Nucleation kinetics of the potassium chloride-water system with predictions of crystal-size

distributions in crystallizers of complex configuration

Item Type text; Thesis-Reproduction (electronic)

Authors Metchis, Steven Geoffrey, 1951-

Publisher The University of Arizona.

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NUCLEATION KINETICS OF THE POTASSIUM CHLORIDE-WATER SYSTEM

WITH PREDICTIONS OF CRYSTAL-SIZE DISTRIBUTIONS

IN CRYSTALLIZERS OF COMPLEX CONFIGURATION

bySt even Geoffrey Metchis

A Thesis Submitted to the Faculty of the

DEPARTMENT. OF CHEMICAL ENGINEERING

In Partial Fulfillment of the Requirements For the Degree of

MASTER OF SCIENCE

In the Graduate College

THE UNIVERSITY OF ARIZONA

1 9 7 4

STATEMENT BY AUTHOR

This thesis has been submitted in partial fulfill­ment of requirements for an advanced degree at The Univ e r ­sity of Arizona and is deposited in the University Library to be m a d e .available to borrowers under rules of the L i ­brary o

Brief quotations from this thesis are allowable without special permission, provided that accurate acknowl­edgment of source is made. Requests for permission for e x ­tended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his judgment the proposed use of the material is in the inter­ests of scholarship. In all other i n s t a n c e s h o w e v e r , per­mission must be obtained from the author.

APPROVAL BY THESIS DIRECTOR

This thesis has been approved on the date shown below:

A.^D. Randolph Professor of

Chemical Engineering

DATE

For my parents and Roslyn

ill

ACKNOWLEDGMENT

The author wishes to express his gratitude to D r «

Alan Do Randolph for his guidance during this research pro­

ject* The Department of Chemical Engineering is also ac ­

knowledged for providing facilities for the project* The

author is indebted to the. National Science. Foundation for

financial support of the project through Grant No. GK-16407 »

Special recognition goes to Roslyn Field whose u n ­

selfish efforts made the long hours in the laboratory more

bearable.

Finally, the author wishes to thank his parents

whose encouragement and understanding helped him to accom­

plish this work *

iv

T A B L E .OF CONTENTS

Page

LIST OF ILLUSTRATIONS „ . . . . . . . . . . . . . „ . vi

LIST OF TABLES ix

ABSTRACT „ . . . . . . . . . . . . . . . . . . . x

INTRODUCTION . . . . . . . . . . . . . . . . . . . . . 1Industrial Crystallization of Potash 8Previous Studies . . . . . . . 12

Crystal Growth and Nucleation Kinetics . . . . 13Computer Simulation of Crystal-Size D i s ­

tributions . , . . . » . . . . . ... . . . . 16

.THEORY . . . . . . . . . . . . . . . . . . . . . . . . 20

EQUIPMENT AND EXPERIMENTAL PROCEDURE . . . . . . . . . 28MSMPR Equipment and Procedure . . . . . . . . . . 28

MSMPR Equipment . . . . . . . . . . . . . . . 28MSMPR Procedure . ... . . . . . . . . . . . . 33

Classifying Crystallizer Equipment and P r o ­cedure . . . . . . . . . . . . . . . . . . . . 39Classifying Crystallizer Equipment . . . . . . 39Classifying Crystallizer Procedure . . . . . . 43

RESULTS . . . . . . . . . . . . . . . . . . . . . . . . 48Nucleation Kinetics . . . . . . . . . . . . . . . 48Stability Analysis . . . . . . . . . . . . . . . . 70Computer Simulation . . . . . . . . . . . . . . . 77

CONCLUSIONS AND RECOMMENDATIONS . . . . . . . . . . . 93

APPENDIX A: POPULATION DENSITY PLOTS . . . . . . . . 96

NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . 106

REFERENCES . . . . . . . . . . . . . . . . . . . . . . 108

v

LIST OF ILLUSTRATIONS

Figure Page

1 World potash production 3

2 Crystal purity in presence of impurities . . . 9

3 Mutual solubility of KC1 and NaCl in water • . 10

4 Kalium Chemical solution mining process . , » 11

5 MSMPR crystallizer 31

. 6 MSMPR experimental equipment 34

7 Schematic of MSMPR equipment 35

8 Schematic of R-z equipment 44

9 Crystallizer-fines trap assembly 45

10 Crystals grown from saturated KC1 solu­tion, Average size = 254 microns . . , 51

11 Crystals grown from saturated KC1 solu-: tion in presence of P b C l ^ » Average

size « 254 microns • . ■ • • • • O . . o « . 51

12 Crystals grown from saturated KC1 s olu­tion in presence of NaCl and M g S O 4 »Average crystal size = 254 microns 0 » „ , 53

13 Variation in solids concentration withtime for run 061474 „ » , , 0. . . . . . 0 56

14 Population density vs crystal size, run021374 V , 0 0 0 0 0 0 , 0 0 0 0 , 0 0 0 0 58

15 Population density vs crystal size, run031274 , , 0 . 0 o o o , o o o o o o o o o o 59

16 Population density vs crystal size, run06 14 7 4 0 0 , 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0

vi

vii

LIST OF ILLUSTRATIONS--Continued

Figure Page

17 Population density vs crystal size, run022674 . . . . . . . . . . . . . . . . 61

18 Nucleation rate as a. function of growthrate o • » • , « 0 » o • . . • . . . ... . . 63

19 Nucleation rate as a function of growthrate and solids concentration . „ » «, » . 67

2 0 r Comparison of theoretical and experimentalsolids concentration » e........... ......... .. 69

21 Effect of fines removal on CSD 0. Q’;: • 72

22 Effect of removal port on CSD . <> e 6 „ 73

23 Variation of solids concentration withtime. Results' of experimental cr y s ­tallization runs 3/10/74 and 3/28/74 . . . 75

24 Variation of solids concentration withtime. Results of experimental crys­tallization runs 4/22/74 and 4/30/74 . . . 76

25 Time-averaged3/10/74

population d ens ity p l o t , run

26 Time-averaged 3/28/74 ,

population density. p l o t , run. 83

27 Time-averaged 4/22/74 ,

population density p l o t , run

28 Time-averaged 4/30/74 ,

population density p l o t , run

29 Variation of solids concentration withtime. Results of computer simulationof runs 3/10/74 and 3/28/74 . . . . ' . »„ . 8 8

30 Variation of solids concentration withtime. Results of computer simulationof runs 4/22/74 and 4/30/74 . . . 89

viii

Figure

31

LIST OF ILLUSTRATIONS— Continued

Page

Variation of solids concentration withtime. Comparison of experimental and simulated r e s u l t s .for run 3/10/74 . , o.. 90

32 Variation of solids concentration withtime. Comparison of experimental and simulated results for run 4/22/74 . „ . . 91

LIST OF TABLES

Table Page

1 Some Potash Minerals . . . . . . . . . . . . . 4

2 Values of the Nucleation Constant for KC1 . . . . 15

3 Units for V a r i a b l e s ,in Table 4 . . . . . . . . 3 9

4 MSMPR Experimental Operating Conditions . . . . 40

5 R-z Experimental Operating Conditions . . . . . 47

6 Chemical Additives Studied as. Habit M o d i ­fiers . . . . . . . . . . . . . . . . . . . . 50

7 Summary of MSMPR Experimental Results . . . . . 55

8 Analysis of Variance, Four Parameter Model . . 6 6

9 Analysis of Variance, Two Parameter Model . . . 6 6

10 Summary of R-z Experimental Results . . . . . . 71

11 Values of C^ for Modelling of Stable Runs . . . 80

12 Values of C^ for Modelling Unstable Runs i . . 81

ix

ABSTRACT

An experimental study was conducted to determine

growth and nucleation kinetics for the crystallization of

potassium chloride from a realistic potash b r i n e . Four in­

dependent variables were studied: residence time, agita­

tion, crystallization temper a t u r e , and feed saturation

t e mperature• Bench scale mixed suspension.mixed product

removal crystallization techniques were used. It was found

that a simple power law model involving the growth rate and

suspension density was successful in correlating the n ucle­

ation rate.

The nucleation kinetic model so determined was used

in the computer simulation of an operating crystallizer of

complex configuration. The purpose was to demonstrate that

this type of simulation can be a valuable design tool. The

steady-state crystal-size distributions for several experi­

ments from this crystallizer were successfully modelled

using as input to the computer program the experimental

operating conditions. The dynamic behavior of the distri­

butions were also successfully modelled. In each case the

x

stability of the distribution was accurately predicted.

In the case of an unstable distribution, the period and

magnitude of the oscillation were accurately r e p r o d u c e d ,

INTRODUCTION

Potassium is the third most important fertilizer

ingredient in terms of the actual tonnage used in the world

for plant nutrient purposes. The large abundance of potas­

sium containing minerals located throughout the world in­

sures that the use of potassium fertilizers will increase

in the coming y e a r s . Potassium does not appear naturally

in its elemental form but is found as various salt com­

pounds. The word "potash" is used to indicate any of these

potassium salts. In the fertilizer industry potash refers

specifically to the oxide, Ka 0. The classification of

fertilizers by their K a 0 content has become a standard in

i n d u s t r y , but is an unfortunate one since this oxide does

not appear n a t u r a l l y . Nonetheless it allows for a simple

and direct comparison of fertilizers. The word "potash" is

derived from a historical manufacturing technique in which

ashes were leached and the resulting solution allowed to

evaporate in iron pots.

Potash has been known and used for over three

c e n t u r i e s . The Gauls and Germanic groups used potash as

1

■ 2a condiment instead of salt. Potash first became a com­

mercial product in the middle of the nineteenth century

when it was found in a well brine in Germany in 1843.

Scientists soon established that it was a good plant food.

By 18 61 commercial production was well u n d e r w a y . Today b e ­

tween 9 0 and 95% of the potash produced in the world is

used for fertilizer purposes.

Potash is found in both soluble and insoluble

(primarily silicate) forms. Only the soluble forms are

economically attractive to process. The soluble forms are

mainly chlorides and sulphates 9 although nitrates and other

forms occur and are processed. Table 1 is a list of the

more common soluble potash forms and their K a 0 c o n t e n t .

The high Ka 0 content of potassium chloride makes it the

most important potash salt. As an ore, potassium chloride

is called sylvite. When found mixed with sodium chloride

(halite) the ore is called sylvinite. A typical analysis

of sylvinite is 23% s y l v i t e , 73% h a l i t e , and 4% other com­

pounds. This analysis can vary considerably.

The recognition that potassium is an excellent

plant food is emphasized by the fact that world-wide potash

consumption is increasing at a rate of 7% per year. Figure

1 shows the corresponding trend in potash p r o d u c t i o n . In

1947 , production of potash was 3.3 million tons of K 2 0.

In 19 6 6 the output rose to 16.2 million tons of K 2 O, an

amazing five-fold increase in nineteen y e a r s .

It has been estimated that if the current trend is

continued, known reserves of potash are sufficient to last

for 1,750 years into the f u t u r e . This figure does not

take into account the discovery of any new ore reserves.

This insures that there will be a sufficient supply of this

very important plant nutrient in the years to c o m e .

ocv|XtotioHtio•H

•rHS

15

10

1950 1955 1960 1965

Figure 1. World potash production

4

Table 1. Some Potash Minerals

Mineral Compo s it ion %Ka 0

Chlorides

Sylvite KC1 63.1

Carnallite K C 1•M g C 1 2 *6 H 20 17.0

Kainite K C 1•M g S 0*•3 H 20 18.9

Hankite K C 1 • 9 N a 2 S0 4 •2N a 2 C 0 3 3.0

Sulphates

Polyhalite K 2SO 4 •M g S O 4 •2 C aS0 4 •2 H 20 15.5

Langbeinite K 2 S O 4 •2 MgS0 4 2 2.6

Leonite K 2 SO 4 •M g S O 4 •4 H 20 25.5

Schoenite K 2 SO 4 *MgS 0 4 •6 H 20 23.3

Krugite K 2SO 4 •MgSO 4 •4CaSO 4 •2H20 1 0 ?

Glasserite 3 K 2SO 4 . N a 2 SO 4 42.6

Syngenite K 2SO 4 •C a S O 4 •H 20 28.8

Apthitalite (K,N a ) 3 (NaSO 4 ) 3 4 2.5

Kalinite K 2SO 4 •A 1 2 (SO 4 ) 3 •24H20 9 .9Alunite : K 2 •A 1 e ( O H ) 1 2 . (SO 4 ) 4 11.4

Nitrates

Niter KNO 3 4 6.5

5

In the developmental years of potash production

crystallization techniques were first used for the pro­

cessing of ores. Crystallization has the advantage of

yielding a product purity in excess of ninety-nine per

cent. It is also a costly p r o c e s s . Manufacturers soon

found that by using a flotation process potash could be

produced much more c h e a p l y . Product purity was lower,

about 9 6 %, but acceptable for marketing. For these

reasons flotation replaced crystallization as the method

for processing potash o r e s . With the development of solu­

tion mining techniques crystallization is again becoming

an important method for processing p o t a s h . If the mineral

is solution mined the potash is already in solution when

processing begins and crystallization is the natural

choice. Crystallization studies of potash have not been

extensive and serious gaps exist in the knowledge of KC1

kinetics. It is the purpose of this work to fill some of

these gaps.

From studies of other systems, it has been found

that such factors as t e m p e r a t u r e , stirring rate, super-

saturation, and residence time in the crystallizer can

affect crystal growth rate and also the rate at which new

crystals are f o r m e d . It has also been found that these

factors may affect different systems in completely

opposite m a n n e r s • While similar correlations can be made

between nucleation.rate and the four factors' listed above,

there appear in these correlations constants which can

only be evaluated empirically for a given system. As yet

no means has been found for prediction of these constants

by theoretical considerations.

Certain modifications to the simple mixed-

suspension mixed-product removal (MSMPR) crystallizer can

be made in order to improve commercial productivity.

These include equipment for removal of small crystals at

a rapid rate, increased removal of large crystals , and

removal of clear liquor from the c r y s t a l l i z e r . These

techniques tend to increase production by limiting the

number of small crystals, removing only product size

crystals, and increasing the suspension density in the

crystallizer. Unfortunately these same techniques tend

to destabilize the system, causing cycling of the crystal-

size distribution (CSD) as evidenced by changes in the

solids concentration.

The objectives of this study were twofold. The

first objective was to evaluate the correlation constants

in a nucleation kinetics model for a potash salt. This

model has been found to be effective in describing other

systems. Potassium chloride was chosen for study since

it is the most important soluble potash form. The kinetic

study was to be accomplished using bench scale MSMPR tech­

niques developed by Randolph and Larson (1971). Secondly,

the kinetic model was to be used in a computer simulation

to match the results of experiments conducted with the same

potash salt but in a crystallizer of more complicated d e ­

sign than the MSMPR crystallizer. The computer program

used was the Mark 111 CSD Simulator developed by Nuttall

(1971)o The purpose was to find the limiting values for

the various removal rates and sizes before destabilization

of the CSD occurred. The system modelled was a classified

product crystallizer with fines removal designed and built '

by E . P. K . Ottens at The University of A r i z o n a , This type

of crystallizer is known as an R-z crystallizer because

small crystals are removed at a rate R times the MSMPR r e ­

moval rate and product crystals are removed at z times the

MSMPR rate. Ottens also conducted the R-z experiments and

his results are reported later in this w o r k . This study

is unique in that it is the first time these three areas of

research--MS^tPR k i n e t i c s , computer simulation, and sta- .

bility analysis--have been brought together to form a sin­

gle, comprehensive study.

8

Industrial Crystallization of Potash

An important technique for refining potash ores is

crystallization. At one time this was the most important

method for potash refining, but was poorly understood, until

recently. As a result, in the past two decades flotation

has become the most important method. This trend could be

reversed with recent advances in the science of crystal­

lization ,

Crystallization has the advantage of being able to

produce a purer and whiter product than flotation, since

iron and other impurities are excluded from the crystal

lattice. Figure 2 shows that a product purity in excess

of 9 9% can be obtained from a solution containing signifi­

cant quantities of sodium c h l o r i d e , More control of pr o d ­

uct size is also possible through crystallization. The

disadvantages are the higher capital and maintenance costs

arising from the handling of hot corrosive brines, and

larger fuel and cooling r e q u i r e m e n t s ,

The basis for the separation of KC1 from NaCl by

c:r y syt a 1 l̂ i z a til on is the unique solubility characteristics

for the system, shown in Figure 3, The solubility of KC1

increases rapidly with increasing temperature. The solu­

bility of NaCl increases only slightly with temperature

but in a common solution with K C 1 , the NaCl solubility

actually drops as temperature rises. Since the tempera­

ture in the crystallizer is kept lower than the tempera­

ture of the feed solution, the KC1 will precipitate out

of solution, but the NaCl will n o t .

100.0

mto 99.8■Uto>•»nCJti•H 99.6O

99.410 20 30

g N a C l /100 g H 20

Figure 2. Crystal purity in presence of impurities (Noyes, 1966).

If the ore has been mined by a conventional shaft

method, it is crushed and brought into contact with hot

brine at 95° - 106 ° C which has been saturated with NaCl but

which is unsaturated with K C 1 . The KC1 is then leached

from the ore by the brine, leaving behind the NaCl in the

ore. The brine is then clarified in a settling tank and

cooled in vacuum c r y s t a l l i z e r s . As the brine cools, the

Figure

10

20 40 60 80Tem pera tu re , °C

100

3. Mutual solubility of KC1 and NaCl in water.

Figure

Quadruple-Effect Evaporators

s =0======s=0===s 0 :CondenserSteam

FeedThickener

(NaCl) Slurry CentrifugeLiquid From Pond

rtH- Crystallizers PIRecycle to Evaporators Salt SolutionCentrifuge t o P o n d

Comp a c tor H yd roclone ‘ _ \ / F l u e Gas

inesScreens RotaryDrier

FlakeBreaker

Dried KC1

To Storage andLoad out

4. Kalium Chemical Solution Mining Process ("Kalium’s Potash Solution Mining Plant Will Go On-Strearn this Fall in Canada," 19 64).

.12KC1 crystallizes 'but the NaCl does not- The product KC1

is washed and dried and the spent brine is recycled to the

leaching operation.

The Kalium Chemical solution mining plant in

Regina, Saskatchewan is unique and should be the forerunner

of other similar plants. A schematic of this operation is

shown in Figure 4. The brine from the mining operation

goes to a bank of quadruple effect evaporators to remove

enough water to bring the brine close to s a t u r a t i o n „ The

solution then goes to a thickener 90 feet in diameter to

settle out any solid NaCl and other, insoluble impurities »

The overflow from the thickener goes to a series of four

Swenson draft tube baffle c r y s t a l l i z e r s , each of which is

responsible for producing a specific size particle. The

crystallizers are fitted with equipment for rapid removal

of the small c r y s t a l s , called f i n e s , and for classification

of the product stream. The product is c e n t r i f u g e d , d r i e d ,

and screened to form different grades of fertilizer. The

Kalium plant is capable of producing 600,000. tons of potash

p er y ear .

Trevious Studies

Little work has been done in the field of potasium

chloride crystallization. This is one of the reasons why

this study was performed. Some previous work is described

13

as follows. Also described is a computer program developed

for use as a design tool for crystallizers of any configur­

ation and which was used in this s t u d y •

Crystal Growth and. Nucleation Kinetics

Lessieux and Svoronos (1966) performed experiments

in which they first obtained an aqueous solution saturated

with both potassium chloride and sodium chloride at a

known temperature, then supersaturated the solution to a

measured degree by lowering the tem p e r a t u r e . At this

point KC1 seed crystals of known mass and surface area ^

were introduced into the solution.. After a time the crys- . tals were removed and the growth rate was measured by a

technique developed by the researchers. Saturation tem-? -

peratures from 30* - 8 0° C were tested.

It was found that the growth rate varied linearly

with the degree of supersaturation for a given initial

crystal surface area. For the same degree of supersatura­

tion , the growth rate increased with increasing saturation

t e m p erature. The increased growth rate did not arise from

any variation in the amount of potassium chloride which

came out of solution since this was essentially the same

for a given degree of supersaturation over the range of

temperatures studied* It was also determined that the

growth rate was a weak function of temperature.

14

Genck and Larson (197 2) carried out a series of ex­

periments to determine the effect of temperature on growth

and nucleation rates of different systems* Their experi­

ments were of the MSMPR type conducted in a well-mixed

cooling crystallizer with a capacity of 1 2 , 5 liters of . "

slurry * The hold-up or retention time in the crystallizer

ranged between 15 - 45 minutes* Conditions were controlled

to maintain a constant solids concentration between all

experiments* Three potassium salts were studied: potas­

sium c h l o r i d e ? sulphate, and nitrate*

Genck and Larson were not able to measure supersat­

uration and so could not verify some of the results of

Lessieux and Svoronos (1966), However they did form a c o r ­

relation between nucleation rate and the crystal growth

rate. For potassium chloride this correlation was:

B° = k G 1 ' n

In this correlation B° is the nucleation rate in number of

nuclei per minute and G is the crystal growth rate in m i l ­

limeters per minute. The kinetic rate c o e f f i c i e n t , 1, was

found to be 2*55* The nucleation constant k n was found to

be a weak function of temp e r a t u r e , The values for kn . d e ­

termined in these experiments are listed in Table 2*

15

For potassium chloride it was found that as tem­

perature increased the nucleation rate increased corre­

spondingly. Under conditions of constant solids

concentration the. growth rate actually decreased with

increasing temperature.

Table 2. Values of the Nuclea- tion Constant for KCl

T, °C kXI

1 2 . 0 K00oo\ 1 0 9

2 0 . 8 1 . 1 2 x 1 0 1 0

3 0.0 1.33 x 1 0 1 0

The experiments of Lessieux and Svoronos (19 6 6 )

were a poor analogy to the conditions actually occurring

in an industrial c r y s t a l l i z e r . As such* their numerical

results should be used cautiously in applications to more

realistic sit u a t i o n s . Their qualitative r e s u l t s 9 however s

do point the way to further r e s e a r c h . It was indicated

that temperature, super s a t u r a t i o n , and solids concentra­

tion may affect the crystal growth rate. Further research

must provide quantitative r e s u l t s .

The work of Genck and Larson (1972) is more real­

istic and the MSMPR technique is the method generally

16

accepted as the best means to determine.crystallization

k i n e t i c s » It was not the purpose of the study to make

a comprehensive analysis of potassium chloride, but to

show the different ways temperature may affect different

systems. They did show in passing the effect of tempera­

ture on the nucleation and growth rates of KC1. Solids

concentration was not considered as a variable in these

e x p e r i m e n t s , and although agitation has been shown to

affect the rate of nucleation in other systems (Randolph

and C i s e , 197 2 ) , its effect of potassium chloride crys- "

tallization was not shown. One of the objectives of the

current study was to identify which factors influence K C 1

crystallization and then to quantify that influence in an

empirical model.

Computer Simulation of Crystal-Size Distributions

Nuttall (1971) presents an excellent history of

crystallizer simulation up to the date of his w o r k . This

history is not repeated h e r e . It was not the purpose of

the current study to develop a computer model for crystal-

size d i s t r i b u t i o n s , but to utilize N u t t a l l ? s model in new

areas of simulation. A brief discussion of N u t t a l l v s work

is appropriate o

Nuttall developed three computer m o d e l s , the Mark

I, II, and III simul a t o r s . The Mark I simulator is the

computer implementation of a g e n e r a l i z e d , steady-state

17

mathematical model of essentially all possible continuous

backmixed c r y s t a l l i z e r s . The basis for the model is the

population balance developed by Randolph and Larson (1971).

The computer model is designed to be able to handle seed­

ing, multiple inlet and outlet streams, fines removal,

classification, staging, size-dependent growth rates, and

secondary nucleation k i n e t i c s . The computer algorithm com­

bines the generality of the mathematical model without re­

quiring internal modification for the study of various

crys,tallizer configurations and conditions. This is made

possible through a subroutine into which the program user

may place specific subfunctions which mathematically d e ­

scribe the physical configuration of the crystallizer being

studied. The user is limited only by his ability to d e ­

scribe physical systems mathematically.

The Mark III simulator is an extension of the

steady-state simulation to the problem of CSD dynamics.

The model employs the distributed dynamic population b a l ­

ance, hut still can solve steady-state problems. The heart

of the program is a Golden Section search r o u t i n e , which

facilitates the steady-state solution by eliminating the

need to iterate through the main loop of the program. The

routine quickly finds the growth rate required to maintain

a particular production rate. Only after this has been

determined is the dynamic solution a t t e m p t e d .

In this study the Mark III simulator was used to

model the dynamic behavior of a single stage crystallizer

with fines removal, liquor advance, and product classifi­

cation. In particular it was desired to simulate condi­

tions which would produce a cycling C S D . These conditions

had previously resulted in a cycling CSD. in a bench-scale

crystallizer of the type being simulated. It was the in-r

tention of this study to show that such computer programs

can be valuable tools for crystallizer design and analysis.

It has been qualitatively known that such processes

as fines destruction, classified product removal, and clear

liquor advance can cause cycling of the C S D . The ability

to be able to predict the limits to which these processes

may be taken before cycling occurs is a major concern for

those who would design an industrial crystallizer. This

was the goal set b y .Beer (1973), who performed a stability

analysis using spectral techniques bn the linearized popu­

lation balance. A Class II classified crystallizer with

fines removal and magma-dependent nucleation kinetics was

studied. Results from Beer f s study were presented as crit­

ical contours of the nucleation/growth rate exponent i =

d (log B ° )/d (log G ) . The most inf luential parameters lead­

ing to CSD instability were found to be the size at which

product classification occurred and the presence of recycle

of dissolved fines back to the crystallizer.

19

To produce a cycling CSD it was necessary to lower

the natural stability limit of i = 21 so that it became

equal to or less than the experimental value of i deter­

mined in the MSMPR studies » The contours presented by Beer

were used as a reference for the amount of classification

and recycle necessary to attain c y c l i n g . Without these

contours much additional work and experimentation would

have been required. B e e r ’s study is an important addition

to crystallization theory and practice.

THEORY

Most physical systems can be completely described

through mass and energy balances, along with kinetic or

equilibrium relationships. More information is required

and vital for a complete description of particulate

dispersed-phase systems. This arises from the fact that

one or more independent properties can be given values for

each individual particle due to the processes which act in

a random manner to produce or influence each particle.

The concept of a population density and its u s eful­

ness in the analysis of particulate systems has long been

recognized. Theoretical relationships for the calculation

of crystal-size distributions were derived by Saeman

(1956). In particular, for a mixed suspension crystallizer

with unclassified d i s c h a r g e , operating at steady-state, and

with growth rate as a function of supersaturation, Saeman

derived the now well-known theoretical size distribution

as :

n = n° e x p [-L/G t ] (1)

21

Several investigators have built upon this early

work of Saeman to form a comprehensive theory for partic­

ulate systems and in particular a theory for cryst alliza­

tion processes. Randolph and Larson (1962) conducted an

extensive study of steady-state and transient operation of

a mixed suspension c r y s t a l l i z e r . This study provided the

basis of the population balance. Randolph (1964) presented

a more rigorous form of the population balance for systems

of countable entities. Other forms of the generalized p o p ­

ulation balance have since been presented by Hulbert and

Katz (1964). For a complete description of the theory b e ­

hind the population balance, the reader is referred to

Randolph and Larson (1971). What follows is the basic co n ­

cept of the population balance as it applies to this study.

Consider a size range from Li to L 2 > with L 2 larger

than Li, and let the difference L 2 - L % be designated A L .

The number of crystals in this size range per unit volume

is AN. The population density is then found by dividing

the number of crystals by the width of the size r a n g e .

Then in the limit as the size range becomes vanishingly

s m a l l :

lira AN dN /oxAL^O AL = dL = n <2 >

The population density must then depend upon the crystal

size at which the derivative in Equation 2 is evaluated.

There are several forms of the population balance

which are useful for describing various system configura­

tions. The most general form is the micro-distributed po p ­

ulation balance:

If + + V * ( v en) - B + D = 0 (3)

In many cases of engineering i n t e r e s t , the pro­

cesses involved in the crystallization system take place in

regions which can be considered to be well-mixed. In these

situations the spatial distribution of the crystals is not

of interest or i m p ortance. The volume of the well-mixed

region can then be averaged into the equations , yielding

the macro-distributed population balance:

It * ^ * » - » * <*>k

For a single stage, mixed suspension mixed product removal

cry s t a l l i z e r , Equation 4 can be considerably simplified

under the following conditions:

1. M c C a b e ’s AL law is applied to the system. This is a law of nature observed by McCabe that for many crystallization systems growth rate is in­dependent of crystal size.

23

2. All feeds to the crys tallizer contain no cry s ­tals.

= 0 ( 6 )

3. The population density of the crystallizer d i s ­charge is identical to that of the mixed sus­pension.

nQ = n (7)

4. No agglomeration or gross crystal fracture o c ­curs .

D = B = 0 (8 )

5. The suspension volume is held constant.

d(log V) = od t

6 . The retention time in the crystallizer is:

(9)

t = (1 0 )O

Under these conditions Equation 4 b e c o m e s :

f t + G ! t - - 7 ( I D

If steady-state operation is also imposed upon the system.

Equation 11 can be directly integrated to obtain the expo­

nential distribution:

n = n° e x p [-L/G t ] (12)

This equation is the steady-state solution of the

population balance for a mixed suspension mixed product

24

removal crys talliz e r . Equation 12 plots as a straight line

on semi-logarithmic graph p a p e r . The intercept of the line

is the natural logarithm of the zero-size population den-

ity, often called the nuclei density, defined as:s

(13)L = 0

The slope of the line has a value of - 1 /G t . Knowing the

residence time, T , for a particular experiment, the growth

rate can be determined from the slope of the line.

The suspension density, or weight of solids per

unit volume, is given by:

M t = 6 pkv n ° (Gt ) 4 (14)

This equation gives the theoretical value of the suspension

density for a given crystal-size distribution. Once the

values for growth rate and nuclei density have been d e ter­

mined, the suspension density can be calculated by Equation

14. It is possible to measure M̂ , directly by collecting a

sample of the crys talliz er slurry , filtering the s a m p l e ,

and weighing the dried crystals. By comparing the values

of resulting from these two processes a consistency

check of the experimental data can be made.

25

In order to prepare a population density plot it is

first necessary to be able to calculate point values of the

population density. These can be calculated easily from

the following r e l a t i o n :

M (dW/dL)n = ------- (15)

P V 3

In this equation L is the average size of two successive

sieve screens, dL is the difference between the sizes of

the two screens, and dW is the weight fraction of crystals

in the sample trapped by the lower screen. The shape fac­

tor, , relates the crystal volume to the cube of the a v ­

erage screen size. All of the quantities on the right-hand

side of Equation 15 can be determined from experiment or a

screen analysis. This equation was derived from the def i ­

nition of the weight fraction of crystals in a size range

being the number of crystals in that size range times the

weight per crystal divided by the weight of all crystals.

An important objective of this research was the d e ­

termination of nuclei densities and growth rates from v a r i ­

ous crystal-size distributions. These distributions were

generated from a series of experiments designed to meet the

conditions leading to the development of Equation 11. Four

variables--retention time, crystallizer temperature, feed

26

saturation temperature, and agitation rate--were studied

as to their effects on the crystal-size distribution.

Equally important in this study was the determination of

the nucleation rate. This is the rate at which crystals of

vanishingly small size are formed and is given by:

L-0 dt(16)

This derivative may be expanded into the following f o r m :

»• - 3T L-*0 £ < i n

It is recognized that the derivative dL/dt is the crystal

growth rate. From Equation 13 it is seen that dN/dL | L->0

is the nuclei density. Then it follows that:

B° = n°G (18)

Thus the nucleation rate can be directly obtained from the

experimental results.

Other investigators (Randolph and Cise, 1972;

Randolph and Youngquist, 19 7 2) have found that a suitable

correlation for the nucleation rate of many systems has the

f o r m :

B° = k n (T,RPM)G 1 M T:j (19)

27where may have the form:

kn = kiex p [ k 2 /T](RPM ) k 3 (20)

A model of this form was used to correlate nucleation rate

to the various physical parameters studied.

The development of the population balance approach

to crystallization has helped to bring this important unit

operation out of the realm of art and into the realm of

science. The ability to analyze experimental data in a

logical and thorough manner is the key to successful design

practices. It is hoped that this study will add to the

growing knowledge of crystallization and lead to more ef fi­

cient and productive crystallization processes.

EQUIPMENT AND EXPERIMENTAL PROCEDURE

The experimental portions of this study fall into

two areaso Initial studies were carried out in a mixed

suspension mixed product removal c r y s t a l l i z e r « These were

followed by experiments with a classified product crystal-

lizer. The discussion here is divided along these lines.

- MSMPR Equipment and Procedure

This section combines two descriptions » First d i s ­

cussed is the construction of the MSMPR crystallizer and

associated e q u i p m e n t „ This is then followed by an outline

of the experimental procedure by which the data were ob­

tained o

MSMPR Equipment

The crystallizer used in this portion of the study

was a ten liter polyethylene vessel, A stainless steel

draft tube was fixed concentric with the vessel and sup­

ported by four stainless steel baffles extending about

three-quarters of the height of the vessel. To the draft

28

29tube was welded a tightly wound cooling coil of 3 / 8 inch

stainless tubing. A three-bladed impeller was fitted into

a seat in the bottom of the vessel and was driven by a m o d ­

el 2-R agitator manufactured by the Bench Scale Equipment

C o m p a n y , This agitator was capable of providing stirring

rates up to 800 r p m . A flexible coupling in the shaft b e ­

tween the motor and the blade eliminated much of the v i b r a ­

tion caused by imprecise placement of the motor mount above

the c r y s t a l l i z e r W a t e r was circulated through the cooling

coil and maintained at constant temperature by a Forma-

Junior Model 2095 bath and circulator obtained from the

Forma-Scientific Company of Marietta, O h i o „

A Model S-3 ,TTherm-0-Watch" electronic controller

manufactured by the I 2R Company maintained constant temper­

ature in the crys t a l l i z e r . When the mercury level in a

thermometer immersed in the slurry moved up to a sensing

clip attached to the thermometer, a solenoid valve was

closed. This valve was located in the cooling water circu­

lation line and when closed stopped flow of the water to a

bypass loop. Thus more water was directed to the crystal­

lizer , which caused the temperature in the crystallizer to

drop. When the temperature dropped sufficiently, about

1 / 2 ° F , the solenoid was opened, and some of the cooling w a ­

ter then bypassed the crystallizer.

30

Liquid level was also controlled in the crystalliz-

ero This was achieved by the use of a Matheson "Lab-Stat"

controller which sensed changes in electrical conductance

of a glass probe filled with a salt solution. The probe

was suspended just above the desired liquid level and its

sensitivity was adjusted so that when the liquid touched

the probe the controller was activated. This caused an

air-operated ball pinch valve to open and an Eastern Model

D-ll centrifugal pump to operate. Slurry was removed for a

specific time period which could be dialed into a delay-

relay in the controller circuit. This time delay was a p ­

proximately four seconds for all of the experiments

conducted s, but was adjusted so that the liquid level was

lowered from 1/4 to 1/2 inch per removal period. A water

flush was continuously run through the pump to avoid crys­

tal b u i l d - u p . Figure 5 shows the crystallizer assembly with

temperature and liquid level p r o b e s .

The port through which the slurry was removed was

located at approximately one-third of the height of the

crystallizer w a l l . Isokinetic removal of the slurry re­

quired that removal be at the same velocity as the circula­

tion rate of the slurry inside the c r y s t a l l i z e r . This was

achieved by connecting the Eastern pump to a powerstat and

adjusting the pump rpm by varying its power i n p u t . Slurry

Figure 5. MSMPR crystallizer .

32

was pumped either to a drain or to a vacuum filtering appa­

ratus if a sample was desired, depending on the position of

two ball valveso

The feed tank was a thirty gallon cylindrical tank

with an inner wall of heavy duty polyethylene and a fiber­

glass outer w a l l » A single-loop heating coil of 3/8 inch

stainless tubing was fitted inside the vessel about one

inch above the bottom and connected through the walls by

"Swagelok" bulkhead unions. Heating was accomplished using

steam. A thermometer protruded into the feed liquor from

the side wall near the bottom of the tank but above the

heating coil. Another "Therm^O-Watch" controller sensed

the feed temperature and opened or closed a steam solenoid

valve as required. The tank had a removable polyethylene

cover through which was fitted an air-operated stirrer

which had as its main function the breaking-up of any ther­

mal gradients. Also attached to the cover was a cooling

water condenser to avoid pressure buildup inside the tank

.by having its contents open to the atmosphere while not

losing any water vapor from the l i q u o r . A drain valve was

also fitted at the bottom of the t a n k .

The feed line was either 3/8 or 1/4 inch stainless-(

steel tubing and was wrapped with heating tapes to avoid

crystallization in the line. The feed was delivered to the

33

crystallizer by a Research Appliance Corporation micro-

bellows pump capable of delivering up to 185 ml/min. There

was no filter in the feed line. A feed sampling port was. " - • ' '

located just upstream from the c r y s t a l l i z e r . A water line

was also tapped into the feed line upstream from the pump.

to allow for washout of any plugging which might occur d u r ­

ing an experimento

Figure 6 shows the complete experimental apparatus

while Figure 7. is a schematic drawing of the equipment.

MSMFR Procedure

The day preceding an experimental run, a batch of

feed solution had to-be prepared. A known volume of water

was put into the feed tank. From the mutual solubility

curve for KC1 and NaCl the amount of each salt to be added

was calculated. These amounts were set such that the r e ­

sulting solution would be under saturated with respect to KC1

by 20°F and just saturated with respect to NaCl. Also added

was 0.75 g Mg/100 g water, in the form of M g S 0 4 »7 H % 0 . This

combination of salts represents a typical brine found in a

solution mining plant. The solution was allowed to sit

overnight at the desired feed temperature to insure that all

solid material was dissolved.

Before the run was started, the crystallizer temper­

ature and level controllers were turned on to allow them to

Figure 6 . MSMPR experimental equipment.u>

Steam

Bellows Pump

Refrigeration Unit

b*— water

Feed Tank

PinchValveCrystallizer

waterFlush

Drain

Vacuum

Trap

Figure 7. Schematic of MSMPR equipment

36

warm up. The crystallizer was charged with saturated li­

quor saved from the previous run. The refrigeration unit

was turned on and water was circulated through the cooling

coil so that the liquor would be near the desired operating

temperature when the experiment was started. In this ini­

tial stage the cooling water actually acted as a heating

medium for the crystallizer charge. At this time the w a ­

ter flush was started through the removal pump* The power

to the heating tapes was turned on to allow the feed line

to come to the feed temperature.

When all of this was accomplished the feed rate was

set to give the desired residence time in the crystallizer.

This was done by adjusting a screw setting on the bellows

pump. Flow was diverted from the crystallizer through the

sampling port so that the flowrate could be checked by a

bucket-and-stopwatch t e c h n i q u e . When the flowrate was at

the correct setting, the feed was allowed to flow into the

crystallizer. The proper agitation was set by adjusting a

speed control knob on the motor until the motion of the

shaft was frozen by a strobe tachometer. The crystallizer

was then seeded with approximately four pounds of potassium

chloride c r y s t a l s . At this point the experiment was in its

operating mode. Frequent checks on the feed flowrate. and

the various temperatures and controllers were made through­

out the course of the experiment to minimize any fluctua-

t i o n s . ;

3 7

Feed samples were obtained at the beginning and end

of each run for later a n a l y s i s • At the end of a run a fil­

tered sample of the crystallizer suspension was also ob­

tained to be subjected to the same analysis. The purpose

of the analysis was to determine the concentration of the

potassium chloride in the stream. The samples were ob ­

tained by allowing some of the feed to be pumped into a

graduated cylinder containing a known volume of distilled

w a t e r . The volume increase indicated the size of the sam­

ple. This technique removed the possibility of losing some

of the sample due to crystallization in the glassware. The

crystallizer sample was obtained by pipetting through a

cotton swab directly from the c r y s t a l l i z e r . A portion of

the pipetted sample was added to distilled water as previ­

ously described.

The analysis consisted of treating the sample with

sodium tetraphenyIboron solution and titrating with a Zeph-

iran chloride solution. The STPB reacts with potassium to

form a white precipitate. The titration indicates the

amount of unreacted STPB 9 thus giving a measure of the po ­

tassium content by b a c k - c a l c u l a t i o n . Difficulties were en­

countered with this; chemical analysis and are discussed in

the section on experimental r e s u l t s .

When a product sample was desired, the water flush

was stopped and the level controller was allowed to operate

38

once to remove- any water from the l i n e s „ Then the ball

valve in the drain line was closed while the valve in the

filter line was o p e n e d . Vacuum was applied to the filter

f l a s k » The next time that the level controller operated 9

flow went to the filter instead of the drain. After the

sample was. obtained the positions of the ball valves were

reversed and the water flush was resumed. The volume of

filtrate was measured and r e c o r d e d . The crystals were

washed and filtered twice with acetone which had been pre­

viously saturated with potassium chloride. The crystals

were weighed and sieved. This sampling technique did not

interfere in any way with the normal operation of the crys-

tal l i z e r .

This procedure was observed for all r u n s . No sig­

nificant deviations were made in the procedure for any run,

except as might occur as technique improved throughout the

course of the research.

Table 4 is a summary of the operating conditions :,

for the individual experimental The units ..for the v a r i ­

ables studied are given in Table 3. The order in which the

experiments were executed was determined by indiscriminantly

selecting an entry from a table of random n u m b e r s . This

was done in order to avoid trends in the data due to any

3 9

unidentified or uncontrolled variables. The experiments

represent a quarter replicate of a full factorial design

for the four independent variables studied.

Table 3. Units for Variables in Table 4

VariableRetention

Time

Crystallizer Temperature

Agitation RPM

Feed KC1 Saturation 0 FTemperature

Classifying Crystallizer Equipment and Procedure

The material in this section was part of a parallel

study conducted by E . P. K . Ottens (n .d .). As his work was

vital to this study, a brief description of the equipment

and procedure used by Ottens is included h e r e ,

Classifying Crystallizer Equipment

The classified product crystallizer had a volume of

21 liters and was constructed of fiberglass. The cooling

assembly consisted of two concentric tight-wound coils. The

Units

minutes

40

Table 4. MSMPR Experimental Operating Conditions

Feed K G 1Run Retention Crystallizer A g i t a t i o n Saturation Time Temperature . Temperature

1 46 100 800 160

2 60 100 750 160

3 60 90 800 160

4 90 90 750 160

5 90 80 800 160

6 120 80 750 160

7 60 100 800 140

8 90 100 750 140

9 120 80 800 140

10 120 90 750 140

11 90 90 800 140

12 46 80 7 50 140

13 4 6 80 7 50 140

outer coil was welded to a stainless steel draft tube sup­

ported, by three baffles. Agitation was achieved using a

Bench Scale Company agitator fitted with a marine propeller.

Temperature and liquid level were monitored using two Math-

eson "Lab-Stat" controllers in a manner similar to that used

in the MSMPR crystallizer.

41

Attached to the side wall of the crystallizer was a

vertical plexiglass c y l i n d e r . This cylinder acted as a

trap for the small crystals. Crystals of all sizes were

forced into the bottom of the cylinder by the action of the

agitator. A peristaltic pump withdrew liquid from the top

of the cylinder at a predetermined flow rate. . The smaller

crystals were carried out the top with the liquid . The

larger c r y s t a l s , being too heavy to flow with the liquid,

fell to the bottom of the cylinder and back into the crys­

tallizer. The maximum size crystal carried out the top of

the trap could be adjusted by changing the flow rate and

could be calculated from S t o k e ’s Law. The cylinder was

compartmentalized by a plexiglass baffle assembly. Liquid

was withdrawn from each of the four compartments via a

stainless steel dip tube. The liquid level control probe

was immersed in one of the compartments because the surface

was less turbulent in the fines trap than in the crystal­

lizer itself.

From the fines trap the slurry was pumped to a

steam-heated tank to dissolve the crystals in the stream.

A fraction of this stream was routed back to the crystal­

lizer after passing through a precooler to remove excess

heat Introduced by the fines dissolver. The remainder of

the stream was pumped back to the feed tank to be incorpo*- -

rated into the feed l i q u o r .

42

A stream of crystals was continuously removed from

the crystallizer in an isokinetic manner using another p e r ­

istaltic p u m p . The system was designed so t h a t .this stream

would pass over a wet screen. The Smaller crystals in the

stream would be washed through the screen and be recycled .

to the crystallizer. The larger crystals would pass over

the screen and return to the feed tank to be dissolved. If.

the liquid level in the crystallizer became too h i g h , the

controller would cause a motor-driven ball valve to rotate.

This valve was part of a flow-direction device and would

make the stream bypass the wet screen and flow directly to

the feed tank. In practice the wet screen was not u s e d .

It was discovered that classification was occurring inter­

nally at the product removal port, making, external classi^

fication an unnecessary complication.

The feed tank was molded from fiberglass and had a

capacity of fifty gallons. A donut-shaped fiberglass d i v i ­

der split the tank into two sections. The bottom section

was steam-heated and was the compartment to which all r e ­

turning streams entered. The crystallizer feed was w i t h ­

drawn from the top section. Both sections were stirred by

a single agitator with two propellor blades fitted to its

s h a f t . The feed line was wrapped with heating tape to

43prevent f o u l i n g . The complete apparatus is pictured in

Figure 8 . Details of the crystallizer-fines trap assembly

are seen in Figure 9.

Classifying Crystallizer Procedure

Feed solution was saved from run to run so it was

not usually necessary to make fresh stock. When it was

necessary the procedure was as described in the MSMPR sec­

tion except that magnesium sulphate was not a d d e d . Freslv

initial charge for the crystallizer was prepared for each

run o Fifteen liters of water were put into the crystal-

lizer, along with enough potassium chloride to form a sat­

urated solution and to act as seed, and sufficient sodium

chloride to form a nearly saturated solution with respect

to that salt. These amounts were determined from the m u t u ­

al solubility curve, Figure 3. Insoluble magnesium ca rbo­

nate p a r t i c l e s , present in the sodium chloride, were

dissolved by adding dilute hydrochloric acid to the solu­

tion.

The crystallizer impeller was started, cooling w a ­

ter was allowed to pass through the coil, and the heating

. tape around the feed line was allowed to warm up. Agita­

tion was set to give a good rolling motion to the suspen-i

s i o n . Proper flow rates for the feed, liquor a d v a n c e , and

fines removal were set by the bucket-and-stopwatch m e t h o d .

F L O W DIRECTION DEVICE

-S—>1"̂c w

W E T SCREEN

DETAILW E T

COOLER SCREENHEATER

LLC]

"M-SAMPLEPOINT

rrrT-frrrrr?PERISTALTICPUM P

V7777/7 / V / y / z vYrrr/TT-nryry A -/nrn c r y s t a l l i z e r peristaltic

AND PUMPFINES TRA P — ™TAP

WATER< v

,-N-DIAPHRAGMCONTROLLEDV O L U M EPUM P

COOLING WATER : SURGE: 1 TANiC:.

STEAM

DRAIN

FEED PREPARATION TANK

Figure 8 . Schematic of R-z equipment.

F i n e sR e m o v a l

C a p a c i t a n c e S e n s o r f o r L L C

C a p a c i t a n c e r t . S e n s o r

f o r T CR e c y c l eF r o mW e t S c r e e n

C o o l i n gW a t e r F e e d

F i n e sT r a p

RX

— > P r o d u c t

Figure 9. Crystallizer-fines trap assembly

4

Steam to the dissolving tank was adjusted so that the solu

tion temperature did not exceed 55 °C „ Water flow to the

precooler tank was set so that the difference between cool

ant and solution temperatures was not more than 3 ° C • The

crystallizer temperature was kept at about 3 2°C for all

runs * Product samples were taken in a manner similar to

the MSMPR sampling m e t h o d „

Table 5 is a summary of the operating conditions

for the R-z experiments. Run 1 was the first test of the

equipment and experimental technique. Runs 2 and 7 were

essentially MSMPR experiments. The purpose of these two

runs was to test the effect on the CSD of rotating the r e ­

moval port. Run 3 duplicated run 2 except that fines r e ­

moval was introduced to test the effects of this process o

the CSD, Run 5 was a test of the principle of liquor ad­

vance and was otherwise identical to run 4, Runs 4 , 6 9 8 ,

and 9 were tests of the stability of the CSD,

Table 5. R-z Experimental Operating Conditions

Fines LiquorRun Feed Removal Advance Removal ml/s ec ml/sec ml/sec Port

1 4.7 5 28.3 3.4 up

2 5.3 - - up

3 5.5 28.5 - up

4 3.7 2 0 . 2 2.9 up

5 3.57 - 2.7 up

6 3.53 20.3 2.6 down

7 3.6 - - down

8 4.0 27.0 2.65 up

9 4.0 27.0 2.7 down

RESULTS

The results from this study are presented in the

three naturally occurring sections which made up the r e ­

search program: nucleation kinetics, stability analysis,

and computer simulation.

Nucleation Kinetics

Initially it was desired that the feed liquor con­

tain only potassium chloride dissolved in water. This

would allow easy analysis of the liquor since instead of

testing directly for potassium, a much simpler titration

for chlorine could be conducted. Since both chlorine and

potassium ions would be present in essentially equal amounts

the potassium chloride concentration should be easily d e t e r ­

minable by this method.

Preliminary shake-down runs of the experimental

equipment with this feed indicated the feasibility of this

type of chemical analysis. However, instead of s i n g l e , c u ­

bic crystals the product contained excessive agglomerates

and rosettes. This type of crystal is undesirable as it

48

49

presents difficulties in analysis and tends to indicate

larger than normal growth rates. It was then 1 necessary to

conduct a brief study of chemical additives to find a suit­

able habit modifier. Such an additive should have the

ability to prevent twinning of the crystals, while not in­

terfering with the nucleation kinetics of the system or

introducing difficulties into the chemical analysis tech­

nique already in u s e .

A list of possible additives was compiled from the

literature and a knowledge of the chemical species present

in an industrial potash crystallizer brine. The substances

tested are listed in Table 6 . Preliminary studies were

conducted in a shaker bath with a temperature controller.

Eight sample could be tested simultaneously in separate

Erlenmeyer flasks. A saturated solution of potassium chlo­

ride containing an additive was placed in the bath, where

it was kept at constant temperature with agitation until

equilibrium was established at a temperature well below the

saturation temperature. The resulting crystals were m i c r o ­

scopically studied to select the more promising additives

for further investigation in the MSMPR e q u i p m e n t .

It was found that crystals produced using lead

chloride as an additive lost all semblance of the natural

cubic shape expected of potassium chloride crystals. The

50

Table 6 . Chemical Additives Studied as Habit Modifiers

SubstanceChemicalFormula

Concentration in Solution

Lead(II) Chloride PbCl 2 500 ppm

Sodium 01 eate Na 2 C 1 e H 3 2 0 2 1 0 0 ppm

P-Toluene Sulfonic Acid (Sodium Salt)

SO 3 ~Na+

0c h 3

500 ppm

TetraethylAmmoniumChloride

C 2 H 5

C 2 H 5 —N — C 2 H 5 —Cl 1C 2 H 5

1 0 0 ppm

Armac T 1 ppm

Sodium Chloride NaCl Saturated Solution

Magnesium Sulphate Mg 2 SO 0.75 g Mg/100 g H 20

product could not be called agglomerated in the sense of two

or more crystals sticking together. Instead it appeared as

if a single crystal grew in all directions in a random m a n ­

ner, completely disregarding any molecular orientation into

a crystal lattice. Figure 10 shows crystals grown from a

solution containing only potassium chloride. The degrada­

tion in crystal habit when lead chloride is also present is

seen by comparison with Figure 11. Obviously lead chloride

had to be rejected as a habit modifier.

51

r W

Figure 10. Crystals grown from saturated KC1 solution Average size = 254 microns.

Figure 11. Crystals grown from saturated KC1 solution inpresence of PbCl 2 » Average size = 254 microns.

52Noticeable improvement in crystal habit was found

from the use of sodium chloride. Single cubic crystals

were present in large amounts in sizes up to approximately

4 00 m i c r o n s , In the larger sizes agglomerates did appear

but the extent of agglomeration was not as severe as when

the additive was not present. Addition of magnesium sul­

phate did,not significantly improve the crystal habit.

Neither did it degrade the habit, and since magnesium and

sulphate ions are present in industrial potash brines it

was decided to retain the magnesium sulphate in the liquor

to make the system more realistic. Figure 12 shows the im­

provement attained in crystal habit when this type of liquor

is u s e d .

The combination of chemicals chosen as a habit m o d ­

ifier complicated the analysis of the feed solution consid­

erably. It was no longer possible to titrate for the

presence of chlorine ions since significant quantities were

introduced in the form of NaCl. Although the test for po ­

tassium is somawhat more complicated it still involves ti-

trimetric techniques. Since no other suitable agent was

found to act as a habit, modifier, it was decided to proceed

with the use of the sodium chloride/magnesium sulphate co m ­

bination.

53

Figure 12. Crystals grown from saturated KC1 solution in presence of NaCl and Mg SO 4 . Average crystal size = 2 54 microns.

54

A series of thirteen experiments was conducted to

determine growth rates and nuclei densities in the manner

previously described. From these experiments, nucleation

rates could also be determined using Equation 18. The r e ­

sults of these experiments are summarized in Table 7.

Whenever possible, two product samples were ob­

tained from a single experiment. These were taken at times

corresponding to eight and nine residence times into the

run. If necessary an experiment could be run for as long .

as eleven residence times before lack of feed solution

forced termination of the experiment. It was found that

steady-state conditions were reached after approximately

seven retention times. This could be checked by following

the variation in solids concentration with time until tran­

sients damped outo The variation in solids concentration

for a typical experiment is shown in Figure 13»

The two samples were treated separately to obtain

in effect two sets of population density data. These were

then plotted on the same semi-log graph and a single line

was f itted through the points by a least-squares technique e

This process yielded average values for the growth rate and

nuclei density. Two samples could not be obtained for each

experiment due to such calamities as a power failure or a c ­

cidental drainage of the crystallizer by the level control­

ler.

Table 7. Summary of MSMPR Experimental Results

Run Date Growth Rate microns/min

Nuclei Density no/cc-micron

SolidsConcentration

g/mlNucleation Rate

no/cc-minute

3 1/22/74 2.11 16.54 0.0546 34.9

1 2/13/74 2.51 2 0.58 0.0525 51.6

7 2/17/74 2.13 . 10.75 0.0335 22.9

12 2/21/7 4* 2.69 15.40 0.0446 41.4

9 2/26/74 1.35 6.08 0.0490 8.2

5 3/02/74* 1.68 14.34 0.0736, 23.1

2 3/12/74* 2.07 18.7 5 0.0566 ( 38,8

8 3/20/74* 1.65 6.24 0.0328 10.3

13 3/22/74* 2.71 16 i 31 0.0438 44.2

10 4/24/74 1.17 8.88 0.0357 10.4

. 11 4/28/74* 1.65 10.18 0.0474 16.8

4 . 6/14/74* 1.67 10.64 0.057 6 17.8

6 6/19/74 1.25 11.08 0.0743 13.8

average of two samples

55

Sol

ids

con

cen

tra

tio

n,

gr/

ml 0.9

0.8

0.7

0.6

100 200 300 400 500 600 700 800Time, minutes

Figure 13. Variation in solids concentration with time for run 061474.

UiON

/ 57

Figures 14 through 17 are typical population de n s i ­

ty plots obtained from the e x p e r i m e n t s • From these graphs

it can be seen that as the residence time increases, the

distribution becomes more spread out , i.e., the slope of

the line becomes smaller. The intercept typically d e ­

creases with increasing residence time also.

Figure 14 is the population density, plot for run

021374« This run exhibited the largest value for the n u ­

clei density of all the runs, 20.58 n o /c c - m i c r o n . . The data

from this run show some deviation from the ideal straight

line expected for an MSMPR experiment. It is believed that

some classification was taking place at the removal port

due to a too high rate of product removal. This is known

as.nonisokinetic removal and is a problem often encountered

due to poor equipment design.

Figures 15 and 16 are examples of the excellent

agreement of the data for two samples of the same r u n . It

was not uncommon for population densities at the same crys­

tal size to lie on top of each other. Such close agreement

of the data between samples is confirmation that steady-

state operation was achieved. It should also be noted that

isokinetic removal was in general achieved throughout the

course of the research, a is was the case for these r u n s .

5810 0 p*’**™0*1

Crystal 1izer Temp = 100*F= 800 RPMAgitation

Sat. KC1 Feed Temp= 160°F

•o

Q.S.

0.01

200 400 600 800 1000Crystal size, microns

Figure 14. Population density vs crystal size , run 0213 74.

100t = 60 mi nCrystallizer Temp = 100°F Agitation = 750 RPM Sat. KC1 Feed Temp= 160°F

CL

O.OI

O.OOI 200 600 800400 1000Crystal size, microns

Figure 15. Population density vs crystal size, run 031274

60100

Crystallizer Temp = 90°F Agi tation = 750 RPM Sat. KC1 Feed Temp= 160°F

in

*oo Sample # I □ Sample # 2

Q.

0.01

0.001 800200 400 600 1000Crystal size, microns

Figure 16. Population density vs crystal size, run 0614 74 .

61100

Crystallizer Temp = 80°F Agitation Sat. KC1 Temp

= 800 RPM = 140°F

*oc 0.1

Cl

0.01

0.001 200 400 600 800 1000Crystal s ize, m icrons

Figure 17. Population density vs crystal size, run 022674.

62

Figure 17 is the population density plot for run

022674. This run had the lowest nuclei density of all the

experiments, 6.08 n o /c c - m i c r o n . This run was subject to

very low driving forces since it had a long retention time

combined with a low temperature difference between feed and

cry s t a l l i z e r .

The population density plots for the remainder of

the runs can be found in Appendix A.

The log of the nucleation rates calculated using

Equation 18 are plotted against the log of the growth rate

in Figure 18. If nucleation is assumed to be independent

of the solids concentration, then the kinetic parameters

for the m o d e l :

B° = knG 1 (21)

can be evaluated from such a plot. This type of model was

used by Genck and Larson (197 2) . Their results for k^ have

previously been given in Table 2. For i, Genck and Larson

found a value of 2.55. Figure 18 indicates that the best

value for i from this data is 1.99.

It should be pointed out that Genck and Larson did

not use a habit modifier and reported that their product

crystals were mostly a g g l o m e r a t e s . The growth rates found

in their study were an order of magnitude larger than those

Nuc

leat

ion

Rat

e,

no

/cc-

min

63100

1.99

10 - °

2 4 6 8 10Growth Rate, m ic ro n s /m in u te

figure 18. Nucleation rate as a function of growth rate

64

found in this study. It was mentioned earlier that exces­

sive agglomeration could result in larger than normal

growth r a t e s . The work of Genck and Larson appears to sup­

port this idea. The discrepancy in the values for i is

very likely attributable to the agglomerated product.

The data collected in this work was fitted to a

model of the f o r m :

B° = knG 1M Tj (RPM)k l e x p[k2/T] (22)

This type of correlation has been found to be suitable for

other systems (Randolph and Cise 1972 , Randolph and Young-

quist 19 7 2) . A multiple linear regression computer program

was used to fit the data. This resulted in the following

c o r r e l a t i o n :

B ° = exp[17 .3]G2,05M T 0 , 8 7 (RPM)_ 1,l4exp[-2885/T] (23)

where temperature is in degrees R a n k i n e . The analysis of

variance for this correlation is given in Table 8. The m o d ­

el has an R 2 value of 0.914 for a correlation coefficient

of 95.,6%. However agitation and temperature are revealed

to be insignificant variables at an F-level of 9 5% and even

much l o w e r . These two variables were discarded and the d a ­

ta was refitted to a simpler model. The correlation resul­

ting from this procedure is:

65

B° = exp[4.0]G2e07M T 0,72 (24)

The analysis of variance for this model is given in Table

9. This model has an R 2 of 0.90 for a correlation coef fi­

cient of 95%. Also both variables are significant above

the 9 5% F-level. Figure 19 is a plot of this model with

the ordinate taken as B °/M ^ 0 * 7 2 „ The slope of the line is

then i = 2.07.

The fact that temperature was not found to be a

significant variable in this study is not inconsistent with

the work of Genck and Larson (1972). In their study a w i d ­

er range of temperatures was studied, namely 54° - 8 6 ° F .

Only a weak temperature dependence of the nucleation kinet­

ics was reported. They also presented a plot of nucleation

rate versus growth rate with the data correlated according

to temperature level. This yielded three lines parallel to

one another. The data from the current study can be plot­

ted in a similar manner to yield three roughly parallel

lines, but the scatter about the lines is such that a sin­

gle line can describe the data equally well. The data from

the experiments with long residence times deviates from the

line much more than do the data from those experiments h a v ­

ing shorter residence times. This is caused by the d iffi­

culties involved in avoiding fluctuations in the operating

conditions over the longer times needed to complete these

long experiments--approximately twenty hours.

66

Table 8» Analysis of Variance, Four Parameter Model

Source of Degrees Sum of MeanVariation of Freedom Squares Square

G 1 3.710 3.710 75.5

m t 1 0.422 0.422 8 . 60

RPM 1 0.017 0.017 0.34 6

T 1 0.055 0.055 1.12

Residual 8 0.393 0.049

Total 12 4.597

Table 9« Analysis of V a r i a n c e , Two Parameter Model

Source of Variation

Degrees of Freedom

Sum of Squares

MeanSquare F-Ratio

G 1 3.710 3.710 79.8

m t 1 0.422 0.422 9.08

Res idual 10 0.465 0.046 5

Total 12 4.597

67

1000

2.07

CM

100

O 80°F □ 90°F AlOO°F

6 8 102 4Growth Rate, m ic ro n s /m in u te

Figure 19. Nucleation rate as a function of growth rate and solids concentration.

68

The solids concentration measured experimentally is

compared to the theoretical value in Figure 20. The theo­

retical values were calculated using Equation 14 » This

type of comparison is a consistency check on the data. It

can be seen from the figure that all of the points lie

within ±20% of the 45° line which would be a perfect check

of the d a t a , *

A mass balance around the crystallizer could not be

m a d e , Feed and crystallizer suspension samples were to

have been titrated to measure their potassium concentra­

tions, Difficulties arose in this procedure which could

not be resolved. These involved the pH sensitivity of the

reaction being used to indicate the end point. In the few

control samples that were titrated the end point was ex­

tremely difficult to identify. The purpose of the mass

balance was to obtain a measure of the supersaturation and

the driving forces in the system. Since potassium chloride

is a Class II system, supersaturation should have been im­

measurably small. This was the case for Genck and Larson

(197 2) who found that the crystallizer suspension was es­

sentially at the saturation concentration for the operating

t emper a t u r e , It would have enhanced this study to have

been able to make this measurement but it was in no means

critical to the results.

0.10

0.08

cn 0.06

<v 0.04

0.02

0 0.02 0.04 0.080.06 0.10Exper imenta l M y , g r / m l

Figure 20. Comparison of theoretical and experimental sol ids concentration.

70Stability Analysis

It was soon discovered that internal classification

of the product stream was occurring at the removal port <,

Furthermore, this classification was of such magnitude as

to make the crystal-size distribution unstable. By rota­

ting the removal port through 180*, so that the port poin­

ted down instead o f . u p w a r d , classification was reduced

enough to stabilize the C S D „ This was an unlooked-for r e ­

sult and caused rethinking of the experimental plan o The

use of the wet screen was subsequently discontinued in lieu

of using the removal port as a source of classification.

This provided an non-off switch" for CSD i n s t a b i l i t y .

A series of nine experiments was conducted with the

R-z equipment to study CSD stability. The results of these

experiments are summarized in Table 10. The listed values

of the solids concentration of the unstable runs are the

averages about which cycling occurred.

The effect on the CSD of fines removal without li ­

quor advance was insignificant, as seen in Figure 21. This

is a. combined population density plot for runs 2/22/74 and

2/27/74. The two sets of data agree so well that a single

line has been used to fit the data. Better agreement could

not be expected between two experiments. It is to be c o n ­

cluded from this plot that the fines removed from the crys-

tallizer either were not being dissolved, they were removed

71Table 10. Summary of R-z Experimental Results

SolidsRun Date Concentration Stability g/ml ___________

1 2/13/74 ±0.160 unstable

2 2/22/74 0.053 stable

3 2/27/74 0.059 s table

4 3/10/74 ±0.170 unstable

5 3/24/74 ±0.160 unstable

6 3/28/74 0.185 stable

7 4/04/74 0.056 stable

8 4/22/74 ±0.260 unstable

9 4/30/74 0.250 stable

at a size too small to have an appreciable effect on the CSD

or they were removed at a rate not sufficiently greater than

the _ product removal rate*

Figure 22 shows the effect of the position of the

removal port on the C S D » This figure is a plot of the p o p ­

ulation densities for runs 2/22/7 4 and 4/04/74. Both of

the distributions are very nearly straight-line MSMPR d i s ­

tributions o It can be concluded from Figure 22 that the

removal port by itself had* no effect on the CSD at low sol­

id con c e n t r a t i o n s 9 i . e . , with no clear liquor advance. In

Popu

latio

n de

nsit

y,

n,

no./c

c sl

urr

y-m

icro

n

72

100.0

10.0

i.o

o.i

_ O N o f i n e s r e m o v a l , n o l i q u o r a d v a n c e

D F i n e s r e m o v a l , n o l i q u o r a d v a n c e ( R = 5 )

0.01 200 600 1000 1200400 800Size, L , microns

Figure 21. Effect of fines removal on CSD.

Popu

latio

n de

nsit

y,

n, no

./cc

slur

ry

-mic

ron

73

100.0

10.0

1.0

0.1

Port up

O R e m o v a l p o r t " u p "

- □ R e m o v a l p o r t " d o w n 1P o r t d o w n

0.01 200 400 600 800 1000 1200Size, L , microns

Figure 22. Effect of removal port on CSD.

7 4

the presence of liquor advance, CSD form and stability were

found to depend solely on the direction in which the port

was pointing, up or down 0

Runs 3/10/74 and 3/28/74 were conducted under the

same conditions except that for run 3/10/74 the removal

port pointed up and for run 3/28/74 it pointed down* Fig­

ure 23 shows the variation in solids concentration for the

two experimentso While the solids concentration for run

3/28/74 maintained a constant value of 0.17 g / m l s for tun

3/10/74 a definite cycling of the solids concentration o c ­

curred. Runs 4/22/74 and 4/30/74 were matched in the same

manner as these other two experiments. Figure 24 presents

the variation in solids concentration for these experiT .

ments. The same qualitative behavior is observed in this

figure as in Figure 23.

A comparison of Tables 5 and 10 lead to the follow­

ing conclusions. First, in every case in which the removal

port pointed down, the CSD was stable. A l s o , w hen liquor

advance was not present, the CSD was always stable. This

includes the case for the removal port pointing up. Only

those runs which had both liquor advance and the removal

port pointing upward exhibited an unstable CSD. One or the

other of these conditions was not sufficient to destabilize

the distribution. It should be noted that clear liquor

Sol

ids

con

cen

tra

tio

n,

gr/

cc

slu

rry

0.20

0.18

0.16

0.14

0.12

- O Run 3 / 1 0 / 7 4 Removal port up -O- Run 3 / 2 8 / 7 4 Removal por t down

0.10 100 200 300 400 500 600 800700 900T im e , m in u te s

Figure 23. Variation of solids concentration with time. Results of experimental crystallization runs 3/10/74 and 3/28/74.

in

Sol

ids

co

nce

ntr

ati

on

, g

r/cc

sl

urr

y0.28

0.26

0.24

0.22

0.20

- O R u n 4 / 2 2 / 7 4 Removal p o r t up -O- Run 4 / 3 0 / 7 4 Removal po r t down0.18

300200100 400T im e , m in u te s

Figure 24. Variation of solids concentration with time. Results of experimental crystallization runs 4/22/74 and 4/30/74.

OX

77advance greatly decreases the product removal flow rate,^

thus exacerbating the classification effects due to removal

port orientation.

Comput er S imula tion

The purpose of the computer simulation was to show

that such models as the Mark III program can be valuable

tools for crystallizer design. It was also to demonstrate

that the nucleation kinetics observed in the MSMPR experi­

ments are independent of the apparatus from which they are

obtained.

The operating conditions of the R-z experiments and

the nucleation kinetics obtained from the MSMPR experiments

were used as input data to the computer program. From the

population density plots of the R-z distributions and a

Stoke*s Law calculation, the various classification func­

tions were estimated. This was the weakness of the study.

The first estimates of the classification functions had to

be modified somewhat to fit the data well. This necessity

arose from the internal classification which occurred at the

removal port. Had isokinetic removal taken p l a c e , classifi­

cation would have been a controlled and known variable by

the use of the wet screen. Predictions as to CSD stability

could then have been made prior to conducting the experi­

ments. As it turned o u t , it was necessary to have the ex­

perimental results before the simulation could be d o n e . -

Four of the R-z experiments were modelled, two of

which exhibited stable CSDs and two of which exhibited u n ­

stable CSDs. Furthermore, the experiments were matched in

such a way that each stable run was conducted under nearly

identical conditions as an unstable run, with the only sig­

nificant difference being the position of the removal port.

In terms of the simulation this meant that the only differ­

ence in the input data between matched runs was the two

classification functions.

The basic equation which the Mark III program uses

is given by:

In this equation is an average flow rate upon which c a l ­

culations are based. The removal function C (L) is definedwas :

MSMPR case, Q q (L) is a constant for all L so that a suitable

choice of will result in a C ^ ( L ) function of unity. For

differs from unity depending upon the various removal r a t e s .

(25)

(26)

where Q q (L) is the total rate of removal at size L. For the

a classified product crystallizer with fines removal, (L)

79

It was necessary in the computer simulation to find

suitable values for the C^(L) function in order to fit the

steady-state data. Tables 11 and 12 list some of the v a l ­

ues of this function which produced the best fits of the

data for the stable and unstable runs m o d e l l e d . There are

three distinct sections in each c a s e . Below a fines size,

k f 5 ^w has a value of R which depends upon the rate at 3 ■ “ ■

which the fines are removed during the e x p e r i m e n t . For the

sizes between L^ and a product size L , C is equal to uni-f p w ^ty o This is the MSMPR section of the d i s t r i b u t i o n . Final­

ly, above size L the C function takes on a value of zP wdetermined by the experiment. As is seen from the two ta­

bles the two stable runs had much lower values of z than

did the two unstable r u n s . This is consistent with the

work of Beer (197 3) who found that large values for the

product classification rate will destabilize the C S D .

The steady-state CSDs for the four runs are plotted

in Figures 25 - 28. The solid lines are the result of the

computer simulation and the circles represent the actual

experimental data. The data points for the unstable CSDs

were obtained by averaging the data obtained throughout the

experiment on the assumption that the CSD was cycling about

a mean v a l u e .

Table 11. Values of for Modelling of Stable Runs

Lmicrons

• 0

9

10

260

300

340

341

CRun 3/28/74

23.0

23 .0

1. 0

1.01.4

1.8 1.8

Run 4/30/74

20.0 20.01.0 1 o 0

1.4

1.8 1.8

81

Table 12. Values of for Modelling Unstable Runs

Run 3/10/7 4 Run 4/22/74

microns w microns W

0 25.0 0 20.0

29 25.0 69 20.0

30 1.0 70 1.0

500 1.0 200 1.0

600 5.0 400 5.0

700 9.0 600 9.0

800 13.0 800 13,0

Popu

latio

n de

nsity

, n,

no./c

c sl

urr

y-m

icro

n

82

100.0

T = 385 min GCaic " 1-25 microns/minn°calc = 15.6 no/cc-micron (C VJcolc = 0 845 /

10.0

Note: Removal Port in up position

0 T

0.1

0.014 0 0200 6 0 0 8 0 0 1000

Size, L, microns

Figure 25. Time-averaged population density p l o t , run3/10/74.

Popu

latio

n de

nsity

, n,

no

./cc

slur

ry

-mic

ron

100.0

10.0

T = 99 minGCaic =2.28 microns/minn°rn|- = 59.6 no/cc- micron (C.V.)calc =0.966

1.0

Note: Removal Port in down position

0.1

0.01 200 4 0 0 6 0 0 8 0 0 1000Size, L, microns

Figure 26. Time-averaged Population density plot, run3/28/74.

Popu

latio

n de

nsity

, n,

no./c

c sl

urr

y-m

icro

n84

100.0

T = 219 minGcaic = 2.58 microns/min n°calc " 26.9 no/cc-micron (C.V.)c a |c = 1.16810.0

Note: Removal Port in up position

0.018 0 0 1000200 6 0 04 0 0

Size, L, microns

Figure 27. Time-averaged population density plot, run4/22/74.

Popu

latio

n de

nsity

, n,

no./c

c sl

urry

-

mic

ron

85

100.0

T = 92 minGCaic = 230 microns/min n°calc =67.7 no/cc-micron (Cv)calc = 0-947

10.0

1.0

Note: Removal Port in down position

O.Ol 200 4 0 0 6 0 0 8 0 0 1000Size, L, microns

Figure 28. Time-averaged population density plot, run4/30/74.

86The first point to be noted about these four plots

is that in each case a hump appears in the distribution at

the size where classification first b e g i n s « This peculiar­

ity is discussed by Nuttall (1971) and is characteristic of

all CSDs from classifying c r y s t a l l i z e r s » The magnitude of

the hump is directly related to the amount of classifica­

tion o c c u r r i n g , . The two CSDs with the large humps are the

steady-state averages of the unstable r u n s » The unstable

runs were subject to greater amounts of classification due

to the position of the removal p o r t »

A mechanism for the internal classification is pr o ­

posed as follows o The action of the agitater forced crys­

tals and slurry up the inside of the draft tube and over the

top of the cooling a s s e m b l y « The smaller crystals tended to

be thrown towards the middle of the annulus between the wall

of the crystallizer and the cooling assembly. The larger

c r y s t a l s , because of their greater momentum, were forced

against the crystallizer wall. The removal port was located

near the wall. When the port was in its upward pointing p o ­

sition the large crystals could flow directly into the port

and out of the c r y s t a l l i z e r . Thus the larger crystals were

preferentially removed and internal classification occurred.

When the port was in its downward pointing position, any

crystal that was to be removed had to be pulled into the

8 7

port. This meant that a change in flow direction had to be

e f f e c t e d , The small crystals could easily make this change.

The large crystals 9 having greater m o m e n t u m 9 resisted the

change in flow direction. Even though there were more large

than small crystals near the port, they could not be removed

as easily as the small crystals. Thus the internal cl assi­

fication effect was d e c r e a s e d ,

The classification functions obtained from the

steady-state simulation of the crystal-size distributions

were used as data for the dynamic simulations. The results

of these simulations are presented for the four runs m o d ­

elled in Figures 2 9 and 30, Stability or instability was

successfully predicted for all four r u n s , Figures 31 and

3 2 are comparisons of the experimental and simulated sol­

ids concentration for runs 3/10/74 and 4/22/74 respective­

ly, These figures show that the period and magnitude of the

oscillations were accurately predicted. However, the pre­

dicted value of the solids concentration was in error.

The Mark III CSD simulater was used in this study

to analyze an operating system. Such questions as "Why does

the CSD cycle?11 and "Why is such a CSD produced ?" can be a n ­

swered in this manner. It is also possible to use this p r o ­

gram for crys talliz er design if the kinetics, of the system

are known. The type of CSD likely to be produced, its sta­

bility, production and growth rates can be determined before

Sol

ids

co

nc

en

tra

tio

n,

gr/

cc

slu

rry

0.20

0.18 -

0.16 -

0.14 -

0.12 -

0.10

3/10/74

3/28/74

100 200 300 400 500T im e , m in u te s

600 700 800 900

Figure 29. Variation of solids concentration with time, lation of runs 3/10/74 and 3/28/74.

Results of computer simu-

00o o

Sol

ids

co

nc

en

tra

tio

n,

gr/

cc

slu

rry

0.19

0.18

0.17

0.16

0.15

0.14

0.13

Figure 30. Variation of solids concentration with time. Results of computer simu- co lation of runs 4/22/74 and 4/30/74.

Run 4 / 2 2 / 7 4

Run 4 / 3 0 / 7 4

100 200 300 400T im e , m in u te s

Sol

ids

co

nc

en

tra

tio

n,

gr/

cc

slu

rry

0.20

0.18

0.16

0.14

Exper imenta lSimula ted

0.12

0.10 100 200 300 400 500 600 700 800 900T im e , m in u te s

Figure 31. Variation of solids concentration with time.and simulated results for run 3/10/74.

Comparison of experimental

VOo

Sol

ids

co

nc

en

tra

tio

n,

gr/

cc

slu

rry

0.26 &

0.24

i.22

0.20

0.18

0.16_Q_ Exper im en ta l — Simula ted ✓

0.14 300 400200100T im e , m in u te s

Figure 32. Variation of solids concentration with time. Comparison of experimental 1-1 and simulated results for run 4/22/74.

92

any experiments are c o n d u c t e d , This type of analysis could

make better use of expensive bench-scale studies. If the

system kinetics are not k n o w n , they can Jbe determined using

relatively simple MSMPR techniques. In this manner much

time and expense can be saved in crystallizer design.

water

These

perature of the crystallization. Neither are they affected

by the agitation in the crystallizer so long as the well-

mixed condition is m e t . A lower limit for the rate of a g i ­

tation exists below which the suspension can no longer be

considered to be well-mixed. This limit was not determined

in this study. Below this limit the conditions leading to

Equation 4 are violated and the results of this study are

not applicable.

When the liquor from which the crystals are grown

is saturated with sodium chloride and contains magnesium

sulphate in the amount of 0.75 g Mg/100 g water, the pro­

duct iA largely single cubic crystals. This is a great

improvement over the.crystals grown from a solution of p o ­

tassium chloride only. Such crystals tend to have a multi-

crystal agglomerated habit.

CONCLUSIONS AND RECOMMENDATIONS

The nucleation kinetics of the potassium chloride-

system can be adequately described by the correlation

B° = exp[4.0]G2 ‘07M T ° ‘72

kinetics are not significantly affected by the tem-

93

94

Improper crystallizer design can cause cycling of

the crys.tal-size distribution. Nonisokinetic removal of

product due to improper design can increase classification

to such a point that the stability limit is exceeded, caus­

ing the CSD to cycle.

Nucleation kinetics determined through MSMPR exper­

iments can be used in computer models such as the Mark III

CSD Simulator. This type of program is useful for cr ystal­

liz er design and system analysis of operating crysta l l i z e r s .

It was shown in this study that the stability of a crystal-

size distribution can be accurately predicted numerically.

It is also possible to predict the shape of the CSD. The

use of computer simulations enables the designer to test a

number of configurations and operating conditions quickly

and economically to find the best possible design for an in­

dustrial c r y s t a l l i z e r .\It is suggested that the MSMPR equipment be rebuilt

so that the crystallizer discharge can be returned to the

feed tank instead of being sent down the d r a i n . This would

stop much waste and eliminate unneeded expense for fresh raw

m a t e r i a l s . It would also allow the experiments to be car-. *

rled out over longer times. Too often an experiment was

unavoidably subjected to a major operational disturbance.

Since insufficient feed stock remained to allow the experi­

ment to recover from the disturbance, the run had to be

95

t e r m i n a t e d , An alternative approach would be to let the

discharge go into a surge tank to dissolve the entrained

crystals and attain saturation before allowing it to return

to the feed tank.

The lower limit of the rate of agitation should be

determined and the effects of surpassing this limit inves­

tigated. Whereas agitation has no effect on the nucleation

kinetics, when the suspension is well-mixed, it is likely

that there will be an effect if the suspension is not well-

mixed o

The product removal port on the classified product

crystallizer should be redesigned so that isokinetic r e m o v ­

al of the product can be achieved. Experiments can then be

conducted for which the classification function is known

explicitely by the use of wet screens. Predictions can then

be made using the Mark III program and verified by experi^

ment. This would demonstrate the usefulness of the program

for design purposes o

APPENDIX A

POPULATION DENSITY PLOTS

This section contains all population density plots

generated during the MSMPE kinetic studies and not included

elsewhere in the.text. The specific values for growth rate

and nuclei density obtained from these plots have previous­

ly been listed in Table 7.

96

97100

Crystallizer Temp = 90°F Agitation = 800 RPM Sat. KC1 Feed Temp= 160°F

u

*o

CL

0.01

0.001 4000 200 600 800 1000Crystal s ize, microns

Figure A 1 . Population density vs crystal size, run 012274.

98100

Crystallizer Temp = 100°F= 800 RPMAgi tation

Sat. KC1 Feed Temp= 140°F

u

CO

CL

O.OI

0.001 800600200 4000 1000Crystal size, microns

Figure A2. Population density vs crystal size, run 0217 74.

99

Crystal 1izer Temp = 80°F Agitation Sat. KC1 Feed Temp= 140°F

= 750 RPM

o Sample # I □ Sample # 2

Q.

aoi

o.ooi 800 1000600400Crystal s ize, microns

200

Figure A3. Population density vs crystal size, run 02217 4.

100100

Crystallizer Temp = 80°F Agitation Sat. KC1 Feed Temp= 160°F

= 800 RPM

10

*u0.1

o Sample # I □ Sample # 2

Q.

0.01

0.001 200 400 600 800 1000Crystal size, microns

Figur e A4 . Population density vs crystal size. run 03 027 4.

101100

Crystal 1izer Temp = 100°F= 7 5 0 RPMAgi tation

Sat. KC1 Feed Temp= 140°F

"O

o Sample # I □ Sample # 2

Q.

0.01

0.001 200 400 600 800 1000Crystal s ize, microns

Figure A 5 . Population density vs crystal size, run 032074.

102100

Crystal!izer Temp = 80°F Agitation = 750 RPM Sat. KC1 Feed Temp= 140°F

*o

Cl

O.OI

0.001 200 400 600 800 1000Crystal size, microns

Figure A 6 . Population density vs crystal size, run 032274.

103100

Crystal!izer Temp = 90°F= 750 RPMAgitation

Sat. KC1 Feed Temp=140°F

T3

CL

0.01

0.001 200 400 600 800 1000Crysta l size, microns

Figure A 7 . Population density vs crystal s i z e , run 042474 .

104

100T = 90 mlnCrystallizer Temp = 90°F Agitation 800 RPM Sat. KC1 Feed Temp= 140°F

u

tn

"O

0 Sample # I a Sample # 2

Q.

0.01

0.001 200 400 600 800 1000Crystal s ize, microns

Figure A 8 . Population density vs crystal size, run 042874.

100x = 0 minCrystallizer Temp = 80°F

= 750 RPMAgitation Sat. KC1 Feed Temp= 60°F

*o

CL

O.OI

O.OOI 200 400 800600 1000Crystal size, m icrons

Figure A9. Population density vs crystal size, run 06197 4.

NOMENCLATURE

B particle birth f u n c t i o n , no/cc-micron-min

B 6 nucleation rate, no/cc-min

C .withdrawal function in computer modelw

D particle death function, no/cc-micron-min

G linear growth rate, micro ns/min

i growth rate exponent in nucleation model

j solids concentration exponent in nucleation model

k nucleation constantn

•-'k volumetric shape factor

ki parameter in kinetic model

k 2 parameter in kinetic model

k g , parameter in kinetic model

L particle size, microns

size at which fines are removed, microns

L size at which product is removed, micronsPM^ solids concentration, g/ml

n population density, no/cc-micron

106

N crystal number density, n o /ml

n° nuclei density, no/cc-micron

Q volumetric flow rate, ml/min

Qg characteristic flow rate, ml/min

R rate of removal of fine crystals

t time, minutes

T temperature, °F

W cumulative weight fraction

V crystallizer volume, ml

v e spatial velocity, microns/min

Sub s cr i p t s

i inlet stream to crystallizer

o outlet stream from crystallizer

Greek letters

p p a r t i c l e d e n s i t y , g / m l

t p a r t i c l e r e s i d e n c e t im e , m i n u t e s

)

REFERENCES

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Hulbert, H* M , and S. Katz* "Some Problems in Particle Technology, A Statistical Mechanical F o r m u l a t i o n ," Chemical Engineering S c i e n c e , 1^, 555 (1964.) »

" K a l i u m v s Potash Solution Mining Plant Will Go On-Strearn this Fall in Canada," Engineering and Mining Journal No* 6, 1_65_, 110(1964) *

L e s s i e u x , J « C 0 and D 0 Svoronos » " Sur la Cristallisationdu Chlorure de Potassium en Solution Aqueuse," Comptes Rendus de 1 vAcademie des S c i e n c e s , Series C , No * 19, 2 6 3 , 1146(1966).

Noyes, R * Potash and Potassium F e r t i l i z e r s , Chemical Pro­cess Monograph, 15(1966)*

Nut tall , Ho Eo "Computer Simulation of Steady-State andDynamic C r y s t a l l i z e r s ," Ph »D 0 Dissertation, University of A r i z o n a (1971) o .

O t t e n s , Eo P * K» Laboratory notebook on crystal-size d i s ­tribution stability experiments. Chemical Engineering D e p a r t m e n t , University of A r i z o n a ( n o d •)•

Randolph, A* D , "A Population Balance for Countable En­tities ," Canadian Journal of Chemical E n g i n e e r i n g , 4 2 , 28 0 ( 1 9 6 4 ) o

Randolph, A* Do and M * D » Cise * "Nucleation Kinetics of the Potassium Sulphate-Water System," AIChE J o u r n a l , 18, 798(1972)*

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109

Randolph, A. D. and M . A. Larson. "Transient and Steady-State Size D i s t r i b u t i o n s ," AIChE Journal, 8, 639(1962).

Randolph, A. D . and M. A. Larson. Theory of Particulate P r o c e s s e s , Academic P r e s s (1971).

R a n d o l p h , A. D . and G . R. Youngquist. "Secondary Nuclea- t ion in a Class II System: Ammonium S u l p h ate-Water,"AIChE Journal , 1_8 , 421 (1972).

Saeman, W. C. "Crystal-Siz e Distribution in Mixed Suspen­sions," AIChE J o u r n a l , _2 , 107 (1956).

12rx /\ rr 1 o