ITB J. Eng. Sci. Vol. 41, No. 1, 2009, 65-76 65 ressure Drop Correlation Covering Dilute to Dense Regimes o Solid article-gas Flow in a Vertical Conveying ipe Y. Bindar, N.A. Sutrisniningrum & D. Santiani Energy and rocessing System o Chemical Engineering Research Group Chemical Engineering rogram Study, Faculty o Industrial Technology Institut Teknologi Bandung Labtek X, Jl. Ganesha 10-Bandung 40132 Email: yazid@che.itb.ac.id Abstract. More general correlations between pressure drop and gas-solid low variables are developed rom the present experimental data. The correlation was modeled or a pneumatic conveying system in a vertical pipe. The transition boundary between dense and dilute regimes is constructed rom the pressure drop correlations. The gas-solid particle low variables are quantiied by the gas Reynolds (N re ) and the solid Froude (F rp ) numbers. The dense low regime is indicated by the decrease o the pressure drop with the increase o the gas Reynolds number. In contrary, the dilute regime exhibits the increase o the pressure drop with the gas Reynolds number. The proposed correlations were built at the range o gas Reynolds number rom 360 to 500 and solid Froude number rom 0,01 to 0,02. Keywords: dense phase; dilute phase; low regimes; pneumatic conveying; pressure drop. 1 Introductions neumatic conveying pipe is one o the methods or the solid particle transportation. Gases are used to carry the solid particle in the pipe. The carrier gas transers its momentum to the solid particles. As a result, the particle lows together with the carrier. However, due to the riction between gas to particles, particles to -particles, gas to wall and particle to wall interaction, the amount o the energy to be supplied to the carrier gases is much higher than the gas low only. The riction in the piping line is indicated by the pressure drop that occurs between the inlet and the outlet o the transport pipe. Thereore, it is essential to predict accurately the total pipeline pressure drop, or example, i we can predict say, p t = 800 ka ±25%, the resulting uncertainty is too great (600 to 1000 ka). This situation could lead to serious operating problems such as inadequate capacity and pipeline blockage. Received March 22 nd, 2009.
66 Y. Bindar, N.A. Sutrisniningrum & D. Santiani Most existing models, such as reviewed [1] are suited only to pure dilute-phase or dense-phase applications. However, the possible modes o low over long distances could occur between these two extremes such as dune-low, sliding beds, and irregular slugging. The pressure drop correlations within such these transition regimes are rarely reported by authors. The solid-gas transport in the pipeline must be able to be operated at wide range o low regimes at sae condition and low maintenance cost. High maintenance cost usually occurs due to high riction actor o the gas-solid particle in which it contributes to higher power consumption. Another reason to high cost is shorter lie time the ducting pipes that is caused by solid particle attrition, and abrasion [2]. Conveying the solid particle at dilute phase low regime is a common method that is applied in industries. However, there are some advantages also to convey the solid particles in the dense phase low regime. aul [3] identiies those advantages as (i) decreased energy usage due to signiicantly reduced volumes o air, (ii) reduced material breakage or degradation due to slower conveying velocities, (iii) reduced pipeline wear due to lower conveying velocities, (iv) smaller conveying pipeline sizes due to heavier line loading capabilities and (v) smaller dust collection requirements at the material destination due to lower conveying air volumes. It is our interest in this paper to ormulate the pressure drop correlation by conducting the experiment. The correlation is applied or dense, transition and dilutes regimes o the solid particle gas lows. The result o this work shows that a general orm o pressure drop correlation to cover all solid-gas low regimes has been successully developed. 2 Fundamental To predict the behaviors o a gas-solid pneumatic system, the low regimes and pressure drop, comprehensive characterization o the gas-solid low is needed. With this inormation, the strategy to minimize power consumption can be set. For an example, the gas low rate can be determined as minimum as possible to carry a required solid particle mass low rate. At minimum gas low rate, the attrition and abrasion can be also minimized. One o the most prominent actors in pneumatic conveying is power consumption or power loss, which can be represented by the pressure drop exhibited by the system. In most cases, the pressure drop in the multiphase low is higher than pressure drop in the one phase low. According to Fan and
Solid article-gas Flow in a Vertical Conveying ipe 67 Zhu [2], in the multiphase low, pressure drop is caused not only by riction o gas molecules, but also by interaction between gas and solids, between solids itsel, and external orces such as gravitational orce, and electrostatic orce. Those orces between solids and external orces cannot aect the gas motion directly, but it has eect on interaction system between gas and solid. The transport characteristic o multiphase low can be dierentiated by the interaction pattern between molecules in the system. Two distinguished types o gas-solid particles low pattern are dense-phase and dilute-phase low [4]. Dilute-phase system occurs in the system with lower solid particles low rate and higher gas low rate than dense phase. In the dilute-phase low, interaction between solid particles is insigniicant compared to that in dense phase. According to Fan and Zhu [2], dilute and dense-phase can be identiied by pressure drop to air velocity relation tendency. The solid-gas low in the pneumatic conveying system is generally characterized by the relation between pressure drop to liner gas velocity. The relation is strongly inluenced the solid particle mass lux in the low, G p. A typical orm o the relation is described by Figure 1. The comparison between dense and dilute-phase characteristics is shown in the Table 1. ressure drop per unit length Dense low Dilute low Linear gas velocity Gas low only Figure 1 General pneumatic conveying system characteristic [2]. The gas-solid low regimes in a vertical pipe are presented in the Figure 2. These low regimes are deined by solid particles concentration, gas velocity, gas and solid particles properties and equipment orientation. The pressure drop at each regime is correlated to these variables. Correlations to predict pressure drop in the gas-solid particles low, acquired by ormer researcher, are presented in Table 2. These correlations only valid in the dilute-phase region and at certain low range [1]. In this matter, only Khan and G p3 G p2 G p1 G p =0 G p = mass lux o solid particles, kg/(m 2 s), G p3 >G p2 >G p1
68 Y. Bindar, N.A. Sutrisniningrum & D. Santiani ei correlation is considered to work under wide range o low regimes. However, this correlation has not been able to arrive on exact situation or zero solid low in which the pressure ratio value should be one. Table 1 Comparison between dense and dilute-phase characteristic [5]. Criterion Dilute low Dense Flow Relati motion between High Low solid particles Solid particles interaction Weak strong erticle diusivity High Low Viscosity Caused by gas and solid particles interaction Caused by solid particles and gas to solid particles interaction Motion over the minimum transport velocity Dilute-phase Stable unstable Dense-phase uniorm transition annular extrusion slugging Decreasing gas velocity with constant solid particles concentration Figure 2 Flow regimes o the gas-solid particles low in a riser [4]. 3 Experimental Method and Apparatus This research was conducted by using sand solid particles. The gas carrier itsel is air. Air is blown to a vertical observation pipe. The observation pipe has the sizes o 0.0504 m diameter and 0.775 m length. The equipment consists o a blower with 20 m 3 /h low rate capability. The apparatus is equipped also with a solid particle Hooper-eeder, an observation pipe segment and a cyclone. The solid particle size ranges rom 250 to 600 m. The pressure drops and low regime data were acquired at varied gas low rate and solid particles low rate.
Solid article-gas Flow in a Vertical Conveying ipe 69 The equipment and the measuring devices are oriicemeter, manometer and rotary valve. The experimental set-up is shown schematically by Figure 3. The solid particles were sized with two standard screens or the sizes o 40 and 60 mesh. Beore being used, the solid particles were dried to remove water vapor contents. Cyclone Figure 3 Experimental apparatus setup. 4 ressure Drop Correlation Development The pressure drop correlations were developed by transorming graphical data in Figure 4 to a mathematical model. The dependent variable in the model is the ratio between the pressure drop o gas-solid particles low ( ) and pressure drop o gas low without solid particles ( ), /. The independent variables are Reynolds number o gas (N re ) and the solid particle Froude number (F rp ). The Reynolds number is deined by N re Observation ipe segment U D Hopper Oriemeter Blower where U, D,, and are gas supericial velocity, pipe diameter, gas density and viscosity respectively. The solid particle Froude number (F rp ) is calculated rom 2 U p F rp gd p (2) (1)
70 Y. Bindar, N.A. Sutrisniningrum & D. Santiani where Up, dp, and g are the particle velocity, particle diameter and the gravity constant. The particle velocity is obtained rom the particle mass low rate, mp, particle density p and the pipe diameter as ollows 4m p U p (3) d2 p p These two variables represent gas and solid particle low identiiers which inluence directly the pressure drop or gas-solid particle low. Most intention in building the pressure drop correlation or solid-gas low in pneumatic conveying pipe was paid to dilute phase low regimes. Some o the correlation or dilute phase regimes is shown in Table 2. The process variables that are involved in those correlation are luid mass lux G, solid mass lux G p, gas Reynolds number N re, solid Froude number F rp, pipe length L, pipe diameter D, pipe cross section area A, particle diameter d p, luid properties, solid properties, gravity constant g, pipe orientation angle, drag coeicient C D, and riction coeicient. Mathur and Klinzing [6] developed a pressure drop correlation or the dense phase regime as is shown by the ollowing equation D0.1 55.5 0.64 0.26 0.91 1- L U d p p U 2 p where is the gas volume raction in the gas-solid low in the pipe. Such this orm o the model has not shown a general orm that can be used in all regime condition. The variables o luid Reynolds number and solid Froude number already represent all geometry, properties and low characteristics o luid and solid. For this pressure correlation development, the dense phase regime is included. These two non-dimensional variables should also apply or dense phase regime as are shown or dilute phase. Our experimental data behavior in Figure 4 presents a kind o decay unction. This decay unction might be represented by an exponential or power unction. Actually, the unction behavior has two boundary conditions. First, / should be equal to one when F rp is equal to zero. Since there is no solid particles loaded at F rp =0, the pressure drop o the gas-solid particle low will same as pressure drop gas without solid particles at the same N re. Second, the (4)
Solid article-gas Flow in a Vertical Conveying ipe 71 gas-solid particles low resembles the ixed bed low when the gas velocity approaches to zero. According to the Ergun equation or ixed bed pressure drop model, at the dense-phase low, / should be diversely proportional to N re. While in the dilute-phase low (high N re ), / approach to a constant value at a spesiied value o F rp. While in the dense-phase low or N re approaching to zero, the value o / become very large. Some assumptions were applied or this model development. The voidage is uniorm at any segment o the vertical pipe. The mass solid particle velocity is constant. The linear solid particle velocity is also constant at any segment. Table 2 [1]. Author Cramp and riestley Farbar Ghosh and Chand ressure drop correlations developed by other authors or dilute phase Correlation G 0,46 L 0,4 U L 2,1 L 0,00092 U * A Up dp tan 3 CD 0,25-0,5 N re F rp 8 p 1 Hariu and Malstad 2 0,192 Up Gp U g D Jones and Allendro 2 2 p Up U L p L ( ) 2 g 2 g D Metha and Smith U p G p U G Razumov 2 p - L L U G p U p pupa D 2g ga Stemerding Gp L U e p D 1 L Us L Up 2 L F rp
72 Y. Bindar, N.A. Sutrisniningrum & D. Santiani Author Correlation Vogt and White 2 D k dp p N re Khan and ei 2 0,5 C d N D p re 2,66 p D F rp -0,5 Base on the the boundary approaching method, the pressure drop correlation is proposed as stated by Equation (5). The model is ormulated to ulill the boundary conditions speciied above. The experimental data are used to it this model. This model should work on all low regimes. / 14 12 10 8 6 4 2 0 1 af rp b Nre c 360 410 460 Figure 4 ressure drop as a unction o N re at various F rp 5 Result and Discussion N r e 0. 001 " Constants o the correlation, a, b, and, c o Equation (5) were obtained by itting this model to the present experimental data. The model was itted or dense and dilute phases. The best values o the model constants are given in Table 3. There are two types o low regimes at linear gas velocity between 0.1-0.12 m/s, slugging and annular. These are deined as the dense-phase low. The slugging regime occurs when the linear gas velocity is smaller than that in the 0. 012 0. 8 10 12 (5)
Solid article-gas Flow in a Vertical Conveying ipe 73 annular regime [4]. When the linear gas velocity is urther decreased, the slugging mode become packed bed mode whereas solids tend to move slowly through the line with a density close to the bulk density o the material. Table 3 Constants o developed model or each low region. Regime a b c Dense-hase 9.613 x 10 8-1630 8.751 Dilute-hase 1.096 x 10 6-287 3.988 Figure 5 Relation between pressure drop with linear gas velocity at mass various solid particle velocity rom the present experimental data. The pressure drop in vertical conveying pipe is contributed by two components. They are wall rictional loss component and gravitational component, Fan and Zhu (1998). The present experimental data exhibit the relation between the solid gas low pressure drops between the linear gas velocities, shown by Figure 5. At high gas velocities (dilute-phase low), pressure drop increases as gas velocity rises. It will increase the wall riction which is signiicantly higher than gravitational component. As the gas velocity is urther reduced, the gravitational component becomes more signiicant. Further decrease o the gas low rate, the regime alls to the dense-phase low. At this condition, the pressure drop is lited up or higher solid low rate. Moreover, the gravitational component becomes predominant. When the change o the pressure drop with the gas velocity becomes lat, the transition
74 Y. Bindar, N.A. Sutrisniningrum & D. Santiani region between dense and dilute phases starts to occur. The wall riction and the gravitational orce are both dominant. The transition line between the dense and dilute phase regimes can then be deined. The line is ormed by connecting the minimum pressure drop point at optimum gas velocity or each solid low rate. Thereore, mathematically this minimum pressure drop is obtained rom the pressure drop correlation o Equation (5) when the gradient o the pressure drop over the gas Reynolds number becomes zero at each value o Froude number as is stated by Equation (6). / N re Frp 0 This line equation is used to predict the transition regime in term o the gas Reynolds number at speciied solid particle Froude number. The transition regime line equation is then obtained as is deined by Equation (7). b 0.0056 N re N re -1.3035 e a b ln N F L re rp 0 N N 2 re re 0.0056 N re 0.073 1 a b N re F rp Table 4 Minimum pressure drop at U minimum or every F rp at transition between dilute-phase and dense-phase low. F rp U minimum minimum 9.97E-03 0.113 8.86 1.15E-02 0.114 10.50 1.29E-02 0.115 12.15 1.44E-02 0.121 18.42 1.59E-02 0.122 21.50 1.74E-02 0.123 28.46 c c (6) (7)
Solid article-gas Flow in a Vertical Conveying ipe 75 The minimum value o the pressure drop is given by the set o the gas velocity and solid particle Froude number. The results are presented in Table 4. From the constructed model above, the low regimes can be remapped rom the present experimental data in a continuous nomograph. This constructed nomograph is shown by Figure 6. The model lines and the present experimental data it closely. Figure 6 Nomograph o low regimes map separated by a transitional line or a vertical pneumatic conveying system. The gas is air and the solid particles are sand particle. The pipe diameter and length are 0.0508 and 0.775 m respectively. The solid points are the present experimental data. The solid lines are obtained rom Equation (5) at solid low rates (m p ) in the range o 0 to 2.453 gr/s. 6 Conclusions The transition low regimes o pneumatic conveying in a vertical pipe is successully deined using the constructed pressure drop correlation. The present pressure drop correlations are considered more general, robust and valid to the boundary conditions. The transition line between dense and dilute regimes is stated in a mathematical equation orm. A nomograph o the low regime o solid-gas conveying low rom dilute to dense with the exact line transition is constructed using the present pressure drop correlation.
76 Y. Bindar, N.A. Sutrisniningrum & D. Santiani Notations A = pipe cross section area, m 2 C D = drag coeicient D = pipe diameter, m d p = particle diameter, m = riction coeicient o gas-solid low = riction coeicient o gas low F rp = solid Froude number g = gravity constant, m/s 2 G = gas mass lux, kg/(m 2 s) G p = solid particle mass lux, kg/(m 2 s) L = pipe length, m m p = solid mass low, kg/s N re, = gas Reynolds number U = gas supericial velocity, m/s U p = characteristic solid velocity, m/s = pressure drop o gas-solid particles low, a = pressure drop o gas low, a = pipe orientation angle = gas volume raction = gas viscosity, kg/(m s) = gas mass density, kg/m 3 p = particle mass density, kg/m 3 Reerences [1] Khan, J.I. & ei, D.C., ressure Drop in Vertical Solid-Gas Suspension Flow, Ind. Eng. Chem. rocess Des. Develop., 12(4), 1973. [2] Fan, L.S. & Zhu, C., rinciples o Gas Solid Flows, Cambridge University ress, 1998. [3] aul, K.D., Dense hase neumatic Conveying Improving Eiciency, owder and Bulk Engr., p. 41, 1991. [4] Cheremisino, N.., Gas Flow ocket Handbook, Gul ublishing Co., Houston, 1984. [5] Soo, S.L., articulate and Continuum: Multiphase Gas Dynamics, Hemisphere, New York, 1989. [6] Mathur, M.. & Klinzing, G.E., The Dense and Extrusion Flow Regime in Gas-Solid Transport, Can. J. o Chem. Engr., 59:590 594, 1981.