CODEN (USA): IJCRGG, ISSN: 0974-4290, ISSN(Online):2455-9555 Vol.10 No.7, pp 157-168, 2017

Abstract : Calcium looping is one of the most promising technology for Carbon Capture and Storage (CCS) purposes. It based on the reversible reaction between sorbent Calcium Oxide (CaO) and Carbon dioxide (CO2). One of the major limitations of this process is that the sorbent loses its activity over multiple cycles. In order to improve the activity of sorbent, intermediate steam hydration step was proposed. This process is based on another reversible reaction where deactivated sorbent is treated with steam to form Ca(OH)2. This Ca(OH)2 undergoes the backward reaction to give back the regenerated sorbent. Several studies have shown encouraging results of the efficiency of this process. Recently, Wang et al. (2013)1 successfully designed a fluidized bed reactor on a pilot-scale. Blamey et al. (2016)2 developed a shrinking core model based on studies carried out on a small experimental reactor. In this study, we are extending the application of this model on a pilot-scale reactor. Modelling of this unit is essential for scale-up and optimization purposes. The model successfully predicts the trends when the operational parameters like steam partial pressure and operating temperature were changed. Keywords : CO2 capture, Calcium Looping, Steam Hydration, Shrinking core model.

Over the last few centuries, anthropogenic activities are leading to unusual phenomenon, which is degrading the environment. Global Warming is one of the most serious threats posed to our environment due to the huge increase in emissions of greenhouse gases like carbon dioxide. A recent study by International Energy Agency (IEA) showed that coal-based power plants are a major source of CO2 emissions3. As a result, government regulations are enforced on such plants to limit the emission of CO2. The industries employ Carbon Capture and Storage (CCS) systems to adhere to the set regulations.

The most widely used technology to carry this out is Amine scrubbing. It is popular because it can be easily retro-fitted with the existing power-plants to include carbon capture in its process. One of the major disadvantages of this process is the energy penalty associated with it. To overcome this problem many alternative technologies have been proposed namely: Membrane separation, Calcium Looping, Chemical Looping, Cryogenic Technology, etc. None of these technologies have been implemented on an industrial scale.4

Among all of the technologies mentioned above, Calcium looping seems to be one of the most promising. Shimizu et al. (1999)5 proposed this novel process of removing CO2 from flue gas using a twin fluidized bed reactor. It makes use of the reversible reaction shown below:

ቆቒቛተቜ ቦ ቆቒቛቤቜ ቿ ቆቆቒቘቛተቜሃ ዠቋቝ ዥ ቭ ቧኔኚኛህን ቨቍሡቪቬቩቢ

A schematic showing the Calcium looping process is shown below:

Fig. 1: Schematic of Calcium looping process

The twin fluidized bed reactors are called carbonator and calciner. In the carbonator, the flue gas is passed through a fluidized bed of calcium oxide (sorbent) at 873 K (600oC), where the CO2 in the flue gas reacts with CaO to produce calcium carbonate which is then sent to the calciner. The CO2 lean flue gas exits the carbonator. Then the calciner is supplied with heat by providing coal and pure oxygen. It favors the backward reaction and CaCO3 decomposes to regenerate the sorbent and also releases CO2 rich flue gas. This is then sent for further processing and sequestration.

This is a cyclic process which would regenerate the sorbent CaO at the end of the calcination step. Later it was found that the sorbent tends to lose its activity after a few cycles.5This can be attributed to the following reasons:

Two major sorbent treatment methods have been proposed. They are Recarbonation and Steam Hydration. This makes the Calcium looping process a three-stage one. Out of these two, extensive studies have been carried out on steam hydration as it was a promising option.

Steam Hydration of the sorbent was first proposed by Manovic et al. (2008)6to improve its activity. It is based on the reversible reaction given below:

ቆቒ ቦ ቋቒ ቿ ቆቛቒቋቜ

A schematic showing the 3-stage Calcium looping process involving steam hydration is as follows:

Fig. 2: Schematic showing 3-stage Calcium looping process.

They carried out experiments in a 75kW calcium looping pilot plant. Steam hydration was carried out at 100OC and atmospheric pressure. The hydrated samples were investigated using Thermo-Gravimetric (TGA) and X-Ray Diffraction (XRD) analysis. The pore surface area, pore volume distribution and swelling showed promising results for hydration. However, one of the major disadvantages observed in the sample was that it was more prone to attrition. Thus, an optimal trade-off between hydration and carbonation is highly desirable.

Ramkumar and Fan (2010)7 carried out a thermodynamic and experimental analysis of 3-stage Calcium looping process with steam hydration. They concluded that operation of the steam hydrator reactor can be carried out below 500OC at atmospheric pressure. For steam partial pressure of 4 atm, hydration occurs at temperatures of 600OC. This enables us to produce high-quality heat which can be used to generate extra electricity. Although, effect on sorbent because of thermal sintering at such high temperatures needs to be investigated. On carrying out steam hydration at 600OC and total pressure ranging from 8-21 atm, they reported that carbon capture capacity of the sorbent increased from 20% to 45% by weight. Phalak et al. (2012)8 then investigated the activity of sorbent when subjected to high-temperature steam hydration in a fixed bed reactor. They demonstrated that there was a negligible reduction in carbon capture capacity over multiple cycles. Wang et al. (2013)1 then designed a bench-scale fluidized bed reactor to carry out steam hydration for sorbent reactivation. Cold-flow tests were carried out and reaction parameters were examined. Internals were installed to promote fluidization of fine Geldart C (CaO) particles which are difficult to fluidize. Satisfactory fluidization was obtained with the aid of rotating agitator and vertical baffles. This lead to a significant improvement in hydration conversion. A linear correlation was observed between hydration conversion and sorbent reactivity. They also discussed the potential for process heat integration to be applied to this process for a variety of applications.

Then Blamey et al. (2016)2established a shrinking core model for steam hydration process describing the kinetics of the process. They reported that it fits the experimental data well. In this work, we are extending the model so that it can be applied to a pilot-scale fluidized bed reactor.

Mathematical Model

An extension of the shrinking core model proposed by Blamey et al. (2016)2 has been used here. The main assumptions of the model are listed below:

A schematic representing the shrinking core model is as follows:

Fig. 3: A schematic representing shrinking core model.

The gas-phase diffusivity was calculated using Wilke-Lee correlation. The correlation is :

ቜዮህቒ

ቖቕቘቑቛቖህቕቝበቕህወ ወ ቜ

ዟዓዟዔ ዟዓዟዔ

ቇዛዜቭ ዷዦ (1)

ሄሀሆዓዔዺቛ ቜ

ሻዓዔ

Air-steam mixture was used in the experiments carried out by Wang et al. (2013)1. The data for molecular separation at collision, energy of molecular attraction and collision function was provided by Treybal9. Using the obtained values of diffusivity co-efficient, the value of Schmidt number was estimated. The fluid properties of steam were obtained from Heat and Mass Transfer Data Book10. The table below provides the estimated values of diffusivity co-efficient and Schmidt number.

Table 1: Calculated values of diffusivity and Schmidt Number (Sc)

Temperature (K)\ Properties | Density of steam (kg/m3) | Viscosity of steam *10 -6(Ns/m2) | ሓሐሑ (m2/s)*10 -5 | Schmidt Number (Sc) |
---|---|---|---|---|

473 | 0.464 | 15.89 | 5.44 | 0.63 |

573 | 0.384 | 20.01 | 7.81 | 0.67 |

673 | 0.326 | 24.32 | 1.03 | 0.72 |

Then, Sherwood Number was estimated using Fröessling correlation: ቖብ ቭ ን ቦ ናህኙቕቢቕህቚቖበቕህቘቘ . (2)11 Then, mass transfer co-efficient was obtained using the dimensionless relation for Sherwood number, ቨዻ ቭ

ዞዓዔ ይዼ

. (3) The table below provides the details of the experimental conditions as reported by Wang et al.

ዸዼ

(2013)1 and the estimated mass transfer co-efficient for each experiment.

Table 2: Overview of experimental conditions and calculated values of mass transfer coefficient for each experiment

Expt. no | Solid feed (mol) | S:Ca | PH20 (atm) | Temp. (K) | Steam feed (l/min) | uo (cm/s) | Re | Sh | kg |
---|---|---|---|---|---|---|---|---|---|

1 | 14 | 1.28 | 1.0 | 573 | 28.3 | 3.72 | 0.0143 | 2.06 | 8.04 |

2 | 14 | 2.56 | 1.0 | 573 | 56.6 | 7.45 | 0.0286 | 2.09 | 8.16 |

3 | 14 | 3.83 | 1.0 | 573 | 85.0 | 11.18 | 0.0429 | 2.11 | 8.24 |

4 | 14 | 2.04 | 0.8 | 573 | 45.3 | 5.96 | 0.0228 | 2.08 | 8.12 |

5 | 14 | 1.53 | 0.6 | 573 | 34.0 | 4.47 | 0.0172 | 2.07 | 8.08 |

6 | 14 | 3.12 | 1.0 | 473 | 56.6 | 7.45 | 0.0435 | 2.11 | 5.74 |

7 | 14 | 2.17 | 1.0 | 673 | 56.6 | 7.45 | 0.029 | 2.08 | 10.71 |

This mass transfer co-efficient can be used to estimate the flux of steam at the surface of the particle by using the following relation: ቍዢዩሂሇሉሆዺድዷዹ ቭ ቧቨዻቆቛትዜ ቧ ትይቜ (4)

The mechanism of diffusion through the product layer was established by Blamey et al. (2016)2. It was reported that Knudsen diffusion also takes place within the product layer. The data for Knudsen diffusion was taken as reported by Blamey et al. (2016)2. The effective diffusivity was estimated taking into account both Fickian diffusion and Knudsen diffusion using the standard expression for resistances in series.

ርዕይቛዡዚቜ ቖ ቖ

ቇዹቭ ቛቦ ቜበቖ (5)

ሼዼዻዾዱ ዞዝ ዞዓዔ

Here, the value of pore tortuosity to consider the non-linear nature of the pores was taken to be 3. This is a typical value suggested by Cussler12, was to be taken in absence of experimental data.

Table 3: Calculated values of Effective Diffusivity

Cycle No. | Ca(OH)2 porosity | Knudsen 473 K | Diffusivity 573 K | 673 K | Effective 473 K | Diffusivity 573 K | 673 K |
---|---|---|---|---|---|---|---|

0 | 0.372 | 3.45 x10 -6 | 3.80 x10 -6 | 4.11 x10 -6 | 4.02 x10 -7 | 4.49 x10 -7 | 4.90 x10 -7 |

2 | 0.196 | 2.79 x10 -6 | 3.08 x10 -6 | 3.33 x10 -6 | 1.73 x10 -7 | 1.94 x10 -7 | 2.11 x10 -7 |

6 | 0.134 | 2.13 x10 -6 | 2.34 x10 -6 | 2.54 x10 -6 | 9.16 x10 -8 | 1.02 x10 -7 | 1.11 x10 -7 |

13 | 0.104 | 1.66 x10 -6 | 1.83 x10 -6 | 1.98 x10 -6 | 5.58 x10 -8 | 6.21 x10 -8 | 6.73 x10 -8 |

For a shrinking core model, the general conversion equation for a spherical particle is as follows13, ቛዝድቛዩዢቜ ቭ ኔ ቧ ቛሆዯቜቘ . (6)

ሆዿ

Blamey et al. (2016)2 carried out a mass balance in the product layer to derive an expression of flux of steam in the product layer. The boundary conditions are: {1} At, ቯ ቭ ቯሇትዢዩሂሆ ቭ ትሇand {2}At, ቯ ቭ ቯዷትዢዩሂሆ ቭ ትዷ. The expression for flux was arrived at in the following form:

ቘሄዿ

በዝዞዱኋኍ በ

ቘሄዯ

ቍዢዩሂሆ ቭ (7)

ሆቛ በ ቜ

ዾዿ ዾዯ

Substituting, ቯ ቭ ቯሇ and ቯ ቭ ቯዷ in equation (7), we get the flux at the particle surface (8) and unreacted core respectively (9).

ቘሄዿ

በዝዞዱኋኍ በ

ቘሄዯ

ቍዢዩሂሆዿቭ (8)

ሆዿቛቖበ ቜ

ዾዯዅዾዿ

ቘሄዿ

በዝዞዱኋኍ በ

ቍዢዩሂ ሆዯ ቭ ቘሄዯ (9)

ዾዯ ዾዯ

ሆዿቛቡ ቁበ ቜ

ዾዿ ዾዿ

From equations (8) and (9), a relation between the flux at the surface of the particle and at the unreacted core was obtained.

ቍዢዩሂ ሆዿ ቭ ቍዢዩሂ ሆዯ ቛሆዯቜ (10)

ሆዿ

Blamey et al. (2016) then carried out a mass balance on Ca(OH)2 formation during reaction. This gives a relation between conversion of Ca(OH)2 and flux of steam at the unreacted core.

ዸዲዕይቛዡዚቜ ቘ ቜሡቘ ዧዕይዡ

ቭ ቧ ቛኔ ቧ ቛዝድቛዩዢቜ ቚዢዩሂሆዷ (11)

ዸለ ሆዥ ሹዕይዡቛቖበቃዕይዡቜ

Since, a first order reaction is taking place and it is related to flux of steam at the unreacted core, the following equation was arrived at:

ሆዯይሂዿዓዝ

ቍዢዩሂሆዯቭቧ ቛትዝቧትዟቜ (12)

ቘ

Here, SV is the BET surface area per unit volume which can be calculated from the expression presented in equation (13)

ቖደ ቭ ቖዜዟዮ ሊዝድዩቛኔ ቧ ዾዝድዩቜ (13)

Substituting, equations (4) and (12) in equation (10), we obtain a relation between the mole fraction of steam at the surface of the particle and the unreacted core which is presented by equation (14)

ሆዯይሂዿዓ ሆዕ

ትሇቭትዜቧ ቛትዝቧትዟቜቛቜ (14)

ቘዿዳ ሆዿ

Equations (6), (9), (11), (12) and (14) are required to completely solve the model and obtain simulation results. The unknowns in the system are xs, xc, rc and XCa(OH)2. A script was written in Matlab to solve this system of equations. Equation (11) is an Ordinary Differential Equation (ODE) which was solved using Euler’s

ሆዯ

method. Using this initial condition, the ratio of can be estimated using equation (6). This obtained value of

ሆዿ ratio was then used to solve equations (9), (12) and (14) to obtain the values of ትሇሂ ትዝand ቍዢዩሂ ሆዯ . The obtained value of ቍዢዩሂ ሆዯ was then used to solve the ODE to give us the value of conversion for the next time interval. This algorithm was repeated to obtain a time-series data of conversion.

The parameters required to solve this system are: C, De, rs, Sv, kA, kg, xE and xB. Concentration C of steam was estimated using ideal gas equation as partial pressure of steam is known. The value of kA was taken from Blamey et al. (2016)2 and equilibrium mole fraction can be calculated from equilibrium partial pressure. Equilibrium partial pressure was estimated using the relation provided by Schaube et al. (2012)14.

ሄዱዽ ቖቝቚ

ኯቡ ቁቭቧ ቦኔኙህኘናኛ (15)

ቖቕቒ

ዮዱዽ

In the experiments carried out by Blamey et al. (2016)2, calcination was carried out for 15 minutes in a calcium looping cycle. However, in the experiments carried out by Wang et al. (2013)1 calcination was carried out for 2 hours. It has been reported in the literature that intensity of calcination affects the sorbent properties. The time of calcination is one of the parameters that affects the intensity of calcination. As a result, no. of cycles for our study was approximated to 8 because 15 minutes of calcination carried by Blamey et al. (2016)2

th 12

is 1/8of 2 hours of calcination carried out by Wang et al. (2013). Since, Blamey et al. (2016)provided data for only 0, 2, 6 and 13 cycles, the parameters for number of cycles being 8 were estimated using linear interpolation.

A table summarizing all the input parameters is given below.

Table 4: Summary of parameters used for modelling

Property | Value |

Mean particle Diameter (µm) | 20 |

Cross-section area of reactor (cm2) | 126.67 |

Sorbent Density (kg/m3) | 3350 |

BET Surface Area (for N=8) (m2/g) | 4.508 |

CaO porosity (for N=8) | 0.562 |

Effective Diffusivity (for N=8) (m2/s) Rate constant per unit area (for N=8) (m/s) | 7.73x10 -8 (473 K); 8.6 x10 -8 (573 K);9.35 x10 -8 (673 K) 3.01x10 -7 (473 K); 1.28 x10 -7 (573 K); 8.73 x10 -8 (673 K) |

Plots of projected conversion versus time for the seven experiments carried out by Wang et. al (2013)1 are shown below.

Fig. 4(a): Plots of estimated conversion as a function of time as calculated by the model developed for actual experiments 1-4 as carried out by Wang et al. (2013)

Fig. 4(b): Plots of estimated conversion as a function of time as calculated by the model developed for actual experiments 5-7 as carried out by Wang et al. (2013)

Wang et al. (2013)1 carried out a detailed study of the reactor performance and effect of various parameters on the reactor performance. The parameters that were investigated are listed below:

In this sub-section, we have made an attempt to validate these experimental findings with our simulation results.

As listed in the literature review section, the sorbent calcium oxide belongs to the family of Geldart C particles. Geldart C particles are most difficult to fluidize. As a result, baffles, agitators and other internals are required to aid fluidization. The simulation does not take into account the difficulty in fluidizing CaO particles. From Figure 5 it can be observed when time is close to zero, the model under-predicts conversion value. This can be attributed to the use of Euler’s method as it is not accurate enough. At higher time, the model over-predicts the conversion value. This can be attributed to the fact that the difficulty in fluidizing sorbent has not been taken into account. Another reason can be the fact that the model does not take into consideration the pore blockage that might occur after certain extent of reaction. However, the model captures the trend of conversion with time reasonably well.

Fig. 5: Conversion versus time with respect to reactor design

While carrying out experiments, it was reported that conversion is directly proportional to the steam partial pressure used to carry out the reaction. From Figure 6, it can be observed that the model successfully captures the effect of change in steam partial pressure on conversion. Although, as stated in the previous section, the model slightly over-predicts the conversion value at higher times.

Fig. 6: Conversion versus time with respect to steam partial pressure

It has been observed that this reaction undergoes Anti-Arrenhius behavior. The conversion decreases on increasing the operating temperature. Again in Figure 7, a similar trend was observed between simulated and actual results. The model over-predicts the conversion at higher times. In this case also, the model successfully predicts the lowering of conversion with respect to temperature.

Fig. 7: Conversion versus time with respect to temperature.

As evident from Figure 4(a), the conversion versus time profiles for the first three experiments, where the steam-flow rate has been varied are strikingly similar. As reported in Wang et al. (2013)1 the final hydration conversion lies within 5 percentage points of each other and more investigation of this parameter is warranted. As a result, we decided not to pursue comparison studies in our simulation for this parameter.

The limitations of this model are listed below:

A fluidized bed reactor model has been extended successfully to a pilot-scale reactor. The experimental trends reported by Wang et al. (2013)1 have been successfully validated. The model successfully captures the trends of change in conversion when two of the major operating parameters are changed: (1) Steam partial pressure and (2) Temperature. Although, the model does not predict conversion at higher times accurately. The reasons for the same have already been discussed in the previous section. In future, we hope to incorporate a more rigorous hydrodynamic model which considers the difficulty in fluidizing Geldart C particles like CaO and the elutriation of fine particles that might occur in the reactor.

Modelling of this unit is essential as it might aid us in future keeping process scale-up in mind. It can also help us in reducing the number of experiments being carried out to carry out optimization studies. Temperature is a very important operating parameter, keeping in mind the costs involved and the flow of process in Calcium looping operation. Thus, temperature optimization studies are of great importance and can be carried out using this model to estimate the optimum temperature at which steam hydration must be carried out in order to obtain the maximum conversion at lowest possible costs.

Nomenclature

C | Molar concentration | mol/m3 |

De | Effective diffusivity within pores | m 2/s |

DAB | Gas-phase diffusivity | m 2/s |

DK | Knudsen diffusivity | m 2/s |

dp | Particle diameter | m |

dpore | Pore diameter | m |

kA | First order rate constant for the reaction of CaO with steam | m/s |

k | Boltzmann constant | J/K |

kg | Mass transfer coefficient | m/s |

M | Molar mass | g/mol |

N | Number of cycles | |

n | Number of moles | mol |

P | Pressure | Pa |

R | Universal gas constant | J/mol/K |

rAB | Molecular separation at collision | nm |

Re | Reynolds number | |

r | Radius | m |

SV | Specific, BET, surface area | m 2/m3 |

Sc | Schmidt number | |

Sh | Sherwood number | |

T | Temperature | K |

t | Time | s |

uo | Fluid velocity | m/s |

W | Molar flux | mol/m2/s |

x | Mole fraction | |

XCa(OH)2 | Conversion to Ca(OH)2 | |

ዾት | Porosity of species | |

λ | Mean free path | m |

ህg | Fluid viscosity | kg/m/s |

ሊg | Gas density | kg/m3 |

ሊx | Density of species | kg/m3 |

ልpore | Pore tortuosity | |

ሔዛዜ | Energy of molecular attraction | J |

ባቛ ቨ ሔዛዜ ቜ | Collision function | |

Subscripts for C, r, X | ||

c/C | At the core of the particle – CaO/Ca(OH)2 interface | |

s/S | At the surface of particles | |

B | In the bulk phase (not applicable to r) | |

E | At equilibrium (not applicable to r) |

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