Kinetics Modelling, Development, and Comparison for the Reaction of

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Catalysis and Kinetics

Kinetics Modelling, Development, and Comparison for the Reaction of Calcium Oxide with Steam Shiladitya Ghosh, John Kokot-Blamey, Matthew E. Boot-Handford, and Paul S. Fennell Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.8b04383 • Publication Date (Web): 29 Apr 2019 Downloaded from http://pubs.acs.org on April 29, 2019

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Kinetics Modelling, Development, and Comparison for the Reaction of Calcium Oxide with Steam Shiladitya Ghosh a, John Kokot-Blamey a, Matthew E. Boot-Handford a, Paul S. Fennell a,* a

Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, England, United Kingdom

Keywords: Fluidised bed reactor, shrinking core, grain catalyst, random pore, calcium looping, hydration, CCS

Abstract

The hydration reaction between calcium oxide (CaO) and steam has applications as (i) a means to increase the reactivity of CaO-based sorbents for calcium-looping (CaL) CO2 capture processes and (ii) a process for thermochemical energy storage (TCES). However, the hydration kinetics of CaO have not been widely investigated in literature, with previous investigations generally performed under diffusion-controlled conditions in a thermogravimetric analyser (TGA). This work uses three particle models including: (i) a developed form of the shrinking core model (D-SCM); (ii) the random pore model (RPM) and; (iii) a developed form of the grain catalyst model (D-GCM), to evaluate the behavior of the reaction between CaO and steam in an atmospheric fluidised bed reactor (AFBR) under typical CaL conditions while minimizing diffusional resistances. The D-SCM was developed to account for particle expansion and changing bulk concentrations while the D-GCM was developed to improve its handling of changing steam concentrations. The suitability of each of the three models is assessed under kinetic-

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controlled conditions by varying particle size (200 – 710 µm), steam concentration (10 – 20 mol%), particle calcination temperature (850 – 950°C), and reaction temperature (300 – 400°C). The D-SCM showed the greatest versatility and demonstrated greater accuracy over the SCM, providing a good fit for experimental data across all experimental conditions tested including data from literature. The RPM consistently bounded the data between a kinetics-controlled and diffusion-controlled prediction, and the D-GCM also showed greater accuracy over the GCM and produced consistent fits across steam concentrations at 300°C but deteriorated at higher reaction temperatures. Further, a quantitative comparison of the modelling results was carried out by 𝜒 2 Goodness of Fit (𝜒 2 -GOF) statistical testing.

INTRODUCTION At the 21st Conference of Parties (COP 21), the Paris Agreement was adopted which decided to reduce anthropogenic greenhouse gas (GHG) emissions to a sustainable level by the end of this century1. The development and wide-scale deployment of carbon capture and storage (CCS) technologies is one way to achieve this.

Calcium looping (CaL) (Figure 1) is one such technology, which exploits the reversible reaction between CaO and CO2 (R1) to selectively remove CO2 from an industrial exhaust stream containing relatively low concentrations of CO2 (e.g. 5-15 vol% for gas and coal-fired power stations respectively) and produce a near-pure stream of CO2 suitable for subsequent compression, transport and storage or reuse.

CaO(s) + CO2(g) ⇌ CaCO3 (s)

(R1)

CaO(s) + H2 O(g) ⇌ Ca(OH)2(s)

(R2)

Ca(OH)2(s) + CO2(g) ⇌ CaCO3(s) + H2 O(l)

(R3)


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In an industrial post-combustion application of this system (Figure 2), an additional hydration step (R2-R3) is often suggested for sorbent reactivity enhancement. In comparison to currently used options such as liquid-gas scrubbing using amines, CaL possesses several distinct advantages: it uses a relatively cheap and naturally abundant material to generate a sorbent, its operating conditions allow high-grade heat to be retained to a large extent, and the chemistry of the process (CaO sorbent as a waste material along with flue gas (CO2) as a feedstock) makes it conducive to integration with and decarbonisation of two major CO2 emitting industries – cement production and power generation.

Figure 1. Conceptual schematic of two-stage Ca-looping process2

Figure 2. Conceptual schematic of three-stage Ca-looping process3


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In the case of CaO, sintering resulting from a gradual expansion of pores within particles leads to continual reduction in reaction surface area and loss in reactivity4. This has been highlighted as a concern for the viability of the CaL process as it is noted that CaO sinters increasingly quickly above 900°C4; this is found to adversely affect carrying capacity5. Previous studies have characterised the rate of decrease in reactivity during looping of the sorbent6, 7. In a fluidised bed, CaO particles are also prone to mechanical degradation through attrition, which reduces the overall reactivity of and changes the fluidisation characteristics of the bed8, 9.

Chemical enhancement of the natural sorbent to tweak its physical and chemical properties is one way to reduce its tendency to undergo sintering, retain a high reaction surface area, and reduce attrition. Manovic & Anthony10 tested the efficacy of preheating treatment, while chemical doping has also been investigated using various ionic materials, with mixed results11-15. Koji et al16 first investigated CaO hydration (R2) with liquid water for this application, with positive results; subsequent studies involving steam have also shown it to consistently increase sorbent porosity17, 18

. In CaO hydration, the advantage of using steam instead of liquid water is that the energy

efficiency of the process is increased as the higher temperatures necessitated allow for better heat recovery.

Blamey19 recently investigated the hydration behaviour of Havelock limestone (500-710 µm) for use in CO2 capture. They examined limestone samples that were cycled (up to 13 times) through a calcination (1173 K) and carbonation (973 K) process in a fluidised bed reactor and were then hydrated, using a TGA, with a steam concentration of 75 mol% at temperatures of 483-678 K. The maximum hydration reaction rate increased with increasing hydration temperature while


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the overall reaction conversion increased at lower hydration temperatures. The projected posthydration CO2 carrying capacities of the sorbents were noted to increase by up to 100% at higher temperatures showing the importance of process conditions on the effectiveness of hydration as a reactivation strategy.

In this paper we set out to assess and develop flexible and physically correct analytical particle models for describing the complex reaction behaviour of CaO with steam at industrially relevant conditions and conversion ranges in a fluidised bed reactor. This allows for measuring and modelling the reaction kinetics while minimizing diffusional resistances within the system, which is important for the development of scaled up CaL systems and steam hydration reactivation strategies.

Several kinetic models, such as the random pore model, the grain catalyst model, and the shrinking core model have been developed for describing the hydration19-23as well as carbonation 24-26

of CaO under a variety of conditions in a TGA.

However it has not been assessed whether these models also successfully describe the reaction behaviour in a fluidised bed setup which significantly mitigates the diffusional resistances encountered in a TGA. This study aims to contribute to building the body of knowledge describing the behaviour of the hydration reaction at a particle level by investigating existing kinetic models and then developing improved models using data from a setup with reduced mass transfer limitations and consequent low diffusional resistances.


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THEORETICAL BACKGROUND Random Pore Model The random pore model (RPM) illustrated in Figure 3 was introduced by Bhatia & Perlmutter21 for improved modelling of fluid-solid reactions. It considers the overall pore size distribution of a material while acknowledging that many particles do not exhibit a regular distribution of pores. The RPM was found to provide a good fit for the carbonation of CaO22, 27. Eq. 1 – 4 describe the general (kinetics-controlled) RPM.

d𝑋 d𝑡

𝐸𝑎

1

= 𝑘𝑎 e−𝑅𝑇 (1 − 𝑋)[1 − 𝛹𝐾 ln(1 − 𝑋)]2

𝛹𝐾 =

4𝜋𝐿0

(2)

𝜌𝑆02 ∞ 𝜐𝑜 (𝑟)

𝑆𝑜 = 2 ∫0 1

𝑟

∞ 𝜐𝑜 (𝑟)

𝐿𝑜 = 𝜋 ∫0

(1)

𝑟2

𝑑𝑟

(3)

𝑑𝑟

(4)

Eq. 1 describes the rate of reaction using Eq. 2 – 4 which calculates the pore structure parameter for the kinetics-controlled model 𝛹𝐾 , reaction surface area 𝑆𝑜 , and the total overlapping pore length 𝐿𝑜 in the system respectively as inputs to Eq. 1, as a means to approximate a random distribution of pores. All of these parameters depend on 𝜐𝑜 , the pore volume distribution of the material which has to be physically measured via porosimetry from the sample material prior to running experiments. Upon measuring 𝜐𝑜 , Eq. 3 – 4 are computed to then calculate 𝛹 via Eq. 2.

Morales-Florez et al26 performed a follow-up study investigating the applicability of the diffusion-controlled RPM to the CaO hydration reaction and obtained a good fit with a


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modification (Eq. 5 – 7) of the fundamental RPM for diffusion control. However, for their study, the experiments were conducted over extended time scales (300-600 h) and under ambient conditions, meaning that the reaction durations and conditions are significantly different compared to those used in CaL and so its suitability for CaO hydration under CaL conditions has yet to be assessed in the literature.

𝛸𝐵 (𝑡) = 1 − 𝛹𝐷 e−𝜔(√𝑡+𝜃) 𝛹𝐷 =

2

(5)

4𝜋𝐿𝑜 (1−𝜀𝑜 )

(6)

𝑆𝑜2 ∞

(7)

𝜀𝑜 = ∫0 𝜐𝑜 (𝑟)𝑑𝑟 (a) (b)

𝒕

Figure 3. (a) Effect of 𝛹 on RPM profile21; (b) illustration of reactive particle surface with randomly-sized pores21 Here an additional term is required to calculate the pore structure parameter for the diffusioncontrolled model 𝛹𝐷 (Eq.6) - porosity 𝜀𝑜 (Eq. 7). This calculated pore structure parameter is then used in evaluating Eq. 5 which describes the conversion of the reactant, along with 𝜔 and 𝜃, which are numerical fitting parameters that have to be iteratively varied to produce a conversion vs time


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profile from the model. The fitting parameters are characteristic to each system and thus are expected to be consistent across experiments from a particular setup. Importantly, as this version of the model is diffusion-controlled, the reaction kinetics are not of importance and they do not directly influence the fitting parameters, hence the rate of reaction described in Eq. 1 is not considered for Eq. 5. Overall, the RPM is a classic reaction model with wide-ranging applicability from which other more specialised models have been developed. Hence it is included in this study to quantify its suitability for the considered reaction and to compare this with the performance of more advanced models.

Grain Catalyst Model CaO hydration kinetics have also been investigated from the perspective of a heat pump/energy storage system23, where Ogura & Zhang noted that previous gas-solid models such as the RPM did not adequately account for heat/mass transfer resistances, changes in pore sizes, and volumetric expansion of the particles, which meant that in many applications the predictions from those models would significantly overestimate the rate of conversion at later stages of reaction as well as the final equilibrium conversions. This led to their introducing the grain catalyst model (GCM) (Figure 4) which makes use of a fundamental catalyst model as a starting point to obtain Eq. 8 – 12.


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Figure 4. Schematic of GCM pore & grains23

d𝛸𝐵

(

d𝑡

) = 3𝐸𝑓 𝑎

2

𝑘1

𝛥𝑃ℎ (1 − 𝛸ℎ𝑦𝑑 )3

(8)

1

(9)

𝑘 1+( 2 ) 𝑘3

1

1

𝐸𝑓 = 𝛷 (𝑡𝑎𝑛ℎ(3𝛷) − 3𝛷) 𝛷𝛸 =

𝑟(𝛸) 3

𝑘 𝜌(𝛸)

√ 𝐷𝑎 (𝛸)

(10)

𝑒

𝜀

𝑇

𝐷𝑒 = 3.067 𝜏 𝑟𝑝𝑜 √𝑀 𝑆

(11)

𝛥𝑃ℎ = (𝑃𝑤 − 𝑃𝑝 )/𝑃0

(12)

−1.096×104 𝑅𝑇

(13)

𝑚𝑔

𝑘1 = 51.1 e 𝑘2 𝑘3

= 5.25 × 104 e

−4.81×104 𝑅𝑇

(14)

It is important to note that this model considers each CaO particle to be made up of multiple grains and thus performs calculations based on individual grains rather than the overall particle. It was developed by Ogura & Zhang based on hydration experiments conducted in a TGA at atmospheric pressure and a range of particle sizes (45-1000 µm) and reaction temperatures (161288°C). The significance of this study and the resulting model is that they demonstrated the


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increasing influence of intra-particle mass transfer resistance with increasing particle size, and accounted for changing particle size during the reaction.

Eq. 8 calculates the actual rate of reaction by accounting for the catalyst effectiveness factor 𝐸𝑓 (Eq. 9), the characteristic reaction rate constant functions (Eq. 13-14), the pressure gradient across the sorbent particle Δ𝑃ℎ (Eq. 12), and the reaction conversion. The catalyst effectiveness factor is used to account for changes in pore size within the particle over the course of the reaction, and is dependent on the Thiele modulus 𝛷𝑋 (Eq. 10) - a dimensionless quantity dependent on the ratio of the reaction rate to the effective diffusivity. The effective diffusivity coefficient 𝐷𝑒 (Eq. 11) accounts for both Knudsen diffusion and effective bulk diffusion phenomenon and is needed for evaluating the Thiele modulus.

The initial inputs into the model are the initial measured average pore radius 𝑟𝑝𝑜 , calculated initial density 𝜌(0), calculated initial grain radius 𝑟(0), all used to evaluate the effective diffusivity, Thiele modulus, and effectiveness factor at the start of the reaction and then calculate the initial rate of reaction, as the pressure gradient is assumed constant. The initial rate is then used to calculate the new grain density and grain radius, resulting in an iterative calculation procedure that ultimately produces a reaction rate vs time profile for the reaction while accounting for changes in particle and pore sizes along with heat and mass transfer effects. This last point is one of the main motivations for examining the GCM in this study, as other models in the literature that attempt to describe this system do not consider changes in particle or pore size, hence it is of interest to ascertain if this proves helpful for improving modelling accuracy.


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Shrinking Core Model The shrinking core model (SCM) (Figure 5) was first proposed by Yagi & Kunii28 as a generalised and parameterized reaction model for fluid-solid reactions while considering kinetic control and film diffusion resistances considered in series and can be applied to model a wide variety of gas-solid reaction systems (Eq. 15). In its basic form it considers particle density (𝜌𝐵 ), mass transfer (𝑘𝑔 ), reactant concentration (𝐶𝐴 ), and changing radii of the particle shell (𝑟𝑆 ) and its unreacted core (𝑟𝐶 ) to predict the extent of conversion achieved at various time intervals.

rS rC

Figure 5. Schematic of SCM29

𝜌 𝑅

3

𝑟

𝑡 = 3𝑘𝐵𝐶 (1 − (𝑟𝐶 ) ) 𝑔 𝐴

(15)

𝑆

Recently Criado et al30 investigated this model for the hydration of CaO through a linear fitting of the maximum rate of reaction (hydration) against the inverse of the average particle diameter. They demonstrated that it could be effectively applied to the reaction under a limited range of


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conditions, with the assumption of equimolar counter-diffusion. Blamey et al20 further developed the SCM (henceforth alluded to as D-SCM) while removing this assumption using Eqs. 16 – 20. However, all investigations thus far have assumed that there is no change in particle size during the reaction; this is known to be untrue as CaO particles expand upon hydration31, 32. Furthermore, the literature has made use of thermogravimetric analysis (TGA) setups exclusively, which can face significant diffusional resistances.

d𝑋𝐶𝑎(𝑂𝐻)2 d𝑡

=

𝑊𝐻2 𝑂,𝑟𝐶 =

−3 𝑟𝑆

(1 − 𝑋𝐶𝑎(𝑂𝐻)2 )

𝜌𝐶𝑎𝑂 (1−𝜀𝐶𝑎𝑂 )

(1−𝑥𝑆 ) ] (1−𝑥𝐶 ) 𝑟 2 𝑟 𝑟𝑆 (( 𝐶 ) − 𝐶 ) 𝑟𝑆 𝑟𝑆

−𝐶𝐷𝑒 ln[

−𝑘𝑔 (𝑋𝐵 − 𝑋𝑆 ) = 𝑘𝑎 =

2/3 𝑀𝐶𝑎𝑂 𝑊𝐻2 𝑂,𝑟𝐶

(17)

(1−𝑥𝑆 ) ] (1−𝑥𝐶 ) 1 ) 𝑟𝑆 (1− (𝑟𝐶 /𝑟𝑆 )

−𝐷𝑒 ln[

(18)

d𝑋𝐶𝑎(𝑂𝐻)2

𝜌𝐶𝑎𝑂 (1−𝜀𝐶𝑎𝑂 )

d𝑡

(1−𝛸𝐶𝑎(𝑂𝐻)2 )𝑀𝐶𝑎𝑂 𝑆0 𝐶(𝑥𝐶 −𝑥𝐸 ) 3

𝑟

(16)

𝑋𝐶𝑎(𝑂𝐻)2 = 1 − (𝑟𝐶 )

(19) (20)

𝑆

Eq. 16 calculates the rate of reaction as a function of Eq. 17-20, as well as the molar weight, density, and voidage 𝜀𝐶𝑎𝑂 of the sorbent. Eq. 17 describes the molar flux of steam 𝑊𝐻2 𝑂 at the interface between the core and product layers of the particle to describe mass transfer across this layer by way of non-equimolar counter-diffusion; this incorporates 𝐷𝑒 to account for intra-particle diffusivity. Eq. 19 gives the rate constant 𝑘𝐴 assuming first-order kinetics, and needs to be calculated iteratively along with Eq. 18 – this allows for Eq. 16 to be fully evaluated. Eq. 20 models the extent of the reaction using a basic shrinking core expression. A more detailed discussion of


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the terms and assumptions involved is provided in the original text20. The SCM is considered in this study as it is a significantly specialised reaction model that has been widely applied in the literature to this system; however it has not been tested on setups involving a fluidized bed. Hence it is of interest to ascertain whether it is suitable to be adapted for such a setup and also quantitatively compare its performance to the other selected models.

MATERIALS & METHODOLOGY Material selection Limestone from Longcliffe Quarries Ltd (LC) was used throughout the study in 3 different particle size ranges: 212-355 µm, 355-425 µm, and 500-710 µm.

According to X-Ray

Fluorescence (XRF) data (Table 1), LC batches were characterised to be 99% CaO by mass in terms of mineral content after calcination.

Table 1. XRF data for untreated Longcliffe limestone Element

SiO2

Al2O3

Fe2O3

MgO

CaO

SrO

LOI

Others

Mass %

0.216

0.065

0.069

0.22

55.101

0.023

44.23

5. A mass of 12 g of sand (355-425 µm)

was used as an inert diluent for the bed to mitigate inter-particle exothermal effects over the course of reaction, resulting in negligible (~3%) bed temperature fluctuations such as in Figure 6. 350

Bed Temperature (°C)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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300 250 200 150 100 50 0 0

40

80

120

Time (s)

Figure 6. Plot of bed temperature data over time for 500-710 µm LC particles, Trxn=300°C For hydration experiments, the reaction vessel containing sand as a bed diluent was first equilibrated at the desired reaction temperature under a pure N2 atmosphere. The heating and


14

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temperature control for the overall system was by means of a custom control interface configured in Agilent VEETM Pro based on a prior design by Blamey29. The bubbler system was then equilibrated at temperatures of 51-68°C (characteristic to this specific setup) corresponding to steam flowrates that would produce the desired steam concentration. The steam supply to the reactor was then switched on and allowed to stabilise, whilst monitored through a VaisalaTM HMT338 relative humidity (RH) probe at the reactor exit; the resulting humidity reading was then converted through a measured calibration curve to give real-time measurements of the steam concentration in the exit stream. Batches of calcined material were then directly injected at the top opening of the reaction vessel. The resulting humidity vs time data over 180 s from the RH probe for each run (a sample is shown in Figure 7) was then processed according to Eq. 21 using sorbent characterisation data to produce conversion vs time plots for each experiment. The calibration on the RH probe was checked prior to each experiment and the mass balance for steam across the system was consistently ≥95%, which made for satisfactorily precise measurements. 25 Measured Steam Conc. (mol%)

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20 15 10 5 0 0

40

Time (s)

80

120

Figure 7. Plot of steam concentration over time for 500-710 µm LC particles, Trxn=300°C (𝑄𝑁 ∗100) 2 −𝑄𝑁2 )+∑𝑡−1 𝑘=0 𝑋𝑡 100−𝑐𝑠𝑡𝑒𝑎𝑚,𝑡

𝑐𝑠𝑡𝑒𝑎𝑚,0 −(

𝑋𝑡 =

𝑚𝐶𝑎𝑂,𝑠𝑎𝑚𝑝𝑙𝑒


(21)

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Experiments were performed to study the effects of varying particle size, calcination temperature, and steam concentration on the quality of the various kinetic models. Several experiments were also performed at 400°C to assess how the models would hold up for conditions close to those likely used in a scaled-up process. Under the conditions tested, the reactions occurred too fast (

Kinetics Modelling, Development, and Comparison for the Reaction of

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