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Growth rate correlation for potassium sulphate crystals in a fluidized bed crystallizer
1290
Shorter Communtcatlons ltWER8Nm 111 Suzulu M and Kawazoe K, 1 Chem Engns Japan 1975 8 379 [21 MUSICD M and Suzuki M , Vrh CHISA J3-1 Praha 1975 Kenkyu 1974 26 275 13) Suzuki M and Kawaqe K , S~ISUII 141 Suzuki M. and Kawazoe K , J Chern Engng Jupan 1975 8 79 ES] Carman P C and Raal F A, Prvc Roy Sot A2O!J38 [6]GdhlandE R.BaddourR F andRussdJ L,AIChE I 1958 4 90 171 SmHh R K and Metzner A B , J Phys Chem 1964 68 2741 [8] Ash R and Barrer R M , Surfncc Scr I%7 8 461 [9] Neretmeks I Chem Engng SCI 1976 31 1029
Callfomra Polytechnrc State Unwersrty YOSHITAKA SUDOt San Lurs Obrspo DRAGOSLAV M MISIC CA 93407 USA
MOTOYUKI SUZUKI
Instrtute of lndustnal Scznce Unrverwty of Tokyo, Roppongr, Mtnato-ku, Tokyo Japan
tOn leave from Tokyo Nattonal Techmcal College, Japan
Hahop,
Growth rate correlation for potassium sulphati in a fluid&d (Recerved 3 &cember
1977, accepted 4 March 1978)
In a previous paper the authors[l] mvesaated growth and dissolution charactenst~cs of potassmm sulphate crystals m a Urn-d bed crystallizer by the mtegral method Previous work, on the growth of potassium sulphate crystals, performed m tierent types of eqmpment under d&rent expenmental condotmns showed v-on m results [ l-81 For a rational comparison of the two methods It ISdesvabk to carry out experunents under smular condItiona m the same laboratory With this view rt IS tho&t desirable to mves@@e the growth rate character~sttcs of potassmm sulphate m the same crystalhzer by the dtierentml method and compare them with previously reported results by the mtegral method In general the overall growth rate depends on temperature, crystal sue, hydrodynamic slNatlon and the presence of unpun-s The overall growth rate may be expressed by an efflplncai relatlonstip as R = aLb exp (-EIRsT)Pg
(1)
where the Arrhemus type temperature dependence and the Bransom type size dependence are used[l, 3.41 The effect of slurry voIdage IS not tncorporated tn eqn (1) because the slurry voidage cannot be defined preclseIy m tlus type of expenment S@cant vartauons m vatues of slurry voldrge may be observed dunn8 the runs The authors [l] and Muihn and Jones[3] showed that the system voidage 18 an m-cant vanable to charactense the hydrodynamic system In the dlfferentud method of analysts a small quantity of closely sized and weighed crystals IS suspended by upward flowm8 stream of the supersaturated soluhon m the growth zones of the Utudned bed crystalllztr In dus type of operation. solutlon concentration ebanges are relatively small but at the same tune measurable sohd deposItion IS aclueved Duect measurement of the crystal we&t change allows to determme the overall growth rate as
RXAW Aht
at a particular tempexature, crystal SW and supersaturatlon level assuming ne8h&e mass deposItion as nuclei The average size and surface area of crystals may be evaluated from the corresponding values of the uutml seed and the linal product The surface area of the seed crystals may be calculated as
&,woF
P&o
crystals
bed crysta&er
(3)
where the average value of the ratio of the surface to the volume shape factors, F, may be taken as seven121 Under the assumptlons of constant shape factors, newble nucleation, breakage and agglomeration, the average size and surface area of the product crystals may be determmed as 213
(4)
(5) -ALTEcENlQuE
The crystalltxer used was the same as that described _ _._ prev~ouslyllJ The expernnental procedure used was sun&u to that used by Mulhn ct al [2.4] A hot, filtered solution of LR grade potassuun sulphate m Qstdled water, of approxunately known Concentration. was charged to the crystallizer The sohttlon was cuculated and mamtamed at 15’C above the workmg temperature A sample (- 20 cm3) for uutml concentraUon analySISwas taken out The mmtml supersaturafiod was aclueved by slow coolm8 When the worlung temperature was attamed, closely sued seeds. previously we@& (-0 085 kg) were char8ed to the crystalhzer The solution velocity was ad~ustea m such a way that the crystals were umformly suspended wlthm the crystalbza~on zone and thus velocity was used for that partuxdar SIX. of seed The seeds were allowed to grow until the total we&t was about 0 01 k8 The d-on of run was dependent on the solututlonsupersaturauon and vaned from 1800 to 7500s At the end of the run the final concentration was measured and the product crystals were removed, dned and carefully sieved Solution temperature was controlled w~thm &O PC and solution concentration measurements were made by evaporatmg the sample to dryness g~vmg an estunated accuracy of more than ?10m4 kg of K2SOJkg of solution The supersaturation was determined by subtractmg the solubtity from actual concentratlon Solubdlty was estunated by relation&p gwen by Mullm and Gaska[S] The change m supersaturation dunng the run was relatively small (< 1 5 x lo-” kg K#OJlrS Ha) The overall growth rate was evaluated by eqn (2) usmg log mean and anthmetx mean values of crystal surface area The maxunum per cent change m the growth rate values was not more than seven Log mean and arrthmetrc average values of
1291 Table 1 Values of the parameters IIIeqn (1) Usmg log mean vanables (r P
Parameter
7oOxlti 045 1s 76 243 097
1 Coefticient, (I 2 Exponent of sue. b 3 Actwation energy. E kJ/mol 4 Orderwrt Poru,g Multiple correlation coefficient
Table 2 Range of vanables used m growth rate data Vanable 1 2 3 4 5 6
Supersaturation Temperature Size of the seed SIX of the product Slurry voldage Run tnne
unit
Range
0 35 x lO-2-l 3 x lo-’ kg K,SO,/kg H,O 34X3-318 K 38x10-‘-65x10-’ m 3 8 x 10-4-l 1 x 10-3 96-99 Gi 1800-7500 s
Table 3 Number balance for a typical growth run 1 Weight of seed crystals, kg 2 Average size of seed crystals, m 3 Crystals In seed, number 4 We&t of product crystals, kg 5 Weight mean size of product crystals, m 6 Relative per cent change (RCN) m number (population) of crystals m product and seed, based on that of seed as gwen by the equatron RCN = (N, - &)/A$,
Mesh size -16 M-18 18-22 22-25 25-30 30-36
497x lo-3 5 5 x lo-’ 2 13x 104 12 61 x lO-3 7 5 x 10-4 110
Size analysis of the product crystals Weight of Cumulauve number of product Cumulatwe Avg size lo6m crystals wt% l@kg 925 n5 650 550 460
0 1957 37730 18398 6 3105 02024 00280
299 445 z: %4
113x 10’ 0 45 4104 244 097
396x104 046 14 69 240 097
59OXld 046 39 57 240 097
value of a might not be exertmg a s&&cant effect on the growth rate The order of the growth process IS about 2 4 m both the metbods[l] The activation energy IS about 15 and 4OkJlmol when SupersaturatIon and relatwe supersaturation are used respechvely as the dnvmg force This difference m activation energres IS due to the posluve temperature dependence of the solubtity wluch IS used m defimtion of relative supersaturation These values are lower than that determmed by the mte& method (- 35 and 60 Wlmol) [ 11 Thrs may be due to the different contnbution of the d&uslonal step to the overall growth process The size dependency which may be observed because of soluhon velocity, crystal shape or surface charactensfic IS found to be comparable m both the methods CONCLUSIONS
The growth rate charactenstlcs of potassuun sulphate III a thudrzed bed crystallizer are mveshgated by a Merentml method Over the range of vanables Investigated tbe order of the growth process with respect to SupersaturaQon IS 2 4, the activation energy IS about 15 kJ/mol and the exponent of the crystal size IS 045 The results are comparable to those of the Integral method, previously reported, under sunllar hydrodynamic condotlons Department of Chemrcal Technology Unrversrty of Bombay Matunga. Bombay400 019
3 41x ld 623x ld 226x104 235x10’ 237x 10’
supersaturatlon and crystal size were also calculated from uutlal and final values The parameter values m eqn (1) were estunated by the least squares multiple hnear regresslon analyst of data of suty experunents usmg log mean or anthmetlc average vmble The analysis was repeated wltb tbe supersaturation bemg replaced by relahve supersaturation wbch may be defined as the ratio of the supersaturation to the solub&y The results are reported 111Table 1 The ranges of the vanables studled are also gwen m Table 2 A number balance of the seeds and product crystals helps m venfymg the assumption of negbgtble nucleatlon The number balance for a typIcal run IS presented m Table 3 In most of the expenments number balance agrees well However, IIIfew expenments at a relatively b&er supersaturation level (> 0 01 kg of K2SOJkg of H20) s@cant nucleation effects (as h& as 40% more crystals) were observed Visual observation m&cated that tbe seed and the product crystals were of sunllar shape The average size calculated by eqn (5) and the we&t mean size of the product crystals were found to be comparable IIImost of the experunents Parameters m eqn (1) except the value of II are the same when tbe log mean and mthmetic mean values are used Probably the
Usmg anthmetuz mean vanables P 0
N S TAVARE M R CHIVATE
NOI’ATION
:
b E F z P i T W AW
coefficient (eqn 1) area of crystals, m2 exponent of size (eqn 1) activation energy, W/m01 rat10 of surface to volume shape factors (= 7 0) order of the growth process crystal sue, m SupersaturatIon, kg K#OJkg Hz0 overall growth rate, kg/m’s umversal gas constant (8 3143 J/molK) run tune, s absolute temperature, K we&t of the crystals, kg we&t dtierence of product and seed crystals, kg
Greek symbols cr relative supersaturation pc density of crystals, kg/m’ Subscripts 0 seed quantltles P product quantlues REpEIlENCEs
[II Tavare N S and Cluvate M R , Tmns Inst Chem Engrs , In press
Shorter Communr&on8
1292 [2] Mulhn J W and Gaska [3] Muhn J W and Jones 51 302 [4] Mulhn J W, Garsrde Filndh 1974 13 299 ES] Muh J W and Gaska
C , Ccvll I Chcm Z31gng 1%9 47 483 A G , Trans Znst Chem J%grs 1973 J, aad Das S N , Id
Engng Ckm
C , J Chem Bngftg I.&to 1973 18 217
[6] Rusen H N and Hulburt H M , Ckm Engng Prvg Symp ser 197117(110) 18 m Rosen H N and Hulburt H M , C&m Engng Z+ag Symp ser 197167(110) 27 [S] Randolph A D and &JpsOpd K , Znd Engng Chem Fnndls 1970 9 165
Shorter Communtcatlons ltWER8Nm 111 Suzulu M and Kawazoe K, 1 Chem Engns Japan 1975 8 379 [21 MUSICD M and Suzuki M , Vrh CHISA J3-1 Praha 1975 Kenkyu 1974 26 275 13) Suzuki M and Kawaqe K , S~ISUII 141 Suzuki M. and Kawazoe K , J Chern Engng Jupan 1975 8 79 ES] Carman P C and Raal F A, Prvc Roy Sot A2O!J38 [6]GdhlandE R.BaddourR F andRussdJ L,AIChE I 1958 4 90 171 SmHh R K and Metzner A B , J Phys Chem 1964 68 2741 [8] Ash R and Barrer R M , Surfncc Scr I%7 8 461 [9] Neretmeks I Chem Engng SCI 1976 31 1029
Callfomra Polytechnrc State Unwersrty YOSHITAKA SUDOt San Lurs Obrspo DRAGOSLAV M MISIC CA 93407 USA
MOTOYUKI SUZUKI
Instrtute of lndustnal Scznce Unrverwty of Tokyo, Roppongr, Mtnato-ku, Tokyo Japan
tOn leave from Tokyo Nattonal Techmcal College, Japan
Hahop,
Growth rate correlation for potassium sulphati in a fluid&d (Recerved 3 &cember
1977, accepted 4 March 1978)
In a previous paper the authors[l] mvesaated growth and dissolution charactenst~cs of potassmm sulphate crystals m a Urn-d bed crystallizer by the mtegral method Previous work, on the growth of potassium sulphate crystals, performed m tierent types of eqmpment under d&rent expenmental condotmns showed v-on m results [ l-81 For a rational comparison of the two methods It ISdesvabk to carry out experunents under smular condItiona m the same laboratory With this view rt IS tho&t desirable to mves@@e the growth rate character~sttcs of potassmm sulphate m the same crystalhzer by the dtierentml method and compare them with previously reported results by the mtegral method In general the overall growth rate depends on temperature, crystal sue, hydrodynamic slNatlon and the presence of unpun-s The overall growth rate may be expressed by an efflplncai relatlonstip as R = aLb exp (-EIRsT)Pg
(1)
where the Arrhemus type temperature dependence and the Bransom type size dependence are used[l, 3.41 The effect of slurry voIdage IS not tncorporated tn eqn (1) because the slurry voidage cannot be defined preclseIy m tlus type of expenment S@cant vartauons m vatues of slurry voldrge may be observed dunn8 the runs The authors [l] and Muihn and Jones[3] showed that the system voidage 18 an m-cant vanable to charactense the hydrodynamic system In the dlfferentud method of analysts a small quantity of closely sized and weighed crystals IS suspended by upward flowm8 stream of the supersaturated soluhon m the growth zones of the Utudned bed crystalllztr In dus type of operation. solutlon concentration ebanges are relatively small but at the same tune measurable sohd deposItion IS aclueved Duect measurement of the crystal we&t change allows to determme the overall growth rate as
RXAW Aht
at a particular tempexature, crystal SW and supersaturatlon level assuming ne8h&e mass deposItion as nuclei The average size and surface area of crystals may be evaluated from the corresponding values of the uutml seed and the linal product The surface area of the seed crystals may be calculated as
&,woF
P&o
crystals
bed crysta&er
(3)
where the average value of the ratio of the surface to the volume shape factors, F, may be taken as seven121 Under the assumptlons of constant shape factors, newble nucleation, breakage and agglomeration, the average size and surface area of the product crystals may be determmed as 213
(4)
(5) -ALTEcENlQuE
The crystalltxer used was the same as that described _ _._ prev~ouslyllJ The expernnental procedure used was sun&u to that used by Mulhn ct al [2.4] A hot, filtered solution of LR grade potassuun sulphate m Qstdled water, of approxunately known Concentration. was charged to the crystallizer The sohttlon was cuculated and mamtamed at 15’C above the workmg temperature A sample (- 20 cm3) for uutml concentraUon analySISwas taken out The mmtml supersaturafiod was aclueved by slow coolm8 When the worlung temperature was attamed, closely sued seeds. previously we@& (-0 085 kg) were char8ed to the crystalhzer The solution velocity was ad~ustea m such a way that the crystals were umformly suspended wlthm the crystalbza~on zone and thus velocity was used for that partuxdar SIX. of seed The seeds were allowed to grow until the total we&t was about 0 01 k8 The d-on of run was dependent on the solututlonsupersaturauon and vaned from 1800 to 7500s At the end of the run the final concentration was measured and the product crystals were removed, dned and carefully sieved Solution temperature was controlled w~thm &O PC and solution concentration measurements were made by evaporatmg the sample to dryness g~vmg an estunated accuracy of more than ?10m4 kg of K2SOJkg of solution The supersaturation was determined by subtractmg the solubtity from actual concentratlon Solubdlty was estunated by relation&p gwen by Mullm and Gaska[S] The change m supersaturation dunng the run was relatively small (< 1 5 x lo-” kg K#OJlrS Ha) The overall growth rate was evaluated by eqn (2) usmg log mean and anthmetx mean values of crystal surface area The maxunum per cent change m the growth rate values was not more than seven Log mean and arrthmetrc average values of
1291 Table 1 Values of the parameters IIIeqn (1) Usmg log mean vanables (r P
Parameter
7oOxlti 045 1s 76 243 097
1 Coefticient, (I 2 Exponent of sue. b 3 Actwation energy. E kJ/mol 4 Orderwrt Poru,g Multiple correlation coefficient
Table 2 Range of vanables used m growth rate data Vanable 1 2 3 4 5 6
Supersaturation Temperature Size of the seed SIX of the product Slurry voldage Run tnne
unit
Range
0 35 x lO-2-l 3 x lo-’ kg K,SO,/kg H,O 34X3-318 K 38x10-‘-65x10-’ m 3 8 x 10-4-l 1 x 10-3 96-99 Gi 1800-7500 s
Table 3 Number balance for a typical growth run 1 Weight of seed crystals, kg 2 Average size of seed crystals, m 3 Crystals In seed, number 4 We&t of product crystals, kg 5 Weight mean size of product crystals, m 6 Relative per cent change (RCN) m number (population) of crystals m product and seed, based on that of seed as gwen by the equatron RCN = (N, - &)/A$,
Mesh size -16 M-18 18-22 22-25 25-30 30-36
497x lo-3 5 5 x lo-’ 2 13x 104 12 61 x lO-3 7 5 x 10-4 110
Size analysis of the product crystals Weight of Cumulauve number of product Cumulatwe Avg size lo6m crystals wt% l@kg 925 n5 650 550 460
0 1957 37730 18398 6 3105 02024 00280
299 445 z: %4
113x 10’ 0 45 4104 244 097
396x104 046 14 69 240 097
59OXld 046 39 57 240 097
value of a might not be exertmg a s&&cant effect on the growth rate The order of the growth process IS about 2 4 m both the metbods[l] The activation energy IS about 15 and 4OkJlmol when SupersaturatIon and relatwe supersaturation are used respechvely as the dnvmg force This difference m activation energres IS due to the posluve temperature dependence of the solubtity wluch IS used m defimtion of relative supersaturation These values are lower than that determmed by the mte& method (- 35 and 60 Wlmol) [ 11 Thrs may be due to the different contnbution of the d&uslonal step to the overall growth process The size dependency which may be observed because of soluhon velocity, crystal shape or surface charactensfic IS found to be comparable m both the methods CONCLUSIONS
The growth rate charactenstlcs of potassuun sulphate III a thudrzed bed crystallizer are mveshgated by a Merentml method Over the range of vanables Investigated tbe order of the growth process with respect to SupersaturaQon IS 2 4, the activation energy IS about 15 kJ/mol and the exponent of the crystal size IS 045 The results are comparable to those of the Integral method, previously reported, under sunllar hydrodynamic condotlons Department of Chemrcal Technology Unrversrty of Bombay Matunga. Bombay400 019
3 41x ld 623x ld 226x104 235x10’ 237x 10’
supersaturatlon and crystal size were also calculated from uutlal and final values The parameter values m eqn (1) were estunated by the least squares multiple hnear regresslon analyst of data of suty experunents usmg log mean or anthmetlc average vmble The analysis was repeated wltb tbe supersaturation bemg replaced by relahve supersaturation wbch may be defined as the ratio of the supersaturation to the solub&y The results are reported 111Table 1 The ranges of the vanables studled are also gwen m Table 2 A number balance of the seeds and product crystals helps m venfymg the assumption of negbgtble nucleatlon The number balance for a typIcal run IS presented m Table 3 In most of the expenments number balance agrees well However, IIIfew expenments at a relatively b&er supersaturation level (> 0 01 kg of K2SOJkg of H20) s@cant nucleation effects (as h& as 40% more crystals) were observed Visual observation m&cated that tbe seed and the product crystals were of sunllar shape The average size calculated by eqn (5) and the we&t mean size of the product crystals were found to be comparable IIImost of the experunents Parameters m eqn (1) except the value of II are the same when tbe log mean and mthmetic mean values are used Probably the
Usmg anthmetuz mean vanables P 0
N S TAVARE M R CHIVATE
NOI’ATION
:
b E F z P i T W AW
coefficient (eqn 1) area of crystals, m2 exponent of size (eqn 1) activation energy, W/m01 rat10 of surface to volume shape factors (= 7 0) order of the growth process crystal sue, m SupersaturatIon, kg K#OJkg Hz0 overall growth rate, kg/m’s umversal gas constant (8 3143 J/molK) run tune, s absolute temperature, K we&t of the crystals, kg we&t dtierence of product and seed crystals, kg
Greek symbols cr relative supersaturation pc density of crystals, kg/m’ Subscripts 0 seed quantltles P product quantlues REpEIlENCEs
[II Tavare N S and Cluvate M R , Tmns Inst Chem Engrs , In press
Shorter Communr&on8
1292 [2] Mulhn J W and Gaska [3] Muhn J W and Jones 51 302 [4] Mulhn J W, Garsrde Filndh 1974 13 299 ES] Muh J W and Gaska
C , Ccvll I Chcm Z31gng 1%9 47 483 A G , Trans Znst Chem J%grs 1973 J, aad Das S N , Id
Engng Ckm
C , J Chem Bngftg I.&to 1973 18 217
[6] Rusen H N and Hulburt H M , Ckm Engng Prvg Symp ser 197117(110) 18 m Rosen H N and Hulburt H M , C&m Engng Z+ag Symp ser 197167(110) 27 [S] Randolph A D and &JpsOpd K , Znd Engng Chem Fnndls 1970 9 165