Rotary Bed Reactor for Chemical-Looping ... - ACS Publications

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Rotary Bed Reactor for Chemical-Looping Combustion with Carbon Capture. Part 2: Base Case and Sensitivity Analysis Zhenlong Zhao, Tianjiao Chen, and Ahmed F. Ghoniem* Department of Mechanical Engineering, Massachusetts Institute of Technology (MIT), 77 Massachusetts Avenue, Cambridge, Massachusetts 02139-4307, United States ABSTRACT: Part 1 (10.1021/ef3014103) of this series describes a new rotary reactor for gas-fueled chemical-looping combustion (CLC), in which, a solid wheel with microchannels rotates between the reducing and oxidizing streams. The oxygen carrier (OC) coated on the surfaces of the channels periodically adsorbs oxygen from air and releases it to oxidize the fuel. A onedimensional model is also developed in part 1 (10.1021/ef3014103). This paper presents the simulation results based on the base-case design parameters. The results indicate that both the fuel conversion efficiency and the carbon separation efficiency are close to unity. Because of the relatively low reduction rate of copper oxide, fuel conversion occurs gradually from the inlet to the exit. A total of 99.9% of the fuel is converted within 75% of the channel, leading to 25% redundant length near the exit, to ensure robustness. In the air sector, the OC is rapidly regenerated while consuming a large amount of oxygen from air. Velocity fluctuations are observed during the transition between sectors because of the complete reactions of OCs. The gas temperature increases monotonically from 823 to 1315 K, which is mainly determined by the solid temperature, whose variations with time are limited within 20 K. The overall energy in the solid phase is balanced between the reaction heat release, conduction, and convective cooling. In the sensitivity analysis, important input parameters are identified and varied around their base-case values. The resulting changes in the model-predicted performance revealed that the most important parameters are the reduction kinetics, the operating pressure, and the feed stream temperatures. transferred to the bulk flow by convection to heat the streams from a low inlet temperature to a high outlet temperature. The rotary wheel consists of a large number of microchannels (Figure 1c), with the OC coated on their inner walls. As shown in Figure 1d, the channel wall has two solid layers, with one being a highly porous OC layer and the other being a bulk dense layer with high thermal inertia and conductivity. Flue streams from a large number of channels merge into two separate streams from the fuel zone and air zone, respectively. Advantages of the rotary design include the intrinsic separation between fuel and air streams, compactness, scale-up feasibility, and periodic and continuous operation without the need to transport particles at high pressures. Potential drawbacks of the rotary reactor design include temperature fluctuation, differential thermal distortion, and carbon deposition. A similar idea of using a rotary reactor with microchannels for CLC was briefly investigated before. Pavone and coworkers25,26 simulated the reduction and oxidation (redox) performances of one channel using a commercial computational fluid dynamics (CFD) package for the initial several cycles. Owing to the limited amount of the solid phase in the channel design, large temperature fluctuations (>500 °C) were observed26 in the OC wash-coat, which could cause severe thermal stresses within the reactor. Little discussion was given regarding the reactor design, periodic performance, or operating conditions.

1. INTRODUCTION Chemical-looping combustion (CLC) is a novel and promising technology for power generation with inherent CO2 capture. In CLC, combustion is performed in two steps. Fuel is oxidized by a metal oxide in a fuel reactor to generate CO2 and water steam. The reduced metal oxide is then regenerated by air in an air reactor. During this two-step process, the looping medium acts as an “oxygen carrier” (OC), which adsorbs oxygen in the air reactor and releases it to oxidize fuel in the fuel reactor. The flue gas from the fuel reactor contains CO2 and H2O only, where CO2 can be readily captured after steam condensation. Thus far, most of the research on the CLC reactor design has been focused on using interconnected fluidized-bed reactors.1−9 Alternative approaches have also been proposed and investigated, including the moving-bed reactor,10−13 the packed-bed reactor,14−16 and the rotating-bed reactor.17,18 A comprehensive review of different types of CLC reactors can be found in the review work by Hossain and de Lasa19 and that by Adanez et al.2 A new rotary reactor concept for gas-fueled CLC is proposed in part 1 (10.1021/ef3014103) of this series. The design of the rotary CLC reactor resembles that of the rotary desiccant wheel20 and the rotary heat exchanger.21−24 The reactor consists of a rotary solid wheel and two stationary chambers at the top and bottom of the wheel, as shown in Figure 1a. The wheel rotates continuously through four sectors (Figure 1b): fuel, air, fuel-purging, and air-purging sectors. Pressurized feed gas (fuel, air, or steam) flows in a co-current pattern from the feeding chamber, reacts with the OC as it passes through the wheel, and leaves the system from the exit chamber. As gas passes through each channel, the heat generated by the conversion of the chemical energy via the surface reaction is © 2012 American Chemical Society

Received: August 28, 2012 Revised: November 6, 2012 Published: November 13, 2012 344

dx.doi.org/10.1021/ef301411g | Energy Fuels 2013, 27, 344−359

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Figure 1. Schematic diagram of the rotary CLC system design: (a) front view, (b) bottom view, (c) individual channel structure, and (d) OC coated on the surface.

The objective of this two-part series is to describe the rotary design for CLC, assess the feasibility of continuous operation, test the performance of the reactor under a periodic stationary state, and identify the key design parameters. A onedimensional model was constructed in part 1 (10.1021/ ef3014103) to simulate the periodic performance of a single channel, with copper oxide used as the OC and boron nitride (BN) as the support material. The model focuses on the reactive plug flow in each channel. At every point along the channel, one-dimensional conservation equations for mass and energy are solved for both the gas and solid phases. The profiles of species mole fraction, temperature, and velocity are calculated along the axis of one channel. Kinetics proposed by Garcia-Labiano et al.27 is used to describe the heterogeneous reactions (see Table 1). Simulations are performed for repeated cycles until a periodic stationary state is obtained. Part 2 of this series deals with the simulation results of the periodic stationary state performance based on the current design parameters and operating conditions, as well as the results of sensitivity analysis to identify input variables and parameters of importance.

Table 1. Properties of the OC and Support Material Used in the Base Case symbol OC reduction reaction oxidation reaction support material density of the bulk support layer porosity of the porous OC layer conductivity of the support active CuO load volume fraction of CuO in the OC layer volume fraction of Cu in the OC layer pre-exponential factor for reduction pre-exponential factor for oxidation activation energy for reduction

2. BASE CASE 2.1. Periodic Performance. The model is used to simulate the operation of the rotary reactor using the design parameters and operating conditions specified in part 1 (10.1021/ef3014103). Simulations are conducted for repeated cycles until periodic operation is achieved. The output of the model consists of the gas flow velocity, the axial profiles of the temperature and gas composition, and the conversion of the OC. As an example, Figure 2 shows the temperature and gas concentration profiles in one cycle as a function of the angle of 345

value

unit

CuO copper oxide 4CuO(s) + CH4(g) → 4Cu(s) + CO2(g) + 2H2O(g) 2Cu(s) + O2(g) → 2CuO(s) BN boron nitride ρs 3450 kg/m3 εs

0.57

ks εCuO

600 10 0.0281

εCu

0.0161

k0,CH4

1.125 × 106

mol0.6 m−1.8 s−1

k0,O2

2.043 × 104

mol0.0 m0.0 s−1

ECH4

60

kJ mol−1

activation energy for oxidation

EO2

15

kJ mol−1

pressure coefficient for reduction pressure coefficient for oxidation reaction order for reduction

aCH4

0.83

aO2

0.68

nCH4

0.4

reaction order for oxidation

n O2

1.0

W m−1 K−1 wt %


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Figure 2. Reactor performance in one cycle for different locations along the channel: (a) z = 0.1 m, (b) z = 0.5 m, and (c) z = 0.9 m. Note that different temperature scales are used for clarity. rotation (from 0 to 2π) for three locations: near the inlet, in the middle, and near the exit of the wheel. Note that different temperature scales are used for clarity. As observed in Figure 2, each curve (temperature or concentration) quickly reaches a quasi-steady state in the fuel sector after a short transition period from the previous purge sector. The fuel concentration gradually decreases from the inlet to the outlet. As seen in Figure 2c, at the wheel exit, the methane concentration is zero all of the time. Thus, the fuel is completely consumed before the exit of the reactor. As the channel enters the fuelpurging sector, the residual fuel is quickly pushed toward the exit of the channel and reacts with the OC near the outlet. All of the residual methane is oxidized by the OC before the channel enters the air sector. Therefore, no direct mixing between the fuel and oxygen is observed, and thus, the safety of the operation is ensured. The black lines in Figure 2 show the solid temperature profiles, which remain almost constant throughout the entire cycle. The maximum temperature variation with time is within 20 K. The limited temperature variation is mainly because of the high thermal inertia of the bulk dense layer in the solid phase, which acts as a heat reservoir to match the energy-transfer processes. However, small temperature jumps are observed in the air sector when the feed air passes through and the oxygen concentration rises. As discussed in part 1 (10.1021/ ef3014103), the copper oxidation rate is highly dependent upon the

local oxygen concentration. Thus, a rapid oxygen concentration rise leads to a fast energy release from the highly exothermic copper oxidation reaction, which significantly exceeds the convective heattransfer rate to the gas flow. Consequently, the energy is temporarily stored in the solid phase, and the solid temperature increases. After these temperature jumps, the solid temperature decreases because energy is transferred out of the channel walls to the flowing gas by convective heat transfer. When panels a−c of Figure 2 are compared, it is observed that the solid temperature gradually increases from the inlet to the outlet. The temperature variation at the outlet is within 0.1 K. The gas temperature profile is directly determined by the solid temperature because of the large specific surface area of the channel and, hence, the high convective heat-transfer rate between the solid phase and the flow. Consequently, the gas temperature fluctuation is limited, and the maximum variation is generally within 20 K. The periodic performance is shown in Table 2. The thermal capacity of the reactor is 1.00 MWth. The combustion efficiency (ηI) and the carbon separation efficiency (ηCO2) at the exit of the channel are defined as follows:

ηI = 1 − 346

∫fuel zone ṁ CH4,exitdt ∫fuel zone ṁ CH4,inletdt

(1)


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describes the unavoidable work loss because of the reaction within the reactor. As a comparison, the second-law efficiency is also calculated for the conventional direct combustion under the same operating conditions. Two cases are considered, as shown in Figure 3, with one being combustion with purging streams mixing and the other being unmixed combustion with steam bypassing. The calculation is also included in the Appendix. As shown in Figure 3a, the efficiency of the first case is 78.45%, which is about 2.5% lower than the rotary design because of the exergy destruction associated with the stream mixing. However, the efficiency for the second case is slightly higher than that for the rotary design, as shown in Figure 3b. This is because the purging flow rate used under current operating conditions is relatively high, such that the exergy loss from the purging gas dilution in the rotary design surpasses the exergy gain associated with the flue gas separation. However, the outlet temperature for this case is higher, and in a real application, effective cooling is required to lower the temperature below the material limit, which lowers the second-law efficiency. In terms of the design optimization, the influences of the purging gas flow rate on the reactor efficiency as well as the flue gas temperature should be considered. Pressure loss is expected as the gas flows through the channel. A higher velocity and a smaller channel lead to a larger pressure drop through the reactor. An accurate prediction of the pressure distribution requires solving the momentum equation along the channel. As an estimate, the pressure drop through the channel can be evaluated on the basis of the classic fully developed laminar flow theory, as follows:28

Table 2. Overall Performance of the Rotary Reactor in a Periodic Stationary State thermal capacity combustion efficiency CO2 separation efficiency second-law efficiency (exergy efficiency) average gas residence time in the fuel sector average gas residence time in the fuel-purge sector average gas residence time in the air sector average gas residence time in the air-purge sector temperature variation between two cycles [see part 1 (10.1021/ef3014103)]

ηCO = 2

value

unit

1.00 100.00 98.06 80.91 6.48 5.78 1.01 0.96 0.001

MW % % % s s s s K

∫fuel zone ṁ CO2,exitdt ∫fuel zone ṁ CO2,inlet + ṁ CH4,inletdt

(2)

The combustion and carbon separation efficiencies are close to unity. Table 3 shows the outlet flue gas velocity, temperature, and mole

Table 3. Steady-State Flue Streams from the Fuel Zone and the Air Zone outlet flue gas

fuel zone

air zone

velocity (m/s) temperature (K)a CH4 mole fraction (%) CO2 mole fraction (%) H2O mole fraction (%) O2 mole fraction (%) N2 mole fraction (%)

0.10 1314.53 0 54.77 45.23 0 0

0.58 1314.53 0 0.44 23.28 10.59 65.69

f=

The simulated flue gas temperature is 2.8 K lower than the adiabatic temperature (1317.29 K) because of numerical error. A non-uniform mesh grid enhances the numerical accuracy. fraction for the fuel zone and the air zone. The flue gas in the chamber downstream of the wheel is a combination of a large number of flow streams, leaving all of the channels in the fuel (or air) zone. The gas velocity in the air zone is higher than that in the fuel zone because of the higher feed velocity. The outlet temperatures are close to each other. Only a small fraction of carbon dioxide leaves the reactor from the air zone. No methane or air is observed in the flue gas from the fuel zone. The second-law efficiency is calculated for the rotary reactor as follows:

̇ ,out Wmax ̇ ,in Wmax

Red < 2300

(4)

where f is the friction factor and Red is the Reynolds number. The pressure drop is estimated to be around 1 kPa. This pressure loss is small compared to the operating pressure (10 atm). 2.2. OC Conversion. During the periodic operation, the OC plays a key role in determining the fuel conversion; therefore, it is crucial for the design of the reactor. Figure 4a shows the OC conversion (X) variation for one cycle along the channel. Note that, in Figure 4a, the conversion contours are plotted as a function of both time and axial location and darker colors represent higher oxygen concentrations in the OC. As seen in Figure 4a, the OC along the channel releases oxygen to oxidize the fuel in the fuel sector and adsorbs oxygen in the air sector. After about 26 s of one cycle (about 2 s before the channel moves to the air-purge sector), all of the copper along the channel is fully regenerated to copper oxide. Thus, the air sector size is large enough to ensure the complete regeneration of the OC. As discussed in part 1 (10.1021/ef3014103), the heterogeneous reaction is closely related to the local temperature and gas concentration: higher temperatures or species concentrations favor conversion. This is evident in Figure 4a. The reduction reaction rate in the fuel sector is lowest at the inlet and outlet because of the low temperature and low fuel concentration, respectively. However, this is not the case for oxidation, as shown in Figure 4a, where the gradients of the conversion contours are almost constant, although the oxidation starts at different times for the different axial locations. This is because oxidation is more sensitive to the oxygen concentration in the gas stream, as discussed in part 1 (10.1021/ef3014103). Therefore, as the gas flows through a channel, the local OC rapidly adsorbs all available oxygen from the bulk flow, leading to a slowly propagating oxygen front, which is evident in the oxygen molar fraction contour shown in

a

ηII =

57 , Red

(3)

where Ẇ max,in and Ẇ max,out are the maximum work that can be extracted in a reversible engine using the feed streams, which are admitted into the rotary reactor, or the flue streams, which are obtained from the exit of the rotary reactor, as the input streams, respectively. For detailed derivation of Ẇ max,in and Ẇ max,out, please refer to the Appendix. The second-law efficiency of the rotary reactor is 80.91%. The value 1 − ηII

Figure 3. Illustration of the conventional direct combustion: (a) steam is mixed with the fuel and air to generate one flue stream, and (b) steam bypasses the reactor without mixing. The second-law efficiency: (a) 78.45% and (b) 82.48%. 347


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Figure 4. OC conversion variation within one cycle: (a) OC conversion contours for the entire channel, (b) OC conversion profiles at four locations, and (c) OC conversion profile and oxygen-added ratio along the channel at the end of the fuel-purge sector. Figure 5a. As the oxygen molar fraction front moves forward, the OC behind the propagating front is already fully oxidized. In contrast, the fuel molar fraction profile in Figure 5a quickly reaches a quasi-steady state after a short transition period from the purge sector to the fuel sector. The methane concentration distribution along the channel remains stable for about 10 s until the channel moves into the fuelpurging sector. Comparing the reduction and oxidation processes, we can conclude that, for copper oxide as an OC, the reactor design and operation are mainly limited by the reduction rate. As shown in Figures 4 and 5, 99.9% of the fuel is completely converted within 0.75 m of the channel. The OC within the top 0.25 m of the channel remains fully oxidized all of the time during one cycle. This 25% of the channel near the exit acts as a “safety margin” to account for the uncertainty of the kinetics and ensure complete fuel conversion at off-design operating conditions. Figure 4b shows the OC conversion profiles at four locations along the channel for one cycle. Among them, the reduction is fastest at 0.40 m, while the OC conversion at 0.80 m remains unity during the entire cycle. When the channel moves into the fuel-purging sector, the fuel concentration contour is shifted slightly upward toward the outlet of the channel (as shown in Figure 5a); the unconverted methane reacts with the copper oxide downstream. As the channel leaves the fuelpurging sector, the OC conversion along the channel reaches the

lowest level during one cycle. The conversion is a bell-shaped curve (the solid line in Figure 4c), with a minimum of 0.26 at 0.40 m and 0.68 at the inlet. The complete reduction of the OC is not observed. Thus, the choice of the fuel sector size and the rotational speed is reasonable. For an optimized design, a non-uniform coating, i.e., coating with first increasing and then decreasing thickness along the axis, may be a good option to make better use of the OCs. The dashed line in Figure 4c represents the oxygen-added ratio ϕ at the end of the fuel-purging sector. The oxygen-added ratio is calculated at local temperatures along the channel, as follows:

ϕ(z) =

nO,added nO,stoic

=

nCuO(z) 4nCH4(z)

t = 21 s

(5)

where nCuO and nCH4 are the moles of copper oxide and methane at axial location z and the factor of 4 in the denominator is the stoichiometric coefficient. The oxygen-added ratio indicates the amount of available oxygen in the porous layer. A smaller oxygenadded ratio means a larger possibility of carbon deposition and a higher risk of failure. For a preliminary analysis, the local species concentration along the channel is assumed to be the same as that in the feed fuel stream (15 vol % methane and 85 vol % CO2), which 348


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and CO2 separation. Therefore, one of our research interests is to investigate the flow in the channel and the coupling with the reactions. Figure 6 shows the bulk flow velocity distribution in the channel while moving through the different sectors. As the gas flows through

Figure 5. Molar fraction of the fuel and oxygen in one cycle: (a) molar fraction contours for the entire channel and (b) molar fraction profiles at four locations. Symbols in panel b are calculated assuming an infinite mass-transfer coefficient hm,i. Figure 6. Bulk flow velocity variation within one cycle: (a) velocity contours for the entire channel and (b) velocity profiles at four locations.

gives the lowest possible oxygen-added ratio under the current operating conditions. As shown in Figure 4c, the oxygen-added ratio is maintained above unity during the entire cycle. Thus, carbon formation should be completely avoided from the perspective of thermodynamic equilibrium. It is worth noting that the results here overestimated carbon formation potential because the fuel is oxidized by the OC as the gas passes through the channel. The local methane volume fraction is lower than 15% (as shown in Figure 5a), and hence, the oxygen-added ratio is expected to be even higher. Figure 5b shows the effects of the external mass-transfer resistance on the OC conversion. The lines are simulated from the model considering the external mass transfer between the bulk flow and the solid surface, while the symbols are calculated assuming an infinitely fast external mass-transfer rate. As observed in Figure 5b, the symbols match the lines perfectly. Thus, the external mass-transfer resistance is less important under the current operating conditions, and the OC conversion is mainly limited by the heterogeneous reactions. 2.3. Gas Velocity Distribution. As the reactor rotates across zones, two time scales are closely coupled with the fluid flow in the channel: the residence time of the channel in each sector and the residence time of the gas in each channel. The first time scale determines the reactor thermal capacity, OC conversion, and regenerability, while the second time scale affects the fuel conversion

the channel, the velocity increases because of the temperature rise. The methane reduction reaction (Table 1) generates two more molecules and, hence, further increases the flow velocity. The gas velocity in the fuel sector is lower than that in the air sector because of the different feed velocities. As seen in panels a and b of Figure 6, there is clearly a steady-state period in each sector where the flow velocity remains almost constant with time. Each two consecutive steady-state periods are connected by a transition region where fast velocity variation is observed. The transition period from the air zone to the fuel zone is smooth. However, strong transient effects are observed in the transition period from the fuel to the air. This flow response is mainly because of the coupling between the physical and chemical processes in the channel. As the channel moves into another sector, a new feed gas stream enters the channel and the flow becomes fully developed within seconds (see the gas residence time in Table 2). Because of the relatively slow reduction rate, the methane molecules span throughout the channel and the OC continuously releases oxygen to oxidize the fuel until the channel leaves the fuel sector. The reaction rate is almost constant during this period, and hence, a steady-state velocity profile is obtained. In the fuel-purge sector, the fast steam flow pushes the residual fuel to the 349


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consumed in the fuel sector, while around 15% of the methane is reacted in the purge sector. The methane concentration decreases monotonically in the fuel sector, while a bell-shaped concentration curve is observed in the fuel-purge sector, with a maximum value of around 10% located close to 0.3 m of the channel. As shown in Table 2, the current operating conditions ensure a similar residence time of the gas in the fuel and fuel-purging sectors. As purging gas flows through the channel, residual methane in the channel is pushed toward the downstream end of the channel, while the OCs continue oxidizing the fuel. Thus, the residual fuel in the purge sector is mostly oxidized within the same region of the channel as that in the fuel sector. As shown in Figure 7, under the current operating conditions, 99.9% combustion efficiency is obtained at 0.75 m of the channel. The extra 0.25 m of the channel is used to ensure redundancy for the fuel conversion, as discussed in section 2.2. If a higher mass flow rate of methane (e.g., higher operating pressure or lower feed stream temperature) is admitted into the channel or a less reactive metal oxide is used as the OC, the concentration profile is expected to be shifted upward. In these cases, the redundant length decreases. Figure 8 shows the CO2 and O2 flux profiles at the outlet of the channel as a function of time. The CO2 flux is normalized by the inlet

exit of the channel, leading to faster reduction rates and, hence, higher flow velocities near the outlet. After the residual fuel is completely removed, a steady-state flow velocity is observed in the fuel-purge sector. As the channel leaves the fuel zone and enters the air zone, the slowly propagating oxygen front (as observed in Figure 5) rapidly oxidizes the OC. The oxidation at the front consumes the majority of oxygen from air and leads to a relatively lower local velocity. When the OC is fully regenerated, the oxygen concentration front moves downstream and the local velocity returns to steady state. Comparing Figures 5a and 6a, it is obvious that the oxygen fraction contours almost coincide with the velocity curves. Therefore, the flow field fluctuation at the beginning of the air sector is attributed to rapid oxidation and complete OC conversion in this region. After 26 s, all of the OC along the channel is fully regenerated and a steady-state flow field is observed. Fluid velocity oscillation in the air sector suggests stronger transient effects in this region, in which non-uniform reactivity along the channel and the slowly propagating oxygen front cause strong variation of the working condition, such as pressure, mass flow rate, composition, etc. However, under periodic conditions, the combination of a large number of transient flow streams coming from the channels in the air zone (or fuel zone) mix well into one steady-state flow. Nevertheless, the flow field fluctuation may impact the mechanical stability, and these transient effects should be considered in the design optimization.

Figure 8. CO2 and O2 flow rates at the outlet of the channel as a function of time for one cycle. carbon flow rate in the fuel sector, including both methane and CO2, while the O2 flux is normalized by the inlet oxygen flow rate. Thus, at steady state, the normalized species flow rate should be unity. As seen in Figure 8 and Table 2, most carbon is captured in the fuel zone, while unreacted oxygen only exits in the air zone. Therefore, dilution between the oxygen and carbon dioxide is avoided. In the fuel sector, at about 8 s, CO2 flow at the outlet reaches steady state, while in the air sector, it takes about 6 s to reach steady state. Steady state in the air sector is indicated by the complete regeneration of the OC. Because of the high velocity, the fuel-purging sector has a spike of species flux. The residue CO2 (1.94%) in the channel is rapidly flushed out at the beginning of the air sector, leading to a spike of the CO2 flux. In the air-purge sector, the oxygen flux drops to zero at about 1 s before the next cycle. Thus, under current operating conditions, the residence time of the channel in each purge sector is long enough to capture most CO2 and ensure complete separation between the fuel and the air. 2.4. Temperature Distribution. The temperature distribution within the channel is critical in determining the OC reactivity as well as the overall energy balance in repeated cycles. Figure 9a compares the time-averaged temperature distribution of the solid and gas phases. The solid temperature increases monotonically from about 1000 to 1300 K. Thus, the maximum temperature rise along the channel is about 300 K. The gas temperature distribution is directly determined

Figure 7. Normalized CH4 concentration in the fuel and purge sectors (solid lines) and the periodic fuel conversion efficiency (dashed line) as a function of the axial location. A total of 99.9% combustion efficiency is achieved at z = 0.75 m. Figure 7 shows the fuel conversion efficiency based on the methane concentration (Figure 5) and the flow (Figure 6). The conversion efficiency along the channel is defined as

ηcomb(z) = 1 − ĈCH4,fuel(z) − ĈCH4,purge(z)

(6)

Ĉ CH4,fuel and Ĉ CH4,purge are the normalized methane concentration

ĈCH4, i(z) =

ṁ CH4, i(z) ṁ CH4,inlet

i = fuel or purge (7)

where ṁ CH4, i(z) is the time-averaged methane flow rate at location z and ṁ CH4,inlet is the inlet methane feed rate. As seen in Figure 7, the fuel conversion efficiency gradually increases. At the outlet of the channel, the fuel conversion is unity. The majority of the methane is 350


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Figure 9. (a) Time-averaged temperature profile as a function of the axial location for the solid (lines) and the flow (circles) and (b) energy flux in the solid phase within one cycle. The dashed line in panel a is the maximum temperature variation of the solid phase in one cycle.

Table 4. Input Parameters, Base-Case Values, and Sensitivities of Outputs to the Input Parameters sensitivity S̃χ→ψ input (χ)/output (ψ) k0,CH4

a

description

base case

units

pre-exponential factor for reduction

OC 1.125 × 106

mol0.6 m−1.8 s−1 −1

ηI 0.0000

ηCO2

ΔTmaxa

L0.99

0.0502

1.4532

−1.5790 0.0009

k0,O2

pre-exponential factor for oxidation

2.043 × 10

s

0.0000

0.0000

−0.0017

ECH4

activation energy for reduction

60

kJ mol−1

−0.0209

−0.2680

−7.6084

7.9137

E O2

activation energy for oxidation

15

kJ mol−1

0.0000

0.0001

0.0026

−0.0014

aCH4

pressure coefficient for reduction

0.83

−0.0070

−0.1003

−2.7555

3.0465

aO2

pressure coefficient for oxidation

0.68

0.0000

0.0001

0.0028

−0.0017

nCH4

reaction order for reduction

0.4

0.0000

0.0402

1.2203

−1.0258

n O2

reaction order for oxidation

1.0

0.0000

−0.0001

−0.0051

0.0028

d H D εM δoc Nud Shd

channel width channel height reactor diameter cross-section area ratio of solid thickness of the porous OC layer Nusselt number Sherwood number

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

−0.0474 −0.2121 0.0000 0.0834 0.0503 −0.0004 0.0000

−1.9867 −0.1345 0.0000 1.7025 1.4469 0.2806 0.0007

1.5360 −0.0101 0.0000 −1.6550 −1.5788 0.0091 −0.0034

P Tin vol % τ uair ufuel ufuel_p uair_p

operating pressure inlet temperature volume fraction of fuel at the inlet one cycle period air flow velocity fuel flow velocity steam velocity of the fuel-purging sector steam velocity of the air-purging sector

−0.0041 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

−0.1102 0.1222 0.1199 0.2374 −0.0893 0.0849 0.1910 −0.0319

−2.7648 4.9109 2.2060 0.6953 −1.6098 0.6588 −0.7612 −0.4709

2.8187 −5.0107 −1.5214 −0.0132 1.5300 −0.5916 0.5641 0.5500

4

Reactor Configuration 2.0 mm 1.0 m 1.70 m 0.45 50 μm 3.61 3.61 Operating Condition 10 atm 823 K 15 % 30 s 0.7 m/s 0.09 m/s 0.11 m/s 0.7 m/s

The maximum temperature fluctuations (ΔTmax) for all tests occur at the inlet. Figure 9b shows the overall energy fluxes in the solid phase during one cycle. As shown in Figure 9b, the overall energy is balanced such that the reaction heat generation is transferred out of the system by convective cooling. The reaction energy release is highest in the middle of the channel, while convective heat transfer is important at the inlet. The solid phase acts as a heat reservoir to match the difference; it stores the heat from the reaction in the middle and

by the solid temperature, except at the inlet, where the feed gas is much cooler than the solid. Therefore, convective heating at the inlet is significant. The dashed line in Figure 9a shows the maximum solid temperature change with time in one cycle. This curve is generally less than 20 K, and therefore, the temporal temperature variation is limited, as discussed in Figure 2 previously. 351


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transfers the heat to the inlet by conduction. Near the exit of the channel, however, all of these curves are close to zero, because the majority of the fuel is converted at about 0.75 m. Thus, the bulk dense layer in the solid phase with a high thermal inertia and high conductivity plays a key role in maintaining the thermal balance in the channel and in stabilizing the cyclic operation.

3. SENSITIVITY ANALYSIS 3.1. Method. Sensitivity analysis is important when certain parameters are unknown, known with some tolerance, or Table 5. Sensitivities of the Thermal Capacity and the Flue Stream Temperature to the Input Parameters sensitivity S̃χ→ψ input (χ)/ output (ψ) D εM P Tin vol % uair ufuel ufuel_p uair_p

description reactor diameter cross-section area ratio of solid operating pressure inlet temperature volume fraction of fuel at the inlet air flow velocity fuel flow velocity steam velocity of the fuel-purging sector steam velocity of the air-purging sector

base case

units

Wth

Texit − Tamb

1.70 0.45

m

2.0000 −0.8182

0.0000 −0.0150

10 823 15

atm K %

1.0000 −0.6381 1.0000

0.0158 0.4412 0.4488

0.7 0.09 0.11

m/s m/s m/s

0.0000 1.0000 0.0000

−0.2206 0.3510 −0.0367

0.7

m/s

0.0000

−0.0793

Figure 11. Time-averaged solid temperature profiles as a function of the axial location for the base case and ±10% variation of the operating pressure.

Sensitivity analysis is performed for the rotary CLC reactor design in the manner described below. The most important outputs for each simulation are identified. These outputs are chosen because they best describe the periodic operation of the reactor. Examples of such outputs include the thermal capacity (Wth), the fuel conversion (ηI) and carbon separation (ηCO2) efficiencies, the flue stream temperature (Texit − Tamb), the maximum solid temperature fluctuation (ΔTmax), and the length of 99% fuel conversion (L0.99). Input parameters whose values are potentially important to these outputs are then identified. Base-case values for these input parameters are chosen on the basis of the design parameters and the operating conditions used in the base case [see part 1 (10.1021/ ef3014103)]. The model is then repeatedly run, allowing for one input parameter at a time to be varied over a range of ±10% around its base-case value. The change of the outputs for a given change in an individual input parameter can then be observed and compared to those of other input parameters for the rotary CLC reactor design. Sensitivity analysis is performed for the design proposed in part 1 (10.1021/ef3014103). The potentially important input parameters for this design, as well as their base-case values, are shown in Table 4. Input parameters are classified as one of three types, as listed in part 1 (10.1021/ef3014103): the OC kinetics, the reactor configuration, and the operating conditions. The model developed in part 1 (10.1021/ef3014103) is run repeatedly with each input parameter changed by −10, −5, +5, and +10% from its base value. Because of their relatively larger influences, four more tests (i.e., −7.5, −2.5, +2.5, and +7.5%) are performed for the analysis of the reduction kinetics. The inlet temperature of the feed streams is varied at −20, −10, +10, and +20 K with respect to the base case. For all sensitivity tests, the feed methane is completely consumed and the fuel conversion efficiency is above 99.4%. One exception is that, as the reduction activation energy (ECH4) is raised over +3%, the residence time of the fuel in the channel is insufficient to ensure complete conversion. A certain fraction of the methane leaves the reactor without being converted, leading to inadequate chemical reaction energy release to heat the feed streams, which

Figure 10. Sensitivity of fuel conversion efficiency to the input parameters.

uncertain, as is the case with most practical simulations. It is used to identify the input parameters or variables that have the greatest influences on the simulation results. Important input parameters or variables identified by sensitivity analysis, whose values are unknown, can then be further investigated to ̃ ) of a improve simulation accuracy. The sensitivity (Sχ→ψ simulation output (ψ) to an input (χ) is defined as follows: Sχ̃ → ψ =

χ Δψ ∂ ln ψ ≈ ψ Δχ ∂ ln χ

(8) 352


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Figure 12. Sensitivity of the exit carbon separation efficiency to the input parameters.

output, relative to other parameters, are omitted for the sake of clarity. 3.2. Results. Figures 10−15 and Table 4 present the results of sensitivity analysis. The base case is also described in Table 4. The fuel conversion efficiency (ηI), the carbon separation efficiency (ηCO2), the maximum solid temperature fluctuation (ΔTmax), and the length of 99% fuel conversion (L0.99) are used as the outputs in the sensitivity analysis because these parameters characterize the capability of the rotary reactor in completely converting the fuel and capturing the CO2 with high stability and robustness. As shown in Figure 10 and Table 4, the fuel conversion efficiency (ηI) is most sensitive to the activation energy for reduction (ECH4) and the pressure coefficient for reduction (aCH4). A higher activation energy and higher pressure coefficient decrease the reduction rate and reduce the fuel conversion efficiency. A higher operating pressure also decreases the efficiency because the convective cooling effects at higher pressures surpass the heating from the extra methane admitted to the channel. Thus, as shown in Figure 11, a higher pressure leads to a lower temperature along the channel and, hence, a reduced fuel conversion rate. Nevertheless, the

lowers the solid temperature, slows the reduction rate, and hence, further decreases the fuel conversion efficiency. In the periodic states, both the exit temperature and the fuel conversion efficiency are low. For instance, with a 4% increase of ECH4, the time-averaged flue gas temperature is 962 K and the fuel conversion efficiency is 27.3%, while for a +3% increase of ECH4, the temperature is 1314 K and the efficiency is 99.6%. Thus, for the sensitivity analysis, the reduction activation energy (ECH4) is only varied between −10 and +3%. In the real industrial application, an active control of the feed stream should be used to maintain the operating temperature and avoid extinction. The results of the sensitivity analysis are shown both graphically and in tables. The results shown in Tables 4 and 5 are the averaged values among the sensitivity tests. In the graphical representations, the x axis shows the percentage change of each input parameter (χ) from its base-case value and the y axis shows the percentage change in output (ψ) because of changes in each parameter. The slope of a line on the plot represents the sensitivity of the output (ψ) to a particular parameter. Parameters that result in very small changes of 353


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the activation energy on the gas residence time becomes less significant when ECH4 is reduced by over 4%. This is because the OC near the inlet is fully reduced, as shown in Figure 13b. In this case, the reaction is mainly limited by the amount of the OC available in the porous layer, and a further decrease of the reduction activation energy has little impact on the temperature distribution along the channel. Figure 14 shows the sensitivity of the maximum temperature fluctuation (ΔTmax) along the channel. For all of the sensitivity tests, the maximum temperature variation occurs at the inlet of the channel. The maximum temperature fluctuation indicates the impact of the thermal distortion on the periodic operation. A larger fluctuation means stronger thermal stresses and a higher risk of failure. As shown in Figure 14 and Table 4, the temperature variation is most sensitive to the reduction activation energy (ECH4), operating pressure (P), and temperature (Tin). A lower activation energy causes a severe temperature variation because a larger fraction of OC is reduced near the inlet, leading to a significantly higher energy release from the highly exothermic reactions in the following oxidizing sector. As discussed in section 2.1, the reaction heat that exceeds the convective heat-transfer rate to the gas flow is temporarily stored in the solid phase and, hence, raises the solid temperature. As the channel travels for one cycle, the excess energy is transferred to the bulk flow by convection and the solid temperature returns to the original state. In contrast, a raised operating pressure and decreased feed stream temperature lead to a lower fuel conversion rate at the inlet because a stronger convective cooling effect lowers the solid temperature. Thus, the temperature rise is inhibited because less OC is reacted near the inlet. Figure 15 shows the sensitivity of the length of 99% fuel conversion (L0.99) to the input parameters. In the base case, 99% of the fuel is converted before 0.70 m of the reactor, leading to 0.30 m of redundant length near the exit to ensure the functionality of the reactor under off-design conditions. In the sensitivity tests, the length of 99% fuel conversion indicates the necessary channel height to ensure complete fuel conversion and maintain periodic operational stability. For all tests, L0.99 is below the height of the channel. The cases with the longest L0.99 are those in which ECH4 is raised by +3% and either P or aCH4 is raised by +10%, as also evident in Figure 10. L0.99 is also sensitive to the inlet temperature because enhanced convective cooling at a lower feed temperature lowers the reaction temperature and inhibits the reduction rate. Sensitivity analysis is also performed specifically for the input parameters that influence the overall thermal capacity (Wth) as well as the flue gas temperature (Texit − Tamb). Table 5 and Figures 16 and 17 present the results of the sensitivity analysis with respect to these parameters. The impact of other parameters on the flue gas temperature is not included because, in these cases, the flue temperature and the thermal capacity remain unchanged and are directly determined by the overall energy conservation. As shown in Figure 16, the thermal capacity is most sensitive to the reactor diameter, because a larger reactor leads to more methane feed. A higher operating pressure, volume fraction of fuel, or fuel flow velocity also increases the thermal capacity because of a higher mass flow rate of methane admitted into the channel. Figure 17 shows that the flue gas temperature is most sensitive to the volume fraction of fuel at the inlet, the feed stream temperature, and the fuel flow velocity.

Figure 13. Effects of the reduction activation energy (ECH4) on the (a) average gas residence time in the channel and (b) profile of conversion at the end of the fuel-purge sector.

efficiency remains close to unity for all of the sensitivity tests, and the maximum drop is within 0.6%. Carbon separation (ηCO2) is most sensitive to the cycle period (τ), the channel height (H), the steam velocity of the fuel-purging sector (ufuel_p), and the activation energy for reduction (ECH4), as shown in Figure 12. The carbon separation efficiency can be improved by either increasing the residence time of the channel in the fuel-purge sector (a lower rotational velocity and a longer period) or reducing the residence time of the gas in the channel (a higher steam velocity and a shorter channel height). The dependence upon the activation energy is negative, indicating that increasing the activation energy leads to reduced CO2 separation. A higher activation energy hinders the reduction rate, leading to a lower temperature and, hence, a lower bulk velocity throughout the channel. Therefore, as shown in Figure 13a, the residence time of the gas in the channel (within the fuel or fuel-purge sector) increases with a higher reduction activation energy and, at the end of the fuelpurge sector, a larger fraction of residual CO2 still remains in the channel. Note that, as shown in Figure 13a, the impact of 354


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Figure 14. Sensitivity of the maximum temperature fluctuation to the input parameters.

3.3. Discussion. From the sensitivity analysis, it is clear that the reduction kinetics has a larger impact on the performance of the rotary reactor than the oxidation kinetics. Among the reduction kinetic parameters, the activation energy influences the periodic operation the most. An increase of the activation energy significantly shifts the fuel conversion toward the downstream, leading to a longer height of the reactor needed for complete conversion. As the activation energy is raised over a certain value (i.e., 4% for the base case), a certain fraction of methane leaves the reactor without being consumed, leading to an insufficient chemical energy release to heat the bulk flow. The fuel conversion is then further reduced because of the lower temperature. In this case, the “positive feedback” effects to the change of the activation energy make the system unstable. In an industrial application, sufficient redundant length or active control of the feed streams is necessary to ensure stability. In contrast to the reduction kinetics, the oxidation kinetics has a limited effect on the performance as long as more than a stoichiometric amount of oxygen is supplied to completely regenerate the OC. Among the reactor configuration parameters, the channel width (d), the thickness of the solid (εM), and the thickness of

the porous OC layer (δoc) have the largest impacts. A thicker porous layer with the channel width (d) unchanged enhances the fuel conversion because the reaction rate is proportional to the thickness of the OC layer, as seen in part 1 (10.1021/ ef3014103). A higher exothermic reaction rate leads to higher solid temperatures near the inlet and, hence, improves the fuel conversion. The side effect is a larger temperature fluctuation because of a higher chemical energy release rate near the inlet. Similar trends can be observed when decreasing the gas passage size (i.e., reducing d or increasing εM) without changing the OC layer. In these cases, the solid temperature is raised because the mass flow rate is lower and, hence, the energy required to heat the bulk flow decreases. The enhanced reaction rate at a higher temperature leads to higher fuel conversion as well as larger temperature fluctuations. In contrast, the periodic performance is insensitive to the Nusselt number (Nud) or the Sherwood number (Shd), which indicates that the convective (heat or mass) transfer is not the rate-limiting step for the operation. The operating pressure and the feed stream temperatures are the most important parameters in determining the proper operating conditions. A higher pressure or lower inlet temperature inhibits the reaction rates by decreasing the solid 355


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Figure 15. Sensitivity of the length of 99% fuel conversion to the input parameters.

Figure 17. Sensitivity of the flue stream temperature to the input parameters.

temperature. The enhanced convective heat-transfer effect also restrains the temperature fluctuation near the inlet, as discussed in section 3.2.

Figure 16. Sensitivity of the thermal capacity to the input parameters.

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(hi − Tosi) is called the flow exergy function and is denoted as ξi. For Ẇ max,in, input streams are the fuel, the air, and the steam. The output streams are CO2, condensed water, and unburned air at standard temperature and pressure (STP) (Figure A1a).

4. CONCLUSION The one-dimensional model developed in part 1 (10.1021/ ef3014103) has been applied to simulate the cyclic performance of the rotary reactor with copper oxide used as the OC and BN as the binder. Simulations were performed for repeated cycles until periodic stationary state performances are reached. Simulation results for the base case show that high fuel conversion efficiency as well as high carbon separation efficiency can be obtained. Because of the relatively low reduction rate of copper oxide, the fuel conversion occurs continuously from the inlet to the end of the reactor, while in the air sector, OCs are rapidly regenerated, consuming a large amount of oxygen from the air. A total of 99.9% of the fuel is converted within 75% of the channel, leading to 0.25 m redundant length near the exit to account for uncertainty and ensure complete fuel conversion under off-design conditions. The external mass-transfer resistance is less important in the base case, and the OC conversion is mainly limited by the heterogeneous reactions. Velocity fluctuation is observed during the transition periods between sectors because of the complete conversion of OCs. The gas temperature increases monotonically from 823 to 1315 K, which is mainly determined by the solid temperature. In the periodic state, the solid temperature variations with time are limited within 20 K. The overall energy in the solid phase is balanced between reaction heat release, conduction, and convective cooling. Preliminary analysis shows great potential of the rotary design for CLC applications. Sensitivity studies are also performed to identify input variables and parameters critical to the operation. Sensitivity analysis for the base case indicates that the reduction kinetics, the operating pressure, and the feed stream temperature are the most important factors affecting the periodic performance of the reactor. Among the reduction kinetics, the activation energy is the most important parameter in determining the fuel conversion efficiency, temperature distribution, and carbon separation efficiency. Experimental tests should be carried out in the future to accurately measure the reduction kinetics for the rotary design.

̇ ,in = ṁ fuel ξfuel + ṁ air ξair + ṁ steamξsteam − ṁ CO ξCO Wmax 2 2 − ṁ H2OξH2O − ṁ O2 + N2ξO2 + N2

Figure A1. Illustration of the maximum work transfer from (a) feed streams and (b) flue streams from the rotary reactor. The output streams from the reversible engine are at STP.

For Ẇ max,out, the input streams are the two flue streams from the fuel and air zones. The output streams are CO2, condensed water, and unburned air (STP) (Figure A1b). Note that, for the base case, CH4 is completely consumed and, thus, omitted in the calculation.

■

APPENDIX For an open-flow system interacting only with the environment at To (298 K) and Po (101 325 Pa), the first and second laws of thermodynamics state that (neglecting kinetic and potential energy) dE = Q̇ − Ẇ + dt Q̇ dS = + dt To

∑ ṁ ihi − ∑ ṁ ihi in

out

∑ ṁ isi − ∑ ṁ isi + Sġ in

out

̇ ,out = ṁ fuel zoneξfuel zone + ṁ air zoneξair zone − ṁ CO ξCO Wmax 2 2 − ṁ H2OξH2O − ṁ O2 + N2ξO2 + N2

∑ ṁ i(hi − Tosi) − ∑ ṁ i(hi − Tosi) − ToSġ in

out

(A5)

For direct combustion, the maximum work from the flue stream is calculated according to Figure A2. The inlet stream temperature is obtained from constant pressure adiabatic combustion, assuming complete fuel conversion. The maximum work is calculated as

(A1)

(A2)

̇ ,steam = ṁ flueξflue − ṁ CO ξCO − ṁ H OξH O Wmax 2 2 2 2

where E and S are the total internal energy and total entropy of the system, respectively. Q̇ and Ẇ are the heat transfer and work transfer with the environment, respectively. ṁ i, hi, and si are the mass flow rate, specific enthalpy, and entropy of stream i, respectively. Sġ is the entropy generation. Substituting eq A2 into eq A1 and integrate in one cycle, we can obtain Ẇ =

(A4)

− ṁ O2 + N2ξO2 + N2

(A6)

̇ ,no steam = ṁ flueξflue + ṁ steamξsteam − ṁ CO ξCO Wmax 2 2 − ṁ H2OξH2O − ṁ O2 + N2ξO2 + N2

(A7)

Therefore, the second-law efficiency can be calculated as ̇ ,out Wmax ηII = for the rotary reactor ̇ ,in Wmax (A8)

(A3)

Therefore, for one cycle, the maximum work transfer rate is obtained when the process is reversible; i.e., Sġ = 0. The term 357


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ṁ CH4, i = time-averaged methane flow rate (kg s−1) ṁ CH4,inlet = inlet methane feed rate (kg s−1) Nud = Nusselt number (Nud = hgsd/kg) n = reaction order nO,added = actual amount of oxygen, added with the oxide and/or with steam (mol) nO,stoic = stoichiometric amount of oxygen for full conversion of the fuel (mol) P = operating pressure (Pa) Red = Reynolds number (Red = ρud/μg) Shd = Sherwood number (Shd = hm,id/Da) Tin = inlet temperature (K) Tamb = ambient temperature (298 K) Texit = flue gas stream temperature (K) u = velocity (m s−1) Ẇ = work (J s−1) Wth = thermal capacity (MW) Greek Letters δoc = thickness of the porous oxygen carrier layer (m) εM = cross-section area ratio of solid ϕ = oxygen-added ratio ηCO2 = carbon separation efficiency ηI = combustion efficiency ηII = second-law efficiency τ = cyclic period time (s) Acronyms BN = boron nitride CLC = chemical-looping combustion OC = oxygen carrier redox = reduction and oxidation

Figure A2. Illustration of the maximum work transfer in direct combustion (a) with and (b) without steam mixing. The output streams from the reversible engine are at STP.

ηII =

̇ ,steam Wmax ̇ ,in Wmax

for direct combustion with steam

mixing ηII =

■

̇ ,no steam Wmax ̇ ,in Wmax

(A9)

■

for direct combustion without

steam mixing

(A10)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This study is financially supported by a grant from the MASDAR Institute of Science and Technology and the King Abdullah University of Science and Technology (KAUST) Investigator Award.

■

REFERENCES

(1) Lyngfelt, A.; Leckner, B.; Mattisson, T. A fluidized-bed combustion process with inherent CO2 separation; application of chemical-looping combustion. Chem. Eng. Sci. 2001, 56, 3101−3113. (2) Adanez, J.; Abad, A.; Garcia-Labiano, F.; Gayan, P.; de Diego, L. F. Progress in chemical-looping combustion and reforming technologies. Prog. Energy Combust. Sci. 2012, 38 (2), 215−282. (3) Linderholm, C.; Mattisson, T.; Lyngfelt, A. Long-term integrity testing of spray-dried particles in a 10-kW chemical-looping combustor using natural gas as fuel. Fuel 2009, 88, 2083−2096. (4) Adanez, J.; Gayan, P.; Celaya, J.; de Diego, L. F.; Garcia-Labiano, F.; Abad, A. Chemical looping combustion in a 10 kWth prototype using a CuO/Al2O3 oxygen carrier: Effect of operating conditions on methane combustion. Ind. Eng. Chem. Res. 2006, 45, 6075−6080. (5) Abad, A.; Mattisson, T.; Lyngfelt, A.; Ryden, M. Chemicallooping combustion in a 300W continuously operating reactor system using a manganese-based oxygen carrier. Fuel 2006, 85, 1174−1185. (6) Proell, T.; Kolbitsch, P.; Bolhar-Nordenkampf, J.; Hofbauer, H. A novel dual circulating fluidized bed system for chemical looping processes. AIChE J. 2009, 55, 3255−3266. (7) Berguerand, N.; Lyngfelt, A. Chemical-looping combustion of petroleum coke using ilmenite in a 10 kWth unit−high-temperature operation. Energy Fuels 2009, 23, 5257−5268. (8) Shen, L.; Wu, J.; Xiao, J.; Song, Q.; Xiao, R. Chemical-looping combustion of biomass in a 10 kWth reactor with iron oxide as an oxygen carrier. Energy Fuels 2009, 23, 2498−2505. (9) Gu, H.; Shen, L.; Xiao, J.; Zhang, S.; Song, T. Chemical looping combustion of biomass/coal with natural iron ore as oxygen carrier in a continuous reactor. Energy Fuels 2011, 25, 446−455. (10) Fan, L.-S.; Li, F. Chemical looping technology and its fossil energy conversion applications. Ind. Eng. Chem. Res. 2010, 49, 10200− 10211.

NOMENCLATURE

Symbols

a = pressure coefficient Ĉ CH4 = normalized methane concentration D = reactor diameter (m) d = channel width (m) Ea = activation energy (J mol−1) f = friction factor H = channel height (m) hm,i = external mass-transfer coefficient (m s−1) k0 = pre-exponential factor (m(3n−3) mol(1−n) s−1, where n is the reaction order) L0.99 = length of 99% fuel conversion (m) 358


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