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The kinetics of ’salting-out’ of neutral sodium sulfate from sulfuric acid solution Okorafor, Ogbonna Charles 1980

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THE KINETICS OF 'SALTING-OUT' OF NEUTRAL SODIUM SULFATE FROM SULFURIC ACID SOLUTION by OGBONNA CHARLES OKORAFOR (B.Sc, Un ivers i ty of Lagos, Niger ia 1977) A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE THE FACULTY OF GRADUATE STUDIES (Chemical Engineering Department) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA May, 1 9 8 0 @ Ogbonna Charles Okorafor, 1 9 8 0 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of Brit ish Columbia, I agree that the Library shall make i t freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department o f , C H e m i CA-L & 7 \ j q A ) C , The University of Brit ish Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date 9 / 6 / SrO ABSTRACT The equ i l i b r ium phase diagram for the system sodium su l fate-methanol / water-su1 fur ic ac id at 35° was determined. The nuc lea t ion , and growth c h a r a c t e r i s t i c s of sodium su l f a te have been studied in a laboratory sca le c r y s t a l l i z e r (Mixed Suspension Mixed Product Removal 'MSMPR') under care-f u l l y con t ro l l ed condit ions o f supersaturat ion, temperature, ag i t a t ion rate and residence time. From a s t a t i s t i c a l ana lys i s of the data i t was found that supersaturat ion, temperature, the interact ions o f supersatura-t ion with temperature and ag i ta t ion rate with temperature had po s i t i ve e f fec t s on growth and nucleat ion rates , while ag i t a t i on rate, residence time, the interact ions of ag i t a t ion rate with supersaturat ion, residence time with supersaturat ion had negative e f f ec t s on growth and nucleat ion rates. The ' o rder ' of the nucleat ion process, b, defined by B = K^S*3 was about 5- The growth rate, def ined by G = KQS c W a s f i r s t order (C = 1). For both processes the ac t i v a t i on energy var ied from 12 to 15 kcal/mol. The growth process was considered to be surface integrat ion cont ro l l ed for the various condit ions tested. The nucleat ion rate was considered e s s e n t i a l l y to be homogeneous nuc leat ion. A non- l inear mathematical re la t ionsh ip was developed for both growth rate and nucleat ion rate in terms of the three f a c t o r s , temperature, super-saturat ion and residence time. In both the growth and nucleat ion rate models the measured data f i t poor ly. This indicates that the model (a react ion rate type) poorly represents the data fo r c r y s t a l l i z a t i o n found in th i s study. TABLE OF CONTENTS CHAPTER PAGE 1 1.1 INTRODUCTION j 1.2 REASON FOR THE STUDY 2 2 LITERATURE SURVEY if 2.1 CRYSTALLIZATION HYPOTHESIS 4 2.2 PREVIOUS WORK ON CRYSTALLIZATION FACTORS 8 2.2.1 EFFECT OF ALCOHOL 8 2.2.2 AGITATION RATE 8 2.2 .3 TEMPERATURE 9 2.2.4 SUPERSATURATI ON 9 2.2.5 RESIDENCE TIME 1 0 2 . 3 SODIUM SULFATE SOLUBILITY 1 0 2.4 PRINCIPLES UNDERLYING EQUIPMENT CHOICE ]\ 3 BASIS AND EXTENT OF EXPERIMENTAL STUDY 1 3 3.1 THEORY 1 3 3 . 2 EXTENT OF EXPERIMENTAL WORK \ 4 4 APPARATUS AND EXPERIMENTAL TECHNIQUE 1 6 4.1 APPARATUS 1 6 4.2 EXPERIMENTAL TECHNIQUE 1 6 4.2.1 PHASE DIAGRAM 1 6 4.2.2 METHOD OF WET RESIDUE PRINCIPLE 1 8 4 . 2 . 3 TECHNIQUE OF DETERMINATION 1 8 4.2.4 ANALYSIS OF PHASE DIAGRAM CRYSTALS 20 4 . 3 CRYSTALLIZATION RATE EXPERIMENT 22 4 .3 .1 TEST SOLUTION PREPARATION 22 4 . 3 . 2 EXPERIMENTAL PROCEDURE 22 4 . 3 . 3 SIEVE TEST ANALYSIS 24 4 . 3 - 4 METHANOL EFFECT 25 5 RESULTS AND ANALYSIS 27 5.1 CRYSTAL SIZE AND POPULATION DENSITY 27 5 . 1 . 2 C R Y S T A L S H A P E F A C T O R 2 8 5 . 2 C R Y S T A L S I Z E D I S T R I B U T I O N 3 1 * 5 . 3 K I N E T I C R A T E V A R I A T I O N A N D K I N E T I C C O N S T A N T 35 5 . 3 - 1 E F F E C T O F S U P E R S A T U R A T I O N A N D T E M P E R A - 3 7 T U R E O N G R O W T H 5 - 3 . 2 E F F E C T O F T E M P E R A T U R E A N D S U P E R S A T U R A - 37 T I O N O N N U C L E A T I O N S.k D E T E R M I N A T I O N O F A C T I V A T I O N E N E R G Y 4 0 5 . 5 F A C T O R I A L A N A L Y S I S 4 3 5 . 6 R E G R E S S I O N A N A L Y S I S 57 5 . 6 . 1 G R O W T H R A T E 58 5 . 6 . 2 N U C L E A T I O N R A T E 5 9 6 D I S C U S S I O N A N D C O N C L U S I O N 6 1 6 . 1 . 1 E F F E C T O F S U P E R S A T U R A T I O N 6 1 6 . 1 . 2 E F F E C T O F A G I T A T I O N R A T E 6 2 6 . 1 . 3 E F F E C T O F R E S I D E N C E T I M E 6 2 6 . 1 . 4 E F F E C T O F T E M P E R A T U R E 63 6 . 1 . 5 E F F E C T O F F A C T O R I N T E R A C T I O N 63 6 . 1.6 E F F E C T O F F A C T O R S O N Y I E L D 6 4 6 . 2 C O N C L U S I O N S 6 5 6 . 3 R E C O M M E N D A T I O N S 6 8 B I B L I O G R A P H Y 69 N O M E N C L A T U R E 72 A P P E N D I C E S 1 S P E C I F I C G R A V I T Y O F M E T H A N O L / W A T E R S O L U T I O N 7 3 2 G R O W T H , N U C L E A T I O N R A T E V E R S U S S U P E R S A T U R A T I O N 75 3 M E A N S I Z E A N D C O E F F I C I E N T O F V A R I A T I O N 80 4 G R O W T H , N U C L E A T I O N C O N S T A N T S A N D A C T I V A T I O N E N E R G Y 8 3 5 C O M P U T E R P R O G R A M 85 6 P O P U L A T I O N D E N S I T Y , C R Y S T A L S I Z E T A B L E 90 7 G R O W T H , N U C L E A T I O N R A T E S V E R S U S S U P E R S A T U R A T I O N ,] 77 P L O T S 8 E Q U I P M E N T L I S T 1.93 9 R E G R E S S I O N A N A L Y S I S P R O G R A M A N D R E S U L T H-9ft iv LIST OF FIGURES 1 SCHEMATIC DIAGRAM OF EQUIPMENT 17 2 PHASE DIAGRAM 21 3 PHOTOGRAPH OF CRYSTALS 26 k POPULATION DENSITY VERSUS CRYSTAL SIZE 31 5 COEFFICIENT OF VARIATION GRAPH 36 6 GROWTH RATE VERSUS SUPERSATURATION PLOT 38 7 NUCLEATION RATE VERSUS SUPERSATURATION PLOT 39 8 GROWTH RATE CONSTANT VERSUS 1/T°K k\ 9 NUCLEATION RATE CONSTANT VERSUS 1/T°K kl LIST OF TABLES 1 GROWTH RATE AND NUCLEATION RATE VERSUS SUPER- 32 SATURATION 2 CRYSTAL SIZE FRACTION VERSUS WEIGHT AT VARIOUS ' 33 RES IDENCE TIME 3 GROWTH AND NUCLEATION RATE CONSTANTS WITH CALCULATED kk ACTIVATION ENERGY k FACTORIAL DESIGN DEFINITION k6 5 GROWTH RATE WITH THEIR CORRESPONDING FACTORS kl 6 ANALYSIS OF DATA YATES'S METHOD FOR GROWTH RATE k8 7 SIGNIFICANCE POINTS TEST (GROWTH) 51 8 ANALYSIS OF VARIANCE FOR GROWTH RATE 52 9 RESULT OF ANALYSIS OF VARIANCE FOR GROWTH 53 10 NUCLEATION RATE WITH THEIR CORRESPONDING FACTORS 53 11 YATES'S METHOD (NUCLEATION) 54 12 SIGNIFICANCE POINTS TEST (NUCLEATION) 56 13 ANALYSIS OF VARIANCE (NUCLEATION) 56 \k RESULT OF ANALYSIS OF VARIATION 57 v ACKNOWLEDGEMENTS I wish to place on record my s incere grat i tude to Dr. K. P inder, under whom this inves t i ga t ion was conducted, for his guidance in helping to carry out th is p ro jec t . I wish to thank my State government (Imo State of Nigeria) for t h e i r f i n a n c i a l support during the course of th i s p ro jec t . I would l i ke to express my deep apprec iat ion for the ass i s tance of Mr. M. Ohanomah in debugging the computer program. My gratefu l acknowledgement is a lso due to my mother for her love and permission given to me to carry out the p ro jec t . vi 1 CHAPTER I INTRODUCTION: Whenever a c r y s t a l l i n e s o l i d is formed out of other phases, whether s o l i d , l i q u i d or gas, the process is known as c r y s t a l l i z a t i o n . It is a commonly used Industr ia l separation and p u r i f i c a t i o n technique. Fundamental research on this unit operat ion has focussed mainly on understanding and pred ic t ing the pa r t i cu l a te nature of the c r y s t a l l i n e phase, recognizing that better knowledge and control of this aspect w i l l permit improvements in the unit operation of c r y s t a l l i z a t i o n , both as a separat ion and p u r i f i -cat ion technique. Although thorough s c i e n t i f i c invest igat ions into the nature of c ry s ta l s t ructure have been ca r r ied out, very l imi ted r e l i a b l e information has been published on the chemical engineering aspects of c r y s t a l l i z a t i o n . In most cases, plant design is s t i l l based almost e n t i r e l y upon experience and t r a d i t i o n rather than on s c i e n t i f i c measurements. In some industr ies where c r y s t a l l i z a t i o n is employed on a very large s ca le , the equipment has been brought to a high s tate of pe r f ec t i on , but this has been mainly an out -come of long experience with the p a r t i c u l a r product. The bas ic p r i n c i p l e s , an exact knowledge of which w i l l enable the chemical engineer to ca l cu l a te the dimensions of an i n s t a l l a t i o n for any s p e c i f i c performance, have not yet been f u l l y analysed. As a r e s u l t , many chemical works are using p r im i -t ive d i s ign methods for c r y s t a l l i z a t i o n un i t s . The c rys ta l s i ze d i s t r i b u -tion (CSD) of the product, which is a bas ic parameter in any c r y s t a l l i z a t i o n process, is a funct ion of the k ine t i c s of the process and in most cases this bas ic informat ion, needed for a s c i e n t i f i c knowledge of c r y s t a l l i z a t i o n , is lacking. The formation of a new phase from a mother phase can be considered as 2 i n v o l v i n g two p r o c e s s e s v i z : t h e f o r m a t i o n o f t h r e e - d i m e n s i o n a l ( i n some c a s e s two d i m e n s i o n a l ) n u c l e i and the growth o f t h e s e c r i t i c a l n u c l e i t o m a c r o s c o p i c d i m e n s i o n s . The former i s known as n u c l e a t i o n and i t s r a t e i s d e f i n e d a s , " t h e number o f n u c l e i formed per u n i t time per u n i t volume o f r e a c t i o n phase;" w h i l e t h e l a t t e r i s the growth r a t e and i s e x p r e s s e d a s , 'the r a t e o f l i n e a r t r a n s l a t i o n o f a growing c r y s t a l f a c e . ' The e x p e r i m e n t a l s t u d y o f n u c l e a t i o n r a t e i s rendered p a r t i c u l a r l y d i f f i c u l t by the f a c t t h a t in the e a r l y s t a g e s o f c r y s t a l l i z a t i o n b oth n u c l e a t i o n and growth t a k e p l a c e s i m u l t a n e o u s l y . The n u c l e i themselves a r e d i f f i c u l t t o o b s e r v e and c o u n t , and i t becomes n e c e s s a r y t o ' d e v e l o p ' them to an o b s e r v a b l e s i z e by growth. A t t e m p t s have been made t o measure the n u c l e a t i o n r a t e w i t h o u t i n t e r f e r e n c e o f the growth phase but o f t e n the c o n d i t i o n s f o r the e x p e r i m e n t s a r e so i d e a l i s e d t h a t they a r e v e r y d i f f i c u l t t o r e p r o d u c e i n p r a c t i c e . Over t h e l a s t 15 y e a r s the e n g i n e e r i n g u n d e r s t a n d i n g o f t h i s u n i t o p e r -a t i o n has r e c e i v e d a tremendous boost from the a p p l i c a t i o n o f t h e c o n c e p t o f 37 the c r y s t a l p o p u l a t i o n b a l a n c e w h i c h was d e v e l o p e d by Randolph and L a r s o n . The approach has f a c i l i t a t e d the m a n i p u l a t i o n o f c r y s t a l s i z e d i s t r i b u t i o n s t o s a t i s f y g i v e n e n g i n e e r i n g and commercial c r i t e r i a . I t has h i g h l i g h t e d the i m p o r t a n c e o f c r y s t a l growth and n u c l e a t i o n r a t e s and the extreme d i f -f i c u l t y o f s c a l i n g up the l a t t e r t o p l a n t c o n d i t i o n s . [1.2] INTEREST FOR THIS STUDY The use o f c h l o r i n e d i o x i d e i n t h e k r a f t p u l p and paper i n d u s t r y , f o r the b l e a c h i n g o f wood p u l p , has become u n i v e r s a l . I t i s e s t i m a t e d t h a t a t l e a s t 200 c h l o r i n e d i o x i d e g e n e r a t o r s a l l o v e r the w o r l d a r e o p e r a t i n g u s i n g the M a t h i e s o n , S o l v a y o r R2 p r o c e s s e s . In the m a j o r i t y o f the m i l l s where e n v i r o n m e n t a l p r o t e c t i o n s laws have been e n f o r c e d the s p e n t a c i d from t h e s e g e n e r a t o r s i s n e u t r a l i z e d w i t h b l a c k l i q u o r and burned i n the r e c o v e r y f u r n a c e . 3 Where prev ious ly there were s u f f i c i e n t losses of sodium su l f a te in the brown stock washers and the furnace to make this f e a s i b l e , the im-proved water u t i l i z a t i o n now pract i ced by most m i l l s and the increas ing consumption of ch lo r ine dioxide mean that there tends to be an excess of sodium and su l f u r in the furnace smelt. Many processes and methods have been suggested to deal with the excess sodium and su l f u r produced during the bleaching react ion. One of these methods is the 'Ac id Recovery Process 1 (ARP) descr ibed by Lobley 23 and Howard. In this process (ARP) the sodium su l f a te is removed from.: the strong (9N) s u l f u r i c ac id so lu t ion by c r y s t a l l i z a t i o n . Rather than use evaporation to produce the required supersaturat ion for c ry s ta l growth, in this process the s o l u b i l i t y of the s a l t is reduced by ' s a l t i n g o u t ' , that i s , an organic so lvent , methanol, is added to the water s o l u t i on . Since th is is not a common chemical engineering method of c r y s t a l l i z a t i o n , the behaviour of such a process is of fundamental i n te re s t . This study has a lso been motivated by the importance of the k ra f t industry to B r i t i s h Columbia and the need to reduce the po l l u t i on caused by the disposal of the cho lor ine d ioxide generator e f f l u e n t . The present ly used c ry s ta l 1izers are simple CSTR's with a ten minute residence time. The e f f e c t of the various design parameters are not understood and no e f f o r t has been made to produce a reactor which w i l l give a good p a r t i c l e d i s tr ibut ion. This work seeks to determine both the growth and nucleat ion rates for the methanol p r e c i p i t a t i o n of a so lu t ion of s im i l a r concentrat ion to that produced i n d u s t r i a l l y , and the e f f ec t s of supersaturat ion, ag i t a t ion rate, residence time and temperature on these rates. 4 CHAPTER 2 LITERATURE SURVEY 2.1 CRYSTALLIZATION HYPOTHESES: Many theories have been put forward to expla in the process of c r y s t a l -l i z a t i o n . According to Becker,^ the rate of nucleat ion is a funct ion of a c t i va t i on energy for d i f f u s i o n and of the work required to form the s u r -face of the nucleus. "The growth process is a lso amenable to the same kind of treatment as that for nuc leat ion on the assumption that c ry s ta l 25 growth is e s s e n t i a l l y a two dimensional nucleat ion process . " McCabe, observed that , "ne i ther nucleat ion nor growth can occur unless the pre-c i p i t a t e d substance has a lower thermodynamic potent ia l a f t e r c r y s t a l l i z a -t ion than before. Also the Gibbs condi t ion for s t a b i l i t y of a c ry s ta l namely,--that for a given volume the surface f ree energy sha l l be a min-imum--, is conf i rmed." Evidence of various kinds have been suggested to show that , there is a d e f i n i t e equ i l i b r ium shape for c ry s ta l s o f a given so lute p r e c i p i t a t i n g from a p a r t i c u l a r so lvent. There is no ten-dency for a macroscopic c rys ta l of non-equi l ibr ium shape to approach an 4 equ i l i b r ium shape unless c rys ta l growth is permitted. Barkhuysen explained the growth of c ry s ta l s by assuming that the rate of growth depends 47 on the d i f f u s i o n rate. Van Hook in his study of the k ine t i c s of sucrose c r y s t a l l i z a t i o n , concluded that the rate of growth of a c ry s ta l is deter -mined p r imar i l y by some i n t e r f a c i a l (homogeneous, chemical) react ion i n -stead of an interboundary (heterogeneous, phys ical ) react ion. This was postulated from the observat ion that d i s to r ted sucrose qrys ta l s were frequent ly produced from impure syrups. Unequal and var i ab le growths of various faces occurred rather than the uniform and ordered growth which would be expected on the basis of a simple d i f f u s i o n mechanism. He 5 showed that, in general the presence of impurit ies in sucrose syrups depressed the normal rate of c r y s t a l l i z a t i o n ; and also confirmed that the r a t e - c o n t r o l l i n g step in sucrose c ry s ta l growth is a surface react ion and not d i f f u s i on of so lute from the bulk of the so lu t ion to the sur face. 20 Laurent derived mathematical re la t ions for the number of nuclei formed in a given time and the rate of c r y s t a l l i z a t i o n , based on the energy of the atom. He u t i l i s e d this law to expla in a l l o t r o p i c t rans -34 formations. In another mathematical approach, Ramberg appl ied thermo-dynamic p r i n c i p l e s and the re l a t i on between mechanical pressure and p a r t i a l vapour pressure (or escaping tendency) to expla in the force or energy of c r y s t a l l i z a t i o n . 3 42 Badger and Seavoy discussed the hypothesis of Ross that , " the process of d i s so l v ing a substance in water involves a chemical react ion resu l t ing in the formation of new compounds which can be designated as 'molten hydrates ' of the s o l u t e . " Continuing th is l i ne of thought, " the formation of a c rys ta l resolves into a process of f reez ing jus t as ice is created from water. Upon lowering the temperature of a s o l u t i o n , a molten hydrate freezes to the s o l i d s ta te . The heat e f fec t s are con-s idered as a combination of the heat of react ion and the heat of fus ion 42 or what is normally c a l l ed the heat of c r y s t a l l i z a t i o n . " Ross ration--a l i zed his hypothesis to account for c ry s ta l growth by presenting photo-graphic evidence to the e f f e c t that, " there is a f i e l d of a t t r a c t i v e force surrounding the o r i g i n a l nucleus and nuclei agglomerates which combine to form the small c r y s t a l s , arid these small c ry s ta l s grow by a t t r ac t i n g nuclei which attach themselves in an order ly arrangement to the growing c r y s t a l s . Each crys ta l substance appears to have i t s own inherent rate of growth which is somehow related to the a t t r a c t i v e force on each d i f f e r e n t face of the c rys ta l with which i t bui lds i t s e l f by the above phenomenon." 6 In the i r study of the growth of magnessium su l f a te heptahydrate 21 c r y s t a l s , L iu et a l , reported that the growth of c rys ta l s from so lu t ion involves two phenomena occurr ing in s e r i e s : " the transport of so lute from the bulk supersaturated so lu t ion to the c ry s ta l sur face , and the incor -porat ion of so lute into the c ry s ta l l a t t i c e , normally ca l l ed surface i n t e -g ra t ion . When the so lut ion is quiescent or only s l i g h t l y ag i ta ted , mass transport is e s s e n t i a l l y due to molecular d i f f u s i on and hence is f requent ly slower than surface integrat ion and is rate l i m i t i n g . When ag i t a t i on of the bulk so lu t ion is s t ronger, convection and eddy d i f f u s i on w i l l i n -crease the mass transport rate so that both steps may be rate l i m i t i n g . With s tronger ,ag i tat ion , the mass transport process becomes the f a s te r one and the growth rate is con t ro l l ed by the surface integrat ion s t e p . " 49 Volmer developed an absorption theory of c r y s t a l l i z a t i o n in which he v i s u a l i z e d the absorbed molecules as wandering qui te f r e e l y over the surface un t i l they were desorbed, attached to the surface at a point of growth, or- formed with other molecules a nucleus for a new l a t t i c e - l a y e r . It has been shown that c ry s ta l nucleat ion occurs by at least three separate mechanisms ca l l ed homogeneous, heterogeneous, and secondary. Homogeneous nucleat ion occurs from c lear so lut ions by molecular d r i v ing f o r ce s , heterogeneous nucleat ion is st imulated by the presence of fore ign substances or substrates wh i le , secondary nucleat ion occurs due to the presence of c ry s ta l s of the so lute phase and commonly occurs at super-saturat ions lower than that required fo r homogeneous or heterogeneous nuc leat ion. In the case of secondary nuc lea t ion , Mason and S t r i c k l a n d -2k Constable suggested that three stages are involved. The f i r s t is i n i t i a l breeding which resu l t s when dry seeds are placed in so lu t ion and microscopic c ry s ta l -dus t washes o f f the dry seed n u c l e i . The second is needle breeding resu l t ing from the breakage of large d e n d r i t i c growth. 7 The th i rd is c o l l i s i o n breeding in which nucleat ion is induced by c o l l i -s ions of seed c ry s ta l s with s o l i d surfaces. 8 2.2 PREVIOUS WORK ON CRYSTALLIZATION FACTORS [2.2.1] EFFECT OF ALCOHOL: 46 Thompson and Molstad determined the s o l u b i l i t y and isotherms fo r potassium and ammonium n i t r a te s in aqueous isopropanol so 1 utions over the temperature range 25 - 70°C. Both s a l t s are very so lub le in water and the i r s o l u b i l i t i e s increase great ly with increas ing temperature. They found, that 15 lb. of isopropanol added to 100 lb. of saturated aqueous so lu t ion of potassium n i t r a t e (KNO^) at 40°C resul ted in the p r e c i p i t a t i o n of f o r t y - f ou r percent of the d i sso lved s a l t . The s a l t recovery would be increased to 68% i f another 50 lb. of isopropanol were added. In other words, an increase in the quantity of added d i luent resul ted in a higher y i e l d of s a l t . D.H. Kohn, I. Yaron et a l , ' ^ found that, the f r a c t i ona l conversion of ac id sodium sufate to the neutral s a l t and the subsequent p r e c i p i t a t i o n of the neutral s a l t as a funct ion of the organic l iquid/aqueous so lu t ion ra t io exh ib i ted an i n i t i a l rapid r i se followed by a slower approach to a maximum value as the r a t i o increased; higher i n i t i a l concentrat ion and lower temperature f a c i l l i -g tated conversion and p r e c i p i t a t i o n . But t le r and Dunn i c l i f f found that the ex t rac t ion of dry sodium b i s u l f a t e with absolute a lcohols ( inc lud ing methanol) gave a mixed s o l i d of the composition Na2S0^- NaHSO^ even a f te r prolonged treatment, whereas moist a lcohol gave neutral sodium su l f a te . [2.2.2] AGITATION RATE The rate at which a s ing le c ry s ta l grows at a given temperature under a constant supersaturat ion condit ion can be a l tered appreciably by ag i ta t ing the l i q u i d or by rotat ing the c r y s t a l in the l i q u i d . The 9 rate of growth increase i n i t i a l l y as the r e l a t i v e v e l o c i t y between c ry s ta l s and l i qu id is increased, but condit ions are soon reached when a further increase in ag i t a t i on rate has no e f fec t . " " * Coulson and Richardson'^ a lso showed,that in a l l cases, ro ta t iona l speeds of c ry s ta l s in excess of about 20 rev/min had l i t t l e e f f e c t on the growth rate. S imi lar r e -48 su i t s have been reported for the growth of sucrose by Van Hook, A and for copper pentahydrate c ry s ta l s from t h e i r supersaturated aqueous so lut ions by McCabe and S (6,13,27,35,44). 20 by McCabe and Stevens, R.P. In 'most cases i t has been observed that, c i r c u l a t i o n rate only increases s ing le c ry s ta l growth up to a l im i t i ng value. 2.2.3 TEMPERATURE The inf luence of temperature upon both conversion of potassium b i -su l f a te to neutral su l f a te and the subsequent c r y s t a l l i z a t i o n of the neutral s a l t has been reported by Kohn, D.H., I. Yaron et a l , ^ who stated that , a decrease in temperature enhanced both conversion and c r y s t a l l i z a t i o n . 9 Chanakya Misra and E.T. White observed that c rys ta l growth var ied as the Arrhenius temperature law, for aluminum t r ihydrox ide . L i u , C.Y., 21 Tsue i , H.S. et al confirmed this model for magnessium su l f a te heptahydrate c r y s t a l s . The growth rate of the hemihydrate and gypsum was reported by A.B. Amin and M.A. Lar son, ' to increase at higher temperatures but the nucleat ion rate to be lower. 2.2.4 SUPERSATURATION FACTOR 28 According to J.W. Mull in and C. Gaska, the growth rate increases with supersaturat ion, slowly at the i n i t i a l stages but more rap id ly as the supersaturat ion is increased. They also observed that growth appar-ent ly ceased below AC = 0.2g K^O^/lOOg H 20. Of in teres t is the fac t 10 that supersaturat ion did not inf luence only the growth and nucleat ion 2,5 ra tes , but a lso the habit and qua l i t y of c r y s t a l s . Tadao Kawakami showed that the rate of growth of copper su l f a te was nearly proport ional to the concentrat ion of copper su l f a te so lu t i on and i t s v i s c o s i t y . I s h i i , 14 T a lso reported a f i r s t order re l a t i onsh ip for potassium s u l f a t e . 33 Nyv l t , J . , stated that for the small degrees of supercool ing normally found in i ndus t r i a l c ry s ta l 1 i zer s , growth rate increased l i n e a r l y with 29 supersaturat ion. In another work, Mull in et al recorded that potassium su l f a te c ry s t a l s in the 250-2500 micron s i ze range grew at a rate propor-41 t iona l to the square of the supersaturat ion. Rosen and Hulburt reported an ident i ca l f u n c t i o n a l i t y for the 60-2000 micron s i z e range. A decrease in nucleat ion rate with increase in supersaturat ion has been reported by Randolph, A.D. and C i se , M . D . , ^ and confirmed by Randolph and R a j a g o p a l . ^ 2.2.5 RESIDENCE TIME It has been reported [A.B. Amin and M.A. Larson]^ that the net resu l t of d i f f e r e n t residence times in continuous c rys ta l 1izers was the generation of a d i f f e r e n t supersaturat ion and consequently d i f f e r e n t growth and nucleat ion rates. For the c r y s t a l l i z a t i o n of calcium su l f a te from phosphoric a c i d , a larger residence time and consequently lower supersatur-43 at ion gave a larger s ized product. 2.3 SODIUM SULFATE SOLUBILITY A search of the l i t e r a t u r e for information on the s o l u b i l i t i e s of inorganic sa l t s in various anhydrous a lcohols w i l l show that comparatively l i t t l e work has been reported. Most of the data have been obtained for 15 sa l t s in aqueous a l coho l s . The s o l u b i l i t i e s of the sa l t s in these a l co -hols show a wide va r i a t i on with d i f f e r e n t inves t i ga tors . "These d i s c rep -11 ancies in resu l ts may be a t t r ibu ted to varying amounts of water in the a l coho l s , or the methods for determination may have permitted moisture to reach the s o l u t i o n s . " ' " ' No reference was found on the s o l u b i l i t y of sodium su l f a te in methanol-water-su1furic ac id s o lu t i on . Larson and 19 Hunt gave data for sodium and potaslsium hal ides at 25°C in absolute 1 2 isopropanol. Ginnings and Chen, have reported resu l t s for potassium c h l o r i d e , ammonium acid phosphate and s u l f a t e , sodium bromide and carbonate at 25°C in aqueous isopropanol so lu t ions . Frankforter and Temple ' ' studied the systems cons i s t ing of the aqueous alcohol and potassium ca r -bonate or f l u o r i d e at 20°C. The s o l u b i l i t i e s of sodium cholor ide and of sodium su l f a te in absolute alcohol are reported by Kirn and Dunlap'"* over the temperature range from 20° to 50°C. l.k PRINCIPLES UNDERLYING EQUIPMENT CHOICE Since supersaturat ion is the molecular d r i v ing force in a l l c r y s t a l -l i z a t i o n processes, a number of techniques have been employed to cause i t : these include ind i rec t coo l ing , evaporation of the so lvent , ad iabat ic vacuum coo l ing , and ' s a l t i n g - o u t ' by the add i t ion of a th i rd component to reduce the s o l u b i l i t y of the c r y s t a l l i z i n g substance. The i nd i rec t cool ing mode, wherein heat is removed through a heat exchanger w a l l , is u t i l i s e d when product s o l u b i l i t y is s trongly temperature dependent. The evaporation technique is su i t ab le for so lut ions with small or negative temperature dependence. Adiabat ic cool ing is used for c ry s ta l s with intermediate types of s o l u b i l i t y curves. In th is work, ' s a l t i n g - o u t ' is u t i l i s e d in the generation of the supersaturated s ta te . The ' s a l t i n g ' substance which may be a l i q u i d , s o l i d or gas is sometimes referred to as a ' d i l u e n t ' or p r e c i p i t a n t . The necessary propert ies for a d i luent are-: i t should be misc ib le with the solvent of the o r i g i n a l s o l u t i o n , 12 at least over the des ired range of concentrat ion; the so lute should be r e l a t i v e l y inso luble in i t and a l so the f i n a l so l vent -d i luent mixture should be capable of easy separat ion, fo r example, by d i s t i l l a t i o n . Equipment for heat ing, coo l i ng , and vacuum generation is not needed as is the case with evaporative or cool ing types of c r y s t a l 1 i z e r s . The use of a non-saturated feed stream el iminates the problem of f e e d - l i n e plugging during operat ion. Insulat ion of the c r y s t a l l i z e r is not necessary; therefore, a transparent vessel can be used enabl ing v i sua l observat ion of the c ry s ta l suspension during operat ion. The maintenance of a constant crys ta l suspension during an {.upset in production rate does not require the simultaneous change of heat input or removal. The above mentioned advantages are e spec i a l l y important when a small c r y s t a l l i z e r is used as in the present workl Probably the biggest disadvantage of ' s a l t i n g -out ' c r y s t a l l i z a t i o n is the need fo r a recovery unit to handle f a i r l y large quant i t ies of the mother l iquor in order to separate the solvent and d i l uen t , one or both of which may be va luable. As 'has been stated e a r l i e r , there are many c r y s t a l 1 i z e r s that have been used i n d u s t r i a l l y but the ARP process uses the ' s a l t i n g ' method because i t gives the desired product e a s i l y and is heat e f f i c i e n t . Since this work was intended to determine some of the design parameters of this (ARP) i ndus t r i a l c r y s t a 1 1 i z e r , a mixed suspension mixed product removal 37 (MSMPR) c r y s t a l l i z e r as recommended by Randolph and Larson was used in the inves t i ga t ion . 13 CHAPTER 3 BASIS AND EXTENT OF EXPERIMENTAL STUDY 3.1 THEORY 3 9 Randolph and Larson described a way in which the rates of the s imu l -taneous processes of nucleation and growth could be quantitatively measured in a backmixed crystal suspension. The essence of the proposed method is to generate in a CSTR a crystal mass with size distribution over some convenient f in i te size range, and to obtain quantitative nucleation and growth rates by f i t t ing the crystal size distribution (CSD) data to the form of CSD predicted by theory. The basic assumptions made are: (i) the system is perfectly mixed, in other words, the agitiation is so effective that there is no product c lass i f icat ion. ( i i ) the product withdrawn from the reactor has the same concentration as that in the reactor and is a representative sample of the vessel contents in shape, s ize, form and habit.: ( i i i ) Crystal nuclei appear with zero s ize; (iv) the growth rate is independent of crystal size (McCabe AL law); (v) there are no crystals in the feed stream; (vi) constant slurry volume (vi i) steady state operation. The analysis of the crysta l l izer data is based on the population 3 9 balance equation given by Randolph as This complex relation is simplified by applying the assumptions made viz constant slurry volume ( d / d t ° n V = 0 ) ; S t e a d y s t a t e R a t i o n [ (^ D- = o) , (B(L) = D (L ) ) ] , a lso the rate of generation is constant at steady s t a te , thus ^ ^' = n7x. where "C = v/Q.) . The s imp l i f i ed equation becomes ^ (Gn) = n_ ( 2 ) n = population density (no. of * t T c ry s ta l ) T- = res idence time G = Growth rate L = s i ze of c ry s ta l 05 The McCabe law assumption is appl ied and equation 2 is integrated to g i ve n = n° exp (-L/QX.) CZ J where n = populat ion density of c rys ta l n° = nuc le i populat ion density L = c rys ta l s i ze A semi-log p lot of n versus L gives a s t ra i gh t l i ne of slope "I/G-TJ, From t h i s , the growth rate G is c a l cu l a ted . The curve is extrapolated to s i ze equal to z e r o — t o give the nuclei population density ( n° ) . The product of n° and growth rate gives the nucleat ion rate. B = n° G (V) 3.2 EXTENT OF EXPERIMENTAL WORK As s o l u b i l i t y cannot be predicted accura te ly , the f i r s t step in the study of c r y s t a l l i z a t i o n rates is to obtain s o l u b i l i t y data for the suggested system in order to estimate the economic f e a s i b i l i t y of the proposed method. In the present work the phase equ i l i b r ium for sodium su1 f a te - -methano l /wate i—su l fu r i c ac id system was determined fo r a meth-anol-water ra t i o of 50 by 50% at a temperature of 35°C. The growth and nucleat ion rates of neutral sodium su l f a te were determined and the e f f e c t of the fo l lowing factors on them tes ted: (i) Supersaturation which serves as an expression of the molecular 15 dr i v ing force of the process and i ts e f f e c t at 0 . 7 , 0 . 8 2 3 and 0 . 9 5 leve ls on the growth and nucleat ion rates was s tud ied. ( i i ) Ag i ta t ion rate at 1 2 6 0 RPM, 1 9 2 6 RPM and 2 4 6 6 RPM was tes ted. ( i i i ) Residence time for 1 7 0 sees, 2 3 5 sees and 3 8 0 sees values were employed and the corresponding e f f e c t measured. ( iv) Temperature of 1 5 ° C , 2 0 ° C , 2 5 ° C and 3 5 ° C were used and the i r e f f e c t on growth and nucleat ion rate was determined. This work could have e a s i l y employed i ndus t r i a l e f f l uen t s but as a pre l iminary study i t was not des i reab le to include a l l the e f fec t s caused by trace elements and other impurit ies in the waste, so instead an a r t i f i c i a l e f f l u e n t of concentrat ion equiva lent to that from the Mathieson process ( 5 0 % sodium su l f a te in 3 7 - 5 % s u l f u r i c ac id so lut ion) was used. A 2 s t a t i s t i c a l f a c t o r i a l design was appl ied in the ana lys i s of the resu l t s because i t was not poss ib le to genera l i se the e f f e c t of a l l the var iab les on growth and nucleat ion rates ju s t by observing the trend in the graphica l representat ion. 16 CHAPTER k APPARATUS AND EXPERIMENTAL TECHNIQUE k.1 APPARATUS The c r y s t a l l i z e r is of the continuous mixed suspension mixed pro-duct removal (MSMPR) type. The vessel is a one l i t r e glass reactor (culture f lask) f i t t e d with a d i r e c t l y dr iven va r i ab le speed ag i t a to r . There are three ports at the top for the introduct ion of spent a c i d , water and methanol. A sample withdrawal port is a lso provided at the top. At the 'neck' of the vessel is an ou t l e t port for product overf low, whi le in the middle on the water j a c k e t , the temperature con t ro l l ed water i n l e t and ou t l e t ports are placed d iagona l ly to each other. Three 0.8 l i t r e containers for spent a c i d , methanol and water are placed above the reactor to give grav i ty feed and are connected to the reactor vessel by tygon tubing. The three flows were measured with (Gilmont s i z e 13) rotameters. A s ta in le s s s tee l heat exchange c o i l was placed in the spent ac id storage vessel and copper heat exchangers in the other two. They were connected in se r ie s to a constant temperature water bath, ( f igure 1) 4.2 EXPERIMENTAL TECHNIQUE 4.2.1 PHASE DIAGRAM DETERMINATION The curves in three-component phase diagrams trace out points of saturat ion with respect to one or more components. Thus, when any mixture of water-methanol , s u l f u r i c ac id and sodium su l f a te was taken which l e f t some c ry s ta l s undisso lved, the ana lys i s of the so lu t ion gave a point on one of the curves. By t e s t i ng a wide range of mixtures a number of saturated so lut ions was obtained and a s u f f i c i e n t number of points L-CONSTANT WATER I TEMPERATURE JACKET FIGURE 1 SCHEMATIC DIAGRAM OF EQUIPMENT 18 was determined to draw a l l the curves in the diagram ( f i g . 2). To complete the diagram i t was necessary to know the form of the s a l t with which each so lut ion was saturated. By f i l t e r i n g and analys ing the c ry s ta l s an ap-proximate formula was found, but th is method was not s u f f i c i e n t l y accurate as some mother l iquor was l e f t in the f i l t e r e d c r y s t a l s . To avoid th is handicap, the method of Wet Residues was employed. 4.2.2 METHOD OF WET RESIDUES PRINCIPLE It .will be remembered that i f any component is marked on a phase diagram i t l i e s on the s t ra i ght l i ne j o i n i n g i t s so lu t ion with i t s s o l i d . If, there fore , some mother l iquor remains with the s o l i d the com-pos i t i on of the wet residue must also l i e on the same s t ra i gh t l i n e , but nearer to the s o l i d . By analysing a so lu t ion and its wet residue two points can be p lot ted on a diagram and a s t ra i ght l i ne is drawn through them. The composition of the so lut ion gives a point on the curve; the composition of the s o l i d phase must l i e somewhere on the s t ra i gh t l i ne beyond the pos i t ion of the wet residue. 4.2.3 TECHNIQUE OF DETERMINATION It.was decided that commercial methanol would be used for making up the aqueous so lu t i ons , provided the s o l u b i l i t y in a test so lu t ion of given composition was the same as that in a so lu t ion of the same composition prepared from p u r i f i e d a l coho l . Since only traces of organic compounds, in addit ion to water, are present as impur i t ies in the com-i mercial methanol, i t was assumed that these would have a n e g i l i g i b l e e f f e c t on the s o l u b i l i t y of sodium su l f a te in the aqueous methanol s o l u -t i on . Moreover, i n d u s t r i a l l y the methanol used is rare ly p u r i f i e d before being used. 19 A 50-50 weight percent mixture of methanol and water was prepared and stored. This was mixed at various weight percents (0, 10, 20, 30, kO, 50, 60, 70, 8 0 , 9 0 , 100) with 9N (37-5 weight %) su fu r i c ac id . About 500 ml of each composition was measured out and d iv ided equal ly into two ir.lenmeyer f l a sk s . A f ixed weight (lOOgm) of sodium su l f a te granules was added to each of the f l a sk s . The f lasks were corked, sealed in order to reduce methanol loss by evaporation.,.,and placed in a water bath main-tained at 35°C. The whole set was ag i tated and allowed to ' s tay ' at this temperature for about seven days with intermittent shaking of the f lasks and the i r contents, so that equ i l ib r ium could be a t ta ined. Equ i l ibr ium was assumed to have been atta ined i f a f t e r seven days, there were s t i l l undissolved granules. If there were no undissolved sodium s u l f a t e , another quantity of sodium su l f a te was added and the 'end po in t 1 test performed at the end of another seven day per iod. At equ i l i b r i um, the mixture was allowed to s e t t l e whi le s t i l l being maintained at 35°C. Some of the c lear so lu t ion was withdrawn from each f l a sk and analysed. 25ml of c l ea r so lu t ion was weighed and heated to dryness, the c rys ta l s were weighed again and the weight of d i s so lved sodium su f fa te ca l cu la ted . A port ion of the so lu t ion was t i t r a t e d with Ferrous Ammonium Su l fa te to determine the weight percent of methanol and thus water/methanol so lu t i on . It should be noted that about a 5% d i f fe rence was observed in the measured methanol concentrat ion and that i n i t i a l l y used. The methanol was p lo t ted as a 50 weight percent water so lut ion on the t r i angu la r diagram. The other port ion of the c lear s o l u -t ion was t i t r a t e d with sodium hydroxide to ca l cu l a te the weight percent of s u l f u r i c a c id . The second f l a sk at the same composition was used to cross-check for the accuracy of the re su l t s . The remainder of the s o l u -t ion in the f l a sk was decanted and the wet residue weighed, and redissolved 20 in s u l f u r i c a c id . This so lu t ion was then analysed as has been descr ibed, but the concentrat ion was ca lcu la ted as a percentage of the weight res -idue and this gave the second point on the diagram. For each o r i g i n a l mixture two analyses were obtained, one representing the s o l u t i o n , the other representing the wet residue. The so lut ion points were jo ined to form the curves. The c ry s t a l s were d isso lved in water and the so lu t ion t i t r a t e d to determine the type of compound produced. h.l.k ANALYSIS OF CRYSTALS The c rys ta l s produced a f t e r the evaporat ion, were d i s so lved in water and the so lu t ion t i t r a t e d . When the t i t e r for each of the new so lut ions was equivalent to 36% t i t r a t a b l e s u l f u r i c a c i d , the c rys ta l was c l a s s i -f i ed as sodium b i s u l f a t e monohydrate. To confirm this , statement, a quantity of the c ry s ta l s was heated and observed to have melted at about 58°C, which corresponds to the melting point of NaHSO^« H^O. But when the t i t e r was equivalent to 18.7% t i t r a t a b l e s u l f u r i c a c i d , sodium sesqu i -su l f a te [Na^H (SO^^] , was assumed to have been formed. If 36% equivalent t i t r a t a b l e s u l f u r i c acid was used but the melting point of the c ry s ta l is above 80°C, sodium b i s u l f a t e was assumed to be the product formed. Both sodium su l f a te (neutral s a l t ) and hydrated sodium su l f a te had not t i t r a t a b l e s u l f u r i c acid equiva lent . The s p e c i f i c g rav i ty of the c ry s ta l s was determined. Crysta l s with s p e c i f i c grav i ty of 1.2 to 1.6 were c l a s s i f i e d as hydrated sodium s u l -fate (Na2S0^ • lQh^O) whi le those with s p e c i f i c grav i ty of about 2.5 were grouped as sodium s u l f a t e . To confirm the observat ion, the i r melting points were measured. The decahydrate was found to melt around 32°C while the neutral s a l t did not melt even at temperatures above 100°C. H20/MeOH FIGURE 2 PHASE DIAGRAM OF Na^O^ - H20/ME0H - H SO^ SYSTEM 22 4 . 3 CRYSTALLIZATION RATE EXPERIMENT 4.3.1 TEST SOLUTION PREPARATION The a r t i f i c i a l waste ac id so lu t ion was prepared by d i s so lv ing a f ixed weight of sodium su l f a te in a 3 7 - 5 weight percent (h^SO^) s u l f u r i c ac id to g(i>ve a 50% sodium su l f a te so lu t i on . The ac id concentrat ion was measured by t i t r a t i n g with standard sodium hydroxide so lu t i on . The so lut ion was placed in a water bath un t i l i t s temperature had r i sen to 5 ° above the expected working temperature. It was removed and f i l t e r e d through a s in tered glass f i l t e r to remove any p a r t i c l e s which could cause nuc leat ion. 4 . 3 - 2 EXPERIMENTAL PROCEDURE The a r t i f i c i a l e f f l uen t so lu t ion was poured into i t s temperature cont ro l led feed reservo i r and the other two containers were f i l l e d with methanol and water. During this time, the constant temperature water was allowed to c i r c u l a t e through the c o i l s of the reservo i r and the jacketted reactor. A su f f i c ient , time was allowed to elapse for the whole system to a t ta in the required temperature. The s t i r r e r was then set at the required speed (the low speed shaft rpm was counted for the number of turns per minute by eye and th£s value was mu l t i p l i ed by 18). The flows were adjusted to give the required rate as shown on the flow meters. This adjustment is very important s ince in a l l cases a f ixed ra t i o of methanol to water has to be maintained at 5 0 - 5 0 1 by weight. This was ca lcu la ted by mul t ip ly ing the volume by the s p e c i f i c g rav i ty . (The spe-c i f i c g rav i ty of a methanol-solution mixture at various volumetric rat ios is l i nea l—append ix 1—). The time to f i l l the reactor vessel and s t a r t overf lowing was noted. 23 At steady state flow conditions (flow in = flow out), a 60 cm* hypodermic syringe with the needle replaced by a 5 mm internal diameter 3 plast ic tubing was used to withdraw about 50 cm of the slurry from the vessel. This was quickly transferred to a sintered glass suction f i l t e r , where the crystals were separated from the mother liquor. About 25 ml of the clear liquor was heated to evaporation and the crystals deposited were weighed to give the concentration of sodium sulfate in the mother liquor. This final concentration (C*) was subtracted from the in i t i a l concentration. This value was then divided by the f inal concentration C -to give the supersation (—g-j. ). TR'rs definition was used for the super-saturation in order to operate under the same basis as the phase diagram values. When the inital concentration of sodium sulfate was less than 50% it became d i f f i cu l t to crysta l l ize neutral sodium sulfate because the addition of a 50-50 methanol-water solution always lead to precipitation of a mixed salt of neutral sodium sulfate and sodium sequisulfate or even sodium bisulfate (Check fig 2, starting point was always on the Na^SO^ - H^ SO^ horizontal l ine since i t was only a two component system then). The crystals were washed with methanol and dried, after which the crystals were weighed, sieved and the sieve fractions weighed. A portion of this crystal was redissolved in water and titrated in order to determine the amount of acidic component present. For neutral salt product, no acidic component was present. Reaction steady state was found by re^peatedly withdrawing samples with the hypodermic syringe and weighing the crystals. A steady state was assumed to have been attained when the difference in any two consecu-tive sample weights was less than 2%. The reactor was then washed to remove any trace of crystals and the whole procedure was repeated for a new condition. Since there is no instrument to measure the point concen-2k t r a t i on during the experiment, a lot of runs have to be made and d i s -carded due to the f ac t that the concentrat ion is measured at only the i n i t i a l and f i n a l states and that using the same condit ions as in the previous experiment, the supersaturat ion may turn out "to be d i f f e r e n t . This would be caused by small temperature va r i a t i on of about 1° which would occur during some runs due to the addi t ion of more methanol and sometimes spent acid to the conta iners. 4.3-3 SIEVE TEST Screen analyses were made using ca l i b ra ted U.S. Standard 3~inch screens. The screens used were the fo l lowing U.S. Standard mesh s i z e s : 60,80,100,140, and 170. Because of the symmetry of the c r y s t a l s , repro-ducib le screen analyses were ea s i l y achieved. To carry out the s ieve analys i s a l l the dr ied c ry s ta l s were weighed and p;laced on the top s ieve in a nest which comprised the f i v e s ieves arranged in order of decreasing aperture ( increas ing mesh number) mounted on a bottom c o l l e c t i n g pan. A top l i d was used to minimise the loss of dust. The nest of s ieves , together with the l i d and c o l l e c t o r pan were held in the l e f t hand, with the s ieve surfaces i nc l i ned downwards towards the l e f t at an approximate angle of 30° to the ho r i zon ta l . The higher s ide of s ieve frame was tapped eight times with the hand. Whilst main-ta in ing the i n c l i n a t i o n of the s ieve , the nest was shaken to and f ro several times, whi le being rotated in the plane of the gauze through an angle of about 60°. These a l ternate tapping and shaking steps were repeated for about 3 to 5 minutes. The top s ieve was removed, inverted over a clean p iece of paper, and tapped gently to remove any c ry s ta l s retained on i t . The bottom surface of the gauze, that i s , the surface 25 that was uppermost with the s ieve in i t s inverted p o s i t i o n , was brushed gently to a id the cleaning operat ion. A l l the discharged material was t ransferred back to the cleaned s ieve mounted on a c o l l e c t o r pan and submitted to a further s iev ing opera t ion , as described above, for about 2 minutes. If the amount of material passing through the s ieve in this 2 minute period was less than 0.5% of the o r i g i n a l test sample weight, s iev ing on this s ieve was considered complete. If the amount passing exceeded 0.5%, the procedure was repeated un t i l the 'end po in t 1 was achieved. A l l the weighed material from the c o l l e c t o r pan was then t rans ferred on to the material retained on the top s ieve of the remaining nest which was submitted to another 3 to 5 minutes s iev ing operat ion. The 'end po int ' test was again appl ied to the top s ieve, and the whole procedure was repeated unt i l a l l the f i v e sieves have been dealt wi th. 4.3-4 METHANOL EFFECT It should be noted that a bas ic assumption made in the experimental procedure was that the purpose fo r r the addi t ion of methanol was to a l t e r the supersaturat ion level of the so lu t i on . In other words methanol acted to change the dr i v ing force in the c r y s t a l l i z a t i o n . Also in the higher temperature experiments both the density and v i s c o s i t y of methanol changed great ly making i t d i f f i c u l t to maintain a steady methanol flow rate. This e f f e c t became very pronounced at temperatures above 35°C, and acted as a constra int in carry ing out the invest igat ion at temperatures above 35°C. FIGURE 3 PHOTOGRAPH OF NEUTRAL SODIUM SULFATE CRYSTALS, AS PRECIPITATED. ON 27 CHAPTER 5 RESULTS AND ANALYSIS 5.1 CRYSTAL SIZE AND POPULATION DENSITY The crys ta l s izes var ied from about 0.1 mm to 0.29 mm and were div ided by screen analyses into f i v e d i f f e r e n t s i ze f rac t ions as pre-v ious ly descr ibed. To enhance the representat ion of the s i ze d i s t r i b u -t ion in terms of population dens i ty , the d i s t r i b u t i o n was converted from the weight f rac t ions obtained from the screen analyses by the fo l lowing method. (i) The mean diameter of each s i z e f r a c t i o n (screen analyses f rac t ion ) was determined. ( i i ) The to ta l weight of the c ry s ta l s of a given s i z e f r ac t i on was then div ided by the c rys ta l dens i ty , the cube of the mean diameter, and an overa l l average shape f ac to r . This gave the number of c ry s ta l s in the s i ze fract ion!; ( i i i ) The number of c ry s ta l s in each f r a c t i o n was then d iv ided by the width of the s i ze range of the f r a c t i o n . This gave the populat ion density of c rys ta l s in the s i ze f r a c t i o n . The actual c a l cu l a t i on was performed by f i r s t converting the d i s c re te values (screen analyses f rac t ions ) of weight to a continuous funct ion by making a cumulative weight percent p l o t . The absc issa of the p lo t was broken into th i r ty - seven equal segments of 0.005 mm width. This width interva l was used in order to reduce the er ror introduced by using 30 the larger value of about 0.05 mm recommended by Mull i n , J . A hypo-the t i ca l diameter was used to represent the mean s i ze of the c ry s ta l s in the i n t e r v a l . This was necessary because i t was r e l a t i v e l y d i f f i c u l t 28 to measure the dimensions of the c ry s ta l s with a microscope or from photographs. The hypothet ica l diameter ( s ize) was ca lcu la ted using the r e l a t i o n : L h =/(A - 0 .025) (A + 0 .025) ( T ) (L^ = hypothet ica l c ry s ta l s i z e , A = mesh opening at u n i -form interva l ) where A = AD(1) + 0 . 0 0 5 ( 1 - 1 ) (6) I = i t e r a t i o n counter (AD = screen s ize) This was ca l cu la ted fo r every 0 .005 mm interva l and the corresponding weight percent on the ord inate was read f o r the segment. The populat ion density for each segment was ca l cu la ted by: suspension density reactor capaci ty c r y s t a l mass increment c ry s ta l density overa l l shape fac tor hypothet ica l c ry s ta l s i z e hypothet ica l c r y s t a l s i ze i ncrement A computer program was wr i t ten that performed th is operat ion (Appendb 5 .1 . 2 CRYSTAL SHAPE FACTOR A value of the overa l l shape f a c t o r , kv is needed for c a l c u l a t i n g the populat ion density from equation ( 7 ) , but as the c ry s ta l s i ze in the present s tudies ranged from about 0 . 3 mm down to a few microns i t was necessary to see i f kv was s ize-dependent. Accord ing ly , sodium s u l f a t e c ry s t a l s produced by c r y s t a l l i z a t i o n were c a r e f u l l y separated with f i v e s i z e f r ac t i ons as described e a r l i e r and the i r volume and surface shape factors were determined separate ly . The volume shape f a c t o r , fv , was determined by weighing about 100 c r y s ta l s from each s ieve f r a c t i on and then apply the re l a t i on . ( n = PsV Am (7) where Ps = P kvL^ AL U W V = "h * h &m = P = kv = L h -* L h = 29 M = nP fv L where L = mean aperture s i ze P = c r y s t a l dens i ty fv = volume shape fac tor n = number of c r y s t a l s M = mass of c r y s t a l s and taking the ar i thmet ic mean aperture s i z e as the c h a r a c t e r i s t i c dimension, L, of each s ieve f r a c t i o n . Within the l im i t s of experiment e r r o r , fv remained constant at 0.6 + 0.03-The surface shape f a c t o r , f s , for the c r y s t a l s in each s ieve f r a c t i o n was determined with the aid of a microscope. It was assumed that the c ry s ta l rested on one of i t s longest faces , i t s average length, x, and breadth,y, were obtained by making s i x readings of each of the two dimen-s ions. The thickness of the c r y s t a l , Z, was derived by taking the mean s ieve aperture s i z e , L, as the cha rac te r i s i ng dimension and assuming the c ry s ta l s to be a p a r a l l e l e p i p e d , that i s , Z = fv L^/xy M U where Z = c ry s ta l thickness L = mean aperture s i z e x = length of c ry s ta l y = breadth of c ry s ta l fv = volume shape fac tor The surface shape fac tor of a c r y s t a l , character i sed by i t s mean s ieve aperture s i z e L, is given by fs = 2(xy + yZ + x Z ) / L 2 (To) where fs = surface shape f ac to r x = length of c ry s ta l y = breadth of c ry s ta l Z = c ry s ta l thickness L = mean aperture Over the s i z e range studied the surface shape fac tor remained reason-ably constant at fs = 3.9 +0.03. Consequently, a constant o v e r a l l shape fac tor kv = f s / f v = 6.5 + 0.5 30 was used when calculating population density from equation ( 7 ) . As can be seen in equation ( 3 ) , a plot of log of the population density versus crystal size should give a straight line with slope equal to (-1/GT) and an intercept of the log of the nuclei population density. A computer program that ut i l i sed the least square method of f i t t i ng a curve was used to determine the growth rate and the corresponding nucle-ation rate for a l l the tested conditions. As can be seen in the semi-log plot of population density versus crystal size (figure k), the plot f i t s 37 the simplified Randolph's model very well. The growth rate was ca l -culated by dividing the inverse of the slope by the residence time. G = - 1 s1 ope X X The slope is negative hence the growth rate is positive. The nu-cleation rate was calculated by multiplying the intercept by the growth rate. See appendix 6 for crystal size and population density results. Table I shows the rates for one set of conditions, a l l the data are given in appendix 4. As can be seen in Table I the growth rate and nucleation rate increase with supersaturation and temperature in a regular manner. Table 2 shows the crystal size distribution obtained from the sieve fractions for one set of conditions, while a l l data are given in appendix 6. The crystal size fractions at various residence times for the same supersaturation, agitation rate and temperature, larger sized pro-duct, as would be expected, is generated at longer residence times. In other words more crystals grew to a large size at longer residence times, which resulted in smaller values of growth rate and corresponding lower nucleation rate values. 31 E E 52 io 7 V E C z UJ Q < _ l 0. o CL 10° F 0.00 AGITATION RATE = 2 466 RPM SUPERSATURATION = 0 9 5 TEMPERATURE = 15 °C RESIDENCE TIME = 170 s 0.10 0.20 SIZE (mm) 0.30 0 4 0 FIGURE k POPULATION DENSITY VS CRYSTAL SIZE (SAMPLE PLOT) 32 TABLE 1 GROWTH RATE, AND NUCLEATION RATE VERSUS SUPERSATURATION AT VARIOUS TEMPERATURES RESIDENCE TIME = 170 sees GROWTH RATE UNIT = (mm/HR) AGITATION RATE = 2466 RPM NUCLEATION RATE UNIT = NUMBERS/HR SUPERSATURATION GROWTH RATE NUCLEATION RATE TEMPERATURE 0.70 0.081 0.7075 X 1 0 7 0.823 0.088 0.82 X 1 0 7 15°C 0.95 0.095 0.9825 X IO 7 0.70 0.0822 0.88 X 1 0 7 0.823 0.0913 1 .0625 X ]07 20°C 0.95 0.10 1.3 X IO 7 0.70 0.0822 0.88 X IO 7 0.823 0.095 1.35 X 10 7 25°C 0.95 0.1066 1.675 X IO 7 0.70 0.08835 1.2125 X 10 7 0.823 o.1005 1.5375 X I 0 7 35°C 0.95 0.1134 1.9875 X IO 7 33 TABLE 2 CRYSTAL SIZE FRACTION VERSUS WEIGHT AT VARIOUS RESIDENCE TIMES SUPERSATURATION = 0.95 AGITATION RATE = 1926 RPM TEMPERATURE = 15°C SCREEN SIZE (mm) WEIGHT (gm) RESIDENCE TIME (sees) 0. 106 0.2/80 0.15 0.3393 0.18 0.02 170 sees 0.25 0.0296 0.297 Q.Q1480 SCREEN SIZE (mm) WEIGHT (gm) RESIDENCE TIME (sees) 0. 106 0.435 0.15 0.558 0.18 0.0696 235 0.25 0.0505 0.297 0.0625 SCREEN SIZE (mm) WEIGHT (gm) RESIDENCE TIME (sees) 0. 106 Q.O894 .0 .15 0.0905 0.18 0.036 380 sees 0.25 0.0547 0.297 0.0433 34 5.2 CRYSTAL SIZE DISTRIBUTION While the most comprehensive method for descr ib ing screen sample is a graphical p r e s e n t a t i o n , — which has been used in th is study to de-termine both growth and nucleat ion r a t e s — , a more convenient method has been suggested by Mull i n , J . ^ The approach uses de s c r i p t i ve methods that are pr imar i l y concerned with the bulk of the product rather than" extremes. This method reports the screen mean aperture of the c ry s t a l s (mean s i ze of c ry s ta l s ) and the c o e f f i c i e n t of va r i a t i on (C.V)) of s i z e . These are found by p l o t t i n g the average p a r t i c l e s i ze against the cummula-t i ve weight retained on each screen on ar i thmet ic p r o b a b i l i t y paper, determining the apertures corresponding to 16% and 84% p r o b a b i l i t y (two standard deviat ions) and comparing the i r d i f f e rence with the average p a r t i c l e s i z e . The c o e f f i c i e n t of va r i a t i on (C.V.) , as a percentage, is defined as fo l lows: C.V. = 100 P - D 16% " P ' D 84%  U ) P - ° 5 0 % 0 where C.V. = c o e f f i c i e n t of v a r i a t i o n P. D 16% = p a r t i c l e diameter at 16% p r o b a b i l i t y P D 84% - p a r t i c l e diameter at 84% p r o b a b i l i t y P. D 50% = mean p a r t i c l e diameter The c o e f f i c i e n t of va r i a t i on of c r y s t a l s in th is study var ied from 3% to 52%. This resu l t agrees very well with Bennett ' s^ value of 25% to 54% f o r n o n - c l a s s i f i e d products. A sample ca l cu l a t i on is shown for a run with: Residence time = 170 sees . , Ag i ta t ion rate = 2466 RPM., Temperature = 15°C and supersaturat ion = 0.95 35 Screen s i ze (mm) Weight retained (gm) Cummulative % wt 0.25 0.03670 4.47998 0. 180 0.0395 9.30176 0.15 0.0332 13.27393 0.106 0.2451 43.27393 0.088 0.4647 100 From the graph (see f i gure 5) P . D ] 6 £ = 0.149 mm; P , C >84% = 0 -°865 mm P.D r . 0 / = 0. 1001 mm Subst i tut ing these values in the C.V. equation gave = 31.2% Mean s i ze = 0.1001 mm. Therefore, the c ry s ta l s can be sa id to have a c o e f f i c i e n t :of v a r i a t i on of 31.2% and mean s i ze of 0.1001 mm. NB: Other resu l ts are in appendix 3 This a lso has confirmed the assumption of per fect mixing used in the theory s ince according to Bennett, R.C, 7 the C.V. for c l a s s i f i e d products var ies from 12% to 38% whi le in th is system, C.V. var ied from 28% to 52% which corresponds c lo se ly to Bennett 's non - c l a s s i f i ed products C.V. range of 25% to 54%. 5.3 KINETIC RATE VARIATION AND KINETIC CONSTANT As has been stated e a r l i e r , the c rys ta l s i z e d i s t r i b u t i o n s a t i s f i e d 39 the s i m p l i f i e d Randolph equation and also th is c h a r a c t e r i s t i c of non-c l a s s i f i c a t i o n of the product has helped in buttress ing the theoret i ca l approach which has been employed. The e f f e c t of the factors v i z super-sa tu ra t i on , a g i t a t i on ra te , residence time and temperature was measured as fol lows : C.V. = 100 0.149 - 0.0865 2 x 0.1001 36 CUMULATIVE % WEIGHT RETAINED FIGURE 5 COEFFICIENT OF VARIATION DETERMINATION 37 5.3-1 EFFECT OF SUPERSATURATION AND TEMPERATURE ON GROWTH A log- log p lot of growth rate versus supersaturat ion is a s t ra i gh t l i n e . The slope of the curve is the ' o rder ' (index of supersaturation) of the re la t ionsh ip between growth rate arid supersaturat ion. For the condit ions s tud ied, th i s ' o rder ' varied from 0.9 to 1.1, thus an average of 1 was used in the f i n a l ana ly s i s . The growth ra te , supersaturat ion re la t ionsh ip is now given as A l inear re l a t ionsh ip of the funct ion was drawn by 'eye ' p l o t t i n g growth rate (G) against supersaturat ion (S). The slope of this curve is equal to the growth rate constant (see f i g . 6 for sample p lot and ap-From the p l o t , i t can be observed that , as would be expected, at higher values of supersaturat ion the c ry s ta l growth rate increased and a lso at increased temperature l e v e l s , the growth rate correspondingly rose. But at increased ag i ta t ion rates and residence times, the growth rate decreased. It was not poss ib le to quant i fy these e f f e c t s from the p l o t s , thus a 2 s t a t i s t i c a l f a c t o r i a l design analys is was employed. Check appendix 2 for a table and appendix 7 for graphs, showing growth rate versus supersaturat ion, with temperature as parameter at various ag i ta t ion rates and residence time l eve l s . 5-3-2 EFFECT OF TEMPERATURE AND SUPERSATURATION ON NUCLEATION A log- log p lot of nucleat ion rate versus supersaturat ion at various leve ls of the other factors was drawn. This gave a l inear re l a t ionsh ip with slope equal to the ' o rder ' (index of supersaturation) of the super-G = kaS where G = Growth rate ka = Growth rate constant S = supersaturat ion pendix 6 for complete data). 38 AGITATION RATE = 2 466 RPM RESIDENCE TIME = 170 s 0.070 1 06 0.7 0.8 09 1.0 SUPERSATURATION , S FIGURE 6 GROWTH RATE VERSUS SUPERSATURATION, TEMPERATURE AS PARAMETER 39 O 2.0 Si E C UJ < UJ o => 0.5 02 AGITATION RATE = 2466 RPM RESIDENCE TIME = 170 3 * « I5°C o . 20°C o . 25°C v = 3 5 » c 0.4 06 SUPERSATURATION , S' 0.8 FIGURE 7 NUCLEATION RATE VS SUPERSATURATI ON, TEMPERATURE AS PARAMETER ho sa tura t ion - - nucleat ion rate equation. B = knS n (13 where kn = k i ne t i c constant B = nucleat ion rate S = supersaturat ion n = order For the conditons tes ted, this ' o rder ' var ied from h.$ to 5-1, an a r i t h -metic average of 5 was assumed. In other words the nucleat ion rate re la t ionsh ip can be represented as B = knS 5 Also in th is case ( f i g . 7) both temperature and supersaturat ion had po s i t i ve e f fec t s on the nucleat ion rate, that i s , promoted nucleat ion whi le a g i -tat ion rate and residence time decreased this rate as the i r values increased, (check appendix 7 fo r more p lots) 5-h DETERMINATION OF ACTIVATION ENERGY The growth rate of a c rys ta l is a funct ion of both the surface integrat ion process and the rate of the molecular transport process. One of the useful c r i t e r i a for d i s t ingu i sh ing which rate controls is the temperature dependence of the overa l l growth constant, ka, which can be estimated by assuming an Ar rltien i us-type re l a t i on of the form. ka = A exp(-Ea/RT) ( f ? ) where ka = k i n e t i c constant A. = Frequency fac tor Ea = Ac t i va t i on energy R = Molar gas constant T = Absolute temperature A log- log p lot of ka (ca lcu lated from the growth rate - supersatur-at ion p lot ) and the inverse of the absolute temperature gave a s t ra ight l i ne of ( f i g . 8) slope equal to (-Ea/R). From this value the ac t i va t i on FIGURE 8 GROWTH RATE CONSTANT VERSUS I/TEMPERATURE °K hi FIGURE 9 NUCLEATION RATE CONSTANT VERSUS I/TEMPERATURE °K 43 energy for the process was est imated. In a l l the condit ions tested the ac t i va t i on energy was in the range from 13 - 15 kcal/mol. These high values of a c t i v a t i o n energy (see table 3 for sample resu l t and appendix 4 for a l l the data) show a strong dependence of growth rate on temperature, as was noted e a r l i e r from the graphs. Coulson and Richardson'^ suggested that , " f o r most reactions the a c t i v a t i on energy l i e s in the range of 10 kcal to 50 kcal which implies a rapid increase in rate constant with temperature." The same approach as has ju s t been described was used in the v e r i -f i c a t i o n of temperature e f f e c t on nucleat ion rate. The ac t i v a t i on energy f e l l with in the range from 12 to 15 kca l /mol , which a lso was an ind i ca t ion of strong temperature dependence, (see f i g . 9 f o r sample p lot and table 3 for some r e s u l t s ) . These high values of a c t i v a t i o n energy combined with the fact that they are independent of s t i r r e r speed s t rong ly suggest a s u r f a c e - i n t e -grat ion c o n t r o l . A dependence of the a c t i v a t i on energy on s t i r r e r speed would have given values in the range from 4.5 to 8 kcal/mol a c t i v a t i on energy and would have suggested a d i f f u s i o n cont ro l l ed mechanism. To buttress the conclusions already made and a l so to quant i fy the e f f e c t of the other factors (ag i ta t ion rate and residence time) a 2^ s t a t i s t i c a l f a c t o r i a l design ana lys i s was u t i l i s e d to fur ther analyse the data. • 5.5 FACTORIAL ANALYSIS 4 A 2 f a c t o r i a l design s t a t i s t i c a l ana lys i s was used to quant i fy the e f f e c t o f the parameters tested as demonstrated in the p lots and table of va lues. This f a c t o r i a l design was employed because of the fo l lowing general advantages over other s t a t i s t i c a l analyses. 44 TABLE 3 GROWTH AND NUCLEATION RATE CONSTANTS WITH CALCULATED ACTIVATION ENERGY AT VARIOUS CONDITIONS AGITATION RATE = 2466 RPM RESIDENCE TIME = 170 sees GROWTH CONSTANT ACTIVATION ENERGY 1/T°K NUCLEATION CONSTANT ACTIVATION ENERGY 2.996 1.8807 1.4550 1.13029 l4.5kcal/mol 0.0032468 0.0033557 0.003413 0.0034722 0.819 0.424474 0.30573 O.2.I2556 15 kcal/mol AG 1 TAT 1 ON RATE = 1926 RPM RESIDENCE TIME = 170 sees GROWTH CONSTANT ACTIVATION ENERGY 1/T°K NUCLEATION CONSTANT ACTIVATION ENERGY 1.9 1.453 1 .30 1 .12 14.4 kcal/mol 0.0032468 0.0033557 0.003413 0.0034722 0.49 0.383864 0.34432 0.3 l4.8kcal/mol AGITATION RATE = 1260 RPM RESIDENCE TIME = 170 sees GROWTH CONSTANT ACTIVATION ENERGY 1/T°K NUCLEATION CONSTANT ACTIVATION ENERGY 2.295 1 .50 1.15 0.9 15 kcal/mol 0.0032468 0.0033557 0.003413 0.0034722 0.4244748 0.3057307 0.2308682 O.I 85 ; 14.5 kcal.mol h5 (i) When there are no interact ions the f a c t o r i a l design gives the maxi-mum e f f i c i e n c y in the est imation of the e f f e c t s . ( i i ) In the f a c t o r i a l design the e f f e c t of a f ac to r is estimated at several levels of the other f a c t o r s , and the conclusions hold over a wide range of condi t ions . ( i i i ) When interact ions e x i s t , t he i r nature being unknown, a f a c t o r i a l design is necessary to avoid misleading conclus ions. ' * ' DEFINITIONS: (a) Factor: is used to denote the feature of the experimental condit ions which was var ied from t r i a l to t r i a l . In these experiments; supersatura-t i o n , ag i ta t ion ra te , residence time and temperature were the factors tested. (b) Levels of a f a c to r : The various values of a fac tor examined in the experiment are known as l e ve l s . (c) Treatment: The set of levels of a l l factors employed in any given t r i a l or experiment is c a l l ed Treatment or Treatment combination. (d) Response: The numerical resu l t of a t r i a l on a given treatment is ca l l ed the Response corresponding to the treatment. In th is case the response ,.was e i the r growth rate or nucleat ion rate. (e) E f fec t of a f ac to r : The e f f e c t of a fac tor is the change in res-ponse produced by a change in the level of the f ac to r . In th is case, where any s ing le fac tor was tested in at least two l eve l s , — the analys i s was based on two l e v e l s , o n l y — , the e f f e c t was simply the d i f fe rence between the average response of a l l t r i a l s ca r r i ed out at the f i r s t <ljevel of fac tor and that of a l l t r i a l s at the second l e v e l . (f) Notat ion: A fac tor is denoted by a cap i ta l l e t t e r , and the two levels of the factor by (one) ' 1 ' for the lower level of t r i a l and the 46 corresponding small l e t t e r representing t r i a l at the higher l e v e l . In the present work, l e t supersaturat ion be represented by A, a g i -tat ion rate by B, residence time by C and temperature by D. Thus, when supersaturat ion is 0.70, which is the lower level of the t r i a l , i t w i l l be denoted by ( l) whi le when i t is 0.95, i t w i l l be represented by (a). TABLE 4  FACTOR LEVELS AND NOTATION  FACTORS LOWER LEVEL ( l) UPPER LEVEL (LETTERS) Supersaturation (A) 0.70 0.95 (a) Ag i ta t ion Rate (B) 1260 RPM 2466 RPM(b) Residence Time (c) 170 sees 380 secs(c) Temperature (D) 15°C 35°C (d) For any t r i a l s in which two or more factors are a t . t h e i r upper l e v e l , the response w i l l be denoted by a combination of the i r small l e t t e r s , fo r instance i f supersaturat ion is 0.95, ag i ta t ion rate = 2466 RPM and temperature = 35°C. , the response w i l l be denoted as abd, while when a l l the factors are at the i r lower l e v e l , the response w i l l be represented as (1). There is a convenient order in which to wr i te the treatment combin-ations and e f f e c t s . For one fac tor A, we simply wr i te ( l ) , a. For two factors A,B, we add b, ab, derived by mul t ip ly ing the f i r s t two by the addi t iona l l e t t e r b. For three factors the standard form is (l) ' , a , b, ab, c , ac, be, abc For four factors as in our case, we have (1), a , b, ab, c, ac, be, abc, d, ad, bd, abd, cd, acd, bed, abcd. 47 TABLE 5 GROWTH RATE WITH THEIR CORRESPONDING FACTORS AT THEIR VARIOUS LEVELS TEMPERATURE OF CRYSTALLISATION D SUPERSATURATION A AGITATION RATE B 15 + 1 (0 35 + 1 (d) RESIDENCE TIME (C) RESIDENCE T ME (C) 170 (1) 380 (C) 170 (1) 380 (C) 0.70 (1) 1260 (1) 2466 (b) 0.0936(1) 0.0810(b) 0.044(C) 0 .04l4(bc) 0.10036(d) 0.08835(bd) 0.04865(cd) 0.0472(bcd) 0.95 (a) 1260 (1) 2466 (b) 0.1057(a) 0.095(ab) 0.0512(ac) 0.0451(abc) 0.12525(ad) 0.1134(abd) 0.06245(acd) 0.0573(abcd) CALCULATION OF EFFECTS AND ANALYSIS OF VARIANCE Yates 1 " ' " method was appl ied in the c a l c u l a t i o n . Procedure: The column marked (l) (see table 6) is derived from the growth (response) column as fo l lows: the f i r s t entry in column (l) is the sum of the f i r s t two responses (0.0963 + 0.1057); the second entry is the sum of the second pa i r of y ie lds (0.0810 + 0.095); the t h i r d and fourth entr ies are the sums of the succeeding pairs (0.044 + 0.0512), (0.0414 + 0.0451) r e spec t i ve l y , this is continued unt i l the last entry in the f i r s t ha l f is f i l l e d by (0.0472 + 0.0573). To f i l l the second part; (middle sect ion of t a b l e ) , the f i r s t entry is (0.1057 - 0.0963), the second (0.095 -0.01810), this is continued unt i l the last entry (0.0573 - 0.0472). The 3rd part is used to cross-check for the presence of any e r ro r . The checks are as fo l lows: ( i) (W + X) in any column = (X + W) + (Z + Y) in previous column. ( i i ) (Y + Z) in any column = (X - W) + (Z - Y) in previous column. This approach is repeated un t i l the 4th column is f i l l e d by u t i l i s i n g the entr ies of the previous column for the new one. The f i r s t entry in TABLE 6 ANALYSIS OF GROWTH RATE DATA YATES'S METHOD SUM OF SQUARES MM/HR = MEAN TREATMENT GROWTH EFFECT = SQUARE = COMBINATION RATE (1) (2) (3) (4) COL 4/8 (COL 4)2/16 (1) 0.0963 0.202 0.378 0.5597 1 .20261 =Total a 0.1057 0.176 0.1817 0.64291 0.10809 =8A 0.0135113 0.0007302 b 0.0810 0.0952 0.42736 0.0343 -0.06511 =8B -0.0081355 0.000265 7 ab 0.095 0.0865 0.21555 0.07379 -0.00239 = 8AB -0.0002988 4 x 1 0 _ / c 0.044 0.22561 0.0234 -0.0347 -0.40811 =8C -0.0510138 0.0104096 ac 0.0512 0.20175 0.0109 -0.03041 -0.03859 =8AC -0.0048238 9.31 x 10";! be 0.0414 0.11105 0.04994 0.0011 0.03461 =8BC 0.0043263 7.49 x 10 ~£ abc 0.0451 0.1045 0.02385 -0.00349 -0.01191 =8ABC -0.0014888 8.9 x 1 0 - b d 0.10036 0.0094 -0.026 -0.1963 0.08321 =8D 0.0104013 0.0004327 ad 0.12525 0.014 -0.0087 -0.21181 0.03949 =8AD 0.0049363 9-75 x ]0~l bd 0.08835 0.0072 -0.02386 -0.0125 0.00429 =8BD 0.0005363 1.2 x 10 I abd 0.1 134 0.0037 -0.00655 -0.02609 -0.00459 =8ABD -0.0005738 1.3 x 10~£ cd 0.04865 0.02489 0.0046 0.0173 -0.01551 =8CD -0.0019388 1.5 x 10 I acd 0.0624 0.02505 -0.0035 0.01731 -0.01359 = 8ACD -O.OOI6988 . 1.15 x \0~b bed 0.0472 0.01375 0.00016 -0.0081 0.00001 =8BCD 1.3 x 10"' 0 -6 abcd 0.0573 0.0101 -0.00365 -0.00381 0.00429 =8ABCD 0.0005363 1.2 x 10 TOTAL 1.20261 SUM OF 1st HALF ODDS SUM OF 1st HALF EVENS X SUM OF 2nd HALF ODDS Y SUM OF 2nd HALF EVENS Z 0.2627 0.297 0.28456 0.35835 0.63386 0.56875 0.05524 0.05285 0.8787 0.432 -0.0451 -0.0224 0.5604 0.6828 -0.1996 -0.224 0.764 0.0552 0.072 0.0256 X + W 0.5597 1.2026 1.3107 1.2432 0.8192 Z + Y 0.64291 0.10809 -0.0675 -0.424 0.0976 X - W - 0.0343 -0.06511 -0.4467 0.1224 Z - Y 0.07379 -0.00239 0.0227 -0.0248 X + W + Z + Y 1.20261 1.3107 1.2432 0.8192 (X-W)+(Z-Y) 0.10809 -0.0675 -0.424 0.0976 TABLE 6 CONTINUED 5 0 column (k) should be equal to the tota l of the response. INTERPRETATION: An estimate of e r ro r variance is required fo r the analys i s of var iance (ANOVA). There was not a s u f f i c i e n t background of information on the c r y s t a l l i z a t i o n system studied to provide an external est imate, and one had to be derived from the experiment i t s e l f . There was no i t rue interna l estimate of e r ro r var iance, s ince only a s ing le r e p l i c a t i o n of the e x p e r i -ment was ca r r i ed out, but assuming that i t was highly un l i ke l y that iner -act ion of two, three or four factors would be apprec iab le ; i t was decided, subject to experimental confirmation of the v a l i d i t y of the step to com-bine some of these in terac t ion factors that have very low Mean square 32 values provided they s a t i s f y Na i r ' s cond i t ion . NAIR'S CONDITION: Suppose there are k mean squares, V|, V^.-.V. V>,based on 0 p 0 2 e t c ; degrees of freedom, and 0 is the tota l number of degrees of freedom, so that the average estimated variance is V = (0.V.)/0 The c r i t e r i o n measuring the divergence in the V s is From ' s i g n i f i c a n t points for M' t ab l e , " " read o f f the M corresponding to k mean squares e i t he r at 9 5 % or 9 9 % confidence l e v e l . If the ca lcu la ted M is greater than the table value, then there is heterogenity in the er ror variance thus e i ther one or more of the in terac t ion mean squares is e l iminated from the variance and the rest t r i e d as above. If there is no heterogenity, sum up the mean square values of these interact ions and use i t as the e r ro r var iance. To s imp l i f y the c a l c u l a t i o n , the Mean square values were mu l t i p l i ed by 10^. Mu l t ip ly ing a l l the mean squares by a constant value did not a f fec t the analys is of var iance. M = 01nV - £ 0 . 1 n V . 51 TABLE 7 SIGNIFICANCE POINTS TEST (M) FOR CRYSTALS GROWTH DATA INTERACTION MEAN SQARE ln (MEAN SQURE) AB 4 1 .3862944 ABC 89 4.4886364 0 ; = 1 BD 12 2.4849067 0 = 5 ABD 13 2.5649494 ABCD 12 2.4849067 TOTAL 130 13.40964 = ^ l n V M = 01nV - £ 0.InV. 1 1 . ' . M = 5 x 4.8675345 - 13.409694 = 10.9279 From Na i r ' s table for k = 5, s i gn i f i c ance point value is 12.0 at 95% conf i n'dence l e v e l . In other words i t can be sa.'nd with 95% confidence that there is no heterogenity in these summed in te rac t i ons , thus the mean squares of these interact ions are summed and use as the e r ro r var iance. -7 -6 -6 -6 That i s , e r ror variance = (4 x 10 + 8.9 x 10 + 1.2 x 10 + 1.3 x 10 + 1.2 x 10" 6) = 0.000013. TABLE 8 ANALYSIS OF VARIANCE FOR CRYSTAL GROWTH MEAN SQUARE SOURCE OF VARIATION DEGREE OF FREEDOM MEAN SQUARES ERROR VARIANCE Supersaturation A , 0.0007302 56.1692 Ag i tat ion Rate B 1 0.000265 20.384615 Residence time C 1 0.0104096 800.73846 Temperature D 1 0.0004327 33-284615 Interactions AC 1 0.0000931 7.1615385 AD 1 0.0000975 7-5 BC 1 0.0000749 5-7615385 BCD 1 0 0 ACD 1 0.0000115 0.8846154 CD 1 0.000015 1.1538462 Error (AB ,ABC, BD, .A...... 5 0.000013 ABD,ABCD) An F -d i s t r i bu t i on table for F( l ,5) gave F = 6.61 at 95% confindence 1 evel . Then, i t could be said with 95% confidence with respect to growth rate that the fo l lowing were s i g n i f i c a n t and with the i r corresponding values. See table 9-53 TABLE 9 ANALYSIS OF VARIANCE RESULT FOR GROWTH RATE SHOWING THE SIGNIFICANT FACTORS AND THEIR VALUES FACTORS VALUES Supersaturation A 0.10809 Ag i ta t ion Rate B -0.06511 Res i dence Time C -0.40811 Temperature D 0.08321 /Supersa tura t ion x \ AC V. Residence Time / -0.0048238 /Supersaturat ion x \ AD Temperature / 0.0049363 Now the same analys i s for nucleat ion rate is shown in tables 10, 1 1 , 12, 13 and 14. TABLE 10 NUCLEATION RATE WITH CORRESPONDING FACTORS AT THEIR VARIOUS LEVELS SUPERSATURATION A AGITATION RATE B TEMPERATURE OF CRYSTALLIZATION (D) 1 5 + 1 (1) 35 + 1 (d) RESIDENCE " DME (C) RESIDENCE TIME (C) 170 (1) 380 (C) 170 (1) 380 (i) 0.70 (1) 1260 (1) 2466 (b) 1.0125 (1) 0.7075 (b) 0.48125(C) 0.45 (be) 1.3125(d) 1.2125(bd) 0.645(cd) 0.6l25(bcd) 0.95 (a) 1260 (1) 2466 (b) 1.23125(a) 0.9825(ab) 0.6875(ac) 0.575(abc) 1.925(ad) 1.9875(abd) 1.2825)acd) 1.1(abed) TABLE 11 ANALYSIS OF NUCLEATION RATE RESULTS YATES'S METHOD SUM OF SQUARES = MEAN TREATMENT NUMBERS/HR EFFECT = SQUARE = COMBINATION NUCLEATION ( l ) (2) (3) (4) COL 4/8 (Co l4 ) Z / l6 (1) 1.0125 2.24375 3-93375 6. 1275 16.205 Total a 1.23125 1.69 2.19375 10. 0775 3-3375 =8A 0.4171875 0.6961816 b 0.7075 1.16875 6.4375 0. 825 - 0 . 9 5 =8B -0 .11875 0 . 0564063 , ab 0.9825 1.025 3.64 2. 5125 - 0 . 0125 =8AB -0 .0015625 9.8 x 10 c 0.48125 3 .2375 0 .49375 - 0 . 6975 -4 .5375 =8C -0 .5671875 1.2868066 ac 0.6875 3.2 0.33125 - 0 . 2525 - 0 . 425 =8AC -0 .053125 0.0112891 be 0.45 1.9275 1.3875 - 0 . 025 0.2325 = 8BC 0.0290625 0.003785 abc 0.575 1.7125 1.125 0. 0125 - 0 . 45 =8ABC - 0 .05625 0.0126563 d 1.3125 0 .21875 - 0 . 55375 - 1 . 74 3-95 =8D 0.49375 0.9751563 ad 1.925 0 .275 -0.14375 - 2 . 7975 1.6875 =8AD 0-2109375 0.1779785 bd 1.2125 0 .20625 -0.0375 - 0 . 1625 0.445 =8BD 0.055625 0.0123766 abd 1.9875 0 .125 - 0 . 2 15 - 0 . 2625 0.0375 =8ABD 0.0046875 8.79 x I O - 5 cd 0.645 0.6125 0.05625 0. 41 -1.0575 = 8CD -0 .1321875 0.0698941 . acd 1.2825 0 .775 -O.O8125 - 0 . 1775 -0.1 -8ACD - 0 .0125 6.25 x 10 bed 0.6125 0 .6375 0 .1625 - 0 . 1375 - 0 .5875 =8BCD - 0 .0734375 0.0215723 abcd 1.1 0.4875 -0.15 - 0 . 3125 - 0 . 175 =8ABCD - 0 .021875 0.0018706 TOTAL 16.205 SUM OF 1st HALF ODDS W SUM OF 1st y HALF EVENS SUM OF 2nd y HALF ODDS SUM OF 2nd HALF EVENS 2.65125 3.47625 3-7825 6.295 8.5775 7.6275 1.675 1.6625 12.2525 7.29 -0.3725 -0.59 6.23 12.35 -1 .63 -3-55 10.95 !2.45 2.75 1.45 X + W 6.1275 16.205 19.5425 18.58 13.4 Z + Y 10.0775 3-3375 -0.9625 -5.18 4.2 X - W 0.825 -0 .95 -4.9625 6.12 -8 .5 Z - Y 2.5125 -0.0125 -0.2175 -1.92 -1-3 X+W+Z+Y 16.205 19.5425 18.58 13.4 (X-W)+(Z-Y) 3-3375 -0.9625 -5..18 . 4.2 TABLE 11 CONTINUED 56 TABLE 12 SIGNIFICANCE POINTS TEST (M) FOR NUCLEATION RATE INTERACTION (MS) In (MS) AB 9.8 2.2823824 ACD 625 6.4377517 ABD 87-9 4.4761998 Total 722.7 13.196334 M = 31n 722.7 - 13.196334 ie 19.748983 - 13.196334 = 6 .5526486. From Na i r ' s table for k = 3 ; M = 77 -6 - 4 -q E r ror Variance = ( 9 .8 x 10 + 6 .25 x 10 + 8.79 x 10 3 ) = 0 .0007227 . TABLE 13 ANALYSIS OF VARIANCE FOR NUCLEATION RATE SOURCE OF VARIATION DEGREE OF FREEDOM MEAN SQUARE MEAN SQUARE ERROR VARIANCE Supersaturation A 0.6961816 ; 963 .30649 Agi tat ion Rate B 1 0.0564063 78.049398 Residence time C 1 1.2868066 1780.5543 Temperature D 1 0.9751563 1349.3238 Interact ions AC 1 0.0112891 15.6207280 BC , 1 0 .003785 4 .6748305 ABC 1 0.0126563 17.512522 AD 1 0 .1779785 246.26885 IBB 1 0.0123766 17.125502 CD 1 0.0698941 96 .712467 BCD 1 0.0215723 29.849592 ABCD 1 0.0018706 2.5883492 Error (AB,ACD,ABD) 3 0.0007227 F - d i s t r i b u t i o n fo r F(l,3) = 10.1 (35% confidence leve l ) 57 There fo re , i t could be sa id with 35% confidence that for nucleat ion rate the fo l lowing were s i g n i f i c a n t and with the i r corresponding values. TABLE 14 FACTORS VALUES Supersaturation A 0.4171875 Ag i ta t ion Rate B -0.11875 Residence Time C -0.5671875 Temperature D 0.49375 Supersaturation x Residence Time AC -0.053125 Supersaturation x Ag i ta t ion x Residence ABC -0.056.25 Supersaturation x temperature AD 0.2109375 Ag i ta t ion x temperature BD o.055625-Residence x temperature CD -0.1321875 Ag i ta t ion x Residence x temperature BCD -0.0734375 ANALYSIS OF VARIANCE RESULT FOR NUCLEATION RATE SHOWING THEIR SIG-NIFICANT FACTORS AND THEIR VALUES. 5.6 REGRESSION ANALYSIS An attempt was. made to der ive a re l a t ionsh ip between growth ra te , nucleat ion rate and the factors studied v i z supersaturat ion, residence time and temperature. It is necessary to point out at this stage that ag i ta t ion rate was not included in the regression analys i s because i t has been shown that the e f f e c t of ag i t a t i on rate on both growth and nucleat ion rates is minimal. Also surface integrat ion was observed to be the con-t r o l l i n g step fo r growth rate whi le nucleat ion rate was homogeneous nuc lea-t ion both of which are independent of a g i t a t i on rate. Many mathematical models of the type found in chemical k ine t i c s and rate equations were t r i e d and the one that gave the lowest standard dev iat ion was chosen to represent the re la t ionsh ip between e i t he r growth rate or nucleat ion rate 58 and the var iab les s tud ied. C r y s t a l l i z a t i o n is a phys ica l t ransformat ion, thus the mathematical model derived may not necessar i l y have the same mathematics as does a chemical t ransformat ion, even though th is form of the re la t ionsh ip is most commonly used. 5.6.1 GROWTH RATE The suggested growth rate model is the normal bas ic rate equation found in c r y s t a l l i z a t i o n k ine t i c s but with some terms included to a l t e r the e f f e c t i v e rate constant to take account of residence time. Thus the growth rate model was found to be 6 - 1 4 1 6 6 . 6 7 ^ - ^ G = KSX e, RT (]] ) where 14166.67 cal/mol is the mean ac t i v a t i on energy for growth rate G = Growth rate (mm/hr) S = supersaturat ion X = residence time (seconds) R = molar gas constant (cal/deg.mol.) T = Temperature (°K) K = constant Logs of both sides of the equation were taken and a non- l inear parameter estimate program was wr i t ten . Also incorporated in the program is the ca l cu la t ionnof the res idue, which is defined as the sum of squares of the deviat ions of the predicted values from the measured va lues, and of the standard dev ia t ion . From the computer p r i n t - o u t , the fo l lowing values were obtained (Appendix 9 f o r program, parameter va lues, residues) 2 7 07471 - 1 4 1 6 6 - 6 7 G = 10 S "C 3 - Q 7 Z t 7 1 6 RT In other words K = 100; . £ = . . 3 . 0 7 4 7 1 sum of squares of Residuals (S0SR) = 224.8826 standard dev iat ion S.D = 1.456549 The r e l a t i v e high values of both standard dev iat ion and sum of 59 squares of res iduals confirmed the problem encountered in t ry ing to use a chemical rate equation type to f i t a phys ica l change as in c r y s t a l l i z a -t i on . Also the po s i t i ve order of residence time in the equation is con-trary to what is observed in the f a c t o r i a l analys i s where a l l the var iab l were allowed to i n te rac t . This discrepancy may be due to the fact that i simple regression ana l y s i s , the i n te rac t i ve e f f e c t of the factors was not taken into cons iderat ion. Since there are no published works on regression analys is invo lv ing temperature, supersaturat ion and residence time, i t is not poss ib le to compare the resu l t to published data. Other workers (10,12,13,27) have used a s im i l a r model but have not allowed for the e f f e c t of residence time on growth rate or on nucleat ion rate. 5.6.2 NUCLEATION RATE The same approach used above was app l ied for the determination of the mathematical model r e l a t i n g nucleat ion rate and the f a c t o r s , super-s a tu ra t i on , residence time, temperature. The re l a t i onsh ip was found to be, fi -13811.11 B = K S 5 - £ D & RT [Y8) where B = nucleat ion rate (number/hr) K = constant S = supersaturat ion i 3 8 l l . l l = mean nucleat ion rate ac t i va t i on energy (cal/mol) R = molar gas constant [cal/deg mol] T = Temperature (°K) t = residence time (seconds) [see Appendix 9b for program and Residuals] The parameter values are as fol lows K = 10 2 ; £ = 7.57801 The sum of squares of Residuals (SOSR) = 315258.2 standard dev iat ion S.D •= 54.53567 60 This high standard deviation can be explained by the poss ibi l i ty that the model is incorrect or that the predicted values were always greater than the measured values. This would confirm the observation 34a made by Ramshaw, C that, 'the nucleation rates measured by the extra-polation of population density versus crystals size to the size equal to zero from sieve analysis is always smaller than., the actual value.' He buttressed his argument by presenting plots of population density versus crystal size for crystals size less than 50yam (measured with electronic counters) which is the limit for most sieve analysis. He found that sizes less than 50pm, the relation ceased to be linear but parabolic (concave upward), thus giving a higher nucleation rate than-that measured. Coupled with this, is the fact that the suspension mass was not considered in the experiment. From nucleation theory, suspension mass has a great effect on nucleation rate. 61 CHAPTER SIX DISCUSSION AND CONCLUSION 6.1 DISCUSSION The f a c t o r i a l analys is indicates the response of the growth rate and nucleat ion rate to var ia t ions in the factors which were tested in th is study. This measure of response was based on the deviat ion of both the growth and nucleat ion rates from zero response, that i s , at a growth rate and a nucleat ion rate equal to zero. A l l po s i t i ve values ind icate increase in both growth and nucleat ion rates while negative values imply a decrease in nucleat ion and growth rates. 6.1.1 EFFECT OF SUPERSATURATION In both growth and nucleat ion rates, a va r i a t i on of supersaturat ion from 0.70 to 0.95 brought a corresponding increase of 0.10809 and 0.4171875 in the rates respect i ve ly . From the analys is of variance (AN0VA) the factor was found to be s i g n i f i c a n t which is i n agreement with the results of other workers. Although not much has been published on sodium su l f a te c r y s t a l l i z a t i o n the e f f e c t of supersaturat ion on growth and nucleat ion rates for other systems l i ke potassium su l f a te have been d i scus sed .^^ '^^ '33 ,41) In a l l these cases a po s i t i ve supersaturat ion e f f e c t had been reported. 36 Randolph and C i se , reported a decrease in nucleat ion rate with increase in supersaturat ion for the same system. This is contrary to the resu l t obtained in this study. Considering the re la t ionsh ip between nucleat ion and growth ra tes , that i s , B = n°G:, an increase in growth rate should cause a corresponding increase in nucleat ion rate. Growth rate is a funct ion of the c rys ta l s i ze 62 d i s t r i b u t i o n (CSD). The greater the c ry s ta l s s i ze displacement to smaller s i ze values the steeper the slopes of the semi-log p lots of populat ion density against c ry s ta l s s i ze w i l l be, which w i l l lead to larger values of nuclei population density ( n ° ) , s ince this is got by ex t rapo la t ion . Thus, an increase in growth rate due to increase in supersaturat ion w i l l resu l t in an increase in nucleat ion rate as has been shown in th i s work. 6.1.2 EFFECT OF AGITATION RATE An increase in ag i t a t i on rate resul ted in a decrease in both growth and nucleat ion rates. An increase in ag i t a t ion rate from 1260 RPM to 2466 RPM gave a negative (decreased)response of -0.06511 and -0.11875 for the growth and nucleat ion rates re spec t i ve l y . This is in agreement with the observations made by Coulson and R ichardson; '^ Van Hook, A ^ and McCabe and Stevens, R .P . 2 6 A host of other workers ^ ' 1 3 ' 3 7 ' 3 5 , Z , Z t ) have reported the same trend. This was expected because at higher ag i t a t i on rates, the a t t r i t i o n e f f e c t w i l l become very pronounced, which w i l l resu l t in low growth and nucleat ion rates. 6.1.3 EFFECT OF RESIDENCE TIME An increase in residence time from 170 sees to 38O sees gave a negative (decreased) e f f e c t of -0.40811 and -0.5671875 on both growth and nucleat ion rates respect i ve ly . This also confirmed what has been reported. ^ ' This was expected s ince the net resu l t of increased residence times was the generation of low supersaturat ions and consequently low growth and nucleat ion rate values. Lower growth rate implies that more c ry s ta l s have grown to larger s izes with a subsequent reduction in the s lope of the semi-log p lo t of population density against c rys ta l s i z e . A lso this s i z e enhance-ment might be pr imar i l y due to the fact that nucleat ion rate decreased to a 63 greater r e l a t i v e degree than growth rate when the residence time was increased from 170 sees to 180 sees. 6.1.4 EFFECT OF TEMPERATURE An increase in temperature from 15°C to 35°C gave an increase of 0.08321 in the growth rate response while the increase in nucleat ion rate was 0.49375 for the same temperature v a r i a t i o n . This resu l t confirmed (l 9 22) the results reported by the other workers ' ' ' who studied other systems. This implies that a decrease in temperature resulted in the production of fewer nuclei and larger c r y s t a l s . This is a lso confirmed by the r e l a t i v e values of the temperature e f f e c t on growth and nucleat ion rates. 6.1.5 EFFECT OF FACTOR INTERACTIONS The in terac t ion of supersaturat ion and residence time gave a decreased rate of growth f ac to r of -0.0048238. This simply implies that at higher supersaturat ion and residence time values, the e f f e c t of residence time predominated over the e f f e c t of supersaturat ion, s ince supersaturat ion as a s ing le factor gave a po s i t i ve growth fac tor whi le residence time gave negative fac tor (growth). As was expected, the in terac t ion of temperature and supersaturat ion resulted in a po s i t i ve growth factor of 0.0049363. The other interact ions were so small that they were used in the e r ro r variance ana lys i s . The in teract ion of supersaturat ion with residence time gave a negative nucleat ion fac tor of -0.053125, whi le the temperature, supersaturat ion in terac t ion resulted in a po s i t i ve nucleat ion fac tor of 0.2109375- The in teract ion between ag i ta t ion rate and temperature gave a po s i t i ve nucleat ion rate fac tor of 0.055625, which shows that the e f f e c t of temperature far out -c lassed that of ag i t a t i on ra te , s ince ag i t a t ion rate as a fac tor had a negative 64 inf luence on nuc leat ion. The net e f f e c t of the in terac t ion of res idence ' time and temperature was a reduction of 0.1321875 in the nucleat ion rate f ac to r . In other words at higher residence times, i t s e f f e c t overshadowed the pos i t i ve e f f e c t of temperature. This conclusion could a l so be made by observing the in terac t ion of the three factors v i z residence time, ag i t a t i on rate and temperature, which resu l ted in a negative nucleat ion fac tor of -0.0734375- The same thing was observed in the in teract ion of supersaturat ion, ag i ta t ion rate and residence time. The e f f e c t was a negative (-0.05625) nucleat ion rate f a c to r . It can ber^seen from the foregoing d iscuss ion that residence time has a more pronounced e f f e c t on both growth and nucleat ion ra tes , than does temperature. It was not poss ib le to determine the r e l a t i v e e f f e c t of both ag i ta t ion rate and supersaturat ion s ince the mean square of the i r i n te rac -t ion was so small that i t was used in the er ror variance c a l c u l a t i o n . The in teract ion e f f e c t of the four factors was not s i g n i f i c a n t . 6.1.6 EFFECT OF FACTORS ON YIELD The y i e l d expressed as the weight of s ing le neutral sodium s u l f a t e -c ry s ta l produced during c r y s t a l l i z a t i o n , in general showed an opposite trend to that of growth and nucleat ion rates. Increase in supersaturat ion and temperature resulted in lower c ry s ta l y i e l d s because more nucle i were formed with a corresponding reduction in growth rate which resul ted in smal ler s i zed p a r t i c l e s and hence low c ry s ta l weights (crys ta l mass is a function of c rys ta l volume). While increase in residence time produced larger s ized p a r t i c l e s and a corresponding increase in c r y s t a l s ' mass. It should be noted that th i s trend could only be observed when s ing le c ry s ta l s were measured but y i e l d in terms of weight of tota l neutral sodium su l f a te c ry s ta l s produced increased with increase in both supersaturat ion 65 and temperature. While increase in residence time and ag i t a t i on rate gave low y i e l d s . This can be explained by the fact that what the c ry s ta l s lost in s i ze at increased supersaturat ion and temperature, they more than com-pensated for by an increase' in c ry s ta l number. The s i n g l e c ry s ta l weight was determined by measuring the dimesions of about a hundred seed c ry s ta l s under the microscope fo r the d i f f e r e n t condit ions tested. The volume of each c ry s ta l was ca lcu la ted and m u l t i -p l i e d by the density of neutral sodium s u l f a t e to g ive the mass. A c ross -check operat ion was performed by measuring the weight of these 100 seed c r y s t a l s and the value d iv ided to give the average volume of the c r y s t a l s . A dev iat ion of about 5% was observed in the two volumes. 6.2 CONCLUSION Nucleation and growth are p a r a l l e l k i n e t i c react ions. Nucleation determines the rate of p a r t i c l e formation (in the absence of a t t r i t i o n or agglomeration); whi le growth determines the rate of depos i t ion of so lute on ex i s t i n g c r y s t a l s . In order to contro l the s i ze d i s t r i b u t i o n of par-t i c l e s , the r e l a t i v e rate of nucle i formation compared to the rate of enlargement is of prime s i g n i f i c a n c e . To increase the mean p a r t i c l e s i z e , p a r t i c l e formation must be suppressed r e l a t i v e to growth, re su l t ing in fewer but larger c r y s t a l s . If a market demands large c r y s t a l s , c r y s t a l l i -zat ion design should be based on increas ing the growth rate r e l a t i v e to nuc leat ion ra te . Since growth is of lower k i n e t i c ' o rder ' than nuc leat ion rate, decreasing supersaturat ion w i l l decrease growth rate less than the corresponding reduction in nuc leat ion rate resu l t ing in a reduced r e l a t i v e c r y s t a l l i z a t i o n rate. Since a c t i v a t i on energy for c ry s ta l growth was p r a c t i c a l l y constant 66 and independent of a g i t a t i on ra te , i t has been suggested that surface integrat ion was the c o n t r o l l i n g res i s tance. It has been shown that a d i f f u s i o n a l mechanism has a lower a c t i v a t i on energy, whi le Coulson and Richardson'^ have shown that for higher values of a c t i v a t i o n energy, the react ion is in genera l , surface react ion r a t e - c o n t r o l l e d . Also f o r d i f f u s i ona l mechanism to be the c o n t r o l l i n g res i s tance, an increase in ag i t a t ion rate should promote growth of c r y s t a l s and a l so the growth should be s i ze dependent. In th is study i t was observed that the growth of c ry s ta l s was s i z e independent and an increase in ag i t a t i on rate decreased growth of c r y s t a l s . Homogeneous nucleat ion is suggested as the mechanism of nuc leat ion for the condit ions studied in these experiments. This conclus ion is drawn from the fact that c lea r so lut ions were used in the study and an increase in supersaturat ion resu l ted in an increase in nuc leat ion rate. If the mechanism had been c o l l i s i o n breeding or by a t t r i t i o n , an increase in ag i t a t i on rate would have resu l ted in an increase in nuc leat ion ra te , but the reverse was the case. A lso there could have been marked breakage points on the c ry s t a l s but as could be seen from the photographs, the break-age points are minimal. A f i r s t ' o rder ' r e l a t i on was found to ex i s t fo r growth rate with supersaturat ion whi le that o f nuc leat ion was f i f t h ' o r d e r ' . The growth rate was found to be independent of the s i z e of the c r y s t a l s , thus the bas ic (McCabeAL Law) assumption made o r i g i n a l l y was co r rec t . The c a l -culated mean s i z e and the c o e f f i c i e n t of v a r i a t i o n confirmed that there was no c l a s s i f i c a t i o n of product in the reactor . A search of the l i t e r a -ture showed that, there have not been any publ ished data on sodium su lpha te— methanol/water--su1fur ic ac id phase diagram, thus an attempt was made to present the data for 35°C. 67 The results of the regression analys is on the data to give a react ion equation of the normal form would ind icate that the form of the model may not be co r rec t s . In the case of nucleat ion rate where the f i t was e s p e c i a l l y poor i t is poss ib le that an account must be taken of the very small nuclei and the suspension mass must be included in the c o r r e l a t i o n . 68 6.3 RECOMMENDATION As a resu l t of this study, the fo l lowing recommendations can be made:-(1) D i f ferent rat ios of methanol-water in the d i luent mixture should be tested and p lo t ted on a phase diagram to get a working combination that w i l l allow greater f l e x i b i l i t y in the va r i a t i on of supersaturat ion. (2) If higher temperatures than 35° C are to be used, a d i f f e r e n t a l c o l hoi p rec ip i t an t should be u t i l i s e d . (3) A la rger reactor capacity should be used to a id the tes t ing of residence time e f f e c t at leve ls above 380 sees. (k) A more soph i s t i ca ted counting method should be employed in order to get a more accurate measure of the number of c ry s ta l seeds with very small s i ze s . (5) The e f f e c t of the presence of t race elements such as chromates ( o r i g i n a l l y in sodium ch lorate) and other corros ion products on growth, nucleat ion rates and y i e l d should be s tud ied. In other words an e f f o r t should be made to use actual i ndus t r i a l e f f l uen t s and to quant i fy the e f fec t s of i t s trace components. (6) The e f f e c t of suspension mass on growth, nucleat ion rates and y i e l d should be inves t i ga ted. (7) With th is added information an attempt should be made to formulate a bet ter mathematical r e l a t i o n s h i p , that p red i c t both growth rate or y i e l d for any s p e c i f i e d operat ing conditons. 69 BIBLIOGRAPHY 1. 2. 3. 4. 5. 6. 8. 9-Amin, A.B and M.A. Larson Badges, W.W. and G.E. Seavoy^ Barkhuysen, F.H.C Becker, R. Bennett, R.C., H.W. Fieldelman £ A.D. Randolph Bennett, R.C. Bu t t l e r , G.S and H.B. Dunn i c l i f f Chanakya Misra & E.T. White 10. Coulson, J.M. and J . F . Richardson 11. 12. 13. 14. 15-16. 17. 18. 19-20. 21 . F rankfor ter , G.B and S. Temple Ginnings, P.M; and Chen, Z.T. Hixson, A.W and K.L Knox I sh i i , T K i r n , E.R. and H.L. Dunlap Kohn, D.H; I Yaron and D. Wolf Lando1t-Bo rns te i n Larson, R.G. and Hunt, H. Laurent, P ier re Ind Eng. Chem Prog. Design S Dev. vol 7 No. 1 Jan 1968 p 134. A . l . Ch.E Journal vol 18, No. 4 Ju ly 1972, p.798. Heat Transfer and c r y s t a l l i z a t i o n Harvey I l l i n o i s , Swanson Evap. Co. (1946) Ind. Eng. Chem 40 Nol Jan 1948 p l l . Am. J . Phys. 32, 128 (1938) Chem. Eng. Prog. 69 No7 p86 July 1973-Chem. Eng. Prog. 58, 9 , p76 Sept. 1962. J . Chem Soc. 17, 649, 1920 Chem. Eng.Prog. Symp. Series No. 10 v o l . 67 53. Chemical Engineering vol 2£3 p8 l7 , p18; Pergamon Press J . Am Chem. Soc. 37, 2697 (1915) J . Am. Chem Soc. 53, 3763 (1931) Ind. Eng. Chem. Eng S Proc Dev. vol 48 No 9 Sept. 1951 p2l44. B u l l e t i n Tokyo Ins t i tute of Technology No. 67 (1965) J . Am Chem Soc. vol 53 Feb 1931 No. 2 p391-Journal of Appl ied Chemistry 13 June 1963 Ibid Phys icka l i sh - Chemische Tabel lan P730-737. J . Phys. Chem 43, 417-23 (1939). Ind. Eng. Chem. vol 40 Nol Jan. 1948. L i u , C.Y. ; H.S. Tsuei and G.R. Youngquist Chem. Eng. Prog. Symp. ser ies No 110 67 53 p43+ 70 22. 23. 24. 25. 26. 27-28. 29. 30. 31. 32. 33. Lob ley , D.C. and Howard, J . Ibid Pulp and Paper Canada, 80, No. 2, T48-T51 Feb. 1979. 34c 35. 36. 37-38. 39. kO. 41. 42. Mason, R.E.A. and R.F. S t r i c k l a n d - Trans. Faraday Sec. 62, 455 Constable 1968. McCabe, W.L. Ind. Eng. Chem. 38, 18 (1946). McCabe, W.L and Stevens, R.P. Chem. Eng. Prog. 47 (1951) 168. M u l l i n , J.W. and G. Gaska Canadian Journal of Chemical Engineering 47 483 (1969) Ibid Trans. Inst. Chem. Eng. 47 T285 (1967) C r y s t a l l i z a t i o n Butterworths Press (1961). Ibid Biometr ika, 35, (1948), 118. Industr ia l c r y s t a l l i z a t i o n from so l u t i on s , Butterworth Press (1971) Ind. 6 Eng. Chem. vol 40. Nol Jan. 1948. Chem. Eng. Oct. 1979 p.691 -A . l . Ch.E Journal vol 18 No4 798. Ibid M u l l i n , J.W. and J . Garside Mul 1 in , J.W. Nai rs Nyv l t , J . 34. Ramberg, Hous Ramshaw, D. Randolph, A.D. and M.D. Cise Randolph, A.D. and Larson, M.A. Theory of Pa r t i cu l a te Processes (1971) Academic Press Ibid Ibid Randolph, A.D. and Rajagopal Rosen, H.N., and H.M. Hulburt Ross, E.T. I & E.C. Fundamentals vol 9 No.1 Feb. 1970 pi65... Chem. Eng. Prog. Symp. ser ies No 110 67, 27 (1970. P a c i f i c Chem. Met. Ind. 2., No. 3, 9 (1938). 71 43. Saeman, W.C. 44. Tadao Kawakami 45. 46. Thompson, A.R. and M.C. Molstad 47- Van Hook, A. 48. 49- Volmer, M and M. Marder 50. Yates 51. Davies, D.L. A.I.Ch.E Journal vol 2 Nol plO March (1956). Nagoya Kogyo Gij'utsu Shikensho Hokoku 14 (3) , 97-101 (1965) Japan. Ibid I S E.C vol 37, No. 12 Dec. 1945-Ind. Eng. Chem. 38, 50 (1946) . Ibid Journal of Physics Chemistry 154 A 97(1931). Design and Analys is of Industr ia l Expt. by Davies Chapt. 7-Design and Analys is of Industr ia l Experiment Chapt. 7-NOMENCLATURE TYPICAL UNITS Mesh opening at uniform interva l s of 0.005 mm mm screen si ze Frequency f ac to r Nucleation Rate c o e f f i c i e n t of v a r i a t i on Ac t i va t i on energy Growth rate Interat ion counter Growth rate constant Nucleation rate constant Overal1 shape fac tor c rys ta l s i ze hypothet ica l c ry s ta l s i ze hypothet ica l c r y s t a l s i ze increment mm c ry s ta l mass increment gm Population density No/mm population nuclei density No/mm P a r t i c l e (crysta l s ize) diameter mm Numbers/hou r percent kcal/mol mm/hr mm/h r Number/hr mm mm Flow rate Molar gas constant Supersaturation Reactor capacity Suspension density c ry s ta l density Residence time cm / sec cal/deg 'mol cm gm/cm' 3 gm/ cm sees APPENDIX 1 S p e c i f i c g r a v i t y o f methano l / w a t e r s o l u t i o n a t v a r i o u s t e m p e r a t u r e s . Temperature = 15°C Volume f r a c t i o n o f methanol S p e c i f i c g r a v i t y 0.2 0.997 0.4 0.978 0.6 0.951 0.8 0.933 1.0 0.909 Temperature = 20°C Volume f r a c t i o n o f methanol S p e c i f i c g r a v i t y 0.2 0.996 OA 0.976 0.6 0.9505 0.8; 0.931 1 .0 0.9087 Temperature = 25°C Volume f r a c t i o n o f methanol S p e c i f i c g r a v i t y 0.2 0.995 OA 0.974 0.6 0.946 0.8 0.929 1.0 0.906 Temperature = 35°C Volume f r a c t i o n o f methanol S p e c i f i c g r a v i t y 0.2 0.994 OA 0.97 0.6 0.946 0.8 0.9265 1.0 0.95 SPECIFIC GRAVITY OF METHANOL/WATER SOLUTION VS VOL. FRACTION OF METHANOL 75 APPENDIX 2 TABLE OF VALUES OF GROWTH RATE, NUCLEATION RATE AT VARIOUS SUPERSATURATION LEVELS, FOR DIFFERENT LEVELS OF TEMPERATURE, AGITATION RATE AND RESIDENCE TIME. RESIDENCE TIME = 170 sees; GROWTH RATE UNITS: (mm/hr) AGITATION RATE = 2466 RPM NUCLEATION RATE UNITS: (NUMBER/HR) SUPERSATURATION GROWTH RATE NUCLEATION RATE TEMPERATURE 0.70 0.823 0.95 0.081 0.088 0.095 0.7075 x IO 7 0.82 x IO7 0.9825 x IO 7 15°C 0.70 0.0822 0.88 x IO 7 0.823 0.95 0.0913 0.10 0.9725 x IO 7 1.3 x IO 7 20°C 0.70 0.823 0.95 0.0838 0.095 0.1066 1.08 x IO 7 1.30 x IO 7 1.675 x IO 7 25°C 0.70 0.823 0.95 ' 0.08835 0.1005 0.1134 1.2125 x 107 1.4975 x IO 7 1.9875 x IO7 35°C 76 AGITATION RATE = 1926 RPM RESIDENCE TIME = 170 sees. SUPERSATURATION GROWTH RATE NUCLEATION RATE TEMPERATURE 0.70 0.823 0.95 0.0995 o.1058 0.1132 1.1 x IO 7 1.2375 x 10' 1.44375 x 10 15°C 0.70 0.823 0.95 0.10075 0,1085 0.1175 1.20375 x IO 7 1.3725 x : i o 7 1.675 x 10' 20°C 0.70 0.823 0.95 0.10325 0.115 0.12075 1.3125 x IO 7 1.5075 x IO 7 1.975 x IO 7 25°C 0.70 0.823 0.95 0.1045 0.11475 0.1255 1.42875 x IO 7 1 . 7225 x IO 7 2.28 x l o ' 35°C AGITATION RATE = 1260 RPM RESIDENCE TIME = 170 sees. SUPERSATURATION GROWTH RATE NUCLEATION RATE TEMPERATURE 0.70 0.823 0.95 0.0963 0.10135 0.1057 1.0125 x \07 1.1 x IO7 1.23125 x l O 7 15°C 0.70 0.823 0.95 0.0981 0.10528 O . U 3 3 1.09375 x l O 7 1.245 x ; ( IO 7 1.43125 x l O 7 20°C 0.70 0.823 0-95 0.1015 0.11048 0.1206 1.2000 x IO 7 1.3875 x io' 1.65 x 1Q7 25°C 0.70 0.823 0.95 0.103O6 0.1142 0.12525 1.3125 x IO 7 1.505 x IO 7 1.925 x IO 7 35°C AGITATION RATE = 2466 RPM RESIDENCE TIME = 235 sees. SUPERSATURATION GROWTH RATE NUCLEATION RATE TEMPERATURE 0.70 0.066 0.66875 x IO 7 0.823 0.07225 0.8 x 10/ 15°C 0.95 0.0781 1.0375 x IO 7 0.70 0.06735 0.875 x IO 7 0.823 0.0769 1 x IO 7 20°C 0.95 0.086 I . l8 l25x IO' 0.70 0.0727 0.98375 x IO 7 0.823 0.08135 1.15625 x \0' 25°C 0.95 0.0915 1.41875 x 10' 0.70 0.07495 1.0825 x IO 7 0.823 0.0857 1.3125 x ]Q' 35°C 0.95 0.09615 . 1.6375 x IO7 AGITATION RATE = 1926 RPM RESIDENCE TIME = 235 sees. SUPERSATURATION GROWTH RATE NUCLEATION RATE TEMPERATURE 0.70 0.0727 0.830625 x IO 7 0.823 0.0763 0.9125 x \0' 15°C 0.95 0.0784 1.0625 x 10' 0.70 0.0742 0.875 x IO 7 0.823 0.0784 I.01875 x IO 7 20°C 0.95 0.0842 1.19375 x 10 0.70 0.07525 0.95625 x IO 7 0.823 0.0827 1.125 x 10/ 25°C 0.95 0.0887 1.4 x 10 X 0.70 0.0772 1.0375 x 1Q 7 0.823 0.08495 1.2925 x ]Qf 35°C 0.95 0.09369 1.61875 x 10 AGITATION RATE = 1260 RPM RESIDENCE TIME = 235 sees. SUPERSATURATION GROWTH RATE NUCLEATION RATE TEMPERATURE 0.70 0.07425 1 x IO 7 0.823 0.0765 1.07 x IO 7 15°C 0.95 0.08025 1.21875 x 10' 0.70 0.0755 1.14125 x IO 7 0.823 0.0791 1.2325 x \0' 20°C 0.95 0.0845 1.4375 x i t r 0.70 Q.07725 1.2625 x IO 7 0.823 0.08195 1.41875 x \0' 25°C 0.95 0.0869 1.65375 x i o ' 0.70 0.07875 1.425 x 1Q7 0.823 0.08435 1.575 x IO 7 35°C 0.95 0.0903 1.86625 x 10 ; AGITATION RATE = 2 4 6 6 RPM RESIDENCE TIME = 3 8 0 sees. SUPERSATURATION GROWTH RATE NUCLEATION RATE TEMPERATURE 0 . 7 0 0 .823 0 . 9 5 0 . 0 4 1 4 0 . 0 4 3 1 0 . 0 4 5 1 0 . 4 5 x 1 Q 7 0 . 5 0 7 5 x IO7 0 . 5 7 5 x IO7 15°C 0 . 7 0 0 .823 0 . 9 5 0 . 0 4 3 3 0 . 0 4 6 0 . 0 4 8 6 5 Q . 5 x 1 Q 7 0 . 6 x 1 Q 7 Q.75625 x IO' 20°C 0 . 7 0 0 .823 0 . 9 5 0 . 0 4 4 7 5 0 . 0 4 8 9 0 . 0 5 3 0 . 5 3 7 5 x 1 0 7 7 0 . 6 9 3 7 5 x i o ' Q . 8 9 3 7 5 x 1 0 ' 25°C 0 . 7 0 0 .823 0 . 9 5 0 . 0 4 7 2 0 . 0 5 1 7 5 0 . 0 5 7 3 0 . 6 1 2 5 x IO 7 0 . 7 9 x IO 7 1.1 x . 1 0 ' 35°C 79 AGITATION RATE = 1926 RPM RESIDENCE TIME = 380 sees. SUPERSATURATION GROWTH RATE NUCLEATION RATE TEMPERATURE 0.70 0.823 0.95 0.041 0.0435 0.0451 0.3375 x IO 7 0.3875 x io' 0.43125 x 10' 15°C 0.70 0.823 0.95 0.0425 0.0462 0.050 0.6875 x IO 7 0.8 x IO 7 0.96625 x IO 7 20°C 0.70 0.823 0.95 0.0435 0.0486 0.0535 0.8 x IO 7 0.9275 x io; 1.125 x 10' 25°C 0.70 0.823 0.95 0.04475 0.05057 0.057 0.90625 x IO 7 1.0625 x IO 7 1.3125 x IO 7 35°C AGITATION RATE = 1260 RPM RESIDENCE TIME = 38O « SUPERSATURATION GROWTH RATE NUCLEATION RATE TEMPERATURE 0.70 0.823 0.95 0.044 0.0475 0.05125 0.48125 x IO 7 0.5175 x IO 7 0.6875 x IO 7 15°C 0.70 0.823 0.95 0.04575 0.0501 0.05515 0.505625 x IO 7 0.6375 x IO 7 0.875 x IO7 20°C 0.70 0.823 0.95 0.047 0.0530 0.05865 0.645 x IO 7 0.8125 x IO7 1.08125 x IO7 25°C 0.70 0.823 0.95 0.04865 0.05565 0.06245 0.7375 x IO 7 0.9425 x IO7 1.2825 x IO 7 35°C 80 APPENDIX 3 MEAN SIZE AND COEFFICIENT OF VARIATION (CV) SUPERSATURATION = 0.95 TEMPERATURE = 15°C AGITATION RATE = 2466 RPM MEAN SIZE (mm) COEFFICIENT OF VARIATION (C .VH RESIDENCE TIME (sees) . . : o . i oo i 31.2 170 0.1006 45 235 0.1009 48 380 SUPERSATURATION = 0.95 TEMPERATURE = 20°C AGITATION RATE = 2466 RPM MEAN SIZE (mm) COEFFICIENT OF VARIATION (C.\l)% RESIDENCE TIME (sees) 0.1003 33 170 0.1007 49 235 0. 101 51 380 SUPERSATURATION = 0.95 TEMPERATURE = 25°C AGITATION RATE = 2466 RPM MEAN SIZE (mm) COEFFICIENT OF VARIATION (C.VH RESIDENCE TIME (sees) 0.1004 32 170 0.1008 46 235 0.1009 52 380 SUPERSATURATION = 0.95 TEMPERATURE = 35°C AGITATION RATE = 2466 RPM MEAN SIZE (mm) COEFFICIENT OF VARIATION (C.\l)% RESIDENCE TIME (sees) 0.1002 28 170 0.1009 42 235 0.1007 43 380 SUPERSATURATION = 0.823 TEMPERATURE = 15°C AGITATION RATE = 1926 RPM MEAN SIZE (mm) COEFFICIENT OF VARIATION (C.V)% RESIDENCE TIME (sees) 0. 100 39 170 0.1003 46 235 0.100 52 380 81 SUPERSATURATI0N= 0.823 TEMPERATURE = 20°C AGITATION RATE = 1926 RPM MEAN SIZE (mm) COEFFICIENT OF VARIATION (C.V)% RESIDENCE TIME (sees) 0.1002 29 170 0.1001 235 0.1005 hi 380 SUPERSATURATION = 0.823 TEMPERATURE = 25°C AGITATION RATE = 1926 RPM MEAN SIZE (mm) COEFFICIENT OF VARIATION (C.V)% RESIDENCE TIME (sees) 0. 1001 33 170 0. 1003 ho 235 0. 1007 hi 380 SUPERSATURATION = 0.823 TEMPERATURE = 35°C RESIDENCE TIME (sees) MEAN SIZE (mm) COEFFICIENT OF VARIATION (C .V )£ RESIDENCE TIME (sees) 0.1003 31 170 0.1002 39 235 0.1008 38 380 SUPERSATURATION = 0.70 TEMPERATURE = 15°C AGITATION RATE = 1260 RPM MEAN SIZE (mm): COEFFICIENT OF VARIATION (C.V)S RESIDENCE TIME (sees) 0. 100 35 170 0.1001 37 235 0.1001 38 380 SUPERSATURATION = 0.70 TEMPERATURE = 20°C AGITATION RATE = 1260 MEAN SIZE (mm) COEFFICIENT OFWARI ATI ON (C.V)% RESIDENCE TIME (sees) 0.1001 32 170 0.10015 33 235 0. 100 hO 380 82 SUPERSATURATION = 0.70 TEMPERATURE = 25°C AG ITAI ON RATE = 1260 MEAN SIZE (mm) COEFFICIENT OF VARIATION (C.V)% RESIDENCE TIME (sees) 0.1001 32 170 0.1002 32 4 235 0.1003 31 5 380 SUPERSATURATION = 0.70 TEMPERATURE = 35°C AGITATION RATE = 1260 RPM MEAN SIZE (mm) COEFFICIENT OF VARIATION (C.V)S RESIDENCE TIME (sees) 0. 100 34 170 0.1001 33.6 235 0.1002 36 380 83 APPENDIX 4 GROWTH AND NUCLEATION RATE CONSTANTS WITH CALCULATED ACTIVATION ENERGY AT VARIOUS CONDITIONS VARIOUS CONDITIONS AGITATION RATE - 2466 RPM RESIDENCE TIME = 170 sees. GROWTH CONSTANT ACTIVATION ENERGY l .T°K NUCLEATION CONSTANT ACTIVATION ENERGY 2.996 0.0032468 0.819 1.8807 14.5kcal/mol 0.0033557 0.424474 15 kcal/mol 1.4550 0.003413 0.30573 1.13029 0.0034720 0.212556 AGITATION RATE = 1926 RPM RESIDENCE TIME = 170 sees. GROWTH CONSTANT ACTIVATION ENERGY 1/T°K NUCLEATION CONSTANT ACTIVATION ENERGY 1.9 0.0032468 0.49 1.453 l4 .4kcal/mol 0.0033557 0.383864 14.8 kcal/mol 1.30 0.003413 0.34432 1.12 0.0034722 0.30 AGITATION RATE = 1260 RPM RESIDENCE TIME = 170 sees. GROWTH CONSTANT ACTIVATION ENERGY 1/T°K NUCLEATION CONSTANT ACTIVATION ENERGY 2.295 0.0032468 0.4244748 1.50 15kcal/mol 0.0033557 0.3057307 l4 .5kcal/mol 1.15 0.003413 0.2308682 0.9 0.0034722 0.185 AGITATION RATE = 2466 RPM RESIDENCE TIME = 235 sees. GROWTH CONSTANT ACTIVATION ENERGY 1/T°K NUCLEATION CONSTANT ACTIVATION ENERGY 2.2 0.0032468 0.3443276 1 .48 l4 .6kcal/mol o.oo33557 0.2867454 13 kcal/mol 1.18 0.003413 O.2567 0.94896 0.0034722 0.230 AGITATION RATE = 1926 RPM RESIDENCE TIME = 235 sees. GROWTH CONSTANT ACTIVATION ENERGY 1/T°K NUCLEATION CONSTANT ACTIVATION ENERGY 1.326 0.0032468 0.381 1.07236 13kcal/mol 0.0033557 0.30573 13.8 kcal/mol 0.90 0.003413 0.270 0.799 0.0034722 0.240 AGITATION RATE = 1260 RPM RESI DENCE TIME = 235 sees • GROWTH CONSTANT ACTIVATION ENERGY 1/T°K NUCLEATION CONSTANT ACTIVATION ENERGY 0.9004 0.0032468 0.301 0.767327 13.2kcal/mol 0.0033557 0.256 13 kcal/mol 0.692 0.003413 0.2056 0.4578357 0.0034722 0.17 AGITATION RATE = 2466 RPM RESIDENCE TIME = 380 sees • GROWTH CONSTANT ACTIVATION ENERGY 1/T°K NUCLEATION CONSTANT ACTIVATION ENERGY 1 .32 0.0032468 0.32491 0.6494067 l4.6kcal/mol 0.0033557 0.21 13 kcal/mol 0.4244748 0.003413 0.173 0.2981129 0.0034722 0.135 AGITATION RATE = 1926 RPM RESIDENCE TIME = 380 sees • GROWTH CONSTANT ACTIVATION ENERGY 1/T°K. NUCLEATION CONSTANT ACTIVATION ENERGY 1 .00 0.0032468 0.323 0.7 l4kcal/mol 0.0033557 0.2308 12.6kcal/mol 0.54 0.003413 0.1853 0.4 0.0034722 0.155 AGITATION RATE = 1260 RPM RES DENCE TIME = 38O sees. GROWTH CONSTANT ACTIVATION ENERGY I /T°K NUCLEATION CONSTANT ACTIVATION ENERGY 1.4 0.0032468 0.44 0.932515 l4.2kcal/mol 0.0033557 0.3038 14.6 kcal/mol 0.753554 0.003413 0.24 0.57735 0.0034722 0.19 . . H I L L . . . 1. - H I L L . . , 2 . , H I L L . . . 3 . . H I L L . . . 4 . . H I L L . . . 5.,. H I L L . . . 6. , H I L L . . . 7 . . HXL I B F S n o . 4 4 4 1 4 6 U n i v e r s i t y o f B C C o m p u t i n g C e n t r e MTS ( I 85 $ S I G N O N COGB P R I N T = T N P A G E S = 3 0 0 T I M E = 1 5 FORa=SEC0iLE C O P I E S = 2 • T H E S I S ' A P P E N D I X 5 cccccccccc cccccccccccc cc cc cc cc cc cc cc cc cc cc cccccccccccc cccccccccc 000000000000 G O O O O O O O O O O O 00 G O 00 00 00 00 00 00 00 00 00 00 00 00 00 00 000000000000 000000000000 GGGGGGGGGG G G G G G G G G G G G G GG GG GG GG GG GG GGGGG GG GGGGG GG GG GG GG GGGGGGGGGGGG GGGGGGGGGG B B B B B B B B B B B B B B B B B B B B B B B BB BB BB BB BB BB B B B B B B B B B B B B B B B B B B B B BB BB BB BB BB BB B B B B B B B B B B B B B B B B B B B B B B B ** ** ** ** ** ** ** ** ** ****** ************ ************ ****** ** ** ** ** ** ** ** ** ** ssssssssss ssssssssssss SS SS SS sss sssssssss sssssssss sss SS SS S S S S S S S S S S S S S S S S S S S S S S S S p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p pp E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E cccccccccc cccccccccccc cc cc cc cc cc cc cc cc cc cc cccccccccccc cccccccccc * * L a s t s i g n o n M a s : 1 4 : 0 1 : 4 9 T o e J u a 1 0 / 8 0 B s e r " C O G B " s i g n e d o n a t 0 1 : 0 9 : 3 5 o n Wed J a n 1 1 / 8 0 $BUN S J 0 * 3 : Q U E B Y E x e c u t i o n B e g i n s 0 1 : 0 9 : 3 6 * * * S E C U R E Q U E R Y : E X E C U T I O N O K « D BY O P E R A T O R E x e c u t i o n t e r m i n a t e d 0 1 : 0 9 : 4 4 . T = G . 0 0 2 RC=0 $ . 0 0 $ C Q P Y P R O J E C T * S I N K * P R O J E C T : PROC O P T I O N S (HA IN) ; / * R E S U L T S AND A N A L Y S I S O F R E S U L T S * / J / * . D E C L A R A T I O N S T A T E M E N T S * / ; D C L (GRV ( 3 , 3 , 3 , 4 ) , NEV ( 3 , 3 , 3 , 4 ) , DAT ( 3, 3 , 3 , 4 , 6) ) F L 0 A T { 1 6 ) ; DCL ( T E H P (4) , A G I T (3) , R E S ( 3 ) , S U P S A T ( 3 ) ) F L O A T (16 ) ; D C L ( L N , L A D , I , J , K , L , I A , M , J A ) F I X E D ; DCL ( AD (*) , X (*) ,CW (*) , N (*) , D (*) , Z (*) ) F L O A T { 16) C T L ; DCL ( S U M _ X , S M D , C U M _ X , A S , D E N , D I F F ) F L Q A T ( 1 6 ) ; DCL ( S U H _ D , S U M _ N , S U M _ N D , S U N 2 _ D , V , RHO) F L O A T (16) ; DCL ( B H 0 _ G , K V , C , G , H D 7 F L O A T ("l6) , (N 0 ( 3 , 3 , 3 , 4) ) F L O A T ( 1 6 ) ; DCL ( R T E M P ( 2 7 , 2 ) , R A G I T ( 3 6 , 2 ) , R R E S ( 3 6 , 2 ) , B S U P S A T (36 ,2 ) ) F L 0 A T ( 1 6 ) ; D C L ( S U H _ G , S a i 3 _ S , S U M _ S G , S U J 5 2 _ S , D S f K S G , P S G ) F L O A T ( 1 6 ) ; 85 OD DCL {SUM_NR,SUM_SN,KSN,PSN,KAG,PAG,DA, SUM_A, SUM_AG) FLOAT (16) ; DCL (SUM_AN,KAN,PAN,SUM_S,SUli_RG,SUS2_R,Dfi) .FLOAT (16.).; DCL (HO,KRG, PRG,SUH_RN,SUMjr,SUM_TGrDT) FLQAI(16); DCL (KTG,PTG, SUM_TN, KTN,PTN, KRN,DG) FLOAT ( 16) ; PUT PAGE LINE(3) EDIT ('ANALYSIS RESULTS' ) (COL (26) , A); POT SKIP(O) EDIT((18) »_•) (COL(26) ,A) ; /* INPUT STATEMENTS */; GET LIST (KV,V,RHQ_G,LAD) ; ALLOCATE AD (LAD) , X (LAD) ,CW (LAD) ; ,'GIT LIST ((AD(JA) DO JA = 1 TO LAD)); LB1: DO L=1 TO 4; DO K=1 TO 3; DO J=1 TO 3; DO 1=1 TO 3; GET LIST (SOPS AT (I) , AGIT (J) , RES (K) ,TEHP (L) # (DAT ( I , J,K ,L,h) DO 15=1 TO 6 ) ) ; END LB 1; /* POPULATION DENSITY COUNT FROM SCREEN HEIGHTS */; LB2: DO L=1 TO 4; DO K=1 TO 3; DO J=1 TO 3; DO 1=1 TO 3; DO M=1 TO 5; X(M) = DAT(I,J,K,L,M) *, END; BHO=DAT(I,J,K,L,6) ; SUH_X=SUM (X) ; CUM_X=0; DO~JA=1 TO LAD; COM_X=CUM_X+X(JA) ; CW (JA) = 100*CUB_X/SUH_X; END; DIFF= ( AD (LAD) -AD ( 1) ) /O. 005; LN=TRUNC(DIFF); ALLOCATE D(LN) ,2 (LN) , N (LN) ; DO IA=1 TO LN-1; AS=AD(1) •0.005*(IA-1) ; DO JA=1 TO LAD-1; IF(AS>=AD(JA) )8 (AS<AD (JA*1) ) J (AS=AD (LAD) ) THEN GOTO LB3; END; LB3: 2 (IA)=CB (JA) + (CB(JA+1) -CB (JA) ) *(AS-AD(JA)) /(AD(JA+1).-'— AD (JA) ) ; D(IA) =SQRT( (AS-. 025) * (AS+.025) ) ; N(IA) = (BBO*V* (2 (IA+1)-Z (IA) ) ) / (BHO_G*K V*D(IA) **3* (D(IA+1)-D (IA) ) ) ; END; D(LN) = 1; N (LN)=1; SUM_D=SUM(D)-B(LN) ; SUH_N=SUM (LOG (N) ) ; SUM ND=SUM ( (D) *LOG (N) ) ; SUM2_D=S0Mf D**2) -D(LN)**2; DEN=SUH_D**2- (LN- 1) *SUfl2_D ; DG=(SOM_D*SUH_N~ (LN-1) *SUM_ND)/DEN; C= (SUM_D*SUM_ND-SUM_N*SUM2_D) /DEN; G=- (1/R£S{K) *DG) ; NO(I,J,K,L) = EXP(C) ; NRV(I,J,K,L) = NO (I,J,K,L) *G ; GRV(I,J,K,L)=G; PUT SKIP (4) EDIT ((68) *_') (COL (4) , A) ; PUT SKIP EDXT{* TEMPERATURE' , 'RESIDENCE TIME',* AGIT AT ION RATE' ,'SUPERSATURATION') (COL (6), A, X (6),A,X (3)>A,X(3) ,A) ; PUT SKIP(O) EDITC(11) (14) •_• , (14) •_», (15) •_•) (COL{6) ,A, X(6) ,A,X(3) ,A,X(3) ,A) ; PUT SKIP (2) EDIT (TEMP (L) /RES (K),AGIT (J),SUP SAT (I) ) (COL (6) , E(10,3),X(6) #E(10 r3) ,X{8) ,E(10,3) ,X(8) ,£(10,3) ) ; POT SKIP(2) ED IT (' POP. AT 0* ) (COL (13), A); PUT SKIP (0) EBIT((9) '_•) (COL(13) , A) ; PUT SKIP EDIT(NO(I,J,K,L) ) (COL(13) ,E(10,3) ) ; PUT SKIP(2) EDIT (* W EIGHT X*,'SCREEN SIZE AD* , * % CUMULATIVE WEIGHT ») (COL(6) ,A,X (6),A,X(4) ,A) ; PUT SKIP (0) EDIT( (8) '_', (14) ' ',(19)' •) (COL (6) , A,X (6) , A,X (4) , A) ; DO JA=1 TO 5; PUT SKIP(2) EDIT(X(JA) , AD( J A) , CW (JA) ) (COL (6) , E (1 0, 3) , X(6) ,E(10,3) ,X(6) ,E (10,3) ) ; END ; PUT SKIP (2) EDIT (' CfiYSTAL SIZE* , * POPULATION DENSITY* , •CRYSTAL SIZE*,'POPULATION DENSITY 1) (COL(6) ,A,X (2) , A,X (4),A,X (2) ,A) ; PUT SKIP(O) EDIT((12) *_«, (18) »_«, (12) «_*,{ 18) »_«) (COL(6) , A,X(2) ,A,X(4) ,A,X(2) ,A) ; DO IA=1 TO LN-1 BY 2; PUT SKIP (2) EDIT (D (IA) ,N (IA) ,D(IA+1) , N(IA+1)) (COL(7) ,E{10,3) ,X{7) , E (10, 3) , X (9) ,E (10 ,3) ,X(7) ,E(10,3)); END; END LB2; /* SUPERSATURATION, GROWTH AND NUCLEATION RATES RELATIONSHIP */; PUT PAGE EDIT (* SUPERSATURATION,GBOWTH AND NUCLEATION RATE RELATION ') (COL ( 4 ) , A); PUT SKIP {0) EDIT((68) « . _ • ) (COL(4) , A) ; LB4: DO L=1 TO 4; DO K=1 TO 3; DO J=1 TO 3; SU«_G=SUM(LOG(GRV(*,J,K,L)) ) ; SU M~S=S DM (LOG (S DPS AT) ) ; SUM~SG=SUM(LOG (SUPSAT) *LOG (GRV(*,J,K,L) ) ) ; S0M2_S=SUM( (LOG (SUPS AT) ) **2) ; DS=SUM_S**2-3*SUM2_S; , KSG=EXP((SUa_G*SUMls-3*SUM_SG)/DS); PSG= (SUM_S*SUM_SG-SUM_G*SUM2_S)/DS; , SUM_NR=SUM (LOG (NRV (*, J,K,L) ) ) ; SUM_SN=SUM(LOG(SUPSAT) *LOG(N«V(*,J,K,L))) ; KSN=EXP { (SUM NR*SUM_S-3*SUM_SN)/DS) ; PSN= (SUM_S*SUM_SN-SOM_NB*SUM2_S) /DS; PUT SKIP (2) EDIT ('TEMPERATURE','RESIDENCE TIME* ,'AGITATION') (COL(6) ,A,X(7) ,A,X(8) ,A) ; PUT SKIP (0) EDIT((11) '_', (14)' », (9)«_«) (COL (6) , A, X (7) ,A , X (8) ,A) ; PUT SKIP EDIT (TEMP (L) ,RES ( K) , AGIT (J) ) (COL (6) , E ( 1 0, 3) , X (9) , E(10,3) ,X(13) ;E(10,3)) ; PUT SKIP (2) EDIT (* GROHT H CONSTANT* ,* GROWTH ORDER* ,* NUC_CONSTANT* , * NUCLEATION ORDEB •) (COL (4) , A ,X (2) , A, X (5) , A,X (5) , A) ; PUT SKIP (0) EDIT ( (15) *_', (12) * 1 , (12) ' (16 ) ' _') (COL(4) ,A,X(2) ,A,X (5) ,A,X(5) , A) ; PUT SKIP EDIT(KSG,PSG,KSN,PSN) (COL (4) , E (1 0, 3) , X (8) , E (10 , 3) ,X (8) , E(10,3) ,X (8) ,E(10,3)) ; END LB4; /* AGITATION,GROWTH AND NUCLEATION RATES RELATIONSHIP */; PUT PAGE EDIT ('AGITATION, GROWTH AND NUCLEATION RATES RELATION') (COL (4) ,A) ; PUT SKIP (0) EDIT ((68) '_• ) (COL (4) , A) ; LB5; DO L-1 TO 4; DO K=1 TO 3 ; oo DO 1=1 TO 3; SUM_A=SUM (LOG ( A G I T ) ) ; SUM G=SUM (LOG (GRV(I,*, K , L ) ) ) ; SUMIAG=SUM (LOG ( A G I T ) *LOG (GgV ( I , * , K , L ) ) ) ; SUM2_A = SUM ( (LOG ( A G I T ) ) * * 2 ) ; DA=SDfl_A**2-3*SUM2_A; KAG=EXP ( (SUM_A*SUM_G~3*SUM_AG) /DA) ; PAG=(SUM_A*SUM_AG-SUM_G*SUM2_G) /DA; SUM NR=SUM (LOG (NBV ( I , * , K,L) ) ) ; SUM~AN=SUH (LOG ( A G I T ) *LOG (NBV ( I , * , K , L) ) ) ; KA N=EXP ( (SUM_NR*SUM_A-3*SUM_AN)/DA) ; P A N = (SUM A*SUH_AN-SUM_NR*SUM2_A) /DA; PUT S K I P (2) E D I T ( ' T E M P E R A T U R E ' , ' R E S I D E N C E T I M E * , * S U P E R S A T U E A T ION •) (COL ( 6 ) ,A,X ( 9 ) , A, X (10 ) , A) ; P U T S K I P ( O ) E D I T { ( 1 1 ) *_« , ( 1 4 ) * _ » , ( 1 5 ) »_») ( C O L (6) , A, X (9) , A, X ( 1 0 ) , A) ; PUT S K I P E D I T ( T E M P ( L ) , RES (K) , S U P S AT ( I ) ) {COL ( 6 ) « E ( 1 0 , 3 ) , X ( 1 1 ) , E ( 1 0 , 3 ) , X ( 1 5 ) , E ( 1 0 , 3 ) ) ; PU T S K I P ( 2 ) E D I T ('GROWTH CONSTANT*,'GROWTH ORDER',» NUC_CONST ANT', ' N U C L E A T I O N OBDER*) (COL (4) , A , X ( 2 ) ,A,X ( 5 ) ,A,X ( 5 ) ,A) ; P U T S K I P (0) E D I T ( ( 1 5 ) ' _ » , ( 1 2 ) «_« , ( 1 2 ) « _ ' , ( 1 7 ) »_») ( C 0 L ( 4 ) ,A,X(2) , A , X { 5 ) ,A,X(5) ,A) ; P U T S K I P E D I T ( K A G , PAG, KAN, PAN) (COL ( 5 ) , £ ( 1 0 , 3 ) , X ( 7 ) ,E ( 1 0 , 3 ) ,X(8) , E ( 1 0 , 3 ) , X ( 8 ) , E ( 1 0 , 3 ) ) ; END L B 5 ; /* R E S I D E N C E TIME,GROWTH AND N U C L E A T I O N B A T E S */; PUT P A G E E D I T ( ' B E S I D E N C E TIME,GBOWTH B A T E AND N U C L E A T I O N fi E L A T I O N • ) ( C C L ( 4 ) ,A) ; P U T S K I P ( O ) E D I T { ( 6 8 ) *_') ( C 0 L ( 4 ) , A ) ; L B 6 : DO 1=1 TO 4; DO J = 1 TO 3; DO 1=1 TO 3 ; SUM B=SUM (LOG ( R E S ) ) ; SUM~G=SUH(LOG (GBV ( I , J , *, L) ) ) ; SUM_RG=SUM (LOG ( R E S ) * L O G (GBV ( I , J , * , L ) ) ) ; SU M 2 _ R = S U H ( ( L O G ( R E S ) ) * * 2 ) ; DR=SUM R ^ * 2 - 3 * S U M 2 B; KRG=EXP ( ( S U M G*SUM_R-3*SUM_RG) /D B) ; PRG=(SUM_R*SUM_RG-SDfi G*SUM2_R) /DR; SUM NR=SUM (LOGINRV ( I , J , * , L ) ) ) ; SUM~RN=SUM (LOG ( R E S ) *LOG (NRV ( I , J , * , L ) ) ) ; KRN=EXP ( (SUM_NR*SUM_R-3*SUM_RN)/D8) ; P R N = (SUM_R*SUM_SN-SUM NE*SUM2 R)/DR; PUT S K I P ( 2 ) E D I T ('TEMPERATURE' ,' A G I T A T I O N ' ,'SUPERS ATU RAT I O N ' ) (COL ( 6 ) , A , X ( 9 ) , A , X ( 1 2 ) , A) ; PUT S K I P ( O ) E D I T ( ( 1 1 ) '_', ( 9 ) »_', ( 1 5 ) •_•) (C O L (fa) ,A,X(9) ,A, X ( 1 2 ) ,A) ; PU T S K I P E D I T ( T E M P ( L ) , A G I T ( J ) , S U P S A T ( I ) ) ( C O L (7) , £ ( 1 0, 3 ) , X (1 0) , E ( 1 0 , 3 ) , X ( 1 5 ) , E ( 1 0 , 3 ) ) ; P U T S K I P ( 2 ) E D I T ( ' GBOWT H CONST ANT* , ' GROWTH ORDER' ,•NUC_CQNS1ANT* , ' N U C L E A T I O N ORDER * ) (CO L ( 4 ) , A , X ( 2 ) , A , X ( 5 ) , A , X ( 5 ) , A) ; PUT S K I P ( O ) E D I T ( ( 1 5 ) '_« , ( 1 2 ) ' _ « , ( 1 2 ) ' _ * , ( 1 6 ) ' _ « ) (COL ( 4 ) , A, X (2) , A , X ( 5 ) , A , X ( 5 ) ,A) ; P U T S K I P E D I T (KRG ,PRG , KB N, PRN) ( C O L ( 5 ) , E ( 1 0 , 3 ) , X ( 7 ) , £ ( 1 0 , 3 ) , X ( 8 ) , E ( 1 0 , 3 ) , X ( 8 ) , E ( 1 0 , 3 ) ) ; END L B 6 ; /* TEMPERATURE,GROWTH AND N U C L E A T I O N B A T E S */; PDT P A G E E D I T ('T EMPERATU RE, GROWTH AND N U C L E A T I O N R E L A T I O N ' ) (COL ( 4 ) , A ) ; PUT S K I P ( O ) E D I T ( ( 6 8 ) * _* ) ( C O L ( 4 ) , A ) ; L B 7: DO K=1 TO 3 ; 89 DO J = 1 TO 3; DO 1=1 TO 3 ; SDH T-SUM (LOG (TEMP) ) ; S U H ~ G = S U M ( L G G ( G B V { I , J , K , * ) ) ) ; S U M _ T G = S U M ( L O G ( T E M P ) * L O G ( G E V ( I , J , K , * ) ) ) ; SUM 2_T=SUM ( (LOG ( T E M P ) ) * * 2 ) ; DT=SUM T * * 2 - 4 * S U M 2 T; K T G = E X P ( ( S U M _ G * S U M I T - 4 * S 0 M _ T G ) / D T ) ; PTG=(SUM__T*SUM_TG-SUM_G*SUM2_T) /DT; SOM NR=SUM (LOG (NRV ( I , J , K , * ) ) ) " ; S U H ~ T N = S U M { L G G ( T E M P ) * L O G ( N R V ( I , J # K , * ) ) ) ; K TN=EXP U S U M _ N R * S U M j r - 4 * S U M _ T N ) / D T ) ; P T N = ( S U M _ T * S U H _ T N - S U M _ N R * S U H 2 _ T ) /DT; POT S R I P ( 2 ) E D I T | ' R E S I D E N C E T I M E * , * A G I T A T I O N ' ,* S U P E R S ATUR A T I G N ' ) 4 C O L ( 6 ) ,A,X ( 8 ) , A , X ( 1 2 ) , A ) ; P U T S K I P ( 0 ) E D I T ( ( 1 4 ) ' • , ( 9 ) *_ • , ( 1 5 ) • *) (COL ( 6 ) » A , X ( 8 ) , A,X ( 1 2 ) , A ) ; PUT S K I P E D I T ( R E S 1 K ) , A G I T ( J ) # S U P S A T ( I ) ) (COL ( 7 ) , E ( 1 G , 3 ) , X ( 1 2 ) , E ( 1 0 , 3 ) , X ( 1 2 ) , E ( 1 0 , 3 ) ) ; P U T S K I P ( 2 ) E D I T ( • G R O W T H CONSTANT*,'GROWTH ORDER',•NUC_CONSTANT', •• N U C L E A T I O N ORDER*) ( C O L ( 4 ) , A,X ( 2 ) , A,X ( 5 ) , A , X ( 5 ) , A ) ; P U T S K I P ( O ) E D I T ( ( 1 5 ) * _ « , ( 1 2 ) «_*, ( 12) •_• , ( 16) •_*) ( C O L ( 4 ) , A, X ( 2 ) , A , X ( 5 ) , A , X ( 5 ) ,A) ; POT S K I P E D I T ( K T G , P T G , K T N , PTN) (COL ( 5 ) , E ( 1 0 , 3) , X ( 7 ) ,E (1 0 ,3) ,X ( 8 ) , , E ( 1 0 , 3 ) , X ( 8 ) , E ( 1 0 , 3 ) ) ; END L B 7 ; R E T U R N ; END P R O J E C T ; 1 1 0 A N A L Y S I S R E S U L T S T E M P E R A T U R E R E S I D E N C E T I M E A G I T A T I O N R A T E S O P EES ATU R A T I O N 1. 5 0 0 E + 0 1 1 . 7 0 0 E + 0 2 2 . 4 6 6 E + 0 3 9 . 5 0 0 E - 0 1 POP. AT 0 1 . 8 2 9 E + 0 8 WEIGHT_X 4 . 6 4 7 E - 0 1 2 . 4 5 1 E - 0 1 3 . 3 2 0 E - 0 2 3 . 9 5 0 E - 0 2 3. 6 7 0 E - 0 2 S C R E E N S I Z E AD 1 . 0 6 0 E - 0 1 1 . 5 0 0 E - 0 1 1 . 8 0 0 E - 0 1 2. 5 0 0 E-01 2 . 9 7 O E - 0 1 C R Y S T A L S I Z E P O P U L A T I O N D E N S I T Y 1 . 0 3 0 E - 0 1 2 . 8 1 0 E + 0 7 % . C U M U L A T I V E WEIGHT 5 . 6 7 3 E * 0 1 8 . 6 6 5 E + 0 1 9 . 0 7 0 E + 0 1 9 . 5 5 2 E + 0 1 1 . 0 0 0 E + 0 2 C R Y S T A L _ S I Z E P O P U L A T I O N D E N S I T Y 1 . 0 8 1 E - 0 1 2 . 4 5 1 E * 0 7 1. 1 3 3 E - 0 1 2 . 1 5 2 E + 0 7 1. 1 8 4 E - 0 1 1. 9 0 0 E + 0 7 1.235E-01 1.337E-Q1 1.438E-01 1.540E-Q1 1.6U1E-01 1.742E-01 1.843E-01 1.944E-01 2.045E-01 2. 145E-0 1 2<.246E-01 2.347E-01 2.447E-01 2..54 8E-01 1.686E + 07 1.445E+52 1-093E+07 8.675E+06 6.829E+06 5.458E*06 4.403E*06 3.58 5E+06 2.950E*06 2.452E*06 2.057E+06 1.739E+06 1.481E+06 1.272E+06 1.286E-G1 l i 388E-Q1 1.489E-01 1.590E-01 1.692E-01 1.793E-01 1.. 89 4 £ - 0 1 1.994E-01 2.095E-01 2. 196E-01 2.296E-01 2.397E-01 2. 498E^01 2.598E-01 5.669E+51 9.971E+45 9.841E+06 7.681E*06 6.094E*06 4.901E*06 3.967E+06 3. 248E+06 2-687E+06 2..243E+06 1.889E+06 1.60 3E+06 U370E+06 1.182E+06 2.648E-01 2.749E-0 1 2.849E-01 1.100E+06 9.575E+05 8. 375E+05 2.698E-01 2.799E-01 1.OOOE+QO 1,026E+06 8. 949E+05 1.OOOE+OO TEM PEBATURE 1. 500E+01 BESIDEMCE TIME 1.70GE + 02 AGITATION BATE SUPERSATURATION 2.466E*-03 8.230E-Q1 POP. AT 0 1.408E+08 WEIGHT, X 6. 149E-01 SCREEN SIZE AD f I CUMULATIVE 8EIGHT 1. 060E-01 4. 080E+01 7.894E-01 1. 50GE-01 9. 318E+01 3. 950E-02 1. 8 ODE-01 9. 580E*01 4.730E-02 2. 500E-01 9. 894E+01 1.600E-02 2. 970E-01 1. OOOE+02 CRYSTAL SIZE POPULATION,DENSITY CRYSTAL_SIZ£ POPULATION DEN £ U030E-01 1.899E+07 1.G81E-01 1.791E*07 1. 133E-01 1.678E+07 1.184E-01 1.565E+07 1.235E-01 1.4561*07 1.286E-01 1.353E+07 1.337E-01 1.256E+07 1.388E-01 1. 166E+07 1.438E-01 1.083E+07 1. 489E-01 9.941E* 06 1»540E-01 8.736E+06 1.590E-0T 7.711E+06 1.641E-01 6.835E+06 1.692E-01 6.082E+06 1.742E-01 5.431E+06 1.793E-01 4.865E+06 1.843E-01 4.363E+06 1.894E-01 3.926E* 06 1.944E-01 3.542E+06 1.994E-01 3.205E+06 2.Q45E-01 2.907E4-06 2.095E-01 2.644E+06 2. 145E-01 2.410E+06 2.196E-01 2. 201E+06 2.246E-01 2.Q15E>06 2.296E-01 1 . 849E+ 06 2,347E-01 1.699E*06 2.397E-01 1. 564E+06 2.447E-01 1. 443E+06 2.498E-01 1.333E*06 2.548E-01 2.64 8E-01 2.749E-01 2.849E-01 1.232E+06 1.058E+06 9. 139E«-05 7.935E+05 2.598E-01 2.698E-01 2.799E-01 1.00OE+OO 1.141E+06 9.827E+05 8.511E+05 1.00GE+00 TEM f£ BAT QBE 1.500E*01 RESIDENCE TIME 1. 700E+02 AGITATION_BATE 2.466E+G3 SDPJIBSATUEAIiSI 7.000E-01 POP* AT 0 8.528E+07 WEIGHT X 3.619E-01 5. 469E-01 1.418E-01 1-790E-01 4.490E-02 SCREEN SIZE AD 1.060E-01 1.500E-01 1.80OE-01 -2.500E-01 2.970E-01 CBYSTAL SIZE POPULATION DENSITY L£OMDLATIVE_WEIGHT 2.840E+01 7.131E»01 8, 243E«-01 9.648E+Q1 1.000E*02 CBYSTAL SIZE POPULATION DENSITY 1.C30E-01 1.383E»07 1.081E-01 1. 334E+07 1..133E-01 1. 271E+07 1. 184E-01 1.201E+07 1.235E-01 1.130E+07 1.286E-01 1*059E+07 U337E-01 9.901E+06 1.388E^01 9.250E+06 1-438E-01 8.636E+06 1.489E-01 7..99 4E+06 1.540E-01 7. 174E+06 1.590E-01 6.462E+Q6 1.641E-01 5.841E+06 1.692E^01 5.298E+06 1.742E-01 4.820E+06 1.793E-01 4.389E* 06 1.843E-01 3.975E+06 1.894E-01 3.611E+06 1.944E-01 3. 289E+06 1.994E-01 3.004E+06 2.045E-01 2.750E+O6 2.Q95E-01 2.524E+06 2.145E-01 2. 321E+06 2. 196E-01 2. 139E*06 2.246E-01 1.975E+06 2.296E-01 1.828E+06 2.347E-01 1.694E+06 2.397E-01 1. 573E+06 2.447E-01 2.54 8E-01 2.648E-01 2.749E-01 2.849E-01 1.46 3E+06 1.262E+06 1.089E+06 9.458E+05 8.2561*05 2.498E-01 2.598E-01 2.698E-01 2.799E-01 1. OOOE+00 93 1.361E+Q6 1. J71E+G6 1.Q14E+06 8.831E+05 1 .OOOE*00 TEMPERATURE 1.5C0E + O1 RESIDENCE TIME 1. 700E + 02 AGITATION BATE SOPJfiS ATU£AT10N 1.926E+03 9.500E-01 POP. AT 0 1.475E+08 2.780E-O1 3.393E-01 2. 000E-02 2.960E-02 1.480E-02 SCBEEN SIZE AD 1.060E-01 1. 500E-O1 1.800E-01 2. 5G0E-O1 2.970E-01 CRYSTAL SIZE PQ PPL AT ION DENSITY i CUMULATIVE HEIGHT 4.078B+01 9.055E+01 9.349E+01 9.783E+01 1.000E+02 CRYSTAL_SIZ£ POPULATION DENSITY 1.030E-01 2.05OE+07 1.081E-01 1. 922E+07 1.133E-01 1.791E+07 1. 184E-01 1. 664E+07 1.235E-01 1.5431+07 1.286E-01 1. 43QE*07 1.337E-01 1.324E + 07 1.388E-01 1. 227E+07 1.438E-01 . 1. 138E*07 1.489E-01 1. 044E+07 1.540E-01 9.177E+06 1.590E-01 8. 107E+06 1.641E-01 7. 190E+06 1.692E-01 6. 402E+06 1.742E-01 5.721E+06 1.793E-01 5. 128E+06 1.843E-01 4.604E+06 1.894E-01 4. 147E+06 1.944E-01 3.745E+06 1.994E-01 3. 392E+06 2.045E-01 3.080E+06 2.095E-01 2. 803E+06 2. 145E-01 2.557E+06 2.196E-01 2. 338E+06 2-246E-01 2. 143E+06 2.296E-01 1. 967E+06 2.347E-C1 1.810E+06 2. 39 7E-01 1 .668 E+06 2.447E-01 1.540E+06 2.498E-01 1.424E+06 2.548E-01 1.318E+06 2.598E-01 1.222E+06 2.648E-01 1.135E+06 2.698E-01 1.Q55E+06 2.749E-01 9.822E+05 2.799E-01 9.157E+05 2.849E-01 8*549E + 05 1.000E+00 1. 000E+00 TEMPEBATUBE RESIDENCE TIM E AGITATION, RATE SUPER SATURATION 1. 500E+01 1.700E+02 1.926E+03 8.230E-01 POP. AT 0 9.628E+07 HEIGHT X SCREEN SIZE AD % CUMULATIVE HEIGHT 3.898E-01 1.060E-01 2.593E+01 8.6C5E-01 1. 500E-01 8.318E+01 1.678E-01 1. 800E-01 9.435E+01 8.150E-02 2.500E-01 9.977E+01 3.500E-03 2. 970E-01 1.000E+02 CRYSTAL SIZE POPULATION DENSITY 1.243E + 07 CRYSTAL SIZE POPULATION DENSITY 1.030E-01 1.081E-01 1.280E+07 1. 133E-01 1. 277E+07 1. 184E-01 1.249E+07 1.235E-01 1.206E+07 1.286E-01 1. 154E+07 1.337E-01 1.098E+07 1.388E-01 1.04QE+07 1.H38E-01 9.831E+06 1.489E-01 9, 171E+06 1.540E-01 8. 20 1E*06 1.590E-01 7.362E+ 06 1.641E-01 6.634E+06 1.692E-01 5.998E+06 1.742E-01 5.441E+06 1.793E-01 4.935E+06 1.843E-01 4.435E+06 1.894E-01 3.997E+06 1.944E-01 3.613E+06 1.994E-01 3.274E+06 2.045E-O1 2.975E + 06 2.095E-01 2.710E+06 2.145E-01 2. 474E*06 2.196E-01 2.264E+06 2.246E-01 2.076E+06 2.296E-01 1.908E+06 2.347E-01 U756E+06 2.397E-01 1.620E+06 2.447E-01 1.497E+06 2.498E-01 1.384E+06 2.548E-01 1.278E+06 2.598E-01 1.183E+06 2.648E-Q1 1.096E+06 2.698E-01 1 .017E+ 06 2.749E-01 9.447E+05 2.799E-01 8.789E+05 2.849E-01 8. 18 8E+05 1.000E+00 1.O00E+00 TEMPERATUBE RESIDENCE TIME AGITATION RATE SUPEBSATURA1I2I •1. 5C0E+O1 1.700E + 02 1.926E+03 7.000E-01 PGP. AT 0 2.249E+08 WEIGHT X SCREEN SIZE AD 5 a CUMULATIVE WEIGHT 1.534E+00 1.060E-01 6.839E+01 5.226E-01 1.500E-01 9.169E+01 6.690E-02 1.800E-01 9.468E+01 6.350E-02 2. 500 E-01 9.751E+01 5.590E-02 2.970E-01 1.000E+02 CRYSTAL SIZE POPULATION DENSITY CfiYSTAL^SIZE POPULATION DENSITY 1.030E-01 3.578£+07 1.081E-01 3..059E* 07 1. 133E-01 2.636E+07 1.184E-01 2. 289E+07 1.235E-01 2.000E+07 1.286E-01 1.758E+07 1.337E-01 1.554E + 07 1.388E-01 1. 381E+07 1.438E-01 1. 232E+07 I.489E-OI 1.099E+07 1.540E-01 9.669E+06 1.590E-01 8.541E+06 1.641E-01 7.576E+06 1.692E-01 6.746E+06 1.742E-01 6.029E+06 1.793E-01 5.402E+06 1.843E-01 4.845E+06 1.894E-01 4.358E+ 06 1.944E-01 3.932E+06 1.994E-01 3. 557E+06 2.045E-01 3. 226E+06 2.Q95E-01 2.933E*06 2. 145E-01 2.672E+06 2. 196E-01 2. 441E+06 2.246E-01 2.234E+06 2.296E-01 2. 049E+06 2.347E-01 1.88 31*06 2.397E-01 1. 733E+06 2.447E-01 1.599E+06 2.498E-01 1. 477£+06 2.548E-01 1.368E+06 2.598E-01 1. 268E+06 2.64 8E-01 1.178E+06 2.698E-01 1. 096E+06 2,749E-01 1.Q20E*06 2.799E-01 9. 517E+05 2.849E-01 8.888E+05 1.QOOE+O0 1. O0OE+O0 TEMPERATURE 1.500E+01 RESIDENCE TIflE 1.700E + 02 AGITATION_RATJ SDPER SAIURATION 1.260E+03 9.50QE-01 POP. AT 0 1.807E+08 WEIGHT X 4.365E-01 1. 182E-01 2. 94GE-02 4. 830E-02 4. 160E-02 SCREEN SIZE AD 1.060E-01 1.500E-01 1.800E-01 2.500B-01 2.970E-01 CRYSTAL SIZE POPULATION DENSITY 1.030E-01 U133E-01 1.f235E-01 1.337E-01 1.438E-01 1.540E-01 1.641E-01 1.742E-01 1.843E-01 1.944E-01 3.152E+07 2. 288E+07 1.714E*07 1.316E+07 1.033B+07 8. 107E*06 6-394E+06 5.121E+06 4. 144E + 06 3. 388 E+06 ; CUMULATIVE WEIGHT 6.476E+01 8.230E+01 8.666E+01 9.383E+01 1.000E+02 CRYSTAL SIZE POPULATION_DENSITY 2.674E+07 1.081E-01 1. 184E-01 1..286E-01 1.388E-01 1.489E-01 1.590E-01 1.692E-01 1.793E-01 1.894E-01 1.994E-01 1.973E* 07 1.498E+07 1.163E+07 9..187E+06 7.185E+06 5..712E+06 4.604E* 06 3.742E+06 3.076E+06 2-.045E-01 2. 145E-01 2.246E-01 2.347E-01 2.447E-01 2 .548E-01 2.648E-01 2.749E-01 2.849E-01 2.800E+06 2.337E+06 1.967E+06 1.669E+06 1.427E+06 1.231E+06 1-0692*06 9.336E+05 8. 197E+05 2.Q95E-01 2.196E-01 2.296E-01 2.397E-01 2.498E-01 2.598E-01 2.698E-01 2.799E-01 1. OOOE+OO 97 2. 555E+06 2. 142E+06 1.81QE+06 1.542E+06 1. 323E+ 06 1.146E+06 9.982E+05 8.742E+05 1. OOOE+00 TEMPERATURE 1.500E+01 BESIDEMCE TIflE 1.700E + 02 AGITATION BATE SUPERS ATI)BAT ION U260E+03 8.2 30E-01 POP. ,. AT 0 1. 490E+08 HEIGHT_X 4. 266E-01 4.713E-01 3. 200E-02 3.670E-02 1. 42OE-02 SCBEEN SIZE AD 1.060E-01 1.500E-01 1.800E-01 2. 500 E-01 2.970E-01 CRYSTAL SIZE POPULATION DENSITY i CUMULATIVE HEIGHT 4.350E+01 9. 155E+01 9.481E+01 9.855E+01 1.0G0E+02 CRYSTAL SIZE POPULATION DENSITY 1.030E-01 2.096E+07 1.081E-01 1. 941E+07 1. 133E-01 1.793E+07 1.184E-01 1. 653E+07 1.23 5 E-01 1. 524E+07 1. 286E-01 1. 4 04E+07 1.337E-01 1.295E+07 1.388E-01 1. 196E+07 1.438E-01 1. 105E+07 1.489E-01 •1. 011E+07 1.54OE-01 8.896E+06 1.590E-01 7. 862E+06 1.641E-01 6.977E+06 1.692E-01 6. 216E+06 1.742E-01 5.557E+06 1.793E-01 4.. 983E+06 1.843E-01 4. 47 2E+06 1.894E-01 4. 025E+06 1. 944E- 01 2. 045E- 01 2. 145E- 01 2. 246E- 01 2. 347E-•01 2. 447E- 01 2. 54 8 E-01 2. 648E- 01 2. 749 E-•01 2. 849E- 01 3.634E+06 2.985E+06 2.477E+06 2.073E+06 1. 749E+06 1.487E*06 1- 271E+06 1.092E+06 9.4421*05 8.205E+05 1.994E-01 2.Q95E-01 2. 196E-Q1 2.296E-01 2. 39 7E-01 2.498E-01 2.598E-01 2.698E-01 2.799E-Q1 1.Q00E+00 3.289E+06 2.716E*06 2.263E+ 06 1. 90 2E+06 1.612E+06 1.374E*06 1. 178E*06 1.Q15E+G6 8.796E*Q5 1. 000E+00 TEMP ERATOBE BESIDENCE TIME i5ITATION_RATE SUPER SATURATION 1.500E + Q1 1.700E+02 1.260E*03 7.000E-01 PGP. AT 0 8.383E+07 HEIGHT X SCREEN S I Z E AD S o CUMULATIVE HEIGHT 3.619E-01 1.060E-01 2.826E + 01 5. 469E-01 1.500E-01 7,096E*01 1.480E-01 1.800 E-01 8.252E+01 1.790E-01 2.500E-01 9.649E*01 4*4901-02 2.970E-01 1.000E*02 CBYSTAL SIZE 1.0 30 E-01 POPULATION DENSITY CBYSTAL SIZE I Q P D M l l O J - S I N S I f Y 1.364E + 07 1.081E-01 1.316E+07 1.133E-01 1.253£*07 1. 184E-01 1 . 185E* 07 1.235E-01 1.114E+07 1.286E-01 1.044E*07 1.337E-01 9.764E*06 1.388E-01 9. 122E+06 1.438E-01 8.516E+06 1.489E-01 7.886E*06 1.540E-01 7.0841*06 1. 590E-01 6.388E* 06 1.641E-01 5.780E*06 1.692E-01 5.247E+06 1.742E-01 4.778E+06 1.793E-01 4.354E+06 1.843E-01 1.944E-01 2,045E-01 2, 145E-01 2.246E-01 2.347E-01 2.447E-01 2.548E-01 2.648E-01 2.749E-01 2-849E-01 3.943E+Q6 3.262E+06 2.727E+06 2.301E+06 1.958E+06 1.679E+06 1.450E+06 1.251E+Q6 1.Q80E+06 9.373E+05 8. 182E+05 1. 894E-01 1. 994E-01 2. 095E-01 2. 196E-01 2. 296E- 01 2, 39 7E-•01 2. 498E- 01 2. 598E-•01 2. 698E-01 2. 799E-•01 1.QOOE+OO 3.581E+06 2.979E+06 2.502E+06 2.121E+06 1 . 812E+06 1. 559E+06 1.349E+06 1. 16 1E+06 1 . 005E+06 8..752E+05 1.000E+00 TEM PERATORE •1. 500E+01 RESIDENCE TIME AGITATION RATE SUPERSATORATION 2.35GE+02 2.466E+03 9.500E-01 POP. AT 0 1.186E+08 H E I G H T X SCREEN SIZE AD 1.060E-01 1.500 E-01 1.800E-01 2. 500 E-01 2.970E-01 4..684E-01 2.472E-01 9.090E-02 1.549E-01 4. 210E-02 CRYSTAL SIZE POPOLATION DENSITY 2. 269E+07 % CUMULATIVE HEIGHT 4.668E+01 7.131E+01 8.037E+01 9.580E+01 1.000E+02 CRYSTAL SIZE POPULATION DENSITY 1.030E-01 1» 133 E-01 1.235E-01 1.337E-01 1.438E-01 1.540E-01 1.641E-01 1.738E+07 1.36 2E+07 1.088E+07 8.829E+06 7.118E+06 5.745E+06 1.081E-O1 1.184E-01 1.286E-01 1.388E-01 1. 489E-01 1.590E-01 1.692E-01 1.979E+07 1.534E+07 1.214E+07 9.781E+06 7.969E* 06 6.383E+06 5.189E+06 1.742E-01 1.843E-01 •1.94-4 E-01 2.045E-01 2.145E-01 2.246E-01 2.347E-01 2.447E-01 2.548E-01 2.648E-01 2.749E-01 2.849E-01 4.703E+06 3.874E+06 3. 215E+06 2.695E+06 2. 281E+06 1.946E+06 1.673E+06 1.448E+06 1.251E*06 1.082E+06 9. 40 8E+05 8.224E+05 1.793E-01 1.894E-Q1 1.994E-01 2.095E-01 2. 196E-01 2.296E-01 2.397E-01 2.498E-01 2.598E-01 2.698E-01 2.799E-01 1.000E+00 100 4.270E+06 3.524E+06 2.940E+06 2.477E+06 2. 105E+06 1.803E+06 1.555E+06 1.349E+06 1.163E+06 1..0Q8E+O6 8.790E+05 1. OOOE+OO TEMPERATURE 1.500E+01 USIDEHCE_TIME 2.350E+02 AGITATION_£ATE SUPERSATURATION 2.466E+03 8.230E-01 POP. AT 0 1.923E+08 WEIGHT X SCREEN SIZE AD 1.060 E-01 1.500E-01 1.800 E-01 2.500E-01 2.970 E-01 2.290E-O1 1.060E-01 1. 450E-02 1.570E-02 5.700E-03 CRYSTAL SIZE POPULATION DENSITY 3.048E+07 1.030E-0 1 •1. 133 E-01 1.235E-01 1.337E-01 1.438E-01 1.540E-01 ; CUMULATIVE WEIGHT 6.174E+01 9.032E*01 9.423E + 01 9.846E+01 1.000E+02 CBYSTAL SIZE POPUJ.ATIOJ_DENSITY 2.641E+07 2. 30 4E+07 1.786E+07 1.414E+07 1.139E+07 9.008E+06 1.081E-01. 1. 184E-01 1.286E-01 1.388E-01 1.489E-01 1.590E-01 2.023E+07 1.585E+07 1.266E+07 1. 022E+07 7.971E+06 1.641E-01 1.742E-01 1.843E-01 1.944E-01 2.045E-01 2. 145E-G1 2.246E-01 2.347E-01 2.447E-01 2.548E-01 2.64 8E-01 2.749E-01 2.849E-01 7.083E+06 5.655E+06 4.557E+06 3.706E+06 3.046E+06 2.52 9E+06 2. 119E*06 1.789E+06 1.522E+06 1.302E+06 1. 1191*06 9.672E+05 8.4071+05 1.692E-01 1.79 3E-01 1.894E-01 1.994E-01 2.095E-01 2.196E-01 2.296E-01 2.397E-01 2. 498E-01 2.598E-01 2.698E-01 2.799E-01 1.000E + 00 i u I 6.317E+06 5.076E+06 4.103E+06 3.356E+06 2.773E+06 2. 313E+06 1 .945E+06 1. 649E+06 1 .407E+ 06 1..206E+06 1.040E+06 9.012E+05 1.000E+O0 TEHPEBATUBE 1.500E+01 BESIDBNCE TIME 2. 350E+02 AGITATION BATE SU PEE 5 AT U BAT ION 2.466E+03 7.000E-01 POP. AT 0 8.651E+07 SCBEEN SIZE AD \ 1.060E-01 1.500 E-01 1. 800E-01 2.500 E-G1 2.970E-01 CBYSTAL SIZE POPULATION DENSITY 1.030E-01 1. 133E-01 1.235E-01 1.337E-01 1.438E-01 1. 170E+07 1.246E+07 1. 1981+07 1.103E+07 9.9411*06 » CUMULATIVE WEIGHT 2..129E+01 7.354E+01 9.466E*01 . 9.894E+01 1.000E+02 CBYSTAL_SIZE POPULATION DENSXTY 1.081E-01 1.232E+07 1.184E-01 1.232E+07 1.286E-01 1. 153E+07 1.388E-01 1.Q49E+07 1.489E-01 9.341E+06 102 U540E-01 8.558E+06 1.590E-01 7. 859E+06 1.641E-01 7.234E+06 1.692E-01 6. 673E+C6 1.742E-01 6. 168E+06 1.793E-01 5. 674E+06 1.843E-01 5.094E+06 1.894E-01 4.. 588E+06 1.944E-01 4.143E+06 1.994E-01 3. 752E*06 2,C45E-01 3.406E+06 2.095E-01 3. 100E+06 2.145E-01 2.8 28E+06 2.196E-01 2. 586E+06 2.246E-01 2.36 9E+06 2.296E-01 2. 175E+06 2.347E-01 2.Q01E»06 2.39 7E-01 1. 844E+06 2.447E-01 1.702E+06 2.498E-01 1. 574E+06 2.54 8E-01 1.455E+06 2.598E-01 1. 347E+06 2.648E-01 1.249E+06 2.698E-01 . 1. 160E+06 2.749E-01 1.079E+06 2. 799E-01 1. 005E+06 2.849E-01 9.367E+05 t.OOOE+OQ 1. OOOE+OO TEH FESATDEE 1.500E + 01 EESIDENCE TIME 2. 350E+02 AGITATION_EATE 1.926E+03 POP. AT 0 1.390E+08 SUPEBSATURATION 9.5 00E-01 WEIGHT X 5.350E-01 6.580E-01 6.960E-02 5. 050E-02 6.250E-02 SCREEN SIZE AD 1.060E-01 1. 500E-01 1.800 E-01 2.500E-01 2. 970E-01 CRYSTAL SIZE POPULATION DENSITY 1.030E-01 1.969E+07 1.133E-01 1.723E+07 1.235E-01 1.486E*07 1.337E-01 1.277E+07 % CUMULATIVE WEIGHT 3.889E+01 8.673E+01 9.179E+01 9.546E+01 1.000E + 02 CRYSTAL SIZE POPUJjATION_DENSIT5f 1.081E-01 1.848E+07 1. 184E-01 1.602E+07 1.286E-01 1.378E+07 1.388E-01 1. 183E+07 I U J 5 1 . 4 3 8 E - 0 1 1 . 0 9 7 E + 0 7 1 . 4 8 9 E - Q 1 1 . 0 0 7 E + 0 7 1 . 5 4 0 E - 0 1 8 . 8 9 8 E + 0 6 1 . 5 9 0 E - 0 1 7 . 8 9 3 E + 0 6 1 . 6 4 1 E - 0 1 7 . 0 3 0 E + 0 6 1 . 6 9 2 E - 0 1 6 . 2 8 5 E + 0 6 1 . 7 4 2 E - 0 1 5 . 6 3 9 E + 0 6 1 . 7 9 3 E - 0 1 5 . 0 7 0 E + 0 6 -1. 8 4 3 E - 0 1 4 . 5 5 0 E + 0 6 1 . . 8 9 4 E - 0 1 4 . 0 9 6 E + 0 6 1 . 9 4 4 E - 0 1 3 . 6 9 8 E + 0 6 1 . 9 9 4 E - Q 1 3 . 3 4 7 E + 0 6 2 . Q 4 5 E - 0 1 3 . Q 3 8 E + 0 6 2 . 0 9 5 E - 0 1 2 . 7 6 4 E + 0 6 2 . 1 4 5 E - 0 1 2 . 5 2 1 E + 0 6 2 . 1 9 6 E - 0 1 2 . 3 0 4 E + 0 6 2 . 2 4 6 E - 0 1 2. 1 1 0 E * 0 6 2 . 2 9 6 E - 0 1 1 . 9 3 7 E + 0 6 2 , 3 4 7 E - 0 1 1 . 7 8 1 E + 0 6 2 . 3 9 7 E - 0 1 1. 6 4 1 E + G 6 2 . 4 4 7 E - 0 1 1 . 5 1 4 E + 0 6 2 . 4 9 8 E - 0 1 1 . 4 0 0 E + 0 6 2 . 5 4 8 E - 0 1 1 . 3 0 0 E + 0 6 2 . 5 9 8 E - 0 1 1-. 2 0 8 E + 0 6 2 . 6 4 8 E - 0 1 1. 1 2 5 E + 0 6 2 . 6 9 8 E - 0 1 . 1 . 0 4 8 E + 0 6 2 . 7 4 9 E - 0 1 9 . 7 8 6 E + 0 5 2 . 7 9 9 E - 0 1 9 . 1 4 8 E + 0 5 2 . 8 4 9 E - 0 1 8 . 5 6 2 E + 0 5 1 . O O O E + O O 1 . 0 0 O E + O 0 T E H P E S A T Q B E R E S I D E N C E T I B E A G I T A T I O N B A T E S U P E R S ATI) B A T I O N 1. 5 0 0 E + 0 1 2 . 3 5 0 E + G 2 1 . 9 2 6 E « - 0 3 8 . 2 3 0 E - 0 1 P O P . AT 0 1 . 0 8 8 E + 0 8 W E I G H T X S C R E E N S I Z E AD % C U H O L A T I V E W E I G H T 1 . 8 2 0 E - 0 1 1 . 0 6 0 E - 0 1 2 . 6 9 3 E + 0 1 4. 1 0 4 E - 0 1 1 . 5 0 0 E - 0 1 8 . 7 6 6 E + 0 1 4. 9 0 0 E - 0 2 1 . 8 0 0 E - 0 1 9 . 4 9 1 E + 0 1 2 . 8 0 0 E - 0 2 2 . 5 0 0 E - 0 1 9 . 9 0 5 E + 0 1 6 . 4 0 0 E - 0 3 2 . 9 7 0 E - 0 1 1 . 0 0 0 E + 0 2 C R Y S T A L S I Z E P O P U L A T I O N D E N S I T Y C R Y S T A L S I Z E P O P U L A T I O N ^ E N S I T Y 1 . 0 3 0 E - 0 1 1 . 3 3 7 E + 0 7 1 . 0 8 1 E - 0 1 1 . 3 8 2 E + 0 7 1 . 1 3 3 E - 0 1 1 . 3 8 3 E + 0 7 1.184E-01 1. 3 5 5 E + 0 7 1 . 2 3 5 E - 0 1 1 . 3 1 1 E + 0 7 1 . 2 8 6 E - 0 1 1 . 2 5 6 E + 0 7 1.337E-01 1.438E-01 1.540E-01 1.641E-01 1.74 2 E-01 1.843E-01 1.944E-01 2. 04 5 E-01 2.145E-01 2.246E-01 2.347E-01 2.447E-01 2.548E-01 2.648E-01 2.749E-01 2.849E-01 1.196E+07 1.072E+07 8. 860E+06 7.054E+06 5. 701 E+06 4.614E+06 3.752E+G6 3.084E+06 2.5601*06 2.144E+06 1.8 10 E+06 1.540E+06 1.3161+06 1.129E+06 9.752E+05 8.465E+C5 1. 388E-01 1.489E-01 1.590E-01 1.692E-01 1.793E-01 1.894E-01 1.994E-01 2.095E-01 2. 196E-01 2.296E-01 2.397E-01 2.498E-01 2.598E-01 2.698E-01 2.799E-01 1.000E+00 104 1. 134E+07 9.991E+06 7.890E+06 6. 330 E+06 5. 14 0E+06 4. 155E+06 3.397E+06 2.807E+06 2.340E+06 1.968E+06 1.668E+06 1. 423E+06 1.218E+06 1. 049E+06 9.080E+05 1.000E+00 TEMP BBA TUBE 1.500E+01 RESIDENCE TIHE 2. 350E + 02 POP. AT 0 1.475E+08 HEIGHT X 3.269E-01 4. 554E-01 3,440E-O2 2.300E-02 1. 100E-02 SCREEN SIZE AD 1.060E-0 1 1.500E-01 1.800 E-01 2, 500E-01 2. 970 E-01 AGITATION_RATE 1.926E+03 S DP ER S AT DBA TI ON 7.000E-01 CRYSTAL SIZE POPOLATION DENSITY 1.C30E-01 1.969E + 07 1.133E-01 1.77 3E+07 % CUMULATIVE HEIGHT 3.843E+01 9.196E+01 9.600E+01 9.871E+01 1.000E+02 CRYSTAL SIZE POPULATION_DENSITY 1.081E-01 1.878E+07 1.184E-01 1.665E+07 105 1. 235E-G1 1.557E+07 1. 286E-01 1.453E+ 0 7 1.337E-01 1.354E + 07 1.388E-01 1. 261E+07 1.438E-01 1. 174E+07 1.489E-01 1. 081E+07 1.540E-01 9.522E+06 1.590E-01 8. 427E+06 1.641E-01 7.488E+06 1.692E-01 6.680E+Q6 1.742E-01 5.980E+06 1.793E-01 5.367E+06 1.843E-01 4.812E+06 1.894E-01 4.328E+06 1.944E-01 3.904E+06 1.994E-01 3.531E+06 2.045E-01 3. 202E+06 2. 095E-01 2.911E+06 2. 145E-01 2.653E+06 2.196E-01 2.422E+06 2.246E-01 2. 217E+06 2.296E-01 2.033E+O6 2.347E-01 1.86 8E+06 2.397E-01 1.719E+G6 2.447E-01 1. 586E+06 2. 498E-01 1 .464E* 06 2.548E-01 1.354E+06 2.598E-01 1.254E+06 2.648E-01 1. 163E+06 2.698E-01 1.081E+06 2.749E-01 1.005E+06 2.799E-01 9.362E+05 2.849E-01 8.732E+05 1.OOOE+00 1. OOOE+00 TEHPERATORE 1.500E+01 BESIDENCE TIME AGITATIOM RATE SUPERS ATU1MIOI 2.350E+02 L26QE+03 9.500E-01 POP. ,.- AT 0 2.014E+08 % CUMULATIVE HEIGHT 6.154E+01 9.399E + 01 9.640E+01 9.877E+01 1.000E+02 CRYSTAL SIZE POPULATION DENSITY CRYSTAL_SIZE POPOLA TIPN DENSITY 1.030E-01 3.053E+07 1.081E-01 2.664E+07 ¥EI GHT_X 6.9C3E-01 3. 640E-01 2.7C0E-O2 2.660E-02 1. 380E-02 SCREEN SIZE AD 1.060E-01 1.500E-01 1. 800E-01 2. 500 E-01 2.970E-01 1. 133E-01 1.235E-01 1.337E-01 1.438E-01 1.540E-01 1.641E-01 1.742E-01 1.843E-01 1.944E-01 2.045E-01 2.145E-01 2.246E-01 2.347E-01 2.447E-G1 2.54 8E-01 2.648E-01 2.749E-01 2. 849E-01 2.338E+07 1.832E+G7 1.46 3E+07 L188E+07 9.387E+06 7.339E+06 5.8 27E+06 4.676E+06 3.792E+06 3.109E+06 2.574E+06 2.150E+06 1.811E+06 1.536E+06 1.312E+06 1.127E+06 9.733E*05 8.454E+05 1. 184E-01 1.-2 8 6 E-01 1.388E-01 t. 48.9E-01 1. 590E-01 1.692E-01 1.793E-01 1.894E-01 1.994E-01 2.095E-01 2. 196E-01 2..2 9-6 E-01 2. 39 7E-01 2.498E-01 2.598E-01 2.698E-01 2.799E-01 1.000E+00 106 2.Q65E+07 1.634E+07 1.316E+07 1.069E+07 8.283E+06 6.527E+06 5.216E+06 H. 205E+06 3.42 9E+06 2.825E+06 2.350E+06 I. 971E+06 1 .666E+06 1. 419E+06 1.215E+06 1. 046E+06 9.066E+05 1.00GE+G0 TEMPERATURE 1.500E+01 POP. AT 0 RESIDENCE TIME AG IT AT ION _B ATE 5UPER SAT DBA TI ON 2. 350E*02 1.260E+03 8.230E-01 1.658E+08 HEIGHT X 4.203E-01 4. 064E-01 4.810E-02 2. 2G0E-02 7.400E-03 S CR J E N_SIZE_ i D 1.060 E-01 1.500E-01 1.800E-01 2.5O0E-01 2. 9 70 E-01 CRYSTAL SI2.E POPULATION DENSITY I_£MULATIVE_WEIGHT 4.6-48E*01 9.143E+01 9.675E+01 9.918E+01 1. 000E+O2 CRYSTAL SIZE POPULA£ION_DENSITY 1 .030 E - 0 1 I.1 3 3 E - 0 1 1 . 2 3 5 E - 0 1 1 , 3 3 7 E - 0 1 1 . 4 3 8 E - 0 1 1 . 5 4 0 E - 0 1 1 . 6 4 1 E - 0 1 1 . 7 4 2 E-01 1 . 8 4 3 E - 0 1 1 . 9 4 4 E - 0 1 2 . 0 4 5 E - 0 1 2 . | 4 5 E-01 2 . 2 4 6 E - 0 1 2 . 3 4 7 E - 0 1 2 . 4 4 7 E - 0 1 2 . 5 4 8 E - 0 1 2 . 6 4 8 E - 0 1 2 . 7 4 9 E - 0 1 2 . 8 4 9 E - 0 1 2 . 3 8 1 E + 0 7 1 .986E+07 1 .659E+07 1 .393E+07 1 .177E+07 9 . 4 8 8 E + 0 6 7 . 4 9 6 E + 0 6 6 . 0 1 3 E * 0 6 4 . 8 4 5 E + 0 6 3. 929E+06 3 . 2 2 2 E + 0 6 2 . 6 6 7 E * 0 6 2 . 2 2 8 E + 0 6 1 . 8 7 7 E+06 1 .592E+06 1 . 3 5 9 E+06 1 .166E+06 1 .007E+06 8 . 7 3 6 E * 0 5 1 . 0 8 1 E - 0 1 1. 1 8 4 E - 0 1 1 . 2 8 6 E - 0 1 1. 3 8 8 E - 0 1 1 . 4 8 9 E - 0 1 1 . 5 9 0 E - 0 1 1 . 6 9 2 E - 0 1 1 . 7 9 3 E - 0 1 1 . 8 9 4 E - 0 1 1 . 9 9 4 E - 0 1 2 . 0 9 5 E - 0 1 2 . 1 9 6 E - 0 1 2 . 2 9 6 E - 0 1 2 . 3 9 7 E - 0 1 2 . 4 9 8 E - 0 1 2 . 5 9 8 E - 0 1 2 . 6 9 8 E - 0 1 2 . 7 9 9 E - 0 1 1 .000E+00 107 2 . 1 7 5 E + 0 7 1..814E+07 1 ,519E+07 1 .279E+07 1. 074E+07 8 . 4 1 6 E + 06 6 . 7 0 1 E + 0 6 5 . 405E+06 4 . 3 5 7 E + 0 6 3 . 5 5 3 E * 06 2 . 9 2 8 E + 0 6 2 . 435E+06 2 . 0 4 3 E + 0 6 1 . 7 2 7 E * 06 1 .470E+06 1 .258E+06 1 . 0 8 3E+06 9 . 3 7 2 E + 05 1 .000E+O0 T E M E E B A T U B B 1 .500E+01 E E S I D E N C J _ T I M E A G I T A T I O N _ R A T E SOPEB SATUBATION 2 . 3 5 0 E + 0 2 1 . 2 6 0 E + 03 7 . Q 0 0 E - 0 1 P O P . AT 0 ~ 1 . 2 5 1 E * 0 8 WEIGHT X 1 . 8 5 8 E - 0 1 1. 5 4 8 E - 0 1 3 . 1 9 0 E - 0 2 5 . 4 S 0 E - 0 2 1. 1 5 0 E - 0 2 S C B E E M S I Z E AD 1 .060 E - 0 1 1. 5 0 0 E - 0 1 1 . 8 0 0 E - 0 1 2 . 5 0 0 E - O 1 2 . 9 7 0 E - 0 1 2-COJ1UL A T I V E _ WEIGHT 4 . 2 3 3 E + 0 1 7 .760E+01 8 . 4 8 7 E + 01 9 . 7 3 8 E * 0 1 1. 000E + 02 108 CBYSTAL SIZE POPULATION DENSITY CRYSTAL_SIZE POPULATION DENSITY 1.030E-01 2. 125E+07 1.081E-01 1.915E+07 1. 133E-01 1.728E+G7 1. 184E-01 1. 564E+07 1.235E-01 1.418E+07 1.286E-01 1 . 289E+07 1.337E-01 1.175E+07 1.388E-01 1.073E+O7 3.438E-01 9.822E+06 1. 489E-01 8.947E+06 1.540E-Q1 7.94 8E + 06 1.590E-01 7.G9GE+06 1.641E-01 6. 349E+06 1.692E-01 . 5. 707E+06 1.742E-01 5.148E+06 1.793E-01 4.655E+06 1.843E-01 4. 209E+06 1.894E-01 3.817E+ 06 1.944E-01 3.472E+06 1.994E-01 3. 166E+06 2.045E-01 2.894E+06 2.095E-01 2.652E+G6 2»145E-01 2.435E+06 2.196E-01 2.241E+06 2.246E-01 2.067E+06 2. 296E-01 1.910E+06 2.347E-01 1.768E+06 2.397E-01 1.640E+06 2-447E-01 1.523E+06 2.498E-01 1.41 5E+ 06 2.548E-01 1.311E+06 2.598E-01 1. 216E+06 2.64 8E-01 1. 129E+06 2.698E-01 1 . 051E+06 2.749E-01 9.786E+05 2.799E-01 9., 128E+05 2.849E-01 8. 525E+05 1.0QOE+Q0 1.000E+00 TEMPERATURE 1. 500E+01 BESIDE NCE TIME AGITATION BATE SUPEBS ATUBATION 3.800E+02 2.466E+03 9.500E-01 POP. AT 0 1.443E+08 WEIGHT X 3. 537E-01 2.463E-01 4. 320E-02 6. 040E-02 SCBEEN SIZE AD 1.060E-01 1.500 E-01 1.800E-01 2. 500E-01 % CUMULATIVE WEIGHT 4.881E+01 8.279E + 01 8.875E+01 9.709E+01 2. 11GE-02 2.970E-01 1.000E+02 ^ CEYSTAL_SIZE POPULATION DENSITY CRYSTAL SIZE POPULATION DENSITY 1.030E-01 2.358E+07 1.081E-01 2.094E+07 -1." 133 E-01 1.868E+Q7 1. 184E-01 1.672E+07 1.235E-01 1.503E+07 1.286E-01 1. 355E+07 1.337E-01 1. 226E+07 1. 388E-01 1.113E+ 07 1. 438E-01 1.013E+07 1.489E-01 9. 180E+06 1.540E-01 8. 126E+06 1.590E-01 7.224E+06 1.641E-01 6.448E+06 1.692E-01 5.777E+06 1 ..742 E-01 5. 19 4E+06 1.793E-01 4.681E+06 1.843E-01 4.217E+06 1.894E-01 3.811E+06 1. 944 E-01 3. 453E+06 1.994E-01 3.138E+06 2.Q45E-01 2.858E+06 2.095E-01 2.6 10E+06 2.145E-01 2. 389 E+06 2. 196E-01 2.191E+ 06 2.246E-01 2.014E+06 2.296E-01 1.855E+06 2.347E-01 1.712E+06 2.397E-01 1.582E+06 2. 447E-01 1.465E+06 2.498E-01 1.358E+06 2.548E-01 1.258 E+06 2. 598E-01 1.167E+06 2.648E-01 1.085E + 06 2.698E-01 1.009E+06 2.749E-01 9. 406E+05 2. 799E-01 8.777E+05 2.849E-01 8.200E+05 1.000E+00 1.000E+00 TEMPEBATUBE RESIDENCE TIME 1.500E+01 3.800E+O2 POP. AT 0 1.078E+08 HEIGHT X SCREEN SIZE AD 1.540E-01 1.060E-01 4.264E-01 1.500E-01 4.330E-02 1.800E-01 AGI1&1IQN_RATE 2.466E + 03 SUPEB SATURATION 8.230E-01 I_CyaULATIVE_HEIGHT 2. 383E + 01 8.982E+01 9.652E+01 1.280E-02 2.500E-01 9.850E+01 HO 9.7G0E-03 2.970E-01 1.000E+02 CRYSTAL SIZE POPULATION DENSITY CRYSTAL^SIZE POP OLA HON DENSITY 1.030E-01 1. 209E+07 1.081E-01 1.309E+07 1. 133E-01 1.348E+07 1.184E-01 1. 347E+07 1.235E-01 1. 322E+07 1.286E- 01 1.281E+ 07 1.337E-01 1.231E+07 1.388E-01 1, 176E+07 1.438E-01 1. 119E*07 1.489E-01 1.Q46E+07 1. 540E-01 9.264E+06 1.590E-01 8. 239E+06 1.641E-01 7.357E+06 1.692E-01 6.594E+06 1.742E-01 5.931E+06 1.793E-01 5.342E+Q6 1.843E-01 4.787E+06 1. 894E-01 4. 303E*06 1.944E-01 3.880E+06 1.994E-01 3.507E+06 2.045E-01 3. 179E+06 2.095E-O1 2. 888E*06 2.145E-01 2.630E+06 2.196E-01 2.401E+06 2.246E-01 2. 196E*06 2.296E-01 2.013E+06 2.347E-01 1.848E+06 2.397E-01 1. 700E+06 2.447E-01 1. 567E+06 2. 498E-01 1 -447E+06 2.548E-01 1.338E+06 2.598E-01 1.240E+Q6 2,648E-01 1. 150E+06 2.698E-01 1.069E+06 2.749E-01 9.943E+05 2.799E-01 9. 26 3E+05 2.849E-01 8.641E+05 1.000E*00 1.000E+0O TEHPJRATORE RESIDENCE TIME 1. 500E+01 3.800E + 02 POP. AT 0 1. 462E+08 HEIGHT X SCREEN SIZE AD 6. 483E-01 1.060E-01 7.694E-01 1. 500 E-01 AGITATION RATE SUPERSJTORATION 2.466E+03 7.000E-01 % COMOLATIVE WEIGHT 4.156E+01 . 9.088E+01 3. 520E-02 4.620E-02 6.080E-02 •1.800E-01 2.500E-01 2.970E-01 CRYSTAL SIZE POPULATION DENSITY 9. 314E+01 H I 9.610E+01 1.000E+02 CRYSTAL SIZE POPULATION DENSITY 1.030E-01 2.018E+07 1.081E-01 1. 885E+07 1. 133E-01 1.752E+07 1. 184E-01 1. 625E+07 1.235E-01 1.504E + 07 1.286E-01 1. 391E+07 1.337E-01 1. 287E+07 1.388E-01 1. 191E+07 1.438E-01 1.103E+07 1.489E-01 1. 011E+07 1.540E-01 8.882E+Q6 1.590E-01 7. 836E+06 1.641E-01 6.942E+Q6 1.692E-01 6. 173E+06 1.742E-01 5.510E+06 1.793E-01 4. 933E+06 1.843E-01 4.425E+06 1.894E-01 3. 981E+06 1.944E-01 3.592E+06 1.994E-01 . 3. 249E+ 06 2.045E-01 2.947E+06 2.095E-01 2. 680E+06 2.145E-01 2.443E+06 2. 196E-01 2. 231E+06 2.246E-01 2.042E+06 2.296E-01 1. 873E+06 2-347E-01 1.722E+06 2.39 7E-01 1 . 585E+06 2.447E-01 1.462E+06 2.498E-01 1. 352E+06 2.54 8E-01 1. 253E+06 2.598E-01 1. 164E+06 2.648E-01 1.083E+06 2.698E-01 1. 009E+06 2.749E-01 9.412E+05 2.799E-01 8.791E+05 2»849E-01 8.222E+05 1.000E+00 1. 000E+00 TEMPERATURE JJSIDJNCJ_TIME AGITATION, RATE SUPERSATURATION 1.50QE + 01 3.800E+02 1.926E+03 9.500E-01 POP. AT 0 1.259E+08 HEIGHT X 2.094E-01 SCREEN SIZE AD 1.060E-01 iLCUMUL_AJI2I_jliIGHT. 4.826E+01 9.050E-02 1.500E-01 6.912E+01 1 1 2 3.6G0E-02 1.800E-01 7.741E+01 5.470E-02 2.'500 E-01. 9.Q02E+01 4. 330E-02 2.97QE-C1 1.000E+02 CRYSTAL SIZE POPULATION DENSITY CBYSTAL_SIZE POPULATION DENSITY 1.Q30E-01 2.434E+07 1.08 IE-01 2. 102E+07 1. 133E-01 1.828E+07 1.184E-01 1. 601E+07 1.235E-01 1.4 10E+07 1.286E-01 1- 249E+07 1.337E-01 1.11 1E + 07 1.388E-01 9, 933E+06 1.438E-01 8.918E+06 1. 489E-01 8. 014E+06 1.540E-01 7. 150E+06 1.590E-01 6. 405E+06 1.641E-01 5.759E*06 1.692E-01 5. 197E+06 1.742E-01 4.705E+06 1.793E-01 4. 267E+06 1.843E-01 3. 86 3E+06 1.894E-01 3. 507E+06 1-944E-01 3.193E+06 1.994E-01 2. 915E+C6 2.045E-01 2.667E+06 2.095E-01 2. 446E+06 2. 145E-01 2.249E+06 2.196E-01 2. 072E+06 2-246E-01 1.912E+06 2. 296E-01 1. 768E+06 2.347E-01 1.639E»06 2.397E-01 1. 521E+06 2.44 7E-01 1.414E+06 2.498E-01 1. 317E+06 2.548E-01 1.231E+06 2.598E-01 1. 151E+06 2-648E-01 1.079E+06 2.698E-01 1. 012E+06 2.749E-01 9.506E+05 2.799E-01 8. 941E+05 2-849E-01 8.419E+0 5 1.000E+00 1. OOOE+00 TEMPERATURE RESIDENCE TIME AGITATION RATE SU PEiBS ATU RATION • -i.50OE*01 3.800E + 02 1.926E+G3 8.23GE-01 POP. AT 0 9.349E+07 WEIGHT X SCREEN SIZE AD % CUMULATIVE WEIGHT 3. 494E-01 1. 060E-01 2.463E+G1 " J 7.317E-01 1.500E-01 7.620E*01 2.677E-01 1.800E-01 9.507E*Q1 5.960E-02 2. 500E-01 9.927E + 01 1.030E-02 2.970E-01 1.000E+02 CBYSTAL SIZE POPULATION DENSITY CgISTAL__SIZE POPULATION DENSITY 1.030E-01 1.2951*07 1.081E-01 1. 319E+07 1. 133E-01 1.307E+07 1.184E-01 1. 272E+07 1.235E-01 1. 223E+07 1.286E-01 1. 167E+07 1. 337E-01 1.108E+07 1.388E-01 1. Q48E+G7 1.438E-01 9.887E+06 1.489E-01 9, 247E* 06 1.540E-01 8.420E+06 1.590E-01 7. 689E+06 1.641E-01 7.040E*06 1.692E-01 6. 463E*06 1. 742E-01 5.947E+06 1.79 3E-01 5. 452E+06 1.843E-01 4.895E*06 1.894E-01 4. 4 07E+ 06 1.944E-01 3.980E*06 1.994E-01 3. 604E+06 2.045E-01 3. 272E*06 2.095E-01 2. 978E+06 2.145E-01 2.716E+06 2.196E-01 2. 483E+06 2.246E-01 2. 275E*06 2.296E-01 2. 089E*06 2.347E-01 1.921E*06 2.397E-01 1. 770E+06 2.447E-01 1.634E*06 2.498E-01 1. 510E+06 2.54 8E-01 1.396E+06 2.598E-01 1. 292E+06 2.64 8E-01 1. 198E+06 2. 698E-01 1. 112E*06 2.749E-01 1.034E+06 2.799E-01 9. 622E*05 2.849E-01 8.968E+05 1.000E+00 1. 000E+00 TEMPEBATUBE RESIDENCE TIHE AGITATION RATE SOPJRSATUEATION 1. 500E*01 3.800E + 02 1.926E+03 7.000E-01 POP. AT 0 1.209E + 08 WEIGHT_X 5.085E-01 9.436E-01 1. 9 10E-Q1 3.880E-02 5- 200E-03 SCREEN SIZE AD 1. 060E-01 1.500 E-0 1 1.800E-01 2. 500 E-01 2.970E-01 CRYSTAL SIZE POPULATION DENSITY % CUMULATIVE HEIGHT 1 1 3-014E+01 8.607E+01 9.739E+01 9.969E+01 1.000E+02 CRYSTALLIZE POP ULAT ION DENSITY 1-030E-01 1.58 3E+07 1.081E-01 1 .578E*- 07 1. 133E-01 1.53 9E+07 1.184E-01 1. 481E+07 1.235E-01 1.413E+07 1.286E-01 1.339E+ 07 1.337E-01 1.26 4E+07 1.388E-01 1. 190E+07 1.438E-01 1. 119E+07 1.489E-01 1. 039E+ 07 1.540E-01 9.291E+06 1.590E-01 8. 337E+06 1-641E-01 7.510E+06 1.692E-01 6.788E*06 1.742E-01 6.155E+06 1.793E-01 5.578E+06 1.843E-01 5.Q0 0E+06 1.89 4E-01 4.496E+ 06 1.944E-01 4.054E+06 1.994E-01 3.666E+06 2.045E-01 3.323E*06 2.095E-01 3.020E+06 2.145E-01 2.751E+06 2.196E-01 2. 511E+06 2.246E-01 2.298E+06 2. 296E-01 2. V06E+06 2.347E-01 1.935E+06 2.397E-01 1.780E+06 2.447E-01 1.641E*06 2.498E-01 1.515E+06 2.548E-01 1.400E+06 2.598E-01 1.295E+06 2.648E-01 1. 200E+06 2.698E^01 1.-113E+06 2.749E-01 1.035E+06 2.799E-01 9.626E+05 2.849E-01 8.968E+05 1.000E+00 1.OOOE+OO lEMPERATURE RESIDENCE TIME AGITATION RATE SUPERS ATURATION 1. 500E+O1 3.800E + 02 1.260E+03 9.500E-01 POP. AT 0 115 1.969E+08 WEIGHT- .X SCREEN SIZE AD % CUMULATIYE WEIGHT 5. 864E-01 1. 06OE-01 5. 874E+01 3.510E-Q1 1. 500 E-01 9. 390E+01 3- 7C0E-02 1. 800E-01 9. 761E+01 7.700E-03 2. 500E-01 9. 838E+01 1.620E-02 2. 9 70E-01 1. 000E+02 CRYSTAL SIZE POPULATION DENSITY CRYSTAL_SIZE POPULATION DEBS. 1.030E-01 2.930E+07 1.081E-01 2.576E* 07 1. 133E-01 2.277E+07 1.1.8 4 E-01 2.022E+07 1.235E-01 1.80 4E+G7 1.286E-01 1.617E+07 1.337E-01 1.455E+07 1.388E-01 1. 313E+07 1.43 8 E-01 1. 190E+07 1. 489E-01 1.074E+07 1.540E-01 9.455E+06 1.590E-01 8.361E+06 1.641E-01 7.425E+06 1.692E-01 6.619E+06 1.742E-01 5.921E + 06 1.793E-01 5.309 E+06 1.843E-01 4.754E+06 1.894E-01 4.26 9E+ 06 1.944E-01 3.846E+06 1.994E-01 3.473E+06 2.045E-01 3. 145E+06 2.095E-01 2.855E+06 2. 145E-01 2.598E+06 2.196E-01 2.369E+06 2.246E-01 2. 165E+06 2.296E-01 1. 983E+06 2.347E-01 1.819E+06 2.397E-01 1.672E+06 2.447E-01 1.540 E+06 2.498E-01 1.421E+06 2,.548E-01 1.314E+Q6 2.598E-01 1. 218E+06 2.648E-01 1. 130 E+06 2.698E-01 1 . G50E+06 2.749E-01 9.769E+05 2.799E-01 9. 102E+05 2.849E-01 8.49 2E+05 1.00QE+00 1.00OE+O0 TEMPEBATUBE 1. 5C0E+O1 RESIDENCE TIME AGITATION BATE SUPERSMOMIIQE 3.800E+02 1.260E+03 8.230E-01 116 POP, AT 0 3.244E+07 1_^GHT_X SCREEN SIZE AD % CUMULATIVE HEIGHT 1.720E-01 1.060E-01 1.236E+01 4.736E-01 1.500E-01 4.639E+01 4. 152E-01 1.800E-01 7.623E+01 3.192E-01 2.500E-01 9.917E + 01 1.16QE-02 2.970E-01 1.000E+02 CRYSTAL SIZE POPULATION DENSITY CRYSTAL SIZE POPULATION.DENSITY 1.030E-01 6.2281*06 1.081E-01 6. 73OE* 06 1. 133E-01 6.925E*06 1.184E-01 6. 921E*06 1.235E-01 6.788E+06 1.286E-01 6. 577E+06 1.337E-01 6.318E+06 1.388E-01 6. Q34E+06 1.438E-01 5.738E+06 1. 489E-01 5. 467E*06 1 .540E-01 5.284E+06 1.590E-01 5. 084E+06 1.641E-01 4.874E+06 1.692E-01 4. 661E+06 1.742E-01 4.45GE+06 1.793E-01 4. 206E+06 1.843E-01 3.844E+06 1.894E-01 3. 523E+06 1.944E-01 3.237E+06 1.994E-01 2. 980E+06 2.045E-01 2.751E+06 2.095E-01 2. 544E+06 2.145E-01 2.357E+06 2.196E-01 2. 188E+06 2.246E-01 2.035E+06 2.296E-01 1. 896E+06 2.347E-01 1.769E+06 2.397E-01 •1. 654E+06 2.447E-01 1.548 E+06 2.498E-01 1 . 446E+06 2.548E-01 1.337E+06 2.598E-01 1. 237E+06 2.648E-01 1. 147E+06 2.698E-01 1 . 065E+06 2.749E-01 9.903E+05 2.799E-01 9. 22QE+05 2.849E-01 8. 59 4E+0 5 1.000E+00 1. 000E+G0 I I / 1. 5C0E + O1 3. 800E+02 1.260E+03 7.000E-01 POP. AT 0 1.017E + 08 WEIGHT X 3.3C1E-01 SCBEEN SIZE AD % CUMULATIVE WEIGHT 1. 060E-01 2. 780E+01 6.148E-01 1.500 E-01 7. 957E+01 2.031E-O1 1. 800E-01 9.668E+01 3.850E-02 2. 500E-01 9. 992E+01 9. 400E-04 2. 970E-01 1 . 000E+02 CRYSTAL SIZE POPULATION DENSITY CRYSTAL SIZE POPULATION DEN' 1.030E-01 1. 410E+07 1.081E-01 1 .406E+07 1. 133E-01 1.373E + 07 1. 184E-01 1. 322E+07 U235E-01 1.26 1E+07 1.286E-01 1.195E+07 1.337E-01 1.129E+07 1.388E-01 1.06 3E+07 1.438E-01 9.989E+06 1. 489E-01 9.309E+06 1.540E-01 8.432E+06 1.590E-01 7.663E+G6 1.641E-01 6.985E+06 1.692E-01 6. 386E+06 1.742E-01 5.853E+06 1.793E-01 5.350E+06 1.843E-01 4.799E+06 1.894E-01 4. 318E+06 1.944E-01 3.896E+06 1.994E-01 3.525E+06 2.045E-01 3. 198E+06 2.095E-01 2.908E*06 2. 145E-01 2.651E+06 2.196E-01 2.422E+06 2.246E-01 2. 217E+06 2.296E-01 2. 034E+G6 2.347E-01 1.870E+06 2.39 7E-01 1.722E+06 2.447E-01 1.588E*06 2.498E-01 1.467E+06 2.54 8E-01 1.355E+06 2.598E-01 1. 253E+06 2.64 8E-01 1.161E+06 2. 698E-01 1 .077E+06 2.749E-01 1.OO0E+06 2.799E-01 9.306E+05 2.849E-01 8.668E+05 1.000E+00 1.000E+00 TEM PERATURE 2. OCOE+01 RESIDENCE TIME I.700E + 02 11 o AGITATION RATE SUPERS ATORATION 2.466E+03 9*5.0 0 E-01 POP, AT 0 ~2.318E+08 HEIGHT X 7.765E-01 2. 722E-01 2, 570E-02 2.900E-02 1.310E-02 SCREEN SIZE AD 1.060E-01 1. 500E-0 1 1.800E-01 2.500E-01 2.970E-01 CRYSTAL SIZE POPULATION DENSITY I CUMULATIVE HEIGHT 6.955E+01 9.393E+01 9.623E+01 9.883E+01 1.000E+02 CR£STAL_SIZE POPULATION D E N S I T Y 1.030E-01 3.633E+07 1.081E-01 3. 109E+07 1. 133E-01 2.682E+G7 1..1842-01 2.. 331E+Q7 1.235E-01 2.Q39E+07 1.286E-01 1. 794E+07 1.337E-01 1.587E+07 1.388E-01 1. 411E+07 1.438E-01 1.260E+07 1.489E-01 1. 124E+07 1.540E-01 9.874E+06 1.590E-01 8, 711E+06 1.641E-01 7.716E+06 1.692E-01 6. 862E+06 1.742E-01 6.124E+06 1.793E-01 5. 482E+06 •1. 84 3 E-01 4.915E+Q6 1.894E-01 4. 421E+06 1.944E-01 3.987E+Q6 1.994E-01 3. 606E+06 2.045E-01 3. 270E+06 2.095E-01 2. 972E+06 2.145E-01 2.708E+Q6 2.196E-01 2. 473E+06 2.246E-01 2. 26 3E+G6 2.296E-01 2. 075E+06 2.347E-01 1.906E+06 2.397E-01 1. 755E+06 2.447E-01 1.618E+06 2.498E-01 1. 494E+06 2.548E-01 1..382E+06 2.598E-01 1. 279E+06 2.64 8E-01 1. 187 E+06 2.698E-01 1. 102E+ 06 2.749E-01 1.025E+06 2.799E-01 9. 546E+05 2.849E-01 8.902E+05 1.Q00E+G0 1. 00OE+0O TEMPERATURE 2. OOCE+01 RESIDENCE TIME 1.700E+02 11S AGI T A T I 0 i ~ R &TE S u i i i s A i u RATION 2.466E+03 8.230E-01 POP. AT 0 2.370E+08 HEIGHT X 1. 119E+00 1.707E-01 4.C7OE-02 4.560E-02 3.860E-02 SCREEN SIZE AD 1.060E-01 1. 500E-01 1.800E-01 2. 500E-01 2.970E-01 CRYSTAL SIZE PQPOLAT ION DENSITY % CUMULATIVE HEIGHT 7.911E+01 9. 117E+01 9.405E+01 9.727E+01 1.G00E+02 CRYSTAL.SIZE POPULATION DENSITY 1.030E-01 3.918E+07 1.081E-01 3.2 80E+07 1. 133E-01 2.772E+07 1.184E-01 2.362E+07 1.235E-01 2.Q28B+07 1.286E-01 1. 753E+07 3.337E-01 1.525E+07 1.388E-01 1. 334E+07 1.438E-01 1.173E+07 1. 489E-01 1. 035E+07 1.540E-01 9.100E+06 1.590E-01 8.037E+06 1.641E-01 7.128E+06 1.692E- 01 6.346E+06 1.742E-01 5.670E+06 1.793E-01 5.081E+06 1.843E-01 4.558E»-06 1.894E-01 4.101E+06 1.944E-01 3.701E+06 1.994E-01 3.349£+06 2.045E-01 3.0 38E+0 6 2.095E-01 2.763E+06 2. 145E-01 2.519E+06 2. 196E-01 2.301E+06 2.246E-01 2. 107E+06 2.296E-01 1.933E+06 2.347E-01 1.777E+06 2.397E-01 1.636E+06 2.447E-01 1. 509E+06 2.498E-01 1.395E+06 2. 548E-01 1.292E+06 2.598E-01 1.J98E+06 2.648E-Q1 1. 113E+06 2.698E-01 1. 03 6E+ 06 2.749E-01 9.650E+05 2.799E-01 9.003E+05 2.849E-01 8. 409E+05 1.000E+00 1 . OOOE+OO 120 TEMPERATURE 2. 00OE+01 RESIDENCE TIME 1.700E + 02 !GITATION_RATE SUPERS AIU RATION 2.466E+03 7.000E-01 POP. AT 0 4.571E+07 WEIGHT X 6, 130E-02 1..210E-01 1. 135E-01 3.230E-02 2.780E-02 SCREEN SIZE AD 1.060E-01 1.500E-01 1.800E-01 2. 500E-01 2.970E-01 CRYSTAL SIZE POPULATION DENSITY % CUMULATIVE WEIGHT 1.722E+01 5.122E+01 8.311E+Q1 9. 219E + 01 1.000E+02 CRYSTAL SIZE POPULATION DENSITY 1.030E-01 8.410E+06 1.081E-01 8.474E+ 06 1. 133E-01 8.331E+06 1.184E-01 8.063E+06 1.235E-01 7.723E+06 1.286E-01 7.346E+06 1.337E-01 6.955E+06 1.388E-01 6. 56 3E+06 1.438E-01 6. 181E+06 1. 489E-01 5.845E+06 1.540E-01 5.632E+06 1.590E-01 5. 405E+06 L641E-01 5. 172E+06 1.692E-01 4.937E+06 1.742E-01 4.706E+06 1.793E-01 4. 431E+06 1.843E-01 3.996E+06 1.894E-01 3.615E+06 1.944E-0 1 3.279E+06 1.994E-01 2.983E+06 2.045E-01 2. 7 20 E+06 2.095E-01 2.486E+06 2. 145E-01 2.277E+06 2.196E-01 2.091E+06 2.246E-01 1.924E+06 2. 296E-01 1.774E+06 2.347E-01 1.638E+06 2.397E-01 1. 516E+06 2.447E-01 1.405E+06 2.498E-01 1.305E+06 2.54 8E-01 1.216E+06 2.598E-01 1.135E+06 2.648E-01 1. 060E+06 2.698E-01 , 9.920E+ 05 2.749E-01 9.295E+05 2.799E-01 8.720E+05 2.849E-01 8. 19 1E+05 1.00OE+0O 1.OOOE+OO 121 TEH FERATURE 2. 0C0E+01 RESIDENCE TIME 1.700E + 02 AGITATION RATE SUPERS ATURATION 1.926E+Q3 9.500E-01 POP. . AT 0 U815E+08 WEIGHT X - SCREEN SIZE AD % CUMULATIVE HEIGHT 8. 288E-01 1. 060E-01 5. 384E+01 5.762E-01 1. 500 E-01 9. 128E+01 6. 430E-02 1. 800E-01 9. 545E+01 5.020E-02 2. 500E-01 9. 871E+01 1.980E-02 2. 970E-01 1. 000E+02 CRYSTAL SIZE POPULATION DENSITY CRYSTAL SIZE POPULATION DEN' 1.030E-01 2.7351+07 1.081E-01 2.429E+07 1. 133E-01 2.166E+07 1.184E-01 1. 939E+07 1.235E-01 1.742E+07 1.286E-01 1. 571E+07 1.337E-01 1.421E+07 1.388E-01 1. 290E+07 1.438E-01 1. 1741+07 1. 489E-01 1. 063E+ 07 1.54OE-01 9.370E+06 1.590E-01 8. 29 5E+06 1.641E-01 7.37 31+06 1.692E-01 6. 579E+06 1.742E-01 5.892E+06 1.793E-01 5. 289E+06 1.843E-01 4.7441+06 1.894E-01 4.269E+ 06 1.944E-01 3.852E+06 1.994E-01 3.486E+06 2.045E-01 3. 162E+06 2.095E-01 2.876E + 06 2. 145E-01 2.622E+06 2. 196E-01 2.395E+06 2.246E-01 2. 193E+06 2.296E-01 2.012E+O6 2.347E-01 1.849E+06 2.397E-01 1.703E+06 2.447E-01 1.571E+06 2.498E-01 1.451E+06 2.548E-01 U342E+06 2.598E-01 1.24 3E+06 2.64 8E-01 1. 153E+06 2. 698E-01 1.071E+06 2.749E-01 9.962E+05 2.799E-01 9.279E+05 2.849E-01 8.654E+05 1.000E+00 1.OOOE+00 TEMPERATURE RESIDENCE TIME 2. 000E+01 1.700E + G2 POP. AT 0 2. 147E+08 122 'AGrTATI0i~SATE SUPERS ATUJATioN 1.926E+03 8.230E-01 8EIGHT , X 1, Q15E + 00 4.074E-01 2. 180E-02 3.420 E-02 2. 830E-02 SCREEN SIZE AD 1.060E-01 1.500E-01 1.800E-01 2.500E-01 2.970E-01 CRISTA! SIZE POPULATION DENSITY I .CUMULATIVE, HEIGHT 6.736E+01 9.440E+01 9.585E+Q1 9.812E+01 1.Q00E+02 CRYSTAL SIZE POPULATION DENSITY 1.030E-01 3.310E+07 1.08 IE-01 2.849E+07 1. 133E-01 2.471E+07 1.184E-01 2. 157E+07 1.235E-01 1.895E+07 1.286E-01 1.674E+07 1.337E-01 1.487E+07 1.388E-01 1.326E+07 1.438E-01 1. 188E+07 1. 489E-01 1. 063E+07 1.540E-01 9.320E+06 1.590E-01 8. 209E+06 1.641E-01 7. 26 1E+06 1.692E-01 6.448E+06 1.742E-01 5.746E+06 1.793E-01 5.138E+06 1.843E-01 4.605E+Q6 1.894E-01 4. 141E+06 1.944E-01 3.734E+06 1.994E-01 3. 376E+06 2.045E-01 . 3.06 1 E+0 6 2.095E-01 2.781E+06 2. 145E-01 2.534E + 06 2.196E-01 2.313E+06 2.246E-01 2. 116E+06 2.296E-01 1 ..940E+06 2.347E-01 1.782E+06 2.397E-01 1. 640E+06 2.447E-01 1.512E+06 2.498E-01 1.396E+06 2.54 EE-01 1.292E+06 2.598E-01 1.197E+06 2.648E-01 1.111E+06 2.698E-01 1 .033E+06 2.749E-01 9.613E+05 2.799E-01 8.960E+05 2.849E-01 8. 36 1E+05 1.000E+00 1.000E+00 T E M P E R A T P R E 2 . OCOE+01 R E S I D E N C E T I M E 1 .700E+02 A G I T A T I O N R A T E 1 .926E+03 1 23 l a 2 J i s j k f i l M I ON 7 . 0 0 0 E - 0 1 POP. AT 0 1 .768E+07 WEIGHT X S C R E E N S I Z E AD ! %, C U M U L A T I V E WEIGHT 7 . 2 4 0 E - 0 2 1. 0 6 0 E - 0 1 1 .366E+01 6 . 0 9 0 E - 0 2 1 .500 E - 0 1 2 . 5 1 6 E + 0 1 •1. 8 1 2 E - 0 1 1. 8 0 0 E - 0 1 5 . 9 9 2 E + 0 1 1 .382 E - 0 1 2 . 5 0 0 E - 0 1 8 . 6 0 0 E + 0 1 7 . 4 2 0 E - 0 2 2 . 9 7 0 E - G 1 1 .000E+02 C R Y S T A L S I Z E P O P U L A T I O N DENSITY C R Y S T A L S I Z E P O P U L A T I O N DENi J . 0 3 0 E - 0 1 6 . 6 4 3 E + 0 6 1 . 0 8 1 E - 0 1 5 . 9 9 0 E + 06 1 . 1 3 3 E - 0 1 5 . 4 1 1 E + 0 6 1 . 1 8 4 E - 0 1 4 . 8 9 9 E + 0 6 1 . 2 3 5 E - 0 1 4 . 445E+06 1 . 2 8 6 E - 0 1 4 . 0 4 3 E + 0 6 1 . 3 3 7 E - 0 1 3 . 6 8 5 E + 0 6 1 . 3 8 8 E - 0 1 3 . 3 6 7 E + 0 6 1 . 4 3 8 E - 0 1 3 .083E+Q6 1 . 4 8 9 E - 0 1 2 . 929E+06 1 . 5 4 0 E - 0 1 3 . 1 2 6 E + 0 6 1 . 5 9 0 E - 0 1 3 . 2 4 2 E + 0 6 1 . 6 U 1 E - 0 1 3. 29 8 E+06 1 . 6 9 2 E - 0 1 3 . 308E+06 1 . 7 4 2 E - 0 1 3 . 2 8 5 E + 0 6 1 . 7 9 3 E - 0 1 3 . 1961+06 1 . 8 4 3 E - 0 1 2 . 9 4 8 1 * 0 6 1 . 8 9 4 E - 0 1 2 . 7 2 6 E + 06 1 . 9 4 4 E - 0 1 2 . 5 2 5 E + 0 6 1 . 9 9 4 E - 0 1 2 . 3 4 4 E + 0 6 2 . 0 4 5 E - 0 1 2. 180E+06 2 . 0 9 5 E - 0 1 2 . 0 3 0 E + 0 6 2 . 1 4 5 E - 0 1 1..895E+06 2 . 1 9 6 E - 0 1 1 .771E+06 2 . 2 4 6 E - 0 1 1 .657E+06 2 . 2 9 6 E - 0 1 1 . 553E+06 2 . 3 4 7 E - 0 1 1 .458E+06 2 . 3 9 7 E - 0 1 1 .370E+G6 2 . 4 4 7 E - 0 1 1 .290E+06 2 . 4 9 8 E - 0 1 1 .214E+06 2 . 5 4 8 E - 0 1 1 .141E+06 2 . 5 9 8 E - 0 1 1 .073E+G6 2 . 6 4 8 E - 0 1 1 .0101+06 2 . 6 9 8 E ^ 0 1 9 . 5 2 5 E + 0 5 2 . 7 4 9 E - 0 1 8 . 9 9 0 E + O 5 2 . 7 9 9 E - 0 1 8. .495E+05 2 . 8 4 9 E - 0 1 8 .Q36E+05 1 .000E+00 1. OOOE+OO TEMPERATURE 2. OOOE+01 RESIDENCE TIME 1.700E + 02 124 lGITATION_fiATE SU PERS ATURATION 1.260E+03 9.500E-01 POP. , AT 0 2. 126E+08 HEIGHT X SCREEN SIZE AD 5 I CUMULATIVE HEIGHT 1.334E+00 1. 060E-01 6. 4 76E+01 •5. 279E-01 1. 500 E-01 9. 038E+01 8. 920E-02 1. 800E-01 9. 471E+01 7.480E-02 2. 500E-01 9. 834E+01 3.420E-02 2. 970E-01 1. OOOE+02 CRYSTAL SIZE POPULATION DENSITY CRYSTAL SIZE POPULATION DEN; 1.030 E-01 3.401E*07 1.08 IE-01 2. 925E+07 -1..1338-01 2.535E+Q7 1.184E-01 2.212E+07 1.235E-01 1.942E+07 1.286E-01 1.715E+07 1.337E-01 1.522E+07 1.388E-01 1.358E+07 1.438E-01 1.216E»07 1. 489E-01 1 . 088E+O7 1.540E-01 9.597E+06 1.590E-01 8. 499E+06 1.641E-01 7.557E*06 1.692E-01 6.745E+06 1.742E-01 6.Q42E+G6 1.793E-01 5. 426E+06 1.843E-01 4. 869E+06 1.894E-01 4.382E+ 06 1.944E-01 3.956E+06 1.994E-01 3.580E+06 2.045E-01 3. 249E*06 2.095E-01 2.956E*06 2.145E-01 2.695E+06 2.196E-01 2.463E+06 2.246E-01 2. 256E+06 2. 296E-01 2.070E+06 2.347E-01 1.903E+06 2.39 7E-01 1..753E + 06 2.447E-01 1.6 18E+06 2.498E-01 1.495E+06 2.54 8E-01 1.383E+06 2.598E-01 1.281E+06 2.64 8E-01 1. 189E+06 2.698E-01 1.105E+06 2.749E-01 1.028E+06 2.799£-01 9.582E+05 2.849E-01 8.9 40E+05 1.000E+00 1.0O0E+00 TEJPEBATU8E 2. 0C0E+01 RESIDENCE TIME 1.700E*02 AGITATION BATE 1.260E+03 .125 "I u H I I JSI I I I I o i 8.230E-01 POP. AT 0 2. 423E+08 HEIGHT X 8.937E-01 1. 119E-01 2. 530E-02 2.400E-02 •1. 940E-02 SCBEEN SIZE AD 1. 060E-01 1.500E-01 1.800E-01 2. 500E-01 2.9 70E-01 CBYSTAL SIZE POPULATION DENSITY % CUMULATIVE HEIGHT 8.319E+01 9.361E+01 9.596E*0t 9.819E + 01 1.000E+02 CBYSTAL SIZE POPULATION DENSITY 1.030E-01 3.950E+07 1.08 IE-01 3. 298E+07 1.133E-01 2.778E+07 1.184E-01 2. 361E+07 1.235E-01 2.021E+O7 1.286E-01 1. 742E+07 1.337E-01 1.512E+07 1.388E-01 1. 319E+07 1.438E-01 1., 157E+07 1.489E-01 1. 018E+07 1.540E-01 8.946E+06 1.590E-01 7. 893E+06 1.641E-01 6.993E+06 1.692E-01 6. 219E+06 1.742E-01 5.551E+06 1.793E-01 4. 970E+06 1.843E-01 4.455E+06 1..894E-01 4. 005E+06 1.944E-01 3.611E+06 1.994E-01 3. 265E+06 2.045E-01 2.960E+06 2.095E-01 2. 690E+06 2. 145E-01 2.450E+06 2.196E-01 2. 237E+06 2.246E-01 2.046E+06 2.296E-01 1. 876E+06 2.347E-01 1.723E+06 2.397E-01 1. 586E+06 2.44 7E-01 1.462E+06 2.498E-01 1. 350E+06 2.548E-01 1.249E+06 2.598E-01 1. 157E+06 2.§48E-01 1.074E+06 2.698E-01 9. 983E+05 2.749E-01 9.291E+05 2.799E-01 8. 659E+05 2.849E-01 8.080E+05 1.000E+00 1. QOQE+00 I J LS j j lMUBE RESIDENCE TIRE AGITATION RATE MPJilSJTURATION 2. 000E+01 1.700E+02 1.260E+03 7.000E-01 POP. AT 0 1.872E + 07 WEIGHT X SCREEN SIZE AD % CUMULATIVE HEIGHT 1. 088E-01 1.060E-01 1.388E+01 9.820E-02 1.500 E-0 1 2.641E+01 2.351E-01 1.800E-01 5.640E+01 2. 867E-01 2.500 E-01 9.298E+01 5.500E-02 2.970E-01 1.000E+02 CRYSTAL SIZE POPULATION DENSITY CRYSTAL_SIZE POPULATION DENSITY 1.030E-01 7. 262E+06 1.081E-01 6. 590E+06 1. 133E-01 5.985E+06 1.184E-01 5. 443E+06 1.235E-01 4.958E+06 1.286E-01 4, 524E* 06 1.337E-01 4.136E+06 1.388E-01 3. 788E+06 1.438E-01 3. 477E+06 1. 489E-01 3. 283E+06 1.540E-01 3.396E+06 1.590E-01 3. 444E+06 1.641E-01 3. 444E+06 1.692E-01 3. 410E+06 1.742E-01 3.351E+06 1.793E-01 3. 247E+06 1.843E-01 3.039E+06 1.894E-01 2. 84 8E+06 1.944E-01 2.671E+06 1.994E-01 2. 509E+06 2.045E-01 2.358E*06 2.Q95E-01 2. 219E+06 2.145E-01 2.091E+06 2.196E-01 1. 972E+06 2.246E-01 1..862S+06 2.296E-01 1. 759E+06 2.347E-01 1.664E+06 2.397E-01 1. 575E+06 2.447E-01 1.49 3E+06 2.498E-01 1. 410E+06 2.548E-01 1.312E+06 2.598E-01 1. 223E+06 2.648E-01 1. 142E+06 2.698E-01 1. 068E+06 2.749E-01 9.996E+05 2.799E-01 9. 370E+05 2.849E-01 8.793E+05 1.000E+00 1. QQOE+00 127 TEMPERATURE 2. 000E+01 RESIDENCE TIME 2.350E+02 AGITATION RATE SUPERSATURATION 2.466E+03 9.500E-01 POP. AT, 0 4.560E+07 WEIGHT X 1. 424E-01 SCREEN SIZE AD S i CUMULATIVE HEIGHT 1.060E-01 2.665E+01 7.800E-02 1. 500E-01 4.125E+01 1. 81 IE-01 1. 800E-01 7.515E+01 1.041E-01 2. 500E-01 9.463E+01 2. 870E-G2 2. 970E-01 1.000E+O2 CRYSTAL SIZE POPULATION DENSITY CRYSTAL_SIZE POPULATION,PENS 1.030E-01 1.2771*07 1.081E-01 1.117E+07 1. 133E-01 9.824E+06 1. 184E-01 8.689E+06 1.235E-01 7.723E+06 1.286E-01 6..897E+06 1.337E-01 6.185E+06 1.388E-01 5.569E+06 1.-43 8 E-01 5.0 32E+06 1. 489E-01 4.651E+06 1.540E-01 4.610E + 06 1.590E-01 4.527E+06 1.641E-Q1 4. 414E+06 1.692E-01 4.282E+06 1.742E-01 4.137E+06 1.793E-01 3.941E+06 1.843E-01 3.59 2E+06 1.894E-01 3.283E+06 1.944E-01 3.008E+06 1.994E-01 2.763E+06 2.045E-01 2.543E+06 2.095E-01 2.346E+06 2.145E-01 2.169E+06 2.196E-01 2.0O9E+06 2.246E-01 1.8651+06 2.296E-01 1.734E+ 06 2.347E-01 1.614E+06 2.397E-01 1.506E+06 2.447E-01 1.407E+06 2.498E-01 1.314E+06 2.54 8E-01 1.221E + 06 2.598E-01 1.136E+06 2.648E-01 1.058E+06 2. 698E-01 9.876E+05 ,2.749E-01 9.228E+05 2.799E-01 8.633E+05 2.849E-01 8.088E+05 1.0O0E+00 1.000E+O0 128 TEMPERATURE BBS IDE MC E~TIfl£ a G I T T i l o i ~ i " & T E SUPESS ATUSAilON 2.OOOE+01 2.350E+02 2.466E+03 8.230E-G1 POP. AT 0 1.940E+08 iUIGHT_X SCEEEN SIZE AD % CUMULATIVE HEIGHT 1.141E+00 1.060E-01 5.933E+01 6.744E-01 1.500E-Q1 9.441E+01 4. 720E-02 1.800E-01 9.686E+01 3.810E-02 2.500E-01 9.885E + 01 2.220E-02 2.970E-01 1.000E+02 CBYSTAL SIZE POPULATION DENSITY CRYSTAL SIZE POPULATION DENSITY 1.Q30E-01 2.897E+07 1.081E-01 2. 544E+07 1. 133E-01 2.247E+07 1.184E-01 1. 995E+07 1 .'23 5 E-01 1.779E+07 1.286E-01 1. 593E+07 1.337E-01 1.433E+07 1.388E-01 1. 293E+07 1.438E-01 1. 171E+07 1. 489E-01 1. 056E+07 1.540E-01 9.279E+06 1.590E-01 8. 187E+06 1.641E-01 7.255E+06 1.692E-01 6. 453E+06 1.742E-01 5.761E+06 1.793E-01 5. 157E+06 1.843E-01 4.622E+06 1.894E-01 4. 155E+06 1.944E-01 3.746E+06 1.994E-01 3. 386E+06 2.045E-01 3. 069 E+06 2.095E-01 2. 788E+06 2. 145E-01 2.539E+06 2.196E-01 2. 318E+06 2.246E-01 2. 120E+06 2.296E-01 1. 943E+ 06 2.347E-01 1.784E + 06 2.397E-01 1.642E+06 2.447E-01 1. 513E+06 2.498E-01 1. 397E+06 2.548E-01 1.291E+06 2.598E-01 1. 19 6E+06 2.648E-01 1. 109E+06 2. 698E-01 1. 030E+ 06 2.749E-01 9.581E+05 2.799E-01 8. 923E+05 2.849E-01 8. 320E+05 1.000E+00 1. 000E+00 TEMEEEATUJE RESIDENCE TIME 2.000E+OI 2.350E + C2 POP. , AT 0 1.589E+08 129 " AGIT ATION~ R ATE SUPERS AT U RATI ON 2.466E+03 7.G00E-01 HEIGHT X 8. 050E-01 7.618E-01 1. 106E-01 6.280E-02 3.530E-02 SCREEN SIZE AD 1.060E-01 1.500 E-01 1.800E-01 2. 500 E-01 2.970E-01 CRYSTAL SIZE POPULATION DENSITY , CUMULATIVE HEIGHT 4.534E+01 8.825E+01 9.447E+01 9.801E+01 1.000E+02 CRYSTAL_SIZE POPULATION DENSITY 1.030 E-0 1 2.348E+07 1.081E-01 2.140E+07 1. 133E-01 1.95IE*07 1.184E-01 1.780E+07 K235E-01 1.625E+07 1.286E-01 1.486E+07 1.337E-01 1.362E+07 1.388E-01 1..249E+07 1.438E-01 1. 149E+07 1.489E-01 1. 049E+07 1.540E-01 9.280E+06 1.590E-01 8. 248E+06 1.641E-01 7.360E+06 1.692E-01 6.593E+06 1.742E-01 5.927E+06 1.793E-01 5. 336E+06 1.843E-01 4.788E+06 1.894E-01 4.3Q9E+ 06 1.944E-01 3.890E+06 1.994E-01 3. 520E+06 2.045E-O1 3. 194E+06 2. 095E-01 2.906E+06 2. 145E-01 2.649E+06 2.196E-01 2.421E+06 2.246E-01 2.217E+06 2. 296E-01 2.034E+06 2.347E-01 1.870E+Q6 2.397E-01 1.723E+06 2.447E-01 1.590E+06 2.498E-01 1.469E+06 2.548E-01 1.360E+06 2.598E-01 1.260E+06 2.648E-01 1. 170E+06 2.698E-01 1.087E+06 2.749E-0 1 1.012E+06 2.799E-01 9.436E+05 2.849E-01 8.807E+05 1.000E+00 1.000E+00 130 TEMPERATURE RESIDENCE TIME AGITATION RATE SUPERSATURATION 2. C00E+01 2. 350E+02 I.926E+03 9.500E-01 POP. AT 0 4.507E+07 WEIGHT X SCREEN SIZE AD 9 5 CUMULATIVE WEIGHT 1. 339E-01 1. 060E-01 2.140E+01 1.405E-01 1.500 E-01 4.386E+01 2. 593E-01 1. 800E-01 8.531E+01 6.730E-02 2. 500E-01 9.607E + 01 2.460E-02 2. 970E-01 1.000E+02 CRYSTAL SIZE POPULATION DENSITY CRYSTAL SIZE POPULATION DEN! 1.030E-01 1.073E+O7 1.081E-01 9. 886E+06 1. 133E-01 9.08 9E+06 1.184E-01 8..351E+06 1.235E-01 7.672E+06 1.286E-01 7.053E+06 1.337E-01 6.490E+06 1.388E-01 5.978E+06 1.438E-01 5.514E+06 1. 489E-01 5.194E+06 1.540E-01 5.237E+06 1.590E-01 5.210E+06 1.641E-01 5. 135E+06 1.692E-01 5.024E+06 1.742E-01 4.889E*06 1.793E-01 4.672E+06 1.843E-01 4. 218E+06 1.894E-01 3 . 82 0E+ 06 1.944E-01 3.469E+06 1.994E-01 3. 159E+06 2.045E-01 2.884E+06 2.095E-01 2.639E+06 2. 145E-01 2.420E+06 2.196E-01 2.225E+06 2.246E-01 2.Q49E*Q6 2. 296E-01 1.891E+06 2.347E-01 1.748E+06 2.39 7E-01 1.619E+06 2.447E-01 1.502E+06 2.498E-01 1.395E+06 2.548E-01 1.294E+06 2.598E-01 1.202E+06 2.648E-01 1. 118E+06 2.698E-01 1.042E+06 2.749E-01 9.716E+05 2.799E-01 9.076E+05 2.849E-01 8. 489E+05 1.000E+00 1.000E+00 TEMPERATURE 2. COOE+01 RESIDENCE TIME 2.350E+02 . 13J AGITATION RATE ~ SUPERS ATORATION 1.926E+03 8-230 E-01 POP. AT 0 1.610E+08 WEIGHT, X 8.907E-01 7.979E-01 7.260E-02 6.950E-02 2.730E-02 SCREEN SIZE AD 1.060E-01 1.500 E-01 1.800E-01 2. 500 E-01 2.970E-01 CRYSTAL SIZE POPULATION DENSITY CRYSTAL^SI CUMULATIVE WEIGHT 4.794E+01 9.088E+Q1 9.479E+01 9.853E+01 1.00QE+02 B ZE POPULATION DENSITY 1.030E-01 2. 355E+07 1. 081E-01 2.136E+07 1..1332-01 1.938E + 07 1.184E-01 1.762E+07 1.235E-01 1.604E+07 1.286E-01 1.463E+07 1.337E-01 1.337E+07 1.388E-01 1.-225E+07 1.438E-01 1. 124E+07 1. 489E-01 1.024E+07 1.540E-01 9.018E*06 1.590E-01 7.980E+06 1.641E-01 7.090E*06 1.692E-01 6.323E+06 1.742E-01 5.66 0E+06 1.793E-01 5.080E+06 1.843E-01 4.559E+06 1.894E-01 4.103E+06 1.944E-01 3.704E+06 1.994E-01 3. 353E+06 2.045E-01 3.0 43E+06 2.095E-01 2. 769E+06 2. 145E-01 2.525E+06 2.196E-01 . 2. 307E+06 2.246E-01 2. 113E+G6 2.296E-01 1. 939E+06 2.347E-01 1.783E+06 2.397E-01 1.643E+06 2.447E-01 1.516E+06 2.498E-01 1.401E+06 2.548E-01 1.296E+06 2.598E-01 1. 200E+06 2.648E-01 1. .1142*06 2.698E-01 1 . 035E+06 2.749E-01 9.627E+05 2.799E-01 8.968E+05 2.849E-01 8. 36 6 E+05 1.000E+00 1.000E+00 132 TEMPERATURE 2 . CCOE+01 R E S I D E N C E T I M E 2 . 3 5 0 E + 0 2 A G I T A T I O N R A T E S U P E R S A T U B A T I O N 1 . 9 2 6 E + 0 3 7 . 0 0 0 E - 0 1 P O P . AT 0 1 . 8 4 9 E + 0 7 W E I G H T X S C R E E N SIZE AD S i C U M U L A T I V E W E I G H T 6. 1 8 0 E - 0 2 1. 0 6 0 E - 0 1 1. 0 3 4 E + 0 1 1. 1 1 3 E - 0 1 1.500E-01 2 . 8 9 8 E + 0 1 2 . 3 1 1 E - 0 1 1. 8 0 0 E - 0 1 6 . 7 6 6 E + 0 1 1 . 0 2 6 E - 0 1 2 . 500E-01 8.483E+01 9 . 0 6 0 E - 0 2 2 . 9 7 0 E - 0 1 1 . 0 0 0 E + 0 2 C R Y S T A L S I Z E P O P U L A T I O N D E N S I T Y C R Y S T A L _ S I Z E P O P U L A T I O N D E N f 1 . 0 3 0 E - 0 1 5 . 1 7 1 E + 0 6 1 . 0 8 I E - 0 1 5 . 1 2 7 E + 0 6 1. 1 3 3 E - 0 1 4 . 9 8 4 E + 0 6 1.. 18 4 E - 0 1 4.783E+06 1 . 2 3 5 E - 0 1 U. 5 5 2 E + 0 6 1 . 2 8 6 E - 0 1 4.3Q8E+06 1 . 3 3 7 E - 0 1 4 . 0 6 2 E + 0 6 1 . 3 8 8 3 - 0 1 3. 8 2 0 E * 0 6 1 . 4 3 8 E - 0 1 3. 587E+06 1. 4 8 9 E - 0 1 3 . 4 6 4 E * Q 6 1 . 5 4 0 E - Q 1 3 . 6 7 5 E + 0 6 1 . 5 9 0 E - 0 1 3 . 7 9 6 E + 0 6 1 . 6 4 1 E - 0 1 3 . 8 4 9 E + 0 6 1 . 6 9 2 E - 0 1 3.853E+06 1 . 7 4 2 E - 0 1 3 . 8 1 9 E + 0 6 1.793E-01 3 . J 0 1 E + 0 6 1.843E-01 3 . 3 7 2 E * 0 6 1 . 8 9 4 E - 0 1 3 . 0 8 0 E + 0 6 1 . 9 4 4 E - 0 1 2 . 8 2 1 E + 0 6 1 . 9 9 4 E - 0 1 2.590E+06 2 . 0 4 5 E - 0 1 2. 384E+06 2.095E-01 2 . 1 9 8 E + 0 6 2 . 1 4 5 E - 0 1 2 . 0 3 2 E + 0 6 2 . 1 9 6 E - 0 1 1 . 8 8 2 E + 0 6 2 . 2 4 6 E - 0 1 1.746E+06 2 . 2 9 6 E - 0 1 1 . 6 2 2 E « - 0 6 2 . 3 4 7 E - 0 1 1 . 5 1 1 E + 0 6 2 . 3 9 7 E - 0 1 1. 4 0 9 E + 0 6 2 . 4 4 7 E - 0 1 1 . 3 1 6 E + 0 6 2 . 4 9 8 E - 0 1 1 . 2 3 2 E + 0 6 2 . 5 4 8 E - 0 1 1 . 1 5 9 E + 0 6 2 . 5 9 8 E - 0 1 1 . 0 9 2 E + 0 6 2 . 6 4 8 E - 0 1 1 . 0 3 0 E * 0 6 2 . 6 9 8 E - 0 1 9 . 7 2 4 E + 05 2 . 7 4 9 E - 0 1 9.192E+05 2 . 7 9 9 E - 0 1 8.698E+05 2 . 8 4 9 E - 0 1 8. 239E+05 1 . 0 0 0 E + 0 0 1 . 0 0 0 E + 0 0 T E J P E B A T J R E 2. 0COE+O1 B E S I D E N C B T I M E 2. 3 5 0 E + 02 133 A G I T A T I Q N~IAT E S U P E R S A I U B A T I Q N 1.260E+Q3 9 . 5 0 0 E - 0 1 POP. AT 0 2 . 9 3 1 E + 0 6 WEIGHT X 2. 8 6 0 E - 0 2 3 . 4 0 0 E - 0 2 1. 6 5 6 E - 0 1 2. 5 2 1 E - 0 1 1. 4 7 4 E - 0 1 S C R E E N S I Z E AD 1 . 0 6 0 E - 0 1 1 . 5 0 0 E - 0 1 1 . 8 0 0 E - 0 1 2. 5 0 0 E - 0 1 2 . 9 7 0 E - 0 1 C B Y S T A L S I Z E P O P U L A T I O N D E N S I T Y % C U M U L A T I V E WEIGHT 4 . 5 5 6 E + 0 Q 9 . 9 7 3 E + 0 0 3 . 6 3 5 E + 0 1 7 . 6 5 2 E + 0 1 1 . 0 0 0 E + 0 2 C B Y S T A L _ S I Z E P O P U L A T I O N D E N S I T Y 1 . 0 3 0 E - 0 1 2. 1 0 0 E + 0 6 1 . 0 8 1 E - 0 1 1.962E+06 1. 1 3 3 E - 0 1 1 . 8 2 4 E + 0 6 1 . 1 8 4 E - 0 1 1.691E+06 1 . 2 3 5 E - 0 1 1. 5 6 6 E + 0 6 1 . 2 8 6 E - 0 1 1 . 4 4 9 E + 0 6 1 . 3 3 7 E - 0 1 1 . 3 4 0 E + 0 6 1 . 3 8 8 E - 0 1 1 . 2 4 1 E + 0 6 1 . 4 3 8 E - 0 1 1 . 1 4 9 E + 0 6 1. 4 8 9 E - 0 1 1 . 1 4 5 E + 0 6 1 . 5 4 0 E - 0 1 1 . 4 0 7 E + 0 6 1 . 5 9 0 E - 0 1 1 . 5 9 3 E + 0 6 1 . 6 4 1 E - 0 1 1.7 20 E+06 1 . 6 9 2 E - 0 1 1..802E+06 U 7 4 2 E - 0 1 1 . 8 5 0 E + 0 6 1 . 7 9 3 E - 0 1 1 . 8 5 6 E + 0 6 1 . 8 4 3 E - 0 1 1 . 7 8 9 E + 0 6 1 . 8 9 4 E - 0 1 1 . 7 2 2 E + 0 6 1 . 9 4 4 E - 0 1 1.654E + 0 6 1 . 9 9 4 E - 0 1 1 . 5 8 8 E + 0 6 2 . 0 4 5 E - 0 1 1 . 5 2 2 E + 0 6 2 . 0 9 5 E - 0 1 1 . 4 5 8 E + 0 6 2. 1 4 5 E - 0 1 1 . 3 9 6 E + 0 6 2 . 1 9 6 E - 0 1 1 . 3 3 7 E+06 2 . 2 4 6 E - 0 1 1 . 2 7 9 E+06 2 . 2 9 6 E - 0 1 1 . 2 2 4 E + 0 6 2 . 3 4 7 E - 0 1 1 . 1 7 2 E + 0 6 2 . 3 9 7 E - 0 1 1. 1 2 2 E + 0 6 2 . 4 4 7 E - 0 1 1 . 0 7 4 E + 0 6 2 . 4 9 8 E - 0 1 1 . 0 2 7 E + 0 6 2 . 5 4 8 E - 0 1 9 . 7 9 3 E + 0 5 2 . 5 9 8 E - 0 1 . 9 . 3 4 1 E + 0 5 2 . 6 4 8 E - 0 1 8 . 9 1 6 E + 0 5 2 . 6 9 8 E - 0 1 8 . 5 1 5 E + 0 5 2 . 7 4 9 E - 0 1 8. 1 3 7 E + 0 5 2 . 7 9 9 E - 0 1 7 . 7 8 0 E + 0 5 2 . 8 4 9 E - 0 1 7 . 4 4 3 E + 0 5 1 . 0 0 0 E + 0 0 1 . 0 0 0 E + 0 0 TEHJPEJ1T5JE 2. 0C0E+G1 R E S I D E N C E T I M E 2 . 3 5 0 E + 0 2 I3jt A G I T A T I O N R A T E I D J E I I A T O R A T I O N 1.260B+03 8 . 2 3 0 E - 0 1 P O P . AT 0 6 . 9 8 2 E + 0 7 WEIGHT X 3 . 6 9 0 E - 0 1 2 . 1 8 3 E - 0 1 4 . 4 5 9 E - 0 1 3 . 9 2 0 B - 0 2 2 . 0 2 0 E - 0 2 S C R E E N S I Z E AD 1 . 0 6 0 E - 0 1 1. 500 E - 0 1 1 . 8 0 0 E - 0 1 2 . 5 0 0 E - 0 1 2 . 9 7 G E - 0 1 C R Y S T A L S I Z E P O P U L A T I O N DENSITY i C O M U L A T I V E WEIGHT 3 . 3 7 7 E + 0 1 5 . 3 7 5 E + 0 1 9 .456E+01 9 . 8 1 5 E + 01 1.0Q0E+02 C R Y S T A L S I Z E P O P U L A T I O N D E N S I T Y 1 . 0 3 0 E - 0 1 1 . 5 3 5 E * 0 7 1. 08 I E - 0 1 1 .348E+ 07 1 . 1 3 3 E - 0 1 1 .191E+07 1 . 1 8 4 E - 0 1 1. 057E+07 1 . 2 3 5 E - 0 1 9 . 4 2 8 E + 0 6 1 . 2 8 6 E - 0 1 8 . 4 4 5 E + 0 6 1 . 3 3 7 E - 0 1 7 . 5 9 4 E + 0 6 1 .38 8 E - 0 1 6 . 8 5 4 E + 0 6 1 . 4 3 8 E - 0 1 6 . 2 0 8 E + 0 6 1 . 4 8 9 E - 0 1 5 . 7 3 5 E + 0 6 1 . 5 4 0 E - 0 1 5 . 6 3 5 E + 0 6 1 . 5 9 0 E - 0 1 5 . 495E+06 1 . 6 4 1 E - 0 1 5 . 3 2 8 E + 0 6 1 . 6 9 2 E - 0 1 5 . 1 4 4 E + 0 6 1 . 7 4 2 E - 0 1 4 . 9 5 1 E + 0 6 1 . 7 9 3 E - 0 1 4 . 6 8 8 E + G 6 1 . 8 4 3 E - 0 1 4. 207E+06 1 . 8 9 4 E - 0 1 3 .786E+06 1 . 9 4 4 E - 0 1 3 . 4 1 8 E + G 6 1 . 9 9 4 E - 0 1 3 . 0 9 3 E + 0 6 2 . 0 4 5 E - 0 1 2 . 8 0 7 E + 0 6 2 . 0 9 5 E - 0 1 2 . 5 5 4 E + 0 6 2 . 1 4 5 E - 0 1 2 . 3 2 8 E + 0 6 2 . 1 9 6 E - 0 1 2 . 128E+06 2 . 2 4 6 E - 0 1 1 .949E+06 2 . 2 9 6 E - 0 1 1 . 788E+06 2 . 3 4 7 E - 0 1 1 . 6 4 4 E * 0 6 2 . 3 9 7 E - 0 1 1 .514E+06 2 . 4 4 7 E - 0 1 1 .397E+06 2 . 4 9 8 E - 0 1 1 .291E+06 2 . 5 4 8 E - 0 1 1 .195E+06 2 . 5 9 8 E - 0 1 1.107E+06 2 . 6 4 8 E - 0 1 1.Q28E+06 2 . 6 9 8 E - 0 1 9 . 5 5 2 E + 0 5 2 . 7 4 9 E - 0 1 8 . 8 9 1 E + 0 5 2 . 7 9 9 E - 0 1 8 . 2 8 6 E + 0 5 2 . 8 4 9 E - 0 1 7 . 7 3 3 E * 0 5 1 .000E+00 1 .000E+O0 135 TEM FERATURE RESIDENCE TIME AGITATION RAT £ SUPERSATUBATION 2. OCOE+01 2. 350E+02 1.260E+03 7.000E-01 POP. - AT 0 2.173E+06 WEIGHT X SCREEN SIZE AD % , CUMULATIVE WEIGHT 2. 57GE-02 1. 060E-01 4. 116E+00 2.090E-02 1. 500E-01 7. 463E+00 9.870E-02 1. 800E-01 2. 327E+01 2.220E-01 2. 500E-01 5. 882E+01 2.571E-01 2. 970E-01 1. OOOE+02 CRYSTAL SIZE POPULATION DENSITY CJXSTAL^SIZE POPULATION DENS 1.030E-01 2.039E+06 1. 081E-01 L833E+ 06 1. 133E-01 1.652E+06 1.184E-01 1 ..492E+06 1.235E-01 1. 35 2 E+06 1.286E-01 1.227E+06 1.337E-01 1.117E+06 1.388E-01 . 1.019E+06 1.438E-01 9.325E+05 1. 489E-01 9.061E+05 1.540E-01 1.054E+06 1.590E-01 1. 156E+06 1.641E-01 1.222E+06 1.692E-01 1.262E+06 1. 742E-01 1.281E+06 1.793E-01 1.284E+06 1.843E-01 1-2-7 2 £+06 1.894E-01 1.252E+06 1.944E-01 1.226E+06 1.994E-01 1.196E+06 2.045E-01 1. 16 4E+06 2.095E-01 1. 129E+06 2. 145E-01 1.094E+06 2.196E-01 1.058 E+06 2.246E-01 1.022E+06 2.296E-01 9.861E+05 2.347E-01 9.509E+05 2.397E-01 9.165E+05 2.447E-01 8.830E+05 2. 498E-01 8.557E+05 2.548E-01 8.482E+05 2.598E-01 8.381E+05 2.64 8E-01 8.259E+05 2.698E-01 8.122E+05 2.749E-01 7.973E+05 2.799E-01 7.814E+05 2.849E-01 7. 6 48 E +05 1.QO0E+00 1.000E+00 T E M P E R A T U R E 2.000E+Q1 PGP. ^ AT 0 136 " R E S I D E N C E T I M I A G I T A T I O N ~ R A T E SUPERS ATU RATI ON 3 . 8 0 0 E + 02 2 . 4 6 6 E + 0 3 9 . 5 0 0 E - 0 1 5.550E+07 WEIGHT X 2..752E-01 4.519E-01 4.070E-01 1.793E-01 1.650E-02 SCREEN SIZE AD 1. Q60E-01 1.500 £-01 1.800E-01 2. 500E-01 2.970E-01 CRYSTAL SIZE POPULATION DENSITY % CUMULATIVE WEIGHT 2.069E+01 5.467E+01 8.528E+01 9.876E+01 1.000E+02 CRYSTAL jSIZE POPULATION DENSITY 1.030E-01 1.0621*07 1.081E-01 1 .037E+07 1. 133E-01 9.970E+06 1. 184E-01 9.491E+06 1.235E-01 8.975E+06 1.286E-01 8.450E+06 1.337E-01 7.933E+06 1.388E-01 7.434E+06 1.438E-01 6.960E+06 1.489E-01 6.542E+06 1.540E-01 6.246E+06 1.590E-01 5.948E+06 1.641E-01 5.654E+06 1.692E-01 5.368E+06 1.742E-01 5.092E+06 1.793E-01 4.781E+06 1-843E-01 4. 326E+06 1.894E-01 3.927E+06 1.944E-01 3.574E+06 1.994E-01 3.261E+06 2.045E-01 2.98 3E+06 2.095E-01 2.735E+06 2. 145E-01 2.514E+06 2.196E-01 2.315E+06 2..246E-01 2. 136E+06 2.296E-01 1.975E+06 2.347E-01 1.830E+06 2.397E-01 1.698E+06 2.447E-01 1.578E+06 2.498E-01 . 1.467E* 06 2.54 8E-01 1.356E+06 2.598E-01 1.256E+06 2.648E-01 1. 165E+06 2. 698E-01 1.082E+ 06 2.749E-01 1.006E+06 2.799E-01 9. 373E+05 2.849E-01 8.74 2E+0 5 1.OOOE+OO 1.000E+00 137 TEMPEBATUBE 2. OOOE+01 BESIDENCB TIKE 3.800E+02 AGITATION BATE SO PEBS ATPJBATION 2.466E+03 8.230E-01 POP. AT 0 ~2.158E+08 H EI G_HT_ jC SCBEEN SIZE AD ! % CUMULATIVE HEIGHT 1.435E+00 1. 060E-01 6. 357E+01 . 7.460E-01 1.500 E-01 9. 662E+01 2. 840E-02 •1. 800E-01 9. 788E+-Q1 2.250E-02 2. 500E-01 9. 887E+01 2.540E-02 2. 970E-01 1. 000E+02 CBYSTAL SIZE POPULATION DENSITY CBYSTAL SIZE POPULATION DEN; 1.030E-01 3. 200E+07 1.081E-01 2.790E+07 1. 133E-01 2.447E+07 1.184E-01 2. 159E+07 1.235E-01 1.915E+07 1.286E-01 1.7G7E+07 1.337E-01 1.528E*07 1.388E-01 1. 374E+07 1.438E-01 1.239E+07 1. 48 9E-01 1.114E*07 1.540E-01 9.766E+06 1.590E-01 8. 599E+06 1.641E-01 7.60 3E+06 1.692E-01 6.749E+06 1.742E-01 6.012E+06 1.793E-01 5.373E+06 1.843E-01 4.8HEf06 1.894E-01 4. 32 2 E* 06 1.944E-01 3.894E+06 1.994E-01 3. 517E+06 2.045E-01 3. 18 5E+06 2.095E-01 2.892E+06 2. 145E-01 2-632E+06 2.196E-01 2, 401E+06 2.246E-01 2.194E+06 2.296E-01 2. 010E+06 2.347E-01 1.84 4E+06 2.397E-01 1.695E+06 2.44 7E-01 1.562E+06 2.498E-01 1.441E+06 2.548E-01 1.332E + 06 2.598E-01 1.233E+06 2.64 8E-01 1. 144E+06 2.698E^01 1.062E+06 2.749E-01 9.880E+05 2.799E-01 9. 201E+05 2.849E-01 8.580E+05 1.000E+00 1.000E*00 TEMPERATURE 2.000E+ 01 138 RESIDENCE TIME AGITATION RATE SUPERSATURATION 3.800E+02 2.466E+03 7.000E-01 POP. . AT 0 1.082E+08 WEIGHT X 5. 046E-01 8.462E-01 2. 358E-01 1.298E-01 2, 770E-02 SCREEN SIZE AD 1.060E-01 1.500 E-01 1. 800E-01 2. 500 E-01 2.970E-01 CRYSTAL SIZE POPULATION DENSITY % CUMULATIVE WEIGHT 2.893E+01 7.745E+01 9.097E+01 9.841E+01 1.000E+02 CEYSTAL_SIZE POPULATION DENSITY 1.030E-01 1.585E+07 1.081E-01 1.554E+ 07 1. 133E-01 1.497E+07 1.184E-01 1. 428E+07 1.235E-01 1.352E+07 1.286E-01 1.275E+07 1.337E-01 1.198E+07 1.388E-01 1.124E+07 1.438E-01 1.053E+07 1. 489E-01 9.773E+06 1.540E-01 8.796E+06 1.590E-01 7. 946E+06 1.641E-01 7.20 2E+O6 1.692E-01 6. 548E+06 1.742E-01 5.972E+06 1.793E-01 5.441E+06 1.843E-01 4.898E+06 1.894E-01 4. 422E+06 1.944E-01 4.003E+06 1.994E-01 3.635E+06 2.045E-01 3. 308E+06 2.095E-01 3. 018E+06 2. 145E-01 2.760E+06 2.196E-01 2. 530E+06 2.246E-01 2. 324E+06 2.296E-01 2. 138E+06 2.347E-01 1.972E+06 2.397E-01 1.821E+06 2.447E-01 1.685E+06 2.498B-01 1. 561E* 06 2.548E-01 1.444E+06 2.598E-01 1.338E+06 2.648E-01 1.241E+06 2.698E-01 1. 153E+06 2.749E-01 1.073E+06 2.799E-01 1..000E+06 2.849E-01 9. 329E+05 1.000E+00 1.0OOE+00 139 TEMPEBATUBE 2. 0COE+O1 RESIDENCE TIME 3.800E+02 AGITATION BATE 1.926E+03 SUPERS ATUBATION 9.500E-01 POP. ..AT 0 1.773E+08 WEIGHT X SCREEN SIZE AD % CUMULATIVE WEIGHT 9. 037E-01 1.060E-01 5. 068E+01 7. 132E-01 1.500 E-01 9. 068E+01 1. 398E-01 1. 800E-01 9. 852E+01 1.820 E-02 2. 500E-01 9. 955E+01 8 . 100E-03 2. 970E-01 1. 000E+02 CRYSTAL SIZE POPULATION DENSITY CBYSTAL SIZE POPULATION DEN£ 1.030E-01 2.630E+07 1.081E-01 2. 358E+07 1. 13 3 E-01 2.121E+07 1.184E-01 1. 913E+07 1.235E-01 1.730 E+07 1.286E-01 1. 568E+07 1,33 7 E-01 1.426E+07 1.388E-01 1. 300E+07 1-4388-01 1. 188E+07 1.489E-01 1. 080E+07 1.540E-01 9.585E+06 1.590E-01 3* 541E+06 1.641E-01 7.640E+06 1.692E-01 6. 860E+06 1.742E-01 6.181E+06 1.793E-01 5. 574E+06 1.843E-01 4. 991 E+06 1.894E-01 4. 4 84E+ 06 1.944E-01 4.03 9E+06 1.994E-01 3. 649E+06 2.045E-01 3.305E+06 2.095E-01 3. 001E+06 2. 145E-01 2.731E+06 2.196E-01 2. 4.91 E+06 2.246E-01 2. 277E+06 2.296E-01 2. 085E+06 2.347E-01 1.913E+06 2.397E-01 1. 759E+06 2.44 7E-01 1.620E+06 2.498E-01 1. 495E+06 2.548E-01 1.381E+06 2.598E-01 1. 278E+06 2.64 8E-01 1. 18 4E+06 2.698E-01 1. 099E+06 2.749E-01 1.021E+06 2.799E-01 9. 504E+05 2.849E-01 8. 856E+05 1.000E+00 1. OOOE+00 TEHPEBATDEE 2. 0C0E+01 B E S I D E N C E T I M E 3 . 8 0 0 E + 0 2 1 AO 'AGITATIQN~JATE SUPJ I s ATOEATIOJ 1.926E+03 8. 230E-G1 POP. AT 0 1.977E+08 BEIGHT_X 1. 281E+00 SCREEN SIZE AD ? % CUMULATIVE WEIGHT 1. 060E-01 5. 842E+01 8.215E-01 1.500 E-01 9. 589E+01 4. 620E-02 1. 800E-01 9. 800E+01 2.470E-02 2. 500E-01 9. 912E+01 1.920E-02 2. 970E-01 1. 000E+02 CRYSTAL SIZE POPULATION DENSITY CBYSTAL SIZE POPULATION DENS 1.030E-01 2.88 9E+07 1.081E-01 2. 551E+07 1. 133E-01 2.264E+07 1.184E-01 2.. 018E+07 1.235E-01 1.806E+07 1.286E-01 1 . 623E+07 1.337E-01 1.464E + 07 1.388E-01 1. 325E+07 1.438E-01 1. 203E+07 1. 489E-01 1-. 086E+07 1.540E-O1 9.53 8E+06 1.590E-01 8. 411E+06 1.641E-01 7.447E+06 1.692E-01 6. 620E+06 1.742E-01 5.906E+06 1.793E-01 5. 284E+06 1.843E-01 4.733E+06 1.894E-01 4. 252E+06 1.944E-01 3.830E+06 1.994E-01 3. 461E+06 2.045E-01 3. 134E+06 2.095E-01 2. 846E+06 2. 145E-01 2.590E+06 2.196E-01 2. 363E+06 2.246E-01 2. 160E+06 2.296E-01 1. 978E+06 2.347E-01 1.816E+06 2.397E-01 1. 669E+06 2.447E-01 1.538E+06 2.498E-01 1. 419E+06 2.548E-01 1.311E+06 2.598E-01 1. 214E+06 2.648E-01 1. 125E+06 2.698E-01 1. 045E+06 2.749E-01 9.716E+05 2.799E-01 9. 046E+05 2.849E-01 8.433E+05 1.0OOE+OO 1. 000E+00 2. 000E+01 RESIDENCE TIME 3.800E+02 m ~AGITATIOH~£ ATE 111111ATUEATI ON 1.926E+03 7.G0 0E-01 POP, AT 0 1.523E+08 WEIGHT X SCREEN SIZE AD ? I CUMULATIVE WEIGHT 8. 559E-01 1. 06OE-O1 4.398E+01 7.458E-01 1. 500 E-01 8.230E+01 1, 980E-01 1. 800E-01 9.247E+01 9.640E-02 2. 500E-01 9.743E+01 5.010E-02 2. 970E-01 1.000E+02 CBYSTAL SIZE POPULATION DENSITY CRYSTAL SIZE POPULATION DENS 1,030E-01 2. 399 E+07 1.Q81E-01 2. 170E+G7 •1. 133E-01 1.965E+G7 1.184E-01 1. 783E+07 1.235E-01 1.621E+07 1.286E-01 1.477E+07 1.3 37E-01 1.348E+07 1.388E-01 1. 233E+07 1.438E-01 1. 131 E+07 1. 489E-01 1.032E+07 1.540E-O1 9.212E+06 1.590E-01 8.257E+06 1.641E-01 7. 4 28 E+06 1.692E-01 6. 706E+06 1.742E-01 6.074E+06 1.793E-01 5.503E+06 1.843E-01 4.944E+06 1.894E-01 4.454E* 06 1.944E-0 1 4.025E+06 1.994E-01 3.647E+06 2.045E-01 3.313E+06 2.095E-01 3.017E+G6 2. 145E-01 2.754E+06 2.196E-01 2. 519E+06 2.246E-01 2.310E+06 2.296E-01 2.122E+06 2.347E-01 1.953E+06 2.397E-01 1. 801E+06 2.447E-01 1.663E+06 2.498E-01 1.539E+06 2.548E-01 1.425E+06 2.598E-01 1.321E+06 2.648E-01 1.227E+06 2.698E-01 1. 142E+06 2.749E-01 1.064E+06 2.799E-01 9.920E+05 2.849E-01 9. 265E+05 1.000E+00 1.000E+00 TEMPERATURE 2. OCOE+01 RESIDENCE TIME 3.800E+02 I hi AGITATION BATE "si?PESS ATUBATION 1..260E+G3 9.500E-G1 POP. AT 0 9.812E+07 HEIGHT X 6. W E - 0 1 9.898E-01 2. 862E-01 2.577E-01 4. 710E-02 SCREEN SIZE AD 1.060E-01 1.500 E-01 1.800E-01 2.500E-01 2.970E-01 CRYSTAL SIZE PQ PU L AT IO M,_ DENSITY , CUMULATIVE HEIGHT 2.895E+Q1 7.344E+01 8.630E+01 9.788E+01 1.000E+G2 CRYSTAL SIZE POPULATION DENSITY 1.030E-01 1.544E+07 1.081E-01 1 .4 93 E+07 1. 133E-01 1.425E+07 1.184E-01 1.349E+07 1.235E-01 1. 270E+07 1.286E-01 1.191E+07 1.337E-01 1.115E+07 1.388E-01 1.042E+07 1.438E-01 9.737E+06 1.489E-01 9.023E+06 1.540E-01 8.122E+06 1.590E-01 7. 337E+06 1.641E-01 6.651E+06 1.692E-01 6.048E+06 1.742E-01 5.516E+06 1.793E-01 5. 030E+06 1.843E-01 4.544E+06 1.894E-01 4. 117E+06 1.944E-01 3.741E+06 1.994E-01 3. 409E+06 2.045E-01 3. 113E+06 2.09 5E-01 2. 850E+06 2. 145E-01 2.616E+06 2.196E-01 2.405E+06 2.246E-01 2.216E+06 2.296E-01 2.046E+06 2.347E-01 1.893E+06 2.397E-01 1.754E+06 2.447E-01 1.628E+06 2. 498E-01 1.512E+06 2.548E-01 1.399E+06 2.598E-01 1.297E+06 2.648E-01 1. 204E+Q6 2.698E-01 1. 120E+06 2.749E-01 1.042E+06 2.799E-01 9.719E+05 2.849E-01 9.072E+05 1.000E+00 1.0QQE+00 TEMJEJATU2E 2. QCOE+01 HESIDEMCE TIME 3.800E+02 AGITATION SAT E 1. 2-60 E* 03 1*3 "Illlis ATO1ATION 8.230E-01 POP. AT 0 1.978E*08 HEIGHT X 1.335E+00 6.370E-01 7, 150E-02 5.300E-02 4.550E-02 SCBEEN SIZE AD 1.060E-01 1. 500 E-01 1.800E-01 2.500E-01 2.970E-01 CBYSTAL SIZE POPDLATION DENSITY ; CUMULATIVE HEIGHT 6.233E+01 9.206E*01 9.540E+01 9.788E+01 1.000E+02 CBYSTAL SIZE POPULATION DENSITY 1.030E-01 3.062E+07 1.081E-01 2.657E+ 07 1.133E-01 2.321E+07 1.184E-01 2.040E+07 1.235E-01 1.804E*07 1.286E-01 1.603E+07 1.337E-01 1.431E+07 1.388E-01 1.283E+07 1.438E-01 1. 155E+07 1. 489E-01 1.Q37E+07 1.540E-01 9.123E+06 1.590E-01 8.064E+06 1.641E-01 7. 157E+06 1.692E-01 6.376E+06 1.742E-01 5.702E+06 1.793E-01 5. 112E+06 1.843E-01 4.583E+06 1.894E-01 4.121E+06 1.944E-01 3.717E+06 1.994E-01 3.361E+06 2.045E-01 3.048E+06 2.095E-01 2.770E+ 06 2. 145E-01 2.524E+06 2.196E-01 2.304E+06 2.246E-01 2. 108E*06 2.296E-01 1.933E+06 2.347E-01 1.776E+06 2.397E-01 1. 635E+06 2.447E-01 1.507E+06 2.498E-01 1.392E+06 2.54 8E-01 1.288E+06 2.598E-01 1. 19 4E+06 2.648E-01 1. 109E*06 2.698E-01 1.031E+06 2.749E-01 9.598E+05 2.799E-01 8.948E+05 2.849E-01 8.353E+05 1.000E+00 1.000E+00 144 TEMPEBATU.BE 2. OCOE+01 RESIDENCE TIME 3.800E + G2 AGITATION .BATE SUPERS AT ULBATI ON 1.26QE+03 7.G00E-01 POP. AT 0 8.386E*07 WEIGHT X 4.612E-01 SCREEN SIZE AD ? I CUMULATIVE WEIGHT 1. 060E-01 2.925E+01 5.336E-01 1.500E-01 6.310E+01 3. 055E-01 1. 800E-01 8.248E+01 2. 142E-Q1 2. 500E-01 9.607E+01 6.2C0E-02 2. 97OE-01 1.000E+02 CRYSTAL SIZE POPULATION DENSITY jCRYSTAL_SIZE POPULATION DENS 1.030E-01 1.559E+07 1.081E-01 1.452E+ 07 1.133E-01 1.346E+07 1.184E-01 1..246E+07 1.235E-01 1. 151E*07 1.286E-01 1.064E+O7 1.337E-01 9.830E+06 1.388E-01 9.089E+06 1.438E-01 8.411E+0 6 1. 489E-01 7.776E+06 1.540E-01 7.146E+06 1.590E-01 6. 582E+Q6 1.64 IE-01 6.074E+06 1.692E-01 5. 616E+06 1.742E-01 5.203E+06 1.793E-01 4.802E+06 1.843E-01 4.348E+06 1.894E-01 3. 94 8E+06 1.944E-01 3.595E+06 1.994E-01 3.282E+06 2.045E-01 3.00 3E+06 2.095E-01 2. 755E+06 2. 145E-01 2.533E+06 2.196E-01 2.334E+06 2.246E-01 2.154E+06 2.296E-01 1.993E+06 2.347E-01 1.84 6E+06 2.397E-01 1.714E+06 2.447E-01 1.59 4E+06 2.498E-01 1.482E+06 2.548E-01 1.375E+06 2.598E-01 1. 277E+06 2.648E-01 1. 188E+06 2.698E-01 1.107E+06 2.749E-01 1.032E + 06 2.799E-01 9.645E+05 2.849E-01 9.021E+05 1.000E+00 1.OOOE+00 TEMPERATURE 2. 5GOE+01 R E S I D E N C E T I M E 1 .700E+02 A G I T A T I O N R A T E 2 . 4 6 6 E + 0 3 J 4 5 SO PERS ATUEATION 9 . 5 0 0 E - 0 1 P O P . AT 0 2 . 2 7 3 E + 0 8 WEIGHT X 1. 451E+00 5 . 4 3 O E - 0 1 3 . 4 0 0 E - 0 2 4 . 1 1 G E - 0 2 3 . 3 5 0 E - 0 2 S C R E E N S I Z E AD 1 . 0 6 0 E - 0 1 1. 500 E - 0 1 1 . 8 0 0 E - 0 1 2. 500 E - 0 1 2 . 9 7 0 E - 0 1 C R Y S T A L S I Z E P O P U L A T I O N DENSITY ^ C U M U L A T I V E WEIGHT 6 . 9 0 1 E + 0 1 9 . 4 8 3 E + 0 1 9 .645E+01 9 . 8 4 1 E + G 1 1 .000E+02 CRYSTAL S I Z E P O P U L A T I O N DENSITY 1 . 0 3 0 E - 0 1 3 . 5 1 0 E+07 1 . 0 8 1 E - 0 1 3 . 012E+07 1. 1 3 3 E - 0 1 2 . 6 0 5 E + 0 7 1 . 1 8 4 E - 0 1 2 . 268E+07 1 . 2 3 5 E - 0 1 1 .988 E+07 1 . 2 8 6 E - 0 1 1 .753E+07 1 . 3 3 7 E - 0 1 1 . 553E+07 1 . 3 8 8 E - 0 1 1 . 3 8 3E+07 1 . 4 3 8 E - 0 1 1. 237E+07 1 . 4 8 9 E - 0 1 1 .105E+07 1 . 5 4 0 E - 0 1 9 . 6 9 3 E + 0 6 1 . 5 9 0 E - 0 1 8 . 5 4 0 E + 0 6 1 . 6 4 1 E - 0 1 7 . 5 5 6 E + 0 6 1 . 6 9 2 E - 0 1 6 . 7 1 1 E + 0 6 1 . 7 4 2 E - 0 1 5 . 9 8 3 E + 0 6 1 . 7 9 3 E - 0 1 5 . 3 5 0 E + 0 6 1 . 8 4 3 E - 0 1 4 . 7 9 5 E + 0 6 1 . 8 9 4 E - 0 1 4..310E+O6 1 .94 4 E - 0 1 3 . 8 8 6 E + 0 6 1 . 9 9 4 E - 0 1 3 . 512E+06 2 . 0 4 5 E - 0 1 3. 183E+Q6 2 . 0 9 5 E - 0 1 2 . 8 9 2 E + 0 6 2 . 145E-01 2 . 6 3 4 E + Q6 2 . 1 9 6 E - 0 1 2 . 4 0 4 E + 0 6 2 . 2 4 6 E - 0 1 2. 199E+06 2 . 2 9 6 E - 0 1 2 . 015E+06 2 . 3 4 7 E - 0 1 1 .851E+06 2 . 3 9 7 E - 0 1 1 .703E+06 2 . 4 4 7 E - 0 1 1 .569E+06 2 . 4 9 8 E - 0 1 1 .449E+06 2 . 5 4 8 E - 0 1 1 .340E+06 2 . 5 9 8 E - 0 1 1 .242E+06 2 . 6 4 8 E - 0 1 1. 152 E+06 2 . 6 9 8 E - 0 1 1 .071E+06 2 . 7 4 9 E - 0 1 9 . 9 6 1 E + 0 5 2 . 7 9 9 E - 0 1 9 . 2 8 2 E + 0 5 2 . 8 4 9 E - 0 1 8 . 6 5 9 E + 0 5 1 .000E+00 1.OOOE+00 2. 5C0E+01 fiESIDENCE TIHE 1.700E+Q2 AGITATION SAT E SUPERS AT U RATION 2.466E+03 8.230E-01 POP. AT 0 2.278E+08 HEIGHT X 8. C52E-01 SCREEN SIZE AD ? I CUMULATIVE HEIGHT 1. 06OE-01 7. 871E+01 1.582E-01 1..500E-0 1 9.417E+01 2. 480E-02 1, 800E-01 9. 660E+01 1.980E-02 2. 500E-01 9. 853E+01 1. 500E-02 2. 970E-01 1. 000E+02 CRYSTAL SIZE POPULATION DENSITY CRYSTAL_SIZE POPULATION DEN£ 1.030E-01 3. 651 E+07 1.081E-01 . 3.072E+ 07 1. 133E-01 2.608E+Q7 1.184E-01 2.233E+07 1.235E-01 1,9 25E+07 1.286E-01 1.671E+07 1.337 E-01 1.46 0E+07 1.388E-01 1.282E+07 1.438E-01 1. 132E+07 1. 489E-01 1.001E+07 1.540E-01 8.794E+06 1.590E-01 7.759E+06 1.641E-01 6.875E+06 1.692E-01 6.J15E+06 1.742E-01 5.459E+06 1.793E-01 4.887E+06 1.843E-01 4.379E+06 1.894E-01 3.937E+ 06 1.944E-01 3.549E+06 1.994E-01. 3.208E+06 2.045E-01 2.907E+06 2.095E-01 2.642E+06 2.145E-01 2.406E+06 2. 196 E-01 2.196E+G6 2.246E-01 2.008E+06 2.296E-01 1.841E+06 2.347E-01 1.690E+06 2.39 7E-01 1.. 55 5 E+06 2,447E-01 1. 433E+06 2.498E-01 1.323E+06 2.548E-01 1.224E+06 2.598E-01 1.134E+06 2.648E-01 1.05 2 E+06 2.698E-01 9.770E+05 2.749E-01 9.090E+05 2.799E-01 8.469E+05 2.84 9E-01 7.900E+05 1.000E+00 1.000E+00 T E N P E R A T Q B E 2. 5 C 0 E + 0 1 R E S I D E N C E T I M E 1 . 7 0 0 E + 0 2 147 "AGITATIQN~j AT E SU PEES ATU R A T I O N 2 . 4 6 6 E + 0 3 7.G0OE-O1 POP. AT 0 1 . 6 1 4 E + 0 8 WEIGHT X 4..747E - 0 1 2 . 2 8 4 E - 0 1 6. 2 2 0 E - 0 2 7 . 5 8 0 E - 0 2 5. 5 1 0 E - 0 2 S C R E E N S I Z E AD 1 . 0 6 0 E - 0 1 1. 5 0 0 E-0 1 1 . 8 0 0 E - 0 1 2. 5 0 0 E - 0 1 2 . 9 7 0 E - 0 1 C R Y S T A L S I Z E P O P U L A T I O N D E N S I T Y I C U M U L A T I V E WEIGHT 5 . 2 9 7 E + 0 1 7 . 8 4 5 E + 0 1 8 . 5 3 9 E + 0 1 9 . 3 8 5 E + 0 1 1 . 0 0 0 E + 0 2 C R Y S T A L S I Z E POPULATIQN D E N S I T Y 1 . 0 3 0 E - 0 1 2 . 8 1 8 E + 0 7 1 . 0 8 1 E - 0 1 2 . 4 4 6 E + 0 7 1. 1 3 3 E - 0 1 2 . 1 3 8 E + 0 7 1. 1 8 4 E - 0 1 1. 8 8 0 E + 0 7 1 . 2 3 5 E - 0 1 1 . 6 6 3 E + 0 7 1 . 2 8 6 E - 0 1 1 . 4 7 8 E + 0 7 1 . 3 3 7 E - 0 1 1 . 3 2 0 E + 0 7 1 . 3 8 8 E - 0 1 1. 183E+07 1 . 4 3 8 E - 0 1 1 . 0 6 5 E + 0 7 1 . 4 8 9 E - 0 1 . 9. 5 8 5 E + 0 6 1 . 5 4 0 E - 0 1 8 . 5 0 8 E + 0 6 1 . 5 9 0 E - 0 1 7. 5 8 3 E + 0 6 1 . 6 4 1 E - 0 1 6 . 7 8 6 E + 0 6 1 . 6 9 2 E - 0 1 6. 0 9 5 E + 0 6 1 . 7 4 2 E - 0 1 5 . 4 9 3 E + 0 6 1 . 7 9 3 E - 0 1 4. 9 6 1 E + 0 6 1 . 8 4 3 E - 0 1 4. 4 7 1 E + 0 6 1 . 8 9 4 E - 0 1 4. 0 4 1 E + 0 6 1 . 9 4 4 E - 0 1 3 . 6 6 3 E + 0 6 1 . 9 9 4 E - 0 1 3. 3 3 0 E + 0 6 2 . 0 4 5 E - 0 1 3 . 0 3 4 E + 0 6 2 . 0 9 5 E - 0 1 2 . 7 7 1 E + 0 6 2 . 1 4 5 E - 0 1 2 . 5 3 7 E + 0 6 2 . 1 9 6 E - 0 1 2 . 3 2 8 E + 0 6 2 . 2 4 6 E - 0 1 2. 1 4 1 E + 0 6 2 . 2 9 6 E - 0 1 1. 9 7 2 E + 0 6 2 . 3 4 7 E - 0 1 1 . 8 2 0 E + 0 6 2 . 3 9 7 E - 0 1 1. 6 8 3 E + G 6 2 . 4 4 7 E - 0 1 1 . 5 5 9 E + 0 6 2 . 4 9 8 E - 0 1 1. 4 4 7 E + 0 6 2 . 5 4 8 E - 0 1 1 . 3 4 6 E + 0 6 2 . 5 9 8 E - 0 1 1. 2 5 3 E + 0 6 2 . 6 4 8 E - 0 1 1. 1 6 9 E + 0 6 2 . 6 9 8 E - 0 1 1. 0 9 1 E + 0 6 2 . 7 4 9 E - 0 1 1 . 0 2 1 E + G 6 2 . 7 9 9 E - 0 1 9. 5 5 8 E + 0 5 2 . 8 4 9 E - 0 1 8 . 9 6 2 E + 0 5 1 . 0 0 0 E + 0 0 1. OOOE+00 2. 5C0E+01 BESIDEMCE IXME 1.700E + 02 _Jk8 i l l l l l iQiL IMJ SUPERS ATU RATION 1.926E+03 9.50GE-01 POP. AT 0 2.326E+08 HEIGHT X U447E+00 5.321E-01 4.130E-02 3.830E-02 3 .060E-02 SCREEN SIZE AD 1. Q60E-01 1.500 E-01 1.800E-01 2. 500 E-01 2.970E-01 CRYSTAL SIZE POPULATION DENSITY CRYSTAL_S CUMULATIVE HEIGHT 6.926E+01 9.473E + 01 9.670E*01 9.854E+01 1.000E+G2 L IZE POP OLA H O N DENSITY 1.030E-01 3.60 0E+07 1.081E-01 3.087E+07 1. 133E-01 2.668E+G7 1.184E-01 2.322E+G7 1.235E-01 2.034E+07 1.286E-01 1.792E+07 1.337E-01 1.587E+07 1.388E-01 1.413E+G7 1.438E-01 1. 263E+07 1. 489E-01 1 . 128E+07 1.540E-01 9.901E*06 1,590E-01 8. 730E+06 1.641E-01 7.728 E+06 1.692E-01 6.869E+G6 1.742E-01 6.127E+06 1.793E-01 5.481E+06 1.843E-01 4.912E+06 1.894E-01 4.415E+06 1.944E-01 3.980E+O6 1.994E-01 3.597E+06 2.045E-01 3. 260E+06 2.095E-01 2. 962E+06 2, 145E-01 2.697E+06 2.196E-01 2 . 461E+G6 2.246E-01 2.251E+06 2.296E-01 2.063E+06 2 .347E-01 1.894E+06 2.397E-01 1.743E+G6 2.447E-01 1.606E+06 2.498E--01 1. 483E+06 2.548E-01 1.371E+06 2.598E-01 1.270E+06 2.64 8E-01 1. 178E+06 2.698E-01 1.095E+06 2.749E-01 1.019E+06 2.799E-01 9.489E+05 2.849E-01 8 .852Er05 1.000E+00 1.000E+00 TEMPEBATORE 2. 500E+01 RESIDENCE TIME 1.700E+02 AGITATION BATE SO PEBS ATngATION 1.926E+03 8.230E-01 POP. AT 0 2.260E+08 HEIGHT X SCREEN SIZE AD 1 I CUMULATIVE HEIGHT 1.188E+00 1. 060E-01 7. 304E+01 3.350E-01 1.500 E-01 9. 365E+01 4. 850E-02 1. 800E-01 9. 663E+01 3.840E-02 2. 500E-01 9. 899E+01 1.640E-02 2. 970E-01 1. OOOE+02 CRYSTAL SIZE POPULATION DENSITY CRYSJCALj_SIZE POPULATION DENf 1.030E-01 3. 592E+07 1.081E-01 3.051E* 07 1.133E-01 2.614E+07 1.184E-01 2.257E+07 1.235E-01 1.962E+07 1.286E-01 1.716E+07 1.337E-01 1.51OE+07 1,388E-01 1.335E+07 1.438E-01 1. 187E+07 1. 489E-01 1 .055E+ 07 1.540E-01 9.281E+06 1.590E-01 8. 198E+06 1.641E-01 7. 271E+06 1.692E-01 6.473E+06 1.742E-01 5.784E+06 1.793E-01 5.18 3E+06 1.843E-01 4.646E+06 1.894E-01 4.177E+06 1.944E-01 3.767E+06 1.994E-01 3.406E+06 2.045E-01 3.088E+06 2.095E-01 2.807E+06 2. 145E-01 2.557E+06 2.196E-01 2.334E+06 2.246E-01 2. 136E+06 2.296E-01 1.958E+06 2.347E-01 1.799E+06 2.397E-01 1.655E+C6 2.447E-01 1.526E+06 2.498E-01 1.409E+06 2.548E-01 1.30 3E+06 2.598E-01 1.206E+06 2.648E-01 1. 118E+06 2.698E-01 1 . 038E+06 2.749E-01 9.657E+05 2.799E-01 8.992E+05 2.849E-01 8. 384E+05 1.OOOE+00 1.OOOE+00 TEM PEBATUBE 2. 500E+01 150 "RESIDENCE TIME JGITATIO KARATE SO PERSAT0 RATI ON 1.700E+Q2 1.926E+Q3 7.00QE-01 8.942E+Q7 WEIGHT X 4. 174E-01 6.836E-01 2.915E-01 1.321E-01 5. 85CE-02 SCBEBN SIZE AD 1.060E-01 1.500 E-01 1.800E-01 2.500E-01 2.9 70E-01 CBYSTAL SIZE POPOLATION DENSITY CBYSTAL_SIZE POP PLAT % CUMULATIVE WEIGHT 2.637E+01 6.955E+01 8. 7 96E+01 9. 6 30E+01 1.000E+02 Y   O ION DENSITY 1.030E-01 1. 4151+07 1.081E-01 1. 382E+07 1.133E-01 1.328E + 07 1.184E-01 1. 264E+07 i l . 23 5 E-01 1. 195E+07 1.286E-01 1. 125E+07 1.337E-01 1.056E+07 1.388E-01 9.. 897E+06 1.438 E-01 9.265E+06 1. 489E-01 8. 623E+ 06 1.540E-01 7.873E+06 1.590E-01 7. 207E+06 1.641E-01 6.614E+06 1.692E-01 6. 085E+06 1.742E-01 5.610E + 06 1.793E-01 5. 155E+06 1.843E-01 4.644E+06 1.894E-01 4. 197E+06 1.944E-01 3.803E+06 1.994E-01 3. 456E+06 2.045E-01 3. 148E+06 2.095E-01 2. 875E+06 2. 145E-01 2.632E+06 2.196E-01 2. 414E+06 2.246E-01 2. 219E+06 2.296E-01 2. 044E+06 2.347E-01 1.886E+06 2.397E-01 1. 744E+06 2.447E-01 1.615E+06 2.498E-01 1. 497E+06 2.548E-01 1.388E+06 2.598E^01 1. 289E+06 2.64 8E-01 1. 1991+06 2.698E-01 1 . 117E+Q6 2.749E-01 1.041E+06 2.799E-01 9. 726E+05 2.849E-01 9.094E+05 1.000E+Q0 1. OOOE+00 151 T E M P E R A T U B E R E S I D E N C E T I M E 2 . 5 0 0 E + 0 1 1 . 7 0 0 E + 0 2 P O P . A T 0 2 . 0 1 2 E + 0 8 A G I T A T I O N S A T E S O P E E S A T O R A T I O N 1 . 2 6 0 E + G 3 9 . 5 0 0 E - 0 1 W E I G H T X S C R E E N S I Z E A D 3 % C U M U L A T I V E W E I G H T 7 . C 1 6 E - 0 1 1 . 0 6 0 E - 0 1 6 . 5 6 6 E + G 1 2 . 6 1 6 E - 0 1 1 . 5 0 0 E - 0 1 9 . 0 1 4 E + 0 1 3 . 5 7 0 E - 0 2 1 . 8 O 0 E - 0 1 9 . 3 4 8 E + 0 1 4 . O 0 0 E - O 2 2 . 5 0 0 E - 0 1 9 . 7 2 2 E + 0 1 2 . 9 7 0 E - 0 2 2 . 9 7 0 E - 0 1 1 . 0 0 0 E + 0 2 C R Y S T A L S I Z E P O P O L A T I O N D E N S I T Y C R Y S T A L S I Z E P O P U L A T I O N D E N f 1 . 0 3 0 E - 0 1 3 . 2 2 9 E + 0 7 1 . 0 8 I E - 0 1 2 . 7 7 Q E + 0 7 1 . 1 3 3 E - 0 1 2 . 3 9 5 E + 0 7 1 . 1 8 4 E - 0 1 2 . 0 8 6 E + 0 7 1 . 2 3 5 E - 0 1 1 . 8 2 8 E + 0 7 1 . 2 8 6 E - 0 1 1 . 6 1 1 E + 0 7 1 . 3 3 7 E - 0 1 1 . 4 2 8 E + 0 7 1 . 3 8 8 E r - 0 1 1 . 2 7 1 E + 0 7 1 . 4 3 8 E - 0 1 1 . 1 3 7 E + 0 7 1 . 4 8 9 E - 0 1 1 . 0 1 6 E + 0 7 1 . 5 4 0 E - 0 1 8 . 9 4 3 E + 0 6 1 . 5 9 0 E - 0 1 7 . 9 0 5 E + 0 6 1 . 6 4 1 E - 0 1 7 . 0 1 7 E + 0 6 1 . 6 9 2 E - 0 1 6 . 2 5 3 E + 0 6 1 . 7 4 2 E - 0 1 5 . 5 9 2 E + 0 6 1 . 7 9 3 E - 0 1 5 . 0 1 5 E + 0 6 1 . 8 4 3 E - 0 1 4 . 5 0 0 E + 0 6 1 . 8 9 4 E - 0 1 4 . 0 5 1 E + 0 6 1 . 9 4 4 E - 0 1 3 . 6 5 7 E + 0 6 1 . 9 9 4 E - 0 1 3 . 3 1 1 E + 0 6 2 . 0 4 5 E - 0 1 3 . 0 0 5 E + 0 6 2 . 0 9 5 E - 0 1 2 . 7 3 4 E + 0 6 2 . 1 4 5 E - 0 1 2 . 4 9 3 E + 0 6 2 . 1 9 6 E - 0 1 2 . 2 7 9 E + 0 6 2 . 2 4 6 E - 0 1 2 . 0 8 7 E + 0 6 2 . 2 9 6 E - 0 1 1 . 9 1 5 E + 0 6 2 . 3 4 7 E - 0 1 1 . 7 6 1 E + 0 6 2 . 3 9 7 E - 0 1 1 . 6 2 3 E + 0 6 2 . 4 4 7 E - 0 1 1 . 4 9 7 E + 0 6 2 . 4 9 8 E ^ 0 1 1 . 3 8 4 E + 0 6 2 . 5 4 8 E - 0 1 1 . 2 8 2 E + 0 6 2 . 5 9 8 E - 0 1 1 . 1 8 9 E + 0 6 2 - 6 4 8 E - 0 1 1 . 1 0 5 E + 0 6 2 . 6 9 8 E - 0 1 1 . 0 2 8 E * 0 6 2 . 7 4 9 E - 0 1 9 . 5 8 0 E + 0 5 2 . 7 9 9 E - 0 1 8 . 9 3 7 E + 0 5 2 . 8 4 9 E - 0 1 8 . 3 4 9 E + 0 5 1 . O O O E + 0 0 1 . O O O E + 0 0 TEMPEEATORE 2. 5C0E+01 RESIDENCE TIME 1.700E + 02 152 "JGITATION RATE SOBERS ATU RATION 1.260E+03 8.230E-01 POP- AT 0 1.079E+08 HEIGHT X SCREEN SIZE AD ? & COHOLATIVE HEIGHT • 5 . 5 8 I E - 0 1 1. 060E-01 4. 813E+01 2-,131 E-01 1.500E-01 6. 651E+01 1.965E-01 1. 800E-01 8.346E+01 1.585 E-01 2. 500E-01 9. 713E*01 3.330E-02 2. 970E-01 1. 000E+02 CRYSTAL SIZE POPOLATION DENSITY CRYSTAL SIZE POPOLATION DENS 1.G30E-01 2-214E+07 1.081E-01 1.901E+07 1. 133E-01 1.646E+C7 1-184E-01 1.434E+07 1.235E-01 1.-258 E+07 1.286E-01 1. 1Q9E+07 1. 33 7 E-01 9.838E+06 1.388E-01 8,765E+06 1.438E-01 7.844E+06 1.489E-01 7.064E+06 1.540E-01 6.440E+06 1,590E-01 5.886E+06 1.641E-01 5.395E*06 1.692E-01 4.957E+06 1.742E-01 4.565E+06 1.793E-01 4.195E+06 1.843E-01 3.798E+06 1-894E-01 3.44 SE* 06 L944E-01 3.140E+06 1.994E-01 , 2.866E+06 2.045E-01 2.623E+06 2.095E-01 2.406E+06 2. 145E-01 2.212E+06 2.196E-01 2.038E+06 2.246E-01 1.88 1E+06 2.296E-01 1 . 740E+06 2.347E-01 1.612E+06 2.397E-01 1. 496E+06 2.44 7E-01 1.39 1E*06 2.498E-01 1.294E+06 2.54 8E-01 1-198E+06 2.598E-01 1.112E+06 2.648E-01 1.033E+06 2.698E-01 9.613E+05 2.749E-01 8-957E + 05 2.799E-01 8.358E+05 2.849E-01 7.808E+05 1.000E+00 1.OOOE+00 TEMPEBATUBE 2. 5C0E+O1 TIME 1.700E+02 . '53 AGITATION BATE SO PEES ATUfiATION 1.260E+03 7.Q0GE-Q1 POP. AT 0 1.945E+08 1. 158E+00 6.348E-01 8. 3 GOB-02 6.440E-02 3. 830E-02 SGBEEN SIZE AD 1.060E-01 1.500 E-01 1.800E-01 2.500E-01 2.970E-G1 CBYSTAL SIZE POPULATION DENSITY I CUMULATIVE HEIGHT 5.852E+01 9.061E+01 9.481E+01 9.806E+01 1 .000E+02 CBYSTAL SIZE POPULATION DENSITY 1.030E-01 3.0171*07 1.081E-01 2. 638E+07 1. 133E-01 2.321E+07 1.184E-01 2. 053E+07 1.235E-01 1.825E+07 1.286E-01 1. 629E+G7 1.337E-01 1.461E+07 1.388E-01 . 1. 316E+07 1.438E-01 1.189 E+07 1. 489E-01 1. 071E+07 1.540E-01 9.443E+06 1.590E-01 8. 360E+06 1.641E-01 7.431E+06 1.692E-01 6. 632E+06 1.742E-01 5.939E+06 1.793E-01 5. 332E+06 1.843E-01 4.7831+06 1.894E-01 4. 304E* 06 U944E-01 3.884E+06 1.994E-01 3. 514E+06 2.045E-01 3. 18 8 E+06 2.095E-01 2. 90OE+06 2. 145E-01 2.643E+06 2.196E-01 2. 415E+06 2.246E-01 2. 211 E+06 2.296E-01 2. 028E+06 2.347E-Q1 1.865E+G6 2.397E-01 1. 717E+06 2.447E-01 1.584E+06 2.498E-01 1. 464E+06 2.548E-01 1.354E+06 2.598E-01 1. 255E+06 2.64 8E-01 1. 1651+06 2.698E-01 1. 083E+O6 2.749E-01 1.008E+G6 2.799E-01 9. 397E+G5 2.849E-01 8.7701+05 1.OOOE+00 1. OOOE+00 TEMJEBATUBE 2. 5C0E*01 RESIDENCE TIME 2.350E + 02 AGITATION BATE 2.466E*03 1 5 4 "sUPEHSJTU R A T I O N 9, 50 0 E-01 POP. AT 0 2.467E+08 HEIGHT X 2. 008E + 00 6.669E-01 4. 580E-02 4.450E-02 1. 430E-02 SCREEN SIZE AD 1.060E-01 1.500 E-01 1.800E-01 2. 500 E-01 2.970E-01 CBYSTAL SIZE POPOLATION DENSITY > COMOLATIVE HEIGHT 7.224E*01 9.624E+01 9.788E+01 9.949E+01 1.000E+02 CBISTAL^SIZE POPULATION DENSITY 1.030E-01 3.808E+07 1.081E-01 3. 253E*- 07 1. 133E-01 2.801E+07 1.184E-01 2. 430E+07 1.235E-01 2. 122E+07 1.286E-01 1. 864E+07 1.337E-01 1.647E+07 1.388E-01 1. 462E+07 1.438E-01 1. 30 4E+07 1.489E-01 1. 162E+07 1.540E-01 1.019E+07 1.590E-01 8. 983E+06 1.641E-01 7.948E+06 1.692E-01 7. 059E+06 1.742E-01 6.293E+06 1.793E-01 5. 627E+06 1.843E-01 5.041E+06 1.894E-01 4. 531E+ 06 1.944E-01 4.083E+06 1.994E-01 3. 690E+06 2.045E-01 3.344E+06 2.095E-01 3. 037E+06 2. 145E-01 2.765E+06 2.196E-01 2. 523E+06 2.246E-01 2.3O7E+06 2.296E-01 . 2. 114E+06 2.347E-01 1.941E+06 2.397E-01 1. 785E+06 2.447E-01 1.645E+06 2.498E-01 1. 518E+06 2.548E-01 1.402E+06 2.598E-01 1. 298E+06 2.648E-01 1.203E+06 2.698E-01 1. 11 6E+ 06 2.749E-01 1.037E+06 2.799E-01 9. 655E+05 2.849E-01 8.998E+05 1.000E+00 1. 000E+O0 TEMPERATURE 2 . 5C0E+Q1 155 " i i s i D E J C E T I M E "A G I T AT 10 N B AT E SUPERS ATU RATION 2 . 3 5 0 E + 0 2 2 . 4 6 6 E + 0 3 8 . 2 3 G E - 0 1 P O P . AT 0 1 .535E+08 H E I G H T X 1. 181E+00 5 . 9 1 6 E - 0 1 2 . 3 3 1 E - 0 1 1 . 3 6 6 E - 0 1 3 . 8 8 0 E - 0 2 S C R E E N S I Z E AD 1 . 0 6 0 E - 0 1 1 .500 E - 0 1 1 . 8 0 0 E - 0 1 2. 5 0 0 E - 0 1 2 . 9 7 0 E - 0 1 C R Y S T A L S I Z E P O P U L A T I O N DENSITY % C U M U L A T I V E H E I G H T 5 . 4 1 4 E + 0 1 8 .127E+01 9 .196E+01 9 . 8 2 2 E + 0 1 1 .000E+G2 CRYSTAL S I Z E P O P U L A T I O N D E N S I T Y 1 . 0 3 0 E - 0 1 2 . 6 1 9 E + 0 7 1 . 0 8 1 E - 0 1 2 . 2 7 8 E + 07 1. 1 3 3 E - 0 1 1 .995E+07 1 . 1 8 4 E - 0 1 1 .757E+07 1 . 2 3 5 E - 0 1 1 .55 6 E+07 1 . 2 8 6 E - 0 1 1 .385E+07 1 . 3 3 7 E - 0 1 1 .239E+07 1 . 3 8 8 E - 0 1 1 .112E+07 1 . 4 3 8 E - 0 1 1 .002E+07 1. 4 8 9 E - 0 1 9 . 0 3 9 E + 0 6 1 . 5 4 0 E - 0 1 8 . 0 7 9 E + 0 6 1 . 5 9 0 E - 0 1 7 . 250 E+06 1 . 6 4 1 E - 0 1 6 . 530E+06 1 . 6 9 2 E - 0 1 5 . 9 0 2 E + 0 6 1 . 7 4 2 E - 0 1 5 . 3 5 2 E + 0 6 1 . 7 9 3 E - 0 1 4 . 8 5 4 E + 0 6 1 . 8 4 3 E - 0 1 4 . 3 6 5 E + 0 6 1 . 8 9 4 E - 0 1 3 . 9 3 7 E + 06 1 . 9 4 4 E - 0 1 3 . 5 6 1 E + 0 6 1 . 9 9 4 E - 0 1 3 . 230E+06 2 . 0 4 5 E - 0 1 2. 9 37 E+06 2 . 0 9 5 E - 0 1 2 . 6 7 7 E + 0 6 2 . 1 4 5 E - 0 1 2 . 4 4 6 E + 0 6 2 . 1 9 6 E - 0 1 2 . 2 4 0 E + 0 6 2 , 2 4 6 E - 0 1 2 . 0 5 5 E + 0 6 2 . 2 9 6 E - 0 1 1 ,890E+06 2 . 3 4 7 E - 0 1 1 .741E+06 2 . 3 9 7 E - 0 1 1 .607E+06 2 . 4 4 7 E - 0 1 1 .486E+06 2 . 4 9 8 E - 0 1 1 .375E+ 06 2 . 5 4 8 E - 0 1 1 .272E+06 2 . 5 9 8 E - 0 1 1 .179E+06 2 . 6 4 8 E - 0 1 1.Q94E+06 2 . 6 9 8 E - 0 1 1 .017E+06 2 . 7 4 9 E - 0 1 9 . 4 6 5 E + 0 5 2 . 7 9 9 E - 0 1 8.820E+05 2 . 8 4 9 E - 0 1 8 . 231E+05 1.OOOE+00 1.OOOE+00 156 TEMFEBATUBE 2. 5G0E+01 BESIDEMCE TIME 2.350E+02 AGITATION BATE 2.466E+03 SOPEBS ATI! BAT I ON 7.000E-01 . POP. AT 0 1.213E+08 HEIGHT X 7.856E-01 1.596E+00 2. 318E-Q1 1.203E-01 2. 810E-02 SCBEEN SIZE AD 1.060E-01 1.500 E-01 1.800E-01 2. 500 E-01 2.970E-01 CBYSTAL SIZE POPULATION DENSITY % CUMULATIVE HEIGHT 2.845E+01 8.623E+01 9.463E+01 9.898E+01 1.000E+02 CB.STAL_SIZE POPULATION DENSITY 1.030E-01 1.555E+07 1. 081E-01 1 . 575E+07 1. 133E-01 1.554E+07 1.184E-01 1. 5G8E+G7 1.235E-01 1. 447E+07 1.286E-01 1. 379E+07 1.337E-01 1.307E+07 1.388E-01 1. 235E+07 1.438E-01 1. 16 4E+07 1. 489E-01 1. 082E+07 1.540E-01 9.621E+06 1.590E-01 8. 587E+06 1.611E-01 7.695E+06 1.692E-01 6. 921E+06 1.742E-01 6.245E+06 1.793E-G1 5. 641E+06 1.843E-01 5.Q65E+06 1.894E-01 4. 561E+06 U944E-01 4.120E+06 1.994E-01 3. 731E+06 2.G45E-01 3. 387 E+06 2.095E-01 3. 083E* 06 2. 145E-01 2.813E+06 2,196E-01 2. 572E+G6 2.246E-01 2.357E+06 2.296E-01 2. 164E+06 2.347E-G1 1.990E+06 2.397E-01 1. 834E+G6 2.447E-01 1.694E»06 2.498E-01 1. 566E+06 2. 548E-01 1.447E+06 2.598E-01 1. 340E+06 2.648E-01 1.243E+06 2.698E-01 1. 154E*06 2.749E-01 1.073Et06 2.799E-01 9. 992E+05 2.849E-01 9. 316E+05 1.00OE+00 1. OOGE+OO TEMPERATURE 2. 5G0E+01 RESIDENCE TIME 2.350E + 02 157 AGITATION RATE SUPERSATURATION 1.926E+03 9.500E-O1 POP. AT 0 1.963B+08 WEIGHT X SCREEN SIZE AD % . CUMULATIVE WEIGHT 1. 581E+00 1. 060E-01 5. 630E+01 1.026E+00 1.500E-01 9. 285E+01 7. 380E-02 1. 800E-01 9. 548E+01 8.090E-02 2. 500E-01 9. 836E+01 4. 600E-02 2. 970E-01 1. 000E+02 CRYSTAL SIZE POPULATION DENSITY CRYSTAL^SIZE POPULATION DENf 1.030E-01 2.940E+07 1.081E-01 2. 598E+07 1. 133E-01 2.307E+07 1.184E-01 2. 058E+07 1.235E-01 1.843E+07 1. 286E-01 1. 657E+07 1.337E-01 1.495E+Q7 1.388E-01 1. 354E+07 1.438E-01 1.230 E+07 1. 489E-01 1. 111E+07 1.540E-01 9.766E + 06 1.590E-01 8. 621E+06 1.641E-01 7.642E+06 1.692E-01 6. 800E+06 1.742E-01 6.072E+06 1.793E-01 5. 439E+06 1.843E-01 4.&78E+06 1.894E-01 4. 388E+06 1.944E-01 3.958E+G6 1.994E-01 3. 581E+06 2.Q45E-01 3. 248E+06 2.095E-01 2. 953E+06 2. 145E-01 2.691E+06 2.196E-01 2. 458E+06 2.246E-01 2.250E+06 2. 296E-01 2. 063E+06 2.347E-01 1.896E+G6 2.397E-01 1. 745E+06 2.447E-01 1.610E+Q6 2.498E-01 1. 487E+06 2.548E-01 1.376E+06 2.598E-01 1. 275E+06 2.648E-01 1. 18 3 E+06 2.698E-01 1 . 099E+06 2. 749E-01 1.023E+06 2.799E-01 9. 529E+05 2.849E-01 8.890E+05 1.OOOE+00 1. OOOE+00 T E M P E B A T U B E 2 . 5C0E+01 R E S I D E N C E T I M E 2 . 3 5 Q E + 02 l 58 ' A G I T A T I O N B A T E l u i i i s j i u i i i i o i 1 .926E+03 8 . 2 3 G E - 0 1 P O P . AT 0 1 .972E+08 H E I G H T X 1. 540E+00 7 . 9 5 7 E - 0 1 8 . 6 4 0 E - 0 2 5 . 5 6 0 E - 0 2 2 . 4 5 0 E - 0 2 S C R E E N S I Z E AD 1 . 0 6 0 E - 0 1 1. 500 E - 0 1 1 . 8 0 0 E - 0 1 2. 5 0 0 E - 0 1 2 . 9 7 0 E - 0 1 C B Y S T A L S I Z E P O P U L A T I O N DENSITY l C U M U L A T I V E WEIGHT 6 . 1 5 5 E + 0 1 9 . 3 3 5 E + 0 1 9 .680E+01 9 . 9 0 2 E + 0 1 1 .000E+02 C B Y S T A L _ S I Z E P O P U L A T I O N D E N S I T Y 1 . 0 3 0 E - 0 1 3 . 0 1 1 E + 0 7 1 .08 I E - 0 1 2 . 6 2 4 E + 0 7 1. 1 3 3 E - 0 1 2 . 3 0 1 E + G 7 1 . 1 8 4 E - 0 1 2 . 029E+07 1 . 2 3 5 E - 0 1 1 .800 E+07 1 . 2 8 6 E - 0 1 1 .604E+07 1 . 3 3 7 E - 01 1 .435E+07 1 . 3 8 8 E - 0 1 1. 290E+07 1 . 4 3 8 E - 0 1 1. 164E+07 1 . 4 8 9 E - 0 1 1 . Q47E+07 1 . 5 4 0 E - 0 1 9 . 2 1 2 E + 0 6 1 . 5 9 0 E - 0 1 8 . 143E+06 1 . 6 4 1 E - 0 1 7 . 228E+Q6 1 . 6 9 2 E - 0 1 6 . 4 4 0 E + 0 6 1 . 7 4 2 E - 0 1 5 . 7 6 0 E + G 6 1 . 7 9 3 E - 0 1 5 . 1 6 4 E + 0 6 1 . 8 4 3 E - 0 1 4 . 629E+06 1 . 8 9 4 E - 0 1 4 . 1 6 1 E + 0 6 1 . 9 4 4 E-01 3 . 7 5 2 E + 0 6 1 . 9 9 4 E - 0 1 3 . 3 9 3 E + 0 6 2 . 0 4 5 E - 0 1 3 . 0 7 5 E + 0 6 2 . 0 9 5 E - 0 1 2 . 7 9 5 E + 0 6 2 . 145E-01 2 . 5 4 6 E + 0 6 2 . 1 9 6 E - 0 1 2 . 3 2 4 E + 0 6 2 . 2 4 6 E - 0 1 2 . 126E+06 2 . 2 9 6 E - 0 1 1 .949E+ 06 2 . 3 4 7 E - 0 1 1 .790E+06 2 . 3 9 7 E - 0 1 1. 647E+06 2 . 4 4 7 E - 0 1 1 .518E+06 2 . 4 9 8 E - 0 1 1 .402E+06 2 . 5 4 8 E - 0 1 1.296E+Q6 2 . 5 9 8 E - 0 1 1. 200E+06 2 . 6 4 8 E - 0 1 1. J 1 2 E + 0 6 2 . 6 9 8 E - 0 1 1 . 033E+06 2 . 7 4 9 E - 0 1 9 . 6 0 6 E + G 5 2 . 7 9 9 E - 0 1 8 . 9 4 5 E + 0 5 2 . 8 4 9 E - 0 1 8 . 339E+05 1 .000E+00 1.OOOE+00 TEMPERATURE 2.5GCE+01 RESIDENCE TIME 2.350E + C2 .159 AGITATION~RATE SUPEBS ATOBATION 1.926E+03 7.0O0E-01 POP. AT 0 1.001E+08 HEIGHT X 6. 981E-01 1. 117E+00 3. 950E-01 1.935E-01 3. 350E-02 SCREEN SIZE AD 1.060E-01 1..500E-Q1 1.800E-01 2. 500 E-01 2.970E-01 CRYSTAL SIZE POPULATION DENSITY > CUMULATIVE HEIGHT 2.865E+01 7.448E+01 9.068E+01 9.863E+01 1.000E+02 CRYSTALLIZE POPULATION DENSITY 1.030E-01 1.5281+07 1.08 IE-01 1. 486E+07 1 . 133E-01 1.425E+07 1. 184E-01 1. 353E+07 1.235E-01 1. 2771*07 1.286E-01 1. 201E+07 1.337E-01 1. 126E+07 1.388E-01 1. 054E+07 1.43 8 E-01 9.8611*0 6 1. 489E-01 9. 159E+06 1.540E-01 8.300E+G6 1.590E-01 7. 546E+06 1.641E-01 6.88 1E*06 1.692E-01 6. 293E+06 1.742E-01 5.770E+06 1.793E-01 5. 279E+06 1.843E-01 4.754E+06 1.894E-01 4. 2 94 E+06 1.944E-01 3.889E+G6 1.994E-01 3. 532E+06 2-045E-01 3. 216E+06 2.095E-01 2. 935E+06 2. 145E-01 2.686E+06 2.196E-01 2. 4621+06 2.246E-01 2. 262E+06 2.296E-01 2. 083E+06 2.347E-01 1.921E+06 2.397E-01 1. 775E+06 2.44 7E-01 1.643E+06 2.498E-01 1. 522E+06 2.548E-01 1.408E+06 2.598E-01 1. 304E+06 2.648E-01 1. 2101*06 2.698E-01 1. 124E+06 2.749E-01 1..045E+06 2.799E-01 9. 739E+05 2.849E-01 9.0841*05 1.OOOE+00 1. 000E+00 TEMPERATURE 2.5CGE*01 RESIDENCE TIME 2.350E + 02 160 AGIT AT ION RATE~ SUJiRS ATfllATigj 1.260E+03 9.50QE-01 POP. AT 0 1.373E+08 HEIGHT X 5.990E-01 7.863E-01 8. 810E-02 4.800E-02 1. 430E-02 SCREEN SIZE AD 1.060E-01 1.500 E-01 1.80OE-01 2. 500 E-01 2.970E-01 CRYSTAL SIZE POPOLATION DENSITY S CUMULATIVE HEIGHT 3.901E*01 9.0211+01 9.594E+G1. 9.907E+01 1.00QE+02 CRYSTAL_SIZE POPULATION DENSITY 1.030E-01 1.886E+07 1.081E-01 1 .784E+ 07 1. 133E-01 1.675E+07 1.184E-01 1.565E+07 1.235E-01 1.458E+07 1.286E-01 1. 356E+07 1.337E-01 1.260E+07 1.388E-01 1, 171E+07 1.438E-01 1.0881+07 1.489E-01 1.001E+07 1.54OE-01 8.8491+06 1.590E-01 7. 856E+06 1.641E-01 7.0031*06 1.692E-01 6.266E*06 1.742E-01 5.627E+06 1.793E-01 5.062E+06 1.843E-01 4.540E+06 1.894E-01 4.085E+06 1.944E-01 3.686E+06 1.994E-01 3.335E+06 2.045E-01 3.Q25E+06 2.O95E-01 2.751E+06 2.145E-01 2.507E+06 2.196E-01 2.290E+06 2.246E-01 2.0971*06 2.296E-01 1.923E+06 2.347E-01 1.768E+06 2.397E-01 1.628E+06 2.44 7E-01 1.50 11*06 2.498E-01 1.387E+06 2.548E-01 1.282E+06 2.598E-01 1. J87E+06 2.648E-01 1. 100E+06 2.698E-01 1.022E* 06 2.749E-01 9.501E+05 2.799E-01 8.846E+05 2.849E-01 8. 247E+05 1.000E+00 1.QOOE+00 TEMPERATURE 2. 5C0E+01 EJSJ[DENCE_TIME 2.350E+02 AGITATION RATE 1.260E+Q3 1 _6 J_ SUPERS ATO RATION 8.230E-01 POP. AT 0 2.027E+08 HEIGHT X SCREEN SIZE AD 5 CUMULATIVE HEIGHT 8. 211E-01 1. 060E-01 6. 443E+Q1 3.717E-01 1. 500 E-01 9. 359E+01 3.620E-02 1. 800E-01 9-643E+01 2.910E-02 2. 500E-01 9. 871E+01 1.640E-02 2. 970E-01 •1. 000E+02 CRYSTAL SIZE POPULATION DENSITY CRYSTAL SIZE POPULATION DEN' L030E-O1 3. 122E+07 1.081E-01 2. 702E+07 1. 133E-01 2.355E+07 1.184E-01 2. 066E+07 1.235E-01 1.823E+07 1.286E-01 J 1. 616E+07 1.337E-01 1.441E+07 1.388E-01 1. 290E+07 1.438E-01 1. 159E+07 1.489E-01 1. 040E+07 1.540E-01 9.139E+06 1.590E-01 8. 070E+06 1.641E-01 7.156E+06 1.692E-01 6. 369E+06 1.742E-01 5.69OE+06 1.793E-01 5. 097E+Q6 1.843E-01 4.569E+06 1.894E-01 4. 1Q8E+G6 1.944E-01 3.705E+06 1.994E-01 3. 350E+06 2,045E-01 3. 037 E+06 2.Q95E-01 2. 760E+06 2. 145E-01 2.514E+06 2.196E-01 2. 295E+06 2.246E-01 2. 100E+06 2.296E-01 - 1. 925E+06 2.347E-01 1.768E+06 2.397E-01 1. 627E+06 2.447E-01 1.50QE+06 2.498E-01 1. 385E+06 2.548E-01 1.281E + 06 2.598E-01 1. 186E+06 2.648E-01 1. 100E+06 2.698E-01 1. 022E+06 2. 749 E-01 9.505E+05 2.799E-01 8. 854E+05 2.849E-01 8.257E+05 1.OOOE+00 1. OOOE+00 TEMPERATURE 2.5COB*01 RESIDENCE TIME 2.350E+O2 I 62 AGITATION RATE SUPERS ATU RATION 1.26QE+03 7.000E-01 POP- AT 0 1-058E+08 IJ I£HT_X 6. 314E-01 1. 187E+00 2. T78E-01 1.595 E-01 4.420E-02 SCREEN SIZE AD 1.060E-01 1 .500 E-01 1.800E-01 2. 500 E -01 2.970E-01 CRYSTAL SIZE POPULATION DENSITY , CUMULATIVE HEIGHT 2.819E+01 8. 118E*01 9.090E+01 9.80 3E + 01 1.000E*02 CRYSTAL_SIZE POPULATION DENSITY 1.030E-01 1.455E*07 1.081E-01 1. 453E* 07 1. 133 E-01 1.420E+07 1.184E-01 1. 368E*07 1.235E-01 1.306E+07 1.286E-01 , 1. 239E+07 U337E-01 1. 170E + 07 1.388E-01 1. 102E+07 1.438E-01 1.036E+07 1.489E-01 9. 630E+06 1.540E-01 8.591E+06 1.590E-01 7. 695E+06 1.641E-01 6.9 19E+06 1.692E-01 6. 243E*06 1.742E-01 5.652E+06 1.793E-01 5. 120E+06 1.843E-01 4.608E+06 1.894E-01 4. 159E+06 1.944E-01 3.765E+06 1.994E-01 3. 417E+06 2.045E-01 3. 109E*06 2.095E-01 2. 836E+06 2. 145E-01 2.593E*06 2.196E-01 2. 376E+06 2.246E-01 2. 182E+06 2.296E-01 2. 008E*06 2.347E-01 1.851E+06 2.397E-01 1. 709E+06 2.447E-01 1.58 1E+06 2.498E-01 1. 465E+06 2.548E-01 1.355E+06 2.598E-01 1. 256E+06 2.648E-01 1. 166E+06 2.698E-01 1. 084E+06 2.749E-01 1.009E+06 2.799E-01 9. 405E+05 2.849E-01 8.778E*05 1.000E+00 1. OOOE+00 TEMPERATURE 2. 5C0E+01 RESIDENCE TIME 3.800E+02 AGITATION RATE 2.466E+03 163 "luPERSATU RATION 9.500E-01 POP. AT 0 2.Q00E+08 WEIGHT X 8- 966E-01 6.313E-01 1. 870E-02 1.580E-02 7, 4G0E-03 SCREEN SIZE AD 1.060E-G1 1.500E-01 1.800E-G1 2.500E-01 2.9 70E-Q1 CBYSTAL SIZE POPULATION DENSITY ; CUMULATIVE WEIGHT 5.712E+01 9.733E+Q1 9.852E+01 9.953E+01 1.00QE+Q2 CBYSTAL_SIZE POPULATION DENSITY 1.030E-01 2.864E+07 1.081E-01 2. 546E+07 1. 133E-01 2.272E+07 1.184E-01 2. 035E+07 1.235E-01 1.830 E+07 1.286E-01 1. 651E+07 •1.33 7 E-01 1.494E+07 1.388E-01 1. 357E+07 1.438E-01 1. 235E+07 1. 489E-01 1. 118E+ 07 1.540E-01 9.797E+06 1.590E-01 8. 625E+06 1.641E-01 7.625E+06 1.692E-01 6. 767E+06 1.742E-01 6.Q28E+06 1.793E-01 5. 386E+06 1.843E-01 4.824E+06 1.894E-01 4. 333E* 06 1.944E-01 3.903E+06 1.994E-01 3. 526E+06 2.045E-01 3. 194E+06 2. 095E-01 2. 900E+06 2. 145E-01 2.639E+06 2.196E-01 2. 407E+06 2.246E-01 2.2001*06 2. 296E-01 2. 015E+06 2.347E-01 1.849E+06 2.397E-01 1. 700E+06 2.44 7E-01 1.566E+06 2.498E-01 1. 444E+06 2.548E-01 1.334E+G6 . 2.598E-01 1. 235E+06 2.648E-01 1.14 41+06 2.698E-01 1. 062E+06 2. 749 E-01 9.869E+05 2.799E-01 9. 185E+05 2.849E-01 8.559E+05 1.OOOE+00 1. OOOE+00 TEMPERATOBE 2. 500E+01 RESIDENCE TIME 3.800E + 02 AGITATION RATE 2.4662+03 164 8.230E-01 POP. AT 0 1.778E+08 HEIGHT X 9.379E-01 5.983E-01 4.410E-02 2.820E-O2 1.720E-02 SCREEN SIZE AD 1.Q60E-01 1.500B-01 1.800E-01 2.500E-01 2.970E-01 CRYSTAL SIZE POPOLATION DENSITY i COMOLATIVE HEIGHT 5.769E+01 9.449E+01 9.721E+01 9.894E+01 1.000E+Q2 CRYSTAL^SIZE POPOLATION DENSITY 1.030E-01 2.630E+07 1.081E-01 . 2. 321E*07 1.133E-01 2.059E+07 1.184E-01 1. 835E+07 1.235E-01 1.642E+07 1.286E-01 1. 475E+07 1.337E-01 1.330E+07 1.388E-01 1. 204E+07 1.438E-01 1.093E*07 1. 489E-01 9. 871E+06 1.540E-G1 8.675E+06 1.590E-01 7. 658E+06 1.641E-01 6.789E+06 1.692E-01 6. 041E+G6 1.742E-01 5.395E+06 1.793E-01 4. 832E+06 1.843E-01 4.329E+06 1.894E-01 . 3. 891E+06 1.944E-01 3.507E+06 1.994E-01 3. 170E+06 2.045E-01 2.873E+06 2.095E-01 2. 609E+06 2. 145E-01 2.376E+06 2.196E-01 2. 168E+06 2.246E-01 1.983E*06 2.296E-01 1. 817E+06 2.347E-01 1.668E+06 2.397E-01 1. 535E+06 2.447E-01 1. 414E+06 2.498E-01 1. 305E+06 2.54 8E-01 1.207E+06 2.598E-01 1. 117E+06 2.648E-01 1.036E+06 2.698E-01 9. 622E+05 2.749E-01 8.948E-r05 2.799E-01 8. 333E+05 2.849E-01 7.770E+05 1.000E+00 1. OOOE+00 TEMPERATURE 2 . 500E+G1 165 " R E S I D E N C E T I M E A G I T A T I O N RATE S U P E R S A T U E A T I O N 3 . 8 0 0 E + 02 2 .466E+Q3 7 . 0 0 0 E - 0 1 POP. AT 0 1 .880E+08 H E I G H T X 1 .044E+00 S C R E E N S I Z E AD % C U M U L A T I V E HEIGHT 1. 0 6 0 E - 0 1 5 . 2 1 4 E + 0 1 9 . 0 4 9 E - 0 1 1. 500 E - 0 1 9 . 7 3 2 E + 0 1 1 . 9 2 0 E - 0 2 1. 8 0 0 E - 0 1 9 .828E+01 1. 9 1 0 E - 0 2 2. 5 0 0 E - 0 1 9 . 9 2 3 E + 0 1 1 . 5 4 0 E - 0 2 2 . 9 7 0 E - 0 1 1.OO0E+G2 C R Y S T A L S I Z E P O P U L A T I O N DENSITY C R Y S T A L L I Z E P O P U L A T I O N DENS 1 . 0 3 0 E - 0 1 2 . 6 1 5 1 * 0 7 1 .08 I E - 0 1 2 . 3 6 4 E + 07 1. 1 3 3 E - 0 1 2 . 1 4 1 E + 0 7 1 . 1 8 4 E - 0 1 1.942E+07 1 . 2 3 5 E - 0 1 1.76 4E+07 1 .28 6 E - 0 1 1 .607E+07 1 . 3 3 7 E - 0 1 1 .467E+07 1 . 3 8 8 E - 0 1 1 .341E+07 1 . 4 3 8 E - 0 1 1. 2 2 9 1 * 0 7 1 . 4 8 9 E - 0 1 1 . 118E+ 07 1 . 5 4 0 E - 0 1 9 . 7 9 4 E + 0 6 1 . 5 9 0 E - 0 1 8 . 6 1 9 E + 0 6 1 . 6 4 1 E - 0 1 7 . 6 17 E+06 1 . 6 9 2 E - 0 1 6 . 757E+06 1 . 7 4 2 E - 0 1 6 . 0 1 7 E + 0 6 1 . 7 9 3 E - 0 1 5 . 3 7 5 E + 0 6 1 - 8 4 3 E - 0 1 4 . 8 1 3 E + 0 6 1 . 8 9 4 E - 0 1 4 . 3 2 3 E + 0 6 1 . 9 4 4 E - 0 1 3 . 8 9 4 E * 0 6 1 . 9 9 4 E - 0 1 3 . 5 1 8 E + 0 6 2 . 0 4 5 E - 0 1 3 . 1861+06 2 . 0 9 5 E - 0 1 . 2 . 8 9 3 E + 0 6 2 , 1 4 5 E - 0 1 2 . 6 3 2 E + 0 6 2 . 1 9 6 E - 0 1 2 . 401E+06 2 . 2 4 6 E - 0 1 2 . 1 9 4 E * 0 6 2 . 2 9 6 E - 0 1 2 . 010E+06 2 . 3 4 7 E - 0 1 1 .844E+06 2 . 3 9 7 E - 0 1 1 .695E+06 2 . 4 4 7 E - 0 1 1 .561 E+0 6 2 . 4 9 8 E - 0 1 1 .440E+06 2 . 5 4 8 E - 0 1 1 .331E+06 2 . 5 9 8 E - 0 1 1 .232E+06 2 . 6 4 8 E - 0 1 1. 142E+06 2 . 6 9 8 E - 0 1 1 .060E+06 2 . 7 4 9 E - 0 1 9 . 8 5 9 E + 0 5 2 . 7 9 9 E - 0 1 9 . 178E+05 2 . 8 4 9 E - 0 1 8 . 5 5 5 E + 0 5 1.OOOE+00 1 .000E+00 TEiSPEEATDfiE 2. 500E+01 166 " R E S I D E N C E T I M E I G I T I T I O N R A T E SO"PERSATURATION 3 . 8 0 0 E + 02 1 . 926E+03 9 . 5 Q 0 E - 0 1 POP. AT 0 T . 6 3 5 E + 0 8 WEIGHT X 7 . 9 5 8 E - 0 1 9 . 5 8 4 E - 0 1 1. 1 7 O E - 0 2 1 . 4 0 0 E - 0 2 1 . 6 5 0 E - 0 2 S C R E E N S I Z E AD 1 . 0 6 0 E - 0 1 1 . 5 0 0 E - 0 1 1 . 8 0 0 E - 0 1 2. 5 0 0 E - 0 1 2 . 9 7 0 E - 0 1 C R Y S T A L S I Z E P O P U L A T I O N DENSITY % C U M U L A T I V E HEIGHT 4 . 4 3 0 E + 0 1 9 . 7 6 5 E + 0 1 9 . 8 3 0 E + 0 1 9 . 9 0 8 E + 0 1 1.Q00E+02 CRYSTAL S I Z E P O P U L A T I O N D E N S I T Y 1 . 0 3 0 E - 0 1 2. 145E+07 1. Q81E-01 2 . 0 0 7 E + 0 7 1 . 1 3 3 E - 0 1 1 .868E+07 1 . 1 8 4 E - 0 1 1 .734E+07 1 . 2 3 5 E - 0 1 1 . 6 0 7 E * 0 7 1 . 2 8 6 E - 0 1 1 .487E+07 1 . 3 3 7 E - 0 1 1 .377E+07 1 . 3 8 8 E - 0 1 1. 275E+07 1 . 4 3 8 E - 0 1 1. 182E+07 1 . 4 8 9 E - 0 1 1 . 0 8 3 E + 07 1 . 5 4 0 E - 0 1 9 . 4 8 1 E + 0 6 1 . 5 9 0 E - 0 1 8 . 339E+06 1 . 6 4 1 E - 0 1 7 . 366E+06 1 . 6 9 2 E - 0 1 6 . 5 3 1 E + 0 6 1 . 7 4 2 E - 0 1 5 . 8 1 2 E + 0 6 1 . 7 9 3 E - 0 1 5 . 190E+06 1 . 8 4 3 E - 0 1 4 . 6 4 7 1 * 0 6 1 . 8 9 4 E - 0 1 4.173E+06 1 . 9 4 4 E - 0 1 3 . 7 5 9 E + 0 6 1 . 9 9 4 E - 0 1 . 3. 395E+06 2 . 0 4 5 E - 0 1 3 .Q74E+06 2 . 0 9 5 E - 0 1 2 . 7 9 1 E + 0 6 2 . 1 4 5 E - 0 1 2 . 5 3 9 E + 0 6 2 . 1 9 6 E - 0 1 2 . 3 1 6 E + 0 6 2 . 2 4 6 E - 0 1 2 . 1161+06 2 . 2 9 6 E - 0 1 1 .938E+06 2 . 3 4 7 E - 0 1 1.778E+Q6 2 . 3 9 7 E - 0 1 1 .635E+06 2 . 4 4 7 E - 0 1 1 .505E+06 2 . 4 9 8 E - 0 1 1 .388E+06 2 . 5 4 8 E - 0 1 1 .283E+G6 2 . 5 9 8 E - 0 1 1. 188E+06 2 . 6 4 8 E - 0 1 1 .102E+06 2 . 6 9 8 E - 0 1 1 .023E+06 2 . 7 4 9 E - 0 1 9 . 5 1 I E * 0 5 2 . 7 9 9 E - 0 1 8 . 8 5 6 E + 0 5 2 . 8 4 9 E - 0 1 8 . 2561+05 1 .000E+00 1 .000E+O0 2. 500E+01 RESIDENCE TIME 3.800E+02 167 AGITATION RATE SUPERS ATP RATION 1.926E+03 8.230E-01 POP. AT 0 2.Q78E+08 HEIGHT X 1. C61E+00 3.542E-01 5. 020E-02 3.560E-02 1. 380E-02 SCREEN SIZE AD 1.060E-01 1.500 E-01 1.800E-01 2.500E-01 2.970E-01 CRYSTAL SIZE POPULATION DENSITY i CUMULATIVE HEIGHT 7.004E+01 9.342E+01 9.674E+01 9.909E+01 1.0O0E+02 l^ISTAL^SIZE POPULATION DENSITY 1.030E-01 3.2781*07 1.Q81E-01 2. 800E+07 1. 133E-01 2.412E + 07 1.184E-01 2.092E+07 1.235E-01 1.8 27 E+07 1.286E-01 1.606E+07 1.337E-01 1.419E*07 1.388E-01 1. 260E+07 1.438E-01 1. J24E+07 1. 489E-01 1.002E+07 1.540E-01 8.818E+06 1.590E-01 7.793E+06 1.641E-01 6.915E+06 1.692E-01 6.160E+06 1.742E-01 5.508E+06 1.793E-01 4.937E+06 1.843E-01 4. 426E+06 1.894E-01 3. 980E+06 1.944E-01 3.589E*06 1.994E-01 3.245E+06 2.045E-01 2.942E+06 2.095E-01 2.674E+06 2. 145E-01 2.436E*06 2.196E-01 2.224E+06 2.246E-01 2.034E+06 2.296E-01 1.865E+06 2.347E-01 1.713E+06 2.397E-01 1. 577E+06 2.447E-01 1.454E+06 2.498E-01 1.342E+06 2.548E-01 1.241E+06 2.598E-01 1.. 148E+06 2.648E-01 1.065E+06 2.698E-01 9.887E+05 2.749E-01 9.193E+05 2.799E-01 8.559E+05 2.849E-01 7,980E*05 1.OOOE+00 1.OOOE+00 168 TEJPEJATJJBE 2. 5C0E+01 RESIDENCE TIME 3.800E + 02 AGITATION RATE 1.926E+03 SUPERS ATUfiATION 7.000E-01 POP. AT 0 2.455E+08 HEIGHT X SCREEN SIZE AD S I CUMULATIVE WEIGHT 1.296E + 00 1. 060E-01 7. 425E+01 4.162E-01 1.500 E-01 9. 810E+01 1. 450E-02 1. 800E-01 9. 893E+01 1.290E-02 2. 500E-01 9. 967E+01 5. 8C0E-03 2. 970E-01 1. OOOE+02 CBYSTAL SIZE POPULATION DENSITY CRYSTAL SIZE POPULATION DEN< 1.030E-01 3.738E+07 1.Q81E-Q1 3. 189E+07 1. 133E-01 2.743E+07 1.184E-01 2.377E+07 1.235E-01 2.074E+07 1.286E-01 1.820E+07 1.337 E-01 1.606E+07 1.388E-01 1.425E+07 -1.438 E-01 1.270 E+07 1.489E-01 1. 131 E+07 1.540E-01 9.907E+06 1.590E-01 8.716E+06 1.641E-01 7.70 1 E+0 6 1.692E-01 6.B30E+06 1.742E-01 6.080E+06 1.793E-01 5.430E+06 1.843E-01 4.862E+06 1.894E-01 4.367E+06 1.944E-01 3.933E+06 1.994E-01 3.552E+06 2.045E-01 3. 216E+06 2.095E-01 2.920E+06 2. 145E-01 2.657E+06 2.196E-01 2.423E+06 2.246E-01 2. 214E+06 2.296E-01 2.027E+ 06 2.347E-01 1.860E+06 2.397E-01 1.710E+06 2.447E-01 1.57 4 E+06 2.498E-01 1.452E+06 2.548E-01 1.341E+06 2.598E-01 1. 241 E+06 2.648E-01 1.150E+06 2.698E-01 1.067E+06 2.749E-01 9.915E+05 2.799E-01 9.226E+05 2.849E-01 8.596E+05 1.00OE+O0 1.000E+00 TEHFEBATORB 2. 500E+01 3.800E + 02 POP, AT 0 1.869E+08 J69 RESIDENCE TIME ~ AGITATION RATE SO PERS JT ] J RATI GN 1.26GE+03 9.500E-01 WEIGHT X 6, 047E-01 SCREEN SIZE AD % COMULATIVE WEIGHT 1.060E-01 5. 483E+01 4.U81E-01 1. 500E-0 1 9. 546B+01 2. 280E-02 1. 800E-01 9. 752E+01 2.Q80E-02 2. 500E-01 9. 941E+01 6. 500E-03 2. 970E-01 •1 .O00E+O2 CRYSTAL SIZE POPOLATION DENSITY CRYSTAL SIZE POPOLATION DENS 1.030E-01 2.702E+07 1.081E-01 2.411E+ 07 1. 133E-01 2.159E+07 1.184E-01 1.940E+07 1.235E-01 1.748E+07 1.286E-01 1.581E*07 1.337E-01 1.434E+07 1.388E-01 1. 304E+07 1.438E-01 1. 189E+07 1.489E-01 1. 078E+07 1.540E-01 9.461E+06 1.590E-01 8.343E+06 1.641E-01 7.38 7E+06 1.692E-01 6. 566E+06 1.742E-01 5.857E+06 1.793E-01 5.241E+06 1.843E-01 4.697E+06 1.894E-01 4.221£*06 1.944E-01 3.805E + 06 1.994E-01 3.440E+06 2.045E-01 3. 117E+06 2.095E-01 2.832E+06 2. 145E-01 2.579E+06 2. 196E-01 2. 354E+G6 2.246E-01 2.153E+06 2.296E-01 1. 973E+ 06 2.347E-01 1.812E+06 2.39 7E-01 1.667E+06 2.447E-01 1.536E+06 2.498E-01 1.418E+ 06 2.54 8E-01 1.310E+06 2.598E-01 1.212E+06 2.648E-01 1. 124E+06 2.698E-01 1.043E+06 2.749E-01 9.695E+05 2.799E-01 9.023E+05 2.849E-01 8. 409E+05 1.000E+00 1.OOOE+00 2. 5COE+01 RESIDENCE TIME 3.800E + 02 170 AGITATIQN~RATE SU PE I J ATOEATIoi 1.260E+03 8.23CE-01 POP. AT 0 2.Q96E+08 WEIGHT X 1.046E+00 4.460E-01 2. 88OE-02 4.170E-O2 1, 51OE-02 SCREEN SIZE AD 1. 060E-01 1.500 E-01 1.800E-01 2.500E-01 2.970E-01 CRYSTAL SIZE POPULATION DENSITY i CUMULATIVE WEIGHT 6.631E+01 9.458E+01 9.64QE+01 9.904E+01 1.000E+02 CRYSTAL SIZE POPULATION DENSITY 1,030E-01 3. 227E+07 1.081E-01 2. 785E+07 1. 133E-01 2.421E+07 1.184E-01 2. 119E+07 1.235E-01 1.865E+07 1.286E-01 1.651 E+07 1.337E-01 1.468E+07 1.388E-01 1.312E+C7 1.438E-01 1.178E+07 1. 489E-01 1 .055E+07 1.540E-01 9.254E+06 1.590E-01 8. 157E+06 1.641E-01 7.219E+06 1.692E-01 6.414E+06 1.742E-01 5.720E+06 1.793E-01 5.J17E+06 1.843E-01 4.588E+06 1.894E-01 4. 127E+06 1.944E-01 3.722E+06 1.994E-01 3.366E+06 2.Q45E-01 3.053E+06 2.095E-01 2.775E+Q6 2. 145E-01 2.528E+06 2.196E-01 2.309E+06 2.246E-01 2. 113E+06 2. 296E-01 1.937E+G6 2.347E-01 1.780E+06 2.397E-01 1.638E+06 2.447E-01 1.511E+06 2.498E-01 1 .395E+06 2.548E-01 1.290E+06 2.S98E-01 1,194E+06 2.64 8E-01 1. 107E+06 2.698£r-01 1.028E+06 2.749E-01 9.559E+05 2.799E-01 8.901E+05 2.849E-01 8. 298E+05 1.OOOE+00 1.000E+00 TEMPERATURE RESIDENCE TIME 2. 5C0E+01 3.800E + 02 POP. AT 0 1.536E+08 . . ]7}_ AGITATION RATE SUPERSATURATION 1.260E+03 7.000E-01 WEIGHT; X 8.665E-01 SCREEN SIZE AD ! % CUMULATIVE WEIGHT 1. 060E-01 4. 299E+01 1.018E+00 1.500 E-0 1 9. 348E+01 9. 100E-02 1. 800E-01 9. 799E*01 2.820E-02 2. 500E-01 9. 939E+01 1. 230E-02 2. 970E-01 1 . 000E*-G2 CRYSTAL SIZE POPULATION DENSITY CRYSTAL_SIZE POPULATION DENf 1.030E-01 2.094E+07 1.08 IE-01 1. 954E+07 1. 133E-01 1.815E+07 1. 184E-01 1. 681E+07 1.235E-01 1.555E+07 1.286E-01 1.438E+07 1.337E-01 1.330E+07 1.388E-01 1..230E+07 1.438E-01 1. 139E+07 1. 489E-01 1.044E+07 1.540E-01 9.209E + 06 1.590E-01 8. 155E+06 1.641E-01 7.252E+06 1.692E-01 6.474E+06 1.742E-01 5.799E+06 1.793E-01 5.206E+06 1.843E-01 4.66 4E+06 1.894E-01 4. 190E+06 1.944E-01 3.776E+06 1.994E-01 3.412E+06 2.045E-01 3.09 1E*06 2.095E-01 2.807E+06 2. 145E-01 2.556E+06 2.196E-01 2.332E+06 2.246E-01 2. 132E+06 2.296E-01 1.953E+06 2.347E-Q1 1.793E+06 2.397E-01 1. 649E+06 2.447E-01 1.519E+06 2.498E-01 1.401E+06 2.548E-01 1.295E+06 2.598E-01 1. 198E+06 2.648E-01 1. 111E*06 2.698E-01 1.031E+06 2.749E-01 9.584E+05 2.799E-01 8.921E+05 2.849E-01 8. 314E+0 5 1.000E+00 1.000E+O0 172 TEMPERATURE AGITATION RATE SUPERSATURATION 3. 500E+01 1. 700E+02 2.466E+03 9.500E-01 POP. , AT 0 1.972E+08 WEIGHT X 6. 229E-01 SCREEN SIZE AD ? I CUMULATIVE WEIGHT 1. 060E-01 5. 636E+01 3.689E-01 1. 500 E-0 1 8.974E+01 5. 810E-02 1. 80OE-01 9. 500E+01, 4.22OE-02 2. 500E-01 9. 881E+01 1. 310E-02 2. 970E-01 1. 000E+02 CBYSTAL SIZE POPULATION DENSITY CRYSTAL ; SIZE POPULATION DENf 1.030E-01 3. 068 E+07 1.081E-01 2.696E+07 1.133E-01 2.381E*07 1.184E-Q1 2.114E+07 1.235E-01 1.885E+07 1.286E-01 1.689E+ 07 1.337E-01 1.519E+07 1.388E-01 1. 37 IE*07 1.438E-01 1.241 E+07 1. 489E-01 1.121E+ 07 1.540E-01 9.899E+06 1.590E-01 8.781E+06 1.641E-01 7.822E+06 1.692E-01 6.993E+06 1.742E-01 6.275E+06 1.793E-01 5.642E+06 1.843E-01 5.063E+06 1.894E-01 4.558E+06 1.944E-01 4. 115E + 06 1.994E-01 3. 725E+06 2.045E-01 3.38 1E+06 2.Q95E-01 3.076E+06 2. 145E-01 2.805E+06 2.196E-01 2.564E+06 2.246E-01 2. 348E+06 2. 296E-01 2. 155E+06 2.347E-01 1.982E+06 2.397E-01 1.826E+06 2.447E-01 1.685E+06 2.498E-01 1.557E+06 2.548E-01 1.440E+06 2.598E-01 1.33 3 E+06 2.648E-01 1. 237E+06 2.698E-01 •1 . 149E+06 2.749E-01 1.068E+06 2.799E-01 9.949E+05 2.849E-01 9. 278E+0 5 1.000E+00 1.OOOE+00 TEMPERATURE 3. 5 DOE* 01 RESIDENCE TIME 1.700E + 02 __J22 i ^ T M I _ l N _ i i ? . J SUPERSATURATION 2.466E+03 8.230E-01 POP. AT 0 2.04 3E+08 HEIGHT X 6. 955E-01 SCREEN SIZE AD ? I CUMULATIVE HEIGHT 1.060E-01 6. 034E+01 3.770E-01 1. 500 E-0 1 9. 305E*01 2. 96GE-02 1. 800E-01 9. 562Er01 . 3..160E-02 2. 500E-01 9. 836E+01 1.890E-02 2. 970E-01 1. 000E+02 CRYSTAL SIZE POPULATION DENSITY CRYSTAL SIZE POPULATION DENS 1.030E-01 3.111E+07 1.081E-01 2. 718E+07 1. 133E-01 2.390E+07 1.184E-01 2. 113E+07 1.235E-01 1.877E+07 1.286E-01 1. 676E+07 1.337E-01 1.502E+07 1.388E-01 1. 352E+Q7 1.438E-01 1.221E+07 1. 489E-01 1 . 099E+07 1.540E-01 9.661E+06 1.590E-01 8. 527E+06 1.641E-01 7.557E+06 1.692E-01 6. 724E*06 1.742E-01 6.004E+06 1.793E-01 5. 377E+06 1.843E-01 4.822E+06 1.894E-01 4. 337E+06 1.944E-01 3.912E+06 1.994E-01 3. 538E+06 2.045E-01 3. 20 9 E+06 2.095E-01 2. 917E+06 2. 145E-01 2.658E+06 2.196E-01 2. 428E+06 2.246E-01 2.222E+06 2.296E-01 2. 038E+06 2.347E-01 1.872E+06 2.397E-01 1. 723E+06 2.447E-01 1.589E+06 2.498E-01 1 . 468E+06 2.548E-01 1.358E*G6 2.598E-01 1. 258E+06 2.648E-01 1. 167E+06 2.698E-01 1 . 085E+06 2. 749E-01 1.010E+06 2.799E-01 9. 407E+G5 2.849E-01 8.776E+05 1.000E+00 1. 000E+00 TEMPERATPRE 3 . 5 C O E * 0 1 R E S I D E N C E T I M E 1.70QE + 02 • m . "AGITATION R A T E SUPERS ATP RATION 2 . 4 6 6 E * 0 3 7 . 0 0 0 E - 0 1 POP. . AT 0 1 .239E+08 H E I G H T X 5 . 7 3 7 E - 0 1 S C R E E N S I Z E AD 1 & C U M U L A T I V E HEIGHT 1 . 0 6 0 E - 0 1 4 . 4 5 5 E * 0 1 3 . 3 2 5 E - 0 1 1. 500 E - 0 1 . 7 . 0 3 7 E * 0 1 1 . 4 9 8 E - 0 1 1, 8 0 0 E - 0 1 8 .201E+01 2 . 0 7 9 E - 0 1 2 . 5 0 0 E - 0 1 9 . 8 1 5 E + 0 1 2 . 3 8 0 E - 0 2 2 . 9 7 O E - 0 1 1 . 0 0 0 E * 0 2 C R Y S T A L S I Z E P O P U L A T I O N DENSITY C R Y S T A L S I Z E P O P U L A T I O N DENS 1 . 0 3 0 E - 0 1 2. 3 9 2 1 * 0 7 1 .081 E - 0 1 2 . 0 9 8 E * 07 1. 1 3 3 E - 0 1 1 . 8 5 1 E * 0 7 1 . 1 8 4 E - 0 1 1 .642E+07 1 . 2 3 5 E - 0 1 1. 463E+07 1 . 2 8 6 E - 0 1 1 .309E+07 1 . 3 3 7 E - 0 1 1 .176E+07 1 . 3 8 8 E - 0 1 1. 061E+07 1 . 4 3 8 E - 0 1 9 . 6 0 4 E * 0 6 1. 4 8 9 E - 0 1 8 . 6 9 7 E * 06 1 . 5 4 0 E - 0 1 7 . 8 1 6 E + 0 6 1 . 5 9 0 E - 0 1 7 . 0 5 0 E + 0 6 1 . 6 4 1 E - 0 1 6 . 3 8 2 E + 0 6 1 . 6 9 2 E - 0 1 5 . 7 9 6 E * 0 6 1 . 7 4 2 E - 0 1 5 . 2 7 9 E + 0 6 1 . 7 9 3 E - 0 1 4 . 8 1 3 E * 0 6 1 . 8 4 3 E - 0 1 4 . 3 6 8 E + 0 6 1 . 8 9 4 E - 0 1 3 . 9 7 5 £ * 0 6 1 . 9 4 4 E - 0 1 3 . 6 2 7 E + 0 6 1 . 9 9 4 E - 0 1 3 . 3 1 8 E + 0 6 2 . 0 4 5 E - 0 1 3 . 0 4 3 E + 0 6 2 . 0 9 5 E - 0 1 2 . 7 9 7 E + 0 6 2 . 1 4 5 E - 0 1 2 . 5 7 6 E * 0 6 2 . 1 9 6 E - 0 1 2 . 3 7 8 E + 0 6 2 . 2 4 6 E - 0 1 2 . 199E+06 2 . 2 9 6 E - 0 1 2 . 038E+ 06 2 . 3 4 7 E - 0 1 1 .892E+06 2 . 3 9 7 E - 0 1 1. 7 5 9 E * 0 6 2 . 4 4 7 E - 0 1 1 .638E+06 2 . 4 9 8 E - 0 1 1 . 5 2 5 E * 0 6 2 . 5 4 8 E - 0 1 1 . 4 1 1 E * 0 6 2 . 5 9 8 E - 0 1 1 . 3 0 8 E * 0 6 2 . 6 4 8 E - 0 1 1 . 2 1 4 1 * 0 6 2. 6 9 8 E - 0 1 1 . 1 2 8 £ * 0 6 2 . 7 4 9 E - 0 1 1 . 0 5 0 E * 0 6 2 . 7 9 9 E - 0 1 9 . 7 8 8 E + 0 5 2 . 8 4 9 E - 0 1 9 . 134E+05 1 . 0 0 0 E * 0 0 1.QOOE+OO TEMPERATURE 3. 5COE+01 BESIDENCE TIME 1.700E + 02 AGITATION BATE 1.926E+03 175 " s o i i i l A T u i l i i G N 9. 500 E-01 POP. AT 0 1.74 2E+08 WEIGHT X 5. 683E-01 5.525E-01 5, 47GE-02 4.050E-02 1.850E-02 SCREEN SIZE AD 1.060E-01 1.500 E-01 1.800E-01 2.500E-01 2.970E-01 CBYSTAL SIZE POPULATION DENSITY i CUMULATIVE WEIGHT 4.603E+01 9. 079E+01 9.522E+01 9.850E+01 1.000E+02 CRYSTAL^SIZE POPULATION DENSITY 1.030E-01 2. 513E+07 1.081E-01 2.297E+07 1. 133E-01 2.099E+07 1. 184E-01 1.918E+07 1.235E-01 1.754E+Q7 1.286E-01 1.607E+07 1.337E-01 1.473E+07 1.388E-01 1.353E+07 1.438E-01 1.245 E+07 1. 489E-01 1. 13 7E+07 1.540E-01 1.0Q2E+07 1.590E-O1 8.878E+06 1.641E-01 7.895E+06 1.692E-01 7.048E+06 1.742E-01 6.315E+06 1.793E-01 5.671E+06 1.843E-01 5. 08 7 E+06 1.894E-01 4.577E+ 06 1.944E-01 4.131E+06 1.994E-01 3.738E+06 2.045E-01 3. 391 E+0 6 2.095E-01 3.084E+06 2. 145E-01 2.811E+06 2.196E-01 2.569E+06 2.246E-01 2. 352E+06 2.296E-01 2. 157E+06 2. 347E-01 1.983E+06 2.397E-01 1..826E+06 2.447E-01 1.685E+06 2.498E-01 1.557E+06 2.548E-01 1.440E+06 2.598E-01 1.334E+06 2.648E-01 1.23 7 E+06 2.698E-01 1.150E+06 2.749E-01 1.070E+06 2.799E-01 9.966E+05 2.849E-01 9. 297E+05 1.OOOE+00 1.000E+00 TEMPEJRATUfiE 3. 5C0E+01 RESIDENCE TIME 1.700E + 02 J76 AG IT ATIO N~£ AT E SUPERS ATU RATION 1.926E+03 8.230E-01 POP. AT 0 1.865E+08 WJIGHT_X 5.445E-01 3.136E-01 4. 620E-02 3.100E-02 1. 380E-02 SCREEN SIZE AD 1.060E-01 1.500 E-01 1.800E-01 2. 500E-01 2.970E-01 CRYSTAL SIZE POPULATION DENSITY i CUMULATIVE WEIGHT 5.737Er01 9.041E+01 9.528E+01 9.855E+01 1.000E+02 CRYSTAL_SIZE POPULATION DENSITY 1.030 E-01 2.888E+07 1.081E-01 2. 533E+07 1.133E-01 2.234E+07 1. 184E-01 1. 980E+07 1.235E-01 1.764E+07 1.286E-01 1. 578E+07 1.337E-01 1.418E+07 1.388E-01 1. 279E+07 1.438E-01 1. 157E+07 1. 489E- 01 1. 04 4 E* 07 1.540E-01 9.213E+06 1.590E-01 8. 167E+06 1. 641 E-01 7.269E+06 1.692E-01 6. 494E+06 1.742E-01 5.823E+06 1.793E-01 5. 232E+06 1.843E-01 4.693E+06 1.894E-01 4. 223E+06 1.944E-01 3.811E+06 1.994E-01 3. 449E+06 2.045E-01 3. 129E+06 2.095E-01 2. 84 5E+06 2. 145E-01 2.594E+06 2.196E-01 2. 370E+06 2.246E-01 2. 170E+06 2.296E-01 1. 990E+06 2.347E-01 1.830E+06 2.397E-01 1. 685E+06 2.447E-01 1.554E+06 2.498E-01 1. 436E+06 2.548E-01 1.328E+06 2.598E-01 1. 230E+06 2.648E-01 1,141E+06 2.698E-01 1. 060E+06 2.749E-01 9.866E*05 2.799E-01 9. 191E+05 2.849E-01 8.573E*05 1.000E+00 1. 000E+00 APPENDIX 7 177 0.130 i — 0.115 h E ' E UJ r-< 0100 5 o OC O 0.085 AGITATION RATE = 1926 RPM RESIDENCE TIME = 170 s x = I5°C o = 20°C ° = 25°C ' = 35°C 0070" 06 __i 0.8 0.7 0.9 SUPERSATURATION , S GROWTH RATE VERSUS SUPERSATURATION, TEMPERATURE AS PARAMETER 178 GROWTH RATE VERSUS SUPERSATURATION, TEMPERATURE AS PARAMETER 179 i i i AGITATION RATE = 1 1 ! 1 2466 RPM 0.095 RESIDENCE TIME = 235 s / x = I 5°C ^ o = 20°C JZZ • = 25°C v = 3 5 ° C E E 0.085 LU r-< or X t— 0 0 7 5 o or e> 0.065 ' 1 1 1 0 6 0 7 0 8 0 9 1.0 SUPERSATURATION , S GROWTH RATE VERSUS SUPERSATURATION, TEMPERATURE AS PARAMETER 180 — l 1 1 r — r AGITATION RATE = 1926 RPM 0.065 H I I i I i i I i I 0 6 07 08 0 9 10 SUPERSATURATION , S GROWTH RATE VERSUS SUPERSATURATI ON, TEMPERATURE AS PARAMETER GROWTH RATE VERSUS SUPERSATURATION, TEMPERATURE AS PARAMETER 182 GROWTH RATE VERSUS SUPERSATURATION, TEMPERATURE AS PARAMETER GROWTH RATE VERSUS SUPERSATURATION, TEMPERATURE AS PARAMETER 184 GROWTH RATE VERSUS SUPERSATURATION, TEMPERATURE AS PARAMETER ION RATE VS SUPERSATURATION, TEMPERATURE AS PARAMETER 1 "o 20 » 1.5 xz\ E 3 C LU cc i.o AGITATION RATE • 1260 RPM RESIDENCE TIME = 170 s x = I5°C O r -< 1 UJ _1 • o ZZ> 0.5 02 04 06 SUPERSATURATION 08 NUCLEATION RATE VS SUPERSATURATION, TEMPERATURE AS PARAMETER 187. i i i i i i i — 02 04 06 08 SUPERSATURATION , S 5 NUCLEATION RATE VS SUPERSATURATION, TEMPERATURE AS PARAMETER 188 AGITATION RATE » 1926 RPM • i 1 ' 04 06 SUPERSATURATION , S 5 NUCLEATION RATE VS SUPERSATURATION, TEMPERATURE AS PARAMETER 189 AGITATION RATE = 1260 RPM RESIDENCE TIME = 235 s ION RATE VS SUPERSATURATION, TEMPERATURE AS PARAMETER 190 NUCLEATION RATE VS SUPERSATURATION, TEMPERATURE AS PARAMETER 19.1 _ j i i . — i —'- 1 — 0.2 04 06 08 SUPERSATURATION , S5 NUCLEATION RATE VS SUPERSATURATION, TEMPERATURE AS PARAMETER 192 * 0 20 E 3 C UJ o r-< UJ 1.5 1.0 1 1 1 1 1 — AGITATION RATE = 1260 RPM RESIDENCE TIME = 380 s x = I5°C o = 20°C a = 25°C v = 35°C O 2 0.5 02 0.4 06 08 SUPERSATURATION , S" NUCLEATION RATE VS SUPERSATURATION, TEMPERATURE AS PARAMETER 193 APPENDIX 8 EQUIPMENT LIST 1. Sartor ius balance CH.E 1518 2. Lauda-Thermostat (constant temp, bath) CH.E 2862 3- Wild Microscope CHI. E 2967 k. Camera (Pentax 35 mm) CH.E 2652 19* A P P E N D I X 9 • • L a s t signon was: 09:40:20 Oser "COGB" signed on at 10:32:26 on Thu Hay 01/80 $LIST PF 1 IMPLICIT RE AL^8 (A-H,0-Z) 2 DIMENSION A (200, 5) , P {2) , PLB {2) , POS (2) 3 EXTERNAL AOX 4 READ (5,10) N,H,NV,NCON 5 10 FORMAT(513) 6 READ (5,20) ((A (I,J) , J= 1,NV) , 1= 1,N) 7 20 FORMAT(5G10.0) 8 READ (5,20) (£ (I) , 1 = 1, H) 9 IF (NCON .EQ, 0) READ(5,20) (PLB (I) , 1 = 1, M) , ( PU B (I) ,1=1, M) 10 LOG=10 11 EPSl=1.D-4 12 EPS2=1. D-4 13 IT=500 14 CALL CLQF(M,N,NV,LOG, A, P, PLB, PUB, EPSl ,EPS2,IT,IERR, NCON,AUX 15 IF (IERR.EQ.0) »RITE(6,40) IT 16 40 FORMAT ('ERROR RETURN ' , 12) 17 STOP 18 END 19 SUBROUTINE AUX (M, A, P, F, D, IND, L ,LS) 20 IMPLICIT REAL*8 (A-H,0-Z) 195 21 DIMENSION & (200, 1) ,P (1) ,D (1) 22 IF (IND. EQ. 3) RETOBN 23 Z=DLOG (A (L,5) ) 24 FE=DLOG (P (1) ) +DLOG (A (L, 1) ) *P (2) * DLOG ( A ( L , 3) ) -14166. 67/(1. 9t 25 F=FE-Z 26 IF (IND. EQ. 1) BETUEN 27 D(1)=1/P(1) 28 D(2) = DLOG(A(L,3)) 29 BETUEN 30 END 31 SUBBOUTINE LIBIT (P,DDB ,1ND,L,C) 32 IMPLICIT BEAL*8 (A-H-O-Z) 33 DIMENSION P(1),DUB(1) 34 BETUBN 35 END End of F i l e $LIST POT 1 108 2 5 0 2 0.7 2466.0 3 0.823 2466.0 4 0.95 2466.0 5 0.7 1926.0 6 0.823 1926.0 7 0.95 1926.0 8 0.7 1260.0 9 0.823 1260.0 10 0.95 1260.0 11 0.7 2466.0 12 0. 823 2466.0 13 0.95 2466.0 14 0.7 1926.0 15 0.823 1926.0 16 0.95 1926.0 17 0.7 1260.0 18 0.823 1260.0 19 0.95 1260.0 20 0.7 2466.0 21 0.823 2466.0 22 0.95 2466.0 23 0.7 1926.0 24 0.823 1926.0 25 0.95 1926.0 26 0.7 1260.0 27 0.823 1260.0 28 0.95 1260.0 29 0.7 2466.0 30 0.823 2466.0 31 0.95 2466.0 32 0.7 1926.0 33 0.823 1926.0 34 0.95 1926.0 35 0.7 1260.0 36 0.823 1260.0 37 , 0.95 1260.0 38 0.7 2466.0 39 0.823 2466.0 40 0.95 2466.0 170. 0 15.0 0.081 170.0 15.0 0.088 170.0 15.0 0.095 170.0 15.0 0.0995 170.0 15.0 0.1058 170.0 15.0 0.1132 170.0 15.0 0.0963 170.0 15.0 0. 10135 170.0 15.0 0.1057 235.0 15.0 0.066 235.0 15.0 0.07225 235.0 15.0 0.0781 235.0 15.0 0.0727 235.0 15.0 0.0763 235.0 15.0 0.0784 235.0 15.0 0.07425 235.0 15.0 0.0765 235.0 15.0 0.08025 380.0 15. 0 0.0414 380.0 15.0 0.0431 380.0 15.0 0.0451 380.0 15.0 0.041 380.0 15.0 0.0435 380.0 15.0 0.0451 380.0 15.0 0.044 380.0 15.0 0.0475 380.0 15.0 0.05125 170.0 20.0 0.0822 170.0 20.0 0.0912 170.0 20.0 0.10 170.0 20.0 0.10075 170.0 20.0 0. 1085 170.0 20.0 0.1175 170.0 20.0 0.0981 170.0 20.0 0.1052 8 170.0 20.0 0. 1133 235.0 20.0 0.06735 235.0 20.0 0.0769 235.0 20.0 0.086 0.7 1926.0 235.0 20.0 0.0742 42 0.823 1926.0 235.0 20.0 0.0784 43 0.95 1926.0 235.0 20.0 0.0842 44 0.7 1260.0 235.0 20.0 0.0755 45 0.823 1260.0 235.0 20.0 0.0791 46 0.95 1260.0 235.0 20.0 0.0841 47 0.7 2466.0 380.0 20.0 0.0433 48 0.823 2466.0 380.0 20.0 0.046 49 0.95 2466.0 380.0 20.0 0.04865 50 0.7 1926.0 380.0 20. 0 0.0425 51 0.823 1926.0 380.0 20.0 0.0462 52 0.95 1926. 0 380.0 20. 0 0.05 53 0.7 1260.0 380.0 20.0 0.04575 54 0.823 1260.0 380.0 20. 0 0.Q501 55 0.95 1260.0 380.0 20.0 0.05515 56 0.7 2466.0 170.0 25.0 0.0833 57 0.823 2466.0 170.0 25.0 0.095 58 0.95 2466.0 170.0 25.0 0.1066 59 0.7 1926.0 170.0 25.0 0. 10325 60 0. 823 1926.0 170.0 25.0 0.1115 61 0.95 1926.0 170.0 25.0 0.12075 62 0.7 1260.0 170.0 25.0 0.1015 63 0.823 1260.0 170.0 25.0 0.1 1048 64 0.95 1260.0 170.0 25. 0 0.12 06 65 0.7 2466.0 235.0 25.0 0.0727 66 0.823 2466.0 23 5.0 25.0 0.08135 67 0.95 2466.0 235.0 25.0 0.09 15 68 0.7 1926.0 235.0 25.0 0.07525 69 0.823 1926.0 235.0 25.0 0.0827 70 0.95 1926.0 235.0 25.0 0.0887 71 0.7 1260.0 235.0 25.0 0.07725 72 0.823 1260.0 23 5.0 25.0 0.08195 73 0.95 1260.0 235.0 25.0 0.0869 74 0.7 2466.0 380.0 25.0 0.04475 75 0.823 2466.0 380.0 25.0 0.046 76 0.95 2466.0 380.0 25.0 0.04865 77 0.7 1926.0 380.0 25.0 0.0435 78 0.823 1926.0 380.0 25.0 0.0486 79 0.95 1926.0 380.0 25.0 0.0535 80 0.7 1260.0 380.0 25. 0 0.047 81 0.823 1260.0 380.0 25.0 0.053 82 0.95 1260.0 380.0 25.0 0.05865 83 0.7 2466.0 170.0 35.0 0.08835 84 0.823 2466.0 170.0 35 . 0 0.1005 85 0.95 2466.0 170.0 35.0 0.1134 86 0.7 1926.0 170.0 35.0 0.1045 87 0.823 1926.0 170.0 35.0 0.1145 88 0.95 1926.0 170.0 35.0 0.1255 89 0.7 1260.0 170.0 35.0 0. 10306 90 0.823 1260.0 170.0 35.0 0. 1142 91 .95 1260.0 170.0 35.0 0. 12525 92 0.7 2466.0 235.0 35.0 0.07495 93 0.823 2466.0 235.0 35.0 O.0857 94 0.95 2466 .0 235.0 35.0 0.09615 95 0.7 1926.0 235.0 35.0 0.0772 96 0.823 1926.0 235.0 35.0 0.08495 97 0.95 1926.0 235.0 35.0 0.09369 98 0.7 1260.0 235.0 35.0 0.07875 99 0.823 1260 .0 235.0 35.0 0.08435 100 0.95 1260.0 235.0 35. 0 0.0903 1.97 101 0.7 2466.0 380.0 35.0 0.0472 102 0.823 2466.0 380.0 35.0 0.05175 103 0.95 2466.0 380.0 35.0 0.0573 104 0.7 1926.0 380.0 35.0 0.04475 105 0.823 1926.0 380.0 35. 0 0.05075 106 0.95 1926. 0 380.0 35.0 0.057 107 0.7 1260.0 380.0 35.0 0.04865 1 08 0.823 1260.0 380.0 35.0 0.05565 109 0.95 1260.0 380.0 35.0 0.06245 110 1.0 1.0 1.0 1.0 1.0 111 0.00001 -1000.0 - 1000.0 -1000.0 -1000 112 1000.0 1000.o 1000.0 1000.0 1000.0 End of F i l e $R *FTN SCARDS=PF PAR=NOSOURCE Execution Begins 10:32:39 No e r r o r s i n MAIN No e r r o r s i n AUX No e r r o r s i n LIMIT NAME NUABER OF ERRORS/WARNINGS SEVERITY MAIN 0 0 AUX 0 0 LIMIT 0 0 Execution Terminated 10:32: 42 T=0.285 RC=0 $.07 $E -LOAD+*NUMLIB 5=POT ==> *NU Mil B IS NOW INCORPORATED IN *LIBfi ARY — 2 APRIL 1979 •LIBRARY IS SEARCHED AUTOMATICALLY. ALL REFERENCES TO •NUMLIB SHOULD BE DELETED FROM YOUR FILES. IT HILL DISAPPEAR. Execution Begins 10:32:43 ITERATION 10 FUNCTION PARAMETERS 99.97456 FUNCTION PARAMETERS 99.97602 28 -19421. 16 EVALUATION 0.6602989 -224.8909 EVALUATION 3.074756 FUNCTION EVALUATIONS 34 DERIVATIVE EVALUATIONS 29 13 PARAMETERS 1 00.000 3.07471 r ' .RES-I-DUALS -2.20292 -2.26469 -0.869365 0.951168 -1.73720 -1.81068 -2. 12394 -2.16370 -1. 11969 1.05386 - 1.68581 -0.599628 -2.05697 - 1.00258 -0.988337 1. 16346 -1.99817 -0.571098 -2.40863 -0.930487 -0.892064 0.880551 -1.91089 -0.539434 -2.30815 -0.865531 0.941460 0.965 887 -1.84708 -0.697232 198' -0.714601 -0.599305 -0.517093 1.31904 1.42043 1. 41609 1.48055 1.26510 1.33505 1. 38343 -1.34144 -1.61441 -1.52989 -1. 46567 -1.59780 -0.268531 -0.218460 -0.193147 -0.30234 1 -0.235534 -0.225813 -0.141566 1.69550 1.82871 1.91723 1.82117 1.64533 1.68706 1. 73012 -0.681693 -0.850140 -0.779652 -0.727877 -0.835682 -0.777029 0.505622 0.53459 1 0.448199 0.515001 0.560950 0.596843 2.41787 2.48868 2.529 34 2. 47229 2.38864 2. 41595 2.44408 SUM OF SQUARES OF RESIDUALS 224. 8826 STANDARD DEVIATION 1.456549 * « # * # # # * # * > * * * * * * * « * * * * * * # # * # # * # # * * * * # * # # « # > * * * * # # « # * « # # * * * * * # # # * * # # * # # # # * # # { # « # # # # # # ! * # # f t # # # # # # # # # # # # # # # # # # # # # # * * # * # * # * # # * * # * # * t * # # # * * * # * * « * # « # ***WARNI NG*** OUTPUT FIELD HIDTH TOO SMALL. CONDITION OCCURRED DURING A i ORtU •SINK*. THE WRITE IS SEQUENTIAL AT RECORD NUMBER 30. FOR THIS I FIELD OF *«S HILL BE HRITTEN. # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # * # * # * # # * « . #######################################################*############# ERROR RETURN** Execution Terminated 10:32:45 T=0.625 RC=0 $.20 $SIG 199 ••Last signon was: 16:51:50 Bon Apr 28/80 User "COGB" signed on a t 09:40:20 on Thu Hay 01/80 $LIST PF 1 IMPLICIT REAL^8 (A-H,0-Z) 2 DIMENSION A (200,5) ,P (2) , PLB {2 ) ,PUB (2) 3 EXTERNAL AUX 4 READ (5,10) N,M,NV,NCON 5 10 FORMAT (513) 6 READ (5,20) ( (A (I , J) , J=1 ,N V) ,1= 1 ,N) 7 20 FORMAT (5G10.0) 8 READ (5,20) (P (I) ,1 = 1 ,M) 9 IF(NCON.EQ.O) READ(5,20) (PLB (I) , 1 = 1, M) , (PUB (I) ,1=1 ,fl) 10 LOG=10 11 EPS 1=1. D-4 12 EPS2=1.D-4 13 IT=500 14 CALL CLQF (M,N,NV,LOG , A,P,PLB,PUB,EPS 1 ,EPS2, IT, IERR, NCON, AUi 15 IF (IERR. EQ.0) WRITE (6,40) IT 16 40 FORMAT ('ERROR RETURN',12) 17 STOP 18 END 19 SUBROUTINE AUX (M,A,P,F,D,IND,L,LS) 20 IMPLICIT HEAL*8 (A-H,0-Z) 200 21 DIMENSION A (200 , 1) , P ( 1) , D ( 1) 22 IF (IND.EQ.3) RETURN 23 Z=DLOG(A(L,5)) 24 FE=DLOG (P ( 1) ) +5*DLOG (A(L,1) ) • P (2) * DLOG (A (L, 3) ) - 138 1 1. 11/(1. 25 F=FE-Z 26 IF(IND.EQ.1) RETURN 27 D(1)=1/P(1) 28 D (2) =DLOG (A (1,3)) 29 RETURN 30 END 31 SUBROUTINE LIMIT (P, DUB, IND,L,C) 32 IMPLICIT BEAL*8 (A-H,0-Z) 33 DIMENSION P(1),DUB(1) 34 RETURN 35 END End of F i l e $ L I S T POT 1 108 2 5 0 2 0.7 2466.0 3 0.823 2466.0 4 0. 95 2466.0 5 0. 7 1926.0 6 0.823 1926,0 7 0. 95 1926.0 8 0.7 1260.0 9 0.823 1260.0 10 0.95 1260.0 11 0.7 2466.0 12 0. 823 2466.0 13 0.95 2466.0 14 0.7 1926.0 15 0.823 1926.0 16 C.95 1926.0 17 0.7 1260.0 18 0.823 1260.0 19 0.95 1260.0 20 0.7 2466.0 21 0.823 2466.0 22 C.95 2466.0 23 0.7 1926. 0 24 0.823 1926.0 25 0.95 1926.0 26 0.7 1260.0 27 0.823 1260.0 28 0.95 1260.0 29 0.7 2466.0 30 0.823 2466.0 31 0. 95 2466.0 32 0.7 1926.0 33 0.823 1926.0 34 C.95 1926.0 35 0.7 1260.0 36 0.823 1260.0 37 0.95 1260.0 38 0.7 2466.0 39 0.823 2466.0 40 0.95 2466.0 170.0 15.0 0.7075E7 170.0 15.0 0.82E7 17 0.0 15.0 0.9825E7 170.0 15. 0 1.1E7 170.0 15.0 1.2375E7 170.0 15.0 1.44375E7 170.0 15.0 1.0 125E7 170.0 15.0 1.1E7 170.0 15.0 1. 23125E7 235.0 15.0 0.66875E7 235.0 15.0 0.8E7 23 5.0 15.0 1.03.75 £7 235.0 15.0 0.830625E7 235.0 15.0 0.9125E7 235.0 15.0 1.0625E7 235.0 15.0 1.0E7 235.0 15.0 1.07E7 235.0 15.0 1.21875E7 380.0 15.0 0.45E7 380.0 15.0 0.5075E7 380.0 15.0 0.575E7 380.0 15.0 0.3375E7 380.0 15.0 0.3875E7 380.0 15.0 0.43125E7 380.0 15.0 0.48125E7 380.0 15.0 0.5175E7 380.0 15.0 0.6875E7 170.0 20.0 0.88E7 170.0 20.0 0.9725E7 170.0 20.0 1.3E7 170.0 20.0 1.20375E7 170.0 20.0 1.3725E7 170.0 20.0 1.675E7 170.0 20.0 1.09375E7 170.0 20.0 1.245E7 170.0 20.0 1.43125E7 235.0 20.0 0.875E7 235.0 20.0 1.0E7 235.0 20.0 1.18125E7 201 41 0.7 1926.0 235.0 20.0 0.875E7 42 0.823 1926.0 235.0 20.0 1.01875E7 43 0.95 1926.0 235.0 20.0 1.19375E7 44 0.7 1260.0 235.0 20.0 1. 14125E7 45 0.823 1260.0 235.0 20.0 1.2325E7 46 0.95 1260.0 235.0 20.0 1.4375E7 47 0.7 2466.0 380.0 20.0 0.5E7 48 0.823 2466.0 380.0 20.0 0.6E7 49 0.95 2466.0 380.0 20.0 0.7562 5E7 50 0.7 1926.0 380.0 20.0 0.6875E7 51 0.823 1926.0 380.0 20.0 0.8E7 52 0.95 1926.0 380.0 20.0 0.96625E7 53 0.7 1260.0 380.0 20.0 O.505625E7 54 0.823 1260.0 380.0 20.0 0.6375E7 55 0.95 1260.0 380.0 20.0 0.875E7 56 0.7 2466.0 170.0 25.0 1.08E7 57 0.823 2466.0 170.0 25.0 1.3E7 58 0.95 2466.0 170.0 25.0 1.675E7 59 0.7 1926.0 170.0 25.0 1.3125E7 60 0.823 1926.0 170.0 25.0 1.5075E7 61 0. 95 1926.0 170.0 25.0 1.975E7 62 0.7 1260.0 170.0 25.0 1.2E7 63 0.823 1260.0 170.0 25.0 1.3875E7 64 0.95 1260.0 170.0 25.0 1.6 5E7 65 0. 7 2466.0 235.0 25.0 0.98375E7 66 0.823 2466.0 235.0 25.0 1. 15625E7 67 0. 95 2466.0 235.0 25.0 1.41875E7 68 0.7 1926.0 235.0 25.0 0.95625E7 69 0. 823 1926.0 235.0 25. 0 1. 125E7 70 0. 95 1926.0 235.0 25.0 1.4E7 71 0.7 1260.0 235. 0 25.0 1.2625E7 72 0. 823 1260.0 235.0 25.0 1.41875E7 73 0.95 1260.0 235.0 25.0 1.65375E7 74 0.7 2466.0 380.0 25.0 0.5375E7 75 0.823 2466.0 380.0 25.0 0.69375E7 76 0.95 2466.0 380.0 25.0 0.89375E7 77 0.7 1926.0 380.0 25.0 0.8E7 78 0.823 1926.0 380.0 25.0 0.9275E7 79 0.95 1926. 0 380.0 25.0 1.125E7 80 0.7 1260.0 380.0 25.0 0.645E7 81 0. 823 1260.0 380.0 25.0 0.8125E7 82 0.95 1260.0 380.0 25.0 1.08125E7 83 0.7 2466.0 170.0 35.0 1.2125E7 84 0.823 2466.0 170.0 35.0 1.4975E7 85 0.95 2466. 0 170.0 35.0 1.9875E7 86 0.7 1926.0 170.0 35.0 1. 42875E7 87 0.823 1926.0 170.0 35.0 1.7225E7 88 0.95 1926.0 170.0 35.0 2.28E7 89 0.7 1260.0 170.0 35.0 1.3125E7 90 0.823 1260.0 170.0 35.0 1.505E7 91 .95 1260.0 170.0 35.0 1.925E7 92 0.7 2466.0 235.0 35.0 1.0825E7 93 0.823 2466.0 235.0 35.0 1.3125E7 94 0.95 2466.0 235.0 35.0 1.6375E7 95 0.7 1926.0 235.0 35.0 1.0375E7 96 0.823 1926.0 235.0 35.0 1.2925E7 97 0.95 1926.0 235.0 35.0 1.6875E7 98 0.7 1260.0 235.0 35.0 1.425E7 99 0.823 1260.0 235.0 35.0 1.575E7 100 0.95 1260.0 235.0 35.0 1.86625E7 202 101 0.7 102 0.823 103 0.95 104 0.7 105 0.823 106 0.95 107 0.7 108 0.823 109 0.95 110 1. 0 111 0.00001 1 12 10C0.0 End of F i l e 2466.0 2466.0 2466.0 1926.0 1926.0 1926.0 1260.0 1260.0 1260.0 1.0 -1000.0 1000.0 380.0 380.0 380.0 380.0 380.0 380.0 380.0 380.0 380.0 1.0 -1000.0 1000.0 35.0 35.0 35.0 35.0 35.0 35.0 35.0 35.0 35.0 1.0 - 1000 . 1000.0 0.61225E7 0.79E7 1.1E7 0.90625E7 1.0625E7 1.3125E7 0.7375E7 0.9425E7 1.2825E7 1.0 0 - 1000 .0 100C.O IR *FTN SCARDS=PF PAB=NOSO0RCE Execut ion Begins 09 :40 :25 No e r r o r s i n MAIN No e r r o r s i n AUX No e r r o r s i n L I M I T NAME NUMBER OF ERRORS/WARNINGS SEVERITY MAIN 0 0 AUX 0 0 LIMIT 0 0 Execut ion Terminated 09:40 :27 T=0. 253 RC=0 $R -LOAD+*NUKIIB 5=POT ==> * N U M LIB IS NOW INCORPORATED IN *LIBRARY — 2 APii lL 1979 •LIBRAEY IS SEARCHED AUTOMATICALLY. ALL REFERENCES TO *NUMLIB SHOULD BE DELETED FROM YO UB F ILES. IT WILL DISAPPEAR. Execut ion Begins 09: 40: 29 ITERATION 10 FUNCTION -315637.2 EARAMETEBS 99.95357 7.238774 EVALUATION 28 FUNCTION -315258.2 PARAMETERS 99.99088 7.578023 FUNCTION EVALUATIONS 32 7.57801 IAEAMETEFS 100.000 EVALUATION 29 DERIVATIVE EVALUATIONS 12 RESIDUALS 17.9524 -142.860 21. 5264 24.7881 18.8555 19.1867 2.49614 18.9253 141. 121 25.4594 •141.898 20.6055 19.1510 20.4625 4.68369 26.0705 17.8329 -139.900 -143.670 -140.088 21.3892 24. 4334 18.5110 21.8323 18.2027 21.5502 8.38236 25.1701 19.0294 20.6055 203 20.3398 -136.035 19.4274 20.8864 21.3296 25. 9210 18.8168 22. 1647 22.5302 25. 5736 SUA OF SQUARES OF STANDARD DEVIATION 21.0723 25.6751 18. 1444 21. 5342 21.8938 24.9503 19. 4392 22.6610 25.759 8 26.1377 RES IDOALS 54.53! 21.6359 24.7958 18.8152 22.0471 25.1327 25.5289 3.75822 21.5904 10. 1961 26.5472 315258.2 -136.374 25.3734 19.2626 20.9147 25.6869 25.9607 18.9016 22. 1800 -134.480 -135. 747 25.7742 - 142. 947 21.5613 26.1511 18.980:* 19.5742 22.6309 25.3676 ##*#####################**##*****##*****#**#****##***#**«**#*# #t *»»**#*****»»* #«##«###i##**«*#»**#***#«****#*>##******##***#*it*********#**#***********##»*» ***WARNING*** OUTPUT FIELD i l D T H TOO SHALL. CONDITION OCCURRED DURING A FORMAT *SINK*. THE 1RITE IS SEQUENTIAL AT RECORD NUMBER 30. FOR THIS AN 1 FIELD OF *>S HILL BE BRITTEN. f*«*«*##«i#t«#####*#***#*****##***#*##******#**i**t*##*#«t#***#*****«*«#######< f######t*#***#*****#*###«*#*####**#**#*****##*##**####*****«###§##>****«t***** E F B O B RETURN** Execution Terminated 09:40 : 31 T=0.613 RC=0 .$.20 $SIG 

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