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THE APPLICATION O F A LITHIUM TRACER METHOD TO RESIDENCE TIME STUDIES IN A SUGAR FACTORY

P.G. Wright and R. ~ roadfdo t

Sugar Research Institute, Mackay, Queensland, Australia

ABSTRACT

The use of lithium salts as a tracer in residence time studies on sugar factory equipment is described, and its application to evap- orators, continuous vacuum pans and continuous cooling crys- tal l izer~ is discussed. The method has several significant advantages over other tracer methods, as long as a good quality flame emission photometer is available for the rapid analysis of the output samples.

Some examples of the application of the method to continuous pans and crystallizers are given, and some techniques for the re- duction and interpretation of the results of tests are described.

I INTRODUCTION

The use of tracer methods for the determination of the residence time, the degree of mixing and the dead space in continuously operating process equipment has been established as a valuable tool for the assessment of equipment design.

In the sugar factory such methods have been applied to clarifier design, evaporator residence time determination and the examination of continuous flow low grade massecuite crystallizers. Ellis and Brain1 gave an account of the use of a radioisotope tracer experiment to determine the flow characteristics of a multifeed clarifier. Mosich2 has recently used a pulse injection of sorbose, with an enzymatic assay of output samples, to deter- mine the residence time in a sugar beet factory evaporator. Foster3 used a heavy addition of common salt to characterise the flow properties of a series of crystallizers, using a flame photometric assay for sodium, but was troubled by a high and variable background level of sodium in the massecuite.

In a paper to the last ISSCT conference, Chen et a14 give a detailed treatment of the application of a radioisotope tracer method to determine the mixing characteristic of a bank of eight low grade crystallizers in series. They also include a discussion of the flow models of Bischoff and Mc- Craken' for the estimation of the residence lime distribution function under different degrees of mixing intensity.

Once an accurate concentration-time input distribution function and the output concentration-time function for the equipment is determined, there are a wide number of methods available to determine the "weighting

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function" associated with the mixing characteristics of the equipment. Some of these have been described by Andersen6. However, if the input concen- tration function is an impulse injection of tracer, it can be approximated by a Delta function, and the mathematical treatment becomes very simple. In fact the output concentration-time curve is the same as the "weighting function" alone. The main problem which still remains is the interpretation of this "residence time distribution function" to obtain an idea of the mixing characteristics of the unit.

The problem of the interpretation of residence time distribution curves has been reviewed by Levenspiel and Bischoff7. These authors have shown process equipment models for tanks-in-parallel (or mixing cells) based on the following flow regions:

(a) Plug flow regions, where the flow takes place without any component of mixing or dispersion;

(b) Back mix regions, where the regions are perfectly mixed;

(c) Dispersed plug flow regions, where turbulence within a plug flow stream can cause axial mixing;

(d) Dead water regions, where the fluid is relatively slow moving and, for all practical purposes, stagnant.

In addition to these regions, combined models may use the following kinds ol flow:

(a) Bypass flow, where portions of fluid bypass the vessel or the particular flow region;

(b) Recycle flow, where portion of the fluid leaves the vessel or region and is returned to mix with the input fluid;

(c) Cross flow, where interchange but no net flow occurs between different flow regions.

The authors review some approaches to modelling interpretation to different systems, and emphasise that it is necessary to simplify the model regions as far as possible to the major likely ones before a mathematical treatment is attempted.

In practice, in crystallizer application,. the major contributors are series backmix tank regions and shortcircuit and stagnant areas. Comparisons of performance can be made using combinations of such simple models (Chen et a14) .

Wolf and ResnickB represented the residence time distribution for real single stage systems by an F function of the form:

F( t ) = 1 - e ~ p ( - ~ ( t - ~ ) / O ) for t > = ~

P.G. WRIGHT AND R. BROADFOOT 2571

or

F( t ) = 0 for O<&t < E

where the symbols are as defined in Appendix 2.

This equation applies for a number of plausible flow models that include plug flow, dead space, short circuiting, response lag and experimen- tal error in the average residence time determination. The model can be extended to describe the experimental results obtained from multistage system as well.

Chemical or radioactive methods are most commonly employed as trac- ers for mixing studies. To compare the effectiveness of different methods, it is considered that a tracer element suitable for residence time distribution studies must, as far as possible:

(a ) behave exactly as the fluid;

(b) possess sufficiently low and constant background concentration to provide good accuracy in detection of added tracer;

(c) be readily analysed for concentration with appropriate accuracy;

(d) be chemically and physically inactive, so as not to be absorbed or to disappear by reaction;

(e) be non-deleterious to future processing operations;

( f ) be non-toxic and require no special safety precautions;

(g) be low in costs, both of materials and analysis.

The sodium tracer used by Foster3 was deficient in respect to (b) due to the high and variable background levels of this element. Radioisotope methods have an advantage in their analysis method (continuous sensing using a scintillation counter), but this is subject to proximity interference. Their main drawback relates to their cost, and to the precautions which have to be taken with use of such a potentially dangerous material. There is also the requirement for a complex correction of the results for activity changes during the test, due to the short half-life of the element which has to be chosen. After a survey of the current methods, the authors examined the use of lithium (as technical grade lithium chloride) as a tracer and, conditional on the availability of an atomic absorption spectrophotometer for the analysis of this element, this material has proven to meet the requirements listed above, and is the best tracer used for this work known to the authors.

It has since been brought to the attention of the authors that Li+ has been used regularly as a tracer in minerals processing research, as it has considerable advantages in this application (Sutherland9).

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In crystallizer investigations lithium chloride (technical grade about $US8 per kg) was mixed with about 10 litres of heavy massecuite, which was then diluted with a little water to render the mixture viscosity similar to that of the massecuite at the point of addition to the process. The amount added was calculated so that, if the tracer was directly mixed with the massecuite held in the crystallizer, the average lithium concentration would be about three parts per million. The addition of the tracer to the inflow stream was made in as short a time as possible, and sampling at the outflow point was then commenced and continued for at least three nominal resi- dence time periods. The samples were then taken at intervals related to the expectation of the outflow concentration curve, with more frequent sampling around the nominal residence time period. A total of 50 to 100 samples were collected with a sample size of 10 to 20 g. During the tests the conditions of operation were kept as steady as circumstances allowed, as the test would be discarded if the flow was interrupted excessively.

The analyses were carried out with the atomic absorption spectropho- tometer settings as in Appendix I. One gram of the sample was diluted with water and aspirated into an atomic absorption spectrophotometer in the flame emission mode of operation, and the resultant reading compared with standards to enable the actual concentration to be obtained by inter- polation. This was then corrected to a basis of the original material.

TREATMENT OF RESULTS

The concentration-time table observed could be plotted to produce an output curve which equates to the residence time distribution curve for the case of an impulse inje~tion of tracer. ~ a c k ~ r o u d a values were generally quite low and there was no difficulty in making the usual corrections for this. However, more information on the flow system can be obtained if the primary data are analysed by a computer programme to compute the frequency and cumulative distribution functions of the output, as well as the mean residence time, and the other moments of the frequency distri- bution curve. The "intensity function" is also computed to aid in the interpretation of the curves, and the use of this as a test for stagnancy has been described by Naor and Shinnarl0.

The experimental curve of residence time distribution has to be cbm- pared to the curves produced by system flow models such as have been described by Levenspiel and Bischoff7 if a complete characterisation is de- sired. These curves are easy to produce in the case of equal residence time backmix elements in series, as there is a rapid analytical solution for this case. In other cases. however. where backmix regions are of uneaual resi-

u

dence time, or where dead regions, bypass flow and plug flow klements are to be considered, the residence time distribution for such systems flow models often requires time-consuming numerical techniques. However, a most useful technique including an analytical solution has been that of Wolf and Resnick8, and this has been used here to fit experimental fre-

P.G. WRIGHT AND R. BROADFOOT 2573

quency distributions by varying the parameters 7 and r in an optimization search programme until the mean square error between the experimental and calculated curves is minimised. The expressions used are outlined in Appendix 2. It should be noted that, as is the case in all model development exercises, a good knowledge of the system under investigation is essential if meaningful results are to be obtained. The optimization search programme for determining the model parameters 7 and 6 considers only the vector space which has realistic significance. This bounded region is mapped by specifying maximum estimated values for plug flow, dead space, amount of short circuiting and response lag.

From the output concentration curve the total integrated area under the curve (after corrections for background have been made) can be com- puted and, when this is corrected with the actual measured flow rate, an estimate of the lithium recovered can be made. In the majority of the tests undertaken the lithium so accounted was within 10% of the actual amount added. In this sense therefore, the method is roughly quantitative and a cross check is available for the analysis.

Tailing of curves

Often, due to plant operation characteristics, it is impossible to con- tinue the output analyses for sufficient time to enable the lithium concen- tration to return to the background level. A tail correction must then be made if a reasonable assessment of the flow system is required.

The method which has been used is to take two suitable concentration- time points on the decaying section of the response curve, and to fit these with an exponential curve asymptotic to the background concentration level at infinite time. Extrapolation points were then taken from this fitted curve to enable a better analysis to be made.

Recycle effects ' >

Care had to be taken to anticipate the effects of recycle streams which might return tracer to the tested process and cause a periodic fluctuation in background concentration. However in most cases, this was not a serious factor. ,

s. APPLICATIONS OF THE METHOD

As examples of the application of the tracer method to the analysis of flow equipment in the sugar factory, the following are given relating (a) to the determination of the residence time distribution in continuous flow cooling low grade crystallizers and (b) to the determination of the mixing characteristics of a continuous vacuum pan, cell. These are given below:

I' 1) ,

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TABLE I. Data for crystallizer tracer trial (Application A).

Time Li + Frequency Cumulative after output concentration concentration

addition distribution distribution (h) ( P P ~ ) (h-I1

0 . 0.158 - - 0.5 0.158 - - 1.0 0.158 - - 1.5 0.158 - 2.0 0.158 A - 2.5 0./i!8 A A

3.0 0':$58 - - 3.5 o. ia8 - - 4.0 0.158 - - 4.5 0.158 - - 5.0 0.158 - - 5.5 0.265 0.0033 0.0014 5.75 0.190 0.0043 0.0025 6 .0 0.218 0.0026 0.0032 6.25 0.282 0.0057 0.0046 6 .5 0.375 0.0107 0.0073 6.75 0.438 0.0156 0.0112 7.0 0.552 0.0212 0.0166 7.25 0.702 0.0296 0.0240 7 .5 0.920 0.0412 0.0343 7.75 1.170 0.0560 0.0483 8 .0 1.210 0.0651 0.0646 8.25 1.888 0.0878 0.0855 8 .5 2.040 0.1141 0.1151 8.75 2.085 0.1203 0.1452 9 .0 1.928 0.1166 0.1744 9.50 1.918 0.1115 0.2301

10.0 1.700 0.1042 0.2823 10.5 1.855 0.1023 0.3334 11.0 1.805 0.1056 0.3862 13.0 1 .840 0.1051 (,# 0.5965 15.0 0.793 0.0730 ' , 0.7427 17.0 0.698 0.0369 0.8165 19.0 0.623 0.0315 0.8795 21.0 0.767 0.0336 0.9469 23.0 0.207 0.0205 0.9880 25.0 0.222 0.0032 0.9945 27.0 0.168 0.0019 0.9984 29.0 0.167 0.0002 0.9988 31.0 0.167 0.0001 0.9992 33.0 0.167 0.0001 0.9995 35.0 0.167 0.0001 0.9997 37.0 0.167 d . 0000 0.9998 39.0 0.167 0.0000 0.9999 41.0 0.167 0.0000 1.0000

P.G. WRIGHT AND R. BROADFOOT

A . Continuous crystallizer residence time distribution

In the actual test some 10 litres of the feed massecuite were mixed with technical grade lithium chloride containing 163.7 g of Li+ and this was added to the input stream to cooling crystallizers. The system consisted of two crystallizers each containing three vertical baffles which directed the massecuite in an underflow-overflow pattern. The crystallizers were arranged in series and were therefore equivalent to an eight compartment flow system. At the time of the tracer study considerable shortcircuiting across the baffles was occurring and it was hoped that an estimate of this could be obtained. Sampling was commenced immediately the lithium addition was made.

Table I shows the concentration of Lif in the output samples, to- gether with the time interval in hours after the addition. Also shown in Table I are some of the concentration-distribution values calculated by computation and corrected for background effects.

Table I1 lists the moments oI the concentration frequency distribution curve which equates to the residence time distribution curve of the system, since the tracer input was a pulse ('delta' function). I t is noted that the integration of the original concentration time curve, corrected for back- ground effects, gives a value of 15.809 ppm-h. Since the mass flow rate averaged 10.03 tone/h, the calculated Li+ recovery was the product of these two values or 158.5 g. This is within 5% of the amount actually added.

TABLE 11. Moments of the concentration-frequency distribution curve.

Crystallizer tracer trial

Mean residence time 12.96 h

Variance 17.55 hZ

Standard deviation 4 . 1 8 h

Third moment 64.03 hS

Total area 15.8094 ppm-h

Figure 1 shows the experimental frequency distribution versus time curve for the system as well as that for eight backmix stages of the same total residence time. This simple model gives a root mean square error of 0.017 when compared with the experimental curve. A closer match (root mean square of 0.0125) was achieved with the Wolf and Resnick8 mul- tistage model for parameter values for 7 and E of 0.7 and 0.48 respectively. A plot of this response curve is also shown in Figure 1. These two values of the model parameters (found by the optimization search programme) indicated that 30% of the flow area was shortcircuiting the backmix region of each stage. A total response lag equivalent to 0.125 of the mean residence time of each stage was also evident.

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FIGURE 1. Residence time frequency fcnction for continuous cooling crystallizers.

x - Response data ( I ) - Eight backmix tanks ( 2 ) - Flow model response

0 0 4 0 8 0 1 2 0 1 6 0 2 0 0 2 4 0 2 8 0 3 2 0 3 6 0 4 0 0

Tlme (hours)

B. Continuous low grade vacuum pan residence time distribution test

Lithium tracer was introduced into the seed feed pipe of a single con- tinuous vacuum pan cell, and the product output stream was then sampled at the outlet pipe. A total of 50 samples were taken over the next four hours and this was equivalent to approximately three nominal residence times in the cell. Table I11 shows the Li+ concentration and time readings and the concentration distribution values derived from these. Values for times over 3.8 h were extrapolated by the technique of fitting an exponential tail to the curve passing through the points 1.966 h, 0.63 Li+ ppm, and 3.80 h, 0.32 Li+ ppm, and dropping exponentially to the background level of 0.22+ ppm at infinite time.

Table IV lists the moments of the concentration-frequency distribution curve, equivalent to the residence time distribution curve for the cell.

The frequency curve is shown in Figure 2 together with the theoretical residence time curve for a single backmix vessel. This curve fits the ex- perimental response curve reasonably well, with a root mean square error of 0.0013. The continuous pan element exhibited very good circulation with turbulent boiling above the top tube plate, and it was expected that the unit would approximate in performance to a single backmix element.

The optimization search programme indicated values of and e in the Wolf and Resnickg single stage model of 1.002 and 0.03 gave the best fit to the response data with a root mean square error of 0.0007. A plot of the frequency curve for this model is also shown in Figure 2. These values of the parameters indicate a plug flow region equivalent to 3% of the total

I TABLE 111. Data for continuous pan element trial (Application B).

Time Li + Frequency Cumulative after output concentration concentration

addition distribution distribution (min) ( P P ~ ) (min")

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TABLE IV. Moments of the concentration-frequency distribution curve. Cor~tir~uous pan element trial

Mean Residence Time 75.13 min Variance 5694.4 min2 Standard deviatioh 75.5 min Third moment 838141. min3 Total area 16.08 ppm-min

volume, corresponding to a plug flow residence time of 2.2 minutes. This precedes the backmix region.

This model is considered to be a realistic approximation to the real situation occurring in the single cell vacuum pan. Here the seed enters at the bottom of the downcomer, travels through the slower moving region below the calandria before entering the tubes and the well-mixed turbulent zone above the tubed calandria.

Thus the residence time distribution of the'cell has been characterised by a realistic model, and the response of groups of such cells can be calculated as required with a good degree of confidence in the result. FIGURE 2 . Residence time frequency function for continuous pan cell.

CONCLUSIONS

The use of lithium as a tracer element Ior residence time distribution studies on sugar factory equipment seems to satisfy well the requirements of a suitable material for this type of work. The more frequent use of such techniques over the range of factory operation should increase the inder- standing of, and improve the design efforts towards improvement of such equipment.

P.G. WRIGHT AND R. BROADFOOT

ACKNOWLEDGEMENT

The authors acknoyvledge the work of Dr. R. Bsooks of the Millaquin Sugar Go., Bundaberg, Queensland in carrying out the crystallizer trial (Application A) .

REFERENCES

1 . Ellis R.W. and Brain L.R. (1960). The use of a radioactive tracer to study flow vatterns in a subsider. Proc. Qd. Soc. Sugar Cane Technol., Twenty-seventh Con- ference, p. 235.

2 . Mosich K. (1976). Untersuchen an einer Verdampfanlange wahrend de Kampagne. Z. Zucker ind., Nr. 5, p. 312.

3 . Foster D.H. (1972). Prospects for continuous crystallizers. Proc. Qd. Soc. Sugar Cane Technol., Thirty-ninth Conference, 379-382.

4 . Chen C.H., Cheng H.T. and Tong J.F. (1974). A method for determining the degree of mixing and dead space of a continuous ciystallizer. Proc. ISSCT, Fifteenth Congress, Durban, Vol. 3, p. 1187.

5 . Bischoff K.B. and McCraken E.A. (1966). Tests in flow systems. Ind, and Eng. Chem., 58, (7), 18-31.

6 . Andersen A.A. (1970). Thesis for ,Ph.D., Univ. of Queensland, Australia. 7. Levenspiel 0. and Bischoff K.B. (1963). Patterns of flow in chemical process

vessels. Advances in Chemical Engineering, (ed. Drew et a l . ) , Vol. 4, Academic Press, New York, p. 159.

8. Wolf D. and Resnick W. (1963). Residence time distribution in real systems. Ind. and Eng. Chem. Fund., 2 (4) , 287.

9. Sutherland D.L. ( 1976). Private communication, C.S.I.R.O., Chemical Eng. Divn., Melbourne, Australia.

10. Naor P. and Shinnar R. (1963). Representation and evaluation of residence time distributions. Ind. and Eng. Chem. Fund., 2 (4) , 278-286.

,'

APPENDIX 1.

Lithium analysis using the atomic absorption spectrophotometer. I Mode: Burner: Angle: Fuel:

Gain: Mode: Backing: Recorder: Concentration range:

Flame emission AB5 1 0 Acetylene 69 kPa gauge, 2 . 7 l/min Support air 103 kPa gauge, 6 . 4 l/min Coarse 8, Fine 6 % transmission 0 . 5 5 mv full scale 0 . 0 to 0 . 2 ppm

APPENDIX 2.

Equations for system model of Wolf and Resnick.

Wolf and Resnick8 consider a flow model consisting of plug flow, dead space, shortcircuiting, system lag and backrnix regions in their analysis of residence time distributions for real systems. For a single stage system of average residence time e (hold-up volume/flow rate) with fraction d of the volume considered to be dead space, then a fraction 1-d represents the effective volume through which the material flows. Assuming the material moves in plug flow through p fraction of the effective volume, and subsequently 1-f fraction of the stream flows through the remainder of the effective volume, which is pcrfectly mixed, yhile the fraction f shortcircuits this

2580 PROCESSING

section and if the combined stream then encounters a lag L, the transfer function for this flow pattern is:

( I - f ) Cu(s)/Cl(s) Lf + (1-p) (1-d) &/(I-f) + 1

] exp (-p(l-d)es) exp (-Ls) . . ( I )

where C,(s) = Laplace transform of the outlet distribution, Ci(s) = Laplace transform of the inlet distribution,

s = Laplace transform operator.

For the inlet function C l ( t ) being a step forcing function, the inversion of expression (1) yields the cumulative distribution function:

F ( t ) = l -e~p(-~(t-e) /O) for t>=e for O<=t<e

where t = time TJ = ( l - f ) / ( l -p ) (1-d)

0

and is considered a measure of the efficiency of mixing of the element.

,/e = ~ / e + p(1-d) + (1-p) (1-d) log. ( l -h / ( l - f ) . . (4)

and is a measure of the phase shift in the system.

The inversion of expression (1 for Cl( t ) approximating an impulse function yields the density distribution function:

f ( t ) = ~ / e exp(-q(t-el/@) . . ( 5 )

The single stage model can be extended to a multistage system of. n identical stages. The expression for the frequency distribution then being as follows:

Expressions ( 3 ) and (4) for the values of TJ and e/B can be modified as different flow models appear relevant, though the model outlined here should suit studies o f sugar factory equipment.

LA APLICACION DE UN METODO TRAZADOR AL LIT10 EN ESTUDIOS SOBRE TIEMPO DE ESTADA EN UNA

FABRICA AZUCARERA

" P.G. Wright y R. Broadfoot

RESUMEN

Se describe el uso de las sales de litio como trazador en estudios sobre tiempo de estada en 10s equipos de una planta azucarera; y su aplicacion a evaporadores, tachos al vacio continuos y cristalizado- res para enfriamiento continuos. Este metodo posee varias ventajas destacadas sobre otros metodos trazadores siempre que se disponga de un fotometro de emision por llama de buena calidad para el ana- lisis rapido de las muestras producidas.

El trabajo da algunos ejemplos de la aplicacion del metodo en tachos y cristalizadores continuos; y ademas describe algunas tecni- cas para la reducion e interpretacion de 10s resultados de 10s ensayos.