High production circulating fluidized bed polymerization reactors

High production circulating fluidized bed polymerization reactors

Journal Pre-proof High production circulating fluidized bed polymerization reactors Dimitri Gidaspow PII: S0032-5910(19)30764-8 DOI: https://doi.o...

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Journal Pre-proof High production circulating fluidized bed polymerization reactors

Dimitri Gidaspow PII:

S0032-5910(19)30764-8

DOI:

https://doi.org/10.1016/j.powtec.2019.09.037

Reference:

PTEC 14711

To appear in:

Powder Technology

Please cite this article as: D. Gidaspow, High production circulating fluidized bed polymerization reactors, Powder Technology(2019), https://doi.org/10.1016/ j.powtec.2019.09.037

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© 2019 Published by Elsevier.

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HIGH PRODUCTION CIRCULATING FLUIDIZED BED POLYMERIZATION REACTORS Dimitri Gidaspow [email protected]

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Illinois Institute of Technology

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ABSTRACT

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This paper is an extension of the Gidaspow invention relating to fluidized bed polymerization reactors, such as the UNIPOL reactor or the later reactors containing cooling tubes. It shows that the polymer production rate can be increased by two or more orders of magnitude over that obtained in the UNIPOL reactor due to the orders of magnitude decreased adiabatic temperature rise. The CFD design of several size polyethylene reactors is described. In all cases the small catalyst particle concentrations are high at the walls showing that electrostatics is not the only mechanism for sheet formation.

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1.Introduction An excellent review of the production processes for polymerization reactors was given in 1994 by T,Xie, et al  1 ..The reactor pressure has been reduced from as high as 3000 atm down to as low as 8 atm 2 . For gas phase polymerization reactors a typical operating pressure is 25 atm and temperature of above 60 C. The reactor is of the order of 15 m high, with an L/D of 3.The catalyst size is about 80 microns or smaller, with the product polymer withdrawn from the reactor of size 100 to 5000 microns. The catalyst residue remains in the polymer and therefore its activity must be large enough to produce more than 50 kg of polymer per gram of catalyst. The high activity catalysts are described in the US patent 4,255,542 . 3 . The rate of reaction is proportional to the monomer concentration and the concentration of polymer sites that decrease with reaction time 4 .The activation energy is about 5 Kcal/mole for ethylene polymerization by chromium oxide catalysts. A typical effective first order rate constant is as high as 8 reciprocal seconds. Hence at near constant temperature for a gas velocity of one m/s and the rate constant of one, the reactor height should be only one meter for a good conversion. Heat removal restricts the conversion to only 2% for both the well stirred and the uncooled fluidized bed bubbling reactors 5 . The heat of reaction is removed by recycling. Two types of fluidzed bed bubbling reactors are used to-day, both developed at Union Carbide in the 1970th .  6 .The first built with an expanded section on top and mostly modeled to-day 7  suffers from severe sheet formation that forces frequent reactor shut-down  8 . The second type of the reactor with internal cooling tubes modeled by X-Z, Chen, et al  9 . may solve the sheet formation problem. But the paper presents too few details to be useful for this purpose.

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2. Description of the figures in the invention Figure 1 shows a simplified UNIPOL reactor  10 .Ethylene, hydrogen and catalyst are fed into this bubbling bed reactor. In this type of the reactor the temperature rise will be 1600 degrees C. 7 . This high temperature rise restricts the conversion of ethylene to only 2%. Sheet formation often limits the operation time. In 2016 .for Fluidization XV, M. Kashyap  11  modeled such a reactor. Similar simulations since that time have shown that the catalyst concentration will be the highest at the walls of the reactor. Table 1 shows typical input data. Figure 2 shows a typical rate of reaction for production of polyethylene based on the data of Yermakov and Zakharov  4 .The rate of reaction is proportional to the monomer and the surface concentrations, as shown above the reaction rate curve in Figure 2.The y axis shows the rate of reaction, 104 g ethylene/g catalyst-hr. This rate is called “ r “ in the species balances equation in “Table 2.Hydrodynamic model “. After initiation the rate decreases slowly. For CFD simulations this slow decrease cannot be included into the calculations due to the long time needed to perform the CFD calculations, typically a day for a 20 second run. Hence, here one typical rate was chosen, with the rate constant, k = 8 sec-1. It is possible to include more than one such rate, a fast rate and a slow rate to include the effect of partially deactivated catalyst. Figure 3 is a simplified illustration of the of the polymer circulating fluidized bed reactor. It is the next generation extension of the bubbling fluidized bed reactors shown in Figures 1 and 2 of the US patent 3,922,322 (1975 )  6  and in the 1981 US patent 4,255,542  3 .In the proposed circulating fluidized bed reactor the heat of reaction is removed by the circulating polymer particles rather than by the cooling tubes described in the 1981 US patent  3 . This major

Journal Pre-proof modification allows an order of magnitude larger polymer production per unit reactor volume and better temperature control. The monomer, such as ethylene with diluent, such as hydrogen, and suspended catalyst particles enter the riser portion of the reactor and flow up the riser, as shown. To fluidize the particles in the riser additional flow is supplied through the recycle system with the power produced by the compressor. From the riser the polymer particles and the unreacted gas and the unreacted catalyst particles enter the downer. The hot particles, P are removed from the downer. They remove all the heat of reaction. This invention removes the need for the cooling tubes in the older generation reactors. To keep the downer fluidized, gases are used to fluidize the downer, as shown . The portion of the polymer particles that are not removed are returned to the riser.

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3. Steady State Energy Balance for a Fluidized Bed Riser Multidimensional, multiphase energy balances are derived in chapter one in Gidaspow’s 1994 book  12 .The energy balance for a riser with conversion of monomer Y and heat of reaction H for a constant cross-sectional area can be written as follows :

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g vggcpg(Tbed-Tin)+svsscps(Tbed-Tin)=gvg gHY (1) Net rate of energy outflow +solids outflow=rate of energy generation

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where the differences between the catalyst and the gas temperatures are small. This balance is similar to that used in the paper by S.Dhodakar, et al 5. The main difference is that in the riser reactor particles enter and leave the reactor. This difference is huge since the solids density, s is of the order of magnitude of 2 to 3 times larger than the density of gas. Therefore the first term in the above equation can be neglected. Hence the rise in temperature becomes as follows :

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Tbed-Tin=(( HY)/(cpss))(g/s)(vgg/vss) (2) Adiabatic riser =Conventional adiabatic x gas to x slip ratio temperature rise temperature rise solids density The volume fractions and the velocities of the gas and the particles are of the same order of magnitude. But the ratio of the gas to solid densities is two to three order of magnitude smaller. Hence the temperature rise in the riser is two to three orders of magnitudes smaller than that in the stirred reactor or in the bubbling bed reactors. Instead of 800 degrees C in the Dhodakar  5  design,. the temperature rise is only of the order of 8 degrees. Similarly the temperature rise in the proposed design is reduced by two or more orders of magnitude from that of the Unipol bubbling fluidized bed. There the temperature rise is 1609 C for ethylene and 850 C for propylene. 7. 4. High production rate

Journal Pre-proof The proposed polymerization reactor, unlike the one shown in the U.S. patent 4,255,542 3  assigned to Union Carbide ,and modeled by X.Z. Chen, et al 9  does not need cooling tubes. The hot polymer particles withdrawn from the reactor remove all the heat of reaction. The steady state energy balance under adiabatic conditions is as follows :

H x rate of reaction = polymer production rate x Cp T

(3)

The polymer production rate is as follows :

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Polymer production = A monomervmonomerYmonomer (4)

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The above polymer production rate equals the rate of catalyst injection described in the US patent 4,255,542  3  which states that the production rate can be controlled simply by increasing the rate of catalyst injection. This is true only when the temperature rise is small, as in the present invention. This patent by Gary L. Brown, et al also describes the catalysts and their method of preparation.

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The low temperature rise in the riser allows the production rate to be increased by more than an order of magnitude. In the fluidized bed reactors used to-day the production rate is limited by the low conversion per pass, of the order of magnitude of 2%.Y in Equation (4) can allowed to be nearly one, increasing the polymer production by 50 times for the same size reactor

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The computational fluid dynamics simulation for the polymerization reactor is similar to that published for the production of Diesel from synthesis gas  13  and to those in Gidaspow’s 1994 book 12 . The method of solution and the computer code are described in Gidaspow and Jiradilok’s 2009 book  14 .

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5.Circulating Fluidized Bed Reactors in Patent Literature The patent literature describes several circulating fluidized bed reactors for polymer production. As proved in section 3, these reactors will have much lower temperature rise than the commercial bubbling bed reactors. In the bubbling bed reactors the up-flow of particles and heat minus the downflow is zero. In the circulating beds the heat is removed by the particles. Hence the temperature rise is very small. This leads to the high production discussed in section 4. None of the patents found discuss these advantages. Ping Cai, et al 15 do not realize that a cooling jacket is not needed in the riser .See their patent Perhaps this is why they designed a small diameter reactor,0.406 meters in their example one. They speak of production of 600 kg polyethylene per hour. Such a reactor should produce 50 times as much, with no need for cooling tubes. Earlier Gabriel Mei, et al 16 had a similar design for polypropylene production, without a discussion of heat transfer or sheet formation problems. Gabriele Govoni and Massimo Covezzi 17 proposed two types of circulating fluidized bed reactors. The first is similar to those already discussed .The second is similar to our design for sorption of sulfur dioxide 18, with two down-comers. Such a geometry has the

Journal Pre-proof advantage of producing symmetry and higher production, but at the expense of a more complex system. An apparent follow up is the 2014 European patent application by G. Meier19 .

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6.CFD Design of a Large Ethylene Reactor 6.1 High Velocity To prevent the formation of sheets at reactor walls due to electrostatics it is best to have high wall velocities. This can be easily achieved using a Westinghouse type reactor geometry, with a cone at the entrance of the reactor  14 . However, many preliminary CFD simulations  20  have shown that the same effect can be achieved with a high velocity central jet entering a simple pipe reactor, with other jets supplying air to keep the particles fluidized. Such a geometry is used in Figure 4,with an outlet on the left side. This simulation shows the time averaged axial velocity of the fluid The velocity of the central jet is about 1500 cm/s and the wall velocity is almost 10m/s, providing a good sweeping effect. The jets contained the gas with a mixture of 0.82 weight fraction of ethylene and 0.18 hydrogen. The two entering solids were the 0.1 cm diameter polymer particles with a volume fraction of 0.1 and the 0.008 cm catalyst particles with a volume faction of 0.005 cm. The details are shown in Table 2, “ Input Data for Large Polymerization Reactor ”. The multiphase CFD code was an extension of that described in great detail in Gidaspow and Jiradilok’s 2009 book for the Westinghouse geometry  14 . It is similar to the MFIX code 21  and the commercial Ansys-Fluent CFD. The earliest CFD simulations for gas phase polymerization reactor were presented at the 1995 ASME meeting in Hawaii and published in 2003  22  . The conservation of mass, momentum, energy and the species equations are a very similar to those used for the CFD design of a slurry bubble column reactor for making diesel fuel using the Fischer-Tropsch reaction  13 . They are shown in Table 1, “ Hydrodynamic model “. Figure 5 shows the time averaged volume fraction of solid 1,the polymer ,in center of the reactor. The jet region up to 15 meters has a slightly higher polymer concentration than the rest of the reactor ,except for the first 2 meter entrance section, with a higher polymer concentration. Figure 5 makes it clear that there exist two regions in this reactor , a dense bottom region and a dilute top region. A comparison to our computed fluidization flow regimes  14,23 shows that we are in the turbulent fluidization flow regime. The turbulent flow regime computed by Jiadilok, et al  24  was for 54 micron FCC particles, with an average velocity of 3.25 m/s and a flux of 99 Kg/sq ms. In our two story unit at IIT we had visually seen a sharp transition between the dense and the dilute regimes for similar conditions. Figure 6 shows the computed time averaged catalyst weight fraction. The catalyst concentration is much higher at the wall, like the high catalyst concentration in the core-annular regime in a single particle riser for flow of FCC particles or the platelet concentration in blood vessels 23 . The blue dots near the bottom in Figure 6 represent two cooling tubes placed into the reactor for safety, in case there are hot spots formed. The high catalyst wall concentration was consistently found in all polymerization reactors, in risers and in bubbling bed reactors, such as the Unipol reactor. Hence the mechanism for the high wall concentration is not just due to the electrostatics. Figure 7 shows the ethylene concentration in this reactor. In the center jet region the ethylene concentration at this high velocity is near 0.8 , the inlet concentration .But at the exit left wall, above the blue splash-cooling plate the exit concentration is near zero. There is more reaction near the wall ,in part, due to higher catalyst concentration at the wall.

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The polyethylene production rate is the product of average gas velocity times the area , the density, and the weight fraction. Here, gas velocity = 2.64 m/s, Area=39.5 sq.m, density = 30 kg/cu m. With complete conversion, the production rate = 3128 kg/s. With the more realistic weight fraction change of 0.6, the production rate = 1876 Kg/s. or 61 million tons per year. This is the ethylene yearly production in the USA. The reactor height can be roughly estimated from the average gas velocity of 2.63 m/s divided by the input effective first order rate constant of 5 reciprocal seconds times the catalyst concentration of roughly 0.02. Hence the reactor height needs to be 26 meters high, as shown in Figure 7. 6.2 Low Velocity Figure 8 shows the average polymer concentration with the gas velocity reduced to 0.88 m/s and the particle size increased to 0.25 cm. At this low velocity ,with the higher polymer size, the dense region increased from about 0.2 to more than 0.6 at the bottom of the reactor. Fig 9 shows that we are again in the turbulent flow regime. At this low gas velocity the time to a steady state increased from one second to 10 seconds. The steady state was determined from plots of volume fractions, temperature, ethylene concentrations, etc as a function of run time. Figure 10 shows the ethylene weight fraction. Since almost complete conversion occurs in 10 meters the reactor is too tall for these conditions. The outlet gas velocity at the left wall was about 25 m/s, with the polymer velocity going into the downcomer of 16m/s and the gas temperature 334 K, a rise of only one degree even at this low velocity. The polymer production rate for this low velocity is 610 kg/s again, an extremely high production rate compared to the commercial UNIPOL reactors. Figure 11 shows temperature peak formations in the reactor. While these temperature peaks are no more than 40 degrees, this low velocity and high rate of reaction are close to the limit of operation. The lower than the inlet temperature of 333 K is due to the cooling splash plate in the riser.

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7. CFD Design of Smaller Reactors To validate the proposed design of the large polymerization reactor it is necessary to perform pilot plant tests with smaller reactors. A number of CFD simulations were done with smaller reactors. Some of the results with an 80 cm diameter reactor are presented here. For the high velocity flow the ethylene weight fraction was very similar to that shown in Figure 7 for the 6 meter diameter reactor. See Figure 12. Figure 13 shows the same core-annular flow, as in Figure 6.Figure 14 shows the variance of the solid 2,the catalyst, velocity. This is a measure of the turbulence. The turbulent granular temperature is approximately the square of the velocity. Figure 15 shows the outlet temperature, starting with the initial temperature of 333 K. The two story IIT circulating fluidized bed with a splash plate used to prevent asymmetrical flow in the 7.5 cm riser 25  can be used for validation of the high production reactor. In the past it was used for flow of Group D particles of a similar size as used here for the polymerization reactor  26 . Solids slugging was observed in this small diameter reactor. Similar slugging was computed here in this high L/D reactor , particularly during the start -up until 8seconds. There were other differences in flow behavior causing incomplete conversion. To obtain complete conversion, the inlet jet velocities were reduced. For the central jet velocity of 3.5 m near complete conversion was achieved, assuring a high production of ethylene.

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Notation

cross sectional area

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General Letters A

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8.Conclusions 1. It is shown that the temperature rise in gas phase circulating fluidized beds is two to three orders of magnitude lower than that in bubbling fluidized beds. This conclusion is obtained from approximate energy balances and from CFD simulations. 2. This small temperature rise allows the circulating fluidized beds to operate with order of magnitude higher monomer conversions. In the bubbling fluidized beds, such as in the UNIPOL reactor, the monomer conversion is only about 2 %. 3. The high monomer conversion increases the polymer production by two to three orders of magnitude for the same size reactor. 4. CFD simulations for several size polyethylene reactors confirm the high production rates. 5. The polyethylene reactor risers operate without bubbles , unlike the UNIPOL reactors used commercially. Formation of large bubbles in the UNIPOL reactors restrict their size due to shaking of the reactors. 6. It is shown that the small catalyst particles move toward the walls for all the reactors studied. Hence sheet formation at the walls is not only due to electrostatics. 7. The ethylene reactors studied were all in the turbulent flow regime, with a dense polymer concentration at the bottom and a dilute region on top, similar to that found for UNUPOL reactors. 8. Operation of the reactors with a high velocity jet at the center produces a high downward flow at the reactor walls that minimizes the bad sheet formation observed in the UNIPOL type reactors. Acknowledgement This study is in part based on provisional US patent application, confirmation No.8603,application number 62/615,798, date 01/19/2018 by Dimitri Gidaspow.

drag coefficient

dk

characteristic particulate phase diameter

Dt

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Cd

g

gravity

G

solid compressive stress modulus

go

radial distribution function at contact

hvk

Gas-phase k heat transfer coefficient

H

enthalpy

Kg

Thermal conductivity of gas

actual or effective tube diameter

Journal Pre-proof rate of generation of phase k

Nuk

Nusselt number

P

continuous phase pressure

Pk

dispersed(particulate) phase pressure

r

rate of reaction, kg”i”/kg catalyst sec

R

Gas constant

Rek

Reynolds number for phase k

T

temperature

t

time

vi

hydrodynamic velocity in i direction

vi

mean velocity in i direction

Yig

weight fraction of the species i in the gas phase

β

interphase momentum transfer coefficient

εk

k

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Greek Letters

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m k

μk

shear viscosity of phase k

θ

granular temperature

ρk

density of phase k

τk

stress of phase k

volume fraction of phase k particle sphericity

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Table 1 Input Data for Large Polymerization Reactor Geometry Height 30 m Width 7m Inlet Jet Width 0.512 m Number of Inlet Jets 5 Outlet Height . Right Wall 1.02 m Splash Plate Width at 26m 3.68 m Solid and Gas Properties Polyethylene Density 0.9 g/cu cm Catalyst Diameter 0.008 cm Catalyst Density 0.9 g/cu cm Inlet Gas Weight Fractions Hydrogen 0.18 Ethylene 0.82 Inlet Conditions Pressure 30.1 atm Temperature 333 K Central Jet Velocity 18m/s Side Jet Velocities 6 & 3m/s, each Polyethylene Weight Fraction 0.1 Catalyst Weight Fraction 0.0005 Grid Sizes Time Step, sec 5x 10-6 Axial 106 x 0.28 m Radial 42 x 0.167 m Initial Conditions Filled Region up to 11.5 m With polymer and Catalyst as at Inlet Gas Velocities in Filled Region 1.8 m/s In Top Gas Region 0.6 m/s

Journal Pre-proof Table 2. Hydrodynamics model Continuity equations Gas phase   g  g      g  g vg   m g t

Solid phases (k  1,2)

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  k  k      k  k vk   m k t

(a)

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Momentum equations Gas momentum

Particulate phases, k  1,..., N 

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N   g  g vg      g  g vg vg   P    gk vk  vg     2 g  g  s vg   g  g g t k 1

Energy Equations

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Gas phase

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N       k  k vk      k  k vk vk    gk vg  vk     kl vl  vk   Gs  k    2 k k  s vk   k  k g t l 1 k  1,2

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N   g  g H g      g  g H g vg    P  vg  P    hvk Tk  Tg     (K g  g Tg ) t  t  k 1

Solid phases

  k  k H k      k  k H k vk   hvk (T f  Tk )    ( K k  k Tk ) t

Species Balances Gas phase  (  g  g Yig ) + .(  g  g Yig v g ) =  s  s r t

Journal Pre-proof Where r has units of kg ethylene/kg catalyst-s Rate of Reaction Rate of reaction = 5 Cethylene Ccatalyst For a high rate of reaction Constitutive equations N

 g  k  1 Hk  H0 ck

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Tk  T0 

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k 1

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g 

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Equations of state – Ideal Gas Law

 k   sk

= constant

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Solids

Fluid phase stress

    f

(b)

f





 f  v f  v f T    v f I   

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(a)

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Constitutive equations for stress

 

2 3

solids phases stress k  1,..., N 

 k    k  v k  v k T  2   v k I 



3

Empirical solids viscosity and stress model (a) Solids viscosity

 k  5 k

Poises

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Pk  G k  k G k   10

8.686 k 8.577

dynes/cm2

Gas-solid drag coefficients k  1,..., N  for  f  0.8 (based on Ergun equation)

d kk   k   g  2

g

 1.75

 g  k  k v g  vk



f

d kk  k   g 

d kk  k   g 



 f 2.65

for Re k  1000 for Re k  1000

g

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 g  g v g  vk d k  k

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Re k 



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 24 1  0.15 Re 0k.687   Re where C D   k    0.44

re

 g  k  k v g  vk

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3 4

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for  f  0.8 (based on empirical correlation)

  CD

Particle-Particle Drag Coefficient



kl k ,l  f

    d  d    3   1  e k l k 3l k 3 l vk  vl 2  k d k  l dl 2

1/ 2

d  where    e  and e  0.95  dk  Gas-Phase Heat Transfer 1.786

 Tf   K f  8.65  10  1400   5

of



 k2  g  k

ro

  150

W/m.K

Journal Pre-proof Gas-Particle Heat Transfer ,k (=s) for f < 0.8 Nu k  2  1.1Re 0.6 Pr1 / 3 S k

Re 200

0.183

 4 Re   200 Re 1000  0.123 S k0.17 d  k  Re1000  0.61Re 0.67 S k For f > 0.8 Nu k  2  0.16 Re 0.67 S k

Re 200 200 Re 1000

 8.2 Re 0.6 S k

Re1000

where,



Re 

of

Sk



 f v f  vk d k

ro

 1.06 Re

0.457

f

6 dk h d Nu  vk k kf

Particulate-Phase Heat Transfer



R   1  f  

f

ur



 *s *SO      1        

  *S  R    *S *SO    B      1           *SO 2      ln    * N  M    B 2  S         N M           B  1 B  1  R     B    N M 2B   

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with,

1  

na

Kk  1 1  f Kf

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re

-p

Sk   k

N  M  1

R    B

1  f B  1.25    f

    



* S 10 / 9

(for spheres)

 R 0.0004C k  T      dk  2 /  r  1  100  3

Journal Pre-proof *S  12.227    7.26  10 8 Ck  5.67  10 8

W/m2.K4 Stefan-Boltzmann Constant

 r  0.93

Emission Ratio

Alternate Expression for Gas-Particle Heat Transfer Coefficient Madhava Syamlal and Sreekanth Pannala in chapter one’ page 40 ,Equation 6.43 give a

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continuous expression for the gas-particle heat transfer coefficient in their book

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,Computational Gas-Solids Flows and Reacting Systems : Theory, Methods and Practice, by

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S.Pannala, M. Syamlal and T.J.O’Brien, , Engineering Science Reference ( 2011 ).

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In both cases the Nusselt number is two for dilute low velocity flow. Without such a

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correction to the previous literature correlations the computed temperatures will be incorrect.

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References 1 Tuyu Xie,K.B. Mc Auley .C.C. Hsu, and D.W. Bacon, Gas Phase Ethylene Polymerization: Production Processes,Polymer Properties, and Reactor Modeling, Ind.Eng.Chem.Res.33 (1994) 449-479 2 Kyu-Yong Choi and W. Harmon Ray, Recent Developments in Transition Metal Catalytic Olefin Polymerization – A Survey. I .Ethylene Polymerization, JMS-REV. MACROMOL.CHEM.PHYS.,C25(1),1-55 (1985) 3 Gary L.Brown, D.F. Warner ,and J.H.Gyon, Exothermic polymerization in a vertical fluid bed reactor system containing means therein and apparatus thereof, US patent 4,255,542, March 10 (1981) 4 Yu.Yermakov and V. Zakharov,One-Component Catalysts for Polymerization of Olefins, Adv.Catal.,24 (1975),173-219 5 Shrikant Dhodapkar,P.Jain and C.Villa, Designing Polymerization Reaction Systems,CEP (2016) Febuary,1-25 6 Dormenval Rogers, H.Laszlo,FR Havas and M. Pierre, Process for dry polymerization of olefins, US patent 3,922,322.November 25 (1975) 7 Ram G. Rokkam, R.O. Fox and M.E.Muhle, Computational Modeling of Gas-Solids Fluidized Bed Polymerization Reactors, chapter 12 in Computational Gas-Solids Flows and Reacting Systems: Theory, Methods and Practice, S.Pannala,M. Syamlal and T.J. O’Brien (Eds)Engineering Science Reference New York ( 2011),pp 375-397 8 George Hendrickson, Electrostatics and gas phase fluidized bed polymerization reactor wall sheeting, Chem.Eng.Science 61 (2006) 1041-1064 9 Xi-Zhong Chen,Z- H Luo, W.-C Yan, Y-H Lu, and I-S Ng, Three-Dimensional CFDPBM Coupled Model of the Temperature Fields in Fluidized Bed Polymerization Reactors, AIChE Journal 57 (2011 ), 3351-3366 10 Mayank Kashyap, Application of multiphase flow CFD in the gas phase polymerization process, in Fluidization XV, J.Chaouki,F.Berruti and R.Cocco (Eds) ECI Symposium Series(2016 ) http://dc.engconfint.org/fluidization-xv/65 11 Mayank Kashyap , Multiphase flow CFD capability development for gas phase polymerization processes, Presented at US Department of Energy ,NETL, July 11 (2016). 12 Dimitri Gidaspow , Multiphase Flow and Fluidization, Academic Press, New York (1994 ) 13 Dimitri Gidaspow, Y. He and V. Chandra, A new slurry bubble column reactor for diesel fuel,Chem. Eng. Science 134 (2015 ) 784-799 14 Dimitri Gidaspow and Veeraya Jiradilok, Computational Techniques, Nova Science, New York (2009 ) 15 Ping Cai, D .Hussein, I.D. Burdeff D.M.Gaines & R.B. Painter, Circulating Fluidized Bed Reactor, US patent 8,129,483 B2, March 6,2012 16 Gabriele Mei, J.T.M. Pater & S. Bertolini , Process and Apparatus for the Polymerization of Propylene ,US patent 7,524,903 B2, April 28,2009 17 Gabriele Govani & Massimo Covezzi, Apparatus for Gas-Phase Polymerization, US patent 6,818,187 B2, November 16,2004 18 Apichai Therdthianwong & Dimitri Gidaspow, Hydrodynamics & SO2 Sorption in a CFB Loop, pp 351-358,in Circulating Fluidized Bed Technology IV, Amos Avidan, ed. AIChE,1994.

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19 Meier, Gerhardus, Polyethylene composition for blow molding having high stress cracking resistance, European patent application, EP 2 818 509 A1, 25 06 2013 20 Dimitri Gidaspow, Design of the Next Generation Polymerization Reactor using CFD, AICE Midwest Conference, IIT, Chicago, Il April 2018 21 Madhava Syamlal, MFIX Documentation : Numerical Techniques.DOE/MC-313465824 NTIS/DE98002029.Springfield, VA: National Technical Information Service,1998. 22 Anne Gobin, H.Neau, O.Simonin, J-R Llinas, V.Rieling and J-L Selo, Fluid dynamic numerical simulation of a gas phase polymerization reactor, International Journal for Numerical Methods in Fluids, 43 ( 2003 ) 1199-1220. 23 Dimitri Gidaspow and M.S. Bacelos, Kinetic Theory Based Multiphase Flow with Experimental Verification, Reviews in Chemical Engineering 34 (2018 ) 299-318. 24 Veeraya Jiradilok, D. Gidaspow,.S.Damronglerd. W.J. Koves and R.Mostofi, Chem .Eng. Science 61 (2006 ) 5544-5559. 25 Mehmet Tartan and D. Gidaspow, Measurement of Granular Temperature And Stresses in Risers, AIChE Journal 60 (2004) 1760-1775. 26 Mayank Kashyap, D.Gidaspow and W.J Koves, Circulation of Geldart D. Type Particles: Part I-High Solids Fluxes Measurements and Computation under Solids Slugging Conditions, Chem. Eng. Science 66 (2011) 1649-1670.