Origen y Curso

phases. One phase involves the study of a group of facts associated with the process—quantities of materials entering process, leaving process or in pro- cess; the compositions of original, intermediate and final products; the necessary details of auxiliary materials used in the process; and the conditions under which the various stages are operated. The second phase deals with attempts to express in figures the merit of the results achieved. In industry generally the purely quantitative relationships provide an adequate index of performance, but this is not usually the case in sugar manufacture. For instance, pol extraction and recovery which are purely quantitative figures are not adequate measures of milling or manufacturing efficiency. Other things being equal, a recovery of 86 per cent is better than one of 85 per cent, but in practice other things are not equal and the lower recovery may re- present the better performance.

In the majority of Queensland sugar factories the analytical and quan- titative data are only approximate. Actual weights are available for only a few of the materials involved, pol is used as an approximation for sucrose, Brix instead of total soluble solids, and various empirical formulae are introduced. This provides a set of figures which are substantially accurate and trustworthy for certain "normal" conditions. Should the existing condi- tions not conform to those assumed the data are rendered incorrect; and the magnitude of the discrepancies which enter depends upon the extent of the divergence from normal. The shortcomings of this control are generally recognized by the mill chemist, but in the absence of means of securing accurate data, the magnitude of the discrepancies at any time cannot be gauged.

These shortcomings of the present empirical system for cane analysis have been well known for many years, but there is no point in discarding an accepted system unless some improved method is available. Several years ago an intensive investigation into the juice weighing system of factory control was carried out. The results of this investigation showed the system to be less prone to the large seasonal variations of the empirical system, but it also brought to light several disturbing sources of inaccuracy in the method. Attention has now moved from juice weighing to the direct analysis of cane using a wet disintegrator for the determination of Brix and pol, and a Spencer or similar type of hot air circulating oven for the determination of moisture. At the time of writing this edition the matter is under investigation, and it may well be that the empirical method of analysis will be superseded by direct analysis of cane.

Quantitative Data

Materials Balances—A materials balance involves a statement of (1) the

total quantity of a particular material entering a process from various sources, and (2) the total quantity of the same material leaving the process through various avenues. In the factory, materials balances may be drawn up to cover a single stage of processing, several stages, or the whole operation, and may deal with pol, Brix, impurities, fibre, crystal, etc.

152 CALCULATIONS INVOLVED IN CHEMICAL CONTROL

Pol Balance (Empirical System)

The most important materials balance is the pol balance of the factory. Pol enters the factory only in the cane, and leaves mainly in bagasse, mud, molasses and sugar. The total of these quantities of pol leaving will normally be less than that of the pol entering, the discrepancy being due to mechanical losses, destruction of pol in the process and errors in the measurements, analyses and formulae. These losses are grouped under the title of "un- determined" losses. For convenience, each quantity of pol leaving the factory is expressed as a percentage of the quantity of pol entering the factory.

Stock—When a materials balance is taken out at an intermediate stage

of operation of a process some of the material involved may be only partly treated and held in stock. Such material may be entered in the materials balance as "in stock", but for the purposes of the pol balance it is customary to presume t h a t all the pol in stock will eventually leave the factory in sugar or final molasses, and to calculate how much of the pol in stock should pass into each of these channels. This involves the use of recovery formulae (see later) or recovery tables. A recovery formula or table will predict the percentage of the total pol in stock which may be expected later to pass out in the sugar. It follows that, if x is the percentage "recovered" as sugar, then 100 — x per cent will enter the molasses.

Normally when taking out a pol balance over a period, account must be taken of stock at both the beginning and the end of the period. The quantities of recoverable and unrecoverable pol in each stock are calculated and those figures for the beginning of the period are subtracted algebraically from the respective figures for the end of the period. The balances may be positive or negative and are accordingly added to or subtracted from the respective figures for pol in sugar and in molasses actually made during the period. Hence the pol balance becomes:—

Pol in sugar, made and estimated, per cent pol in cane Pol loss in bagasse per cent pol in cane

Pol loss in mud per cent pol in cane

Pol loss in molasses, made and estimated per cent pol in cane Undetermined loss

100

Pol in Cane—The quantity of pol entering the factory is not measured

directly but determined from the weight of the cane and the analysis of the first expressed juice, with the aid of an empirical formula—thus:—

Tons pol in cane = tons cane x pol per cent cane

Pol Loss in Molasses—This is derived from the weight of molasses and

the pol per cent molasses, with correction for stock.

where F = fibre per cent cane

Pol Loss in Bagasse—From the definition of pol extraction it follows t h a t

Pol loss in bagasse = 100 — pol extraction.

Pol Loss in Mud—This is derived from the weight of mud and the pol

Undetermined Loss—This is a residual, calculated by difference, either

in tons or per cent pol in cane. Pol Balance (Direct Analysis)

The only difference between this system and the empirical system just set out, is that pol per cent cane is determined directly, using the wet dis- integrator. Thus the empirical formula for pol in cane is not used in this method and one possible source of error is avoided.

The accuracy of the direct analysis system, as with all other analytical systems, depends of course, on the accuracy and adequacy of sampling techniques, plus strict adherence to good analytical procedures.

Overall Recovery—Overall recovery, frequently simply called recovery is the tons of pol recovered in sugar expressed as a percentage of the tons of pol in cane.

CALCULATIONS INVOLVED IN CHEMICAL CONTROL 153 Pol loss in molasses =

Pol in Sugar—This is derived from the weight of sugar and the pol of

the sugar, with correction for stock. Pol in Sugar =

and is identical with the figure for pol in sugar per cent pol in cane. Boiling House Recovery—In the boiling house recovery, the quantity of pol in sugar, made and estimated, is expressed as a percentage of the quantity of pol entering the boiling house, i.e., in the juice leaving the mills. It follows by simple reasoning that

Extraction—This is an important figure from a commercial point of view, since it relates the quantity of pol extracted by the milling plant to the quantity of pol in the cane. It also provides an estimate of the percentage of the pol in cane which enters the boiling house, and thus forms a basis for the evaluation of boiling house recovery. The extraction is calculated from the analysis of bagasse and cane as follows:—

Let— Pc = pol per cent cane Fc = fibre per cent cane

Pb = pol per cent bagasse Bb = Brix per cent bagasse W = moisture per cent bagasse Fb = fibre per cent bagasse

Then since bagasse consists of fibre, soluble solids and water—

154 CALCULATIONS INVOLVED IN CHEMICAL CONTROL I n p r a c t i c e Bb i s f r e q u e n t l y c a l c u l a t e d b y a s s u m i n g t h a t t h e p u r i t y o f t h e j u i c e i n t h e b a g a s s e i s e q u a l t o t h e p u r i t y o f l a s t e x p r e s s e d j u i c e , a n d f r o m t h i s a s s u m p t i o n : — T h e e x t r a c t i o n o b t a i n e d b y e a c h i n d i v i d u a l m i l l e x p r e s s e d a s a p e r c e n t a g e o f t h e p o l i n t h e feed t o t h e m i l l c a n b e c a l c u l a t e d b y c a r r y i n g o u t a m a t e r i a l s b a l a n c e o v e r t h e m i l l i n g t r a i n . w h e r e en = p o l e x t r a c t i o n at t h e wth m i l l e x p r e s s e d as a p e r c e n t a g e of p o l in t h e b a g a s s e f r o m t h e p r e v i o u s (n — 1) m i l l . En = p o l e x t r a c t e d p e r c e n t p o l in c a n e for n m i l l s of t h e t r a i n . En - i = p o l e x t r a c t e d p e r c e n t p o l in c a n e for n — I m i l l s of t h e t r a i n .

For example:—Consider t h e f o l l o w i n g list of p o l e x t r a c t i o n s p e r c e n t

p o l i n c a n e . N o . 1 m i l l — 7 0 . 0 N o . 2 m i l l — 8 2 . 0 N o . 3 m i l l — 9 0 . 0 N o . 4 m i l l — 9 5 . 0 T h e n e x t r a c t i o n b y n u m b e r t h r e e m i l l , e x p r e s s e d a s a p e r c e n t a g e o f t h e p o l i n n u m b e r t w o m i l l b a g a s s e : — T h e e x t r a c t i o n o b t a i n e d b y i n d i v i d u a l m i l l s s u b s e q u e n t t o N o . 1 mill c a n also b e c a l c u l a t e d a s a p e r c e n t a g e o f t h e p o l i n t h e b a g a s s e f r o m t h e p r e v i o u s m i l l i n t h e following m a n n e r : — w h e r e C = p u r i t y of l a s t e x p r e s s e d j u i c e T h i s a s s u m p t i o n i s n o t u s u a l l y c o r r e c t , t h e p u r i t y o f j u i c e i n t h e b a g a s s e b e i n g n o r m a l l y l o w e r t h a n t h e p u r i t y o f l a s t e x p r e s s e d j u i c e , b u t t h e e r r o r i n t r o d u c e d i s n o t l a r g e a n d i s f r e q u e n t l y t o l e r a t e d .

A s n o fibre i s lost o r g a i n e d i n t h e p r o c e s s , t h e q u a n t i t y o f fibre w h i c h e n t e r s m u s t e v e n t u a l l y a p p e a r i n t h e b a g a s s e . T h e r e f o r e , t h e r e a r e Fc p a r t s o f fibre e n t e r i n g a n d p a s s i n g t o t h e b a g a s s e , p e r 100 p a r t s o f c a n e , s o t h a t —

CALCULATIONS INVOLVED IN CHEMICAL CONTROL 155

Maceration—The quantity of maceration is logically considered as a percentage of fibre. It is strongly recommended that the maceration water be weighed or measured, since this gives an accurate figure for the water used, which moreover is immediately available as a guide to the correct regulation of the added water. The maceration water per cent fibre for any period is then readily calculated from the weight of water, weight of cane and average fibre in cane for the period.

The proportion of water added is often conveniently reported in terms of "dilution", i.e., the portion of the maceration water which passes into the mixed juice. This may be expressed as a percentage of undiluted juice or as a percentage of fibre in cane.

Dilution per cent Undiluted Juice—This is calculated by a Brix balance,

since the added water introduces no solids and the quantity of Brix in the diluted juice is identical with that in the undiluted juice.

Let— 100 — weight of undiluted juice,

B = Brix of undiluted juice, b = Brix of diluted juice,

x = weight of maceration water in diluted juice,

and 100 + x = weight of diluted juice (mixed or clarified juice).

Dilution per cent Fibre—This is obtained by multiplying the dilution

per cent undiluted juice by the weight of undiluted juice extracted from cane, expressed as per cent fibre, thus—

Dilution % fibre =

The expression for undiluted juice in cane is derived from the first part of the c.c.s. formula from which we have—

Filter Washing Water—The water used in washing filter cake (or in diluting mud prior to filtering) should be metered and the quantity expressed as a percentage of the dry substance in filter cake. The weight of filter cake is determined for rotary niters as described under sampling.

Pol Added to Filter Cake by Bagacillo—Some of the pol contained in rotary filter cake was present in the bagacillo added to assist nitration and theoretically had been accounted for as pol lost in bagasse. Hence a portion of the pol in the bagacillo is included in both the pol loss in bagasse and the pol loss in mud.

In measuring retention, the values Mf and Mc, Ff and Fc are determined as described in Chapter I X . There are other methods of obtaining an estimate of retention, one of which was shown in the previous edition of this manual. However, the method listed above is the only mathematically correct one which can normally be carried out in practice, and it is recommended t h a t this method be used in preference to the more approximate alternatives.

Clarified Juice per cent Cane—This quantity is obtained by means of a pol balance, thus—

Tons pol in clarified juice = tons pol in cane — tons pol in bagasse — tons pol in mud

156 CALCULATIONS INVOLVED IN CHEMICAL CONTROL

A method of correcting the observed pol loss in mud to the basis of original mud without added bagacillo was outlined in a previous edition of this Manual. Some of the reasoning involved in the calculation is open to question and the method is not recommended for adoption. The actual correction is of the order of ten per cent of the observed mud loss and there- fore is a relatively small factor on the actual pol balance.

Retention (Rotary Filters)—The calculation of retention is based on the assumption that all fibre (bagacillo) in the feed is retained in the cake.

Let— Mf and Mc be the mud solids contents per cent, and Ff and Fc the fibre (bagacillo) contents per cent,

in feed and cake respectively. Then—

Concentration and Evaporation Formulae—These formulae are similar to those for Dilution, and are calculated as follows:—

Let— 100 = weight of original juice, etc.

b = Brix of original juice, etc. B = Brix of final product,

x = water evaporated, as percentage by weight of

original juice, Then— 100 b = (100— x)B

Overall Evaporation Coefficient of Effets—This figure represents the weight of water, in pounds, evaporated per hour per square foot of heating surface, and is readily calculated with the aid of the two preceding formulae as follows:—

N.B.:—The calculation of heating surface area for effets or other vessels

CALCULATIONS INVOLVED IN CHEMICAL CONTROL 157 t o b e m a d e . T h e m e t h o d o f c a l c u l a t i o n o f h e a t i n g s u r f a c e i s l a i d d o w n i n t h e S.A.A. B o i l e r Code, A S . C B 1 , w h e r e a p p e n d i x A , s e c t i o n R - 9 s t a t e s : — " E v a p o r a t o r s , V a c u u m P a n s , E t c . — F o r e v a p o r a t o r s , v a c u u m p a n s , h e a t e r s a n d o t h e r s i m i l a r u n f i r e d vessels, t h e h e a t i n g s u r f a c e s h a l l i n c l u d e t h e t o t a l a r e a o f t u b e s , i n c l u d i n g c i r c u l a t i n g t u b e s (if a n y ) , t h e t u b e p l a t e s e x c l u d i n g t h e a r e a o f t h e t u b e holes, a n d i n t h e c a s e o f b a s k e t c a l a n d r i a s , t h e a r e a of t h e shell. F o r t h i s p u r p o s e t h e a r e a o f t h e t u b e s shall b e b a s e d o n t h e e x t e r n a l d i a m e t e r o f t h e t u b e s a n d t h e i r l e n g t h b e t w e e n t h e o u t e r s u r f a c e s o f t h e t u b e p l a t e s . T h e n e t t u b e p l a t e a r e a shall b e t h e t o t a l a r e a o f t h e t u b e p l a t e , c a l c u l a t e d o n t h e e x t e r n a l d i a m e t e r o f t h e c a l a n d r i a , m i n u s t h e a r e a o f t h e t u b e holes. I n t h e c a s e o f b a s k e t c a l a n d r i a s t h e u p p e r t u b e p l a t e , m i n u s t h e t u b e h o l e s , a n d t h e a r e a o f t h e s t e a m i n l e t s h a l l b e m e a s u r e d , a n d also, i n t h e b a s k e t t y p e , t h e a r e a o f t h e shell shall b e b a s e d o n t h e o u t s i d e d i a m e t e r a n d t h e l e n g t h b e t w e e n t h e o u t e r surfaces o f t h e t u b e p l a t e s . I n t h e c a s e o f e v a p o r a t o r s w i t h coils, h e a t i n g surface s h a l l b e b a s e d o n t h e e x t e r n a l d i a - m e t e r o f t h e coil a n d t h e coil l e n g t h b e t w e e n t h e i n l e t a n d t a i l p i p e . " R e c o v e r y F o r m u l a e — T w o r e c o v e r y f o r m u l a e a r e i n c o m m o n u s e ; t h e S . J . M . a n d t h e W i n t e r - C a r p . E a c h i s t a k e n t o r e p r e s e n t t h e p e r c e n t a g e o f t h e pol i n t h e o r i g i n a l m a t e r i a l r e c o v e r a b l e a s pol i n s u g a r . T h e S . J . M . f o r m u l a i s d e r i v e d a s f o l l o w s : — L e t — 100 = w e i g h t of p r i m a r y p r o d u c t , J = p u r i t y of p r i m a r y p r o d u c t , P = p o l of p r i m a r y p r o d u c t , S = p u r i t y of s u g a r p r o d u c e d , M = p u r i t y of final m o l a s s e s , x = r e c o v e r y of p o l p e r c e n t p o l in p r i m a r y p r o d u c t ,

Hence arises the common impression t h a t the Winter-Carp formula is a special case of the S. J.M. formula. Originally intended to express the recovery of raw sugar, the Winter-Carp formula is now used, like the S.J.M., to express the recovery of pol from the quantity of pol present in the original material.

Example—

Given 130 tons of massecuite of Brix 95 and pol 66.5—hence 70 per cent purity, calculate the quantity of sugar recoverable.

S.J.M. Formula—Assuming 100 purity for sugar, and molasses purity of 35—

It is found that by substituting S = 100 and M = 28.57 in the S.J.M. formula, the Winter-Carp formula may be derived thus—

158 CALCULATIONS INVOLVED IN CHEMICAL CONTROL The Winter-Carp formula was originally derived from the assumption that for every 100 parts of impurity in juice 40 parts of sucrose would be rendered unrecoverable. (Compare this with the c.c.s. formula.)

To derive the Winter-Carp formula consider a juice of purity J containing 100 parts of sucrose. Then

M o l a s s e s in Stock—The estimation of molasses in stock follows simply from the calculation of recoverable pol, for—

Tons pol in molasses = tons pol in stock — tons recoverable pol. The figure for pol in molasses thus derived may be used directly in the calculation of the pol balance. If it be desired to express the quantity as molasses, then

Taking Stock—All pans, tanks, and other holding vessels should be calibrated so that the volume of the product in stock may be determined readily. Stocktaking is then usually carried out by recording the volume and temperature of each product, analysing a sample for Brix and pol, and entering the results into a table of the following form:—

Stock Sheet Material A Massecuite AB Massecuite B Massecuite C Massecuite A Molasses AB Molasses B Molasses Syrup Juice Magma Temp. ° C 1 Gal- lons 2 Brix 3 *Brix at T ° C 4 ** Fac- tor 5 P o l 6 Totals Purity 7 Weight in Tons 8 Tons Brix 9 Tons Pol 10

* Brix corrected for temperature from tables supplied. ** From tables.

Column 1 shows the actual temperature of the material when the volume (column 2) is measured. Columns 3, 6, and 7 are obtained from the analytical data. The values for column 4 must be corrected to the value corresponding to the actual temperature of the material when sampled. The factors of column 5 are obtained from Table XX. The weight in tons (column 8) is obtained by multiplying column 2 by column 5 and dividing by 100, while columns 9 and 10 are calculated by multiplying column 8 by columns 3 and 6 respectively. Totals are obtained for columns 9 and 10, and their ratio multiplied by 100 shows the average purity of the materials in stock. Then from this value and the total tons of pol, the recoverable sugar may be calculated by applying the Recovery Formula. The volume of molasses expected may also be estimated, as outlined above.

The method of measuring stock outlined above is not applicable to final molasses, which, after brief storage, is usually found to be highly aerated. The quantity of molasses in storage should be determined using a weight measuring device such as the pneumercator. This device has been available for a number of years and is well described in the paper by W. R. Dunford,

160 CALCULATIONS INVOLVED IN CHEMICAL CONTROL