Modeling of solids segregation in circulating fluidized bed boilers

Abstract

Segregation always occurs in a circulating fluidized bed (CFB) because of the wide distribution of particle size and density of the bed material. Terminal velocity has a significant influence on solids segregation; thus, it is convenient to describe the segregation tendency using single particle terminal velocity u_t. This paper proposes a segregation model in CFB boilers based on the Cell Model. In each cell along the riser, varied-sized particles have different tendencies toward segregation; finer particles are carried out more easily, while coarser ones tend to sink into the cell. It is assumed that the average terminal velocity \overline{u_t}, corresponding to the mean particle size in the cell, has a segregation index of x = 1.0 as the reference point. The segregation index of particles with higher terminal velocity is lower than 1.0, while that for finer particles is larger than 1.0. The empirical formulae of segregation parameters, namely x₀ and k₁, are derived by optimizing experimental data in published literature. The test result of ash size distribution in a 220 t/h CFB boiler validates the reasonableness of the model.

Keywords

segregation / model / terminal velocity / circulating fluidized bed (CFB)

Introduction

The bed material of a circulating fluidized bed (CFB) boiler consists of various types of particles such as coal, ash, and limestone. In general, these particles are of different sizes and densities. The smaller or lighter solid particles, whose terminal velocities are smaller, are more easily elutriated by the fluidizing gas, while the bigger or heavier ones tend to remain at the bottom of the bed. This common process in CFB boilers is referred to as solid segregation. In contrast, the process against solid segregation, called solid mixing, is mainly caused by the gaseous turbulence and interaction between solids, in particular, the interaction between upward flowing particles and downward moving particles. Dynamic equilibrium between solid mixing and solid segregation is maintained in CFB combustors [1,2].

The Wen-Chen model is commonly used to simulate the elutriation and entrainment phenomena in a CFB riser. The model validly describes the solid segregation over the freeboard in a bubbling fluidized bed. However, the capacity of the model to describe solid segregation for the combustor of a CFB boiler, where the entire flow field is a superposition of a fast or a pseudo-fast bed on the top and a bubbling bed at the bottom, is questionable. Solid segregation occurring in different sections is dominated by different mechanisms.

Relatively large particles tend to move downward to the bottom of a CFB combustor because their large terminal velocities interact with rising gaseous bubbles. The strong gas-solid interaction induces strong gas-solid mixing in the bubbling bed. There is solid segregation occurring in this section, controlled by the interaction between down-moving particles and rising bubbles. The dominant factors are particle properties and particle-gas interaction [2].

Above the dense bed, in the fast or pseudo-fast bed region of a CFB combustor, the particles are relatively small and have relatively small terminal velocities. In this section, the solid segregation depends on the particle properties and the particle-particle interaction [3].

The particle properties play a significant role in both mechanisms. Since the terminal velocity, u_t, is generally used as a parameter to characterize a particle using its size and density, it is reasonable to assume that u_t could be conveniently used as a parameter to describe the tendency of solid segregation as well. Under this hypothesis, a novel solid segregation model in CFB boilers is developed. Two parameters, x₀ and k₁, as expressed by empirical formulae, are derived and optimized using experimental data in published literatures.

Segregation model

In the segregation model, it was assumed that bed materials are composed of particles of constant density that have broad distribution in size. This is reasonable because over 95% of the bed materials in a CFB boiler are coal ash. The particles were divided into several discrete groups with different sizes. The CFB riser was divided into a series of cells along the axial direction. In different cells, particles with different sizes and terminal velocities have different segregation tendencies. The finer particles tend to be carried up by the gas flow, while the coarser ones tend to sink. Segregation index, x, was used to describe the segregation tendency of the particles. For particles of average terminal velocity \overline{u_{\mathrm{t}}} corresponding to the mean size of all particles in a cell, \overline{d_{\mathrm{p}}}, x = 1.0. For particles with a terminal velocity larger than \overline{u_{\mathrm{t}}}, x<1.0. For particles with a terminal velocity less than \overline{u_{\mathrm{t}}}, x>1.0.

Without segregation, the upward flow rate of particles with size j is

(1){\dot{m}}_{\mathrm{u}\mathrm{p}j}=W_{\mathrm{u}\mathrm{p}}·{\displaystyle \frac{m_j}{m}}.

With segregation, the upward flow rate of size-j particles is

(2){\dot{m}}_{\mathrm{u}\mathrm{p}j}=W_{\mathrm{u}\mathrm{p}}·{\displaystyle \frac{m_j}{m}}·{\xi }_j.

where x_j is the segregation index of size-j particles, m_j is the mass of size-j particles, m is the total solid mass in the cell, and W_up is the total upward flow rate of particles from the cell.

For mass conservation, x_j satisfies

(3){\displaystyle \sum _j{\displaystyle \frac{m_j}{m}}·{\xi }_j=\mathrm{1.}}

In general, x_j is a function of particle diameter and density:

(4){\xi }_j=f\left({\displaystyle \frac{d_j}{\overline{d}}},{\displaystyle \frac{{\rho }_j}{\overline{\rho }}},{\displaystyle \frac{m_j}{m}}\right).

Based on previous study, the function could be an exponential type if the terminal velocity, u_t, is used as a variable. In the model, when the diameter of group-j particles was smaller than the mean diameter, {\overline{d}}_p, the segregation index was assumed simply as

(5){\xi }_j=\mathrm{1}+({\xi }_{\mathrm{0}}-\mathrm{1})\left[\mathrm{1}-\exp \left(-{\displaystyle \frac{\overline{u_{\mathrm{t}}}-u_{\mathrm{t},j}}{k_{\mathrm{1}}}}\right)\right],

where, k₁ is defined as the segregation ability, reflecting the segregation intensity. A larger k₁ represents a weaker segregation in the CFB combustor. The variations of segregation index with the terminal velocity at different k₁ are shown in Fig. 1.

When the diameter of group-j particles is larger than the mean diameter \overline{d_{\mathrm{p}}}, it is assumed as

(6)\xi =\exp \left(-{\displaystyle \frac{u_{\mathrm{t}}-\overline{u_{\mathrm{t}}}}{k_{\mathrm{2}}}}\right).

To obtain the same slope of x_j at mean terminal velocity \overline{u_{\mathrm{t}}} for Eqs. (5) and (6), k₂ and k₁ should satisfy

(7)k_{\mathrm{2}}=k_{\mathrm{1}}·{\displaystyle \frac{\mathrm{1}}{{\xi }_{\mathrm{0}}-\mathrm{1}}}.

Assuming that the downward flow rate for size-j particles is proportional to the mass fraction in the cell (Fig. 2), the mass balance for size-j particles in a specific cell can be expressed as

(8)W_{\mathrm{u}\mathrm{p},i-\mathrm{1}}·{\displaystyle \frac{m_{i-\mathrm{1},j}}{m_{i-\mathrm{1}}}}·{\xi }_{i-\mathrm{1},j}-W_{\mathrm{u}\mathrm{p},i}·{\displaystyle \frac{m_{i,j}}{m_i}}·{\xi }_{i,j}+W_{\mathrm{d}\mathrm{n},i+\mathrm{1}}·{\displaystyle \frac{m_{i+\mathrm{1},j}}{m_{i+\mathrm{1}}}}-W_{\mathrm{d}\mathrm{n},i}·{\displaystyle \frac{m_{i,j}}{m_i}}·{\xi }_{i,j}=\mathrm{0.}

Experimental data resource

Although solid segregation in CFBs has attracted much attention, experiments investigating this mechanism remain inadequate. Among the number of studies available, aside from those with binary solid mixtures, such as Nakagawa et al. [4] and Jiang et al. [5], only a few have reported on particles with a wide distribution in size. Two experiments have been found to validate the segregation model proposed in this paper: the experiment conducted by Hirschberg and Werther [6] in a CFB riser with quartz sands, and the study by Moortel et al. [7] in the dilute zone of a CFB cold pilot using a phase Doppler particle analyzer. The mean particle sizes along the axial direction have been reported in both experiments. The operational conditions of both are summarized in Table 1.

Under the working conditions of the experiment conducted by Hirschberg and Werther [6], the cyclone efficiency was assumed as 100% and no additional particles were fed or drained. Given axial solid volume concentrations, and if the interactions between particles are ignored, the upward flow rate in cell i can be calculated as

(9)W_{\mathrm{u}\mathrm{p}}=A\rho (\mathrm{1}-ϵ)\left(u_{\mathrm{g}\mathrm{a}\mathrm{s}}/ϵ-\overline{u_{\mathrm{t}}}\right).

Derivations of empirical parameters

An empirical equation that can describe the parameters in the segregation model can be derived using the available experimental data. Using the FORTRAN IMSL, important parameters such as x₀ and k₁ were optimized. By analyzing the values of x₀ and k₁, at the same gas velocity, the segregation index x₀ can be expressed in terms of the upward flow rate in cell i, W_up(i), kg/s, and circulating rate G_s, kg/m² as

(10){\xi }_{\mathrm{0}}=\mathrm{1.0}+{\displaystyle \frac{a}{u_{\mathrm{g}\mathrm{a}\mathrm{s}}}}·{\displaystyle \frac{W_{\mathrm{u}\mathrm{p}}(i)-G_{\mathrm{s}}A}{G_{\mathrm{s}}A}},

(11)k_{\mathrm{1}}={\displaystyle \frac{b}{u_{\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{m}}}}·u_{\mathrm{g}\mathrm{a}\mathrm{s}}^{\mathrm{2}},

where, a and b are empirical constants.

From the optimization results, the values of a and b can be derived (Table 2).

The mean particle diameter profile along the axial direction can be recalculated by integrating x₀ and k₁ into the model. The calculated results are plotted in Fig. 3, along with the comparison of original experimental data. It can be seen that the segregation model agrees with the experimental data very well, except for the case of u_gas = 7.5 m/s. The reason for this could be due to high gas velocity and high G_s that causes a fierce friction, leading to a high pressure-drop in the cyclone and valves in the experimental system. To maintain the pressure balance of the circulating loop, more relatively coarse solids are accumulated in the return leg, resulting in a smaller average diameter of particles in the riser.

There have been no reports on the solid feeding and voidage distribution along the riser in the experimental data of Moortel et al. [7]; thus, the derived segregation model and the voidage calculated by Kunni [8] and Rhodes [9] were used to calculate the size distribution along the riser. By comparing the modeling results with the experimental data, the reliability of the derived model can be validated.

In the model, the voidage along the riser is described as an exponential function [8]:

(12){ϵ}_{\mathrm{h}}={ϵ}_{\infty }+({ϵ}_{\mathrm{0}}-{ϵ}_{\infty })\exp (-{\alpha }_j(h-H_{\mathrm{b}\mathrm{e}\mathrm{d}})).

The voidage in dense bed, {ϵ}_{\mathrm{0}}, and the voidage over TDH, {ϵ}_{\infty }, were calculated using the Rhodes model. The exponential decay coefficient, a_j, which is a function of particle size, can be expressed as

(13)a_j={\displaystyle \frac{a{u}_{\mathrm{t},j}}{u_{\mathrm{g}\mathrm{a}\mathrm{s}}}}.

In the present calculation, the decay constant a_j was chosen as 2.0. In the simulation of a real CFB boiler, however, it is suggested that the decay constant be optimized through the field test data.

Figure 4 depicts the modeling results under the experimental conditions of Moortel’s experiments [7]. The modeling results are in good agreement with the experimental data, indicating that the segregation model can work for fluidization beds with relatively small gas velocities.

Model validation in industrial boilers

To validate the segregation model, the mass balance of one 220 t/h CFB boiler was calculated. The details of the mass balance model have been reported previously [10]. Table 3 shows the operating conditions and calculated segregation parameters of the CFB boiler. The decay constant, α, was optimized through the field test data. The calculated and measured ash size distributions in the 220 t/h CFB boiler validated the reasonableness of the segregation model (Fig. 5).

The segregation parameters are functions of the operating conditions and should be optimized by comparing the calculated data with the field measured ones.

Conclusions

A solid segregation model has been developed. In general, the calculation results of the segregation model agree well with the experimental data, indicating that the segregation model is reasonable.

After validating with the experimental data, the empirical formulae for x₀ and k₁ have been derived as

{\xi }_{\mathrm{0}}=\mathrm{1.0}+{\displaystyle \frac{a}{u_{\mathrm{g}\mathrm{a}\mathrm{s}}}}·{\displaystyle \frac{W_{\mathrm{u}\mathrm{p}}(i)-G_{\mathrm{s}}A}{G_{\mathrm{s}}A}},

k_{\mathrm{1}}={\displaystyle \frac{b}{u_{\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{m}}}}·u_{\mathrm{g}\mathrm{a}\mathrm{s}}^{\mathrm{2}}.

The parameters a and b are influenced by the operating conditions and should be adjusted with the field test data.

References

[1] Bai D, Nakagawa N, Shibuya E, Kinoshita H, Kato K. Axial distribution of solid holdups in binary solids circulating fluidized beds. Journal of Chemical Engineering of Japan, 1994, 27(3): 271-275

[2] Bodelin P, Delabarre A. Behaviour of single solids and their binary mixtures in a circulating fluidized bed. In: Large J F, Claude L, eds. Fluidization VIII. New York: Engineering Foundation, 1996, 270-279

[3] Cammarota A, Chirone R, Marzocchella A, Salatino, P. Relevance of attrition to bed solids inventory and particle size distribution in circulating fluidized bed coal combustors. In: Grace J R, Zhu J-X, de Lasa H I, eds. Proceeding of 7th International Conference on CFB, Ottawa: Canada Society of Chemical Engineering, 2002, 1661

[4] Nakagawa N, Bai D, Shibuya E, Kinoshita H, Takarada T, Kato K. Segregation of particles in binary solids circulating fluidized beds. Journal of Chemical Engineering of Japan, 1994, 27(2): 194-198

[5] Jiang P, Bi H, Liang S, Fan L. Hydrodynamic behavior of circulating fluidized bed with polymeric particles. AIChE Journal, 1994, 40(2): 193-206

[6] Hirschberg B, Werther J. Factors affecting solids segregation in circulating fluidized bed riser. AIChE Journal, 1998, 44(1): 25-34

[7] Van den Moortel T, Azario E, Santini R, Tadrist L. Experimental analysis of the gas-particle flow in a circulating fluidized bed using a phase doppler particle analyzer. Chemical Engineering Science, 1998, 53(10): 1883-1899

[8] Kunni D, Levenspiel O. Fluidization Engineering. 2nd ed. Boston: Buterworth-Heinemann, 1991, 223-225

[9] Rhodes M J, Geldart D. Model for the circulating fluidized bed. Powder Technology, 1987, 53(3): 155-162

[10] Yang H, Xiao X, Wang X, Lu J. Model research on material balance in a circulating fluidized bed boiler. In: Xu X C, Zhao C S, eds. Proceedings of the 5th International Symposium on Coal Combustion, Nanjing, China, Southeast University Press, 2003, 251-255

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