NUMERICAL MODELLING OF CALCINATION OF LIMESTONE

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Abstract

Calcination is important for modern society as we know it since products from the reaction is used in several industries. Calcination is a chemical reaction where a solid particle, e.g., limestone, is exposed to high temperature which causes volatile impurities to be released from the particle.

One of the main challenges with lime production is the mere scale of commercial production. Ensuring good calcination and high-quality lime in laboratory scale is relatively easy, whereas commercial lime kilns produce 100 – 800 tons lime each day, causing the conditions to be much more challenging. The environment inside a lime kiln is extreme, with temperatures exceeding 1200°C, and a moving stone bed makes measurements difficult to perform. To obtain information about the calcination process and the extreme environment that arises in commercial lime kilns, companies and researchers have developed simulation programmes to evaluate how changes in ambient condition affect the calcination process.

In this project, a shrinking core model has been used to simulate calcination of limestone with varied geometry and size in different ambient condition. A transient model was used to simulate the heating phases before and after the calcination phase. The results obtain from the simulation are compared to measured data obtain by others.

There are many similarities between the measured data and the simulation, a reoccurring

phenomenon is that the transit model, during the pre-heating, heats the limestone faster compared to the measured data. However, in one case, the transient model is slower. A reason for this may be that the transient model does not account for morphological effects, as they are included in the heat transfer coefficient instead, such as the thermal conductivity coefficient and specific heat transfer coefficient. The post heating phase, after the reaction phase, required further work.

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Acknowledgements

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Nomenclatures

t = Time [s] ∆t = Time step [s] V = Volume [m3_]

P= Partial pressure of CO2 [bar]

P0 = Pre-exponential pressure coefficient [bar] T = Temperature [K]

Q = Heat flow rate [W]

α = Heat transfer coefficient [W/(m2_∙K)] β = Mass transfer coefficient [m/s] DP_{= Mass diffusion coefficient [m/s]} k = Reaction coefficient [m/s] λ = Thermal conductivity [W/(m∙K)] ρ = Density [kg/m3_] σ = Stefan-Boltzmann constant [W/(m2_∙K4_)] ε = Emissivity [-] µ = Dynamic Viscosity [kg/(m∙s)] ν = Kinematic Viscosity [m2_/s] A = Area [m2_] r = Radius [m] ∆r = Radius step [m] D = Diameter [m] LC = Characteristic length 𝑚̇ = Mass flow rate [kg/s] m = Mass [kg]

𝑉̇ = Volumetric flow rate [m3_/h] u = Velocity [m/s]

∆H = Reaction enthalpy [kJ/mol] ∆h = Specific reaction enthalpy [kJ/kg] R = Universal gas constant [J/(mol∙K)]

RCO2 = Individual gas constant for CO2 [J/(kg∙K)] Rσ = Heat transfer resistance [s]

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1 Introduction

Limestone is a carbonate sedimentary rock that mainly consists of calcium (Ca), carbon (C) and oxygen (O). The main elements in limestone exist as carbonate minerals. Limestone is found all over the world in limestone deposits, that have been formed during various sedimentation mechanism throughout million years [1].

Calcium carbonate (CaCO3) is the main component in limestone. Upon thermal treatment of limestone, lime is formed, of which the main component is calcium oxide (CaO). The process of converting limestone into other materials with different chemical properties has been known to mankind for several millennia [2]; the earliest civilization used limestone and lime for

construction, bleaching, medicine and for agriculture purposes [3, 4]. In modern society, limestone and lime are a highly sought after product with a wide range of application in multiple sectors [5], such as steel, metal and construction industry. As of 2019, the annual world-wide lime production was 420 Mt [6].

Lime is produced in lime kilns, where limestone is heated until the limestone is converted to lime and carbon dioxide (CO2). This thermal treatment of limestone is called calcination, and can be described as CaCO3 → CaO + CO2. Calcination is a highly endothermic reaction, causing the energy requirement to be high for the process. In addition, calcination of each CaCO3 molecule results in the release of one CO2 molecule, causing the CO2 emissions of the process to be high as well. On average, the lime industry contributes to approximate 1.3 ton CO2 for 1 ton of produced lime, and as of 2018, the annual production of lime in Sweden was approximate 2 M ton [7, 8]. The heat required for the calcination is commonly achieved by direct firing of fuels. Common fuels are oil, coal, coke, waste gas, and natural gas. Approximately 30% of the CO2 emissions are related to the fuel used and the remaining emission are process emissions [8]. There are several initiatives within the lime industry and the kiln manufacturers to lower CO2 emissions, where research is being done on alternative fuels and kiln optimization to reduce emissions [2, 8, 9]. The availability and price for new fuel is usually a problem for the industry since the lime kiln usually is

strategically located in relation to fuel. The energy cost is almost 50% of the total production cost [2].

One of the main challenges with lime production is the mere scale of commercial production. Ensuring good calcination and high-quality lime in laboratory scale is relatively easy, whereas commercial lime kilns produce 100 – 800 tons lime each day, causing the conditions to be much more challenging [9]. The environment inside a lime kiln is extreme, with temperatures exceeding 1200 °C and a moving stone bed. This makes it difficult to conduct measurements, even

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1.1 Aim

The aim of the project was to find a model that describes the physical behaviour of a limestone particle that undergoes calcination and investigate how relevant parameters such as; size and shape of the limestone particle, ambient temperature, and CO2 partial pressure affects the

calcination duration. The model should be based upon fundamental equations for energy and mass transport between the limestone particle and the surrounding environment.

The model will be compared with experimental data published by others to validate the results.

2 Background

2.1 Calcination Reaction

The kinetics and chemical mechanism regarding calcination of carbonates has been widely discussed during the last decades [15, 16]; especially calcination of CaCO3 [17], because of its technological importance and its simplistic stoichiometry that is, Reaction (1) [18]. There are many aspects not well understood about the reaction [19]. Several Reaction (1)-(3), has been presented since there is no agreement upon the mechanism.

𝐶𝑎𝐶𝑂3 (𝑠) → 𝐶𝑎𝑂(𝑠) + 𝐶𝑂2(𝑔), ∆𝐻𝑅 = +168 𝑘𝐽/𝑚𝑜𝑙 (1)

𝐶𝑎𝐶𝑂3 (𝑠) ↔ 𝐶𝑎𝑂∗(𝑠) + 𝐶𝑂2(𝑔) ↔ 𝐶𝑎𝑂(𝑠) + 𝐶𝑂2(𝑔) (2)

𝐶𝑎𝐶𝑂3 (𝑠) ↔ 𝐶𝑎𝑂(𝑔) + 𝐶𝑂2(𝑔) ↔ 𝐶𝑎𝑂(𝑠) + 𝐶𝑂2(𝑔) (3)

Hyatt et al, propose the existence of metastable structure of CaO. It is supposed that the active CaO, denoted as CaO*_{in Reaction (2), acts as a bridge between the freshly made CaO crystal and} the unreacted CaCO3 [16]. Another approach, proposed by L’vov is that CaCO3 decompose into gaseous species of CaO and CO2 and simultaneous condensation of low volatility CaO as seen in Reaction (3) [20].

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2.2 Calcination Models

To investigate the calcination reaction, a suitable process model is necessary. Several models have been proposed for calcination reaction and each model are designed to solve a specific task, such as determine pore parameters with pore models, or to determine pre exponentials kinetics

parameters with an Arrhenius approach. In early studies, it was common to investigate calcination of micro-sized particles [15], hence, several existing models are adapted for rapid calcination reaction, where the reaction is completed after a few seconds. A consequence is that physical-chemical resistance is neglected [20, 24].

There are three main groups that divides the models: particle models, grain models, and pore models [15]. In particle models, the particle is regarded as a homogeneous cylinder, sphere, or a plate and the model analyzes how the process dynamics vary as a function of time. In this model, the chemical reaction occurs at a reaction front between layers of product and the unreacted region and moves towards the centre [25]. The grain model is similar to the particle model except that instead of the reaction process begin a function of time, it is instead a function of surface area [15, 25]. Pore models are similar to grain models since both are a function of surface area. The pores are considered as cylinders with an initial diameter and as the reaction proceed, the pore diameter grows and the surface area increases until it reaches a maximum value before falling to zero [15]. Kainer et al. [26, 27], proposed a time dependent system of analytical equations for the particle model called Shrinking Core Model (SCM), to study calcination of a single limestone particle. The analytical system is based upon heat and mass transfer equations so that the calcination reaction can either be viewed form a heat- or mass balance perspective. During the reaction phase, there is a balance between heat necessary for the reaction and mass transport through the porous zone caused by the reaction. Hence, heat and mass transfer are interconnected with the chemical kinetics and their respective thermal- and mass resistance [26]. The SCM can be used to calculate thermal material properties during the reaction phase, such as heat capacity and thermal

conductivity, or reaction parameters such as reaction enthalpy or reaction coefficients. The SCM has been deployed in various dissertations and studies [11-14, 28-31], and will be the model used in this study.

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2.3 Material Properties

The chemical composition and structure of limestone varies even within same quarry, as there are different layers that may separates structure and composition of the limestones [32]. Thus, the thermal behavior varies, since thermo-physical properties e.g., specific heat capacity, thermal conductivity and reaction enthalpy varies with temperature [12].

Thermal conductivity is defined as the rate at which heat is transferred through a material and is usually measured by investigating the materials ability to conduct heat [33]. Thermal energy is passing through material by valence electron moving towards the colder part of the material and passing their energy to other atoms [34]. The thermal conductivity varies with material and temperature. During phase changes, the thermal conductivity of the material may dramatically change [35]. The thermal conductivity usually falls within 3-0.6 [W/(m∙K)] for limestone at 0-700°C, and for lime 1.7-0.3 [W/(m∙K)] at 100-1100°C.

The specific heat capacity is defined as the amount of energy that is required for a mass unit to increase in one unit temperature. The heat capacity varies with material and phase [35]. Reported values for limestone ranges from 0.6-1.7 [J/(g∙K)] and for lime 0.7-1 [J/(g∙K)] [12, 29, 34]. For lime, it was found that the average heat capacity is independent of temperature, however, the heat capacity of lime differs individual due to different morphology within each lime.

The reaction enthalpy is independent of origin and is published as 178 [kJ/mol] at atmospheric conditions. However, at calcination temperature, the reaction enthalpy varies between 160-172 [kJ/mol], since the calcination temperature has been reported to vary between 850-925°C when comparing limestone samples from all over the world [29].

4 Shrinking Core Model

The proposed SCM model by Kainer et al, is schematic described in Figure 1. To simulate and describe the calcination process behavior with the proposed analytical system, some necessary assumption is needed: 1) Heat supplied to the particle are symmetric. 2) The particle to be

examined, must have a spherical, cylindrical or plate shape. 3) Chemical composition and structure of the sample must be homogeneous. 4) The formation of CaO is uniform and starts at the particle surface and always forming a smooth geometric CaO layer and moves towards the center. 5) The condition inside the reactor is constant, e.g., temperature and pressure. 6) For small temperature changes, heat transfer coefficient and mass transfer coefficient are constant. 7) An effective heat transfer coefficient which contains radiation and convection effects is used to describe the heat transfer to the carbonate particle [26].

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energy and thus heat flowing further into the core is negligible during reaction. As heat is supplied, the chemical reaction, k, occurs. Diffusion, DP_{, of CO}₂_{occur through the porous CaO layer to the} particle surface from the reaction front and passes by convection, β, to the surrounding

environment [26].

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4.1 Theory of SCM

When the particle surface reaches calcination temperature, Tf, the reaction begins and moves towards the centre. The degree of conversion of any particle is defined as the ratio between the initial CO2 mass the released CO2 mass, see Eq (4),

𝑋 =𝑚(𝑡=0)− 𝑚(𝑡) 𝑚(𝑡=0) = 1 − (𝑟𝑓 𝑟𝑠 ) 𝑏 . (4)

In Eq (4), b is a shape factor equal to 2 or 3 for a cylindrical or spherical particle geometry, respectively [27]. In the case of complete calcination, the degree of conversion is equal to 1. The calcination time associated with the degree of conversion is given by Eq (5) and (6) for a heat- or mass transfer perspective,

𝑡 = 𝑅𝛼∙ 𝑓1(𝑋) + 𝑅𝜆∙ 𝑓2(𝑋), (5)

𝑡 = 𝑅𝛽∙ 𝑓1(𝑋) + 𝑅𝐷𝑃∙ 𝑓2(𝑋) + 𝑅𝑘∙ 𝑓3(𝑋). (6)

Where fi(X) is a form functions based upon X and the geometrical shape of the particle, and are summarized in Table 1. Ri denotes the resistance for respective physical transport phenomenon and reaction. Rα is the resistance due to heat transfer from the surrounding, Rλ is the resistance due to heat conduction through the particle, Rk is the resistance due to the calcination reaction, RDP is the resistance due to diffusion of CO2 through the porous material and, Rβ is the resistance due to mass transfer of CO2 from the particle surface to the surrounding. The four transport resistances are interconnected with the chemical resistance, where each individual resistance is connected in series and is visually presented in Figure 2, and the resistances are summarized below. 𝑅𝛼= 𝜌𝐶𝑂₂∙ ∆ℎ 𝑇𝑎− 𝑇𝑓 ∙ 𝑟𝑠 𝑏 ∙ 𝛼. (7) 𝑅𝜆= 𝜌𝐶𝑂2∙ ∆ℎ 𝑇𝑎− 𝑇𝑓 ∙ 𝑟𝑠 2 2 ∙ 𝑏 ∙ 𝜆. (8) 𝑅𝛽 = 𝜌𝐶𝑂₂∙ 𝑅𝐶𝑂2∙ 𝑇𝑓 𝑃𝑒𝑞− 𝑃𝑎 ∙ 𝑟𝑠 𝑏 ∙ 𝛽. (9) 𝑅_𝐷𝑃= 𝜌𝐶𝑂2∙ 𝑅𝐶𝑂2∙ 𝑇𝑓 𝑃𝑒𝑞− 𝑃𝑎 ∙ 𝑟𝑠 2 2 ∙ 𝑏 ∙ 𝐷𝑃. (10) 𝑅𝑘= 𝜌𝐶𝑂₂∙ 𝑅𝐶𝑂2∙ 𝑇𝑓 𝑃𝑒𝑞− 𝑃𝑎 ∙𝑟𝑠 𝑘. (11)

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Peq is the equilibrium pCO2, β is the mass transfer coefficient, DP is the pore diffusion coefficient, and k is the reaction coefficient.

Figure 2: Circuit schedule for the resistances within the calcination mechanism.

The equilibrium pCO2 is given by an Arrhenius approach correlation as

𝑃𝑒= 𝑃0∙ exp (−

∆𝐻𝑅

𝑅 ∙ 𝑇𝑓

). (12)

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Table 1: Form function fi(X) for spherical and cylindrical sample geometries. These are the form functions used in SCM. Sphere Cylinder 𝑓1(𝑋) = 𝑋 𝑓1(𝑋) = 𝑋 𝑓2(𝑋) = 3 ∙ (1 − (1 − 𝑋) 2 3 ⁄_{) − 2 ∙ 𝑋} _𝑓 2(𝑋) = 𝑋 + (1 − 𝑋) ∙ ln(1 − 𝑋) 𝑓3(𝑋) = 1 − (1 − 𝑋) 1 3 ⁄ _𝑓 3(𝑋) = 1 − (1 − 𝑋)1/2 By linearizing Eq (5) as 𝑡 𝑓1(𝑋) = 𝑅𝛼+ 𝑅𝜆∙ 𝑓2(𝑋) 𝑓1(𝑋) (13) and Eq (6) as 𝑡 − 𝑅𝛽∙ 𝑓1(𝑋) 𝑓3(𝑋) = 𝑅_𝐷𝑃+ 𝑅_𝑘∙ 𝑓2(𝑋) 𝑓3(𝑋) , (14)

the resistances can be obtained from the slope and interception and the material properties such as λ, DP_{, and k can be calculated provided that the reaction duration t, X, and T}_f_are

measured/known. Otherwise, X and Tf can be predicted if the material properties are known. The remaining material properties α and β can be predicted based upon flows around bodies by using the definition of Nusselt and Sherwood number [14, 26, 35].

During the reaction, heat is transferred to the particle surface from the surrounding environment and transferred through the calcinated material by conduction as

𝑄 = −𝜆 ∙ 𝐴(𝑟) ∙𝑑𝑇 𝑑𝑟

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where r is the local position between the reaction front and the surface. The balance between mass transfer and the heat necessary for the reaction is given as

𝑄 = 𝑚̇𝐶𝑂₂∙ ∆ℎ. (16)

The mass transport of CO2 from the particle surface to the surrounding environment is given by

𝑚̇𝐶𝑂2= 𝛽 𝑅𝐶𝑂₂∙ 𝑇𝑓

∙ 𝐴𝑠∙ (𝑃𝑠− 𝑃𝑎) (17)

where RCO2 is the individual gas constant for CO2. The transport of CO2 that occurs through the porous material, from the reaction front to the surface is given by

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where r and P is the local position and pressure, respectively. From the reaction front, the mass transport of freshly converted CO2 is given as

𝑚̇𝐶𝑂2 = 𝑘 𝑅𝐶𝑂2∙ 𝑇𝑓

∙ 𝐴𝑓∙ (𝑃𝑒𝑞− 𝑃𝑓) (19)

4.2 Transient modelling

Due to the necessary equilibrium requirements in the fundamental Eq (5)-(6), the SCM is unable to predict heating of the sample before and after the calcination reaction [12]. To enable modelling of the entire process, including heating before and after the calcination reaction, an explicit transient heating model is proposed, that will enable preheating and when the reaction occurs, the temperature is fixed at Tf and when the reaction is complete, the heat is initiated until the sample reached Ta.

The transient model is based upon heat conduction equation in cylindrical coordinates 𝜕𝑇 𝜕𝑡 = 𝜆 𝜌 ∙ 𝑐𝑝 ∙ (1 𝑟∙ 𝜕𝑇 𝜕𝑟+ 𝜕2𝑇 𝜕𝑟2) (20)

and in spherical coordinates 𝜕𝑇 𝜕𝑡 = 𝜆 𝜌 ∙ 𝑐𝑝 ∙ (2 𝑟∙ 𝜕𝑇 𝜕𝑟+ 𝜕2_𝑇 𝜕𝑟2) (21)

[36]. The transient model in discretizing form, finite difference method, the sample is divided into shells with thickness ∆r, for cylindrical coordinates, see Eq (21).

𝑇𝑖,𝑗+1= 𝑇𝑖,𝑗+ ∆𝑡 ∙ (𝜆𝑖 𝜌𝑖∙ 𝑐𝑝𝑖 ⁄ ) 𝑟𝑖∙ ∆𝑟 ∙ [𝑟𝑖+1/2∙ ( 𝑇𝑖+1,𝑗− 𝑇𝑖,𝑗 ∆𝑟 ) − 𝑟𝑖−1/2∙ ( 𝑇𝑖,𝑗− 𝑇𝑖−1,𝑗 ∆𝑟 )] (22)

Where i and j represent the spatial and time domains, ∆t is the time step, ρ, λ, and cp is the local density, thermal conductivity, and specific heat capacity. If the length to diameter ratio of the sample is greater than 4, heat transfer in the axial direction is insignificant compared to heat transfer in the radial direction, hence a one dimensional approach is valid.

For spherical geometry, the one dimensional discretizing is given as

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4.3 Determination of heat and mass transfer coefficient

The heat transfer coefficient is a combination of both radiation and convection and is given as

𝛼 = 𝛼𝑟𝑎𝑑+ 𝛼𝑐𝑜𝑛𝑣. (24)

Where the radiation heat transfer coefficient is given by

𝛼𝑟𝑎𝑑= 𝜀 ∙ 𝜎 ∙ (𝑇𝑠2+ 𝑇𝑎2) ∙ (𝑇𝑠+ 𝑇𝑎), (25)

Since the temperature inside the theoretical RC is constant and the surface temperature of the particle is initially at 20°C, αrad is low in the beginning and as the particle surface is heated, αrad increases until the surface temperature reached Ta and then αrad converges and remains constant throughout the entire process.

The convection heat transfer coefficient is a result from a fluid flow inside the RC. To keep the pCO2 inside the RC as close to constant as possible, it is necessary to introduce a gas flow to flush away the produced CO2 from the calcination reaction. The convection heat transfer coefficient based upon fluid flow is defined based on the Nusselt number, Nu, as

𝛼𝑐𝑜𝑛𝑣=

𝑁𝑢 ∙ 𝜆𝑎

𝐿𝑐

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Where λa is the thermal conductivity of the ambient gas inside the RC and LC a characteristic length for the sample. For a cylindrical sample, LC has been chosen to be the length and for a spherical geometry, the radius. The definition of Nu varies for the RC, the Nu is defined as

𝑁𝑢 = 0.644 ∙ 𝑅𝑒1/2_{∙ 𝑃𝑟}1/3_. ₍₂₇₎

Pr is the dimensionless Prandtl number, defined as the ratio of momentum diffusivity and thermal diffusivity, and Re is the dimensionless Reynolds number, defined as the ratio between inertial forces and viscous forces within a media as

𝑅𝑒 =𝑢 ∙ 𝐿𝑐

𝜈 =

𝑢 ∙ 𝐿𝑐∙ 𝜌

𝜇

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where u is the velocity of the flowing media, ν and µ is the kinematic and dynamic viscosity. The mass transfer coefficient β is defined as

𝛽 =𝑆ℎ ∙ 𝐷𝐶𝑂2−𝑅𝐶 𝐿𝐶

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𝑆ℎ = 0.644 ∙ 𝑅𝑒1/2_{∙ 𝑆𝑐}1/3_. ₍₃₀₎

Where Sc is the dimensionless Schmidt number, which is defined as the ratio between momentum diffusivity and mass diffusivity as

𝑆𝑐 = 𝜈 𝐷𝐶𝑂2−𝑅𝐶 = 𝜇 𝜌 ∙ 𝐷𝐶𝑂2−𝑅𝐶 (31)

5 Implementation of SCM

A theoretical reaction chamber (RC) was created using Visual Basic for Applications in Microsoft Excel 2021 [37]. The chamber was designed to theoretically mimic a tube furnace, DRC = 0.1 m, with a continuous volumetric flow rate, 𝑉̇𝑛 = 7 m3/h, of hot gas to heat the sample and to flush away

newly formed CO2 gas. The hot gas is assumed to be an ideal gas and is used to calculate Rα and Rβ with the mention theory. The temperature and pressure inside the RC are assumed to be constant, due to the flow of hot gas. With Eq (24)-(31) and the volumetric flow rate, the heat transfer and mass transfer coefficient are calculated and listed in Table 2. For further information on variables used in the simulations, see Table A1 in appendix.

The sample was initially (t=0) at room temperature and was immediately exposed to the RC ambient temperature Ta, starting the heating process of the sample. At every time step, ∆t, the algorithm checks if the surface temperature has reached Tf, and simultaneously the temperature at next spatial domain is raised. When the surface temperature reaches Tf, the calcination reaction begins at the surface and the temperature is locked at Tf until the surface is fully calcinated. When the surface is fully calcinated, the heating process is resumed until next spatial domain reaches Tf. During calcination, the heating slows down due to the locked temperature and based on how much that is calcined, the algorithm changes the material properties, such as λ, ρ and cp. Figure 3 shows a schematic of the algorithm used for the entire heating and calcination process.

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5.1 Model validation

A study by Do [30], three cylindrical limestone samples from different regions in Germany were calcined. All three samples were calcined under same ambient condition while the X, t, Tf were measured. The samples were calcinated in a furnace at Ta=1000°C with a flow of pure air to avoid any build-up of CO2. Figure 4 and Figure 5 shows the measured conversion and temperature profile. It can be read that the calcination duration varies between 45 – 65 minutes for sample LGe1 and LGe3 and that Tf varies between 860 – 890°C for LGe2 and LGe3.

Figure 4: Conversion profile from calcination of sample LGe1-LGe3. Adapted from [30].

Figure 5: Temperature profile from calcination of sample LGe1-LGe3, the temperature profile is measured in the sample core. Adapted from [30].

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and the other with CO2 as ambient gas and Pa = 0.85 bar. The furnace temperature Ta is 1045°C in both cases. The measured conversion and temperature profile can be seen in Figure 6 and Figure 7. Both samples behave similarly, except that F2A is completely calcined after 56 minutes and F2C after 60 minutes, and Tf is slightly lower for F2A at 893°C than F2C at 910°C.

Figure 6: Conversion profile from calcination of F2A and F2C, A and C denotes their respective ambient gas. Adapted from [12].

Figure 7: Temperature profile from calcination of sample F2A and F2C. Adapted from [12].

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6 Result and discussion

6.1 Sample LGe 1 – LGe 3

The measured conversion profile, for sample LGe 1 – 3, compared with the simulated profile are seen in Figure 8. It appears that the conversion profiles vary to some extent between the different samples. For example, the simulation managed to predict the behaviour of sample LGe1 and LGe2 well in relation to LGe3. The predicted profile for LGe2 is almost identical to the measured conversion.

Figure 8: Conversion profile from sample LGe1 - LGe3 compared to the simulated conversion profile.

As for the temperature profiles for LGe 1-3 seen in Figure 5, it appears that the measured temperature begins at 700°C, which is considered unlikely since the simulations is only about 200°C at the same time which is consistent with other measurements performed in [12, 14]. The simulated temperature profiles shown in Figure 9, Figure 10 and Figure 11 are therefore fitted against the measured profiles.

The heating phase, before calcination phase, matches well with the measured profile, which indicates that the chosen transient model is a good model for the preheating. It can be noted that the transient model heats all samples slower compared to the measured profile, which is

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Figure 9: Compared temperature profile from sample LGe1 to the simulation.

Figure 10: Compared temperature profile from sample LGe2 to the simulation.

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Based on the measured conversion in the Figure 4 and Figure 6, the mass flow of CO2 can be calculated and compared with the simulated cases. See Figure 12, Figure 13, and Figure 14 for the measured and simulated LGe1 – LGe3 samples.

Figure 12: Measured CO2 massflow rate vs simulated for sample LGe 1.

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Figure 14: Measured CO2 massflow rate vs simulated for sample LGe 3.

From Figure 12, Figure 13 and Figure 14, it appears that the simulations are faster compared to the reference data. This is most likely because the reaction coefficient is lower for the measured data compared to the simulated cases. The reaction coefficient for the measured data ranges from 0.0098 – 0.0054 for sample LGe 1 – Lge 3 [30], and for the simulation it ranges from 0.035 – 0.0088. The reason why the simulated reaction coefficients are higher is most likely that everything in the simulation and the material is homogeneous and that the heat distribution is completely symmetrical to the sample, which is not the case for a real limestone which may contain other substances [32], and the heat distribution in a real furnace is not 100% symmetrical.

6.2 Sample F2A – F2C

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Figure 15: Conversion profile from sample F2A compared to the simulated conversion profile.

Figure 16: Conversion profile from sample F2C compared to the simulated conversion profile

In Figure 17 and Figure 18, the comparison between the measured and the simulated temperature profiles are shown. In this case, the simulated profile is not fitted against the measured profile and the simulated profile coincides, almost perfect, in this case. This supports the assumption that the transient model is a suitable tool to simulate the preheating. However, in both cases, the

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Figure 17: Compared temperature profile from sample F2A compared to the simulation.

Figure 18: Compared temperature profile from sample F2C compared to the simulation.

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mass flow is faster in the beginning in a CO2 rich environment compared to an environment with air. However, the model is predicting an equal CO2 in both environments.

Figure 19: Measured CO2 massflow rate vs simulated for sample F2A.

Figure 20: Measured CO2 massflow rate vs simulated for sample F2C.

6.3 Shape distribution

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calcination of spherical geometries could not be obtain, the geometrical aspect of the simulation cannot be verified, yet.

There is massive increase in calcination duration of Cyl Sim compared to LGe 2 Sim, an increase of 75 mm of the radius results in an increased calcination duration of 70 minutes.

Figure 21: Comparison between conversion profile from a simulation with a cylindrical and a spherical sample with same radius and material properties.

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Figure 22: Comparison between temperature profile from a simulation with a cylindrical and a spherical sample with same radius and material properties.

6.4 Size distribution

Figure 23 shows the conversion of spherical samples with same material properties and with different radius. The sample with the smallest radius, R2.5, is fully converted after almost 40 minutes. As the radius increases, so does the calcination duration. Sample R2.5, R3 and R4 all have a larger radius compared to the previous spherical sample Sph Sim. Despite this, Sph Sim is significantly slower converted compared to the samples in R2.5 and R3. The material properties for R2.5, R3 and R4 are set as too pure CaCO3 and CaO and affect the calcination duration significantly. The parameter that has the greatest impact on this case is the thermal conduction coefficient, where the calcination duration increases with a low thermal conductivity coefficient.

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Figure 24 shows the temperature profile for the different sizes. The size of the particle significantly affects the calcination and heating time. This is expected because it is a larger volume that require more energy to heat and to convert. The flow of CO2 during calcination is also affected by the size of the particle as the distance on which the mass is to travel becomes longer with larger volumes [17, 38].

Figure 24: Comparison of temperature profile between spherical samples with different radius.

6.5 Material properties

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Figure 25: Linearization with Eq (13), the slope represent Rλ and the intersection with the y-axis represents

Rα.

Figure 26: Linearization with Eq (14), the slope represent RK and the intersection with the y-axis represents

RDP.

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Table 3: Heat and mass transfer resistance for each simulation. Values are based on linearization with Eq (13) and (14). Sample Rλ Rα Rk RDP λ [W/(m2_K)] α [W/(mK)] k [m/s] DP₁₀-5 [m2_/s] LGe1 Sim 2114 614 551 1921 0.7 385 0.035 3.2 LGe2 Sim 1319 1579 465 2437 0.74 128 0.0079 13 LGe3 Sim 2212 1334 2245 1416 0.73 193 0.0088 4.4 F2C Sim 2653 975 2016 1951 0.47 211 0.02 6.4 F2A Sim 2550 943 235 2468 0.44 194 0.083 2.4 R2.5 1909 312 317 1774 0.8 391 0.13 10 R3 2727 383 321 2599 0.8 383 0.16 9.8 R4 4888 507 253 4780 0.8 386 0.27 9.5 Cyl Sim 2996 1823 5017 987 0.74 119 0.0062 10 Sph Sim 4410 2633 3906 3054 0.74 123 0.0079 5

Sample LGe1 Sim was converted fastest among those compared with. Although LGe1 Sim had the lowest thermal conductivity but the reaction coefficient was highest and the diffusion coefficient the least. This results in a faster conversion compared to LGe2 Sim and LGe3 Sim.

For sample F2C and F2A we can see that F2C has a higher heat conduction but that it converted more slowly compared to F2A and this is because F2C was calcined in a CO2 rich environment and this has affected the other coefficients significantly compared to F2A. The diffusion for F2C is higher while the coefficient of reaction is lower, which is consistent with others [12].

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7 Conclusion

The goal of the project was to model a limestone particle that undergoes calcination and investigate how relevant parameters such as; Size of limestone, ambient temperature and CO2 partial pressure affects the calcination process. This was done using the Shrinking core model to simulate the calcination phase and a transient model to simulate the heating phases between the reaction. The models included fundamental equation for energy and mass transport between the limestone particle and the surrounding environment.

Effects caused by morphology are not treated within the model. However, morphology effects are included in other parameters such as thermal conduction coefficient, reaction coefficient and diffusivity.

It has been shown that the transient model is a suitable tool to simulate the heating phase before the reaction phase, however, the post heating phase requires further work. It has been shown that material properties significantly affect every aspect of the calcination simulation with the SCM, even the emissivity of the material must be treated with caution since it significantly affects the heat transfer coefficient which affects the preheating and the thermal resistance caused by heat transfer to the particle from the surrounding environment.

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8 Further studies

The one dimensional shirking core model in combination with transient heating model has been used to simulate the preheating, calcination, and post heating of limestone samples with various geometry, sizes, and different ambient environment in a theoretical small scale laboratory furnace. Based on the simulation performance and simulation results, further outlooks are suggested: The simulations have been numerically unstable, which affected the spatial domains and time step. For each reduction on ∆r, ∆t also needed a reduction. This resulted in that all geometries were dived into 6 shells and a time step corresponding to 0.5 seconds. Resulting in an enormous amount of cells to perform calculation in. It was estimated that calculation of 1 cell took 3 physical seconds and sample Cyl Sim required 19200 cells calculation. If the time step increased to decrease the number of cells, the temperature began to fluctuate between positive and negative infinity.

• An improvement could be to implement the model in something rather than Microsoft Excel Visual Basic for Application 2021. For example, MATLAB or Star-CCM+.

Balancing the spatial and time domains in these simulations required extensive work, however, Excel allowed for quick error-checking.

Simulation of calcination has shown that the reaction is very sensitive and requires precision in the choice of parameters. To make the simulations possible, knowledge of the material's thermal conductivity or reaction coefficients is required. As shown in the results, there parameters vary between every individual cases.

• A comprehensive investigation of material properties of limestone and lime.

All simulations of the temperature profile have been quite good except for the last part when the whole stone is calcined. Additional work is required on the post heating mechanism.

• Adjusting the post heating mechanism.

For industrial application, limestone particle is rarely of cylindrical shape, or spherical for that matter, but more spherical than cylindrical. Based on the results, the geometry of the particle affects the calcination process and therefore it is important to investigate the spherical aspect of the model.

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References

[1] S. Ram, "Calcium Carbonate – From the Cretaceous Period into the 21st Century," vol. 83, ed: Current Science Association, 2002, pp. 328-329.

[2] H. Piringer, "Lime Shaft Kilns," Energy procedia, vol. 120, pp. 75-95, 2017, doi: 10.1016/j.egypro.2017.07.156.

[3] F. M. Lea, "Lea's chemistry of cement and concrete," Chemistry of cement and concrete, 1998.

[4] F. Schorcht, I. Kourti, B. M. Scalet, S. Roudier, and L. Delgado Sancho, "Best available techniques (BAT) reference document for the production of cement, lime and magnesium oxide: Industrial Emissions Directive 2010/75/EU (integrated pollution prevention and control)," vol. 26129, 2013.

[5] Competitiveness of the European cement and lime sectors: summary of the final report.

Luxembourg: Publications Office, 2018.

[6] USGS. "Lime Statistics and Information." https://www.usgs.gov/centers/nmic/lime-

statistics-and-information?qt-science_support_page_related_con=0#qt-science_support_page_related_con (accessed 18/11, 2020). [7] "Branschstatistik | Svenska kalkföreningen," 2021.

[8] M. Stork, W. Meindertsma, M. Overgaag, and M. Neelis, "A Competitive And Efficient Lime Industry," 2014.

[9] "PFR Kilns for soft-burnt lime - Maerz Ofenbau AG," 2021-03-26 2020.

[10] B. Krause et al., "3D-DEM-CFD simulation of heat and mass transfer, gas combustion and calcination in an intermittent operating lime shaft kiln," International journal of thermal

sciences, vol. 117, pp. 121-135, 2017, doi: 10.1016/j.ijthermalsci.2017.03.017.

[11] D. Hai Do and E. Specht, "Measurement and Simulation of Lime Calcination in Normal Shaft Kiln," Materials performance and characterization, vol. 1, no. 1, p. 104351, 2012, doi: 10.1520/MPC104351.

[12] P. Sandaka, "Calcination behavior of lumpy limestones from different origins," Doktoringenieur, Fakultät für Verfahrens- und Systemtechnik, Otto-von-Guericke-Universität Magdeburg, Otto-von-Guericke-Universität Magdeburg, 2015.

[13] B. Agnieszka, "Dynamic Process Simulation of Limestone Calcination in Normal Shaft Kilns," Doktoringenieurin, Fakultät fur Verfahrens und Systemtechnik, Otto von Guericke Universität, Universität Magdeburg, 1332, 2005.

[14] C. Cheng and E. Specht, "Reaction rate coefficients in decomposition of lumpy limestone of different origin," Thermochimica acta, vol. 449, no. 1, pp. 8-15, 2006, doi:

10.1016/j.tca.2006.06.001.

[15] B. R. Stanmore and P. Gilot, "Review-calcination and carbonation of limestone during thermal cycling for CO2 sequestration," Fuel processing technology, vol. 86, no. 16, pp. 1707-1743, 2005, doi: 10.1016/j.fuproc.2005.01.023.

[16] E. P. Hyatt, I. B. Cutler, and M. E. Wadsworth, "Calcium Carbonate Decomposition in Carbon Dioxide Atmosphere," Journal of the American Ceramic Society, vol. 41, no. 2, pp. 70-74, 1958, doi: 10.1111/j.1151-2916.1958.tb13521.x.

[17] S. Takkinen, J. Saastamoinen, and T. Hyppänen, "Heat and mass transfer in calcination of limestone particles," AIChE journal, vol. 58, no. 8, pp. 2563-2572, 2012, doi:

10.1002/aic.12774.

(37)

of theoretical & computational chemistry, vol. 12, no. 6, p. 1350049, 2013, doi:

10.1142/S0219633613500491.

[19] F. García-Labiano, A. Abad, L. F. de Diego, P. Gayán, and J. Adánez, "Calcination of calcium-based sorbents at pressure in a broad range of CO2 concentrations," Chemical

engineering science, vol. 57, no. 13, pp. 2381-2393, 2002, doi:

10.1016/S0009-2509(02)00137-9.

[20] B. V. L’vov, L. K. Polzik, and V. L. Ugolkov, "Decomposition kinetics of calcite: a new approach to the old problem," Thermochimica acta, vol. 390, no. 1, pp. 5-19, 2002, doi: 10.1016/S0040-6031(02)00080-1.

[21] G. D. Silcox, J. C. Kramlich, and D. W. Pershing, "A mathematical model for the flash calcination of dispersed calcium carbonate and calcium hydroxide particles," Industrial &

engineering chemistry research, vol. 28, no. 2, pp. 155-160, 1989, doi:

10.1021/ie00086a005.

[22] C. R. Milne, G. D. Silcox, D. W. Pershing, and D. A. Kirchgessner, "Calcination and sintering models for application to high-temperature, short-time sulfation of calcium-based sorbents," Industrial & engineering chemistry research, vol. 29, no. 2, pp. 139-149, 1990, doi: 10.1021/ie00098a001.

[23] R. H. Borgwardt, "Calcination kinetics and surface area of dispersed limestone particles,"

AIChE journal, vol. 31, no. 1, pp. 103-111, 1985, doi: 10.1002/aic.690310112.

[24] B. V. L’vov, "The physical approach to the interpretation of the kinetics and mechanisms of thermal decomposition of solids: the state of the art," Thermochimica Acta, vol. 373, no. 2, pp. 97-124, 2001, doi: 10.1016/S0040-6031(01)00507-X.

[25] T. Donald, "Analysis of limestone calcination and sulfation using transient gas analysis," PhD, Mechanical Engineering, Iowa State University, Iowa State University, 1996. [26] H. Kainer, E. Specht, R. Jeschar, and C. Zellerfeld, "Reaction, Pore Diffusion and Thermal

Conduction Coefficients of Various Magnesites and their Influence on the Decomposition Time," ZKG, vol. 4, pp. 248-268, 1986.

[27] H. Kainer, E. Specht, and R. Jeschar, "Die Porendiffusions-, Reaktions- und

Värmeleitkoeffizienten verschiedener Kalksteine und ihr Einfluss auf die Zersetzungszeit,"

ZEMENT-KALK-GIPS, vol. 5/1986, pp. 259-268, 1986.

[28] M. Silva, "Experimental investigation of the thermophysical properties of new and representative materials from room temperature up to 1300°C " Doktoringenieur, Fakultät für Verfahrens- und Systemtechnik, Otto-von-Guericke-Universität Magdeburg, Universität Magdeburg, 2009.

[29] M. Silva, E. Specht, and J. Schmidt. (2010) Thermophysical properties of limestone as a function of origin (Part 2): Calcination enthalpy and equilibrium temperature ZKG. 51-57.

[30] D. H. Do, "Simulation of Lime Calcination in Normal Shaft and Parallel Flow Regenerative Kilns " Doktoringenieur, Fakultät für Verfahrens- und Systemtechnik, Otto-von-Guericke-Universität, Magdeburg 2012.

[31] A. Abdelwahab, "Modeling of Solid Reaction Behavior in Direct Heated Rotary Kilns," PhD, Faculty of Process and Systems Engineering, Otto-von-Guericke-University of Magdeburg, University of Magdeburg, 2017.

(38)

[33] D. M. C. Bacon, "The science and engineering of materials: Donald R. Askeland Third SI edition, SI adaptation by Frank Haddleton, Phil Green and Howerd Robertson Chapman & Hall, 1996, ISBN 0-412-53910 1, 854pp, paperback, £24.99," Materials in engineering, vol. 17, no. 1, pp. 57-58, 1996, doi: 10.1016/0261-3069(96)83775-7.

[34] M. Silca, "Experimental investigation of the thermophysical properties of new and representative materials from room temperature up to 1300°C " Doktoringenieur, Fakultät für Verfahrens- und Systemtechnik, Otto-von-Guericke-Universität Magdeburg, Universität Magdeburg, 2009.

[35] Y. A. Çengel, A. J. Ghajar, and M. Kanoglu, Heat and mass transfer : fundamentals and

applications, 5th ed. in SI units ed. New York: McGraw-Hill, 2015.

[36] J. Thibault, S. Bergeron, and H. Bonin, "On Finite-Difference Solutions of the Heat Equation in Spherical Coordinates," Numerical heat transfer. Part B, Fundamentals, vol. 12, no. 4, pp. 457-474, 1987, doi: 10.1080/10407798708551436.

[37] "Microsoft - Official Home Page." https://www.microsoft.com/sv-se (accessed 31/05, 2021).

[38] Y. Wang and W. J. Thomson, "The effect of sample preparation on the thermal

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Appendix

Table A1: Values of various parameters used in the simulations.

Variable Unit Sample

LGe1 LGe2 LGe3 F2A F2C R2.5 R3 R4 Cyl Sph

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