Flue Gas Desulphurization in Circulating Fluidized Beds

Abstract

Sulphur dioxide (SO₂) is mostly emitted from coal-fueled power plants, from waste incineration, from sulphuric acid manufacturing, from clay brick plants and from treating nonferrous metals. The emission of SO₂ needs to be abated. Both wet scrubbing (absorption) and dry or semi-dry (reaction) systems are used. In the dry process, both bubbling and circulating fluidized beds (BFB, CFB) can be used as contactor. Experimental results demonstrate a SO₂-removal efficiency in excess of 94% in a CFB application. A general model of the heterogeneous reaction is proposed, combining the external diffusion of SO₂ across the gas film, the internal diffusion of SO₂ in the porous particles and the reaction as such (irreversible, 1st order). For the reaction of SO₂ with a fine particulate reactant, the reaction rate constant and the relevant contact time are the dominant parameters. Application of the model equations reveals that the circulating fluidized bed is the most appropriate technique, where the high solid to gas ratio guarantees a high conversion in a short reaction time. For the CFB operation, the required gas contact time in a CFB at given superficial gas velocities and solids circulation rates will determine the SO₂ removal rate.

1. Introduction

1.1. An Overiew of the Sulphur Problem

SO₂ is mostly related to energy generation from fossil fuels. The International Energy Agency (IEA) reported that fossil fuels account for over 80% of the word energy supply [1]. In China, about 70% of the energy is provided by coal and fuel oil. Although the combustion of fossil fuels is the dominant contribution for anthropogenic CO₂ emission [2], the combustion-derived emissions of NO_x and SO₂ are also important towards atmospheric pollution. The ultimate analysis of some fuels determines the composition and the extent of the possible SO₂ problem.

Table 1. Characteristics of combustion feedstock.

Parameters	Used in the Present Research			Petroleum Fuels Oil
	Coal (Columbia)	Wood Bark	Sludge	No.1 Fuel Oil (41.5° A.P.I.)	No.2 Fuel Oil (33° A.P.I.)	Low Sulfur (12.6° A.P.I.)	High Sulfur (15.5° A.P.I.)
Ash content (wt.% dry)	7.7–9.2	0.2–0.3	7.0–22.9	<0.01	<0.01	0.04	0.02
C (wt.%)	60.1–62.1	17.8–22.3	10.3–15.7	86.4	87.3	87.26	84.67
H (wt.%)	4.22–4.25	1.11–2.72	1.39–2.09	13.6	12.6	10.49	11.02
S (wt.%)	0.58–0.59	0.02–0.05	0.05–0.06	0.09	0.22	0.84	3.97
N (wt.%)	1.26–1.35	0.04–0.17	0.05–0.09	0.003	0.006	0.28	0.18
O (wt.%)	8.92–8.97	16.42–18.82	12.71–15.13	0.01	0.04	0.64	0.38

illustrates some example compositions. Even biomass or waste activated sewage sludge contain non-negligible S-contents.

The NO_x problem related to combustion has been extensively dealt with by Mahmoudi et al. [3]. The emission and abatement of SO₂ merits a further attention, especially in the field of in-situ removal in the combustor. Although sulphur dioxide (SO₂) is mostly emitted from coal-fueled power plants, from waste incineration and fuel combustion, it also originates from sulphuric acid manufacturing, from clay brick plants and from treating nonferrous metals.

Its presence in the atmosphere is one of the major environmental concerns, since it contributes to acid rain formation [4,5], has various other environmental impacts such as localised cooling (by reflecting sunlight back into space) [6] and is hazardous to human health resulting in many types of respiratory illnesses such as asthma and bronchitis [7,8]. The emission of SO₂ by industrial activities also needs to be limited.

Two types of SO₂-loaded off gases need to be distinguished. Power plant flue gases generally contain low concentrations of SO₂ (less than 0.5% by volume), but are emitted at high volumetric flow rates: A coal-fired power plant burning 1% sulphur coal (by weight) produces 20 kg of SO₂ for every ton of coal burned, and this at over 10,000 Nm³/t of exhaust gas [6]. Similarly, a clay brick kiln will emit about 6 g/Nm³ of SO₂ at high flue gas flow rates (~ 100,000 Nm³/h for a medium size brick kiln). These “dilute” SO₂ gases will mainly rely on a “throw-away” reactant for the abatement, as further described in Section 1.2 below.

Highly loaded off gases are produced by e.g., smelter operations, containing SO₂ at a concentration of about 10% by volume. These concentrated gases will be mostly water-scrubbed in a counter-current absorption tower, and the resulting liquid will be upgraded to sulphuric acid (H₂SO₄). The upgrading of sulphuric acid to commercial grade (>95%) is necessary for making this method economically feasible [9,10,11,12].

1.2. Review of De-SO₂ Techniques

There are two approaches to SO₂ emission control, i.e., the removal of sulphur from the fuel before it is burned, by using low-sulphur fuels [13], or the end-of-pipe removal of SO₂ from the exhaust gases before emission into the atmosphere. In the flue gas treatment, both wet (scrubbing) and dry systems (sorbent injection) are used. The present research only deals with SO₂ removal from flue gases, since the complete removal of S from the fuel prior to combustion is at present neither technically nor economically viable [13]. Some relevant references are given in

Table 2. Relevant literature findings for end-of-pipe deSOx.

Author	Methods	Characteristics
[14,15]	Semi-dry flue gas desulphurization (FGD)	Contact with slurry of Ca(OH)2 Production of CaSO4 (in some cases reusable in building industry)
[11,16]	Scrubbing (H2O)	Scrubbing with water in countercurrent adsorption tower Formation of H2SO4 Concentration to technical grade H2SO4 needed
[17,18,19]	Thiosorb lime wet scrubbing	Reagent of 3–6 wt% MgO acts as catalyst for SO2 removal by lime Reliable and cost-effective process for high-sulphur applications
[20,21,22,23]	Regenerative alumina process	Simultaneous removal of NOx and SO2 by of alumina pellets with sodium aluminates Spent sorbent is regenerated No longer used in practical applications
[24,25]	Dry limestone	Most practical method, using dry limestone or lime Application in fluidized beds
[26,27,28]	Electron beam flue gas treatment (EBFT)	Simultaneous dry removing of SO2 and NOx Flue gas irradiation with fast electrons initiating chemical reactions High capital and operating costs
[29]	Oxy-fuel combustion	The substitution of N2 by O2 in oxy-fuel combustion does not affect the release of sulphur from the coal during combustion. Increased retention will reduce the SO2 emission rate

. A further description is given below.

Various “throw-away” techniques for desulphurisation have been developed in semi-dry or dry flue gas desulphurisation (FGD). Hydrated lime (Ca(OH)₂) and/or sodium bicarbonate (NaHCO₃) are commonly used as SO₂ reactants, with solid reaction product (CaSO₄ / Na₂SO₄) removed with the gas exhaust of the contactor and partly recycled (till exhausting the active reactant) or finally recovered in a collection device (fabric filter or electrostatic precipitator). A portion of solids is recycled, mixed with fresh reactant and fed (semi-) dry to the contactor. Dry reaction products are obtained. In the dry process, both bubbling and circulating fluidized beds (BFB, CFB) can be used as contactor [30,31,32,33]. In this process no waste water is produced and dry calcium sulphate is the product of reaction [14].

In a wet scrubbing process [16], SO₂ is removed by scrubbing with water or alkali solutions in a counter-current absorption tower, and sulphuric acid is formed. The concentration of sulphuric acid to commercial grade (>95%) is necessary for making this method economically feasible.

The Thiosorb process is an example of a mixed deSO_X process and requires the use of lime reagent with 3–6 wt% magnesium oxide (MgO) for SO₂ capture in a wet flue gas desulphurization system. Absorbent slurry is sprayed into the gas containing SO₂. The pure lime scrubbing process has a number of deficiencies and desulphurization is exceptionally low (removal efficiency of 50% to 85%). A large volume of slurry has to be brought into contact with flue gas for abatement of SO₂ and it needs a significant amount of energy for pumping. By addition of MgO, which acts as catalyst and reactant, lime scrubbing can achieve SO₂ removal of 99% with high sulphur coal. This system is recognized as a reliable process for high-sulphur applications and is cost-efficient [17,18].

A system based on sorption on alkalised alumina simultaneously removes SO₂ and NO_x uses a fluidized bed of alumina pellets with sodium aluminate. Flue gas in the range of 120–150 °C passes through a fluidized bed which contains the active sorbent to remove SO₂ and NO_X and form sodium sulphate, sulphite and nitrate. Spent sorbent, recovered separated from the absorption reactor, is regenerated in a number of steps: initially, the sorbent is heated with hot air and the stripped gas is subsequently sent to a selective catalyst reduction to transform NO_x to N₂, and finally to a multistage regenerator to react with steam and natural gas to obtain hydrogen sulphide (H₂S) and SO₂. This technology was developed by the U.S. Bureau of Mines, but it has subsequently been abandoned [20].

One of the most practical methods to reduce SO₂ emissions is using dry lime [CaO, Ca(OH)₂] or limestone (CaCO₃). This method will be further investigated in this paper. Limestone and/or lime are used to enable SO₂ gas to chemically react with CaCO₃ or CaO forming calcium sulphate (CaSO₄) and calcium sulphite (CaSO₃) as can be seen in the following reactions.

CaCO₃(s) + SO₂(g) + 0.5O₂ (g) → CaSO₄ (s) + CO₂ (g)

CaCO₃ (s) + SO₂ (g) → CaSO₃ (s) + CO₂ (g)

CaO(s) + SO₂ (g) + 0.5O₂ → CaSO₄(s)

A continuous circulating fluidized bed (CFB) is commonly chosen as the most appropriate processing unit due to the high velocity of air being used, thus reducing the plant size and providing very good mixing and contact for the desired removal. The flue gas is forced into the riser via a fan and a distributor situated at the bottom of the riser. After the distributor, the flue gas will be in contact with limestone or lime being both fed from the L-valve, and injected as fresh reactant. The excellent mixing achieved in the CFB promotes mass transfer between the limestone and the flue gas. As the air/solid mixture leaves the riser, it enters the cyclone. The cyclone will collect coarser solids and recycle them to the riser. Over time, particles erode and become smaller, they become saturated with chemisorbed SO₂ and need to be removed from the system. Very small solids together with the flue gas will leave the system from the top of the cyclone, at approximately the same temperature as the inlet flue gas, and are directed to a polishing filtration.

CFB technology was commercially introduced by Lurgi in the early eighties for the abatement of acid gases, especially for flue gas desulphurization using Ca²⁺ compounds. Numerous plants based on this CFB desulphurization technology are in commercial operation [34,35,36,37]. Leuschke et al. [38], have shown that it is possible to achieve desulphurization efficiencies in excess of 99%, reducing residual SO₂ emissions to about 50 mg/Nm³. The model developed in the present paper will theoretically demonstrate that these high efficiencies can indeed be achieved.

1.3. Objectives and Novelties of the Present Researach

Despite numerous previous researches, as highlighted in 1.2 above, the SO₂ capture by alkali sorbents is not fully understood towards (1) the reaction rate; (2) the application in a large-scale combustor.

The present study offers answers to these questions. The de-SO₂ efficiency is analyzed in a large-scale CFBC, with cheap Ca(OH)₂ as alkali sorbent. It moreover develops a theoretical model approach, applicable to any alkali sorbent of different particle size, by developing model equations that combine gas film diffusion, reaction rate and gas diffusion in the pore of the sorbent.

Application of the overall model to sorbents of small particle size will determine that the reaction of SO₂ with CaO is the dominant factors in the reaction rate. The conversion can be predicted when the SO₂ to sorbent ratio and the gas-solid contact time are determined.

The continuous circulating fluidized bed (CFB) is demonstrated to be the most appropriate processing unit due to both the high gas velocity (U) and solid circulation flux (G) being used, thus reducing the plant size, and providing very good mixing and contact between SO₂ and reactant for the desired removal [39,40,41]. A cyclone will collect solids and recycle them to the riser of CFB. When the size of solids becomes smaller due to attrition, the particles have a higher surface area per unit volume to react with the SO₂. Usually very fine solids are SO₂-saturated and can no longer be separated by the cyclone. These very fine particle will exit the system together with the fly ash and flue gas, and need subsequent cooling before a fabric filter or electrostatic precipitator [42,43].

2. Experimental Set-Up and Results

The specific reactions of SO₂ with Ca²⁺ in the circulating fluidized bed combustor of biomass were examined in a large scale CFB combustor of UPM-Kymmene (UK) Ltd (Caledonian paper mill, Irvine, Ayrshire, Scotland, UK) while burning coal, wood bark and sewage treatment sludge. The layout of the plant and its operational conditions are illustrated in Figure 1. Relevant dimensions are given in

Table 3. Relevant dimensions of the CFB.

Riser			Cyclone
Square	Total length	Length above L-valve	Diameter cylinder	Length cylinder	Length conical part	Solids apex	Gas outlet
3780 mm	18,450 mm	14,000 mm	4560 mm	5460 mm	5000 mm	1310 mm	1860 mm

. The feedstock of the CFB was given in Table 1. Due to the high percentage of coal used (2.1 kg/s for a total of 2.5 kg/s), the SO₂ formed is between 1.25 and 1.4 g/m³ as measured in the stack exhaust. Measurements were made continuously while adding Ca(OH) ₂ to the feed of the CFB. Since Ca(OH)₂ decomposes to CaO and H₂O at ~ 580 ℃, the reaction of SO₂ at the operating temperature of ≥800 ℃ should consider CaO as reactant. Due to the fact that the CFB combustor is essential in the paper manufacturing process to supply process steam, variations in the CFB operation were limited (towards operating temperature (T), superficial gas velocity (U), and solids circulation flux (G)).

Experimental results are expressed as percentage SO₂-removed in function of the operating temperature, with the operating superficial gas velocity (U) and solid circulation flux (G) as additional parameters. Hydrated lime [Ca(OH)₂] of particle size <<100 μm was added within the fuel feed, at such a mass flow rate that the resulting CaO inventory in the CFB was between 1 and 2 wt%. Due to particle attrition in the CFB, reacted lime (as CaSO₄) was removed with the fly-ash in the electrostatic precipitator. Due to particle attrition in the CFB, reacted lime (as CaSO₄) was removed with the fly ash in the electrostatic precipitator.

Ca(OH)₂ consists of soft hexagonal crystals. Its particle size is illustrated in Figure 2. The figure also includes the laser diffractometry size analysis of the fines collected (CaSO₄ and flyash) collected. Since both flyash and CaSO₄ cannot be separated from the discharge of the electrostatic precipitators, both are jointly analyzed.

The BET of the Ca(OH)₂ used was 40.6 m²/g, against only 3.4 to 4.9 m²/g for the flyash-CaSO₄ discharge. These Malvern results clearly indicate that Ca(OH)₂ is a brittle sorbent, reduced to smaller particle sizes by reaction, thermal decrepitation and attrition. BET results also tentatively demonstrate that the formation of CaSO₄ reduces the porosity of the sorbent. This is expected, since the molar volume of CaSO₄ is 74.69 cm³/mol, against 31.66 cm³/mol for Ca(OH)₂: CaSO₄ with a higher molar volume tends to block the Ca(OH)₂ pores upon reaction.

Additional measurements for Ca(OH)₂ include the pore size distribution, and field emission scanning electron microscopy (FESEM). Nitrogen adsorption-desorption isotherms were measured using a ASiQwin, ver.5.2, Quantachrome Instruments, as shown in Figure 3 and

Table 4. BET results of Ca(OH)₂ nanoparticles.

Component	Pore Volume (cm3/g)	BET SUrface Area (m2/g)	Type of Porosity
Ca(OH)2	0.20	40.6	Mesoporous 5–12 nm

. The surface morphology of the adsorbent was determined by JEOL JSM-7800F field emission scanning electron microscope (FESEM), as illustrated in Figure 4.

The pores of the Ca(OH)₂ particles are all mesopores. The pore size of Ca(OH)₂ is anyway larger than CaSO₄. Similar measurements could not be made for the reaction product, CaSO₄, since it was collected together with the flyash fines. SEM images reveal the porous and irregular structure of the Ca(OH)₂ particles.

The SO₂ abatement experiments reveal SO₂ removal efficiencies between 95% and 99.5%, as a function of operating superficial air velocity, solid circulation flux and temperature (Figure 5).

The results will be further compared with model predictions in Section 5. An increasing G increases the efficiency of SO₂ removal, irrespective of U. Increasing values of U at a given G reduce the removal efficiency. Both effects are in accordance with the hydrodynamic expectations: An increasing U will reduce the SO₂-CaO contact (residence) time, thus reducing the reaction potential; an increasing G on the contrary will increase the amount of CaO present in the riser, thus enhancing the reaction by the increasing CaO/SO₂-ratio [44]. These effects will also be further discussed when model equations are applied.

3. Development of a General Gas-Solid Model for SO₂ Capture

3.1. Model Equations

The reaction of the solid reactant with SO₂ follows a first order kinetics in SO₂, provided O₂ is present in high concentrations [45,46]. This is always the case in combustion flue gases in view of the legal obligation to emit them into the atmosphere at minimum 6 vol % O₂.

As shown in Figure 6, three combined factors are important in the SO₂ /particle reaction:

• The external diffusion of SO₂ across the gas film, determined by the Sherwood number, and a function of the turbulence of the system and therefore of the type of reactor;
• The internal diffusion of SO₂ in the porous particles, expected to play a role in particles of large diameter, only;
• The reaction as such (1st order), function of the reaction rate constant and the contact time.

These 3 factors are combined in general model equations, although the gas film diffusion is expected to only control the overall reaction rate in the early stages of conversion when no product layer is present: A product layer will introduce a pore-diffusion resistance. Since CFB attrition might however remove the product layer, gas film diffusion was included in the calculations.

To develop a model that spans a wide range of particles sizes of the CaO reactant, a shrinking core model is used, which assumes a sharp boundary between the un-reacted core and the formed product layer [47]. CaO particles, are assumed spherical and of uniform size. The overall mass balance is expressed in terms of the SO₂ and CaO conversion by:

$${C=C}_g{/C}_{g0}{=1-M}_{R}X$$

(1)

C_g0 and C_g, Initial SO₂ concentration, and SO₂-concentration at any time (mol/m³)

M_R, Molar ratio of Ca²⁺-reactant/SO₂ (mol/mol)

X, Fractional conversion of Ca²⁺-reactant (-)

The relationship between the conversion X, and the radius of the shrinking core, r_c, as a function of its initial radius, R₀, is given by:

$${1-X=(r}_c{/R}_0{)}^3$$

(2)

The reaction rate can be expressed in terms of the determining factors where gas film mass transfer (k_g), pore diffusion (D_e) and reaction rate constant (k_c) are combined [47,48].

$$-\frac{{\rho }_P}{M_s}\frac{{dr}_c}{dt}=\frac{C_g}{\frac{r_c{}^2}{R_0{}^2{k}_g}+\frac{{(R}_0{-r}_c{)r}_c}{R_0{D}_e}+\frac{1}{k_c}}$$

(3)

r_c and R₀, Radius of the reaction boundary and Initial radius (m), respectively; M_s, Molar mass of solid reagent (CaO) (kg/kmol); ρ_p, Particle density (kg/m³); k_g, Gas film mass transfer coefficient (m/s); D_e, Effective Diffusivity of SO₂ in the porous reagent (m²/s); k_c, Reaction rate constant (m/s).

Introducing M_R and X from Equations (1) and (2) respectively, together with a dimensionless reaction time τ according to Equation (4), and dimensionless groups that include the relevant reaction resistances (Bi, Da), yields:

$$\tau =\frac{D_e{M}_s{C}_{g0}}{R_0{}^2{\rho }_p}t$$

(4)

$$\frac{dX}{d\tau }=\frac{3{\left(1-X\right)}^{\frac{1}{3}}}{1-\left(1-\frac{1}{Bi}\right){\left(1-X\right)}^{\frac{1}{3}}{+Da}^{-1}{\left(1-X\right)}^{-\frac{1}{3}}}{(1-M}_{R}X)$$

(5)

t = Reaction time (s); τ = Dimensionless time (-); B_i = Biot number = k_gR₀/D_e, incorporating film and intra-particle (pore) diffusion; Da = Damkohler number = k_cR₀/D_e, including reaction rate constant and pore diffusion.

This equation is solved with the following boundary conditions: at τ = 0, X = 0 (no CaO conversion at t = τ = 0) and C = 1 (C_g = C_g0 at t = τ = 0)

Introducing further appropriate ratios and equations provides a general solution [48]:

$$\alpha =(\frac{{1-M}_g}{M_g}{)}^{1/3}$$

(6)

$${\gamma =(1-X)}^{1/3}$$

(7)

$${\tau =(1+\alpha }^3{\left)\right(g}_1{\phi }_1{+g}_2{\phi }_2{+g}_3{(g}_4{-\phi }_3\left)\right)$$

(8)

$$g_1=\frac{1}{2\alpha }\left(1-\frac{{Da}^{-1}}{\alpha }\right)$$

(9)

$$g_2=\frac{1}{3}\left({1-Bi}^{-1}\right)-\frac{1}{6\alpha }\left(1-\frac{{Da}^{-1}}{\alpha }\right)$$

(10)

$$g_3=\frac{1}{\alpha \sqrt{3}}\left(1+\frac{{Da}^{-1}}{\alpha }\right)$$

(11)

$$g_4{=tan}^{-1}\left(\frac{2-\alpha }{\alpha \sqrt{3}}\right)$$

(12)

$${\phi }_1=ln\left(\frac{\gamma +\alpha }{\gamma -\alpha }\right)$$

(13)

$${\phi }_2=ln\left(\frac{{\gamma }^3{+\alpha }^3}{{1+\alpha }^3}\right)$$

(14)

$${\phi }_3{=tan}^{-1}\left(\frac{2\gamma -\alpha }{\alpha \sqrt{3}}\right)$$

(15)

The integrated reaction equation includes the dominant parameters. Physical properties are included in the Biot-and Damköhler numbers. The required reaction yield can be predicted for any value of M_R and/or τ provided these parameters are calculated.

3.2. Evaluation of the Model Parameters

3.2.1. External Diffusion

The rate coefficient of gas diffusion, k_g, is commonly expressed in terms of the Sherwood number, Sh, being the ratio of the mass transfer coefficient at the particle surface and the gas diffusivity.

Different expressions are used in powder-gas systems:

$$\mathrm{Sh}=\mathrm{f}\left(\mathrm{Re},\mathrm{Sc}\right)=\left(\frac{k_g{d}_p}{D_g}\right)$$

(16)

Sh, Sherwood number, kgdp/Dg	(-)
Re, Reynolds number, dpUslρg/μg	(-)
Sc, Schmidt number, μg /ρg Dg	(-)
Dg, Diffusivity of SO2 in the gas flow	(m2/s)
dp, Particle diameter	(m)
kg, Gas film mass transfer coefficient	(m/s)
Usl, Slip velocity (i.e., ~ U-Ut)	(m/s)
U, Superficial gas velocity in the CFB	(m/s)
Ut, Particle terminal velocity	(m/s)
${\mu }_g$, Gas viscosity	(Pa.s)
${\rho }_g$, Gas density	(kg/m3)

All gas-related parameter values need to be calculated at the operating temperature. Powder related parameters are nearly insensitive to the temperature.

Equations for the Sherwood number are given by Li and Wang [49], Zevenhoven and Jarvinen [50], and Gunn [51]. A CFB combustor, the UPM-Kymmene (UK) Ltd (Caledonian paper mill, Irvine, Ayrshire, Scotland, UK) application with a riser of 3.78$\times$3.78 m² being a typical example, operates at temperatures between 1023 K and 1173 K, with small particles (Ca²⁺-reactant is injected with particle size ≤74 μm). The slip velocities, being the difference of the superficial gas velocity, U, and the calculated terminal (free fall) velocity of the particle, U_t, are around 3 m/s [52]. Application of the literature equations leads to the following predictions of k_g, as illustrated in Figure 7.

Although predicted values differ among the equations, the k_g value exceeds 200 m/s for reactant particle sizes below 74 μm, being closer to 300 m/s for an average particle size of ~40 μm.

From these calculated k_g-values, it is also clear that the effect of the gas diffusion resistance can be assumed negligible ($\frac{r_c^2}{R_0^2{k}_g}$<<) for fine particles, as will also be proven by further calculations.

3.2.2. The Effective Internal Diffusion Coefficient, D_e

The effective pore diffusivity D_e determines the resistance to gas penetration within the particle. It depends on pressure, temperature, particle porosity, and particle size. As previously experienced [52], it only plays a role for coarser particles. For fine particles the contribution of the pore diffusion resistance is small. The effect of the internal pressure is limited, and pressure is assumed to remain atmospheric in a CFB environment. At atmospheric pressure, and using sorbent particles between 2 and 106 µm at absorption temperatures between 773 and 1123 °C, the effective diffusivity in m²/s was determined by various researches, as illustrated in

Table 5. Table of effective diffusivities, measured for different systems at atmosphere pressure.

Authors	T(K)	Composition	Particle Size(μm)	De (m2/s)
[55]	773–1213	SO2: 0.3%; O2: 5%; CO2: 95%	2–106	7.341$\times$10−7
[53]	923–1173	SO2: 0.25%; O2: 3.6%; CO2: 96.4%	2–106	6.34$\times$10−10
[54]	1073	SO2: 0.1%–0.5%; O2: 10%; CO2: 70%	4–5.4	2.1$\times$10−9

. Values differ by several orders of magnitude i.e., from 6.4 × 10⁻¹⁰ [53], to 2.1 × 10⁻⁹ [54] and 7.3 × 10⁻⁷ [55]. The effect of pressure is not outspoken [56,57,58,59].

It is common to use D_e ~10⁻⁹ m²/s in reaction rate calculations.

3.2.3. The Reaction Rate Constant, k_c

This key parameter for all gas-solid reactions. For limestone it is of the order of 10⁻⁴ to 10⁻³ m/s [54,55,57,59,60]. It is between 10⁻² to 10⁻³ m/s for CaO [45,46,59,61,62]. Since the sulphation of Ca²⁺ is an exothermic process, reaction rates are lower at high temperatures and higher at lower temperatures.

3.2.4. The Molar Ratio M_R (Expressed as Ca/S or CaO/S)

To find the molar ratio, the molar flow rate of CaO (or CaCO₃)₎ and molar flow rate of SO₂ are required operational variables. With a solid circulation flux, G (kg/m²s) and cross-sectional area of the riser, A (m²), the molar flow rate of solids is known.

$$\mathrm{Molar}\mathrm{flow}\mathrm{rate}\mathrm{of}\mathrm{solid}\mathrm{reactant}=\frac{{GA(\%CaCO}_3)}{{MM}_{{CaCO}_3}}\mathrm{or}\frac{GA(\%CaO)}{{MM}_{CaO}}$$

(17)

Where,

G, Solid circulation flux	(kg/m2s)
A, Cross sectional area of the riser	(m2)
MMCaCO3, molecular weight of CaCO3	100 kg/kmol
MMCaO, molecular weight of CaO	56 kg/kmol
%CaCO3/%CaO, weight percentage in G	-

Similarly, for a superficial gas velocity, U (m/s) in the same riser dimensions, the molar flow rate of SO₂ is also defined.

Molar flow rate of SO₂ = $\frac{AU}{{MV}_{SO2}}\frac{{SO}_2{(ppm}_v)}{{10}^6}\ast \frac{273}{(T+273)}$

MV _SO2, molar volume of SO₂              22.4 Nm³/kmol

$$M_R=\frac{\frac{GA(\%CaO)}{56}}{UA\frac{{SO}_2{(ppm}_v)}{{10}^6}\ast \frac{273}{22.4(T+273)}}\mathrm{or}{M}_R=\frac{\frac{{GA(\%CaCO}_3)}{56}}{UA\frac{{SO}_2{(ppm}_v)}{{10}^6}\ast \frac{273}{22.4(T+273)}}$$

(18)

3.2.5. Evaluation of the Model Parameters

During the experiments, the CFB of UPM-Kymmene (UK) Ltd (Caledonian paper mill, Irvine, Ayrshire, Scotland, UK) was operated at 1107–1135 K, for superficial velocities of 2.5 to 4.8 m/s and solids circulation fluxes of 36 to 71 kg/m²s. The initial SO₂ concentration was between 1250 and 1400 mg/m³ i.e., 438 to 525 ppm_v. The transport velocity of the bed material was 0.8 m/s. The amount of CaO in the bed was between 1 to 2 wt%, and was continuously kept at that level by adding fresh CaO [as Ca(OH)₂].

Under these specific operating conditions, the essential parameters can be retrieved from previous equations and data, whilst M_R and the contact time t are calculated below:

• D_e: 10⁻⁷ to 10⁻⁹ m²/s, commonly adopted as 10⁻⁹ m²/s
• k_g: Allowing for a safety margin, k_g is taken at a conservative average of 300 m/s, for the particle size range (<74 μm) under scrutiny
• k_c: 5 × 10⁻² m/s
• The M_R ratio is calculated according to the equations before, and illustrated in Figure 8.
• The residence time distribution of the gas phase in the riser of a CFB was studied by [39]. The average contact time is given by:
  $\overline{t}$ = 0.54(U-U_TR)^−0.25G^−0.2H with $\overline{t}$ in s and H, the riser height in m (19)

It should be remembered that U is the superficial gas velocity, whereas U_TR is the superficial gas velocity whereby a CFB operating mode is initiated [31,63,64].

Considering a riser of 14 m height above the solids recycle feed as in the UPM-Kymmene (UK) Ltd (Caledonian paper mill, Irvine, Ayrshire, Scotland, UK) case, operating at an average velocity of 3.5 m/s for particles with U_TR, of 0.8 m/s, yields $\overline{t}$-values of $\overline{t}$= 2.98 s for G = 30 kg/m²s and 2.52 s for G = 10 kg/m²s.

4. Application of the Model Equations and Comparison with Experimental Result

4.1. Effect of Contact Mode

From the model application, Figure 9 illustrates that a short time contact time, τ, is needed in a CFB, and an average τ in a BFB. The required residence times in a pneumatic conveying line (>>100 s) make this solution in practice impossible since extremely long piping would be needed at a velocity of e.g., 2 m/s.

4.2. The CFB Contact Mode

Using the parameters of 3.2, the model equations can be used to predict SO₂ capture efficiencies and parameter influences.

1. Prior to performing detailed predictions, the effect of both k_g and D_e were assessed. All other parameters remaining within the predicted range of 4.2, the effects of both k_g and D_e are negligible. Increasing k_g from 200 to 2000 m/s has a negligible effect on the predicted time for a given conversion: this was indeed expected due to the high Reynolds number in the riser, where flue gas film diffusion is of negligible influence.

Similarly, the variation of D_e by 2 orders of magnitude, at k_g~300 m/s for an average particle size of 40 μm, has an effect well below 10% on the expected conversion. Pore diffusion is not a rate-limiting resistance when using small particles, as is common in CFB combustors.

2. Using k_g ~ 300 m/s, D_e = 10⁻⁹ m²/s and k_c = 5 × 10⁻² m/s, the model equations predict the required time (t) for a given conversion. This is illustrated in Figure 10 below, M_R being the remaining variable.

Since the average gas-solid contact time in the CFB-riser is between 2.5 and 3 s and M_R-values exceed 500, very high SO₂-removal efficiencies are predicted.

3. The effect of CaO-particle size is important. For e.g., M_R = 400, k_g = 300 m/s, D_e = 10⁻⁷ m²/s, the required contact time is between 2 sec (for 90% SO₂ removal) and 3 sec (for 98% SO₂ removal) when using 25 µm sorbent particles. Since for a continuous reaction system, required times are proportional with the particle size, these required contact times need to be multiplied by 2, respectively 4, when using sorbent particles of 50 or 100 µm.

Clearly, operating with coarser CaO-particles, increases the required reaction time for a required conversion. Commercial Ca(OH)₂ normally has a particle size <<74μm, with an average around 40 μm: efficiencies well in excess of 95% can then be expected in the CFB.

Since particles in a CFB are subjected to attrition, their particle size will progressively decrease. They will be carried out of the system when their particle size is lower than the cut-size of the CFB cyclone [42]. The attrition will not affect the gas-solid contact mode, since the bulk CFB bed material will either be an inert powder (e.g., sand), and fresh reactant is continuously added. However, the reaction rate for small particles is inversely proportional to the particle size. Finer particles will therefore be more rapidly converted, thus providing a safely margin towards the required reaction time predicted by the model on the basis of the average particle size.

4. When using the model equations to predict the SO₂ removal rate over the range of operating conditions of the UPM-Kymmene (UK) Ltd (Caledonian paper mill, Irvine, Ayrshire, Scotland, UK) application the correspondence of predicted and measured removal yields is illustrated in Figure 11 (with k_c at a conservative 0.03 m/s).

A very fair agreement is obtained. The limited over/or underestimation might be due to the k_c-value taken at 0.03 m/s (at k_c = 0.025 m/s, the predicted removal efficiencies decrease on average by about 0.2%); a slight overestimation of the reaction time, and/or the use of an average particle size of 40 μm: since the lime used has a wide size distribution and decreases due to attrition, the average particle size can be below 40 μm.

The experimental and model comparison however stresses the reliability of the model approach.

This was a further assessed for the case of using CaCO₃-filler, with commonly quoted efficiencies of >99.9% [38], and widely applied in the Lurgi CFB-SO₂ removal plants. In these applications, a CaCO₃ circulating bed is used. At an average conversion of 50%, the CaCO₃-content of the bed can be assumed as 50%. M_R values in this case vary between 5000 and 14,000 for SO₂ = 600 ppm_v and U decreasing from 6 to 3 m/s respectively. For SO₂ = 400 ppm_v the M_R-values increase to 11,000 and 21,000 respectively at 6 and 3 m/s.

It is hence clear that SO₂ removal efficiencies in a CFB-riser are excellent and are achieved by a simple direct contact between the Ca²⁺ reactant and SO₂.

5. Conclusions

The SO₂ capture by alkali sorbents is examined for a large-scale CFBC (58 MW_th) of coal, biomass and sludge.

Experimental results demonstrate a removal efficiency of >94.5 at high superficial gas velocity and low solid circulation flux. Efficiencies of over 99.5% are reached at lower operating velocities and higher solid circulation flux.

A theoretical reaction model was developed to encompass gas film diffusion, gas diffusion in the sorbent pores, and the chemical reaction at the unreacted particle core.

From the evaluation of the model parameters, the chemical reaction is the major resistance in the overall reaction rate.

The application of the model equations moreover demonstrate that a CFB is a better gas–solid contacting mode than a BFB. A pneumatic reactor is practically unacceptable.

The fair agreement between experimental and model results stress the reliability of the model approach.