A Simulation of the Accumulation of Solid Particles in Coal

Catalytic Hydrogenation of HyperCoal (Ashless Coal) and Reusability of Catalyst. Koji Koyano , Toshimasa Takanohashi and Ikuo Saito. Energy & Fuels 20...
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Ind. Eng. Chem. Res. 2000, 39, 2866-2875

A Simulation of the Accumulation of Solid Particles in Coal Liquefaction Reactors Based on the NEDOL Process Masaki Onozaki,† Yasuki Namiki,† Toshihiro Aramaki,† Tsutomu Takagi,† Masatoshi Kobayashi,† and Shigeharu Morooka*,‡ Nippon Coal Oil Co., Ltd., KS Bld., 2, Sanban-cho, Chiyoda-ku, Tokyo 102-0075, Japan, and Department of Materials Physics and Chemistry, Kyushu University, Fukuoka 812-8581, Japan

A direct coal liquefaction plant was constructed in Kashima, Japan, based on the concept of “NEDOL Process”, and successfully processed 150 tons of Tanitorarum coal per day during 19971998. The plant was equipped with three reactors: 1 m in diameter and 11.8 m in length, connected in series. During the operation, solid particles were accumulated mainly in the first reactor. Slurry samples were directly removed from the reactors, and size distributions of solid particles were determined. Two types of particles were found: particles with cores and particles without cores. The size of the former particles was in the range of 10-200 µm, while that of the latter particles was 1-80 µm. The growth rate of the particles was estimated to be 0.10 nm s-1 under the reaction conditions. The solid accumulation in the first reactor was classified into a dense region in the lower part of the reactor and a lean region extending above the dense region. The former region was expressed as a three-phase fluidized bed model, and the latter was expressed by a one-dimensional sedimentation-dispersion model. These reactor models were validated on the basis of pressure differences and particle size distributions. It was confirmed by the simulation that removing a small amount of solids from the bottom of the first reactor was effective to achieve a long-term continuous operation without accumulation of coarse solid particles. 1. Introduction A coal liquefaction pilot plant, having a capacity of 150 tons of coal per day, was in successful operation during 1997-1998 in Kashima, Japan. The pilot plant (Figure 1) consists of four sections: (1) the coal slurry preparation section including the pulverizing, drying, and mixing units; (2) the liquefaction section, including a preheating unit, liquefaction reactors, and a highpressure separation unit; (3) the distillation section with atmospheric and vacuum towers; and (4) the solvent hydrogenation section, which contains a solvent hydrogenation reactor with six Ni/Mo catalyst beds. The goals of the project were to obtain engineering data suitable for scale-up and to demonstrate the reliability of the “NEDOL Process” developed by the New Energy and IndustrialTechnologyDevelopmentOrganization(NEDO), Japan. The NEDOL Process features liquefaction using a finely divided pyrite catalyst and hydrogenation of recycle oil at a connected plant. The direct coal liquefaction plant in Kashima was equipped with three reactors connected in series. Five runs were performed using three coals. In each run, the pressure drop between the top of the reactor and the inlet line connected to the bottom of the reactor gradually increased with passing operation time. The accumulation of solid particles reduced the effective volume of the reactor. Slurry samples removed from the * Correspondence concerning this article should be addressed to Shigeharu Morooka, Department of Materials Physics and Chemistry, Kyushu University, Fukuoka 8128581, Japan. Telephone: 81-92-642-3551. Fax: 81-92-6515606. E-mail: [email protected]. † Nippon Coal Oil Co., Ltd. ‡ Kyushu University.

reactor contained particles, which were from a few micrometers to about 500 µm in diameter. Ueda et al. (1999) and Aramaki et al. (2000) investigated the structure of relatively large particles recovered from the Kashima pilot plant. Those particles were composed of a core which contained SiO2 as the major component and FeS and Al2O3 as minor components, in addition to a peripheral region which contained CaCO3, FeS, and MgCO3. Sedimentation of solids has also been reported in other direct coal liquefaction reactors. Wakely et al. (1979) found that particles recovered from a coal dissolver at the Wilsonville SRC pilot plant were largely calcium carbonate particles which were 50-150 µm in diameter. Each particle was composed of a distinct layer, surrounding the core. Okuma et al. (1999) analyzed sediments in a liquefaction reactor using a Victorian brown coal and found that the solids were multilayered carbonates of Ca, Mg, and Na. Mochizuki et al. (1997) analyzed deposits from reactors of a process supporting unit (PSU), which was designed and operated based on the NEDOL Process (capacity, 1 ton of coal per day; reactor dimensions, 0.175 m in diameter and 1.75 m in height). The cores of these particles contained Si and Al, and the concentric shells outside of the cores were largely composed of Ca. Morooka et al. (1986) discussed the hydrodynamics of particle sedimentation in liquefaction reactors, based on balances among entrainment, growth, and axial dispersion of solid particles. However, the theory was not validated with experimental data obtained in actual liquefaction reactors. The objective of the present study is to characterize the solid deposits and to evaluate the solid accumulation, based on the data of the Kashima pilot plant.

10.1021/ie990746+ CCC: $19.00 © 2000 American Chemical Society Published on Web 06/16/2000

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Figure 1. Flow sheet of the Kashima pilot plant. Table 1. Properties of Tanitoharum Coal proximate analysis (dry coal basis) volatile matter fixed carbon ash moisture in feed coal

47.0 wt % 48.0 wt % 5.0 wt % 16.2 wt %

ultimate analysis, wt % daf basis C; 76.9 H; 5.8 N; 1.9 S; 0.15 O (difference); 15.25 ultimate analysis of ash, wt % as oxide SiO2; 27.7 Al2O3; 20.9 Fe2O3; 10.5 MgO;4.4 CaO; 12.9 P2O5; 1.4 SO3; 17.4 Na2O; 3.0 Others; 1.8

2. The Operation of the Kashima Pilot Plant and Analysis of Solid Particles Table 1 shows the properties of the Tanitoharum coal, which was processed in the Kashima pilot plant. The feed was prepared from pulverized coal (0-50 µm, 50 wt %; 50-150 µm, 48 wt %; 150-250 µm, 2 wt %), recycle oil, pyrite (FeS2) powder (average diameter ) 0.7 µm), and hydrogen-rich recycle gas. The feed was heated to 660-690 K in a slurry heat exchanger and a fired heater, and then introduced into the first reactor through an upward nozzle which was 107 mm in diameter. Figure 2 shows the dimensions of the reactor. The axial position was measured from the height of the boundary between the cylindrical and conical sections at the bottom of the reactor. This line is referred to as the bottom tangential line. The distance between the bottom and top tangential lines was 11.0 m. Three pressure taps and sampling nozzles, 20 mm in diameter, (A-C) were installed in each reactor, and another (D) was installed in the feed line to the reactor. Two downward injection nozzles for the quench gas were installed at different heights. Table 2 shows three major operating conditions, at which the continuous operation was performed. After

Figure 2. Dimensions of the liquefaction reactors.

allowing 9 days for start up, the conditions of case 1 were maintained for 18 days, and the conditions of case 2 were maintained for 11 days. Finally, the coal concentration was increased to about 50 wt %, and the conditions for case 3 were maintained for 15 days. The recycle gas was fed into the reactors as feed and quench

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Table 2. Operating Conditions and Data for the Kashima Pilot Plant case 1 recycle gas average molecular weight fraction of hydrogen, vol % makeup slurry recycle oil feed rate, kg h-1 coal feed rate, dry coal basis, kg h-1 slurry feed rate, kg h-1 coal concentration in slurry, wt %, dry coal basis catalyst (pyrite powder) in slurry, wt %, dry coal basis reaction operating pressure, MPa operating temperature at the top of the first reactor, K Gr/Lf,a m3(STP)/kg-slurry Gr/Lf,b m3(STP)/kg-slurry yields, wt % daf coal basis gas water oil (C4 to bp 811 K fraction) residue total hydrogen consumption, wt % daf coal basis

case 2

case 3

5.48 86

5.71 85

5.78 85

9540 6480 16200 40 3

8470 6750 15400 43.7 3

6340 6180 12700 48.5 3

16.6-16.8 728 0.55 0.71

16.6-16.8 728 0.55 0.70

16.6-16.8 733 0.71 0.90

17.2 10.2 51.0 26.1 104.5 4.5

20.0 9.9 53.1 21.6 104.6 4.6

20.4 9.9 55.6 18.8 104.8 4.8

a (Volumetric flow rate of recycle gas fed to the feed slurry)/(mass flow rate of makeup coal slurry). recycle gas fed to the three reactors)/(mass flow rate of makeup coal slurry).

b

(Volumetric flow rate of total

Figure 3. Operation conditions and timings of the sampling.

gas. The compositions of the recycle gas were slightly different for cases 1, 2, and 3. The flow rate of the recycle gas is given as the volume (STP) per unit time and is denoted as Gr. The flow rate of the slurry, which was a mixture of coal, recycle oil, and catalyst powder, is given in units of mass per unit time and is denoted as Lf. The feed consisted of recycle gas and slurry. Figure 3 shows the sampling sequence. A total of six samples were withdrawn from the reactors during the operation through nozzles (B) (middle) and (C) (bottom) of the first reactor, and a total of six samples through nozzle (B) of the second and third reactors during the operation. Each sample was withdrawn into a highpressure container which was 0.0164 m3 in size, and the slurry was depressurized into a low-pressure container using a needle valve. After cooling, the liquid and solid were separated, and the solid particles were washed with hexane. The morphology of the solid particles was observed using a scanning electron microscope (SEM), and size distributions were determined with a laser diffractiometer using a suspension of the samples in ethanol under ultrasonic irradiation. The crystallinity of the particles was determined by polarization microscopy, and the elements were determined by X-ray spectrometry and energy-dispersive X-ray spectrometry (EDX).

Figure 4. SEM image of particles.

3. Properties of the Solid Particles The recovered solid particles can be classified into coarse particles with cores and fine particles without cores (Aramaki et al., 2000). Particles with cores consist of both the central region and the peripheral region. This structure was clearly observed by SEM. Figure 4 shows the sectioned faces of sedimented particles with cores and without cores, which were recovered at 40 days after the start of liquefaction. Larger particles were selected in order to clearly show the structures of particles. According to the X-ray spectrometry and EDX, Particle 1 without a core consists largely of Si. Particle 2 consists of Ca, Fe, and S as the major components, with Al and Mg as the minor components. The granular material in particle 2 is FeS, formed from the catalyst powder. Some particles without cores consist mainly of Fe, S, Al, and coal fragments. Particle 3 has a core which is composed of Si, and the peripheral region which consists of Ca, Fe, S, Al, and Mg. Only less than 1 wt % of organic carbon is contained in these particles. The solid particles were not always spherical, and the cores assumed a variety of shapes, including cylinders and long spheroids. The size of the particles with cores was

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Figure 7. Particle size distributions of samples withdrawn from the middle of the first reactor: solid line, 19th day; broken line, 32th day; thin line, 51th day.

Figure 5. Effect of operation period on the oxide content of particles withdrawn from the bottom of the first reactor: 9, SiO2; [, Fe2O3; 0, Al2O3; 4, CaO; O, MgO. Solid lines, correlations of Fe2O3 and CaO.

Figure 6. Particle size distributions of samples withdrawn from the bottom of the first reactor: solid line, 24th day; broken line, 37th day; thin line, 56th day.

largely in the range of 10-200 µm, and that of the cores was largely in the range of 1-80 µm (the peak of frequencies of size ) ∼25 µm). The size of particles without cores was also in the range of 1-80 µm. The average density of the solid particles was determined to be 2700 kg m-3. As shown in Figure 5, the calcium content of the particles which were recovered from the first reactor increased, while the iron content decreased, with increasing operation periods. This result, as well as Figure 4, suggests that the particle growth was caused mainly by the deposition of calcium compounds on the cores. Figures 6 and 7 show the volume-based cumulative size distributions of the particles, which were sampled from the bottom part of the first reactor through sampling nozzle (C) and from the middle part of the first reactor through sampling nozzle (B), respectively. The sampling times are the same as shown in Figure 3. The particles recovered on the 51st and 56th days show dualpeak distributions, with fewer particles in the 30-80

Figure 8. Effect of operation period on diameter of solid particles withdrawn from the bottom of the first reactor: 9, 100% of cumulative frequency; ], 95% of cumulative frequency; O, 90% of cumulative frequency. Solid line, correlation of 100% of cumulative frequency.

µm range. Smooth size distributions were found for the other particles. Figure 8 shows time-dependent changes in diameter of 100%, 95%, and 90% of the volume-based cumulative frequency of the particles, which were sampled from the bottom part of the first reactor operated under the conditions of cases 1, 2, and 3. The growth rate of the particles, Kg, based on the maximum particle sizes in the first reactor, is ∼0.10 nm s-1. 4. Pressure Drop and Accumulated Solid Particles Figure 9 shows the time-dependent changes in pressure differences between pressure tap A and pressure tap D in the first reactor during the operation of cases 1, 2, and 3. The pressure drop between A and D, Pd, determined at 12 h after the start of liquefaction, can be considered to be the standard pressure drop, which is caused by the mass of the gas and slurry phases with no accumulated coarse particles present:

Pd/H ) (gFg + slFsl)g/1000

(1)

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5. Modeling of Solid Accumulation

Figure 9. Changes in pressure differences in the reactors.

where g is the gravitational acceleration, Fg the density of the gas phase, Fsl the density of the slurry phase without coarse particles, g the gas holdup, sl the slurry holdup, and H the height of the reactor. The holdup of the gas phase in the first reactor was 0.47, as reported by Onozaki et al. (1998). Thus, the density of the slurry phase was determined to be 743 kg m-3 from the slope of the pressure difference along the reactor height. The pressure difference remained unchanged in the second and third reactors during the entire reaction period. However, the pressure difference rose gradually with operation time in the first reactor, and increased by 45 kPa after 2 months of operation. Since no severe scaling was observed on the walls of any of the reactors by visual inspection after the operation, it would appear that this increase is caused by an accumulation of coarse solid particles in the first reactor. The particle density is 2700 kg m-3 as described above. Immediately after the startup of liquefaction, most particles are less than 10 µm. The terminal velocity of a particle with a diameter of 10 µm is ∼0.0002 m s-1, which is much smaller than the superficial liquid velocity in the reactor (typically 0.0038 m s-1). Thus, the slurry phase is assumed to be a homogeneous pseudo-liquid. However, larger particles appeared in the lower part of the reactor after a long liquefaction period. If the coarse particles are homogeneously suspended in the first reactor, the increase in the pressure difference, Pd, is given by

Pd/H ) (gFg + slFsl + sFs)g/1000

The fine particles without cores are included in the slurry phase, and most of them are carried out along with the ascending liquid flow. However, some particles remain in the reactor as a result of the axial dispersion and grow to coarse particles, which cannot be entrained by the liquid flow. A portion of the coarse particles can be discharged from the reactor also by the axial dispersion. As the operation continues, coarse particles are concentrated at the bottom and rarely discharged from the reactor. After the concentration of solid reaches a threshold value, a condensed zone is formed. This condensed zone is named a lower dense region, while the part above the lower dense region is named an upper lean region. As the particles grow, the boundary between the upper lean region and the lower dense region gradually rises. Upper Lean Region. A one-dimensional sedimentation-dispersion model is applied to the lean region. The population balance of coarse solid particles proposed by Morooka et al. (1986) is described as follows:

-

∂CL(y,x,t) ∂2CL(y,x,t) ∂CL(y,x,t) + (up - u) + Ep ∂t ∂x ∂x2 ∂ {K C (y,x,t)} ) 0 (3) ∂y g L

where CL(y,x,t) is the concentration of coarse solid particles per particle size, t the time, x the axial height of the reactor, y the coordinate of the particle size, u the linear velocity of the slurry, up the sedimentation velocity of coarse particles, and Ep the axial dispersion coefficient of coarse solid particles. The second and third terms on the left-hand side of eq 3 are the concentration of coarse solid particles transported by the liquid flow and the axial dispersion per unit time, respectively. The fourth term is the concentration of coarse solid particles transferred by the particle growth along the y axis per unit time. The time constant, for which solid particles are grown, is of the order of several days. Meanwhile, a concentration profile of coarse solid particles with a size of yn can be stabilized in the reactor in a time period shorter than several hours. It is then reasonable to assume that a concentration profile of coarse solid particles is always established for a prescribed particle size distribution. Thus eq 3 is reduced to a quasi-steady-state equation for CLt(yn,x) as follows:

(2)

where s and Fs are the holdup and density of the coarse particles, respectively. In this report, the slurry itself consists of liquid and fine particles but does not include the coarse solid particles. The application of eq 2 indicates that ∼14% and ∼18% of the volume of the first reactor were occupied by accumulated coarse solid particles at the end of the operation of cases 2 and 3, respectively. On the basis of the material balance of calcium, ∼1.2 wt % of the calcium which had been contained in the feed coal had accumulated in the first reactor at the end of the operation of case 3. Since the average size of the cores is ∼25 µm, the particles with the diameter larger than 25 µm are hereafter referred to as the coarse solid particles. The solid particles, which are smaller than 25 µm, are, as a definition, included in the slurry phase.

(up - u)

dCLt(yn,x) dx

+ Ep

d2CLt(yn,x) dx2

)0

(4)

The boundary condition at the top of the reactor is described by the following equation:

dCLt(yn,H) dx

)0

(5)

Thus, the concentration of coarse particles with a diameter of yn at a height of x is given as

CLt(yn,x) ) CFt(yn)

[

{

}

up up - u exp (H - x) up - u Ep

]

u (6) up - u

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where CFt(yn) is the concentration of coarse particles with a diameter of yn in the feed stream at the inlet nozzle. The amount of the coarse particles with a diameter of yn in the reactor, WLt(yn), is obtained by integrating CLt(yn,x) over the range of x ) 0 - H:

∫0HCL (yn,x) dx

WLt(yn) ) A

(7)

t

where A is the cross sectional area and H is the height of the reactor. WLt(yn) is increased to WLt(yn+1) by a factor of (yn+1/ yn)3 if no coarse particles are entrained to the outside by the liquid flow. Actually, however, the mass of the coarse particles, which are carried out due to the entrainment and artificially removed from the reactor at the height of HR, should be subtracted from WLt(yn):

WLt(yn+1) )

{

WLt(yn) -

(

(

2 CLt(yn,HR) + CLt(yn+1,HR)

FT∆t -

) }( )

2

FR∆t

yn+1 yn

3

(8)

where FT is the flow rate of the effluent slurry causing the entrainment and FR is the removal rate from the reactor. CLt(yn,x) can be calculated from eqs 6-8. The feed concentration of core particles, CFt(y0), is related to the concentrations of ash and catalyst and is assumed to be constant in the present simulation:

CFt(y0) ) constant

(9)

where y0 is the diameter of the core particle. The core particles grow at a rate Kg, which is assumed to be independent of particle size. Thus, yn+1 and yn are connected by the following equation: 9

yn+1 ) yn + Kg∆t × 10

(10)

where ∆t is the time interval in which yn increases to yn+1 at a linear growth rate Kg. The total concentration of particles at x, SL(x,t), is then calculated by integrating CLt(y,x) over the particle size, y:

SL(x,t) )

∫y

ye 0

CLt(y,x) dy

Smax ) sDFs

(12)

When the total concentration of particles at the bottom, SL(0,t), is more than Smax, a dense region is formed. In this region, SD(x,t) is constant and referred to as Smax. It can be assumed that solid concentration, a function of operation period, t, in the dense region, CD(y,t) is independent of the axial position. In the lean region, the solid concentration is calculated from the following equation as a function of operation period t:

CL(yn,x,t) ) CF(yn,t)

{

[

} ]

up up - u (H - x) exp up - u Ep u (13) up - u

)

CLt(yn,H) + CLt(yn+1,H)

dense region, sD, which is constant with respect to the axial position:

(11)

where ye is the maximum diameter at t. y0 is assumed to be 25 µm in the present case. Lower Dense Region. The behavior of the coarse particles in the lean region above the dense region is described by the sedimentation dispersion model, as expressed in the preceding section. When the concentration of coarse particles exceeds a threshold value, however, a dense region of coarse particles appears in the lower region. Kato et al. (1985) reported that the threshold of the solid holdup, defined for coarse particles, in the dense region was ∼0.5. In the present study, however, the threshold value of the solid holdup is decided to be 0.4, since fine particles which are homogeneously suspended in the slurry phase may increase the drag force. The height of the dense region is assumed to be equal for all solid particles with cores, irrespective to their particle diameters. The threshold concentration, Smax, is related to the solid holdup in the

where HD(t) e x e H and where HD(t) is the height of the dense region. The boundary condition between the lean and dense regions is expressed by

CL(yn,HD,t) ) CD(yn,HD,t)

(14)

Assuming CF(yn,t) and HD, the mass of grown particles having a diameter yn in the dense region, W(yn,t), is successively calculated by the way shown in the previous section so as to satisfy eq 12, using eqs 13 and 14. Thus, the pressure difference along the reactor length, Pd, is calculated from

Pd(t) )

∫yy {CD(y,t)HD(t) + ∫HH (t)CL(y,x,t) dx}g dy/1000 e

0

D

(15)

6. Estimation of Parameters Used in the Model Gas Holdup. It has been reported that the gas holdup at elevated pressures is several times larger than the data measured with air-water systems at ambient conditions (Tarmy et al., 1984; Takeshita et al., 1989). Onozaki et al. (1998) found that the data obtained in the Kashima pilot plant were in agreement with the correlation proposed by Tarmy et al. (1984) for ug ) 0.05-0.07 m s-1:

ug ) (ug + usl) + ub(1 - g)m g

(16)

where ub is the ascending velocity of an isolated bubble obtained to be 0.09 m s-1 and m was obtained to be 0.65 (Tarmy et al., 1984). Equation 16 was used in the calculation of the present study. Axial Dispersion Coefficient. Several correlations have been reported for the axial dispersion coefficient of the liquid phase in vertical bubble columns as functions of column diameter and superficial gas velocity. The majority of data (Deckwer et al., 1974; Hikita and Kikukawa, 1974; Field and Davidson, 1980) were obtained for air-water systems under ambient conditions. Deckwer et al. (1974) proposed the following equation:

El ) 0.678Dt1.4ug0.3

(17)

where Dt and ug are expressed in the unit of meters and meters per second, respectively. In coal liquefaction reactors, however, liquid dispersion coefficients, as

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Table 3. Model Parameters and Simulation Conditions for Case 1 gas phase density, kg m-3 calculated superficial velocity, m s-1 liquid phase density of liquid, kg m-3 viscosity of liquid, kg m-1 s-1 calculated superficial velocity, m s-1 solid particle density, kg m-3 initial diameter of particle, µm conversion ratio from ash and catalyst of feed slurry to cores, wt % growth rate of particles, nm s-1 calculated gas holdup calculated axial dispersion coefficient, m2 s-1 maximum solid holdup

48 0.056 670 0.0007 0.0038 2700 25 10 0.10 0.47 0.024 0.4

determined by tracer tests, were found to be much smaller than those estimated from the above correlations (Tarmy et al., 1984; Pittsburgh & Midway Coal Mining Co., 1982; Panvelker et al., 1982). At the Kashima pilot plant, Sakai et al. (2000) used a neutron absorption tracer technique and determined El ) 0.018 and 0.029 m2 s-1 at ug ) 0.058 and 0.056 m s-1, respectively. These values can be correlated using the following equation which is derived by modifying:

El ) Kdug0.3

(18)

where Kd is 0.042 and 0.069 for ug ) 0.058 and 0.056 m s-1, respectively, and the average value is 0.056. Physical Properties of Gas and Slurry. Properties of coal liquids are dependent on characteristics of processes (Tsonopoulos et al., 1986; Gray et al., 1983). In the Kashima pilot plant, coal liquids were fractionated, and physical properties of each fraction were determined. These data, including reaction rate coefficients and vapor-liquid equilibria, were stored in the simulator, which was developed by Hiraide et al. (1999). The flow rates of the gas and liquid in the reactors were estimated using the simulator, as shown in Table 3. Details of the simulation will be published separately. Sedimentation Velocity. Kato et al. (1972) measured the mean settling velocity of solid particles, which were suspended in bubble columns. The particles were glass spheres, the average diameters of which were 74162 µm. Their data are correlated as

up ) 1.33ul

() ug ut

0.25

Q2.5

(19)

where

Q)

l l + s

(20)

Kato et al. (1985) extended the above correlation to the lean region of the three-phase fluidized bed and proposed the following correlation:

{

( )}

up ) ul 1 + 1.5

ug ut

0.30

Q2.5

(21)

where ut is the terminal velocity of an isolated solid particle. However, the drag coefficient of particles highly depends on particle shapes and flow properties. Thus, the terminal velocity of an isolated particle in the

Figure 10. Pressure difference in the first reactor: solid line, experiment; thin lines, calculation.

reactors of the Kashima pilot plant is determined by the following equation:

ut ) Kpy2(Fs - Fl)g/18µl

(22)

Since the holdup of coarse particles is much smaller than the liquid holdup in the lean region, Q in eq 20 is assumed to be unity. up is calculated from eq 21, where Kp is used as an adjustable parameter in the present calculation. 5. Results The pressure difference between the pressure taps A and D was calculated for case 1 as a typical condition. Table 3 shows the data, as well as estimated values, used for the simulation for case 1. When 10 wt % of ash and catalysts in the feed slurry were converted to the core particles, the calculated pressure drop was coincident with the measured value. The concentration of the core particles fed to the reactor, CFt(y0), was estimated by this ratio. Figure 10 shows the time-dependent changes in the pressure difference along the reactor length, as a function of Kp defined by eq 22. The calculation is closest to the data when Kp is assumed to be 2.5. When Kp is increased to 2.8, the pressure difference starts to increase too early. When Kp is reduced to 1.0, on the other hand, the pressure difference increases too slowly. CFt(y0) rarely affects the timedependent change in the pressure difference. Once the dense region appears, the height of the dense region increases rapidly, as shown in Figure 11. Figure 12a shows the particle size distributions which were obtained for the samples recovered at the middle of the first reactor on the 19th and 51st days from the start. These data are good in agreement with the calculation, as shown in Figure 12b, where the estimated weight-based distributions are transformed to the number-based distributions. Particles less than 25 µm in diameter are added to the calculated distribution in Figure 12b to compare them with the experimental

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Figure 11. Estimated dimensionless heights of dense region in the first reactor.

Figure 13. Effect of axial dispersion coefficient on the dimensionless heights of the dense region in the first reactor.

Figure 14. Relationship between minimum removal rate of slurry and particle growth rate to avoid the accumulation of coarse solid particles.

6. Discussion

Figure 12. Estimated particle size distributions at the middle of the first reactor: (a) experiment; (b) calculation; solid line, on the 19th day; thin line, on the 51th day.

distributions. Experimental distributions are broader than the calculated distributions due to a variety of sizes of core particles. As the time proceeds, the particles between 30 and 80 µm in diameter are entrained, and only a few of those particles remain in the reactor on the 51th day.

Column diameter and gas velocity affect the axial dispersion coefficient, as shown in Figure 13. If Kd in eq 19 is increased by 4 and 16 times, the appearance of the dense region is substantially delayed. However, the pressure drop increases in any case. The time-dependent change in particle size is calculated for a growth rate of 0.1 nm s-1, assuming that the solid particles are continuously removed at the bottom tangential line (HR ) 0) to the outside. Even if the removal rate is as small as 0.0055 wt % of the feed rate, the accumulation of solid particles is effectively prevented. Figure 14 shows the minimum removal rate of

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the slurry to maintain the pressure difference at the same level. For a growth rate of 0.20 nm s-1, the solid accumulation can be avoided, when 0.06 wt % of the feed slurry is removed from the bottom of the reactor. 7. Conclusions During the operation of the Kashima pilot plant, two types of solid particles were produced, i.e., particles with cores, and particles without cores. The average size of the former particles was 10-200 µm, while that of the latter particles was 1-80 µm. The size of the core, included in the larger particles, was as equivalent in size to that of the smaller particles without cores. The cores, as well as the particles without cores, were largely composed of SiO2, with lesser amounts of FeS and carbon. These materials were probably formed from ash, catalyst, and coal fragments. The particles grew in size by additional deposition of the materials on the cores, and the growth rate of the particles in the first reactor was estimated to be 0.10 nm s-1 under the reaction conditions of the Kashima pilot plant. The solid accumulation, which increased the pressure drop in the first reactor, was simulated using a model, consisting of a lean region at the upper part and a dense region at the lower part. A one-dimensional sedimentation-dispersion model was applied to the lean region, and a fluidized-bed model was applied to the dense region. The simulation was validated from the changes in pressure differences along the reactor length, as well as particle size distributions in samples removed from the reactors. The particle size and the height of the dense region were increased as the operation time passed. Acknowledgment The authors acknowledge the support by the New Energy and Industrial Technology Development Organization (NEDO) in line with the New Sunshine Project. Nomenclature A ) cross sectional area of the reactor, m2 C ) concentration of solid particles per particle size, kg m-4 Dt ) diameter of reactor, m El, Ep ) axial dispersion coefficients of liquid and solid particles, m2 s-1 F ) slurry flow rate, m3 s-1 Gq ) volumetric flow rate of quench gas, m3(STP) s-1 Gr ) volumetric flow rate of recycle gas, excluding gas and oil vapor which are evolved by reactions, m3(STP) s-1 g ) gravitational acceleration, m s-2 H ) effective length of the reactor including top and bottom portions, m HD ) height of dense region, m Kd ) correction factor of eq 18 Kg ) growth rate of solid particle, nm s-1 Kp ) correction factor of eq 22 Lf ) mass flow rate of makeup slurry, kg s-1 m ) parameter of eq 16, Pd ) pressure difference along the reactor length, kPa Q ) liquid ratio in slurry phase, S ) concentration of solid particles in slurry phase, kg m-3 t ) time, s u ) liner velocity of slurry, m s-1 ug, ul, usl ) superficial velocity of gas, liquid, and slurry, m s-1 up ) sedimentation velocity of a particle, m s-1

ut ) terminal velocity of a particle, m s-1 W ) mass of grown particles in the reactor per particle size, kg m-1 x ) axial position, m y ) coordinate of diameter of a particle, m ∆t ) time interval, s g, sl, s ) gas, slurry, and solid holdup µl ) viscosity of liquid, kg m s-1 Fg, Fsl, Fs ) density of gas including oil vapor, that of slurry including fine particles, and that of coarse solid particles, kg m-3 Subscripts 0 ) at initial point b ) isolated bubble D ) dense region e ) at end point F ) feed g, l, sl, s ) gas, liquid, slurry and solid phase, respectively L ) lean region max ) maximum n, n+1 ) at n and n+1 step, respectively p ) particle T, R ) position of outflow and removal t ) pseudo-steady state at time t

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Received for review October 12, 1999 Revised manuscript received February 21, 2000 Accepted April 25, 2000 IE990746+