Dynamic Modeling and Control Studies of a Two-Stage Bubbling

Article pubs.acs.org/IECR

Dynamic Modeling and Control Studies of a Two-Stage Bubbling Fluidized Bed Adsorber-Reactor for Solid−Sorbent CO2 Capture Srinivasarao Modekurti,†,‡ Debangsu Bhattacharyya,*,†,‡ and Stephen E. Zitney‡ †

Department of Chemical Engineering, West Virginia University, Morgantown, West Virginia 26506, United States AVESTAR Center, National Energy Technology Laboratory, U.S. Department of Energy, Morgantown, West Virginia 26507, United States

‡

ABSTRACT: A one-dimensional, nonisothermal, pressure-driven dynamic model has been developed for a two-stage bubbling fluidized bed (BFB) adsorber-reactor for solid−sorbent carbon dioxide (CO2) capture using Aspen Custom Modeler (ACM). The BFB model for the flow of gas through a continuous phase of downward moving solids considers three regions: emulsion, bubble, and cloud-wake. Both the upper and lower reactor stages are of overflow-type configuration, i.e., the solids leave from the top of each stage. In addition, dynamic models have been developed for the downcomer that transfers solids between the stages and the exit hopper that removes solids from the bottom of the bed. The models of all auxiliary equipment such as valves and gas distributors have been integrated with the main model of the two-stage adsorber reactor. Using the developed dynamic model, the transient responses of various process variables such as CO2 capture rate and flue gas outlet temperatures have been studied by simulating typical disturbances such as change in the temperature, flow rate, and composition of the incoming flue gas from pulverized coal-fired power plants. In control studies, the performance of a proportional-integral-derivative (PID) controller, feedback-augmented feedforward controller, and linear model predictive controller (LMPC) are evaluated for maintaining the overall CO2 capture rate at a desired level in the face of typical disturbances.

1. INTRODUCTION With the increase in power demand all over the world, it is anticipated that fossil fuel consumption will continue to grow in the coming decades. In the U.S., it is estimated that consumption of fossil fuels will increase by 27% in the next 20 years.1 When generating electricity, the combustion of fossil fuels is the major source for the emission of CO2, a key greenhouse gas. The U.S. Department of Energy’s Carbon Capture Simulation Initiative (CCSI) is focused on commercialization of CO2 capture technologies from discovery to development, demonstration, and ultimately the widespread deployment to hundreds of power plants. One element of the CCSI is focused on improving the operation and control of carbon capture systems since this can have a significant impact on the extent and the rate at which commercial-scale capture processes will be scaled-up, deployed, and used in the years to come. As part of this work, dynamic simulation and control models, methods, and tools are being developed for CO2 capture and compression processes and their integration with a baseline commercial-scale supercritical pulverized coal (SCPC) power plant. Solid−sorbent-based postcombustion CO2 capture technology was chosen as the first industry challenge problem for CCSI because significant work remains to define and optimize the reactors and processes needed for successful sorbent capture systems. The traditional aqueous amine systems for CO2 capture suffer from high energy penalties due to the latent heat for water evaporation that needs to be provided in the regenerator reboiler.2,3 Due to the low energy requirement for regeneration, solid−sorbents are capable of reducing the parasitic power load associated with capture systems that remove CO2 from flue gas. In moving and fluidized bed © 2013 American Chemical Society

processes, the heat load for regeneration decreases with an increase in the sorbent capacity.4 In view of this, the current paper focuses on development of a dynamic model of a solid− sorbent CO2 adsorber-reactor and an analysis of its control and transient performance with respect to several typical process disturbances. Bubbling fluidized beds (BFBs) are an attractive option for solid−sorbent CO2 capture as these beds offer higher mass and heat transfer due to large contact area.5 Samanta et al.6 have presented a comprehensive review of postcombustion of CO2 capture using solid sorbents. Comparison of different solid sorbents and a technoeconomic analysis have been discussed in this review paper. Abanades et al.7 have evaluated the sorbent cost and performance in CO2 capture systems in comparison to the well-established monoethanolamine (MEA) systems. A few experimental and modeling studies can be found in the existing literature on CO2 capture using different solid sorbents. Khatri et al.8 have experimentally studied the thermal and chemical stability of regenerable amine sorbent for CO2 capture. Roy et al.9 have designed and constructed a three-stage fluidized bed countercurrent adsorber for chemisorption of CO2 using porous granular calcium oxide particles. From the experimental studies, the authors have concluded that the superficial gas velocity, solids velocity, and weir height have strong influence on CO2 removal efficiency. The study shows that 75% removal of CO2 is possible using the developed three-stage fluidized bed adsorber. Fang et al.10 have conducted experiments in dual Received: Revised: Accepted: Published: 10250

March 16, 2013 June 18, 2013 June 23, 2013 June 24, 2013 dx.doi.org/10.1021/ie400852k | Ind. Eng. Chem. Res. 2013, 52, 10250−10260

Industrial & Engineering Chemistry Research

Article

Figure 1. A schematic of the two-stage BFB adsorber-reactor for CO2 capture with overflow-type configuration.

reactor for the sorption of CO2 using hydrated lime particles. The simulated results of CO2 removal efficiency are compared with their experimental data. Recently, Lee and Miller20 have presented a one-dimensional (1-D) three region model of a BFB adsorber-reactor for solid−sorbent CO2 capture. In recent years, a large body of research has investigated the dynamic modeling and control of solvent systems for CO2 capture.21−25 However, to the best of the authors’ knowledge, there are very few papers in the open literature that have focused on dynamic modeling of BFB reactors for solid− sorbent CO2 capture processes. Dynamic models of BFBs have been presented by Ikonen and Kortel26 for a coal combustion system, Yuan et al.27 for nonisothermal reacting BFBs, and Mahecha-Boteroet et al.28 for a catalytic reactor respectively. Bollini et el.29,30 have studied the dynamics of CO2 adsorption on amine adsorbents in the packed bed reactors. In addition, the dynamic model of a packed-bed solid−sorbent CO2 capture process has been presented by Gaspar and Cormos31 and Li.32 Lawal al.33 have investigated postcombustion CO2 capture in a full scale 500 MWe subcritical power plant through dynamic simulations. Harrison et al.34 have designed a closed-loop control system via proportional-integral-derivative and adaptive controllers to control the voidage of the BFB by manipulating the gas flow rate. In this work, development of a one-dimensional nonisothermal pressure-driven dynamic model for a solid−sorbent CO2 capture process using a two-stage BFB adsorber-reactor is presented. Various control strategies are implemented to study the response of the system for a disturbance in the flue gas flow rate. The developed control system is then used to study the

BFBs to capture CO2 using calcium-based sorbent. The authors have shown experimentally that about 95% CO2 capture is feasible. Li et al.11 have developed nanolayered solid−sorbents for CO2 capture. From their studies, the authors have concluded that the nanolayered solid−sorbents require less heat for regeneration than CO2 scrubbing. Monazam et al.4 have studied equilibrium and adsorption kinetics of CO2 experimentally using solid-supported-amine sorbent. Zhao et al.12 have investigated the thermal stability of a supported amine sorbent and continuous CO2 capture from flue gases in a dual fluidized bed reactor. Hasan et al.13 have modeled, simulated, and optimized pressure swing adsorption and vacuum adsorption for CO2 capture. Comprehensive theoretical foundations of bubbling fluidized beds were laid out by Kunii and Levenspiel.14 Kobayashi et al.15 developed models for predicting the spatial variation of bubble distribution, solid circulation, and mixing in bubbling fluidized beds. Yi et al.16 experimentally studied the performance of potassium-based dry solvent in a fast fluidized bed carbonator and a BFB regenerator under continuous solid circulation mode. Garg et al.17 have developed a continuum CFD model for potassium-based solid−sorbent CO2 capture. Choi et al.18 have developed a simplified model for an entrained-bed absorber and a bubbling-bed regenerator for CO2 capture using a particle population balance model. From the parametric studies using the developed models, the authors have concluded that the temperature has significant effect on CO2 capture efficiency in comparison to gas velocity, bed height, and moisture content. Mohanty and Meikap19 have developed a two-phase model for the countercurrent three-stage BFB 10251

dx.doi.org/10.1021/ie400852k | Ind. Eng. Chem. Res. 2013, 52, 10250−10260


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transient response in the face of other disturbances that are typical of operating power plants.

2. DYNAMIC MODEL DEVELOPMENT The dynamic model of a two-stage BFB adsorber-reactor for solid sorbent CO2 capture has been developed in Aspen Custom Modeler (ACM) by modifying the steady-state singlestage BFB model presented by Lee and Miller.20 A brief description of the BFB model that is relevant to the current dynamic model is given here mainly focusing on the key differences from the work of Lee and Miller.20 For more detailed discussions of the single-stage steady-state model developed in ACM, the readers are referred to the work of Lee and Miller.20 The schematic of the two-stage BFB adsorber is shown in Figure 1. A countercurrent configuration is considered for the gas and solid sorbent flows. Flue gas enters at the bottom of the lower bed (ADSB), whereas fresh sorbent enters at the top of the upper stage (ADSA). The clean flue gas from the upper stage goes to the stack. In this overflow-type configuration, the solids from the upper stage go to a downcomer before entering the lower bed. Finally, the solids go to an exit hopper before exiting to the regeneration process. The gas is distributed through a distributor in between the stages. The exit pressure losses for the downcomer are accounted through a nozzle equation. A single dynamic model has been developed by integrating the bed model with the controllers and the models of the auxiliary equipment/hardware including the immersed heat exchangers, distributors, downcomer, flue gas stack, and exit hopper. To remove the heat generated due to adsorption, internal heat exchangers have been considered in both the stages. Dynamics of the heat exchanger have been neglected in this work. Details about the heat exchanger model can be found in the work of Lee and Miller.20 The following assumptions have been made while developing the dynamic model: i. Transport variables vary only in the axial direction. ii. Each BFB stage consists of three regions, namely bubble, emulsion, and cloud-wake, and each region exhibits plug-flow behavior. iii. Bubbles are spherical in shape and move upward with gas velocity. iv. Elutriation and entrainment are negligible. v. Heat capacities for gas and solids and density for solids are constants. vi. Particle size throughout the bed is constant. vii. Solids always leave from the top of the bed (overflowtype configuration). viii. Dynamics in the tube side of the immersed heat exchangers are neglected. 2.1. BFB Stage Model. The BFB is divided into three regions i.e., bubble, cloud-wake, and emulsion. A schematic of the model structure in a control volume is shown in Figure 2. At each CV, solid adsorption takes place in both cloud-wake and emulsion regions. Mass and heat transfer takes place between the regions and also between the phases in each region. In particular, mass and heat exchange is considered between emulsion and cloud-wake regions in both gas and solid phases, whereas the mass and heat exchange between bubble and cloud-wake regions is considered to take place only in the gas phase. An additional bulk term is considered to account for the exchange of mass and heat between the bubble and

Figure 2. A schematic of the model structure (redrawn from Lee and Miller20).

emulsion regions. Additional details about the bed characterization can be found in the work of Lee and Miller.20 2.1.1. Mass and Energy Conservation Equations. Material and energy balances have been written for all the chemical components in all three regions for both gas and solid phases. The kinetics used in this work have been taken from Lee et al.35 The kinetic model assumes that the adsorption of CO2 and water occurs through a three-reaction scheme. H2O(g ) ↔ H2O(phys)

(1)

R 2NH+2

2R 2NH + CO2 (g) ↔

−2

+ R 2NCO

(2)

R 2NH + CO2 (g) + H 2O(phys) ↔ R 2NH+2 + HCO−3 (3)

The first reaction is for the formation of physisorbed water, the second reaction represents the formation of bicarbonate ions, and the third reaction represents the formation of carbamate ions. In the model development, CO 2 , H 2 O, and N 2 components have been considered for gaseous phase and carbamate, bicarbonate, and adsorbed water considered for the solid phase. 2.1.1.1. Bubble Region. Since it is assumed that the bubble phase contains no solids, the mass and energy balances have been written for gaseous species alone. Equations 4 and 5 are written for the species and energy conservations, respectively. ∂(δxACb , j , x) ∂t

=−

∂(yb , j , i Gb , x) ∂x

− δxAKbc , j , x(Cb , j , x − Cc , j , x) + K g , bulk , j , x (4)

∂(Cbt , xAδxCp , g , b , x(Tg , b , x − Tref ))

=−

∂t ∂(Gb , xCp , g , b , x(Tg , b , x − Tref )) ∂x

− AδxHbc , x(Tg , b , x − Tg , c , x) + Hg , bulk , x

(5)

In eq 4, the first term represents the accumulation of species i, the second term represents the axial flow of gas through bubble region, and the third and last terms represent flow between the bubble and cloud-wake regions and emulsion and bubble regions, respectively. Equation 5 represents the bubbleregion energy balance. Similar to eq 4, the terms in eq 5 10252



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represent the heat flows between the bubble region and the other two regions. Detailed explanations about the terms other than the accumulation terms can be found in Lee and Miller.20 2.1.1.2. Cloud-Wake Region. The cloud-wake region consists of both gaseous and solid components. In addition to the mass and heat transfer, solid-sorption reaction takes place here. The mass and energy balances for both gas and solid components are given below. Gas phase Component balance: ∂(δxαxACc , j , x) ∂t

∂(A(1 − αxδx − δx)εdCe , j , x) ∂t = δxAKce , j , x(Cc , j , x − Ce , j , x) − K g , bulk , j , x + (1 − αxδx − δx)(1 − εd , x)Arg , e , j , x

Energy balance: ∂(Cet , xA(1 − αxδx − δx)εdCp , g , e , x(Tg , e , x − Tref )) ∂t = AδxHce , x(Tg , c , x − Tg , e , x) − Hg , bulk , x

= δxAKbc , j , x(Cb , j , x − Cc , j , x)

− A(1 − αxδx − δx)(1 − εd , x)ρs aphp , x(Tg , e , x − Ts , e , x)

− δxAKce , j , x(Cc , j , x − Ce , j , x) + αxδx(1 − εd , x)Arg , c , j , x

+ A(1 − αxδx − δx)(1 − εd , x) ×

(6)

∑ (rg ,e ,j , xCp, g , j , e , x(Tg , e , x − Tref )) (11)

j

Energy balance:

Solid phase Adsorbed species balance:

∂(Cct , xAαxδxεdCp , g , c , x(Tg , c , x − Tref ))

∂(A(1 − αxδx − δx)(1 − εd , x)ρs ne , i , x)

∂t = AδxHbc , x(Tg , b , x − Tg , c , x) − AδxHce , x(Tg , c , x − Tg , e , x)

= −A

− Aαxδx(1 − εd , x)ρs aphp , x(Tg , c , x − Ts , c , x) + αxδx(1 − εd , x)A ∑ (rg , c , j , xCp , g , j , c , x(Tg , c , x − Tref ))

∂(Aαxδx(1 − εd , x)ρs nc , i , x)

= −A

(12)

∂t ∂(Je , x (Cp , s(Ts , e , x − Tref ) + hads , e , x)) ∂x

+ Hs , bulk , x + Aδxρs Kce , bs , x(Cp , s(Ts , c , x − Tref )

− Ks , bulk , x − Aδxρs Kce , bs , x(nc , i , x − ne , i , x)

+ Aαxδx(1 − εd , x)rs , c , i , x

+ Ks , bulk , x + Aδxρs Kce , bs , x(nc , i , x − ne , i , x)

∂(A(1 − αxδx − δx)(1 − εd , x)ρs Cp , s(Ts , e , x − Tref ))

Solid phase Adsorbed Species balance:

∂x

∂x

Energy balance:

(7)

∂t ∂(Jc , x nc , i , x)

∂t ∂(Je , x ne , i , x)

+ A(1 − αxδx − δx)(1 − εd , x)rs , e , i , x

j

= −A

(10)

+ hads , c , x − (Cp , s(Ts , e , x − Tref ) + hads , e , x))

(8)

− A(1 − αxδx − δx)(1 − εd , x) ×

Energy balance:

∑ (rg , e , j , xCp, g , j , e , x(Tg , e , x − Tref )) j

∂(Aαxδx(1 − εd , x)ρs Cp , s(Ts , c , x − Tref ))

= −A

+ A(1 − αxδx − δx)(1 − εd , x)

∂t ∂(Jc , x (Cp , s(Ts , c , x − Tref ) + hads , c , x))

× ρs aphp , x(Tg , e , x − Ts , e , x) + πdHX ht , xΔTHX , xNHX Cr (13)

∂x

2.1.2. Hydrodynamic Correlations. All hydrodynamic correlations used in this work are the same as those used by Lee and Miller.20 2.2. Auxiliary Equipment Submodels. 2.2.1. Distributor Design. The pressure drops in the gas distributors have been calculated using standard equations for an orifice and are assumed to be 30% of the bed pressure drop.5 The number of holes used in each distributor is 2200 per m2. 2.2.2. Valve Design. It is assumed that the solids flow rates to the upper adsorber stage and from the exit hopper are regulated by (throttle) valves. The following equation is used to model these valves.36

− Hs , bulk , x − Aδxρs Kce , bs , x(Cp , s(Ts , c , x − Tref ) + hads , c , x − (Cp , s(Ts , e , x − Tref ) + hads , e , x)) − αxδx(1 − εd , x)A ∑ (rg , c , j , xCp , g , j , c , x(Tg , c , x − Tref )) j

+ Aαxδx(1 − εd , x)ρs aphp , x(Tg , c , x − Ts , c , x)

(9)

2.1.1.3. Emulsion Region. Similar to the cloud-wake region, the emulsion region also consists of both gas and solid phases. Adsorption reaction also takes place in this region along with heat and mass transfer. Gas phase Component balance:

Q = CvX 10253

ΔP ρ

(14)



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In the above equation, Q represents the volumetric flow rate, Cv represents the valve coefficient, X is the percentage opening of the valve, ΔP is the pressure drop across the valve, and ρ is the density of the flowing gas/solid. Valve coefficients are calculated assuming 50% opening and 15 psi pressure drop at the steady-state operating conditions. The solids distributors and the flue gas stack are modeled by dropping X from eq 14. 2.2.3. Downcomer. The solids from the upper stage flow to the lower stage through the downcomer.5 The pressure drop in the downcomer is calculated using the hydrostatic expression ΔPd = ρs (1 − ϵd)g hd

and the level control of the exit hopper. In the subsequent discussion, open-loop system means that no control action is used for regulating the CO2 capture. 4.1.1. Open-Loop System. In this study, the overall capture of CO2 is not controlled. A 20% step change in the flue gas flow rate is introduced as a disturbance. The sorbent flow rate is maintained at its initial value. The transient response of overall CO2 capture rate is shown in Figure 3. Due to less residence time of the flue gas in the reactor, overall CO2 capture decreases.

(15)

where ΔPd is the pressure drop in the downcomer, and hd is the level of solids in the downcomer. The dynamic change of the solids level in the downcomer is calculated from the following mass balance equation. d(hdρs (1 − εd)Ad ) dt

= mdin − mdout

(16)

The exit hopper is modeled similar to the downcomer.

3. DYNAMIC MODEL SOLUTION The transient model equations are formulated, discretized, and solved in ACM using the method of lines. The solution of the system of equations for the base case conditions given in Table 1 is first obtained for steady state. This solution is used as the initial conditions for the dynamic simulations. The Implicit Euler method is used for numerical integration.

Figure 3. Transient in CO2 capture due to 20% step increase in the flue gas flow rate.

4.1.2. Proportional-Integral-Derivative (PID) Controller. PID controllers are the most commonly used controllers in industrial control systems. Therefore, the performance of a PID-only control for overall CO2 capture is evaluated. The flow of the solid sorbent to the upper stage is the manipulated variable. As before, a 20% step change in the flue gas flow rate is introduced as a disturbance. For tuning the PID controller, a first-order transfer function model is constructed from the open-loop process response, and the control performance is observed for the tuning parameters calculated by the following tuning rules: Ziegler-Nichols, Cohen-Coon, time-integral, and Internal Model Control (IMC). Figure 4 shows the transients

Table 1. Base Case Conditions design parameters

gas conditions Gb,in Tg,in yg,CO2,in

1875 313.15 0.132

3000

yg,H2O,in

0.055

4.55 × 10−4 m2 per orifice

yg,N2,in

0.813

Dt Lb dHX

10 6 0.03

NHX ao

m m m

HX fluid conditions

solid conditions Fsorb,in Tsorb,in nHCO3,in

166.67 395 31.38

kg/s K mol/m3

Lower Stage FHX,in 400 THX,in 305.35 K

nH2O,in

239.74

mol/m3

Upper Stage

376.07

3

nNHCO2,in

mol/s K

mol/m

FHX,in

300

THX,in

305.35 K

kg/s

kg/s

4. RESULTS AND DISCUSSION 4.1. Control System Design. Operating power plants generally vary their load over time in response to fluctuations in the power demand. Such load following results in variations in the flue gas flow rate which, in turn, can cause significant deviation from the CO2 capture target if the CO2 capture rate is not being controlled. In the current work, various control strategies have been developed for a two-stage adsorber-reactor to maintain the desired CO2 capture rate when the flue gas flow rate changes. A flow controller has been considered for manipulating the sorbent flow rate. A level controller has been designed to maintain the level of solids in the exit hopper. Traditional proportional-integral-derivative (PID) controllers have been used for the flow control of solids to the upper stage

Figure 4. Transient in CO2 capture due to 20% step increase in the flue gas flow rate using PID controller.

in CO2 capture rate for the “best” tuning parameters that were obtained by modifying the tuning parameters obtained by the tuning rules mentioned above. The transient in the process variable (PV) exhibits a large undershoot and long settling time to reach the desired set point (SP). 4.1.3. Feedback-Augmented Feedforward Controller (FBAUGFF). To improve on the PID controller performance, a feedback-augmented feedforward controller (FBAUGFF) is 10254



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Figure 5. Comparison of the identified process model and data for step change in the sorbent flow rate.

Figure 6. Comparison of the identified process model and data for step change in the fluegas flow rate.

designed. The process and disturbance models required for designing this controller have been obtained by using the inputoutput data generated by simulating step changes in the sorbent flow rate for the process model and flue gas flow rate for the disturbance model. The model parameters are regressed to the data in MATLAB. The process model is approximated as a firstorder transfer function without any time-delay. The comparison of the process model to the data is shown in Figure 5. The disturbance model is approximated as a second-order transfer function with pure gain and no time-delay. An excellent fit to the data similar to Figure 6 is obtained. After obtaining the process and disturbance models, the FBAUGFF controller is implemented in ACM. The same 20% step increase in flue gas flow rate is introduced as a disturbance. As before, the PID controller is tuned to obtain the “best” performance. The closed-loop performance of the FBAUGFF controller is shown in Figure 7. Even though the control performance is superior to

the PID-only control, the FBAUGFF control still suffers from an overshoot and long settling time.

Figure 7. Transient in CO2 capture due to 20% step increase in the flue gas flow rate using the FBAUGFF controller. 10255



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Figure 8. Comparison between the data and the identified ARX process and disturbance model.

Figure 9. Simulink schematic of the LMPC control strategy for CO2 capture.

4.1.4. Linear Model Predictive Controller (LMPC). To improve the control performance further, a linear model predictive controller (LMPC) is designed. The combined process and disturbance model is identified using the System Identification tool box in MATLAB. The input-output data are generated by introducing a step change in both sorbent and flue gas flow rates simultaneously. The identified model is the AutoRegressive with eXogenous inputs (ARX) model. Figure 8 shows the comparison between the data and identified model. The identified model is given below.

A(q)y(t ) = B(q)u(t ) + e(t )

(17)

where A(q) = 1 − 1.408q−1 − 0.1453q−2 + 0.5946q−3 − 0.04143q−4 B(q) = −0.07178q−1 − 0.01151q−2 + 0.01254q−3 + 0.07076q−4 10256



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Table 2 shows a comparison between the performance of all the controllers in terms of integral absolute error (IAE), integral

The LMPC is implemented in Simulink. The ACM model of the adsorber system is embedded in Simulink using an available custom block. The Simulink flowsheet is shown in Figure 9. The disturbance in the flue gas flow rate is also implemented in Simulink and passed on to the ACM process model. Since a linear model is used even though the process has strong nonlinearity, the controller suffered from offset (deviation from set-point). To eliminate the offset, two different strategies have been used. In the first strategy, an additional integrator with a gain value of 0.05 has been used (named as LMPC-I). In the second strategy, the unmeasured disturbances have been estimated (named as LMPC-II) using the advanced estimation feature available in the MATLAB MPC toolbox. The performances of both LMPC-I and LMPCII are shown in Figure 10 for the disturbance of 20% increase in

Table 2. Error Analysis of All the Controllers controller

IAE (h)

ISE (h)

ITAE (h2)

PID FBAUGFF LMPC-I LMPC-II

0.8111 0.4751 0.3913 0.4007

1.7551 0.5502 0.6138 0.6386

1.12 × 10−04 6.60 × 10−05 5.57 × 10−05 6.30 × 10−05

squared error (ISE), and integral time-weighted absolute error (ITAE). Both IAE and ITAE are less for LMPC-I in comparison to the other controllers. Overall, either of the LMPC strategies is preferred to the others. However, if implementation or computational issues are of concern for the LMPC strategies, the FBAUGFB controller can be used if the overshoot can be tolerated. 4.2. Transient Studies for Other Disturbances. In the controller study presented above, only the flue gas flow rate has been considered as the disturbance in the identified model used in the LMPC strategies. However, the controller should also perform satisfactorily in the face of unmodeled disturbances and so that is the focus of the study presented below. Though the performances of both LMPC-I and LMPC-II are similar, the computational time is much lower for LMPC-II than LMPC-I. Since unmeasured disturbances are estimated in the LMPC-II strategy, it is envisaged that this controller would perform better in the face of unmodeled disturbances. Hence, LMPC-II is used in the following study, where two unmodeled disturbances have been considered, and the results are compared with the open-loop system. 4.2.1. Change in the Flue Gas Inlet Temperature. A ramp change of 10 °C (from 40 to 50 °C) for duration of 5 s is introduced in the flue gas inlet temperature. The dynamics of the CO2 capture are shown in Figure 12 for both open-loop

Figure 10. Performance of the LMPC strategies for maintaining CO2 capture in the face of 20% step increase in the flue gas flow rate.

the flue gas flow rate. From the figure, it can be observed that the response of both the controllers is good. Further, their response is almost similar. 4.1.5. Comparison of Control Performance. The performance of all the controllers presented above is compared in Figure 11. Representing an approximate measure of the “best”

Figure 12. Performance of LMPC-II for a 10 °C increase in the inlet flue gas temperature.

and closed-loop LMPC-II designs. A rapid decrease in CO2 capture is observed initially when the gas temperature is increased. This is due to a quick change (increase) of temperature in the lower stage. It is observed that the LMPC-II controller successfully eliminates the offset but results in a minor overshoot that has not been observed in the previous case when the change in the flow rate was considered as the disturbance. The dynamics of the exit bubble phase (flue gas exit) temperature and CO2 concentration are shown in Figures 13 and 14, respectively. As expected, the temperatures of the gas and solid increase with an increase in the flue gas inlet

Figure 11. Performance comparison of all the controllers.

performance that can be achieved in this system, a plot named “Best” has been generated by increasing the sorbent flow rate to the ultimate value instantaneously immediately after the introduction of the disturbance. As mentioned earlier, the PID controller has a long undershoot. The FFAUGFB controller has an overshoot and long settling time. The performances of both LMPC-I and LMPC-II are superior to the previous controllers and very close to the “Best” performance. 10257



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Figure 15. Performance of the LMPC-II controller in the face of a 10% increase in the CO2 composition in the flue gas inlet. Figure 13. Transient response of the flue gas exit temperature for each stage for a 10 °C increase in the inlet gas temperature.

Figure 16. Transient response CO2 mole fraction at the exit for a 10% increase in the CO2 composition in the flue gas inlet. Figure 14. Transient response of the CO2 mole fraction at the exit of each stage for a 10 °C increase in the inlet gas temperature.

5. CONCLUSIONS A one-dimensional, nonisothermal, pressure-driven dynamic model of a two-stage BFB adsorber-reactor has been developed for solid−sorbent CO2 capture. Mass and energy conservation equations are written for the gas and solid phases, as appropriate, in the bubble, cloud-wake, and emulsion regions. Dynamic models of the downcomer, exit hopper, and other auxiliary equipment such as valves and gas distributors are developed and integrated with the main adsorber model in ACM. Various control strategies are developed and tested for maintaining the CO2 capture rate at the desired level under different disturbances. As the flue gas flow rate is expected to be the dominant and most frequent disturbance for a CO2 capture process, a 20% step increase in the flue gas flow rate is introduced to evaluate the performance of the control strategies. The PID-only controller exhibits a large undershoot and long settling time. The performance of the FBAUGFF controller is superior to the PID-only control, but the settling time is still unacceptable in addition to a minor overshoot. The performance of both linear model predictive controllers, LMPC-I and LMPC-II, is superior to the others. Using the LMPC-II controller design where unmeasured disturbances have been estimated, the transient responses of various process variables have been studied for other disturbances such as change in the inlet gas temperature and composition of the flue gas. The designed LMPC-II controller is found to reject all the disturbances successfully.

temperature. However, the change in the inlet gas temperature has a relatively larger effect on the lower stage than on the upper stage as seen in Figure 13. Since CO2 adsorption reaction is exothermic and equilibrium-limited, the extent of reaction decreases with the increase in temperature of the beds. Hence, the concentration of CO2 at the exit increases. As the effect of temperature is more in the lower stage than the upper stage, the extent of increase of exit CO2 concentration is more in the lower stage than in the upper stage as shown in Figure 14. 4.2.2. Change in the Flue Gas Inlet Composition. The CO2 composition in the flue gas inlet is step increased by 10% (from 0.132 to 0.1452) at 5 s. To keep the summation of mole fractions for the flue gas inlet equal to unity, the compositions of nitrogen and water vapor have been reduced accordingly. The dynamics of CO2 capture are shown in Figure 15 for both open-loop and closed-loop LMPC-II systems. Due to the increase in partial pressure of CO2 in the flue gas inlet, the overall CO2 capture increases initially. However, due to the higher extent of the exothermic adsorption reactions, the bed temperature increases. If the sorbent flow rate remains the same, as in the case of the open-loop system, the CO2 loading of the sorbent also increases resulting in a decrease in the overall CO2 capture. Again the performance of the LMPC-II is found to be satisfactory. The dynamics of the exit CO2 concentrations are shown in Figure 16. Similar to before, the effect is more on CO2 capture in the lower stage.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +1-3042939335. Fax: +1-3042934139. E-mail: [email protected]. 10258



Article

Kg,bulk - rate of gas phase bulk flow between bubble and emulsion regions (mol/m-s) Ks,bulk - rate of solid phase bulk flow between could-wake and emulsion regions (mol/m-s) Lb - depth of fluidized bed (m) m - mass flow rate (kg/s) n - concentration of adsorbed species in adsorbent (mol/kg sorbent) NHX - number of heat exchanger tubes (-) P - pressure (Pa) Q - volumetric flow rate (m3/s) r - rate of reaction (mol/m3s) T - temperature (K) ΔTHX - temperature difference between heat exchanger tubes and emulsion region (K) Tref - reference temperature (K) X - percentage of opening (-) y - gas phase mole fraction (-)

Notes

This journal article was prepared as an account of work sponsored by an agency of the United States Government under the Department of Energy. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. The authors declare no competing financial interest.

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Greek Characters

ACKNOWLEDGMENTS As part of the National Energy Technology Laboratory’s Regional University Alliance (NETL-RUA), a collaborative initiative of the NETL, this technical effort was performed under the RES contract DE-FE0004000.

α - cloud-wake to bubble volume ratio (-) δ - bubble volume fraction (-) ε - cross-sectional average voidage (-) εd - emulsion region voidage (-) ρg - gas density (kg/m3) ρs - solids density (kg/m3)

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NOMENCLATURE ao - area of distributor plate per orifice (m2/kg) ap - specific surface area of solid particle (m2/kg) A - cross-sectional area of fluidized bed (m2) C - gas phase concentration (mol/m3) cp - heat capacity (J/mol-K) cp,s - heat capacity of unloaded sorbent (J/mol-K) Cr - empirical coefficient (-) Cr - valve coefficient (-) Dt - diameter of reactor vessel (m) dHX - diameter of heat exchanger tubes (m) FSorb - flow rate of solids (kg/s) g - acceleration due to gravity (m/s2) Gb - bubble region gas axial flow rate (mol/s) hads - specific enthalpy of adsorbed species (J/kg sorbent) Hbc - bubble to cloud-wake region gas phase heat transfer coefficient (J/m3s-K) Hce - cloud-wake to emulsion region gas phase heat transfer coefficient (J/m3s·K) hd - heat transfer coefficient between heat exchanger and emulsion packet (W/m2-K) Hg,bulk - rate of heat transfer between bubble and emulsion regions due to bulk flow of gas (W/m) hp - gas−solids heat transfer coefficient (W/m2-K) Hs,bulk - rate of heat transfer between bubble and emulsion regions due to bulk flow of solids (W/m) ht - heat exchanger heat transfer coefficient (W/m2-K) ΔHrxn - specific heat of reaction (J/mol) J - superficial solids flux (kg/m2-s) Kbc - bubble to cloud-wake region gas phase mass transfer coefficient (1/s) Kce - cloud-wake to emulsion region gas phase mass transfer coefficient (1/s) Kce,bs - cloud-wake to emulsion region solids phase mass transfer coefficient (m3 solid/m3 bubbles. 1/s) Kd - bubble to emulsion region gas phase bulk flow coefficient (m2/s) kg - thermal conductivity of gas (W/m-K)

Subscripts

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b - bubble region c - could-wake region d - downcomer e - emulsion region g - gas phase i - adsorbed species j - gaseous species k - reaction r - region s - solid phase t - total x - value at height x

REFERENCES

(1) Figueroa, J. D.; Fout, T.; Plasynski, S.; McIlvried, H.; Srivastava, R. D. Advances in CO2 Capture TechnologyThe U.S. Department of Energy’s Carbon Sequestration Program. Int. J. Greenhouse Gas Control 2008, 2, 9−20. (2) Hoffman, J. S.; Richards, G. A.; Pennline, H. W.; Fischer, D.; Keller, G. Factors in Reactor Design for Carbon Dioxide Capture with Solid, Regenerable Sorbents. Proceedings of 33rd International Technical Conference on Coal Utilization and Fuel Systems, Clearwater, FL, June 1−5, 2008. (3) Gray, M. L.; Hoffman, J. S.; Hreha, D. C.; Fauth, D. J.; Hedges, S. W.; Champagne, K. J.; Pennline, H. W. Parametric Study of Solid Amine Sorbents for the Capture of Carbon Dioxide. Energy Fuels 2009, 23, 4840−4844. (4) Monazam, E. R.; Shadle, L. J.; Siriwardane, R. Performance and Kinetics of a Solid Amine Sorbent for Carbon Dioxide Removal. Ind. Chem. Eng. Res. 2011, 50, 10989−10995. (5) Kunii, D.; Levenspiel, O. Fluidization Engineering, 2nd ed.; Butterworth-Heinemann: Boston, 1991. (6) Samanta, A.; Zhao, A.; Shimizu, G. K. H.; Sarkar, P.; Gupta, R. Post-Combustion CO2 Capture Using Solid Sorbents: A Review. Ind. Chem. Eng. Res. 2012, 51, 1438−1463. (7) Abanades, J. C.; Rubin, E. S.; Anthony, E. J. Sorbent Cost and Performance in CO2 Capture Systems. Ind. Chem. Eng. Res. 2004, 43, 3462−3466. 10259



Article

(8) Khatri, R. A.; Chuang, S. S. C; Soong, Y.; Gray, M. Thermal and Chemical Stability of Regenerable Solid Amine Sorbent for CO2 Capture. Energy Fuels 2006, 20, 1514−1520. (9) Roy, S.; Mohanty, C. R.; Meikap, B. C. Multistage Fluidized Bed Reactor Performance Characterization for Adsorption of Carbon Dioxide. Ind. Chem. Eng. Res. 2009, 48, 10718−10727. (10) Fang, F.; Li, Z.; Cai, N. S. Continuous CO2 Capture from Flue Gases Using a Dual Fluidized Bed Reactor with Calcium-Based Sorbent. Ind. Chem. Eng. Res. 2009, 48, 11140−11147. (11) Li, B.; Jiang, B.; Fauth, D. J.; Gray, M. L.; Pennline, H. W.; Richards, G. A. Innovative Nano-Layered Solid Sorbents for CO2 Capture. Chem. Commun. 2011, 47, 1719−1721. (12) Zhao, W.; Zhang, Z.; Cai, N. Investigation of Thermal Stability and Continuous CO2 Capture from Flue Gases with Supported Amine Sorbent. Ind. Chem. Eng. Res. 2013, 52, 2084−2093. (13) Hasan, M. M. F.; Baliban, R. C.; Elia, J. A.; Floudas, C. A. Modeling, Simulation, and Optimization of Postcombustion CO2 Capture for Variable Feed Concentration and Flow Rate. 2. Pressure Swing Adsorption and Vacuum Swing Adsorption Processes. Ind. Chem. Eng. Res. 2012, 51, 15665−15682. (14) Kunii, D.; Levenspiel, O. Fluidized Reactor Models.1.For Bubbling Beds of Fine, Intermediate, and Large Particles. 2. For the Lean Phase: Freeboard and Fast Fluidization. Ind. Chem. Eng. Res. 1990, 29 (7), 1226−1234. (15) Kobayashi, N.; Yamazaki, R.; Mori, S. A Study on the Behavior of Bubbles and Solids in Bubbling Fluidized Beds. Powder Technol. 2000, 113, 327−344. (16) Yi, C.-K.; Jo, S. H.; Seo, Y.; Lee, J.-B.; Ryu, C.-K. Continuous Operation of the Potassium Based Dry Sorbent CO2 Capture Process with Two-Fluidized Bed Reactors. Int. J. Greenhouse Gas Control 2007, 1, 31−36. (17) Garg, R.; Shahnam, M.; Huckaby, E. D. Continuum Simulations of CO2 Capture by Dry Regenerable Potassium Based Sorbents. 7th International Conference on Multiphase Flow, 2010, pp 1−10. (18) Choi, J.-H.; Yi, C.-K.; Jo, S.-H. A Model on an Entrained BedBubbling Bed Process for CO2 Capture from Flue Gas. Korean J. Chem. Eng. 2011, 28 (4), 1144−1147. (19) Mohanty, C. R.; Meikap, B. C. Modeling the Operation of a Three-Stage Fluidized Bed Reactor for Removing CO2 from Flue Gases. J. Hazard. Mater. 2011, 187, 113−121. (20) Lee, A.; Miller, D. A 1-D Three Region Model for a Bubbling Fluidized Bed Adsorber. Ind. Chem. Eng. Res. 2013, 52, 469−484. (21) Mac Dowell, N.; Samsatli, N. J.; Shah, N. Dynamic Modelling and Analysis of an Amine-Based Post-Combustion CO2 Capture Absorption Column. Int. J. Greenhouse Gas Control 2013, 12, 247−258. (22) Jayarathna, S. A.; Lie, B.; Melaaen, M. C. Amine Based CO2 Capture Plant: Dynamic Modeling and Simulations. Int. J. Greenhouse Gas Control 2013, 14, 282−290. (23) Mac Dowell, N.; Shah, N. Identification of the Cost-Optimal Degree of CO2 Capture: An Optimization Study Using Dynamic Models. Int. J. Greenhouse Gas Control 2013, 13, 44−58. (24) Arce, A.; Mac Dowell, N.; Shah, N.; Vega, L. F. Flexible Operation of Solvent Regeneration Systems for CO2 Capture Processes Using Advanced Control Techniques: Towards Operational Cost Minimisation. Int. J. Greenhouse Gas Control 2012, 11, 236−250. (25) Ziaii, S.; Rochelle, G. T.; Edgar, T. F. Dynamic Modeling To Minimize Energy Use for CO2 Capture in Power Plant by Aqueous Monoethanolamine. Ind. Chem. Eng. Res. 2009, 48, 6105−6111. (26) Ikonen, E.; Kortela, U. Dynamic Model for a Bubbling Fluidized Bed Coal Combustor. Control Eng. Practice 1994, 2 (6), 1001−1006. (27) Yuan, T.; Cizmas, P. G.; O’Brien, T. A Reduced Order Model for a Bubbling Fluidized Bed Based on Proper Orthogonal Decomposition. Comput. Chem. Eng. 2005, 30, 243−259. (28) Mahecha-Botero, A.; Grace, J. R.; Elnashaie, S. S. E. H.; Lim, C. J. Time-Scale Analysis of a Fluidized-Bed Catalytic Reactor Based on a Generalized Dynamic Model. The 12th International Conference on Fluidization - New Horizons in Fluidization Engineering, 2007, Vol. RP.4, pp 623−630.

(29) Bollini, P.; Brunelli, N. A.; Didas, S. A.; Jones, C. W. Dynamics of CO2 Adsorption on Amine Adsorbents. 1. Impact of Heat Effects. Ind. Chem. Eng. Res. 2012, 51, 15145−15152. (30) Bollini, P.; Brunelli, N. A.; Didas, S. A.; Jones, C. W. Dynamics of CO2 Adsorption on Amine Adsorbents. 2. Insights into Adsorbent Design. Ind. Chem. Eng. Res. 2012, 51, 15153−15162. (31) Gáspár, J.; Cormos, A. M. Dynamic Modeling and Validation of Absorber and Desorber Columns for Post-Combustion CO2 Capture. Comput. Chem. Eng. 2011, 35, 2044−2052. (32) Li, M. Dynamics of CO2 Adsorption on Sodium Oxide Promoted Alumina in a Packed-Bed Reactor. Chem. Eng. Sci. 2011, 66, 5938−5944. (33) Lawal, A.; Wanga, M.; Stephenson, P.; Obi, O. Demonstrating Full-Scale Post-Combustion CO2 Capture for Coal-Fired Power Plants through Dynamic Modeling and Simulation. Fuel 2012, 101, 115−128. (34) Harrison, A. J. L; Lim, C.-N.; Gilbertson, M. A. Modelling and Control of the Dynamics of Bubbling Fluidized Beds. Proc. Inst. Mech. Eng., Part E 2005, 220, 43−53. (35) Lee, A.; Mebane, D.; Fauth, D. J.; Miller, D. C. A model for the adsorption kinetics of CO2 on amine-impregnated mesoporous sorbents in the presence of water, 28th International Pittsburgh Coal Conference, Pittsburgh, PA, USA, 2011. (36) Turton, R.; Bailie, R. C.; Whiting, W. B.; Shaeiwitz, J. S.; Bhattacharyya, D. Analysis, Synthesis and Design of Chemical Processes, 4th ed.; Prentice Hall: 2012.

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Dynamic Modeling and Control Studies of a Two-Stage Bubbling

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