et al. 2011; Han et al. 2013). In capture and sequestration (CCS). This concept entails the One promising alternative to curb CO emissions is carbon One promising to curb CO emissions is carbon capture andofsequestration (CCS). This22CO concept entails the of suitable OC materials; on the other hand, very few studies have been reported (Noorman et al. 2011; Han et al. 2013). In generation aalternative highly concentrated stream (>90%) 2 on dynamic modelling and performance performance forHan CLC packed beds on dynamic modelling and CLC beds have beenstudy, reported (Noorman etoptimization al. 2011;for et packed al. 2013). In One promising alternative to curb CO emissions is carbon a recent a multi-period formulation with generation of a highly concentrated stream (>90%) 2CO 2 capture and sequestration (CCS). This concept entails the capture and (CCS). for Thisinjection concept the on (>90%) generation ofsequestration a highly concentrated CO dynamic modelling and performance for CLC packed beds 2 stream ahave recent study, a multi-period optimization formulation with making it economically feasible inentails geologic beenstudy, reported (Noorman et al. 2011; 2011; Han et al. al. 2013). 2013). In been reported (Noorman al. Han et In a recent a multi-period optimization formulation with capture sequestration (CCS). for Thisinjection concept the have the objective to maximize heat et recovery was presented (Han et making it feasible in geologic generation of highly concentrated CO (>90%) 2 generation of highly concentrated CO stream (>90%) making and it economically economically feasible for injection inentails geologic 2 stream have beenstudy, reported (Noorman al. 2011; Han et al. 2013). In the objective to maximize maximize heat et recovery was presented (Han et formations, suchaa as depleted oil and gas fields (Klara et al., the a recent study, a multi-period optimization formulation with a recent a multi-period optimization formulation with objective to heat recovery was presented (Han et generation of a highly concentrated CO stream (>90%) al., 2016). In that work, the control variables were assumed to formations, such as depleted oil and gas fields (Klara et al., 2 making it economically feasible for injection in geologic making it economically feasible forgas injection in currently geologic formations, such as depleted oil and fields (Klara et al., aal., recent study, a multi-period optimization formulation with 2016). In that work, the control variables were assumed to 2003). The most advanced technological pathways the objective to maximize heat recovery was presented (Han et the objective maximize recovery wasTo presented (Han to et 2016).constant In to that work, theheat control variables were making it economically feasible forgas injection in currently geologic remain during each period. theassumed authors’ 2003). The most advanced technological pathways currently formations, such as depleted oil and and gas fields (Klara et al., al., al., formations, such oil fields (Klara et 2003). The advanced pathways the objective to maximize heat recovery was presented (Han et remain constant during each period. To the authors’ available formost CCSas indepleted powertechnological generation are post-combustion al., 2016). In that work, the control variables were assumed to al., 2016). In that work, the control variables were assumed to remain constant during each period. To the authors’ formations, such as depleted oil and gas fields (Klara et al., knowledge, a control study that shows the dynamic operability available for CCS in power generation are post-combustion 2003). The most advanced technological pathways currently 2003). The technological pathways currently available formost CCSadvanced in power generation are post-combustion al., 2016). In that work, the control variables were assumed to knowledge, a control study that shows the dynamic operability capture, pre-combustion capture, and oxy-fuel combustion. To knowledge, remain constant during each period. To the authors’ remain constant during eachshows period. To theoperability authors’ a control study 2003). The advanced technological pathways currently CLC packed beds is not that available inthe thedynamic literature. Thus, it capture, pre-combustion capture, and combustion. To available formost CCS in power generation are post-combustion available for power generation are post-combustion capture, pre-combustion capture, and oxy-fuel oxy-fuel combustion. To of remain constant during eachshows period. To theoperability authors’ of CLC packed packed beds is not not that available inthe thedynamic literature. Thus, it it date, most ofCCS the in CCS technologies available are energy knowledge, aatocontrol study knowledge, control study that shows the dynamic operability of CLC beds is available in the literature. Thus, available for CCS in power generation are post-combustion is important gather more insight in CLC dynamic modeling date, most of the CCS technologies available are energy capture, pre-combustion capture, and oxy-fuel oxy-fuel combustion. To capture, pre-combustion and combustion. date, most of the CCScapture, technologies available are energy knowledge, a control study that shows the dynamic operability is important to gather more insight in CLC dynamic modeling intensive. Chemical-looping combustion (CLC), which can To be is of CLC packed beds is not available in the literature. Thus, it of CLC packed beds is not available in the literature. Thus, it important to gathertomore insightdemonstrate in CLC dynamic capture, pre-combustion capture, and oxy-fuel combustion. optimization further the modeling technical intensive. Chemical-looping combustion (CLC), which can be date, most of technologies available are energy date, most ofas the the CCS technologies available areattractive energy intensive. Chemical-looping combustion (CLC), which can To be and of CLC packed bedsto not available in the dynamic literature. Thus, it and optimization toismore further demonstrate the modeling technical categorized an CCS oxy-fuel alternative, is an is important to gather more insight in CLC dynamic modeling is important to gather insight in CLC and optimization further demonstrate the technical date, mostChemical-looping ofas CCS technologies available areattractive energy of this technology to capture CO2. categorized an oxy-fuel alternative, is intensive. combustion (CLC), which can be intensive. Chemical-looping combustion (CLC), which can be feasibility categorized as the an simultaneously oxy-fuel alternative, is an an attractive is important gather insight in CLC dynamic feasibility oftothis this technology to capture capture CO2. technology that can produce power using a gas and optimization tomore further demonstrate the modeling technical and optimization to further demonstrate the technical feasibility of technology to CO2. intensive. Chemical-looping combustion (CLC), which can be technology that can simultaneously produce power using a gas categorized as an oxy-fuel alternative, is an attractive categorized as can andirect oxy-fuel isand anfuel, attractive technology simultaneously produceairpower using a gas and optimization to further demonstrate the technical turbine and that avoid contactalternative, between hence In this work we present a sensitivity analysis on key feasibility of this technology to capture CO2. feasibility of this technology to capture CO2. categorized as an oxy-fuel alternative, is an attractive turbine and avoid direct contact between air and hence In this this work work we we present present aa sensitivity sensitivity analysis analysis on on key key technology simultaneously produce using aacore gas technology that can simultaneously produce power using gas In turbine and that avoid direct contact between airpower and fuel, fuel, feasibility of and this technology capturestudy CO2. to improve the production ofcan nitrogen dilutions is circumvented. Thehence parameters, an optimalto control the technology that can simultaneously produce power using a gas the production of nitrogen dilutions is circumvented. The core parameters, and an optimal control study to improve the turbine and avoid direct contact between air and fuel, hence In this work we present a sensitivity analysis on key turbine and avoid direct contact between air and fuel, hence In this work we present a sensitivity analysis on key the production of nitrogen is circumvented. The to core andexhaust an optimal to the improve the idea is the intervention of dilutions a metal/metal oxide, referred as parameters, duration of an hot aircontrol streamstudy during oxidation turbine and avoid direct contact between air and fuel, hence In this work we present a sensitivity analysis on key idea is the intervention of a metal/metal oxide, referred to as duration of an exhaust hot air stream during the oxidation the production of (OC). nitrogen dilutions is circumvented. circumvented. The core parameters, and an optimal optimal control study to improve the the of nitrogen dilutions is core parameters, and an study to improve the ideaproduction is the intervention of a metal/metal referred to as duration of an hot aircontrol stream during the oxidation oxygen carriers The oxidation ofoxide, the OC isThe highly process using a exhaust dynamic model for a packed bed reactor that the production of (OC). nitrogen dilutions is circumvented. The core parameters, and an optimal control study to improve the oxygen carriers The oxidation of the OC is highly process using a exhaust dynamic model for a packed packed bed reactor that idea is the intervention of a metal/metal oxide, referred to as duration of an exhaust hot air stream during the oxidation idea is the intervention of a metal/metal oxide, referred to as duration of an hot air stream during the oxidation oxygen carriers (OC). The oxidation of the OC is highly process using a dynamic model for a bed reactor that exothermic, which is used to heat up the air stream that drives was adapted from the literature (Han et al. 2013). idea is the intervention of a metal/metal oxide, referred to as duration of an exhaust hot air stream during the oxidation exothermic, which is used to heat up the air stream that drives was adapted from the literature (Han et al. 2013). oxygen carriers (OC). The oxidation of the OC that is highly highly process usingfrom dynamic model(Han for aaetpacked packed bed reactor reactor that that oxygen carriers (OC). The oxidation the OC is process using aa dynamic model for bed which is used to heat up theof airthe stream drives adapted the literature al. 2013). aexothermic, gas turbine for power generation whereas reduction of the was oxygen carriers (OC). The oxidation the OC that is highly usingfrom a dynamic model(Han for aet bed reactor that aexothermic, for generation whereas reduction of which is to up the air stream drives was the al. exothermic, which is used used to heat heat up theof airthe stream that drives was adapted adapted from the literature literature (Han etpacked al. 2013). 2013). a gas gas turbine turbine for power power generation whereas the reduction of the the process exothermic, is used to heat up the airthe stream that drives aa gas for generation whereas reduction of gas turbine turbinewhich for power power generation whereas the reduction of the the was adapted from the literature (Han et al. 2013). a gas turbine for power generation whereas the reduction of the

Copyright © 2019, 2019 IFAC 850Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © IFAC (International Federation of Automatic Control) Copyright © 2019 IFAC 850 Copyright 2019 responsibility IFAC 850Control. Peer review©under of International Federation of Automatic Copyright © 2019 2019 IFAC IFAC 850 Copyright © 850 10.1016/j.ifacol.2019.06.168 Copyright © 2019 IFAC 850

2019 IFAC DYCOPS Florianópolis - SC, Brazil, April 23-26, 2019 Marco Lucio et al. / IFAC PapersOnLine 52-1 (2019) 850–855

851

2. PROCESS DESCRIPTION. In CLC the use of an OC has the purpose of completing a cycle between two reactors. The CLC process is composed of an oxidation process (also known as air reactor) and a reduction process (also known as fuel reactor). This method of burning carbon-based fuels has the advantage of inherent sequestration of carbon dioxide without the need for additional energy consumption requirements. In the oxidation (R1), the OC is in direct contact with an air stream; thus, OC particles are oxidised by oxygen (exothermic reaction). 2𝑀𝑀𝑀𝑀𝑦𝑦 𝑂𝑂𝑥𝑥−1 + 𝑂𝑂2 → 2𝑀𝑀𝑀𝑀𝑦𝑦 𝑂𝑂𝑥𝑥

(R1)

In the reduction process, the OC particles are regenerated via the use of fuel reacting with the oxygen available in the OC to produce CO2 and water (R2). Note that CLC minimizes NOx formation due the lack of flame and low operating temperatures (<1200 °C) (Hossain and De Lasa, 2008). 𝐶𝐶𝑛𝑛 𝐻𝐻2𝑚𝑚 + (2𝑛𝑛 + 𝑚𝑚)𝑀𝑀𝑀𝑀𝑦𝑦 𝑂𝑂𝑥𝑥 → 𝑛𝑛𝐶𝐶𝐶𝐶2 + 𝑚𝑚𝐻𝐻2 𝑂𝑂 + (2𝑛𝑛 + 𝑚𝑚)𝑀𝑀𝑀𝑀𝑦𝑦 𝑂𝑂𝑥𝑥−1

Figure 1. Schematic of the packed bed CLC reactor.

(R2) 3. PROBLEM FORMULATION.

In principle, CLC can achieve high overall energy efficiencies if the operation takes places at high pressures (approx. 20 bar), which can be achieved with a packed bed reactor design.

3.1 Model description. A dynamic model adapted from that reported by Han et al. (2013) has been used in this work to study the transient behaviour of this process. The model is a dynamic heterogeneous model, which accounts for mass and heat transport resistances from the bulk fluid phase to the OC particle phase and within the particle. In this study, we focus on a one-dimensional heterogeneous model, i.e. only the axial direction in the reactor is considered. The heterogeneous model considered in this work is shown in equations (1)-(11). The assumptions considered in the development of this model are: i) spherical particles of the OC, ii) constant volume of the particle, iii) macroscopically uniform particle structure that is not affected by the reaction, iv) uniform OC distribution within the particle and the reactor. The gas concentrations and temperature inside the pores of the particle are assumed to be functions of OC radial direction and axial direction. Also, the model assumes that the gas at any point inside the particle is at the same temperature as the solid, and that the thermal conductivity of the gas is negligible compared to the solid. Similarly, a perfectly well mixed feed stream in the crosssectional area of the reactor is considered; hence, radial effects across the reactor are neglected. In addition, the model assumes that there is considerable difference between solid and fluid conditions. The intraparticle resistance is also considered (eq. 6 and 7), since limitations to diffusive transport inside the pores can significantly limit the reaction rates inside large particles (Han et al., 2013).

The fixed bed CLC reactor operation is a batch process; the reactions take place on a single reactor, operated in successive cycles involving oxidation, heat recovery, and reduction (see Figure 1). In this set-up, the reactor’s outlet temperature and composition are used to control the transient switching between each process in the cycle. As shown in Figure 1, the oxidation is initiated by feeding air into the reactor. As the reaction evolves, the exothermicity of the oxidation will generate a heat front within the reactor. The system is switched to heat recovery when the heat front reaches the reactor’s outlet. During this process, the reactor’s outlet stream is used to drive a gas turbine for power generation. The heat recovery process is stopped when the outlet air stream’s temperature drops, which is an indication that the reaction is completed due full oxidation of the OC (conversion), and the air stream cannot longer be used to feed the turbine. The reactor is then purged, and the reduction reaction process is carried out. During this process, a fuel gas stream is fed into the reactor until complete (reduction) conversion is reached. This can be detected when a fuel slip in the outlet stream occurs and the CO2 capture efficiency (recovery and purity) diminishes. The reactor is then purged before returning to the oxidation process to complete the cycle. The downstream gas turbine requires specific conditions to operate properly, e.g. solids concentration, temperature of the driving gas. Fluctuations in the reactor exhaust stream during the transient heat removal can damage the turbine by causing thermal/mechanical stress thus shortening the lifetime of the turbine. Hence, appropriate heat management of the CLC reactor is needed. The dynamic model used to study the transient behaviour of the packed bed CLC oxidation process is presented next.

Reactor’s mass and energy balances: 𝜀𝜀𝑏𝑏

𝜕𝜕𝐶𝐶𝑖𝑖 𝜕𝜕𝜕𝜕

+

𝜕𝜕𝐹𝐹𝑖𝑖 𝜕𝜕𝜕𝜕

𝜀𝜀𝑏𝑏 𝐶𝐶𝑝𝑝,𝑓𝑓 𝐶𝐶𝑇𝑇

851

𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕

= 𝜀𝜀𝑏𝑏

𝜕𝜕

𝜕𝜕𝜕𝜕

(𝐷𝐷𝑎𝑎𝑎𝑎,𝑖𝑖

+ 𝐶𝐶𝑝𝑝,𝑓𝑓 𝐹𝐹𝑇𝑇

𝜕𝜕𝜕𝜕

𝜕𝜕𝐶𝐶𝑖𝑖 𝜕𝜕𝜕𝜕

) + 𝑘𝑘𝑐𝑐,𝑖𝑖 𝑎𝑎𝑣𝑣 (𝐶𝐶𝑐𝑐,𝑖𝑖 |𝑅𝑅𝑅𝑅 − 𝐶𝐶𝑖𝑖 )

(1)

=

𝜕𝜕𝜕𝜕 𝜕𝜕 𝜕𝜕𝜕𝜕 𝜀𝜀𝑏𝑏 (𝜆𝜆𝑎𝑎𝑎𝑎 ) 𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕

+ ℎ𝑓𝑓 𝑎𝑎𝑣𝑣 (𝑇𝑇𝑐𝑐 |𝑅𝑅𝑅𝑅 − 𝑇𝑇)

(2)

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Boundary conditions for the reactor phase: 𝜕𝜕𝐶𝐶𝑖𝑖

𝜀𝜀𝑏𝑏 𝐷𝐷𝑎𝑎𝑎𝑎,𝑖𝑖 𝜀𝜀𝑏𝑏 𝜆𝜆𝑎𝑎𝑎𝑎

| 𝜕𝜕𝜕𝜕 𝑧𝑧=0

𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕

𝜕𝜕𝐶𝐶𝑖𝑖

| 𝜕𝜕𝜕𝜕 𝑧𝑧=𝐿𝐿

= (𝐹𝐹𝑖𝑖 |𝑧𝑧=0 − 𝑦𝑦𝑖𝑖,𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝐹𝐹𝑖𝑖𝑖𝑖 )/𝐴𝐴𝑐𝑐

(3)

|𝑧𝑧=0 = (𝑇𝑇𝑐𝑐 |𝑧𝑧=0 − 𝑇𝑇𝑖𝑖𝑖𝑖 )𝐶𝐶𝑝𝑝,𝑓𝑓 𝐹𝐹𝑇𝑇 /𝐴𝐴𝑐𝑐

=

𝜕𝜕𝜕𝜕

| 𝜕𝜕𝜕𝜕 𝑧𝑧=𝐿𝐿

Table 1. Properties of the oxygen carrier in this work Han et al. (2013) Active material NiO Support Al2O3 Weight fraction of the metal oxide (wt.%) 0.21 Solid porosity 0.5 Particle size (mm) 1.4 Melting point of reduced metal (°C/K) 1455/1728 The kinetic model considered for the OC particle is as follows:

(4)

=0

(5)

Mass and energy balances for the particle phase: 𝜀𝜀𝑐𝑐

𝜕𝜕𝐶𝐶𝑐𝑐,𝑖𝑖 𝜕𝜕𝜕𝜕

=

1

𝜕𝜕

(𝐷𝐷𝑒𝑒,𝑖𝑖 𝑟𝑟𝑐𝑐 2

𝑟𝑟𝑐𝑐 2 𝜕𝜕𝑟𝑟𝑐𝑐

𝜕𝜕𝐶𝐶𝑐𝑐,𝑖𝑖 𝜕𝜕𝑟𝑟𝑐𝑐

) + 𝜌𝜌𝑠𝑠 𝛴𝛴𝑅𝑅𝑖𝑖

((1 − 𝜀𝜀𝑐𝑐 )𝜌𝜌𝑠𝑠 𝐶𝐶𝑝𝑝,𝑠𝑠 + 𝜀𝜀𝑐𝑐 𝐶𝐶𝑝𝑝,𝑐𝑐 𝐶𝐶𝑇𝑇,𝑐𝑐 𝜌𝜌𝑠𝑠 𝛴𝛴𝑅𝑅𝑖𝑖 (−𝛥𝛥𝐻𝐻𝑖𝑖 )

𝜕𝜕𝑇𝑇𝑐𝑐 𝜕𝜕𝜕𝜕

=

𝜕𝜕𝑇𝑇 (𝑟𝑟 2 𝑐𝑐) 𝑟𝑟𝑐𝑐 2 𝜕𝜕𝑟𝑟𝑐𝑐 𝑐𝑐 𝜕𝜕𝑟𝑟𝑐𝑐 𝜆𝜆𝑠𝑠 𝜕𝜕

(6)

𝑅𝑅𝑖𝑖 = 𝛴𝛴 𝑟𝑟𝑖𝑖

+

For the oxidation process ri is defined as follows: (7)

−𝐸𝐸𝑎𝑎

𝑟𝑟𝑂𝑂2 = 𝑎𝑎0 (1 − 𝑋𝑋)𝑘𝑘0 𝑒𝑒 ( 𝑅𝑅∗𝑇𝑇 ) 𝐶𝐶𝑂𝑂2 𝐶𝐶′𝑁𝑁𝑁𝑁

Boundary conditions for the particle phase: 𝜕𝜕𝐶𝐶𝑐𝑐,𝑖𝑖 𝜕𝜕𝑟𝑟𝑐𝑐

|𝑟𝑟𝑐𝑐 =0 =

−𝐷𝐷𝑒𝑒,𝑖𝑖 −𝜆𝜆𝑠𝑠

𝜕𝜕𝐶𝐶𝑐𝑐,𝑖𝑖

𝜕𝜕𝑇𝑇𝑐𝑐

𝜕𝜕𝑟𝑟𝑐𝑐

| 𝜕𝜕𝑟𝑟𝑐𝑐 𝑅𝑅𝑝𝑝

𝜕𝜕𝑇𝑇𝑐𝑐 𝜕𝜕𝑟𝑟𝑐𝑐

|𝑟𝑟𝑐𝑐=0 = 0

|𝑅𝑅𝑝𝑝 = 𝑘𝑘𝑐𝑐,𝑖𝑖 (𝐶𝐶𝑐𝑐,𝑖𝑖 |𝑅𝑅𝑝𝑝 − 𝐶𝐶𝑖𝑖 ) = ℎ𝑓𝑓 (𝑇𝑇𝑐𝑐 |𝑅𝑅𝑅𝑅 − 𝑇𝑇)

𝐹𝐹𝑖𝑖𝑖𝑖 = 𝐺𝐺 ∗ 𝐴𝐴𝑐𝑐 ∗

𝐶𝐶𝑖𝑖𝑖𝑖

𝜌𝜌𝑎𝑎𝑎𝑎𝑎𝑎

(12)

𝑑𝑑𝑑𝑑(𝑟𝑟,𝑧𝑧) 𝑑𝑑𝑑𝑑

(8)

=

(13)

(2∗𝑟𝑟𝑟𝑟)

(14)

𝐶𝐶′𝑁𝑁𝑁𝑁

where a0 is the initial specific surface area of the OC (0.002 m²/kg OC); X (r, z) is the OC conversion, which depends on the radial position within the particle and the axial position within the reactor, respectively. k0 is the frequency factor for OC oxidation reaction (4.6e-1 m/s) whereas Ea is the activation energy (22,000 J/mol); R is the gas constant (8.3145 J/mol K), and C’Ni is the initial Ni concentration in the OC (0.21 kg Ni/kg OC). Table 2 shows the base case conditions for the oxidation phase obtained from Spallina et al. (2015). These conditions were used in the present analysis because they report data for the complete CLC process cycle.

(9) (10) (11)

Ci represents the concentration of the gas species i in the fluid phase (mol/m³), T is the temperature in the fluid phase (K), Cc,i is the concentration of gas species i in the particle (mol/m³), Tc represents the temperature inside the particle (K), r is the radial spatial domain within the particle whereas z is the axial spatial domain in the reactor; Rp and L are the particle radius and bed length (m), respectively. Fi is the molar flow rate of the gas species i entering the reactor (mol/s), Fin is the molar flow rate of gas species i at the inlet (9,101 mol/s), G is the mass flux of the gas phase (6.0 kg/m²/s); εb (0.37) and εc (0.5) are the bed and particle porosities, respectively; likewise, Dax,i (3.8756e-3 m²/s) and λax (8.0265 W/m/K) are the axial dispersion and heat dispersion coefficients of species i, respectively; kc,i (0.833 m/s) and hf (1,476 W/m²/K) are the mass and heat transfer coefficients between bulk fluid and OC particle, respectively; av is the external particle surface area per unit volume (2,700 1/m); Cp,f is the heat capacity of the gas mixture of the fluid phase (34.53 J/mol K); CT (332.72 mol/m³) and FT (40,197 mol/s) are the total concentration and total flow rate, respectively, whereas Cin (76.52 mol/m³) is the molar concentration of gas species i entering the reactor; yi,feed is the mole fraction of the gas species in the feed; Ac is the cross sectional area of the reactor tube (23.76 m²); Ri is the rate of reaction (mol/m³s); ρs is the density of the oxygen carrier (4,480 kg/m³) and ρair is the density of air at the reactor’s inlet conditions; De,i is the effective diffusion coefficient of species i (2.788e-7 m²/s); λs is the thermal conductivity of the OC (0.0028 W//m K); ΔHi is the heat of reaction (-479,400 J/mol); Cp,c (31.63 J/mol/K) and Cp,s (1,055 J/kg/K) are the heat capacities of the gas mixture of the solid phase and the oxygen carrier, respectively. CT,c is the total gas concentration in solid phase (332.72 mol/m³). The model considered in this work represents a high-pressure fixed bed reactor with Ni/NiO as OC supported in alumina. The kinetic data for this system was obtained from Dueso et al. (2012). Table 1 shows the properties of the OC implemented in this work.

Table 2 Base case and operating conditions for this work Reactor configuration Length (m) Diameter (m) Initial bed temperature (°C/K) Initial O2 concentration in bed (mol/m³) Oxygen stream Inlet temperature (°C/K) Pressure (bar) Air composition (wt. %)

11 5.5 600/873 0

450/723 20 O2 23% N2 76%

4. RESULTS AND ANALYSIS. The dynamic heterogeneous model presented in the previous section was implemented in Python 3.6 using PYOMO library. The model was discretized using centered differences; the resulting in a set of non-linear algebraic equations, which were solved using the interior-point optimization algorithm combined with the linear solver MA97. Previous studies have used the same finite difference discretization scheme (Han et al. 2013). The number of discretization elements per domain were determined a priori from trial and error simulations, i.e. the number of points was increased until no further improvement in the model predictions were observed while keeping a reasonable computational time. Accordingly, 18 and 14 discretization elements were employed for the reactor’s axial domain (z) and the particle’s radius (r), respectively. Likewise, for the base-case operating condition reported above, the number of discrete elements for the time domain was set to 30 for a simulation timespan of 5,400 seconds. This 852

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resulted in a model composed of 90,000 nonlinear algebraic equations that need to be solved simultaneously. This problem was solved using the direct transcription dynamic optimization approach. Each simulation required on average 1,000 CPU seconds (2.5GHz i5-7200U processor).

853

4.2 Sensitivity analysis. To gain insight on the system’s transient behaviour. A dynamic sensitivity analysis on key variables and model parameters was performed on the CLC oxidation process.

4.1 Model validation. The dynamic model was validated by comparing the resulting oxidation temperature profiles to those reported in the literature (Noorman et al., 2007; Han et al., 2016). To the author´s knowledge, there are no other studies or reports available that provide the required information to further validate our simulation results (e.g. particle and/or reactor conversion and concentration profiles). Figure 2 shows the conversion profile within the particle at different positions within the reactor. The results suggest that the particles closer to the reactor’s inlet have not fully reached conversion, whereas the OC particles far away from the reactor’s inlet are almost fully converted due the heat front enhancing the reaction rate within the reactor. The results indicate that the concentration quickly reaches steady state since diffusion across the particle is not the controlling step in the oxidation process; this observation agrees with recent reports in the literature (You et al., 2018).

Fig.

3. Temperature profile at different times; z is the axial reactor position. 4.2.1 Effect of the air inlet mass flux.

The air mass flux plays a key role in controlling the reactor’s performance; at lower mass fluxes we may reach the OC’s melting point harming the fixed bed whereas higher mass fluxes may undershoot the minimum operating temperature for the gas turbine. Thus, the maximum achievable temperature in the reactor is highly sensitive to the air mass fluxes at the inlet. To analyse its effect on the reactor’s performance, a change in the air mass flux of +/- 10% was considered. As shown in Figure 4, higher temperatures are reached when lower air mass inlet fluxes are considered. Also, the results show that higher conversion is reached faster in the oxidation process (not shown for brevity), an aspect that is crucial in the heat recovery process for the downstream gas turbine.

Fig. 2. Conversion profile of the particle (OC) in the radial direction r at 5,400 seconds; z is the axial reactor position. The temperature profiles within the reactor at different times are shown in Figure 3. As shown in this figure, the exothermic reaction can reach temperatures above 800 °C, which is the minimum temperature for driving the downstream gas turbine (Brooks, 2000). As expected, the results show that the reactor’s temperature increases drastically when the conversion in the OC is relatively low (not shown for brevity). Furthermore, after 1,000 seconds, the temperature drops as the conversion increases within the OC particles, which is expected for the CLC oxidation process. Based on the above, the present dynamic model captures the main characteristics of the oxidation process in CLC.

Fig. 4. Effect of varying the air mass flux on the outlet temperature profile. Selecting a suitable air inlet temperature (450°C) may be instrumental in the CLC oxidation process. At higher mass fluxes, the air stream cools down the CLC packed bed. Likewise, increasing the inlet temperature would translate in 853

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greater heat recovery. Thus, a crucial aspect in the reactor’s performance is maintaining an air mass flux that allows the heat transfer from the exothermic reaction to be greater than the cooling caused by the air mass flux moving within the reactor. Note that the air inlet temperature of 450 °C is related to the preheating process between the air fed to the reactor and the gas turbine exhaust (500-600°C). Future work in this research will consider the integration of the turbine and the preheater alongside the packed bed CLC reactor.

system’s performance since it causes significant nonlinear changes in the reactor’s temperature.

4.2.2 Effect of the reactor’s length. Changes on the reactor’s main design parameters such as the reactor’s length were also carried out by changing this parameter by +/- 10%. Figure 5 shows similar profiles as Fig. 4, with slightly lower temperature values.

Fig. 6. Effect of varying the specific surface area on the outlet temperature profile 4.2.4 Optimal air mass flux control. An adequate control in the oxidation process will translate in a more efficient energy production by the downstream turbine thus diminishing the energy penalty that entails CCS (Spallina et al. 2013). As mentioned above, the air inlet mass flux (G) has a significant impact on the CLC oxidation process. This section presents an optimal controllability study on the CLC packed bed reactor using the air mass flux as the manipulated variable. The goal is to extend the heat recovery within this process by maintaining the reactor’s outlet stream temperature constant at 800°C (𝑇𝑇800°𝐶𝐶 ) during the oxidation process. This optimal control problem can be formulated as a dynamic optimization problem and is as follows:

Fig. 5. Effect of varying the reactor length on the outlet temperature profile. Figure 5 also shows that the peak temperature occurs at different times while using different reactor sizes, being 85 seconds the maximum difference between peak temperatures. This condition would affect the timing of the switching from the oxidation stage to the heat recovery stage when the two stages are performed, i.e. if the change is done towards the end of the oxidation process, we would be wasting energy production in the gas turbine, but if it is done too early we would damage the turbine due low air inlet temperature. Note that at around 4,800 seconds the temperature in the reactor converge towards the air inlet temperature (450 °C); this is expected since the OC is almost depleted (fully oxidized) and the heat produced has been consumed.

2 min ∑𝐾𝐾 𝑘𝑘=0(𝑇𝑇800°𝐶𝐶 − 𝑇𝑇(𝑘𝑘𝑘𝑘𝑘𝑘)) 𝐺𝐺(𝑘𝑘)

(15)

Subject to: 𝐶𝐶𝐶𝐶𝐶𝐶 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚, 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 (1 − 14) 𝑡𝑡 = [0, Δ𝑡𝑡, 2𝛥𝛥𝛥𝛥, … . . , 𝑘𝑘𝑘𝑘𝑘𝑘, … … , 𝐾𝐾𝐾𝐾𝐾𝐾] ˅ k = 1, 2, 3, ….,K 3 ≤ 𝐺𝐺(𝑘𝑘𝑘𝑘𝑘𝑘) ≤ 7

4.2.3 Effect of the OC’s surface area. The properties of the oxygen carriers vary depending on particular characteristics of the particle, e.g. size, preparation, supported material. The specific surface area of the OC is key in the oxidation process. Figure 6 shows the reactor’s temperature response at the outlet when this parameter was changed by +/- 10%. The results show that the temperature peak increases as the OC’s specific surface area is increased. This behaviour is expected since more surface area would enhance the reaction between the OC and the oxygen. This figure also shows that this parameter is highly sensitive to the

Fig. 7. Reactor’s exhaust air stream temperature profile and air mass flux control profile. 854

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The optimization problem converged in 600 seconds using the interior-point optimization algorithm. The results correspond to the base case operating conditions presented in Table 2. Figure 7 shows the reactor’s outlet stream temperature profile when the optimization is performed and when manual step changes in the air mass flux were implemented, which is the common engineering practice. Moreover, figure 7 presents the control variable profiles of the air mass flux for both cases scenarios. The results show that an optimal control profile is able to maintain a fairly constant outlet reactor temperature close to its desired set-point value. On the other hand, significant deviations in the outlet temperature are observed when a manual air mass flux profile is considered. As mentioned above, having significant changes in the reactor’s outlet stream temperature may harm the downstream turbine; thus, an optimal air mass flux profile allows for a smoother and efficient turbine operation.

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REFERENCES Brooks, F.J. (2000). GE Gas Turbine Performance Characteristics. Schenectady, NY. Dueso, C., Ortiz, M., Abad, A., Garcia-Labiano, F., de Diego, L.F., Gayan, P., Adanez, J. (2012). Reduction and Oxidation Kinetics of Nickel-based Oxygen-carriers for Chemical-looping Combustion and Chemical-looping Reforming. Chemical Engineering Journal, 188, 142-154. Halmann, M., Steinberg, M., (2000). Greenhouse Gas Carbon Dioxide Mitigation: Science and Technology. Lewis Publishers, Boca Raton, Fl. Han, L., Zhou, Z., Bollas, G.M. (2013). Heterogeneous Modeling of Chemical-Looping Combustion. Part 1: Reactor Model. Chemical Engineering Science, 104,233249. Han, L., Bollas, G.M. (2016). Dynamic Optimization of fixed bed chemical-looping combustion processes. Energy, 112, 1107-119. Hossain, M.M., De Lasa, H.I. (2008). Chemical-looping Combustion (CLC) for Inherent Separation-a Review. Chemical Engineering Science, 63, 4433-4451. Klara, S.M., Srivastava, R.D., McIlvried, H.G. (2003). Integrated Collaborative Technology Development Program for CO2 Sequestration in Geologic Formations. Department of Energy R&D. Energy Conv. Manage, 44, 2699-2712, USA. Mattisson, T., Johansson, M., Jerndal, E., Lyngfelt, A. (2008). The reaction of NiO/NiAl2O4 particles with alternating methane and oxygen. The Canadian Journal of Chemical Engineering 86, 756–767. Noorman, S., van Sint Annaland, M., Kuipers, J.A.M. (2007). Packed Bed Reactor Technology for Chemical Looping Combustion, Industrial & Engineering Chemistry Research, 46, 4212-4220. Noorman, S., Gallucci, F., van Sint Annaland, M., Kuipers, J.A.M. (2011). A Theoretical Investigation of CLC in Packed Beds. Part 1: particle model, Chemical Engineering Journal, 167, 297-307. Spallina, V., Gallucci, F., Romano, M.C., Chiesa, P., Lozza, G., van Sint Annaland. (2013). Investigation of Heat Management for CLC of Syngas in Packed Bed Reactors. Chemical Engineering Journal, 225. Spallina, V., Chiesa, P., Martelli, E., Gallucci, F., Romano, M.C., Lozza, G. (2015). Reactor Design and Operation Strategies for a Large-scale Packed-bed CLC Power Plant with Coal Syngas. International Journal of Greenhouse Gas Control, 36. You, H., Yuan, Y., Li, J., Ricardez-Sandoval, L. (2018). Multiscale Model for CO2 Capture: A Nickel-based Oxygen Carrier in Chemical-looping Combustion. 10th IFAC International Symposium on Advance Control of Chemical Processes, Shenyang, Liaoning, China.

Note that the air mass flux profile obtained from problem (15) is non-trivial since it depends on the stage of the oxidation process, e.g. the time at which the system reaches the set-point for the first time. Thus, by lowering the mass flux we are hindering the cool down of the packed bed caused by convection with the air stream going across the reactor. Han et al. (2016) showed similar results when they performed a multiperiod optimization by using the air inlet flow rate (mass flux) as decision variable on every period and maximizing the heat recovery stage. A key difference is that they assume that the air mass flux would remain constant throughout the oxidation process. This work demonstrates that the efficiency in the heat recovery process can be further improved if optimal time-dependent control profiles are implemented for the oxidation process, as shown in Figure 7. 5. CONCLUSIONS The dynamic model and optimal control of a packed bed reactor for CLC have been presented. The heterogeneous model was solved using Python/PYOMO. Using the base case reactor and conditions, the model was validated, showing reasonable behaviour in both, the concentrations profiles and the temperature time-dependant profiles. The model was then subjected to a sensitivity analysis of few parameters that have never been studied before for this process. The results showed reasonable tendencies and responses to those changes, which captures the expected transient behaviour of this process. This study showed that the air mass flux is the most convenient parameter to adjust in an effort to optimally control the reactor’s outlet stream temperature and extend the heat recovery stage. Results from the present optimal control formulation showed that this control approach may improve the energy production in the downstream gas turbine. Thus, this work provides more insight into the dynamic operation of packed bed CLC technology and shows that this process is a promising and economically attractive CCS alternative to diminish CO2 emissions to the atmosphere. Future work in this research considers modelling of the reduction stage that involves CO2 generation. Also, the oxidation and reduction stages will be added to this present oxidation model to investigate effective switching strategies for the complete packed bed CLC cycle process. 855