\(Microsoft Word - \\322\\355\\344\\310 \\330\\307\\341\\310\) Al-Qadisiya Journal For Engineering Sciences Vol. 3 No. 2 Year 2010 212 MATHMATICAL MODELING OF MASS TRANSFER FROM AN IMMERSED BODY TO A FLUIDIZED GAS BED Zainab Talib Abidzaid al-Sharify Al-Mustansiryiah University/College of Engineering Environmental Engineering Department Iraq - Baghdad /Bab-AL- Muthem/P.O. Box 14150 Zainab_talib2009@yahoo.com Abstract: Fluidization process is widely used by a great assortment of industries worldwide; one of these processes is the mass transfer from an immersed body to a fluidized gas bed. This work presents an experimental study of a continuous gas-solid fluidized bed with a porous material placed at the bottom of the column to support the packing material. Sand-air-naphthalene system has been used in this work. Sand with sizes distributed between 75-250 microns was used as solid fluidizing particles and air was used for fluidization in a 70 cm height and 8 cm inside diameter fluidization Column. Naphthalene was selected for this study as the immersed object, this have been done by making a spheres of wood of 2.9 cm outside diameter and coating this spheres wood with Naphthalene by dipping this spheres into a bath of molten naphthalene (at about 900C). An empirical correlation was developed for mass transfer of naphthalene vapor into air-sand fluidized bed by using experimental data of many variables such as temperature, air velocity, and sand particle size. The experimental results of the mass transfer in the present work have been compared in curve in Yokota,s coordinate with many documented experimental literatures data. The comparison gave a very good agreement, and show that Sherwood number increased slowly with the increase in gas velocity at constant surface temperature and particle size. Key Words: fluidization, mass transfer, sand-air-naphthalene system, Ziegler equation, Sherwood number, minimum fluidizing velocity, mass transfer coefficients. غاطس الى طبقة غازية مميعة جسمنتقال المادة من النمذجة الرياضية الشريفي عبدزيد زينب طالب الجامعة المستنصرية كلية الھندسة قسم ھندسة البيئة :الملخص سم ان عملية التميع واسعة االستعمال في الصناعات العالمية المتعددة واحدة من هذه العمليات هي انتقال المادة من ج الصلب مع مادة مسامية وضعت -لغازا للتميع المستمر لنظام هذا العمل يقدم دراسة تجريبيةان .غاطس الى طبقة غازية مميعة ان الرمل المستعمل كجسيمات الصلب .نفثالين-هواء- تم في هذا العمل استخدام نظام رمل. مواد الحشوةفي أسفل العمود لدعم تم استخدام عمود تميع زجاجي .ان سائل التميع كان الهواء، مايكرون ٢٥٠ - ٧٥ة تتراوح بين المتميع استخدم بأحجام مختلف حيث تم طالء كرات خشبية ، تم في هذه الدراسة استخدام المادة المغمورة وهي النفثالين. سم 8سم وبقطر داخلي 70بأرتفاع تم تطوير . درجة سليزية ٩٠ن المنصهر بدرجة حرارة حوالي سم وذلك بإنزال هذه الكرات في حمام النفثالي ٢.٩قطرها الخارجي Al-Qadisiya Journal For Engineering Sciences Vol. 3 No. 2 Year 2010 212 وذلك بدراسة العملية لعدة ، عالقة رياضية تربط معامل إنتقال المادة لبخار النفثالين الى الطبقة الغازية المميعة من الهواء والرمل ألنتقال المادة في العمل الحالي تمت ان النتائج التجريبة. معدل جريان الهواء وحجم الدقائق،درجة حرارة السطح ك متغيرات وتم وضعها في رسومات على احداثيات ، هرت مطابقة جيدة جداظوهذه المقارنة ا. مقارنتها مع التجارب العملية الموثقة علميا .حيث تم ايجاد ان رقم شيروود يتزايد ببطء مع زيادة سرعة الغاز بثبوت حرارة السطح والجسيمات، يوكوتاس Notations Units Notations Symbols mole /m3 Concentration at the surface. = Cs mole / m3 Bulk concentration. = Cb Relative and mean relative mass capacity respectively = Cm , mC kg / kg Specific mass capacity of gas and particles respectively = Cmf ,Cms m2 / s Molecular diffusivity in a gas = Df m2 / s Effective and mean effective diffusivity in a particle respectively = Ds , sD m2 /s Diffusivity of transferable component and at 00C respectively. = Dv, Dv0 m Diameter of the bed. = d m Fluidizing particle diameter. = dp m/s2 Gravitational force. = g kg /m2. s Gas mass velocity. = G kg /m2. s Gas mass minimum velocity. = Gmf kg / m2.s Surface-to-inert bed mass transfer coefficient = ky' kg / m2.s Surface-to-bubble mass transfer coefficient = kyb' kg / m2.s Surface-to-packet mass transfer coefficient = kyp kg / m2.s Surface-to-packet mass transfer coefficient for Cms=0 = kyp' m/s Mass transfer coefficient. = kg m Length of the column = L kg Particle mass 3 / 6s s sm dπ ρ= = ms m3 / kg Mass capacity of particles = Ms kg/m2.s Total surface-to-bed mass flux = N mm Hg Bed pressure drop. = ∆P mm Hg Saturation partial pressure. = Ps - Reynolds number based on the diameter of the inert particles. = Rep m2. s /kg Mass transfer packet and contact resistance respectively = Rmp, Rmw - Sherwood number. kg ds / Dv = Sh - Sherwood number in empty bed. = She - Sherwood number in packet bed. = Shp 0C Temperature = T 0C Saturation partial temperature. = Ts m/s Minimum fluidizing velocity. = Umf m/s Gas velocity = U kg/kg Concentration of gas (mass of transferred substance per unit mass of inert gas) = Y Greek Letters µ = Viscosity kg/ s.m µo = Viscosity of air at 0C kg/ s.m ρ = Gas density. kg/m3 ρp = Particle density. kg/m 3 , sfρ ρ = Gas and solid density respectively kg/m 3 ψ = Sphericity. - τ = Time s bb ττ , = Bubble residence contact time and its mean value respectively s Al-Qadisiya Journal For Engineering Sciences Vol. 3 No. 2 Year 2010 212 pp ττ , = Packet residence contact time and its mean value respectively s ε = Porosity - εp = Packet porosity - Subscripts b Bubble f Gas m Mass (minimum) p packet s Solid(particle) Introduction: Fluidized beds are commonly employed in chemical, biochemical and petrochemical industries in processes such as hydrocarbon cracking, drying of solid particles, combustion and gasification of coal and biomass, synthesis reactions and coating of particles. Gas-solid fluidized systems are characterized by temperature uniformity and high heat transfer coefficient due to the intense mixture of the solid material with the gas bubbles normally present (Pécora and Parise, 2006). A number of correlations for mass transfer in fluidized beds have been proposed, most of these involve a single-line relationship between Reynolds number and the product of Sherwood number by some power of Schmidt number (Wankhede, 2009). Resnick (Resnick, 1949) calculated the mass transfer coefficient of naphthalene crystals of five different sizes ranged from 250 to 1000 microns in air, hydrogen, and carbon dioxide at a temperature of 298K and rates between 0.01 and 1.5 kg/m2.s. Gamson (Gamson, 1951) utilized the available mass transfer data for packed and fluidized beds related the mass transfer modulus to the modified Reynolds group. Gupta and Thosad (Gupta and Thosad, 1962) correlated the mass transfer factor with the conventional Reynolds number utilizing all the available data. Markova and Martyushin (Markova and Martyushin, 1965) studied the effect of fluidized particle size on mass transfer coefficient with particle diameter of 0.565, 0.488 and 0.347 mm. They concluded that the increasing air velocity increases the mass transfer coefficient. Shirai (Shirai, et al., 1966) studied heat and mass transfer between fluidized bed and surface of single sphere fixed in the bed. Sand was employed as fluidizing particles for mass transfer study and the solid sphere was made of brick and the system used is air-water system. They found that the value of Sherwood number is only 1.5 times that for mass transfer between particles and fluid. Ziegler and Holmes (Ziegler and Holmes, 1966) studied mass transfer from fixed surface to gas fluidized beds. Mass transfer coefficients were measured for the diffusion of water vapor from a saturated porous sphere into various air-fluidized beds of solid particles. Naphthalene diffusion from coated flat plate into fluidized beds was also studied. Gunn (Gunn, 1987) studied the mass transfer in gas-solid fixed and fluidized beds operated in a wide range of velocities and porosities. He developed a theoretical correlation that expresses the mass transfer between the particles and fluids processes. Kaneko (Kaneko et al., 1999), Rhodes (Rhodes et al., 2001) and Kafui (Kafui et al., 2002) studied the general characteristics of a fluidized bed, such as the gradual change in particle characteristics and size distribution in the bed, and also studied the impact of inter particle forces on fluidization. Schmidt and Renz (Schmidt and Renz, 2005) investigate numerical analysis of the heat transfer between fluidized bed of mono-dispersed glass beads and an immersed heater tube. An Eulerian approach has been used for the solution of the mass, momentum and energy equations of both phases. Pécora and Parise (Pécora and Parise, 2006) presents an experimental study of a continuous gas-solid fluidized bed with an immersed horizontal tube. Silica sand of 254µm diameter was used as solid particles and air was used for fluidization in a 900mm long and 150mm wide heat exchanger. An empirical correlation for the heat transfer coefficient was proposed as a function of solid particle and gas mass flow rate, number of baffles and gas velocity. Wankhede (Wankhede, 2009) study the effect of surface temperature on average heat transfer coefficients in a sound assisted fluidized bed of fine powders. He found that for both coarse grained and fine particles, the heat transfer rates can be improved by increasing Al-Qadisiya Journal For Engineering Sciences Vol. 3 No. 2 Year 2010 212 the surface temperatures. He presents the data as a function of excess air velocity and sound pressure level. The objective of this work is to: 1- Writing a mathematical model for mass transfer from an immersed body to a gas fluidized bed depending on variables affecting the mass transfer. 2- Study the effect of different factors on the gas-solid system, such as fluid properties, fluidized properties, and nature of the flow, as well as the effect of each one on the others. 3- Determine the dependence of mass transfer coefficient on fluidized bed variables. Many variables effect mass transfer have been investigated such as: air velocity, sphere surface temperature, size of fluidizing particles and sphere size. 4- Predicate the mass transfer coefficient from the knowledge of mass transfer coefficient in the absence of fluidizing particles, plus a term that describes the effect of fluidizing solid particles on transfer rate coefficients. Minimum Fluidizing Velocity When the gas is passed upwards through a fluidized bed unrestrained at its upper surface, the pressure drop increases with gas velocity increasing, the drag on an individual particle excess the force exerted by gravity. Then an excess pressure is required to free the particles that are interlocked at the fluidized state and theoretical pressure drop. The velocity at the point that the pressure drop falls back is called the minimum fluidizing velocity (Umf) (Gupta and Sathiyamoorthy, 1999). Leva (Leva et al., 1951) worked with round and sharp sands of 0.05-0.40 mm using 0.1 m diameter with various depths fluidized by air. He noted that the smaller particles require an extra of energy for fluidization. The Wen and Yu produced an empirical correlation for Umf for gas fluidization. Wen and Yu (Wen and Yu, 1966) correlation is often taken as being most suitable for particles larger than 100 µm, whereas the correlation of Baeyens and Geldart (Baeyens and Geldart, 1974) is best for particles less than 100µm, which is shown in eq. 1: 1.8 0.934 0.934 0.87 0.066 ( ) 110 p p mf d g U ρ ρ µ ρ − = (1) Model for Mass Transfer in Fluidized Bed The process of mass transfer from an immersed body to a gas fluidized bed has not yet been intensively investigated. To describe the process mathematically Baskakov (Baskakov and Suprun, 1970) and Prozorov (Prozorov, 1976) assumed that mass is transmitted from the surface by packets of particles and by gas bubbles as follows: (1 ) y yp yb k f k f kο ο′ ′ ′= − + (2) Where: b pb f ο τ τ τ = + (3) In contrast to heat transfer theory where the heat within a packet is transferred through gas and particles and the accumulation of heat within particles plays a dominant role. These workers assumed that mass within a packet is transferred only by gas between particles occurs. Thus the mass transfer coefficient to a packet was found to be (Markova and Martyushin, 1965; Baskakov and Suprun, 1972; Baskakov et al., 1973): 1/ 2 2 fyp p D k ρ πτ′         = (4) 1/ 2 2 bfyb b D k ρ πτ′         = (5) Al-Qadisiya Journal For Engineering Sciences Vol. 3 No. 2 Year 2010 212 It must be remembered that all the above considerations apply to an inert fluidized bed (Baskakov, 1974). If adsorption of a transported substance onto the particles takes place the mass transfer coefficient rises and the ratio (ky/kyf ) may then reach values from 3 to 15 (Ziegler and Holmes, 1966). For such cases, on the basis of the packet theory and allowing for mass accumulation on particles, Yokota (Yokota et al., 1975) derived the following expression: 1/ 2 (1 )p s s pf yp f p D M k ε ρ ε ρ τ         − = (6) Eq. 6 transformed into the dimensionless form, as shown below: 1/ 22(1 )p s s p pf M L Sh D ε ε ρ τ         − = (7) In this work the mass capacity process was investigated and described on the basis of the modified packet model including the mass contact resistance. For the contact resistance control region the alternative simplified packet model was developed. In order to derive the simplified packet model equations, two assumptions are made: 1- For sufficiently short packet contact times which correspond to vigorous fluidization and for relatively large particles, only the first layer of particles, i.e. those in contact with the surface, participate in surface-packet mass transfer. 2- During the time that a packet remains at the surface, a particle in the first layer adsorbed to the surface. Dimensional Analysis: The dimensionless group, Y, is a function of all the variables and dimensionless constant which take into account the influence of particles motions. These factors may be arranged in a suitable form of dimensional analysis using Buckingham’s π theorem (Buckingham, 1914), such as: ( , , ( ), , , ( ), )p p mfY f d G G gψ ρ ρ ρ µ= − − (8) (9) The common groups for mass transfer are Sherwood number, Schmidt number and Reynolds number. In Buckingham’s π theorem, the dimensions of a physical quantity are associated with mass, length and time, represented by symbols m, L and θ respectively, each raised to rational powers. The number of dimensionless groups obtained from the dimensional analysis are equal to the number of variables, n=5, minus the number of fundamental dimensions, r=3, and hence two dimensionless groups will be obtained. In term of fundamental dimensions: (10) From these results we obtain (11) 2 ( ) ( ) ( )( ) [ ] [ ] ( ) p p pb emf mf g d d G G Y G G ρ ρ ρ ψ ψ µ −− −= − (12) From the above equation, one can notice that the first term is the invert of Froude number (Fr) and the second is the modified Reynolds number (Re). 2 6 2 2 [ ] [ ] [ ] [ ] [ ]1 a b c d e m m L m L LL L θθ θ = 2[ ] [( ) ] [ ] [ ] [ ]e b b b e b ep p mfY d G G gψ ρ ρ ρ µ − − − −= − − [ ] [( ) ] [ ]a b c d ep p mfY d G G gψ ρ ρ ρ µ= − − Al-Qadisiya Journal For Engineering Sciences Vol. 3 No. 2 Year 2010 212 Experimental Set-Up and Method Sand-air-naphthalene system has been used in this work. Sand was employed as fluidizing particles, which can be regarded as a non-absorptive material. A sand bed material was employed in this investigation with three different particle sizes, with range of 75-250 micron, in order to get a smooth fluidization. The properties of sand particles used in this work are shown in Table 1. The immersed object used has a spherical shape of 2.9 cm outside diameter made of wood, which was coated with hard smooth surface of naphthalene. This was done by dipping the spheres into a bath of molten naphthalene at about 90°C. The immersed object was fixed in the center of the column by suspending it with a steel rod. The spherical shape was used in order to minimize the dead zone around the immersed object, and because spherical shapes have many applications in the industrial. A photographic picture of the apparatus used is shown in Figure 1. The experimental system, as outlined in Figure 2, consists of the main components: fluidization column, air compressor, air flow meter, U-tube manometer, bed material (sand), immersed work piece, heating equipment (heating element, variac), and temperature measurement device. The fluidization Column was made of glass column (Q.V.F) 8 cm inside diameter and 70 cm height. A porous material was placed at the bottom of the column to support the packing material. Air compressor was used to supply air with a surge tank to store the air and minimize the fluctuation. An automatic regulator in the compressor was used to regulate the pressure of the air inside the tank. The amount of air which left the compressor was controlled by the use of the tank and valve. A calibrated air flow meter was used to measure the air flow rate which entered the column. The range of the air flow meter is 0-16 m3/hr. The pressure drop across the bed was measured by the use of U-tube manometer which made of glass with total length of 0.75 m. The manometer was placed on a wide sheet of wood with a measuring tape for the measurement of the level difference of the liquid (water) inside the tube. An electrical heater placed inside 2" Q.V.F. glass tube has been used as the heating equipment. The variation in heat supplied from the heater was controlled by the use of a variac connected directly to the heater. Two thermocouples were used for temperature measurement; the thermocouples were located in two different locations in order to measure the temperature about 3 cm under and above the spheres. These thermocouples were connected to digital readers that show the value of temperature. Experimental Procedure The pressure drop of the bed was determined by subtracting the pressure drop of distributor from total pressure drop that are found for a range of superficial gas velocities after loading known weight of sand particles having known diameter into the bed to a static level of 30 cm. Curves of pressure drop across the bed versus superficial gas velocity are shown in Figures 3, 4, 5 and 6. Mass transfer coefficient value in empty bed has been determined experimentally, by placing two thermocouples and other devices and connected them to the column. The compressor started blowing air into the tank until it reached the desired pressure to turn the compressor off by the automatic regulator. The tanks valve was turned on. The air flowed through the rotameter to the bed until rotameter read a constant desired value of the air flow rate. At the same time the heater was turned on for the desired power which was controlled by the use of the variac. The measurements of the pressure drop across the bed were made by the use of the U-manometer. When the conditions reach to steady state (constant flow rate and constant temperature), the coated sphere was lowered inside the column 15 cm above the distributor surface. Every 5 minutes, the sphere was taken out of the bed and the change of weight was measured by digital balance. This have been repeated for arrange of air superficial velocities and a range temperatures. The Mass Transfer coefficient value from the sphere sand to the fluidized bed has been determined experimentally, by weighting a quantity of sand and poured it into the column from the top for a known and constant height of 30 cm for all runs carried in the work. Two thermocouples in their place were connected to the column. The compressor started blowing air into the tank until it reached the desired pressure to turn the compressor off by the automatic regulator. The tanks valve was turned on. The air flowed through the rotameter to the bed until rotameter read a constant desired value of the air flow rate. At the same time the heater was turned on for the desired power that was controlled by the use of the Al-Qadisiya Journal For Engineering Sciences Vol. 3 No. 2 Year 2010 212 variac. When conditions reach to steady state (constant flow rate and constant temperature); the coated sphere was lowered inside the column 15 cm above the distributor surface. Results And Discussion: A set of experiments at different air velocities and different temperatures were performed for mass transfer in empty bed (air stream only), to check the results with previous works. Operational conditions and experimental results for mass transfer coefficient for each experimental test are presented in Table 2 and 4. From Table 4 it can be seen clearly that experiments were carried out at temperature below 70℃, to avoid naphthalene melting. A set of experiments were performed to determine the value of mass transfer coefficient from the sphere to the fluidized bed, the experimental conditions and results for this experiments are listed in Table 3 and 5. The air velocity is chosen to be within the range (1-1.4) Umf, because this range of flow is usually used in industrial practice. The particle size of sand was selected to be as fine particles in order to get a smooth fluidization. ntal ResultsCorrelations of the Experime Many variables are influence mass transfer coefficient such as diffusivity of the active component through the fluid, superficial flow rate of the fluid, density and viscosity of the fluid, and shape and size of the spaces between the particles in the bed. A number of assumptions were made to get accurate relationship of the variables influence on mass transfer coefficient: 1- Neglect the abrasion effects and assume the weight loss of naphthalene is mainly due to evaporation. 2- Void fraction of fluidizing sand particles equals the void fraction at minimum fluidizing velocity. 3- Partial pressure of naphthalene at the surface everywhere equal to the saturation partial pressure of vapor at the surface temperature of the solid sphere, the partial pressure of naphthalene at the bulk of air stream was equal to zero. Change in surface area of the sphere along the experiment was neglegted. Surface temperature of the solid sphere everywhere equal to the average value of the temperature reading of the thermocouples below and above the sphere. The experimental results must be correlated by: 1-The viscosity of air can be calculated from eq.13, where µo is the viscosity of the air at 0℃ which equals to 0.017 in centipoises and n equals to 0.677 (Perry, 1973): 273 n T ο µ µ       = (13) 2- Experimental value of mass transfer coefficients was calculated from eq. 14, in which Cb is equal to zero (Perry, 1973, Prins et al., 1985): ( )g s bN k C C= − (14) 3- The correlation for diffusivity of naphthalene vapor in air with temperature is made by eq. 15, where the diffusivity of naphthalene vapor in air at 0℃ was taken equal to 0.0513 cm2/s and m=1.823(Perry, 1973): 273 m Dv T Dv ο       = (15) 4- Vapor pressure of solid naphthalene is given by equation 16 where Ps in mHg and Ts in K, for the range of (0-80℃) (Perry, 1973): (16) 5- Values of Sherwood number for mass transfer from the sphere to the bed of fluidized particles were calculated by the eq. 17; in which f(y) describes the effect of particles motion on transfer rate, and y is a dimensionless group determined by dimensionless analysis (Perry, 1973): 3729.3 log 11.450s s P T = − + Al-Qadisiya Journal For Engineering Sciences Vol. 3 No. 2 Year 2010 212 ( )eSh Sh f y= + (17) 6- The value of Sherwood number for mass transfer in empty bed calculated from equ.18, where C1, C2 and C3 are constants and determined from the experimental results in empty bed (Ranz, 1952) 32 12 Re cc e pSh C Sc= + (18) Equation 18 for mass transfer in empty bed was fitted for air flow through fluidized bed, by assuming the limiting value of Sherwood number, at zero Reynolds number, is equal to 2 because it agrees with the theoretical approach. The experimental results were correlated by using statistical fitting, as shown below: 1/ 2 1/32 0.657 Ree pSh Sc= + (19) With correlation coefficient of 0.9907 and percentage of average errors of 0.62%. For experiments that carried out at minimum fluidizing velocity, the value of the dimensionless group, Y, is inconsistent with other experiments due to the term (G-Gmf) which is equal to zero at minimum fluidizing velocity, so results obtained at minimum fluidization are neglected. The term f(y) in equation 17 is chosen as a power function of Y , that is: 2 1( ) C f y C y= (20) Two attempts have been made to correlate the experimental results: 1. The first attempt was made by choosing the dimensionless function, Y, as given by Ziegler (Ziegler and Holmes, 1966), i.e.: 2 1 2 ( ) [ ] ( ) ( ) Cmf e p p G G Sh Sh C d g µ ψ ρ ρ ρ − = + − (21) Eq. 21 was fitted for air flow through fluidized bed using the experimental results at minimum fluidization velocity, and was correlated by the following equation: 014.0 2 6.9                                 − − += g pp d mf GG eshsh ρρρψ µ (22) With the correlation coefficient of 0.976 and percentage of average errors of 1.57%. Fig. 7 shows a comparison of eq. 22 with the experimental data. It can be seen from this figure, that the correlation suggested by Ziegler and Holmes don’t fit the experimental results of this work. 2. The second attempt was made by taking the dimensionless group, Y , as obtained from the dimensionless analysis, i.e.: 32 1 2 ( ) ( ) ( )( ) [ ] [ ] ( ) CCp p p mf e mf g d d G G Sh Sh C G G ρ ρ ρ ψ ψ µ − − = + − (23) Eq. 23 was fitted using statistical fitting for the experimental results of air flow through fluidized bed at minimum fluidization velocity, the constants of the equation C1, C2 and C3 have been found to be equal to 16.8574, 0.07497 and 0.1284 respectively. With the correlation coefficient of 0.914 and percentage of average errors of 1.544 %. Fig. 8 shows comparison of eq. 51 with the experimental data. From this Al-Qadisiya Journal For Engineering Sciences Vol. 3 No. 2 Year 2010 212 figure it can be notice that this correlation shows a better agreement with experiments, in which 97% of the points have an error less than 25%, consequently this correlation obtained from the present work. Comparison of Experimental Results with Previous Works and Model Solid mass capacity has an essential affect on surface-to-fluidized bed mass transfer. For (Cms=0) low mass transfer coefficients are attained and there is no similarity with surface-to-bed heat exchange. In the case of non-zero solid mass capacity, mass transfer coefficients are greater and for small values of (Cms) they may be predicted from the theory proposed by Yokota (Yokota, 1975). For relatively large values of ( psmsdC τ/ 2 ) greater than 10-5 m2/s the contact resistance is dominant and the surface-to-packet mass transfer coefficient is inversely proportional to (ds). For small values of psmsdC τ/ 2 less than 10-10 m2/s the packet resistance predominates and the surface-to-packet mass transfer coefficient is independent of particle size as represented in Table 6. Fig. 9 show a comparison between the experimental results of mass transfer and those obtained from documented experimental literatures data; this comparison are represented in Yokota,s coordinate. For very large mass capacities, Sherwood numbers predicted from Yokota,s theory considerably overestimate experimental ones, so there must be an additional mass transfer resistance. It is apparent that this resistance depends on particle size and rises as (ds) increases, which agrees with the contact resistance concept and don’t show any appreciable (ds) dependence. Studying the Variables Affecting Mass Transfer Coefficient: Many variables effect mass transfer have been investigated such as: air velocity, sphere surface temperature, size of fluidizing particles and sphere size. The range of sphere surface temperature varied from ambient temperature to a temperature below the melting point of naphthalene. Figs. 10 and 11 show the effect of air temperature on Sherwood number, Fig. 12 shows the effect of air flow rate on Sherwood number, Figs. 13, 14 and 15 show the effects of both air temperature and particle size on Sherwood number, the effects of both air flow rate and particle size on Sherwood number are showed in Figs. 16, 17 and 18 the effects of both particle size and different temperature on Sherwood number are showed in Figs. 19, 20, 21 and 22. Conclusions: In this work, a mathematical model for mass transfer was introduced depends on one dimensionless group which results from the merge of the two dimensionless groups derived in this work and was fitted for air flow through fluidized bed using the experimental results at minimum fluidization velocity. The mathematical model had successfully describes the effects of different parameters on the mass transfer coefficient such as air velocity, sphere surface temperature, size of fluidizing particles and sphere size, when compared with the experimental results and gives a good improvement rather than Ziegler equation. Sherwood number increased slowly with the increase in gas velocity at constant surface temperature and particle size, although it is increasing with decreasing surface temperature of the sphere at constant U/Umf and particle size, and Sherwood number increased with decreasing particle size at constant U/Umf and temperature. The ratio of Sherwood number for mass transfer in the presence of solid particles (fluidized bed) to that in absence of solid particles (empty bed) was found to be varied up to 30. References: Al-Qadisiya Journal For Engineering Sciences Vol. 3 No. 2 Year 2010 212 1. Baeyens J. and Geldart D., 1974, "An Investigation into Slugging Fluidized Beds", Chem. Eng. Sci. Vol. 29, pp. 255. 2. Baskakov A. P. and Suprun V. M., 1970, “Mass transfer from a freely moving single sphere to the dense phase of a gas fluidized bed of inert particles”. Sov. Chem. Ind. Vol. 9, pp. 61. 3. Baskakov A. P., 1974, “Critique of the modified packet theory”. Journal of Engineering Physics and Thermophysics, Vol. 28, No. 5, pp. 584-586. 4. Baskakov A. P., B.V. Berg, O.K. Vitt, N.F. Filippovsky, V.A. Kirakosyan, J.M. Goldobin and V.K. Maskaev, (1973), “Heat transfer to objects immersed in fluidized beds”. Powder Technology, Vol. 8, pp. 273-282. 5. Baskakov, A. P. and Suprun V. M., 1972, "The determination of the convective component of the coefficient of heat transfers to a gas in a fluidized bed". Int. Chem. Eng., Vol. 12, pp. 53. 6. Buckingham, Edgar, 1914, "On Physically Similar Systems: Illustrations of the Use of Dimensional Analysis". Phys. Rev. Vol. 4, pp. 345. 7. Gamson B.W., 1951, “Heat and mass transfer in fluidized and packed beds”, Chem. Eng. Progress, vol. 74, no. 1, pp. 19-28. 8. Gunn D. J., 1987, "Axial and Radial Dispersion in Fixed Bed ". Eng. Sci., Vol. 42, pp. 363-373. 9. Gupta C.K. and Sathiyamoorthy D., 1999, "Fluid Bed Technology in Material Processing". CRC Press, Florida, pp. 38. 10. Gupta, A.S. and Thodas, G., 1962, “Liquid-phase mass transfer in fixed and fluidized beds of large particles”. A.I.Ch.Eng., Journal, Vol. 20, No. 1, pp. 20–26. 11. Kafui K.D., Thornton C. and Adams M.J., 2002, "Discrete-Continuum Fluid Modeling of Gas- Solid Fluidized Beds", Chemical Engineering Science, Vol. 57, pp. 2395-2410. 12. Kaneko Y., Shiojima T., and Horio M., 1999, "DEM Simulation of Fluidized Beds for Gas- Phase Olefin Polymerization", Chemical Engineering Science, Vol.54, No. 24, pp. 5809- 5821. 13. Kopec J., 1981, “The Kinetics of a Low-Temperature Drying in a Fluidized Bed”. Ph. D. Thesis, Warsaw Technical University. 14. Leva M., Weinfraub M., Grummer M., Pollchik M. and Storch H. H., "Fluid Flow through Packed and Fluidized Systems". U. S. Bureau of Mines Bulltin, 504(1951). 15. Markova M. N. and Martyushin I. G., 1965."An investigation of mass transfer during the vaporization of water from the surface of objects immersed in a fluidized bed of finely divided particles", Chem. Eng. Vol.5, pp. 20-22. 16. Pécora A. A. B. and Parise M. R., 2006, “An Analysis of Process Heat Recovery in a Gas-Solid Shallow Fluidized Bed”. Brazilian Journal of Chemical Engineerin,g Vol. 23, No. 04, pp. 497 - 506. 17. Perry R.H. and Chiton C.H., 1973, Chemical Engineers Handbook. (5th Edition). McGraw- Hill, New York, NY. 18. Prins W., Casteleijn T. P., Draijer W. and. Van Swaaij W. P. M, 1985,” Mass transfer from a freely moving single sphere to the dense phase of a gas fluidized bed of inert particles”. Chem. Eng. Sci., Vol. 40, No. 3, pp. 481-497 Al-Qadisiya Journal For Engineering Sciences Vol. 3 No. 2 Year 2010 212 19. Prozorov E. N., 1976, “kinetics of the removal of liquid from capillary porous bodies in a fluidized bed under nonisothermal conditions”. Izuest. VUZ-ov Khim. Technol., Vol. 30, No. 6, pp. 1127–1137. 20. Ranz W. E. and Marshall W. R., 1952, "Evaporation from Drops". Chem. Eng. Prog. Vol. 48, pp. 141-173. 21. Resnick W. and White R. R., 1949, “Mass transfer in systems of gas and fluidized solids”. Chem. Eng. Prog. Vol. 45, pp. 377. 22. Rhode, M.J., Wang X.S., Nguyen M., Stewart P., and Liffman K. (2001),"Use of discrete element method simulation in studying fluidization characteristic: influence of antiparticle force", Chemical Engineering Science, Vol. 56. p. 69. 23. Schmidt A., Renz U., 2005, “Numerical prediction of heat transfer between a bubbling fluidized bed and an immersed tube bundle”, Heat-Mass Transfer, Vol. 41, pp. 257–270. 24. Shirai, T., Yoshitome, H. and Shoji Y., 1966, “Heat and Mass transfer on the Surface of Solid Spheres Fixed within Fluidized”. Kagaku Kogaku, Vol. 4, pp. 880 – 884 25. Wankhede U. S., 2009, “Effect of Increase in Surface Temperature on Heat Transfer in a Sound Assisted Fluidized Bed of Fine Powders”. International Journal of Engineering Studies, Vol. 1, No. 1, pp. 31–38. 26. Wen Y.C. and Yu Y.H., 1966, “Mechanics of Fluidization”, Chemical Engineering Progress Symposium Series, Vol. 62, pp. 100-111. 27. Yokota T., Hidaka Y. and Yasutomi T., 1975, “Mass transfere”, Kagaku Kogaku Ronbunshu, Vol.1, p. 399. 28. Ziegler, E. N. and Holmes J. T., 1966,” Mass transfer from fixed surfaces to gas fluidized beds”. Chem. Eng. Sci., Vol. 21, pp. 117-118. Al-Qadisiya Journal For Engineering Sciences Vol. 3 No. 2 Year 2010 205 Table 1: Property of Sand Particles Particle Density (Kg/ m3) Range Particle Size (micron) Range of Particle Size (micron) 2600 112.5 75-150 2600 165 150-180 2600 215 180-250 Table 2: Operational conditions for experiment of mass transfer in empty bed without naphthalene Test 1 For sphere of diameter 2.9 cm and weight 8 gm, air flow rate 2.8 m3/hr, ambient temperature 39 0C, pressure drop 0.9 cm H2O Test 2 For sphere of diameter 2.9 cm and weight 8 gm, air flow rate 2.8 m3/hr, ambient temperature 39.1 0C, pressure drop 0.9 cm H2O Test 3 For sphere of diameter 2.9 cm and weight 8 gm, air flow rate 3.7 m3/hr, ambient temperature 39.1 0C, pressure drop 1.4 cm H2O Time (min) Wt. Loss (gm) T2(℃) T1(℃) Wt.(gm) Wt. Loss (gm) T2(℃) T1(℃) Wt.(gm) Wt. Loss(gm) T2(℃) T1(℃) Wt.(gm) 0 - 39.0 39.0 10.21 - 51.3 51.3 10.2 - 66.0 66.0 12.45 5 0.087 39.1 39.1 10.12 0.2884 51.1 51.2 9.93 1.0717 66.1 66.2 11.38 10 0.079 39.1 39.0 10.04 0.2514 51.3 51.4 9.68 1.0215 66.1 66.2 10.36 15 0.072 39.0 39.0 9.968 0.3102 51.3 51.4 9.37 0.7172 66.1 66.0 9.637 20 0.083 39.0 39.1 9.884 0.1913 51.2 51.2 9.17 0.6251 66.0 66.1 9.013 25 0.079 39.0 39.0 9.805 0.1241 51.1 51.3 9.05 0.6765 66.1 66.0 8.337 Note: T1 = Temperature below the sphere, T2 = Temperature above the sphere. Al-Qadisiya Journal For Engineering Sciences Vol. 3 No. 2 Year 2010 212 Table 3: Operational conditions for experiment of mass transfer in fluidized bed without naphthalene Tests Test 1 for sphere of diameter 2.9 cm and weight 8 gm, air flow rate 4 m3/hr, ambient temperature 390C, pressure drop 21 cm H2O Test 2 for sphere of diameter 2.9 cm and weight 8 gm, air flow rate 4.8 m3/hr, ambient temperature 39.30C, pressure drop 23 cm H2O Test 3 for sphere of diameter 2.9 cm and weight 8 gm, air flow rate 5.2 m3/hr, ambient temperature 39.40C, pressure drop 25 cm H2O Time (min) Wt. Loss(gm) T2(℃) T1(℃) Wt.(gm) Wt. Loss(gm) T2(℃) T1(℃) Wt.(gm) Wt. Loss(gm) T2(℃) T1(℃) Wt.(gm) 0 - 39.1 39.1 12.74 - 51.2 51.2 12.35 - 66.1 66.2 15.56 5 0.1147 39.0 39.1 12.63 0.45317 51.0 51.0 11.89 1.5197 66.1 66.1 14.04 10 0.1954 39.0 39.0 12.43 0.48788 51.1 51.2 11.40 1.4178 66.0 66.1 12.63 15 0.1721 39.1 39.2 12.26 0.39927 51.1 51.1 11.01 1.5503 66.1 66.0 11.07 20 0.1229 39.1 39.0 12.13 0.47188 51.0 51.1 10.53 1.2799 66.1 66.3 9.795 25 0.1627 39.2 39.2 11.97 0.5561 51.1 51.0 9.98 1.6998 66.0 66.0 8.095 Al-Qadisiya Journal For Engineering Sciences Vol. 3 No. 2 Year 2010 205 Table 4: Operational conditions and results for mass transfer in empty bed She Rep Weight Loss (gm/hr.m 2) Temp 0C Air Flow rate(m3/hr) Tests no. 17.3135 285.1003 16.0007 39.0 2.8 1 18.7098 345.8269 17.4398 39.1 3.4 2 19.3947 377.7627 18.3160 39.2 3.7 3 19.9931 406.7856 18.4545 39.0 4.0 4 21.0113 458.6925 19.6208 39.1 4.5 5 22.3181 529.8438 20.6403 39.0 5.2 6 17.1085 277.7204 46.3716 51.3 2.8 7 16.9799 272.8329 65.2329 55.3 2.8 8 16.8026 266.4974 148.507 66.1 2.8 9 18.4820 336.7652 49.6271 51.2 3.4 10 18.3388 330.7357 68.0483 55.2 3.4 11 18.1415 323.0021 160.042 66.1 3.4 12 19.1685 368.4121 51.7253 51.2 3.7 13 19.0308 362.3935 71.6804 55.3 3.7 14 18.7530 350.6095 163.612 66.0 3.7 15 19.7436 396.0089 52.5007 51.1 4.0 16 19.5742 388.2574 73.0415 55.3 4.0 17 19.3535 378.8475 171.623 66.2 4.0 18 20.7647 447.5064 56.4473 51.3 4.5 19 20.6113 440.0929 77.5178 55.3 4.5 20 20.2874 424.9063 179.185 66.2 4.5 21 22.0536 516.9524 59.3788 51.2 5.2 22 21.8811 507.9866 82.1496 55.3 5.2 23 21.5112 489.2557 189.438 66.2 5.2 24 *Air flow rate measured at ambient temperature. Table 5: Experimental conditions for mass transfer in fluidized bed Sand Mean Particle Size (micron) Exp. No. Air Flow Rate (m3/hr) U/Umf Temp. 0C Wt. Loss (gm /hr .m2) Rep She 215 1 4.0 1.081 39.1 30.550 943.71 254.612 2 4.4 1.189 39.1 31.754 964.75 258.791 3 4.8 1.297 39.2 33.483 972.29 262.413 4 5.2 1.405 39.2 34.911 982.71 269.751 5 4.0 1.081 51.0 84.836 951.64 214.622 6 4.4 1.189 51.0 89.614 967.90 225.704 7 4.8 1.297 51.2 94.233 971.53 243.950 8 5.2 1.405 51.3 98.408 979.46 257.568 ٩ 4.0 1.081 55.2 121.607 916.60 203.815 10 4.4 1.189 55.1 124.457 945.03 217.780 11 4.8 1.297 55.2 130.413 969.87 247.502 12 5.2 1.405 55.0 132.781 972.37 227.235 13 4.0 1.081 66.3 285.096 884.27 172.751 14 4.4 1.189 66.1 295.131 989.40 194.224 15 4.8 1.297 66.0 297.444 944.85 203.705 Al-Qadisiya Journal For Engineering Sciences Vol. 3 No. 2 Year 2010 212 16 5.2 1.405 66.3 313.011 961.19 214.443 165 1 3.0 1.071 39.0 25.509 661.73 281.599 2 3.4 1.214 39.0 27.221 753.69 305.431 3 3.8 1.714 39.2 29.075 839.76 334.890 4 4.0 1.428 39.1 29.756 889.36 344.508 5 3.0 1.071 51.1 73.244 648.80 264.114 6 3.4 1.214 51.3 78.891 734.67 283.170 7 3.8 1.714 51.0 81.180 822.97 295.800 8 4.0 1.428 51.1 84.641 871.43 307.709 9 3.0 1.071 55.0 100.240 640.28 247.105 10 3.4 1.214 55.1 107.812 728.69 265.401 11 3.8 1.714 55.3 115.400 814.63 281.715 12 4.0 1.428 55.2 117.142 857.09 299.552 13 3.0 1.071 66.0 240.074 629.50 227.746 14 3.4 1.214 66.1 256.227 713.26 239.534 15 3.8 1.714 66.2 270.089 782.94 252.753 16 4.0 1.428 66.3 280.120 827.04 274.766 112.5 1 2.4 1.091 39.0 23.162 524.39 349.553 2 2.8 1.272 39.1 25.077 611.68 364.710 3 3.0 1.363 39.2 25.833 650.19 377.455 4 3.2 1.454 39.0 26.042 692.23 389.107 5 2.4 1.091 51.1 64.938 505.76 327.114 6 2.8 1.272 51.2 70.487 591.29 339.415 7 3.0 1.363 51.3 74.378 639.27 359.770 8 3.2 1.454 51.0 75.018 683.96 378.105 9 2.4 1.091 55.3 91.653 500.88 314.211 10 2.8 1.272 55.2 99.647 593.28 332.154 11 3.0 1.363 55.1 100.780 630.22 351.005 12 3.2 1.454 55.0 103.917 676.43 368.417 13 2.4 1.091 66.0 212.427 489.99 305.215 14 2.8 1.272 66.1 230.876 573.56 319.419 15 3.0 1.363 66.3 682.796 930.62 335.498 16 3.2 1.454 66.2 698.345 992.66 357.794 Table 6: Comparison of the orders of magnitude of the experimental parameters Silica gel-air-water (Rmp/Rmw ~ 0) Sand-air-water (Rmp/Rmw~∞) Sand-air-naphthalene (Rmp/Rmw~∞) (m2/s) 10-3 10-2 10-2 /m msC C 10 2 102 103 (m2/s) 10-5,10-6 10-11,10-12 10-9,10-10 Al-Qadisiya Journal For Engineering Sciences Vol. 3 No. 2 Year 2010 212 Fig. 1: Photographic picture of the Experimental Equipment 1. Rotameter 2. Variac 3. Heating Equipment 4. Temperature Reader 5. Fluidization Column 6. Manometer Fig. 2: Experimental setup. Al-Qadisiya Journal For Engineering Sciences Vol. 3 No. 2 Year 2010 212 0.01 0.10 1.00 10.00 Velocity (Cm/s) 0.01 0.10 1.00 10.00 P b e d ( C m H 2 O ) Fig. 3: Distributor Pressure Drop Fig. 4: Bed Pressure Drop vs. Air Velocity (Sand Particle Size = 215 Micron) 1.00 Air Velocity (Cm/s) 1.00 10.00 ^ P b e d ( C m H 2 O ) 10.00 P̂ B ed ( C m H 2 O ) 1.00 Air Velocity (Cm/s) Fig. 5: Bed Pressure Drop vs. Air Velocity (Sand Particle Size = 165 Micron) Fig. 6: Bed Pressure Drop vs. Air Velocity (Sand Particle Size= 112.5 Micron) 100.00 200.00 300.00 400.00 Sh (exp. ) 100.00 200.00 300.00 400.00 S h ( c a lc .) All point within solid lines are of error less than 25 % All points within dashed lines are of error less than 15 % 100.00 200.00 300.00 400.00 Sh (exp. ) 100.00 200.00 300.00 400.00 S h ( ca lc .) All point within solid lines are of error less than 25 % All points within dashed lines are of error less than 15 % Fig. 7: A comparison of eq. 50 with the experimental data Fig. 8: A comparison of eq. 51 with the experimental data 1.00 Air velocity (Cm/s) 10.00 ̂P b e d ( C m H 2 O ) Al-Qadisiya Journal For Engineering Sciences Vol. 3 No. 2 Year 2010 212 Fig. 9: Comparison of Experimental Data with The Packet Theory Systems is follows: Silica gel-air-water [(o) ds=0.548mm, ( ∆ ) ds=0.875 mm, (� ) ds=1.342mm]. Sand-air-water [(◊) ds=0.496mm].Sand-air-naphthalene [(� )ds=0.351mm] (Yokota, 1975). Sand-air-naphthalene (present work) [(▪) ds=215 micron, (▪) ds=165 micron, (▪) ds= 112.5 micron] 20.00 40.00 60.00 80.00 Temperature ( C ) 100.00 200.00 300.00 400.00 S h ( e x p . ) Part. Size= 215 micron Part. Size=165 micron Part. Size=112.5 micron 0.00 20.00 40.00 60.00 80.00 Temperature( C ) 100.00 200.00 300.00 400.00 S h ( ex p .) Part.Size = 215 micron Part. Size = 165 micron Part.Size = 112.5 micron Fig. 10: Experimental Sh. vs. Temperature at Air Flow Rate = 1.2 Umf Fig. 11: Experimental Sh. vs. Temperature at Air Flow Rate = 1.4 Umf Al-Qadisiya Journal For Engineering Sciences Vol. 3 No. 2 Year 2010 212 0.00 0.40 0.80 1.20 1.60 2.00 Flow (U / Umf) 100.00 200.00 300.00 400.00 S h ( e xp . ) Part. Size=215 micron Part. Size=165 micron Part. Size =112.5 micron Temperature = (51.0 _ 51.2) C 20.00 30.00 40.00 50.00 60.00 70.00 Temperature ( C ) 100.00 150.00 200.00 250.00 300.00 S h ( c a lc .) 1.2 Umf 1.4 Umf 1.3 Umf Particle Size = 215 micron Fig. 12: Experimental Sh. vs. Air Flow Rate Fig. 13: Effect of Temperature on Calculated Sh. No 20.00 30.00 40.00 50.00 60.00 70.00 Temperature ( C ) 100.00 200.00 300.00 400.00 S h ( ca lc .) Particle Size = 165 micron 1.2 Umf 1.4 Umf 1.3 Umf 20.00 30.00 40.00 50.00 60.00 70.00 Temperature ( C ) 280.00 320.00 360.00 400.00 S h ( c al c .) Particle Size = 112.5 micron 1.2 Umf 1.4 Umf 1.3 Umf Fig. 14: Effect of Temperature on Calculated Sh No. Fig. 15: Effect of Temperature on Calculated Sh. No. 1.00 1.20 1.40 Flow (U/Umf) 100.00 150.00 200.00 250.00 300.00 S h ( ca lc .) 39 C 51 C 55 C 66 C Part. Size = 215 micron 1.20 1.60 2.00 Flow (U/Umf) 100.00 150.00 200.00 250.00 300.00 350.00 S h ( c al c .) 39 C 51 C 55 C 66 C Part. Size = 165 micron Fig. 16: Effect of Air Flow Rate on Calculated Sh. No. Fig. 17: Effect of Air Flow Rate on Calculated Sh. No. Al-Qadisiya Journal For Engineering Sciences Vol. 3 No. 2 Year 2010 212 0.80 1.20 1.60 2.00 Flow (U/Umf) 100.00 200.00 300.00 400.00 S h ( c al c .) 39 C 51 C 55 C 66 C Part. Size =112.5 micron 120.00 160.00 200.00 240.00 Particle Size (micron) 100.00 200.00 300.00 400.00 S h ( c a lc .) 1.2 Umf 1.4 Umf 1.3 Umf Temperature = 39 C Fig. 18: Effect of Air Flow Rate on Calculated Sh. No. Fig. 19: Effect of Sand Particle Size on Calculated Sh. No 100.00 150.00 200.00 250.00 Particle Size (micron) 100.00 200.00 300.00 400.00 S h ( ca lc .) 1.2 Umf 1.4 Umf 1.3 Umf Temperature = 51 C 120.00 160.00 200.00 240.00 Particale Size (micron) 100.00 200.00 300.00 400.00 S h ( c al c. ) Temperature = 55 C 1.2 Umf 1.4 Umf 1.3 Umf Fig. 20: Effect of Sand Particle Size on Calculated Sh. No. Fig. 21: Effect of Sand Particle Size on Calculated Sh. No Al-Qadisiya Journal For Engineering Sciences Vol. 3 No. 2 Year 2010 212 120.00 160.00 200.00 240.00 Particale Size (micron) 100.00 200.00 300.00 400.00 S h ( ca lc .) Temperature = 66 C 1.2 Umf 1.4 Umf 1.3 Umf Fig. 22: Effect of Sand Particle Size on Calculated Sh. No.