Gas mixing in a multi-stage conversion fluidized bed (MFB) with secondary air injection. Part I: an experimental study

Abstract

This paper investigated the distribution of secondary air after injection into a multi-stage conversion fluidized bed (MFB) cold model. Carbon dioxide (CO₂) was used as the tracer and its concentration was tested. The effects of the velocity of the primary air and secondary air, the particle circulating rate, and the diameter, number and included angle with the central line of the riser of injectors on the distribution of CO₂ were studied. Single- and multi-injector systems were applied, in which different designs of the secondary-air injectors were used. The radial gas dispersion coefficient was calculated by the dispersed plug flow model (DPFM). The concentration profile of the tracer and calculated radial gas dispersion coefficients indicated that lower velocity of primary air, higher velocity of secondary air and particle circulating rate, bigger size of injectors and smaller included angles of injectors helped the gas mixing of the secondary air in the MFB. The tangential injection of secondary air would induce a gathering of gasification agents in the region near the wall, which was undesirable for the operation of the MFB gasifier. The variation of the penetration depth of the secondary air indicated that the penetration depth under multi-injector system was smaller than that under single-injector system when other operational parameters were uniform. Thus, according to numbers of injectors, taking the included angles between injectors and the central line of the riser into consideration, the penetration depth of the secondary air was correlated with operational parameters.

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1. Introduction

For wide coal adaptability, effectiveness in the control of pollutant emission and lower operational cost, the circulating-fluidized-bed (CFB) gasifier has been widely applied in the industry of coal gasification.^1–3 However, several drawbacks such as low conversion rate of the carbon, low capacity per unit and so on still exist.⁴ One of the main reasons for the low conversion rate of coal particles lies in the fact that fine particles entrained out of the gasifier include too much carbon which has not been reacted.⁵ Thus, as one particular kind of CFB coal gasifier, a novel concept which was called a multi-stage conversion fluidized bed (MFB) was proposed to optimize the process of coal gasification.⁶ The main operational characteristics and advantages over conventional fluidized-bed gasifiers have been discussed in previous work.⁶ The MFB couples an enlarged-diameter ash agglomerated fluidized bed (AFB) with a reduced-diameter riser, and its essential concept is shown in Fig. 1. The basic hydrodynamic characteristics of the MFB have been investigated in detail in a cold model in previous work,⁶ which focused mainly on solid hydrodynamics. Unfortunately, the secondary air was not introduced in that work. Nevertheless, one of the main characteristics of the design of the MFB is that the gasification agents would be introduced into the bed by multiple stages.

Fig. 1 Schematic diagram of coal gasification process in the MFB.

Introducing secondary air into the upper reduced-diameter riser, which may be oxygen, steam or a mixture of both, is thought to be beneficial to the process of coal gasification from several aspects. Firstly, the injected gas could strengthen the fluctuation of the local fluid field, which always means the mixing of the gas and solid would be better.⁷ Secondly, the up-flow production gas including hydrogen, carbon monoxide and light hydrocarbons could react with the secondary air. The heat released by these reactions could increase the temperature in the riser, and this may promote the cracking of tar.⁸ More significantly, the increased temperature and existing secondary air could further consume the fine coal particles which are entrained out of the AFB by the reactions of pyrolysis and gasification, which would result in increasing the conversion rate of the raw material and thus the capacity.^9,10 Based on the analysis above, the distribution of secondary air after injection into the MFB needs to be investigated carefully, since it could affect the local flow field and the intensity of reactions in different areas in the riser.

The effects of secondary air on the distribution of solid holdup along the axial direction, particle velocity profiles and gas dispersion have been investigated by various researchers.^11–16 They mainly aimed at optimizing the combustion process in the CFB boiler. However, research on the operation and hydrodynamics of secondary air in the gasifier is relatively rare, compared with that in the boiler. The chemical reactions in the gasifier happen in the atmosphere of deficient oxygen, while the scenario in the boiler is reversed, based on the different aims of these two kinds of reactors. For the boiler, an oxygen-rich atmosphere is essential to combust coal particles as much as possible, and thus the amount of secondary air injected into the boiler is always in excess. While in a coal gasifier, the amount of injected secondary air is remarkably smaller than that in a boiler, since a reducing atmosphere is needed to produce more syngas and/or methane.

From previous literature,^11–21 it could be found that the diameter of the injector, the design of the secondary air injection devices, the ratio of secondary air to primary air and the height of the injecting points are all key parameters which affect the hydrodynamic characteristics of the secondary air in the CFB. Different designs of secondary air injecting devices used by researchers are shown in Fig. 2. It needs to be noticed that these types of injectors, no matter radial, tangential, mixed or circumferential, are all in one kind of plane that is perpendicular to the axial central line of the riser, which means that all these secondary-air injectors are normal to the central line of the riser. Nevertheless, injectors which have a downward axial included angle with the central line of the riser have been applied much less. For the operation of the MFB, such type of injection of secondary air might be beneficial to increase the conversion rate of coal particles, for it would increase the residence time and thus the reaction time of the secondary air.

Fig. 2 Types of secondary-air injectors used in previous experimental researches. T, tangential injection; R, radial injection; M, mixed injection (T + R); C, circumferential injection.

As one kind of CFB reactor, gas mixing in the riser plays a significant role in the contacting of coal particles and gas phase.^22–24 From the literature available,^25–34 two kinds of dispersion model to characterize gas mixing in the CFB were applied, named as dispersed plug flow model (DPFM) and mean square displacement model (MSDM).

Another concern of the operation of the secondary air in the MFB is the penetration depth of the secondary air. Neither too large nor too small a penetration depth is desirable for the stable and safe operation of the gasifier. The wall opposite the secondary-air injector of the gasifier would be eroded seriously and thus the refractory would be damaged under large penetration depth. Insufficient rigidity of the secondary air, on the other hand, would induce the gathering of the fuel gas along the injecting wall, and result in slag adhering to the wall, which would damage the refractory and wall, reduce the capacity and lead to abnormal shut-down of the MFB. Despite the significance to the operation of the secondary air in the gasifier, research on the penetration depth of the secondary air in the CFB gasifier is still insufficient. Table 1 shows the correlations to calculate the penetration depth of the secondary air and experimental descriptions by several researchers. It needs to be noted that their correlations were based on single-injector system, and their injectors were all in the plane normal to the central line of the riser.

Table 1 Experimental research on the penetration depth of the secondary air injected into a circulating fluidized bed

Researcher	Size of the riser (m)	Bed material	Correlations	Tracer
Savolainen^35	0.07 × 0.5 × 0.5	—		CO2
		151 μm
Ljungdahl^36	0.3 × 0.4 × 8.0	3300 kg m^−3; 240 μm		CO
Chen^37	0.65 × 0.68 × 3.5	620 kg m^−3; <83 μm		Heat air
Yang^38	0.3 × 0.3 × 4.0	2400 kg m^−3; 240 μm		Heat air
Wang^39	0.25 × 0.25 × 6.07	2550 kg m^−3; 274 μm		CO2

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This paper investigated the distribution of the secondary air after injection into the MFB cold model. In addition to the conventional secondary-air injectors, injectors which had axial downward included angles with the central line of the riser were applied too. The DPFM was used to characterize radial gas mixing in the riser in single-injector system. The penetration depths of secondary air were studied under single- and multi-injector systems, and according to numbers of injectors, correlations taking the included angle between injectors and the axial central line of the riser into consideration were deduced.

2. Experiment and radial gas dispersion model

2.1 Experimental apparatus

The experimental apparatus is similar to what has been illustrated in a previous study,⁶ except the secondary-air injecting devices. A schematic diagram of the experimental system is shown in Fig. 3. The MFB and standpipe were both made of clear Plexiglas. The MFB was comprised of three parts: a jetting fluidized bed (JFB) at the bottom with an inner diameter (i.d.) of 0.3 m and height between the gas distributor and reducing pipe of 1.5 m, a reducing pipe that connects the JFB and riser and a riser with i.d. of 0.15 m and height of 8 m. The riser was assembled by sections for ease of disassembling and replacing different sections according to designs of secondary air injectors. The standpipe has an inner diameter of 0.305 m and height of 5 m, and the total solid inventory is about 90 kg. The standpipe and the MFB are connected by a two-stage cyclone system. A bag filter is installed at the exit of the secondary cyclone to collect escaped particles. The L-valve, located at a height of 2.40 m above the gas distributor, is used as a loop seal to recycle particles, and the solid circulating rate is controlled by the air blown into the valve by a gas compressor.

Fig. 3 Schematic diagram of the experimental apparatus. (1) Gas compressor. (2) CO₂ cylinder. (3) Jetting fluidized bed. (4) Reducing pipe. (5) Secondary-air injecting ports. (6) Riser. (7) Bag filter. (8) Secondary cyclone. (9) Primary cyclone. (10) Revolve valve. (11) Storage. (12) Standpipe. (13) Non-mechanical valve. (14) Butterfly valve. (15) Roots-type blower.

The fluidization air, which was used as the primary air, was supplied by a Roots-type blower and fed into the MFB at the bottom. The secondary air was controlled by an independent system. Different designs of secondary-air injectors are illustrated in Fig. 4. For realizing designs of the secondary-air injection, four pipes with a height of 0.5 m each and the same diameter as the riser were prepared beforehand, and every pipe was to one of the designs. Injectors were fixed by supports and the angles were examined carefully and repeatedly to make sure that the directions of the secondary-air jets were desirable. When the experiments with one kind of design of secondary air injection were accomplished, the pipe would be replaced by another one. All injectors were arranged at a height of 2.65 m above the gas distributor. The designs of secondary-air injectors used in this paper could be classified into four kinds: radial, tangential, 30 degrees and 60 degrees downward axial included angle with the central line of the riser, as shown in Fig. 4. Every design consisted of four injectors, and the injecting points quartered the cross-section of the riser. The flow rate in every injector was controlled by an independent rotameter to make sure that the exit velocity of each nozzle was uniform.

Fig. 4 Designs of secondary-air injectors used in this work and the sampling line.

2.2 Experimental description and procedure

At the beginning of the experiment, a small amount of secondary air was injected into the riser to prevent particles entering the injectors. After the MFB had run for at least 20 minutes to obtain a steady solid circulating rate, the tracer was introduced and mixed with the air, and then the velocities of the secondary air in every injector were adjusted and examined to make sure that they were uniform. Particles (bed material) used in this work were silica gel, which would be fluidized in experiments. Their properties in detail are given in Table 2. The variations of operational parameters in experiments are shown in Table 3.

Table 2 Properties of the bed material used in this work

Properties	Values
Mean diameter (μm)	250
Bulk density (kg m^−3)	480
Particle density (kg m^−3)	1020
Terminal velocity (m s^−1)	0.79
Minimum fluidization velocity (m s^−1)	0.016

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Table 3 Values of the operational parameters in the experiments

Parameter	Values
Velocity of primary air ub (m s^−1)	3.0, 4.4, 5.0
Particle circulating rate Gs (kg m^−2 s^−1)	0, 20, 40, 60, 85
Number of injectors n	1, 2, 4
Diameter of injectors d0 (mm)	5, 8, 10
Designs of injectors	Radial, tangential, 30°, 60°
Velocity of secondary air uj (m s^−1)	11.64, 20, 30, 40

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For its low price, safety and negligible absorption to the particles, CO₂ was chosen as the tracer gas, which was premixed with air before being injected into the riser as the secondary air. A dimensionless concentration (C*) was defined to describe the CO₂ concentration:

where C₀, C₁, C are the volume concentrations of CO₂ in primary air, at the exit of the riser and at different locations in the riser, respectively.

The concentrations of CO₂ were tested at ten axial heights of 2.65 m, 2.90 m, 3.15 m, 3.65 m, 4.65 m, 5.15 m, 5.65 m, 6.65 m, 7.85 m and 9.05 m above the gas distributor (not in all experiments), which included bottom dense, transient and upper dilute region according to previous work.⁶ At any height, data were taken at 11 radial locations from r* = −0.95 to r* = 0.95. Here, a dimensionless radius (r*) was defined to denote the radial position along the sampling line:

where r is the radial distance between testing point and original point (the center point of the cross section of the riser at any given height), and R is the radius of the riser. The sampling line is shown in Fig. 4. The diameter of the sampling pipe was 6 mm. A KP-810-type online gas detector was used to test the volume concentration of CO₂. It has a measuring range and a resolution of 0–10% vol and 0.01% vol, respectively, with a response time of 20 s. The sampling time at any location lasted for at least 15 minutes. All data were collected during the testing and the average value was calculated to represent the real concentration of CO₂ at that location.

2.3 Radial gas dispersion model

According to the mass balance on a differential volume element of the riser, the DPFM could be expressed bywhere z is the axial distance from the injection points to the sampling line, positive in the upward direction, and r, C′, D_r, D_a, u_b are the radial distance between the sampling point and the center, the calculated concentration of CO₂ by the DPFM, the radial and axial gas dispersion coefficients, and the velocity of primary air, respectively. The boundary conditions are:

Z = −∞, c′ = 0 (5)

Z = ∞, c′ = c₀ = U_CO2/(U_pri + U_Sec) (6)

A previous study⁴⁰ has derived an analytical solution for eqn (3) with the boundary conditions given by eqn (4)–(6):

whereand J₀ is the zero-order Bessel function, and K_n is the n-th root of the first-order Bessel function, J₁(K_n) = 0. In eqn (7), D_r and D_a are both variables, which mean that the numbers of equations are not enough to obtain numerical solutions for eqn (7). In this case, treating D_a and D_r as adjustable parameters with certain time steps, a method of parameter estimation could be applied:where C and C₀ are concentrations of CO₂ tested at different locations and at the exit of the riser respectively. By eqn (9), D_r could be estimated.

The procedure of the process of estimating D_a and D_r is illustrated in Fig. 5. The process was implemented by means of a self-written program which was written in the Visual Basic language. During the process, firstly, the zero- and first-order Bessel functions were solved by a self-written program which was also written in the Visual Basic language, from which K_n, J₀ and J₀² could be worked out. Then, the initial and terminal values of D_a and D_r and suitable time step were set. Combined with R, u_b and c₀ which were all operational parameters, the analytical solution for eqn (3) could be used to calculate the term “c′”. In the process, each team of D_a and D_r could obtain an “S” in eqn (9). Thus, many “S” could be outputted during the process. The term “S” in eqn (9) indicates the deviation between the calculated c′ and the experimental measured c. Thus, the minimum value of “S” means the best agreement between the calculated c′ and measured c within the calculation range. Then, D_a and D_r corresponding to S_min could be considered as suitable dispersion coefficients. It needs to be noticed that the calculation range was not decided randomly, but based on literature^25–34 and the boundary conditions of eqn (3), which are written as eqn (4)–(6).

Fig. 5 The procedure of the process of estimating the D_a and D_r.

In addition, during the process of estimating D_a and D_r, data fitting was applied to select optimized D_a and D_r; thus, a comparison between the calculated and measured values of the concentration of CO₂ is needed. This work has been done and is discussed in the following Section 3.

3. Results and discussion

3.1 Single secondary-air injection

3.1.1 Without particle circulation. For a basic understanding of the rule of gas mixing in the MFB with secondary air operation, experiments with only one injector and without particle circulation were conducted firstly. Fig. 6(a) shows the distribution of the dimensionless concentration of CO₂ at different heights above the injection points. It could be found that the concentration profiles flattened with an increase of the distance from the injection port to the sampling line. The distribution of concentration of CO₂ became nearly uniform from a height of 5.65 m above the distributing plate and on.

Fig. 6 (a) The measured dimensionless concentration profile of CO₂ at different axial heights along the riser. (b) A comparison of measured concentration of CO₂ with that calculated by the DPFM.

Fig. 6(b) compares the concentration of CO₂ measured in experiments at five axial heights along the riser with that calculated by the DPFM at the same positions. From Fig. 6(b), the maximum deviation between the tested and calculated concentration of CO₂ could be found at the position where z = 3.65 m and r* = 0.6, where the tested and calculated concentrations of CO₂ were 0.92% and 0.77% respectively; thus the maximum deviation would be 16.3% . At other positions, however, the deviations between measured and calculated concentrations of CO₂ were all within ±5%, which meant that the DPFM could reasonably predict the concentration profile of CO₂ in the riser when no particle was circulated. From another aspect, the radial gas dispersion coefficients (D_r) estimated by the DPFM were credible.

3.1.2 With particle circulation. Fig. 7 shows the distribution of CO₂ at different axial heights when only the velocity of the primary air was changed. From Fig. 7(a), it could be found that as the velocity of the primary air (u_b) declined from 5.0 m s⁻¹ to 3.8 m s⁻¹, the position where the maximum value of C* emerged moved further away from the radial position of the secondary-air injector, which meant that the secondary air could penetrate further with an increase of the velocity of the primary air. On the other hand, it could be found also that when u_b increased, the maximum values of C* increased too, which meant that the fluctuation of C* strengthened as the velocity of the primary air increased. This might indicate that the radial dispersion of the secondary air was faster under lower velocity of primary air.

Fig. 7 Profiles of dimensionless concentration of CO₂ under different velocities of the primary air: (a) axial height, 2.90 m; (b) axial height, 4.65 m.

From Fig. 7(b), it could be found that when the axial height increased to 4.65 m, the dimensionless concentration profiles of CO₂ flattened compared with those at the height of 2.90 m, with no respect to the velocity of the primary air. While on the other hand, the distribution of C* was nearly uniform when the velocity of primary air was as low as 3.8 m s⁻¹. While when u_b increased up to 4.4 m s⁻¹ and 5.0 m s⁻¹, the uniformity of the concentration of CO₂ became worse.

Fig. 8 shows the radial gas dispersion coefficients (D_r) under different velocities of the primary air. It could be found that D_r decreased as the velocity of the primary air increased, which meant that the gas mixed more quickly under slower primary air. This was consistent with what has been found in experiments.

Fig. 8 The radial gas dispersion coefficients (D_r) under different velocities of the primary air.

Fig. 9 compares the concentration of CO₂ measured in experiments at different locations with that calculated by the DPFM. It could be found that the maximum deviation between them occurred at the position where z = 2.90 m and r* = 0.6, where measured and calculated concentrations of CO₂ were 0.88% and 0.62%, respectively. Thus, the maximum deviation between the tested and calculated concentration of CO₂ was 29.5% . At other locations, however, the deviations between them were within the range of ±10%, which meant that the DPFM could predict the concentration profile of CO₂ in the riser for cases with particle circulation. As a matter of fact, the deviations between the tested and calculated concentration of CO₂ for other operational conditions have been investigated and they were all in reasonable agreement. This meant that the DPFM could be used to estimate the radial gas dispersion coefficients (D_r) in the MFB.

Fig. 9 A comparison of tested concentration of CO₂ with that calculated by the DPFM.

Fig. 10 shows the distribution of CO₂ under different velocities of the secondary air (u_j). It could be found from Fig. 10(a) that as u_j increased from 11.64 m s⁻¹ to 40 m s⁻¹, the location where the maximum value of C* occurred moved further towards the wall opposite to the injecting port, which meant that the secondary air could arrive further along the riser with increasing u_j. While on the other hand, the fluctuations of C* weakened with increasing u_j, which meant that a higher velocity of the secondary air could promote the radial gas mixing in the riser. From Fig. 10(b), it could be found that the fluctuations of C* were not as significant as those in Fig. 10(a) under the different velocities of the secondary air.

Fig. 10 The dimensionless concentration profiles of CO₂ under different velocities of the secondary air: (a) axial height, 2.90 m; (b) axial height, 3.15 m.

Fig. 11 shows the radial gas dispersion coefficient estimated by the DPFM under different velocities of the secondary air. It could be found obviously that D_r increased with increasing u_j, which is consistent with the analysis above.

Fig. 11 The radial gas dispersion coefficients (D_r) under different velocities of the secondary air.

Fig. 12 shows the distribution of the secondary air at three axial heights under different particle circulating rates. It could be found from Fig. 12(a) that when the particle circulating rate declined from 85 kg (m² s)⁻¹ to 40 kg (m² s)⁻¹, the secondary air could penetrate the bed further, which might mean that the particles could suppress the penetration of the secondary air. Besides, as G_s increased, the fluctuation of C* became less remarkable, which indicated that particles could help the radial gas mixing in the riser. It also could be found from Fig. 12(a)–(c) that as the axial heights increased, the profiles of C* flattened. However, it could be found obviously that the secondary air nearly became uniform at a height of 3.65 m when G_s was 85 kg (m² s)⁻¹, while when G_s was 60 kg (m² s)⁻¹, the height needed to be 5.65 m to get a uniform distribution of CO₂. This meant that the gas mixed faster in the axial direction under higher particle circulating rate.

Fig. 12 The dimensionless concentration profiles of CO₂ under different particle circulating rates: (a) axial height, 2.90 m; (b) axial height, 3.65 m; (c) axial height, 5.65 m.

Fig. 13 shows the radial gas dispersion coefficients when only the particle circulating rate was changed. It could be found that D_r increased remarkably with an increase of the particle circulating rate.

Fig. 13 The radial gas dispersion coefficients (D_r) under different particle circulating rates.

Fig. 14 shows the concentration profile of CO₂ at three heights under different diameters of the injector (d₀) when other parameters were set to be uniform. It could be seen that with an increase of the size of the injector, the fluctuations of C* declined, since the peak value of C* dropped obviously, regardless of the heights (2.90 m and 3.65 m). Besides, when inspecting C* at the height of 2.65 m, which was the same height at which the secondary air was injected, the peak value became higher when the diameter of the injector increased, especially when the diameter of the injector was 10 mm. In addition, from Fig. 14(c), it could be found that when the size of the injector increased, the radial gas distribution became more uniform, which was similar to what has been found when the solid flux increased. The radial gas dispersion coefficients which are shown in Fig. 15 also indicated that D_r increased when the size of the injector was increased.

Fig. 14 The dimensionless concentration profiles of CO₂ under different diameters of the secondary-air injector: (a) axial height, 2.65 m; (b) axial height, 2.90 m; (c) axial height, 3.65 m.

Fig. 15 The radial gas dispersion coefficients (D_r) under different diameters of the secondary-air injector.

Fig. 16 illustrates the distribution of the secondary air after injection into the riser under different axial included angles between the injector and the central line of the riser (α). It could be found from Fig. 16(a) that as the angles increased from 30° to 90°, the peak of C* moved towards the wall opposite to where the secondary air was injected, which meant that the secondary air could penetrate the bed further under larger included angles between the injector and the central line of the riser. Besides, from Fig. 16(a), it also could be found that the fluctuation of C* was more narrow under smaller angles, which indicated that the smaller angles between the injector and the central line of the riser were beneficial to the radial gas mixing when the secondary air was introduced. From Fig. 16(a)–(c), it could be found that as the axial heights increased, the profiles of C* became more flat, regardless of the angles. However, differences could be found on the other hand. When the axial heights increased to 3.65 m, it could be found that the concentrations of the secondary air were nearly uniform under 30° injection, while for the other two cases (60° and 90° injection), the scenarios were different. This meant that smaller angles could help axial gas mixing in the riser.

Fig. 16 The dimensionless concentration profiles of CO₂ under different axial included angles between the injector and the central line of the riser: (a) axial height, 2.90 m; (b) axial height, 3.15 m; (c) axial height, 3.65 m.

Fig. 17 shows the variation of D_r under different axial included angles between the injector and the central line of the riser. It could be found that as the angles increased, D_r declined obviously, which meant that smaller angles of injection of the secondary air help the radial gas mixing in the riser. This is consistent with the analysis above.

Fig. 17 The radial gas dispersion coefficients (D_r) under different axial included angles between the injector and the central line of the riser.

3.2 Multiple secondary-air injection

3.2.1 Two streams of radial injection of the secondary air. Fig. 18 shows the dimensionless concentration profiles of CO₂ when two streams of secondary air were introduced into the riser with opposite radial directions and with different velocities, which were 11.64 m s⁻¹, 30 m s⁻¹ and 40 m s⁻¹ respectively. From Fig. 18(a)–(c), it could be found that no matter what velocity of secondary air was applied, the profile of C* flattened with axial heights, which was similar to what was found under single-injector system in Section 3.1. In Fig. 18(a), two obvious peaks of C* axially relatively close to the injectors could be found at heights from 2.90 m to nearly 3.65 m when the velocity of the secondary air was selected as 11.64 m s⁻¹ for both injectors, while the concentration of CO₂ in the center region was remarkably lower at these heights compared with that in the area near the wall. It meant that the secondary air could hardly arrive at the center region at lower heights under such velocity. When the velocity increased to 30 m s⁻¹, such peaks of C* near the wall could only be found at heights of 2.90 m and 3.15 m, and they vanished completely when the velocity was up to 40 m s⁻¹, which can be seen in Fig. 18(b) and (c). For ease of comparison of the trends under different velocities, data at a height of 2.90 m were extracted and plotted in one diagram, which is shown in Fig. 18(d). It could be found from Fig. 18(d) that when the velocity of secondary air increased from 11.64 m s⁻¹ to 30 m s⁻¹, not only did the maximum value of C* decline, but also the position where the peaks appeared moved from the region relatively near the wall to the center. This meant that, on the one hand, increasing the velocity of the secondary air could help the radial gas mixing in the riser, and, on the other hand, the secondary air could penetrate the bed more markedly when its velocity increased. While when the velocity increased up to 40 m s⁻¹, the tendency of the dimensionless concentration profiles of CO₂ totally changed, in which the peaks near the wall vanished and only one peak appeared in the center of the riser. For the remarkable variation in terms of the tendency, these three velocities were selected for the following four-injector experiments.

Fig. 18 The effects of the velocity of the secondary air on the distribution of the dimensionless concentration profiles of CO₂: (a) u_j = 11.64 m s⁻¹; (b) u_j = 30 m s⁻¹; (c) u_j = 40 m s⁻¹; (d) z = 2.90 m under different velocities of the secondary air.

The type of concentration profiles illustrated in Fig. 18(d) (especially for u_j = 11.64 m s⁻¹ and 30 m s⁻¹) could be called a “hump distribution”, with respect to the shape of the profiles. From the perspective of the hot model experiments of coal gasification (especially pilot-scale tests), such a type of distribution of the secondary air could affect the performances of the MFB from several aspects. On the one hand, the local particle concentration in the region near the wall was higher than that in the center area,⁶ which meant that the probability of consumption of coal and char in the region near the wall by the secondary air could be increased with such a type of “hump distribution” of the secondary air, and the total conversion rate of the coal would be improved. On the other hand, however, the local particle and gas velocity in the region near the wall was always remarkably lower than that in the center,⁶ which meant that the heat released by the reactions between secondary air and coal, char and production gas could not be carried away quickly. This would generate a region in which the temperature was significantly higher; thus the risk of slagging needed to be considered seriously in such a case.

3.2.2 Four injectors of different designs. Four types of injector designs under a four-secondary-air-injector system have been applied in this paper, which were radial, tangential, 30°, and 60° axial included angle with the central line of the riser respectively. As a matter of fact, the design of radial injection could be seen as 90° secondary-air injection, compared with the design of 30° and 60° injection. Three different velocities, which were 11.64 m s⁻¹, 30 m s⁻¹ and 40 m s⁻¹ respectively, have been selected as the velocity of the secondary air, and the solid circulating rates were set as 20 kg (m² s)⁻¹ and 60 kg (m² s)⁻¹ respectively.

Fig. 19 shows the dimensionless concentration profiles at three axial heights of the riser under the same operational conditions but with different design of injectors. It could be found from Fig. 19(a)–(c) that the fluctuations of C* became less and less remarkable as the axial heights increased from 2.90 m to 6.65 m, with no respect to the designs of injectors, which was similar to what has been found for the single secondary-air injection system. When the tangential injectors were applied, it could be found that at all three heights, the concentration of CO₂ in the region near the wall was remarkably higher than that in the central area, and as a matter of fact, the concentration of CO₂ in the center was so low that it could be thought that the secondary air could hardly arrive in this area, especially at lower heights of the riser. Such a concentration profile is not desirable for the process of coal gasification in the MFB, because the gathering of secondary air (gasification agents) at the wall always results in slagging and thus unstable operation. The tendencies under the other three designs of injectors at three heights, however, were opposite to that under tangential injection, which meant that the concentrations of CO₂ were higher in the center compared with that near the wall. On the other hand, it could be found that the range of fluctuation of concentration profile of CO₂ was relatively narrow when the included angle was 30° at all three heights, which meant that the radial gas mixing was better in such a case. When the height was 6.65 m (which is shown in Fig. 19(c)), the distribution of CO₂ was nearly uniform under 30° injection, compared with the other three designs. Thus, the axial gas mixing was better when the 30° injectors were applied too.

Fig. 19 The dimensionless concentration profiles of CO₂ at three different heights under different designs of injectors: (a) axial height, 2.90 m; (b) axial height 3.65 m; (c) axial height, 6.65 m.

Fig. 20 shows the dimensionless concentration profile of CO₂ at a height of 2.90 m under different velocities of secondary air and designs of injectors. From Fig. 20(a), it could be found that when the secondary-air velocity was 11.64 m s⁻¹, the concentration of CO₂ in the central region was significantly lower than that in the region at the wall, which was opposite to the tendencies under 30 m s⁻¹ and 40 m s⁻¹. It could be found from Fig. 20(b) and (c) that when the velocities of the secondary air were 30 m s⁻¹ and 40 m s⁻¹, the profiles of C* were obviously higher in the center than at the wall. Besides, when the included angle between injectors and the central line of the riser increased from 30° to 90° with a secondary-air velocity of 11.64 m s⁻¹, two peaks of C* emerged gradually in the region near the wall and the position where the peaks emerged moved to the center as the angle increased. It could be seen from Fig. 20(a) that when the included angle was 30°, the concentration of CO₂ declined monotonically from the wall to the center region, while when the included angle was 60°, two peaks emerged at radial positions of −0.8 and 0.8, compared with −0.6 and 0.6 when the angle was 90°. Anyway, the overall tendency of the distribution of CO₂ with a secondary-air velocity of 11.64 m s⁻¹ meant that the secondary air could not penetrate into the central region of the riser under such a velocity. When the velocity of secondary air increased to 30 m s⁻¹ and 40 m s⁻¹, it could be found that either the peak values or the fluctuations of the dimensionless concentration of CO₂ increased with an increase of the included angles between injectors and the central line, which meant that the gas mixed more quickly under smaller included angle injectors. In addition, it could be found from Fig. 20(c) that there were platforms of C* in the central area under 60° and 90° included angle injectors with a secondary-air velocity of 40 m s⁻¹. This might be attributed to the fact that when the velocity was up to 40 m s⁻¹, the secondary air from four injectors all arrived at the central area, which would create a relatively wide region with higher and relatively uniform concentration of the tracer. As for the tangential injection of the secondary air, it could be found from Fig. 20(d) that the concentration of CO₂ was remarkably higher in the region near the wall than in the center, irrespective of the increase of the velocity of secondary air.

Fig. 20 The dimensionless concentration profiles of CO₂ under different velocities of the secondary air and designs of injectors: (a) u_j = 11.64 m s⁻¹; (b) u_j = 30 m s⁻¹; (c) u_j = 40 m s⁻¹; (d) tangential injection.

The effect of solid circulating rate on the radial gas mixing under different designs of injectors is illustrated in Fig. 21. It could be found that when the tangential injectors were applied, the concentration profile still had a different tendency compared with the other three designs, and such a tendency was not desirable for the stable and safe operation of the MFB, as discussed before. As for the other three designs, it could be found that with the an increase of the solid circulating rate from 20 kg (m² s)⁻¹ to 60 kg (m² s)⁻¹, the concentration of CO₂ in the region near the wall increased, while it declined in the center, which meant that higher particle flux helped the radial gas mixing, although such a tendency was not so obvious when the 60° and 90° injectors were applied. From the perspective of the peak value, it could be seen that as the included angle increased from 30° to 90°, the peak value increased gradually, especially when comparing the data under both 30° and 90° injection with a solid flux of 60 kg (m² s)⁻¹. This also meant that a smaller included angle between injectors and the axis of the riser led to better radial gas mixing.

Fig. 21 The effect of the solid circulating rate on the radial gas mixing under different designs of injectors: (a) 30° injection; (b) 60° injection; (c) 90° injection; (d) tangential injection.

3.3 Penetration depth

3.3.1 Experimental results. In this work, the penetration depth of the secondary air (L) was defined as the radial distance between the position where the first maximum dimensionless concentration of CO₂ emerged and the wall where the secondary air was injected at a height of 2.90 m above the distributing plate (0.25 m above the injection ports). The definition of the penetration depths of the secondary air under single- and multi-injector systems is illustrated in Fig. 22. Such definition of the penetration depth was based on the concern of the position where the secondary air (gasification agents) would gather in the MFB gasifier, since it could affect the intensity of chemical reactions in different areas and thus the stable operation of the MFB. From Fig. 22(a), it could be found that there was only one peak of C* that emerged under single-injector system, while as for the multi-injector system (Fig. 22(b)), the number of the peaks of C* depended on the experimental conditions.

Fig. 22 The definition of the penetration depth of the secondary air under different experimental conditions: (a) single-injector system; (b) multi-injector system.

Fig. 23 shows the effects of various experimental conditions on the penetration depth of the secondary air, including the velocity of the primary air and secondary air, the particle circulating rate, the diameter of injectors and included angles between injectors and the central line of the riser. It could be found from Fig. 23 that the penetration depth declined when the solid circulating rate and the velocity of the primary air increased, while it increased with an increase of the velocity of the secondary air, the diameter of the injector and the included angle between injectors and the central line of the riser. The penetration depth of the secondary air could be expressed by the ratio of the momentum between the secondary air and primary air,⁴¹ which means the larger such a ratio is, the longer the secondary air could penetrate. According to such analysis, the results for the tendencies of the penetration depths of the secondary air under different operational parameters illustrated in Fig. 23 were reasonable.

Fig. 23 The effects of different experimental conditions on the penetration depth of the secondary air: (a) velocity of the primary air; (b) velocity of the secondary air and the diameter of injectors; (c) particle circulating rate; (d) included angles between injectors and the central line of the riser.

The penetration depths of the secondary air under single-injector system and two-opposite-radial-injectors system with the other operational conditions being the same are illustrated in Fig. 24. It needs to be noticed that the penetration depth under two-radial-injectors system in Fig. 24 refers to the penetration depth of each injector. It could be found that the penetration depths were less when two opposite radial injectors were used than when only one radial injector was applied. This might be attributed to the change of the concentration of particles and the local velocity of the gas in the up-flow in the central region when another stream of secondary air was introduced from the opposite wall, and this change may suppress the penetration of the original secondary air. This remarkable difference also indicated that the correlations derived for the single-injector system could not be applied to the multi-injector system directly. Besides, the penetration depths under four-radial-injector system have been investigated too; however, no significant differences have been found compared with the two-radial-injector system. This might be due to the fact that the effects of the secondary air from the normal directions were too inconspicuous to be detected.

Fig. 24 The comparison of the penetration depths of the secondary air under different number of injectors.

The effect of the included angle between injectors and the central line of the riser on the penetration depth of the secondary air under four-injector system is shown in Fig. 25. It could be found that the penetration depth increased with an increase of the included angle. This could be explained by the collision of two streams of momentum. Assuming the streams of secondary air under different injection angles were collided by the up-flow mixture of gas and solid with the same momentum, the horizontal velocity component of the secondary air would decide the distance to which the secondary air could penetrate to a large extent. Obviously, the horizontal velocity component was smaller under small included angle when the total velocity of the secondary air was the same. Thus, the penetration depth under the included angle of 30° was the smallest.

Fig. 25 The effect of included angles between injectors and the central line of the riser on the penetration depth of the secondary air under four-injector system.

In addition, from the concentration profile under tangential injectors, it could be found that the concentration of CO₂ was always the largest at the location close to the wall, and thus the penetration depth under such operational conditions could not be defined.

3.3.2 Theoretical approach. From the analysis above, it could be found that the velocity of primary and secondary air (u_b and u_j), the diameter of injectors (d₀), the solid circulating rate (G_s), numbers of the injectors (n) and the injecting angle (α) were all parameters affecting the penetration depth of the secondary air, and, on the other hand, they are also the operational conditions of the MFB. Thus, a correlation to calculate the penetration depth of the secondary air (L) could be obtained based on all these parameters:

L = f(u_b, u_j, d₀, G_s, n, α) (10)

Since the penetration depth could be written as a function of the ratio between the momentums of up-flow suspension of gas and solids and secondary air, eqn (10) could be expressed as:

where ξ and m are constants, and ε_s is the concentration of solids in the up-flow primary stream, which could be found in previous work,⁶ since the quantity of the secondary air was so small that the effects of it on the flow field in the whole bed could be neglected. Then, putting the penetration depths measured in experiments and corresponding operational parameters into eqn (11), correlations according to the number of injectors could be obtained as:

It needs to be noticed that the penetration depths calculated using the correlations above were based on the axial height of 2.90 m above the distributing plate, since in a few cases, when the axial height increased to 3.15 m, the distribution of CO₂ was nearly uniform such that no obvious peak of C* could be found to define the penetration depth.

Fig. 26 analyzes the accuracy of the correlations above, and compares the calculated penetration depths of the secondary air by these correlations and those of others^36,38 with the tested ones in experiments. It could be found that the deviations between the calculated penetration depths of the secondary air by the correlations and the tested ones were almost within the range of ±30%, which meant that the deduced correlations could be applied to calculate relatively precisely the penetration depth of the secondary air injected into the MFB. While as for the correlations derived by other researchers,^36,38 the deviations between the computational and experimental results all exceeded the range of ±30%, which meant that their correlations were not suitable to calculate the penetration depth of the secondary air in the MFB. This may be attributed to the differences in terms of the experimental apparatus, the bed material used in experiments and the tracer technology between this work and that of others.

Fig. 26 The comparison of the tested penetration depths of the secondary air (L) with the calculated ones by the correlations deduced in this work and previous literature.

Compared with the correlations to calculate the penetration depth of the secondary air proposed in previous works,^36,38 the correlations deduced in this work took into consideration the number of injectors and the axial included angle between injectors and the central line of the riser.

4. Conclusions

The aim of this work was to investigate the distribution of secondary air after injecting into the riser of the MFB cold model. In addition to the conventional injectors, different designs in which the injectors had downward axial included angles with the central line of the riser were applied too. The radial gas dispersion coefficients were calculated under single-injector system. The penetration depth of the secondary air was correlated with operational parameters. The main conclusions are summarized below:

(1) The dimensionless concentration profiles of CO₂ flattened with an increase of the axial distance between the sampling line and injectors, regardless of numbers and designs of injectors (including inclined injection of the secondary air).

(2) A smaller axial included angle between the injectors and the central line of the riser always meant better gas mixing, while as for the tangential injection, the tracer always gathered in the region near the wall, which was undesirable for the stable and safe operation of the MFB.

(3) The penetration depth of secondary air declined when the solid circulating rate and the velocity of the primary air increased, while it increased with an increase of the velocity of the secondary air and the diameter of the injector. Besides, the penetration depth increased with an increase of the included angle between injectors and the central line, which could be explained by the fact that the horizontal component of the velocity of the secondary air declined as the included angle decreased.

(4) The penetration depth under multi-injector system was smaller than that under single-injector system when other operational parameters were uniform, which might be attributed to the increase of the particle concentration and local velocity of the mixture of gas and solid in the central area when another stream of secondary air was introduced from the opposite wall.

(5) According to numbers of injectors, the penetration depths of the secondary air were correlated with the operational parameters taking the included angle between injectors and the central line of the riser into consideration. The range of deviations between the calculated penetration depths of the secondary air and tested results was within ±30%.

Abbreviations

C*	Dimensionless residual concentration
C0	Volume concentration of CO2 in primary air, %
C1	Volume concentration of CO2 at the exit of the riser, %
C	Volume concentration of CO2 tested at different locations, %
C′	Calculated concentration of the tracer, %
d0	Diameter of injectors, mm
Da	Axial gas dispersion coefficient, cm^2 s^−1
Dr	Radial gas dispersion coefficient, cm^2 s^−1
Gs	Particle circulating rate, kg (m^2 s)^−1
J0	Zero-order Bessel function
J1	First-order Bessel function
Kn	n-th root of the first-order Bessel function
r*	Dimensionless radius
r	Radial distance between the sampling point and the center, mm
R	Radius of the riser, mm
ub	Velocity of the primary air, m s^−1
uj	Velocity of the secondary air, m s^−1
up	Velocity of particles, m s^−1
up−a	Velocity of particles in the annular region, m s^−1
up−c	Velocity of particles in the core region, m s^−1
z	Distance from injectors to the sampling line, m
ρj	Density of secondary air, kg m^−3
ρg	Density of primary air, kg m^−3
ρs	Apparent density of particles, kg m^−3
εs	Cross-sectional average solids holdup, %
εs−j	Average solids holdup at the cross-section of jet and up-flow mixture, %
εs−a	Average solids holdup in the annular region, %
εs−c	Average solids holdup in the core region, %
α	Included angles between injectors and the central line of the riser, °

Acknowledgements

This work was financially supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (XDA07050100), the Natural Science Fund of Shanxi Province (2014021014-7) and the National Natural Science Foundation of China (no. 21506242).

Notes and references

1. C. S. Zhao, L. S. Lin, K. L. Pang, W. G. Xiang and X. P. Chen, Fuel Process. Technol., 2010, 91, 805–809.
2. X. M. Meng, W. de Jong, N. J. Fu and A. H. M. Verkooijen, Biomass Bioenergy, 2011, 35, 2910–2924.
3. C. L. Lin, T. H. Peng and W. J. Wang, Powder Technol., 2011, 207, 290–295.
4. L. Q. Qu, Coal Convers., 2007, 30, 81–85.
5. P. Mondal, G. S. Dang and M. O. Garg, Fuel Process. Technol., 2011, 92, 1395–1410.
6. Z. Y. Wang, Z. H. Cheng, Y. T. Fang, J. J. Huang, Z. H. Hao and Y. Wang, Fuel Process. Technol., 2013, 115, 99–109.
7. M. Koksal and F. Hamdullahpur, Chem. Eng. Res. Des., 2004, 82, 979–992.
8. C. Higman and M. Van der Burgt, Gasification, Gulf Professional Publishing, 2003, pp. 526–529.
9. Y. T. Fang, Z. Tang, M. Li, J. M. Zhang and Y. Wang, J. Fuel Chem. Technol., 1996, 24, 143–149.
10. J. H. Wu, Y. T. Fang, H. Peng and Y. Wang, Fuel Process. Technol., 2004, 86, 261–266.
11. L. E. Ersoy, M. R. Golriz, M. Koksal and F. Hamdullahpur, Powder Technol., 2004, 145, 25–33.
12. Y. Kang, P. S. Song, S. J. Yun, Y. Y. Jeong and S. D. Kim, Chem. Eng. Commun., 2000, 177, 31–47.
13. J. H. Kim and K. Shakourzadeh, Powder Technol., 2000, 3, 179–185.
14. L. E. Ersoy, M. Koksal and F. Hamdullahpur, Proceedings of 14^th Conference on FBC, 1997, vol. 2, p. 1247.
15. A. Marzocchella and U. Arena, Powder Technol., 1996, 87, 185–191.
16. Y. J. Cho, W. Namkung, S. D. Kim and S. Park, J. Chem. Eng. Jpn., 1994, 27, 158–164.
17. X. S. Wang and B. M. Gibbs, Circulating Fluidized Bed Technology III, 1991, pp. 225–230.
18. W. Namkung and S. D. Kim, Powder Technol., 2000, 113, 23–29.
19. L. E. Ersoy, M. Koksal and F. Hamdullahpur, Circulating Fluidized Bed Technology VI, 1999, pp. 417–422.
20. C. Brereton and J. R. Grace, Preprints of CFB IV, 1997, pp. 169–174.
21. G. Sun, H. Liu and M. Shi, Circulating Fluidized Bed Technology VII, 2002, pp. 373–379.
22. E. R. Gilliland and E. A. Mason, Ind. Eng. Chem., 1949, 41, 1191–1196.
23. E. R. Gilliland and E. A. Mason, Ind. Eng. Chem., 1952, 44, 218–224.
24. Y. C. Lin and C. S. Chyang, Powder Technol., 2003, 131, 48–55.
25. G. Yang, Z. Huang and L. Zhao, Fluidization, 1984, pp. 145–152.
26. R. Bader, J. Findlay and T. M. Knowlton, Circulating fluidized bed technology II, 1988, pp. 123–137.
27. J. Werther, Circulating fluidized bed technology IV, 1993, pp. 1–14.
28. J. Werther, Circulating fluidized bed technology VII, 1992, pp. 257–263.
29. J. Werther, E. U. Hartge and M. Kruse, Powder Technol., 1992, 70, 293–301.
30. F. Wei, Y. Jin, Z. Yu and J. Liu, Chem. Eng. Technol., 1995, 18, 59–62.
31. J. Sterneus, F. Johnsson and B. Leckner, Chem. Eng. Sci., 2000, 55, 129–148.
32. P. Gayan, L. F. Diego and D. J. Adanez, Powder Technol., 1997, 94, 163–171.
33. M. L. Mastellone and U. Arena, Can. J. Chem. Eng., 1999, 77, 231–237.
34. J. Sterneus, F. Johnsson and B. Leckner, Powder Technol., 2002, 126, 28–41.
35. K. Savolainen and R. Karvinen, Advances in Fluid Mechanics Series, 2001, vol. 29, pp. 87–96.
36. B. Ljungdahl and B. Zethrnus, Proceeding of 5^th Int. Conf. On Circulating Fluidized Beds, 1996, pp. 31–36.
37. J. H. Chen, X. F. Lu, H. Z. Liu and J. Liu, Powder Technol., 2008, 185, 164–169.
38. J. H. Yang, H. R. Yang and G. X. Yue, Chinese Journal of Powder Engineering, 2008, 28, 509–513.
39. S. Z. Sun, Z. Y. Wang, M. K. Du and H. Chen, J. Eng. Therm. Energy Powder, 2010, 25, 51–56.
40. A. Klinkenberg, H. J. Krajenbrink and H. A. Lauwerier, Ind. Eng. Chem., 1953, 45, 1202–1208.
41. M. Patrick, J. Inst. Fuel, 1967, 40, 425–426.

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