Ind. Eng. Chem. Res. 1989, 28, 684-688
684
High-Velocity Fluidized Bed Hydrodynamic Modeling. 1. Fundamental Studies of Pressure Drop Ronald W. Breault' and Virendra K. Mathur* Department of Chemical Engineering, University of New Hampshire, Durham, New Hampshire 03824
High-velocity fluidization is a relatively new concept used in circulating fluidized bed systems. Part 1 of this study investigates pressure drop correlations for high-velocity fluidization. In this study of a bench-scale circulating fluidized bed system, the loop fluidized bed has been successfully designed, fabricated, and installed. Pressure drop data using sand, limestone, and gypsum particles have been obtained. A new solid friction factor as a function of solid fraction has been proposed. For nearly 15 years, considerable effort has been made on the development of fluidized bed combustion of coal. This process holds a number of attractions, all stemming from the concept of maintaining low temperatures in the range 1100-1200 K in the combustion chamber. However, it is reported that one of the main disadvantages of a fluidized bed combustion system is that turndown of combustion rate is difficult. Fluidized beds are not operable over wide ranges of loads. Circulating fluidized bed processes have been proposed recently to eliminate some of the problems encountered in conventional fluidized beds. The high-velocity fluidized bed (HVFB) is a transport reactor system in which the solids and gas go through many different flow regimes. The loop fluidized bed (LFB) shown in Figure 1 is one such circulating fluidized bed which is being considered for pressurized combustion of coal in the presence of a sulfur sorbent such as dolomite. This study has been conducted to provide fundamental knowledge of the hydrodynamics in the LFB with special reference to the riser section which operates in the highvelocity fluidization regime. Experimental data have been used for the development of a mathematical model to predict pressure drop in the riser section.
Background Vertical upward gas-solid transport has been studied extensively. However, most of these studies have concentrated on pneumatic transport of the solids and not on the solid-gas transport regime of high-velocity fluidization. The investigations on high-velocity fluidization have been primarily conducted by Yerushalmi and co-workers (Yerushalmi et al., 1975,1976,1978;Squires, 1976; Yerushalmi and Cankurt, 1978,1979). The riser section (Figure 1)of the LFB operates in a fast fluidization regime. The fast fluidization term is used to describe the phenomena of dense strands and clusters moving to and fro, rising and falling, and forming and breaking apart, as the solid particles are conveyed through the riser (Yerushalmi et al., 1975). Yerushalmi and co-workers conducted investigations in three experimental setups: (1)a rectangular, two-dimensional bed; (2) a 3-in.-diameterbed and (3) a 6-in.-diameter bed. They developed a pressure drop correlation (Yerushalmi et al., 1978) based on the following assumptions: (1) all solid particles are in densely packed clusters, (2) clusters are spherical, (3) there are no wall or acceleration effects, (4) clusters have a voidage equal to that at minimum fluidization, and ( 5 ) clusters are discreetly distributed in the bed. Present address: Riley Stoker Corporation, Worcester, MA 01610.
On the basis of these assumptions, the pressure drop per unit length can be described by the following equations:
where (3) (4)
The index n in eq 2 is called the Richardson-Zaki index and describes the voidage in a fluidized bed. This index is developed for solid-liquid particulate fluidization, and its value ranges from 4.65 to 2.4 for terminal Reynolds number less than or equal to 0.2 to greater than or equal to 500. The pressure drops obtained from these equations agree with experimental data. The cluster voidage is essentially an adjustable parameter which is used to allow the model to fit the data. Yerushalmi et al. (1978) calculated the cluster diameter as a function of the solid concentration. The data fall about a single curve, obtained from the equations, showing good agreement between the experimental data and the model. The disadvantage of this model is that it requires many unmeasurable parameters, namely, N , ,E, d,, and Uc,sl. Thus, our approach of considering the riser as a pneumatic transport reactor required a better understanding of the hydrodynamics of the system. The riser is the key section of a high-velocity fluidized bed combustor, since it is in this region where coal combustion and sulfur removal occur. The riser operates in the fast fluidization mode which lies between the regimes of pneumatic transport and fluidized bed flow. No suitable model representing the flow behavior and pressure drop in this region is available in the literature. Many investigators (Stemerding, 1962; Reddy and Pei, 1969; Van Swaaij et al., 1970; Capes and Nakamura, 1973;Yang, 1978; Klinzing, 1979) have proposed additive pressure drop models based on the Bernoulli force balance. In these models, the total pressure is considered to be the sum of the pressure drop contributions from the solid and gas kinetic energy changes, the solid and gas potential energy changes, the solid and gas interphase friction, the particle-particle friction, and the solid and gas wall friction. These mathematical models are represented in the most general form by the equation APT = PSKE + PGKE + USPE + UGPE + USGF + USSF + PSWF + UGWF (5) 1989 American Chemical Society
Ind. Eng. Chem. Res., Vol. 28, No. 6, 1989 685
-AUBURN MASS FLOW METER
\ I
A~
\
/
A
CYCLONE -SEPARATOR
L:/fl\ AIR
Table I. Solid Friction Factor Correlations effects of increasing solid slip investigation solid model friction velocity velocity Van Swaaij e t f, = 0.08/US no effect decrease no effect al., 1970 Stermerding, f, = 0.003 no effect no effect no effect 1962 Reddy and Pei, f, = 0.046/U, no effect decrease no effect 1969 Capes and f, = 0.48/U,1~22 no effect decrease no effect Nakamura, 1973 Yang, 1978 f, = no effect no effect increase 0.01025(1 - t ) t((1 - t)(Ret/Re,l))1,021
8A- B C RISER DISENGAGINGZONE C-D STANDPIPE D-A EDUCTOR ZONE
AIR
Figure 1. Loop fluidized bed.
The high-velocity fluidized bed will, in general, be operating in steady-state fashion. Therefore, the changes in solid and gas kinetic energies are zero. The resulting equation for the pressure drop then becomes
UT= USPE + UGPE + USGF + USSF + USWF + PGWF (6) The first two terms on the right in eq 6 are the solid and gas potential energy changes, commonly referred to as the solid and gas heads, respectively. The solid head loss is Figure 2. High-velocity fluidized bed experimental unit. given by enter the eductor zone, and are entrained in the high-veUSPE = - 6)gU (7) locity air stream at this zone. The air is supplied from an and the gas head loss is Ingersoll-Rand compressor. The flow rate is measured with four Dwyer rotameters. The particles conveyed upward UGPE = pgcgU (8) travel through an Auburn mass fraction monitor located at the middle of the 2.1-m-high riser outside the accelerThe third term, A P S G F , represents the interphase solid and ation region as shown by height-pressure data (Mathur, gas frictional losses. The fourth term, U S S F , represents 1984). The monitor continuously measures the percent the solid-solid particle interaction frictional losses. To solids of the two-phase stream as it flows past. The Audate, these two terms, third and fourth, have been conburn monitor consists of two separate units, the sensor sidered negligible when compared to the head terms and spool and the electronics. The sensor spool is constructed wall frictional losses. The fifth and sixth terms represent from a heavy steel pipe which has an inner diameter of the solid-wall and gas-wall frictional losses, respectively. 0.038 m (11/2 in.). Six individual sensor points are supplied The solid-wall frictional losses have been extensively around the spool. The electronics monitor the signals and studied for pneumatic transport; however, no uniformly analyze them to give an output voltage proportional to the agreed upon single model exists for this term. Most invoidage of the flowing suspension. The pressure drop vestigators have used the modified Fanning equation across the monitor is measured with a Validyne differential 2f,P,(l - C)US2U pressure transducer-indicator system. These instruments (9) @SWF = give analog outputs proportional to the corresponding 4 variables. The analog outputs are recorded by a Coleto model the solid-wall friction. The solid-wall friction Palmer strip chart recorder. The solid particles and gas factor, f,, is the term in dispute. This factor has been travel through the remainder of the riser and then loop investigated by several research workers and will be disaround the top via a 135’ bend and a 45’ bend. The gas cussed in detail. A summary of various solid friction factor exists via a 135’ bend, while the solid particles return to correlations is given in Table I. the standpipe. The air containing a small amount of solid particles flows through a cyclone and a bag filter (not Experimental Setup and Procedure shown in Figure 2); the solids leave the loop through the The experimental unit shown in Figure 2 has been ascyclone bottom. Pressure ports are provided approxisembled from a 0.038-m (11/2-in.)Pyrex glass pipe. There mately every m around the loop for monitoring pressure are five nozzles, No, N1, N2,N3,and N4,located at the lower with water manometers. The total height between the part of the loop which supply air at high velocity to fluidize lower and upper loops is 2.3 m. and entrain the solid particles. Solid particles are placed Experiments are carried out at operating conditions: in the feed hopper and fed manually to the LFB at the top temperature = 298 K, pressure = 10-50 kPa gauge, nozzle flow rates = (0-7.5) x m3/s, and superficial velocity of the standpipe through a ball valve. The particles traverse the standpipe, 1.2 m in height, in moving bed flow, = 3.9-7.6 m/s. The solids used in this study are sand, .#R i * O Y CoYPRLP3Oi
686 Ind. Eng. Chem. Res., Vol. 28, No. 6, 1989
in the AAPD range of 37.95 for gypsum to 41.51 for sand. The friction factor correlation has the same form as that of Van Swaaij et al. except that the proportionality constant is approximately 40% lower in this model. As a result, the error is larger. Capes and Nakamura (1973) obtained a correlation for the solid friction factor which stated that the solid friction factor was inversely proportional to the solid velocity raised to the 1.22 power. The AAPD for this correlation ranged limestone, and gypsum particles with average sizes of 300, from 40.93 for gypsum to 45.05 for sand. The larger AAPD 452, and 296 l m , respectively. Limestone and gypsum for this correlation suggests that increasing the power of have been chosen since these will be present in the HVFB the solid velocity term is inappropriate. coal combustion system. Details are given elsewhere The correlation by Yang (1978) was developed using (Breault, 1985). data available in the literature. The model by Yang incorporates the solid fraction and the slip velocity. The Discussion experimental data are compared against the predictions. Pressure drop data are obtained for the riser section The AAPD range from 40.31 for gypsum to 52.41 for using sand, limestone, and gypsum particles in order to limestone particles. The agreement at low pressure drop develop a mathematical model for this section of the is acceptable. The error increases greatly for exvalues HVFB. These measurements are made across the Auburn perimental pressure drops in excess of 500 kg/ (m2s2). The monitor to simultaneously obtain accurate solid fraction agreement at low pressure drops suggests that the solid data as well. friction factor should be a function of the slip velocity and Existing Models. To illustrate the deficiency of exthe solid fraction as well as the solid velocity. The values isting gas-solid flow models to predict the pressure drop of solid fraction and slip velocity are unavailable in the in HVFB flow, a comparison of the predicted results using literature from which Yang developed the model. It is the mathematical models obtained from the literature and possible that a great error was introduced due to erroneous the experimental data is made. In general, these models estimates of these values. are represented by the equation Development of a New Solid Friction Factor CorUT= USPE + UGPE + U G W F + PSWF (10) relation. The large deviation between the predictions and the experimental data suggests that the existing models The solid potential energy loss term, U S p E is obtained are not correctly describing the physical phenomena ocfrom eq 7. The gas potential energy loss term, APGPE, is obtained from eq 8. The solid wall friction loss, USWF,curring in high-velocity fluidization, which is a special case of gas-solid transport. High-velocity fluidization is the is obtained from eq 9 with the solid wall friction factor term used to describe the phenomena of dense strands and obtained from Table I. The gas wall frictional loss, APGwF, clusters moving to and fro, rising and falling, and forming is obtained from the Fanning equation. and breaking apart, as the particles are conveyed through The predicted pressure drop values for each model the riser. The pressure energy losses associated with such studied in this investigation are compared against the a flow behavior must be greater than those losses due to corresponding experimental values. The absolute average solids transported pneumatically where the solids flow in percent deviations (AAPD) between the model predictions stream lines with very little or no interaction between the and the experimental data range from 23.78 to 58.67 as particles. shown in Table 11. Graphical plots are available elsewhere The frictional pressure drop terms which incorporate the (Breault, 1985). Klinzing (1979) has also reviewed these losses due to the complex flow phenomena in the HVFB models. He reports that the deviation in experimental are (1)APs, (the solid wall friction), (2) ilpss~(solidsolid pressure drop versus predicted pressure drop was between friction), and (3) APsGF (solid-gas friction). The effect of -30% and +50%. The percent deviations obtained from these three terms has been neglected in the past. This most of the models in Table I1 agree with this error range. omission would cause erroneous estimates of the solid The AAPD for the predicted pressure drop using the fraction and solid velocity. The solid fraction would be correlation by Van Swaaij et al. (1970) range from 23.78 estimated higher than it actually is, while the solid velocity for gypsum to 29.58 for sand particles. The error magwould be lower than it is. Errors in the estimates of these nitude is quite reasonable considering the application of parameters have not caused serious problems when the this model outside the region for which it was originally equipment is used only to transport solids. However, the developed. However, a plot of the experimental data solid fraction and solid velocity are very critical parameters versus the predicted values by this model shows the in high-velocity fluidized bed reactors. The pressure losses agreement to be in the acceptable range for pressure drops due to A F ' S W , P s F , and must be considered when below 600 kg/(m2 s2) but unacceptable above this value. modeling solid-gas reacting flow systems. The solid wall The large deviation at high pressure drop between the data friction pressure loss is the only one of three terms that and the model predictions is probably due to the inadehas been studied to date. quacy of the solids friction factor model to account for the solid-solid particle interaction, the solid-gas interaction, The effects of each of the above factors on the total pressure drop have not been separated but combined into and the effect of the solid fraction. one term, the solid frictional loss term. This term is The AAPD in the predicted pressure drop using the modeled by the friction factor approach and has essentially correlation developed by Stemerding (1962) range from been considered as only the wall friction. The solid fric55.11 for gypsum to 58.67 for sand particles. The model tional loss term will be influenced by the solid velocity, always underpredicts the observed pressure drop. The use of a constant solid friction factor gives unacceptable the solid fraction, and the gas-solid slip velocity. It is expected that increasing the solid velocity would decrease pressure drop predictions. the frictional losses as is in the case of gases. Increasing The pressure drop predictions using the solid friction the solid fraction should increase the friction factor since factor correlation developed by Reddy and Pei (1969) are Table 11. Absolute Average Percent Deviation between Experimental and Predicted Pressure Drop Data sand limestone gypsum Van Swaaij et al., 1970 29.58 28.67 23.78 Stemerding, 1962 58.67 56.53 55.10 Reddy and Pei, 1969 41.51 41.37 37.95 Capes and Nakamura, 1973 45.05 43.15 40.93 Yang, 1978 43.31 52.41 40.31
Ind. Eng. Chem. Res., Vol. 28, No. 6, 1989 687 more solids are available for collision. Similarly, increasing the slip velocity should increase the friction factor since greater drag will be exerted on the particles. The solid friction factor models available in the literature and the effects of the above parameters on the friction factor are shown in Table I. Table I shows that only the model developed by Yang (1978) considers the effect of the solid fraction on the solid friction factor. Yang's model predicts the expected increase in the solid friction factor for an increase in the solid fraction. The models by Van Swaaij et al. (1970), Reddy and Pie (1969), and Capes and Nakamura (1973) predict the expected decrease in the solid friction factor for an increase in solid velocity. The Stemerding (1962) and Yang (1978) models do not consider the effects of solid velocity. The only model that considers the influence of the slip velocity on the solid friction factor is by Yang. The model predicts the expected increase in the solid friction factor for an increase in the slip velocity. The solid friction factor models are in disagreement when extrapolated to the conditions of high-velocity fluidization, for example, at solid velocity equal to 1m/s, solid fraction equal to 0.003, and slip velocity equal to 5 m/s. As seen from Table I, solid friction factors (pressure drop) differ widely for these models. Disagreement of such magnitude eliminates all possibility of using these equations to develop correlations for predicting losses due to solid-solid and solid-gas effects. Consequently, the node1 developed in this study for predicting the overall pressure drop due to the solid frictional effects has not considered these two losses separately but included them in the solid frictional term. The proposed mathematical model is represented by
USF = USWF + USSF +~
S G F
= 2fsus2ps(l - c ) u / d t
O0
W
g
1000
v, W v,
a
n A
F Z W
z
a W
500
i
0
0
/
0
0 0 0
o
SAND LIMESTONE
a W X
o ~ , , "500 l l ' l ' I Ol0 0 , l , l I 5'0 0, , l 2000 , l PREDICTED PRESSURE DROP ( k g / m 2 s 2 )
Figure 3. Experimental pressure drop in the riser versus predicted using the proposed solid friction factor correlation.
(11)
The pressure loss, U S F , is modeled by a Fanning-type equation similar to that used by previous investigators. Equation 11 can be written as U S F
/ ZOOOF
P W
0
W X
(12)
The solid friction factor, f,, in the above equation is considered as a function of the solid velocity, the solid fraction, and the slip velocity. The slip velocity contributes primarily to the term describing the solid-gas losses which are assumed to be negligible. Thus, the solid friction factor can be expressed as f, = alJ,b(l - € ) e / &
(13)
Information from the literature and experimental data from the present study have been used to estimate values of the constants a, b, c, and d. The model for the solid friction factor by Van Swaaij et al. predicts that the solid friction factor varies inversely with the solid velocity (f, ULl). Since this model provides the best agreement with the present experimental data for pressure drop (see Table 111, the value of b is taken as -1.0. The Ergun equation in the viscous dominated region of the packed bed flow states that the solid friction factor is proportional to (1e ) / e 3 . Thus, the values of c and d are taken to be 1.0 and -3.0, respectively. Therefore, the solid friction factor can be represented by f, = a ( l - e)/U,c3
(14)
This leaves only one unknown constant, a. The sand and limestone experimental data are used to determine a by a least-squares regression technique. The regression estimated the value of a to be 12.2, which resulted in the AAPD for sand and limestone to be 17.266 and 16.312,
Conclusions In this study, a bench-scale loop fluidized bed (LFB) made of Pyrex glass has been successfully designed, fabricated, and installed. The LFB has been operated using sand, limestone, and gypsum particles. The data have been obtained to study the effect of air flux, solid flux, and solid fraction on the pressure drop in the high-velocity fluidization (riser) section of the bed. The major findings are as follows: (1)The pressure drop in the riser section of a HVFAB can be expressed by the sum of the individual energy loss terms: U = USPE + UGPE + @SF + UGWF (2) The pressure drop due to the solid frictional losses can be modeled by a Fanning type of equation:
688
I n d . Eng. C h e m . Res. 1989,28, 688-693
*SF
=
2fAl - 4P,US2AL dt
(3) The proposed solids friction factor, f,, can be expressed by eq 15.
Literature Cited
Acknowledgment This study has been supported in part by the US.Department of Energy (Morgantown Energy Technology Center) under Contract DE-AC21-82MC19372.
Nomenclature Cd = drag coefficient d = diameter, m f = friction factor g = gravitational constant, 9.807 m/s2 G = mass flux, kg/m2/s AL = transport length, m n = Richardson-Zaki index N = cluster number P = pressure, kg/(m s2) AF' = pressure drop, kg/(m s2) Re = Reynolds number U = velocity, m/s Greek S y m b o l s t
= voidage
p = p =
SPE = solid potential energy SSF = solid-solid friction SWF = solid-wall friction t = tube, terminal T = total
gas viscosity, kg/(m s) density, kg/m3
Subscripts
Breault, R. W. Hydrodynamic Characteristics and Coal Combustion Modeling of a High Velocity Fluidized Bed. Ph.D. Dissertation, The University of New Hampshire, Durham, 1985. Capes, C. E.; Nakamura, K. Vertical Pneumatic Conveying: An Experimental Study with Particles in the Intermediate Turbulent Flow Regimes. Can. J. Chem. Eng. 1973, 51, 31. Klinzing, G. E. Vertical Pneumatic Transport of Solids in the Minimum Pressure Drop Region. Ind. Eng. Chem. Process Des. Dev. 1979, 18(3),404. Mathur, V. K. Pressurized High Velocity Fluidized-Bed Combustion Modeling. Report DOE/MC-19372-4 submitted to Morgantown Energy Technology Center, May 1984; Morgantown, WV. Reddy, K. V. S.; Pei, D. C. T. Particle Dynamics in Solids-Gas Flow in a Vertical Pipe. Ind. Eng. Chem. 1969, 8(3), 490. Squires, A. M. Application of Fluidization Beds in Coal Technology. In Alternate Energy Sources; Hartnett, J. P., Ed; Hemisphere Publishing Corp.: Washington, DC, 1976. Stemerding, S. The Pneumatic Transport of Cracking Catalyst in Vertical Risers. Chem. Eng. Sci. 1962, 17, 599. Van Swaaij, W. P. M.; Buurman, C.; von Breusel, J. W. Shear Stresses on the Wall of a Dense Gas-Solid Riser. Chem. Eng. Sci. 1970,25, 181. Yang, W. C. A Correlation for Solid Friction Factor in Vertical Pneumatic Conveying Lines. AIChE J. 1978, 24(3), 548. Yerushalmi, J.; Cankurt, N. T. High - Velocity Fluid Beds. CHEMTECH 1978, Sept, 564. Yersuhalmi. J.: Cankurt. N. T. Further Studies of the Regimes of Fluidization: Pouder' Technol. 1979, 24, 187. Yerushalmi, J.; Cankurt, N. T.; Geldart, D.; Liss, B. Flow Regimes in Vertical Gas-Solid Contact Systems. AIChE Symp. Ser. 1978, 74(176), 1. Yerushalmi, J.; Gluckman, M. J.; Graff, R. A,; Dobner, S.; Squires, A. M. Production of Gaseous Fuels from Coal in the Fast Fluid Bed. In Fluidization Technology; Keairns, D. L., Ed.; Hemisphere Publishing Corp.: Washington, DC, 1975; Vol. 11. Yerushalmi, J.; Turner, D. H.; Squires, A. M. The Fast Fluid Bed. Ind. Eng. Chem. Process Des. Dev. 1976, 15(1),47. Y
c = cluster g = gas f = friction
GKE = gas kinetic energy GPE = gas potential energy GWF = gas-wall friction mf = minimum fluidization s = solid sl = slip velocity SF = solid friction SGF = solid-gas friction SKE = solid kinetic energy
Received for review J u n e 13, 1988 Revised manuscript received February 10, 1989 Accepted February 25, 1989
High-Velocity Fluidized Bed Hydrodynamic Modeling. 2. Circulating Bed Pressure Drop Modeling Ronald W. Breaultt and Virendra K. Mathur* Department of Chemical Engineering, University of N e w Hampshire, Durham, N e w Hampshire 03824
Circulating high-velocity fluidized beds (HVFB) have been proposed to eliminate some of the problems encountered in conventional fluidized beds. The loop fluidized bed is one such system being considered for pressurized combustion of coal in the presence of a sulfur sorbent such as dolomite. This study has been conducted to obtain fundamental knowledge of the hydrodynamics of the one particular HVFB, the loop fluidized bed (LFB), which operates in various flow regimes. Experimental data obtained from a bench-scale unit have been used for the development of a mathematical model to predict the pressure profile in the LFB. The model requires solid flow rate, gas flow rate, equipment geometry, and solid fraction as inputs to predict the pressure a t any point in the system. The predicted pressures have been compared with experimental data and show good agreement. Part 1 of this study (Breault and Mathur, 1989) has described a test fluidized bed which has several advantages
-
'Present address: Rilev Stoker CorDoration. Worcester. MA 01610.
0888-5885/89/2628-0688$01.50/0
over a conventional fluidized bed. A high-velocity fluidized bed (HVFB) can overate over a wide range of gas throughputs.' The ga$ rate may be reduced to such a ;egree that the bed becomes turbulent or even enters the bubbling regime without losing uniformity of the bed 0 1989 American Chemical Society
