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Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 3, 1979
Vertical Pneumatic Transport of Solids in the Minimum Pressure Drop Region George E. Klinzing Chemical and Petroleum Engineering Department, University of Pittsburgh, Pittsburgh, Pennsylvania 1526 1
The minimum pressure drop region in vertical pneumatic transport of solids was analyzed as a means of distinguishing between dilute and dense phase regions of flow. None of the existing correlations was found to be satisfactory to represent this dense phase flow regime for all cases considered. A new correlation for frictional contribution due to the presence of solids in the gas flow is given for the minimum pressure drop region. Particle size effects on the pressure drop are reviewed.
Introduction In the design of industrial processes involving liquid and gas transport the general guidelines and procedures are well defined for delivering or discharging these fluid streams. Not everything is known about fluid flow phenomena, but in comparison to systems involving the movement of solids, the state of knowledge and level of reliance in design is much greater. Presently, a large number of processes involve the handling of solids. The number of processes involving the handling of solids has been increasing and will continue to increase, especially when one considers the anticipated use of coal, for example, in the many energy conversion processes such as coal combustion, coal gasification, and magnetohydrodynamics. In designing transport lines for these solid delivery systems one is presented with much data and several correlations that have been formulated over the years. Each solid processing plant undoubtedly has its own limits and criterion for operation controlled by the kinetic rates of those operations. This present work is oriented predominantly to vertical pneumatic transfer of solids; however, much of the analysis is applicable to horizontal flow as well. As a guideline for optimum design based on the minimum utilization of energy, the minimum pressure drop as a function of superficial gas velocity is stressed. Doig (1975) has recently commented on the utility of basing the design of pneumatic systems on this criterion. Development Operation in the region of the minimum of the pressure drop as a function of superficial gas velocity has, in addition to the advantage of consuming less energy, the advantage of delivering a minimum quantity of gas to the process. This decrease in the amount of gas transferred is often a requirement for the operation. If one is moving the gas for a pneumatic system by a blower, Doig (1975) and Leung et al. (1971) have pointed out the difficulty inherent in such a design in balancing the energy needed to transport the solids with the blower requirements. These two operations are coupled and the minimum pressure drop region adds instability much the same as the laminar flow instability phenomena (Black et al., 1977). If a blower system is not used for the movement of the solids, one will not encounter this instability. When viewing the concept of operation a t a minimum point in the pressure drop vs. superficial gas velocity, concern may be raised as to sharpness of the minimum and the difficulty in maintaining an operation at such a precise operating point. In most cases this minimum is quite broad, making control at this point easy, and the possibility 0019-7882/79/1118-0404$01.00/0
of driving the flow to a choked condition less likely. Figure 1shows an example of the broadness of these minima using the Konno-Saito (1969) model to represent solid friction for varying coal flow rates in a 1 / 2 in. diameter pipe. Reviewing the literature, one finds papers by several investigators who have been concerned with dilute phase transfer of solids by a gas, e.g., Hinkle (1953), Stermerding (19621, Konno-Saito (19691, Reddy-Pei (19691, van Swaaj et al. (19701, Capes-Nakamura (1973), Yang (19761, etc. The definition of dilute phase is indeed not clearly defined. Doig has attempted to quantify the dilute and dense character of pneumatic transfer. Fine distinctions still appear to be lacking. In Figure 1 one sees a typical plot of pressure drop vs. superficial gas velocity. A tentative definition of dense and dilute phase of transport regions is proposed by noting that the region to the right of the minimum can be classified as dilute, while that to the left, as choked flow is approached, can be called the dense phase region. Many people have used solids loading as the criterion for quantifying the difference between dilute and dense phase operations; the higher the solids loading, 30 to 100 lb of solids/lb of gas, the more dense the transport. Recently, investigators have avoided such definitions and have correctly looked a t the densities of the solid and gas phases involved in the transfer as well as the loadings. The present proposed method of distinguishing between dense and dilute phase requires determination of the pressure drop as a function of superficial gas velocity either experimentally or by a model in order to classify the flow regime. Another aspect of the pneumatic transport of solids is the particle size of the solids flowing. Obviously, one never has a single particle size but a distribution of sizes. A few of the basic dilute phase transfer models involve the particle size of the solids in their analysis as, for example, that of Yang and Hinkle. The question thus arises as to what particle size should be employed. From an industrial viewpoint a sieve analysis appears to he the easiest measure of the size distribution. The sieve analysis essentially gives a weight mean diameter. This average diameter is most appropriate in settling phenomena where gravity effects are important. The fundamental mechanism for the transport of solids in pneumatic systems is one of momentum transfer; thus, the length mean diameter is more appropriate. In order to analyze a sample of particles for this length mean diameter, microscopic work which involves costly equipment and generally more tedious analysis is required. Analysis of some recent coal samples has shown roughly a 1 : l O ratio of length mean diameter to weight mean diameters. Since microscopic analysis of
0 1979 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 3, 1979
405
Table I Capes-Nakamura Van Swaaij e t al. Reddy-Pei Stermerding Konno-Saito Yang
0.206[ Up]-'.zz 0.263[Up]-' 0.151[Up]-' fp = 0.003 fp = 4(0.0285)Jgz[ Up]-' f p = 0.0206(1 - € ) / e 3 X [(l- € ) U t / U g- U p ] - 0 . 8 6 9
fp = fp= fp =
3
50-
1000 l b l h r
0
O
I
'
Ap/Lgxp
0
/
7
/
/'
Ib, /ft2/1!
Figure 2. A P / L c a i c d vs. ilP/LeXptlfor Konno-Saito model; selected data points.
From this definition of the particle velocity the voidage can be determined.
Further analysis of the shear stress gives (3)
A number of investigators have found various correlations for the frictional term, fp. (See Table I). In all solid-gas flow studies the voidage and actual solid velocity are used in the analyses. These quantities are quite difficult to measure experimentally and in few studies have the authors been able to actually determine these values independently. Most investigators use the difference between the gas velocity and the terminal velocity as the particle velocity
This expression for the particle velocity encounters difficulty in calculations of some flow systems in which the terminal velocity of the average particle size is larger than the gas velocity but in which solid transport occurs experimentally nevertheless. Table I1 shows a number of these experimental points. Also when applying the standard correlations mentioned above for the calculation of the minimum pressure drop point, the small particle velocities as defined by eq 4 do not give realistic predicted results when compared with experimental findings. These experimental points are also noted in Table 11. There thus appears to be difficulty in using the particle velocity as expressed in eq 4 in the dense phase for calculating minimum pressure drop values. Figure 2 gives the results of the predicted vs. experimental pressure drop for the Konno-Saito model using only the 18 out of 30 experiment points for which reasonable values could be predicted. These difficulties in using the existing models are not surprising when one notes that Capes and Nakamura experimentally found some unique behavior of the solid particles flow in a gas stream at low gas velocities. They noted a waviness in the solids trajectories and appearance of particles floating near the wall. Recirculation of the particles was also seen moving down from the wall then back to the core of the pipe. In order to apply the basic momentum balance equation to the minimum pressure drop region without difficulty, the solid friction factor was correlated with the gas velocity and terminal velocity instead of the particle velocity. Results and Analysis As stated previously, the main concern of this work is the minimum pressure drop region for vertical pneumatic transport. Data from eight investigators on the minimum
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Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 3, 1979
Table 11. Experimental Values Minimum APIL and Velocities ~~~
process Svnthane PDU (coal) (Saroff) Zenz (rape seeds)
(sand)
(salt) Capes-Nakamura (1973) (glass) Sandy et al. (1970), (alumina) Knowlton and Bachovchin (1975), (lignite) (siderite) Konchesky et al. (1975), (coal) Rose and Barnacle ( 1 9 5 7 ) a
~~~~
~
~~
part. diam., d,, ft
part. dens., p , , 1b,/ft3
tube diam., D,,ft
solids flow, W, lblh
lb,/m2
0.00033
75
0.025
400
2.39
614.7
12.8
0.410
0.1458 0.1458 0.1458 0.1458 0.1458 0.1458 0.1458 0.1458 0.1458 0.1458 0.1458 0.1458 0.1458 0.1458 0.1458 0.250 0.250 0.0417 0.0417 0.2417 0.2417 0.2417 0.2417 0.2417 0.45 0.45 0.45 0.104 0.104
234 487 842 1287 1743 162 721 1563 80.6 229 577 1912 136 499 854 186 1206 25 75 3395 4935 6875 2603 8077 5800 10000 21200 247 301
0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.351 0.351 0.351 2.46 0.783 0.075 0.075 0.075 0.075 0.075
14.7 14.7 14.7 14.7 14.7 14.7 14.7 14.7 14.7 14.7 14.7 14.7 14.7 14.7 14.7 14.7 14.7 14.7 14.7 70 70 70 490 156 14.7 14.7 14.7 14.7 14.7
30 30 30 25 22 28 26 32 27 27 30 32 16 17 21 59 76 22 28 46 48 50 23.5 24.5 108 128 135 31 35
22.26 22.26 22.26 22.2b 22.2a 14.3 14.3 14.3 25.3b 25.3b 25.3b 25.3b 3.04 3.04 3.04 47.1b 47.1b 5.89 5.89 3.25 3.25 3.25 1.81 2.22 143.P 143.P 143.P 24.Bb 24.Bb
0.0055 0.0055 0.0055 0.0055 0.0055 0.001925 0.001925 0.001925 0.00305 0.00305 0.00305 0.00305 0.00055 0.00055 0.00055 0.0095 0.0095 0.0 0 0 6 6 0.00066 0.00119 0.00119 0.00119 0.00119 0.000515 0.167 0.167 0.167 0.00655 0.00655
68 68 68 68 68 155 155 155 165 165 165 165 131 131 131 178 178 248 248 78.6 78.6 78.6 78.6 244 94.2 94.2 94.2 71.25 71.25
pg3
pressure drop region yielded 30 separate data points which were used for analysis. These data points represent a wide variety of materials, particle sizes, and pipe diameters. Table I1 lists the data. Acceleration contributions were calculated for both the gas and solid phases in order to determine the frictional contribution due to the solids. In most of the cases considered, these contributions to the overall pressure drops were small due to the long length of the test sections. Note that Table I1 includes some recent coal processing systems which operate a t high pressures for which the effect of gas density is significant. The models of Yang, Capes-Nakamura, and KonnoSaito were studied using the tabulated data to test their ability to predict the minimum pressure drop point and its associated superficial velocity. As noted previously, when using the particle velocity Up in the representation of friction due to the presence of solids, difficulty was encountered in predicting all the experimental results. This is not to say the models studied are incorrect, but that these models were predominantly developed for the dilute phase flow regime, not dense phase flow. The dense phase flow regime suffers from the many nonuniform effects as previously noted by Capes and Nakamura. Utilizing the same basic balance equation as KonnoSaito, Capes-Nakamura, and Yang, the frictional effect due to the solids was determined for each of the 30 experimental points considered, and a model was developed dependent on the gas velocity and other factors. The forms of the solid frictional effect considered were f p = a,Ugbl (6) = a2UgbzUtbstb4
(7)
The coefficients were determined by use of a multiple
27 0.707 1.27 2.26 3.54 4.95 0.594 2.26 4.10 0.707 1.13 1.98 4.81 0.386 2.12 4.53 0.498 1.00 0.95 2.0 1.66 a . 39 3.16 3.95 4.67 1.04 1.76 2.83 0.861 1.12
Small particle velocities as defined by eq 4.
Terminal velocity of the average particle size greater than gas velocity.
fp
min total velocity U, pressure press., at min, terminal drop, P,, Urn, velocity, APIL, lbf/in.2 ftls ftls lbf/ft2/ft
gas dens.,
/
/30‘* 5.0
/
1
/
/
/’SO*.
1
1.0
I
I
2.0 b
p/Lexp
30 lb{tt2/1
1
I
4.0
50
t
Figure 3. AP/Lcalcdvs. AP/Lexptlfor four-parameter model; fp = a2Ugb2tb3U>.
regression analysis. The best parameters were found to be a, = 0.061; u2 = 0.287; bl = 4.90; b2 = -1.51; b3 = 0.509; b4 = 4.08. The experimental vs. the calculated values for eq 7 are shown in Figure 3. One sees that for this new form of the solid friction term all the data scatters evenly about the corelation line. The results lying between -30% and +50% includes practically all of the data. The use of the additional parameters given in eq 7 yields an improvement on the correlation given by eq 6 by reducing the spread. Particle Size Effect Capes-Nakamura, Konno-Saito, and Yang’s analyses of dilute phase transfer include the effect of particle size
Ind. Eng.
Chem. Process Des. Dev., Vol.
18, No. 3, 1979
407
Table 111. Montana Rosebud Coal sieve anal. size mesh 20 40 80
1 on
%
1.0 5.05
21.21 11.1
omnicon microscow d , = 9.4 ern
I 10
10
60
a0 PAI,,
