Heat Transfer in Gas
Content
Gas-solid Heat transfer during solid flows- An overview and prospects Introduction: Process industries handle large amount of powders and granules during transportation, storage, processing etc. Nearly 70% of the raw materials and 50% of the products are in the granular form. Fre uently the solids are su!"ected to operations li#e si$e reduction, heat e%change and reactions. &ranular materials can easily !e transported from one process unit to the other using a gas medium. 'he mo(ement of gas and solid can !e of two modes: co)current, cross current and countercurrent mode. *o)current, cross current and counter current flow ta#e place in mo(ing !eds whereas in pneumatic con(eying, the co)current flow of gas and the solid ta#es place. *ounter current flow in dilute phase is called raining solid system+*,-.. In counter current mo(ing !eds, solid and gas flow in opposite directions with solid mo(ing downwards and gas mo(ing upwards, as in the case of mo(ing !ed reactors, adsor!ers, solid coolers etc. 'he flow of solid in a direction inclined to the hori$ontal ta#es place in rotary dryers, #iln etc where the gas tra(els in counter current direction to the solids. In co)current mode, !oth the solids and the gas mo(e downwards in the same direction. 'he mo(ement of solids and gas in the perpendicular direction, resulting in the contact !etween the solids and the gas is the cross flow mode practiced in drying, cooling etc. /o(ing !eds are used for fairly large granules easily deacti(ated catalyst and for large)scale operations. 'emperature gradients can !e controlled !y proper gas flow and can !e minimi$ed !y sufficiently large solid circulation. /o(ing !eds ha(e the ad(antages of plug flow and low catalyst handling costs. /o(ing !eds ha(e !een employed in the past for heating of cold solids using e%haust gases in mo(ing !eds. 0nother application is the sand crac#er for crac#ing gas, using sand as a heat carrier in which sand descends down in an upward flow of gas. 'he co)current mo(ement of gas and solid ta#es place in pneumatic con(eying. Pneumatic con(eying refers to the transportation of solid particles using air at (elocities greater than the terminal (elocity of the solids. Pneumatic con(eying finds wide applications in con(eying of solids !ecause of the ad(antages of dust free transportation, fle%i!ility in routing, ease of maintenance etc.+1.. 'he pneumatic transport of solids is !roadly classified into two regimes) dilute phase and dense phase transport. 2ilute phase transport is characteri$ed !y high gas (elocities typically greater than 30m4s, low solids concentration 5less than 1%6 and low pressure drop per unit length of the transport line. 7nder these dilute flow conditions the solid particles !eha(e as indi(iduals, fully suspended in the gas with no particle)particle interaction +3.. 'he dense phase flow is characteri$ed !y low gas (elocities 5less than 5m4s6, high solids concentration and high pressure drop per unit length of the pipe. In dense phase transport, particles are not fully suspended and there is much interaction !etween the particles +3.. Industrially important materials li#e cement, fuel ash, polyethylene powder, flour e%hi!it dense phase transport +8..
9ecause of the o!(ious differences !etween two modes of pneumatic con(eying, their hydrodynamic characteristics are different from that of each other. :ydrodynamics of pneumatic con(eying in dilute phase and dense phase transport has !een widely pu!lished +;,5.. :eat transfer in gas)solid flows: &as)solid heat transfer is important in many industrial applications. 2rying of granular materials is a (ery common operation in chemical, pharmaceutical, food industries etc. Fre uently, the raw materials are preheated using e%haust flue gases. 'he products are cooled using incoming cold air. 0ll the a!o(e operations in(ol(e heat transfer !etween gas and solid in co)current and counter current !eds. 'he commercial applications of operations in(ol(ing gas)solid heat transfer during flow can !e categori$ed as preheating4heating of solids, drying, cooling of solids, reactions li#e com!ustion, crac#ing etc. Preheating4:eating of solids: <olids are heated using hot gases flowing in co)current direction during transportation or reaction. In circulating fluidi$ed !eds, heat is transferred from the gases to the solids so that the solids are heated resulting in reactions, as in the case of circulating fluidi$ed !ed !oilers using coal. 'he spent catalyst from the fluidi$ed !ed crac#er needs to !e regenerated to remo(e the deposition of car!on on the surface of the catalyst. 'he catalyst is repeatedly transported !etween the reactor and the regenerator, during which heat transfer !etween the gas and solid ta#es place. Preheating of #iln feed using e%haust gases from the #iln in cement industries is an important e%ample of gas)solid heat transfer during preheating. 'he #iln feed and hot gases mo(e in counter current direction in the rotary #iln where the necessary reactions ta#e place. 'he e%it temperature of the e%haust gases from the #iln is around 1000 *. 'he heat of the gases is used to preheat the cold solid feed. For this purpose, multistage cyclone separators with pneumatic con(eying ducts !etween them are used in cement industries. In !etween the cyclone separators, the solids are con(eyed pneumatically resulting in the heat transfer !etween the solids and the gases. 9y this way solids are preheated and temperature of air is reduced to around 550 = !efore they enter >lectrostatic Precipitator. 2rying of heat sensiti(e solids: *ertain solids li#e pharmaceutical products? food materials etc are highly heat sensiti(e. 'he e%posure of these materials to high temperature for longer duration will result in the degradation and loss in the uality of the product. 9ut, in(aria!ly these products need to !e dried to reduce the moisture content re uired to meet the deli(ery specifications. 'his is achie(ed in pneumatic con(eying dryers where the residence time is (ery short in the order of few seconds. Pneumatic con(eying dryers are continuous,
con(ecti(e dryers with dilute phase transport suita!le for drying of heat sensiti(e, e%plosi(e, degrada!le or flamma!le materials. :ot air supplies the drying energy and transports the solids through a (ertical pipe +@.. 'ypical applications include drying of alumina, poly(inyl chloride, calcium car!onate etc. 'he other solids that are dried in a pneumatic dryer in industries are animal feed, catalysts, cellulose, clay, corn fi!ers, epsum salt, gypsum, #aolin, pigment, poly propylene, poly styrene, proteins, silica, $eolites etc. 'he schematic diagram of a flash dryer is shown in figure no.1.
>%haust air
Bet <olid 2ried <olid
9lower
:eater
Figure no.1: <chematic diagram of a flash dryer
Figure no.3: <chematic diagram of a cyclone preheater system
*ooling of solids: In certain cases, the solids are to !e cooled to the deli(ery specifications after passing through a high temperature reaction or separation. 'he e%amples are cooling of hot polyethylene granules from the dryer, cooling of flyash during its transportation to disposal site etc. 'hese in(ol(e either counter current mo(ing !eds or co)current pneumatic con(eying system. Aeactions in(ol(ing com!ustion and crac#ing: 'he pyrolysis of oil shale is carried out in a fluidi$ed !ed. 'he (olatile matter is dri(en off in a retort, and the car!onaceous residue is !urnt in a second location to pro(ide the heat necessary. 'his is done in a circulation system where the shale is transported !etween the retort and the heater. 'he transport of shale from the retort to the
heater is !y pneumatic con(eying, whereas its transport from the heater to the retort includes !oth mo(ing !eds and pneumatic transport. *orrelations for gas)solid heat transfer: 'he widespread application of heat transfer in gas)solid flow systems in process industries and power plants moti(ated research in this area in the past two decades. 'he researchers around the world are acti(ely carrying out a large uantum of wor# in this field. 'he re(iew of literature in the gas)solid heat transfer re(eals the following correlations a(aila!le for the calculation of heat transfer coefficient !etween the gas and the solid. 1. 9aeyens)&eldart e uation for pac#ed !ed +@..
Nu
p
=0.010@ Ae 1.;C ...................................................516
(
)
3. =othari e uation for fluidi$ed !ed +@.
Nu
p
=0.08 Ae 1.8 .......................................................5 36
(
)
8. Batson e uation for fluidi$ed !ed +@.
d Nu p = 0.003D Ae1.7 p D
(
)
− 0.3
...................................586
;. &amson e uation for fluidi$ed !ed +@,D.
Nu p =0.010@ Ae 0.5C Pr 0.88 .......................................5 ;6
(
)
5. 2e 9randt e uation for pneumatic dryer +@,D,C..
Nu p =0.1@ Ae 1.8 Pr 0.@7 ............................................556
(
)
@. Aan$)/arshall e uation e uation for e(aporation from water droplets +C..
Nu p =3 +0.@ Ae 0.5 Pr 0.88 ............................................5@6
(
)
7. 9aeyens e uation for pneumatic drying of surface moisture +@,D,C.
Nu p = 1.0@(Ae ).............................................576
D. /odified Aan$)/arshall *orrelation for drying of single wet particle in air +D.
3 + 0.@ Ae 0.5 Pr 0.88 Nu p = 0.7 ..........................5 ;6 (1 + B )
C. =emp et al e uation for drying +C.
Nu p = 3 +0.5 Ae 0.5 Pr 0.88 +0.0@ Ae 0.D Pr 0.88 .............5C6
10. /a"son et al e uation for drying of P> pellets +C..
n Nu p = 3 +0.@rg Ae 0.5 Pr 0.88 ?. Ae < 300.............5106 n n Nu p = 3 +0.5rg Ae 0.5 Pr 0.88 +0.03rg Ae 0.0D Pr 0.88 ?300 < Ae <1500.....5116 n Nu p =3 +0.0000;rg Ae1.D ? Ae >1500................5136
5 nE 8.5 for 8mm Pe pellets6 11. 9androws#i , =ac$mar$y# e uation +C.
0.5CD; Nu p = 0.0011; Ae 0.D15C rs− ?0.00035 < rs < 0.05 , 1D0 < Ae <1D00...........5186
13. =ato correlation for heat transfer !etween oil shale particles and air +10.
8 }0.C7 .........................51;6 Nu p =3.8De − Ae n { ∈1−∈
n = 3.;D ∈ 1− ∈
(
) −0.3D
In the a!o(e e uations, Ae =
Nu p = Pr =
d p ρg vr
µg
h pg d p kg kg
C pg µ g
B=
C pv T g − Td H
fg
(
)
/ason et al +8. made a model for non)suspension gas)solids flow of fine powders in pipe. 'he authors modeled the dense phase transport of powders using the two)layer concept de(eloped for li uid)solids flow. 'he dense phase transport is modeled as two layers: a dilute gas)solid mi%ture a!o(e a dense gas)solids mi%ture. 'he conser(ation e uations for mass, momentum and energy were sol(ed for !oth the gas and the solid phase. 'he model showed good agreement with the e%perimental data in terms of the (ariation of layer height, (elocity and solids concentration. 'hey also concluded that the (ariation of the initial conditions for the same gas and solid mass flow rates had only a small effect on the prediction of fully de(eloped flow.
9aeyens et al +@. descri!ed a procedure for the design of industrial pneumatic con(eying dryer using large)scale e%perimental data. 0ccording to them, hydrodynamics of the pac#ed !ed and the fluidi$ed !ed does not correspond to the hydrodynamics of the pneumatic con(eying, the use of 9aeyens F &eldart e uation, =othari e uation, Batson e uation and &amson e uation will predict erroneous results. 2e9randt e uation and Aan$)/arshall e uation were found to o(erestimate the heat transfer coefficient. 'he authors proposed a correlation for the gas Fsolid heat transfer coefficient in pneumatic drying of surface moisture from PG* and calcium car!onate. 'he authors predicted the temperature and moisture profiles using their correlation and found the profiles to fit the e%perimental data well. 'he draw!ac# of their correlation is that the effects of solids flow rate, porosity are not included. Aadford +7. presented a simple model for particulate drying in pneumatic con(eying systems that can !e implemented easily. 'he model assumed the particles to !e non)hygroscopic, discrete with no interaction with other particles, spherical and of uniform si$e and the flow of gas to !e tur!ulent. :ence the model is (alid only for dilute phase transport of particles of same si$e and spherical shape. In the drying model, the duct was considered to !e made up of a large num!er of segments with each segment representing an e ual incremental time in the duct. 'he model can !e implemented on a spread sheet. 'he pu!lished correlations were tried and did not yield meaningful results, as the correlations were highly specific. Frant$ correlation and 2onsi , Ferrai correlations were found to !e effecti(e for the drying of alumina particles in air. 'he model was simulated using Fran$ correlation for drying of alumina particles and found that the simulated (alues matched the e%perimental data well. 'he applica!ility of the model for drying of particulate solids other than alumina has not !een tried. 0(i -e(y et al +D. sol(ed a steady state one)dimensional flow model for a pneumatic dryer !y ta#ing into account of mass, momentum and heat transfer !etween the gas and the particles phases, to predict the temperature and moisture profiles along the length of the dryer. 0 two) phase continuum model was used to descri!e the steady state flow of wet solid particles and gas through a pneumatic dryer. 'he &amson correlation and modified Aan$ ) /arshall correlation were found to o(erestimate the heat transfer. 'he authors also concluded that for non)adia!atic conditions and for (arying wall temperature, 2e9randt and 9aeyens e uation predict the heat transfer well. 'heir model is applica!le for dilute phase con(eying only. /ason et al +C. made a computational in(estigation of transient heat transfer n pneumatic transport of granular particles of 8 mm polypropylene pellets using a 2istinct >lement /ethod 52>/6 to model heat transfer in gas solid flow systems. 'he e%periments were conducted to study heat transfer in !oth dilute and dense phase pneumatic transport. 'he authors made a re(iew of e%isting e uations for heat transfer in dilute phase and dense phase con(eying. Aan$)/arshall e uation was found to apply for particles with small AeynoldHs num!er 5AeI3006. 9aeyens e uation was found to o(erestimate the heat transfer for 8 mm polyethylene pellets. 'he authors modified the e uation of =emp et al !y su!stituting different constants in the original e uation to account for the tur!ulent !oundary layer that would de(elop for large particles. 'hey
proposed a correlation for gas)solid heat transfer of polyethylene pellets and suggested that the effect of particle si$e, density on the empirical constants needs to !e e(aluated. 'he influence of particle concentration on the performance of the system was predicted and found to consistent with the e%perimental data. 'he time consumed !y the 2>/ model for large num!er of particles is more and hence, the model was not e%tended for dense phase flow. 9ertoli et al +10. made an analytical study on the radiati(e and con(ecti(e heat transfer on pneumatic transport of particles. 'hey found that =atoHs correlation predicts that heat transfer well. 9ut the empirical constants used were specifically for heat transfer !etween the oil shale particles and air. 'he analytical solution was compared with the e%perimental data in the literature and found to predict the particle and fluid temperature well. 'hey concluded that the performance of any model to predict the temperature profile depends on the correlation used for the estimation of the particle Nusselt num!er. *ollado et al +11. simulated the mass and energy !alances in one)dimensional two phase flow at steady state !y assuming uniform gas (elocity, uniform solid (elocity and uniform solid distri!ution o(er the cross section of the ducts !y adding a new e uation to the classical mass !alance e uation for the two)phase flow. 'he energy !alance resulted in new correlations for the pressure drop in pneumatic con(eying which predicted the e%perimental data (ery well. /ason et al +13. descri!ed a simulation system for pneumatic con(eying to o(ercome the pro!lem encountered during design, optimi$ation and up gradation of these systems. *orrelations used to predict the pressure drop and their limitations in terms of fle%i!ility were presented. 'he simulation system presented impro(ed the fle%i!ility of the model. Future Prospects: 'he figure no.8 shows the comparison of predicted (alues of Nusselt num!er for same Aeynolds num!er !y different e uations a(aila!le. It is clear from the figure that the e uations a(aila!le for the design of systems in(ol(ing gas)solid heat transfer contradict each other and (ary widely for similar operating conditions. 0ll the parameters that affect the heat transfer in gas)solid flow ha(e not !een accounted for. 'he e uations 1 to 10 do not ta#e the effect of solids (olume concentration or the (oidage in to account. 'he correlations are (ery specific and cannot !e used for other systems as they either tend of underestimate or o(erestimate heat transfer+3)C.. 0 generali$ed e uation is necessary for the presentation of heat transfer in gas)solid flow systems, which will !e useful for the design of such systems, as e(ident from the literature.
Com parison betw een the correlations for gas-solid heat transfer in pneum atic conveying 4500 4000 3500 Nusselt Num ber 3000 2500 2000 1500 1000 500 0 0 500 1000 1500 Reynolds Num ber 2000 2500 3000 ()* Kot+ar! *amson ,e)(randtl R)M (aeyens
Figure no. 8: *omparison !etween prediction of different correlations for similar conditions.
150
Re = 1750 (Majson et al) Re = 1750 (Kato et al)
Nusselt Number (Nu)
100
50
0 0 0.01 0.02 0.03 0.04 0.05 0.06
Reynolds Number (Re) !"ure no.4# $om%ar!son bet&een Majson et al and Kato et al data 'or same Reynolds number
'he e uations suggested !y /a"son et al and =ato et al correlate the Nusselt num!er with Aeynolds num!er, solid (olume fraction and Prandtl num!er. It is e(ident from the figure no.; that the two correlations (ary widely in their prediction for same operating conditions i.e. for the same Aeynolds num!er and solid (olume fraction. 'he de(iations could !e due to the use of different solid materials in the respecti(e e%periments. =ato et al used oil shale particles while /a"son et al reported the results for 8 mm polyethylene pellets. 'he particle si$e has !een ta#en into account in the Aeynolds Num!er 5Ae6, while the density of the particle has not !een accounted for in !oth these correlations. :ence, the de(iation !etween the correlations can !e o(ercome !y ta#ing the density of the particles in to account. 0n attempt is made to propose a correlation, which fits the data of !oth =ato et al and /a"son et al. 'he data of =ato et al and that of /a"son et al are calculated from their correlations. 0n e uation of the following form is o!tained !y modifying the =atoHs correlation to account for the density of the particles.
Nu p = 3.8De
−8
Ae
n
{∈1−∈ }
0.C7 ρ p
n = 3.;D ∈ 1− ∈
m E f5Ae, 1)ε6
(
) −0.3D
........................5156 ρ
m
ρp E Particle density 5#g4m86 ρE 3800 #g4m8 Following forms for JmH were o!tained !y comparison of data of /a"son et al and =ato et al. 5i6 For Ae I 300,
)} + B?...(1−∈) < 0.01 m = A{ Ln(1−∈
m = C (1−∈ ) 3 + D(1−∈) + E?....0.01 < (1−∈) < 0.08
) + G?.......(1−∈) > 0.08 m = F (1−∈
A = 0.1;C ln ( Ae ) −1.010C B =1.0@;@ ln ( Ae ) −@.D785 C = −3;3.;8 ln ( Ae ) +1;71.8 D = 38.0;1 ln( Ae ) −118.;7 E = 0.1D53 ln( Ae ) −1.3858 F = D.88@1 ln( Ae ) − [email protected] G = 0.;151 ln( Ae ) − 3.558;
5ii6 For 300IAeI1500,
m = A(1−∈ ) 3 + B(1−∈ ) +C ?...(1−∈ ) < 0.00; m = D (1−∈ ) 3 + E (1−∈ ) + F ?....0.00; < (1−∈ ) < 0.08 m = G{ Ln (1−∈ )} + F ?.......(1−∈ ) > 0.08
A = −11073 ln ( Ae ) +1117D0 B =113 Ln( Ae ) −100;.3 C = −0.3857 ln ( Ae ) +1.C8C7 D = −8C7.18 ln ( Ae ) + [email protected] E = 3C.1;C ln ( Ae ) −[email protected] F = −0.0000C( Ae ) −0.180; G = 7.C338 ln ( Ae ) − 3;.175
5iii6 For Ae K 1500,
m = A1( Ae ) + B1?..51−∈ 6 < 0.01 m = A3( Ae ) + B 3?..51−∈ 6 > 0.01
01 E C.5;18L-n5Ae6)83.D5C 91 E )1.1818L-n5Ae6MD.383@ 03 E C.5;18L-n5Ae6)83.D5C 93 E )1.1818L-n5Ae6MD.383@ 'he figure no. 5 shows the (ariation of Nusselt num!er with Aeynolds num!er as predicted !y the e uation 1@ and the data of /a"son et al for AeI300. <imilar plots are made in the figure no.s @ , 7 for 300IAeI1500 and AeK1500 respecti(ely. 'he figure no.D shows the (ariation of Nusselt num!er with Aeynolds num!er as predicted !y e uation 1@ and the data of /a"son et al for the range of Aeynolds num!er !etween 10 to 5000. 0ll the a!o(e plots ha(e !een made at two different solid concentrations to predict the effect of solid concentration on the Nusselt num!er. It can !een seen from the figure no.s 5 to D that the present e uation predicts the e%perimental data of /a"son et al (ery well. 0 plot is made in figure no. C !etween the Nusselt num!er of /a"son et al and that predicted !y the e uation 1@. 'he predicted (alues fit with the e%perimental data well with a slope of 1.00;3 and a correlation coefficient greater than 0.CC 'he present correlation needs to !e (erified with more e%periments conducted for particles of different denisites and with higher Aeynolds num!er. <ince the e uation is highly empirical, further refinement can !e made from more e%perimental results.
. 7 Nusselt Number (Nu) 6 5 4 3 2 1 0 0 20 40 60 -0 Reynolds Number (Re) 100 120 140
rs = 0.05 (Majson et al) rs = 0.05 (%red) rs = 0.004 (Majson et al) rs = 0.004 (%red)
!"ure no.5# /ar!at!on o' Nusselt number &!t+ Reynolds number u% to 200.
30
25
Nusselt Number (Nu)
20
15
10
rs = 0.05 (Majson et al) rs = 0.05 (%red) rs = 0.004 (Majson et al)
5
rs = 0.004 (%red)
0 0 200 400 600 -00 1000 1200 1400 1600 Reynolds Number (Re)
!"ure no.6# /ar!at!on o' Nusselt number &!t+ Reynolds number bet&een 200 0 1500
200 1-0 160 Nusselt Number (Nu) 140 120 100 -0 60 40 20 0 0 1000 2000 3000
Reynolds Number (Re)
rs = 0.05 (Majson et al) rs = 0.05 (%red) rs = 0.004 (Majson et al) rs = 0.004 (%red)
4000
5000
6000
!"ure no.7# /ar!at!on o' Nusselt number &!t+ Reynolds number "reater t+an 1500
200 1-0 160 Nusselt Number (Nu) 140 120 100 -0 60 40 20 0 0 1000 2000 3000 Reynolds Number (Re) !"ure no.-# $om%ar!son bet&een t+e data o' Majson et al and t+e %red!1ted data us!n" t+e e2uat!on 16. 4000 5000 6000 rs = 0.05 (Majson et al) rs = 0.05 (%red) rs = 0.004 Majson et al) rs = 0.004 (%red)
200 1-0 160 Nusselt Number (4red!1ted) 140 120 100 -0 60 40 20 0 0 50 100 Nusselt Number (Majson et al) !"ure no. .# $om%ar!son bet&een t+e %red!1ted 5alues and t+e data o' Majson et al. 150 200
y = 1.00423 R2 = 0...-.
*onclusions: 'he gas)solid heat transfer during flows ta#es place in mo(ing !eds, rotary #ilns and in pneumatic transport for preheating, cooling, drying etc. 'he estimation of heat transfer coefficient !etween gas and the solid is difficult !ecause of the limitations of the a(aila!le correlations in the literature for the prediction of heat transfer coefficient. 0 correlation relating the heat transfer coefficient with the properties of solid, gas and their (elocities, concentration will !e useful in the design and analysis of such systems. 'he present correlation needs to !e (erified and refined with more e%perimental results. :ence, further e%periments are necessary to study the effect of following parameters on gas)solid heat transfer: 1. /ass flu% of the solids. 3. <i$e distri!ution of the solids. 8. <olids of (arious nature with different densities, conducti(ities etc. ;. <olids concentrations in the pipeline. 0 relia!le correlation can !e o!tained using the data from the a!o(e studies. 0n e uation of the form similar to e uations 1 to 1; can !e deduced with additional parameters4dimensionless num!ers to ma#e it suita!le to predict the heat transfer for a wide range of gas)solid systems and applications.
Nomenclature: <ym!ol 2 9 rg, ε rs n Nup hpg dp #g ρg (r µg *pg *p( Ae Pr 'g :fg 2escription 2iameter of the dryer <palding num!er Golume fraction of the gas Golume fraction of the solids *onstant Nusselt num!er for gas)solid heat transfer :eat transfer coefficient !etween the gas and the solid 2iameter of the particle 'hermal conducti(ity of the gas 2ensity of the gas Aelati(e (elocity !etween the gas and the solid Giscosity of the gas <pecific heat of the gas <pecific heat of the water (apour Particle Aeynolds num!er Prandtl num!er 'emperature of the gas -atent heat of (apourisation of water.
0!stract
'he widespread application of heat transfer in gas)solid flow systems in process industries and power plants has moti(ated research in this su!"ect. 'ypical applications include transfer of hot particles 5cooling6, preheating of solids, com!ustion of coal in circulating fluidi$ed !eds , !oilers, transport of F** catalyst !etween reactor and regenerator, pneumatic drying of heat sensiti(e products, transportation of hot fly ash to the disposal plants etc. 'hese applications are critical and re uire careful design of these systems. 'he re(iew of literature clearly shows the enormous wor# !eing done in this field. 'he models a(aila!le for the design of these systems contradict each other and (ary widely for similar operating conditions. 0lso, the parameters that affect the heat transfer in gas)solid flow ha(e not !een accounted for completely. 0 generali$ed e uation is necessary for the presentation of heat transfer in gas)solid flow systems, which will !e useful for design and analysis of such systems, as e(ident from the a(aila!le literature. In the present proposal, heat transfer studies will !e made in counter current mo(ing !eds, co)current pneumatic transport systems for preheating, cooling and drying of solids. 'he effect of mass flu% of air, mass flu% of solid, solid density, si$e , si$e distri!ution, moisture content etc. on the gas)solid heat transfer will !e studied. 9y factorial design, appropriate e%periments will !e conducted to study the effect of a!o(e (aria!les on the gas)solid heat transfer. *orrelations will !e o!tained using dimensionless num!ers for (arious gas)solid heat transfer applications. 'hese correlations will ena!le the calculation of heat transfer coefficient, to !e used in the design and performance analysis of these systems. Nn successful completion of the pro"ect, the results of the pro"ect will !e applied in the process industries, to design a new gas)solid heat transfer system and retrofit the e%isting ones.
9ecause of the o!(ious differences !etween two modes of pneumatic con(eying, their hydrodynamic characteristics are different from that of each other. :ydrodynamics of pneumatic con(eying in dilute phase and dense phase transport has !een widely pu!lished +;,5.. :eat transfer in gas)solid flows: &as)solid heat transfer is important in many industrial applications. 2rying of granular materials is a (ery common operation in chemical, pharmaceutical, food industries etc. Fre uently, the raw materials are preheated using e%haust flue gases. 'he products are cooled using incoming cold air. 0ll the a!o(e operations in(ol(e heat transfer !etween gas and solid in co)current and counter current !eds. 'he commercial applications of operations in(ol(ing gas)solid heat transfer during flow can !e categori$ed as preheating4heating of solids, drying, cooling of solids, reactions li#e com!ustion, crac#ing etc. Preheating4:eating of solids: <olids are heated using hot gases flowing in co)current direction during transportation or reaction. In circulating fluidi$ed !eds, heat is transferred from the gases to the solids so that the solids are heated resulting in reactions, as in the case of circulating fluidi$ed !ed !oilers using coal. 'he spent catalyst from the fluidi$ed !ed crac#er needs to !e regenerated to remo(e the deposition of car!on on the surface of the catalyst. 'he catalyst is repeatedly transported !etween the reactor and the regenerator, during which heat transfer !etween the gas and solid ta#es place. Preheating of #iln feed using e%haust gases from the #iln in cement industries is an important e%ample of gas)solid heat transfer during preheating. 'he #iln feed and hot gases mo(e in counter current direction in the rotary #iln where the necessary reactions ta#e place. 'he e%it temperature of the e%haust gases from the #iln is around 1000 *. 'he heat of the gases is used to preheat the cold solid feed. For this purpose, multistage cyclone separators with pneumatic con(eying ducts !etween them are used in cement industries. In !etween the cyclone separators, the solids are con(eyed pneumatically resulting in the heat transfer !etween the solids and the gases. 9y this way solids are preheated and temperature of air is reduced to around 550 = !efore they enter >lectrostatic Precipitator. 2rying of heat sensiti(e solids: *ertain solids li#e pharmaceutical products? food materials etc are highly heat sensiti(e. 'he e%posure of these materials to high temperature for longer duration will result in the degradation and loss in the uality of the product. 9ut, in(aria!ly these products need to !e dried to reduce the moisture content re uired to meet the deli(ery specifications. 'his is achie(ed in pneumatic con(eying dryers where the residence time is (ery short in the order of few seconds. Pneumatic con(eying dryers are continuous,
con(ecti(e dryers with dilute phase transport suita!le for drying of heat sensiti(e, e%plosi(e, degrada!le or flamma!le materials. :ot air supplies the drying energy and transports the solids through a (ertical pipe +@.. 'ypical applications include drying of alumina, poly(inyl chloride, calcium car!onate etc. 'he other solids that are dried in a pneumatic dryer in industries are animal feed, catalysts, cellulose, clay, corn fi!ers, epsum salt, gypsum, #aolin, pigment, poly propylene, poly styrene, proteins, silica, $eolites etc. 'he schematic diagram of a flash dryer is shown in figure no.1.
>%haust air
Bet <olid 2ried <olid
9lower
:eater
Figure no.1: <chematic diagram of a flash dryer
Figure no.3: <chematic diagram of a cyclone preheater system
*ooling of solids: In certain cases, the solids are to !e cooled to the deli(ery specifications after passing through a high temperature reaction or separation. 'he e%amples are cooling of hot polyethylene granules from the dryer, cooling of flyash during its transportation to disposal site etc. 'hese in(ol(e either counter current mo(ing !eds or co)current pneumatic con(eying system. Aeactions in(ol(ing com!ustion and crac#ing: 'he pyrolysis of oil shale is carried out in a fluidi$ed !ed. 'he (olatile matter is dri(en off in a retort, and the car!onaceous residue is !urnt in a second location to pro(ide the heat necessary. 'his is done in a circulation system where the shale is transported !etween the retort and the heater. 'he transport of shale from the retort to the
heater is !y pneumatic con(eying, whereas its transport from the heater to the retort includes !oth mo(ing !eds and pneumatic transport. *orrelations for gas)solid heat transfer: 'he widespread application of heat transfer in gas)solid flow systems in process industries and power plants moti(ated research in this area in the past two decades. 'he researchers around the world are acti(ely carrying out a large uantum of wor# in this field. 'he re(iew of literature in the gas)solid heat transfer re(eals the following correlations a(aila!le for the calculation of heat transfer coefficient !etween the gas and the solid. 1. 9aeyens)&eldart e uation for pac#ed !ed +@..
Nu
p
=0.010@ Ae 1.;C ...................................................516
(
)
3. =othari e uation for fluidi$ed !ed +@.
Nu
p
=0.08 Ae 1.8 .......................................................5 36
(
)
8. Batson e uation for fluidi$ed !ed +@.
d Nu p = 0.003D Ae1.7 p D
(
)
− 0.3
...................................586
;. &amson e uation for fluidi$ed !ed +@,D.
Nu p =0.010@ Ae 0.5C Pr 0.88 .......................................5 ;6
(
)
5. 2e 9randt e uation for pneumatic dryer +@,D,C..
Nu p =0.1@ Ae 1.8 Pr 0.@7 ............................................556
(
)
@. Aan$)/arshall e uation e uation for e(aporation from water droplets +C..
Nu p =3 +0.@ Ae 0.5 Pr 0.88 ............................................5@6
(
)
7. 9aeyens e uation for pneumatic drying of surface moisture +@,D,C.
Nu p = 1.0@(Ae ).............................................576
D. /odified Aan$)/arshall *orrelation for drying of single wet particle in air +D.
3 + 0.@ Ae 0.5 Pr 0.88 Nu p = 0.7 ..........................5 ;6 (1 + B )
C. =emp et al e uation for drying +C.
Nu p = 3 +0.5 Ae 0.5 Pr 0.88 +0.0@ Ae 0.D Pr 0.88 .............5C6
10. /a"son et al e uation for drying of P> pellets +C..
n Nu p = 3 +0.@rg Ae 0.5 Pr 0.88 ?. Ae < 300.............5106 n n Nu p = 3 +0.5rg Ae 0.5 Pr 0.88 +0.03rg Ae 0.0D Pr 0.88 ?300 < Ae <1500.....5116 n Nu p =3 +0.0000;rg Ae1.D ? Ae >1500................5136
5 nE 8.5 for 8mm Pe pellets6 11. 9androws#i , =ac$mar$y# e uation +C.
0.5CD; Nu p = 0.0011; Ae 0.D15C rs− ?0.00035 < rs < 0.05 , 1D0 < Ae <1D00...........5186
13. =ato correlation for heat transfer !etween oil shale particles and air +10.
8 }0.C7 .........................51;6 Nu p =3.8De − Ae n { ∈1−∈
n = 3.;D ∈ 1− ∈
(
) −0.3D
In the a!o(e e uations, Ae =
Nu p = Pr =
d p ρg vr
µg
h pg d p kg kg
C pg µ g
B=
C pv T g − Td H
fg
(
)
/ason et al +8. made a model for non)suspension gas)solids flow of fine powders in pipe. 'he authors modeled the dense phase transport of powders using the two)layer concept de(eloped for li uid)solids flow. 'he dense phase transport is modeled as two layers: a dilute gas)solid mi%ture a!o(e a dense gas)solids mi%ture. 'he conser(ation e uations for mass, momentum and energy were sol(ed for !oth the gas and the solid phase. 'he model showed good agreement with the e%perimental data in terms of the (ariation of layer height, (elocity and solids concentration. 'hey also concluded that the (ariation of the initial conditions for the same gas and solid mass flow rates had only a small effect on the prediction of fully de(eloped flow.
9aeyens et al +@. descri!ed a procedure for the design of industrial pneumatic con(eying dryer using large)scale e%perimental data. 0ccording to them, hydrodynamics of the pac#ed !ed and the fluidi$ed !ed does not correspond to the hydrodynamics of the pneumatic con(eying, the use of 9aeyens F &eldart e uation, =othari e uation, Batson e uation and &amson e uation will predict erroneous results. 2e9randt e uation and Aan$)/arshall e uation were found to o(erestimate the heat transfer coefficient. 'he authors proposed a correlation for the gas Fsolid heat transfer coefficient in pneumatic drying of surface moisture from PG* and calcium car!onate. 'he authors predicted the temperature and moisture profiles using their correlation and found the profiles to fit the e%perimental data well. 'he draw!ac# of their correlation is that the effects of solids flow rate, porosity are not included. Aadford +7. presented a simple model for particulate drying in pneumatic con(eying systems that can !e implemented easily. 'he model assumed the particles to !e non)hygroscopic, discrete with no interaction with other particles, spherical and of uniform si$e and the flow of gas to !e tur!ulent. :ence the model is (alid only for dilute phase transport of particles of same si$e and spherical shape. In the drying model, the duct was considered to !e made up of a large num!er of segments with each segment representing an e ual incremental time in the duct. 'he model can !e implemented on a spread sheet. 'he pu!lished correlations were tried and did not yield meaningful results, as the correlations were highly specific. Frant$ correlation and 2onsi , Ferrai correlations were found to !e effecti(e for the drying of alumina particles in air. 'he model was simulated using Fran$ correlation for drying of alumina particles and found that the simulated (alues matched the e%perimental data well. 'he applica!ility of the model for drying of particulate solids other than alumina has not !een tried. 0(i -e(y et al +D. sol(ed a steady state one)dimensional flow model for a pneumatic dryer !y ta#ing into account of mass, momentum and heat transfer !etween the gas and the particles phases, to predict the temperature and moisture profiles along the length of the dryer. 0 two) phase continuum model was used to descri!e the steady state flow of wet solid particles and gas through a pneumatic dryer. 'he &amson correlation and modified Aan$ ) /arshall correlation were found to o(erestimate the heat transfer. 'he authors also concluded that for non)adia!atic conditions and for (arying wall temperature, 2e9randt and 9aeyens e uation predict the heat transfer well. 'heir model is applica!le for dilute phase con(eying only. /ason et al +C. made a computational in(estigation of transient heat transfer n pneumatic transport of granular particles of 8 mm polypropylene pellets using a 2istinct >lement /ethod 52>/6 to model heat transfer in gas solid flow systems. 'he e%periments were conducted to study heat transfer in !oth dilute and dense phase pneumatic transport. 'he authors made a re(iew of e%isting e uations for heat transfer in dilute phase and dense phase con(eying. Aan$)/arshall e uation was found to apply for particles with small AeynoldHs num!er 5AeI3006. 9aeyens e uation was found to o(erestimate the heat transfer for 8 mm polyethylene pellets. 'he authors modified the e uation of =emp et al !y su!stituting different constants in the original e uation to account for the tur!ulent !oundary layer that would de(elop for large particles. 'hey
proposed a correlation for gas)solid heat transfer of polyethylene pellets and suggested that the effect of particle si$e, density on the empirical constants needs to !e e(aluated. 'he influence of particle concentration on the performance of the system was predicted and found to consistent with the e%perimental data. 'he time consumed !y the 2>/ model for large num!er of particles is more and hence, the model was not e%tended for dense phase flow. 9ertoli et al +10. made an analytical study on the radiati(e and con(ecti(e heat transfer on pneumatic transport of particles. 'hey found that =atoHs correlation predicts that heat transfer well. 9ut the empirical constants used were specifically for heat transfer !etween the oil shale particles and air. 'he analytical solution was compared with the e%perimental data in the literature and found to predict the particle and fluid temperature well. 'hey concluded that the performance of any model to predict the temperature profile depends on the correlation used for the estimation of the particle Nusselt num!er. *ollado et al +11. simulated the mass and energy !alances in one)dimensional two phase flow at steady state !y assuming uniform gas (elocity, uniform solid (elocity and uniform solid distri!ution o(er the cross section of the ducts !y adding a new e uation to the classical mass !alance e uation for the two)phase flow. 'he energy !alance resulted in new correlations for the pressure drop in pneumatic con(eying which predicted the e%perimental data (ery well. /ason et al +13. descri!ed a simulation system for pneumatic con(eying to o(ercome the pro!lem encountered during design, optimi$ation and up gradation of these systems. *orrelations used to predict the pressure drop and their limitations in terms of fle%i!ility were presented. 'he simulation system presented impro(ed the fle%i!ility of the model. Future Prospects: 'he figure no.8 shows the comparison of predicted (alues of Nusselt num!er for same Aeynolds num!er !y different e uations a(aila!le. It is clear from the figure that the e uations a(aila!le for the design of systems in(ol(ing gas)solid heat transfer contradict each other and (ary widely for similar operating conditions. 0ll the parameters that affect the heat transfer in gas)solid flow ha(e not !een accounted for. 'he e uations 1 to 10 do not ta#e the effect of solids (olume concentration or the (oidage in to account. 'he correlations are (ery specific and cannot !e used for other systems as they either tend of underestimate or o(erestimate heat transfer+3)C.. 0 generali$ed e uation is necessary for the presentation of heat transfer in gas)solid flow systems, which will !e useful for the design of such systems, as e(ident from the literature.
Com parison betw een the correlations for gas-solid heat transfer in pneum atic conveying 4500 4000 3500 Nusselt Num ber 3000 2500 2000 1500 1000 500 0 0 500 1000 1500 Reynolds Num ber 2000 2500 3000 ()* Kot+ar! *amson ,e)(randtl R)M (aeyens
Figure no. 8: *omparison !etween prediction of different correlations for similar conditions.
150
Re = 1750 (Majson et al) Re = 1750 (Kato et al)
Nusselt Number (Nu)
100
50
0 0 0.01 0.02 0.03 0.04 0.05 0.06
Reynolds Number (Re) !"ure no.4# $om%ar!son bet&een Majson et al and Kato et al data 'or same Reynolds number
'he e uations suggested !y /a"son et al and =ato et al correlate the Nusselt num!er with Aeynolds num!er, solid (olume fraction and Prandtl num!er. It is e(ident from the figure no.; that the two correlations (ary widely in their prediction for same operating conditions i.e. for the same Aeynolds num!er and solid (olume fraction. 'he de(iations could !e due to the use of different solid materials in the respecti(e e%periments. =ato et al used oil shale particles while /a"son et al reported the results for 8 mm polyethylene pellets. 'he particle si$e has !een ta#en into account in the Aeynolds Num!er 5Ae6, while the density of the particle has not !een accounted for in !oth these correlations. :ence, the de(iation !etween the correlations can !e o(ercome !y ta#ing the density of the particles in to account. 0n attempt is made to propose a correlation, which fits the data of !oth =ato et al and /a"son et al. 'he data of =ato et al and that of /a"son et al are calculated from their correlations. 0n e uation of the following form is o!tained !y modifying the =atoHs correlation to account for the density of the particles.
Nu p = 3.8De
−8
Ae
n
{∈1−∈ }
0.C7 ρ p
n = 3.;D ∈ 1− ∈
m E f5Ae, 1)ε6
(
) −0.3D
........................5156 ρ
m
ρp E Particle density 5#g4m86 ρE 3800 #g4m8 Following forms for JmH were o!tained !y comparison of data of /a"son et al and =ato et al. 5i6 For Ae I 300,
)} + B?...(1−∈) < 0.01 m = A{ Ln(1−∈
m = C (1−∈ ) 3 + D(1−∈) + E?....0.01 < (1−∈) < 0.08
) + G?.......(1−∈) > 0.08 m = F (1−∈
A = 0.1;C ln ( Ae ) −1.010C B =1.0@;@ ln ( Ae ) −@.D785 C = −3;3.;8 ln ( Ae ) +1;71.8 D = 38.0;1 ln( Ae ) −118.;7 E = 0.1D53 ln( Ae ) −1.3858 F = D.88@1 ln( Ae ) − [email protected] G = 0.;151 ln( Ae ) − 3.558;
5ii6 For 300IAeI1500,
m = A(1−∈ ) 3 + B(1−∈ ) +C ?...(1−∈ ) < 0.00; m = D (1−∈ ) 3 + E (1−∈ ) + F ?....0.00; < (1−∈ ) < 0.08 m = G{ Ln (1−∈ )} + F ?.......(1−∈ ) > 0.08
A = −11073 ln ( Ae ) +1117D0 B =113 Ln( Ae ) −100;.3 C = −0.3857 ln ( Ae ) +1.C8C7 D = −8C7.18 ln ( Ae ) + [email protected] E = 3C.1;C ln ( Ae ) −[email protected] F = −0.0000C( Ae ) −0.180; G = 7.C338 ln ( Ae ) − 3;.175
5iii6 For Ae K 1500,
m = A1( Ae ) + B1?..51−∈ 6 < 0.01 m = A3( Ae ) + B 3?..51−∈ 6 > 0.01
01 E C.5;18L-n5Ae6)83.D5C 91 E )1.1818L-n5Ae6MD.383@ 03 E C.5;18L-n5Ae6)83.D5C 93 E )1.1818L-n5Ae6MD.383@ 'he figure no. 5 shows the (ariation of Nusselt num!er with Aeynolds num!er as predicted !y the e uation 1@ and the data of /a"son et al for AeI300. <imilar plots are made in the figure no.s @ , 7 for 300IAeI1500 and AeK1500 respecti(ely. 'he figure no.D shows the (ariation of Nusselt num!er with Aeynolds num!er as predicted !y e uation 1@ and the data of /a"son et al for the range of Aeynolds num!er !etween 10 to 5000. 0ll the a!o(e plots ha(e !een made at two different solid concentrations to predict the effect of solid concentration on the Nusselt num!er. It can !een seen from the figure no.s 5 to D that the present e uation predicts the e%perimental data of /a"son et al (ery well. 0 plot is made in figure no. C !etween the Nusselt num!er of /a"son et al and that predicted !y the e uation 1@. 'he predicted (alues fit with the e%perimental data well with a slope of 1.00;3 and a correlation coefficient greater than 0.CC 'he present correlation needs to !e (erified with more e%periments conducted for particles of different denisites and with higher Aeynolds num!er. <ince the e uation is highly empirical, further refinement can !e made from more e%perimental results.
. 7 Nusselt Number (Nu) 6 5 4 3 2 1 0 0 20 40 60 -0 Reynolds Number (Re) 100 120 140
rs = 0.05 (Majson et al) rs = 0.05 (%red) rs = 0.004 (Majson et al) rs = 0.004 (%red)
!"ure no.5# /ar!at!on o' Nusselt number &!t+ Reynolds number u% to 200.
30
25
Nusselt Number (Nu)
20
15
10
rs = 0.05 (Majson et al) rs = 0.05 (%red) rs = 0.004 (Majson et al)
5
rs = 0.004 (%red)
0 0 200 400 600 -00 1000 1200 1400 1600 Reynolds Number (Re)
!"ure no.6# /ar!at!on o' Nusselt number &!t+ Reynolds number bet&een 200 0 1500
200 1-0 160 Nusselt Number (Nu) 140 120 100 -0 60 40 20 0 0 1000 2000 3000
Reynolds Number (Re)
rs = 0.05 (Majson et al) rs = 0.05 (%red) rs = 0.004 (Majson et al) rs = 0.004 (%red)
4000
5000
6000
!"ure no.7# /ar!at!on o' Nusselt number &!t+ Reynolds number "reater t+an 1500
200 1-0 160 Nusselt Number (Nu) 140 120 100 -0 60 40 20 0 0 1000 2000 3000 Reynolds Number (Re) !"ure no.-# $om%ar!son bet&een t+e data o' Majson et al and t+e %red!1ted data us!n" t+e e2uat!on 16. 4000 5000 6000 rs = 0.05 (Majson et al) rs = 0.05 (%red) rs = 0.004 Majson et al) rs = 0.004 (%red)
200 1-0 160 Nusselt Number (4red!1ted) 140 120 100 -0 60 40 20 0 0 50 100 Nusselt Number (Majson et al) !"ure no. .# $om%ar!son bet&een t+e %red!1ted 5alues and t+e data o' Majson et al. 150 200
y = 1.00423 R2 = 0...-.
*onclusions: 'he gas)solid heat transfer during flows ta#es place in mo(ing !eds, rotary #ilns and in pneumatic transport for preheating, cooling, drying etc. 'he estimation of heat transfer coefficient !etween gas and the solid is difficult !ecause of the limitations of the a(aila!le correlations in the literature for the prediction of heat transfer coefficient. 0 correlation relating the heat transfer coefficient with the properties of solid, gas and their (elocities, concentration will !e useful in the design and analysis of such systems. 'he present correlation needs to !e (erified and refined with more e%perimental results. :ence, further e%periments are necessary to study the effect of following parameters on gas)solid heat transfer: 1. /ass flu% of the solids. 3. <i$e distri!ution of the solids. 8. <olids of (arious nature with different densities, conducti(ities etc. ;. <olids concentrations in the pipeline. 0 relia!le correlation can !e o!tained using the data from the a!o(e studies. 0n e uation of the form similar to e uations 1 to 1; can !e deduced with additional parameters4dimensionless num!ers to ma#e it suita!le to predict the heat transfer for a wide range of gas)solid systems and applications.
Nomenclature: <ym!ol 2 9 rg, ε rs n Nup hpg dp #g ρg (r µg *pg *p( Ae Pr 'g :fg 2escription 2iameter of the dryer <palding num!er Golume fraction of the gas Golume fraction of the solids *onstant Nusselt num!er for gas)solid heat transfer :eat transfer coefficient !etween the gas and the solid 2iameter of the particle 'hermal conducti(ity of the gas 2ensity of the gas Aelati(e (elocity !etween the gas and the solid Giscosity of the gas <pecific heat of the gas <pecific heat of the water (apour Particle Aeynolds num!er Prandtl num!er 'emperature of the gas -atent heat of (apourisation of water.
0!stract
'he widespread application of heat transfer in gas)solid flow systems in process industries and power plants has moti(ated research in this su!"ect. 'ypical applications include transfer of hot particles 5cooling6, preheating of solids, com!ustion of coal in circulating fluidi$ed !eds , !oilers, transport of F** catalyst !etween reactor and regenerator, pneumatic drying of heat sensiti(e products, transportation of hot fly ash to the disposal plants etc. 'hese applications are critical and re uire careful design of these systems. 'he re(iew of literature clearly shows the enormous wor# !eing done in this field. 'he models a(aila!le for the design of these systems contradict each other and (ary widely for similar operating conditions. 0lso, the parameters that affect the heat transfer in gas)solid flow ha(e not !een accounted for completely. 0 generali$ed e uation is necessary for the presentation of heat transfer in gas)solid flow systems, which will !e useful for design and analysis of such systems, as e(ident from the a(aila!le literature. In the present proposal, heat transfer studies will !e made in counter current mo(ing !eds, co)current pneumatic transport systems for preheating, cooling and drying of solids. 'he effect of mass flu% of air, mass flu% of solid, solid density, si$e , si$e distri!ution, moisture content etc. on the gas)solid heat transfer will !e studied. 9y factorial design, appropriate e%periments will !e conducted to study the effect of a!o(e (aria!les on the gas)solid heat transfer. *orrelations will !e o!tained using dimensionless num!ers for (arious gas)solid heat transfer applications. 'hese correlations will ena!le the calculation of heat transfer coefficient, to !e used in the design and performance analysis of these systems. Nn successful completion of the pro"ect, the results of the pro"ect will !e applied in the process industries, to design a new gas)solid heat transfer system and retrofit the e%isting ones.
