study of the c-curve fluctuation analysis for a cstr reactor

Study of the C-curve fluctuation analysis for a CSTR reactor

by

Kao Shiung-Pin

Thesis submitted to the Faculty of the

Virginia Polytechnic Institute and State University

in partial fulfillment of the requirements for the degree of

Master of Science

Kenneth Konrad

in

Chemical Engineering

APPROVED:

Roland. A. Mischke, Chairman

June, 1986

Blacksburg, Virginia

E. A. Manus

Study of the C-curve fluctuation analysis for a CSTR reactor

by

Kao Shiung-Pin

Roland. A. Mischke, Chairman

Chemical Engineering

(ABSTRACT)

The purpose of this study was to determine whether the fluctuations of concentration in the

exit stream for a RTD were statistically random.

A 460ml one inlet, one outlet CSTR (Continuous Stirred Tank Reactor) was set up to perform

the RTD (Residence Time Distribution) test. A electrical conductivity probe capable of meas-

uring concentration variations in volume elements of the order of 3.00 x 10- 5ml was used to

detect the tracer {sodium chloride) response. Flow rates ranging from 52 -..!!J/-to 213 rn_J min min

and agitation speeds from 0.00 rpm to 200 rpm were covered. The C-curve (concentration

curve) was found to be reproducible to within ± 5 % at agitation speed greater than 20 rpm.

The fluctuations for a C-curve were extracted and standard deviation was used to characterize

these fluctuations. The fluctuations were found to be not random statistically a:id the standard

deviation of fluctuation was reproducible to within ± 8%.

Acknowledgements

The author would like to express his deep appreciation to Dr. R. A. Mischke, Associate Pro-

fessor in the Department of Chemical Engineering, who was the thesis advisor for this inves-

tigation. The author has benefited from his knowledge, skill and attitudes towards academic

work. Furthermore, it was his advice, guidance and great understanding that made this thesis

possible. The author feels deeply indebted to him.

The author would also like to thank Dr. Peter R. Rony, Professor of Chemical Engineering, for

providing equipment as well as advice for this investigation.

Acknowledgements iii

Table of Contents

Introduction ............................................................ 1

Literature Review . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Nonideal flow reactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Stimulus-Response type analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Mixing models .......................... ·. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Data acquisition techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

Purpose of investigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

Plan of experimentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

Design and construction of the experimental apparatus. . . . . . . . . . . . . . . . . . . . . . . . 37

Reactor flow system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

Conductivity probe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

Data acquisition section .............................................. 42

Motor speed sensing section

Calibration of the apparatus.

Table of Contents

.......................................... 44

. ........................................... 46

iv

Calibration of the rotameter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

Calibration of the conductivity probe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

Calibration of the motor speed sensing section . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

Determination of the exit tracer response. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

Determination of fluctuations of exit tracer response. . . . . . . . . . . . . . . . . . . . . . . . . . . 50

Determination of standard deviation of fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

Determination of frequency of occurrence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

Determination of FFT spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

Discussion of literature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

Discussion of procedures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

Determination of exit tracer response. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

Determination of fluctuations of the exit tracer response. . . . . . . . . . . . . . . . . . . . . . . 103

Determination of standard deviation of fluctuations. . . . . . . . . . . . . . . . . . . . . . . . . . . 104

Determination of frequency of occurrence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

Determination of FFT spectrum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

Discussion of results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

Conclusions ............ , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

Summary ............................................................ 111

Bibliography. . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

Table of Contents V

Appendices .......................................................... 117

A. Design of apparatus.

Reactor flow system.

Conductivity probe.

117

117

124

Circuitry for data acquisition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

Circuitry for motor speed sensing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

B. Notes on calibration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

Calibration of the rotameter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

Calibration of the conductivity probe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

Calibration of the A/D converter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

Calibration of the motor agitation speed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

C. Sample calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

D. Materials and apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

Table of Contents vi

List of Illustrations

Figure 1. Typical C-curve for a delta input function ............................. 7

Figure 2. Plug flow reactor with side entrances. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Figure 3. Two-environment model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Figure 4. Micro- and macro-mixed model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Figure 5. Partial segregated model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Figure 6. Block diagram of a typical conductivity measurement system . . . . . . . . . . . . 31

Figure 7. Transfer and Error function for an ideal 3-bit A/0 converter . . . . . . . . . . . . . . 33

Figure 8. Schematic flow diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

Figure 9. Block diagram of probe circuitry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

Figure 10. Block diagram of data acquisition circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Figure 11. Block diagram of motor speed sensing circuit. ........................ 45

Figure 12. Rotameter calibration curve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

Figure 13. Conductivity probe calibration curve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

Figure 14. Standard deviation of fluctuations; 213 ml/min . . . . . . . . . . . . . . . . . . . . . . . . 60


Figure 16. Standard deviation of fluctuations; 147 ml/min ........................ 62


Figure 18. Standard deviation of fluctuations; 52 ml/min . . . . . . . . . . . . . . . . . . . . . . . . . 64


Figure 20. Standard deviation of fluctuations; 184 ml/min ........................ 66


List of Illustrations vii


Figure 23. Standard deviation of fluctuations; 52 ml/min . . . . . . . . . . . . . . . . . . . . . . . . . 69

Figure 24. Standard deviation of fluctuations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

Figure 25. Corelation of intercepts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

Figure 26. Corelation of slopes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

Figure 27. Effects of tracer concentration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

Figure 28. Effects of tracer width; 4ml tracer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

Figure 29. Effects of tracer width; 2ml tracer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

Figure 30. Tracer fluctuation plot; 4ml tracer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

Figure 31. Tracer fluctuation plot; 2ml tracer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

Figure 32. Sample test 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89



Figure 35. Fluctuation plot for sample test 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92



Figure 38. Frequency of occurrence distribution. ·. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

Figure 39. FFT spectrum analysis of tracer response. . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

Figure 40. Dimensions of the reactor ....................................... 119

Figure 41. Baffle dimensions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

Figure 42. Agitator dimensions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

Figure 43. Pulsing port construction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

Figure 44. Probe port construction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

Figure 45. Conductivity probe assembly. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

Figure 46. Probe signal conditioning circuit schematic. . . . . . . . . . . . . . . . . . . . . . . . . . 127

Figure 47. Analog to digital converter circuit schematic. . . . . . . . . . . . . . . . . . . . . . . . . 129

Figure 48. Motor speed sensing circuitry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

Figure 49. Motor speed sensing subroutine. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

List of Illustrations viii

List of Tables

Table 1. Standard deviation of fluctuations: now rate= 213ml/min . . . . . . . . . . . . . . . . 55

Table 2. Standard deviation offluctuations: flow rate= 184 ml/min ................ 56

Table 3. Standard deviation of fluctuations: now rate= 147 ml/min . . . . . . . . . . . . . . . . 57

Table 4. Standard deviation of fluctuations: now rate= 103 ml/min . . . . . . . . . . . . . . . . 58

Table 5. Standard deviation of fluctuations: flow rate= 52 ml/min . . . . . . . . . . . . . . . . 59

Table 6. Intercept data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

Table 7. Slope data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

Table 8. Tracer concentration effects: 213 ml/min . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

Table 9. Tracer concentration effects: 147 ml/min . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

Table 10. Tracer concentration effects: 52 ml/min . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

Table 11. Effects of tracer pulse width. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

Table 12. Rotameter calibration data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

Table 13. Conductivity probe calibration data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

Table 14. Sample AID converter data -1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

Table 15. Sample AID converter data -2

Table 16. Sample concentration data -1

Table 17. Sample concentration data -2 ................................... .

Table 18. Sample fluctuation data -1 ...................................... .

Table 19. Sample fluctuation data -2

List of Tables

146

147

148

153

154

Ix

Introduction

A stimulus-response type experiment is commonly used to obtain the residence time distrib-

ution response of a vessel to be used as a flow reactor, and this information in turn can be

used to predict the performance of the vessel as a reactor.

Frequently, because of the difficulties involved in predicting the extent of conversion for a

second or higher order reaction using the residen_ce time distribution information alone, some

mixing patterns must generally be assumed at the intermolecular level. These models are

then interconnected in various ways in order to emulate the residence time distribution re-

sponse obtained experimentally and at the same time predict the extent of conversion ade-

quately.

In going from the C-curve to the E-curve, we usually use a smoothed version of the C-curve

since this is usually adequate enough to determine the over-all shape of the E-curve or RTD

<1>.

The purpose of this investigation was to process the unsmoothed time record of the tracer

concentration response collected at the reactor exit stream in order to obtain more informa-

tion about the reactor and therefore provide, in addition to the moments < 2,3 > of the resi-

Introduction 1

dence time distribution itself, a parameter which can be used to further characterize a CSTR

reactor. Any additional parameter so obtained must be reproducible, consistent and relate to

the controlled operating conditions imposed upon the reactor system.

Introduction 2

Literature Review

This section presents a brief survey of the literature pertinent to this investigation. The fol-

lowing list outlines the topics presented:

• Non-ideal now reactors.

• Stimulus-response type analysis.

• Data acquisition techniques.

• Mixing models.

Nonideal flow reactor

The study of fluid flow in agitated tanks can be classified into three distinct categories as fol-

lows

Literature Review 3

• Gross now- Over-all flow measurements, general flow patterns, agitator pumping capaci-

ties, etc < 4 > .

• Statistical turbulence- Average velocity measurements, turbulence intensities, energy

spectra, etc < 5,6 >.

• Structural turbulence- Flow structure identification, velocity and turbulence measure-

ments, conditional sampling techniques, etc < 7 >.

The last two techniques deal with traditional flow mechanics and rely heavily upon sophisti-

cated experimental equipment. Recently, a new technique which employes digital image

processing for tracking the turbulence flow pattern has also been used < 8,9 >. The gross

flow technique for studying the fluid flow is the one employed in this investigation.

In 1940's the studies of mixing were mainly concerned with factors like drag on an impeller,

pumping capacity of an impeller, total circulating fluid in a tank, and the effects of baffles on

turbulence generation and vortex suppression. In 1953 Dankwerts < 10> proposed a concept

called RTD ( residence time distribution) for the study of general flow pattern through reactors

( vessels, beds, tubes, etc. ).

The two most commonly used idealized flow patterns in continuous flow reactor systems are

plug flow (i.e. piston type flow with complete radial mixing) and mixed flow (i.e. completely

homogeneous at any instant and location within a fluid). In real reactors some deviations from

these flow patterns will usually result because of the extent of macromixing (differences in

velocity profile) and micromixing (interactions at molecular level) that the fluid elements take

along the path from vessel inlet to outlet. For example, in plug flow deviation may be caused

by velocity profile, eddy and molecular diffusion, presence of packing, etc.. While in mixed

flow deviations may be caused by low agitation rate or viscous fluids < 11 >. In other words,

the non-ideality is a combined effect of the differences in the extent of macromixing ( mixing

Literature Review 4

on the large scale fluid dynamics level that is primarily of a convective nature < 12 > ) and the

differences in the extent of micromixing ( mixing on the molecular scale < 12-15 > ) that the

fluid elements undergo in the reactor. Therefore, while channeling of fluid, recycling of fluid,

and crossflow of fluid could be combined to account for the nonideal behaviors in the macro-

mixed level for the fluid flow through a vessel. The interactions of these fluid elements at the

intermolecular level (micromixing) could only be approximately described by assumptions of

well defined mixing models like segregated, dispersed and mixed flow models < 2 >. These

mixing models ,in general, provide reasonable physical contacting patterns among molecules

ofa fluid <16>.

Stimulus-Response type analysis

In 1953 Dankwerts < 10> published a paper which described the evaluation of reactor per-

formance by means of the residence time distribution which gives information about the frac-

tion of fluid that resides a certain time in the vessel. The details of exactly where the fluid was

during its stay are not considered and so information about point-to-point changes of the

variables is not available < 17 >. In other words, it describes the gross flow pattern of fluid

elements passing through a reactor vessel. This analysis is based upon the concept that fluid

elements taking different routes through a vessel may require different lengths of time to pass

through the vessel. The distribution of these times for the fluid elements leaving the vessel

is called the exit age distribution E, or the residence time distribution RTD of fluid. This E-

curve is usually expressed in a normalized form such that the area under the E-curve is unity,

or stated mathematically < 18 >

Ja°°Edt = 1 [1.0)

Literature Review 5

where:

t = time (min.)

The RTD distribution, or residence time frequency function as it is sometimes referred to, for

a particular vessel can be obtained by using a stimulus-response type experiment which uti-

lizes an inert tracer input into the flow stream entering the vessel as the stimulus, and the

response is a complete time record of the tracer leaving the vessel at the exit stream. The

tracer input can be of any arbitrary shape but step function, sinusoidal function, and Dirac

delta function (unit quantity at t =O, zero at all other time) are the most popular. Also, the

tracer can be of any material as long as it can be detected and does not disturb the flow pat-

tern in the vessel. Techniques required in actual detecting and recording the tracer response

as a function of time will be described later.

If a delta function tracer input signal is applied at the upstream of a vessel, then the down-

stream tracer concentration response as a function of time after normalization is called a C-

curve

Cdt = - = 1 SCX) SCX) C 0 0 Q [2.0)

where;

Q = J000 cdt= Total area under C-curve

c = measured tracer concentration response; mg/I

Figure 1 shows a typical C-curve for an impulse tracer test.

Literature Review 6

C

o function tracer input

I l I I I l I I I

Tracer output C curve

I ----,-------- -

I I

t t

Figure 1. Typical C-curve for a delta Input function: Levenspiel, 0., 'Chemical Reaction Engi-neering•, Page 257. John Wiley and Sons Inc. New York, N. Y. 1972.

Literature Review 7

It has also been shown by Levenspiel < 18 > that at steady-state flow, the C-curve gives di-

rectly the E-curve, e.g.

C(t) = E(t) (3.0]

where;

t = time (min.)

This relationship will only hold true if the vessel under test can be considered a closed vessel

by which we mean that there is no backmixing at the point in the flow stream where the tracer

is introduced and the point where the measurement is taken.

For a perfectly mixed vessel, the E curve is defined as < 10, 18, 19 >

-vt E(t) = x e-v-

V

where;

t= time; min.

v= inlet flow rate; ml/min.

V= volume of the reactor; ml

[4.0]

For most E-curves obtained experimentally, deviations from the perfectly mixed exit age dis-

tribution exist. Plug flow regions, by-passing, and deadwater regions are the major causes

for these deviations.

Plug flow regions are regions of fluid within the vessel which experience little or no axial

mixing. By-passing of fluid occurs when part of the fluid passes directly to the flow of the, exit

stream after entering the vessel. Deadwater regions refer to regions of fluid within the vessel

that are stagnant.

Literature Review 8

Therefore, the E-curve obtained experimentally can be used to describe the velocity variations

within the vessel and the average time available for the fluid elements to react within the ac-

tual reactor vessel. But the difficulties involved in applying this information to the prediction

of conversion lie in the fact that the extent of micromixing is not fully defined by the RTD

< 16, 19 > . Put another way, the E-distribution information for a particular vessel alone is in-

sufficient in terms of predicting the conversion ratio in situations where nonlinear reactions

are involved. A mixing model must be proposed which on one hand will be consistent with

the E-curve obtained experimentally while on the other hand will provide some well defined

intermolecular activities for the fluid elements passing the vessel in order to perform the

conversion prediction more precisely. Therefore, some assumptions must be made on the

extent of micromixing within the vessel. In order to accomplish this, various mixing models

were proposed to provide a better defined fluid contacting pattern ( i.e. extent of micromixing

) in the vessel and at the same time simulate the RTD ( i.e. state of macromixing ) obtained

experimentally for that vessel to a reasonable extent.

Mixing models

Mixing models are used to describe the extent of micromixing in a reactor vessel. Generally,

these models are not based on any physical reality but rather they provide a simple but ade-

quate mechanism to describe the observed reactor performance.

For reactors operating in an inherently well defined mixing condition such as in the case of

plug flow, laminar flow, or well mixed flow, the RTD can be derived analytically without any

experimental data. This analysis involves using the velocity profile in the solution of the

transient mass balance equation for the actual reactor system.

Literature Review 9

In cases where the experimentally obtained RTD differs notably from the well defined situ-

ations mentioned above, a suitable mixing model is proposed to help describe the perform-

ance of the vessel as a reactor. These models serve to interpret the tracer response data,

by simulating the gross flow pattern using dead space, short channeling etc., while at the

same time improving the accuracy of conversion prediction by providing a contacting pattern

on the molecular scale < 31 >.

It is possible to interpret a single RTD response with different states of micromixing taking

place < 19 >; therefore, more than one mixing model can be used to emulate the RTD ob-

tained experimentally. Exactly which mixing model best describes the actual extent of macro-

and micro-mixingin a vessel can only be determined by a model's ability predict the conver-

sion of a non-linear reaction taking place in that vessel.

Macrofluids and microfluids.: The concept of macrofluids and microfluids <13,18> can be

defined as follows;

• A macrofluid describes the intermolecular level activities of the individual fluid elements

as regions of batch reactors, each responsible for its own mixing activity. Therefore, in

a macrofluid there exists lumbs of fluid (aggregates) which stay as a whole and do not

react with molecules from other lumbs during their entire stay within the vessel. The

mixing state that produces the situation described above is defined as macromixing and

assumes that fluid enters the reactor in aggregates which remain as such throughout

their stay in the reactor with each aggregate acting as a batch reactor.

• A microfluid is defined as a fluid whose individual molecules lose their identities com-

pletely. As a result, the molecules are distributed uniformly within the vessel and there-

fore exhibit no segregation (lumbs of fluid) anywhere within the vessel. The mixing state

which would produce the fluid described above is called micromixing which inherently

assumes instantaneous mixing and uniformity of fluid elements throughout the vessel.

Literature Review 10

Segregated flow model: In vessels where fluid elements experience a minimum amount of

intermixing, the mixing state can be approximated by macromixing, since in macromixing the

aggregates do not mix and therefore represent a condition with late intermixing. This model

is called the segregated flow model < 13,19 >. This model can be expressed mathematically

as

- 00-c = Jo Cbatch x E(t) x dt

where;

C = Fraction of reactant unreacted

= CA CAO

Cbatch = Fraction of reactant remaining in an aggregate between time t and t + dt

E(t) = Fraction of exit stream consisting of aggregates between time t and t + dt

CA = exit concentration of the reactor

CAo = input concentration of reactant A

C = reduced concentration

[5.0]

To use equation 5.0 for predicting the exit concentration of a reaction, the E-curve must be

obtained experimentally and the reaction rate-equation must be known in order to calculate

~atch· This model will simulate a vessel having a minimum amount of micromixing.

Maximum mixedness flow model: A maximum mixedness flow model, non-segregated flow

model <·19 >, has also been proposed. It describes a mixing state in which the intermolec-


ular mixing is performed as early as possible throughout the vessel and therefore maximum

intermixing is obtained and minimum degree of segregation achieved. This model divides the

residence time of a molecule into two parts, the time the molecule has spent in a vessel and

the time that it will spend in the vessel (life expectation), or

t, =a+ 'A, [6.0]

where:

t, = residence time of a molecule (min.)

a = age of a molecule (min.)

'A, = life expectation of a molecule (min.)

Two functions have further been defined. The life expectancy distribution F('A,) states that at

the entrance of a reactor, the life expectation of the molecule equals the maxi mun residence

time and decreases to zero at the exit of the reactor. This life expectancy frequency function

f('A,) is then stated as

/{'A,) = dF(A) d'),,,

therefore

For a reactor system as shown in Figure 2 on page 14 Zweitering < 13 > stated that

de = R(c) + _r,_(A_)_ ( ) d'A, 1 - F(A) x c - co

Literature Review

[7.0]

[8.0)

[9.0]

12

where;

c = concentration of fluid ( moles) I

c0 = concentration of incoming fluid ( mo;es)

R(c) = reaction rate ( mole~ ) Ix mm


parallel feed line -~ ., ,, 'I, 'I, ,if ,if

inlet outlet -. ... ,

V <

Figure 2. Plug flow reactor with side entrances.: Zwietering, T. N., "The degree of mixing in continuous flow systems·, Chem. Eng. Sci., 11,9 (1959)


de = ....!.... x R(c) + f(y) x c - 1 dy Co 1 - F(y)

where;

y = ...?:_= reduced time 't

-r = = space time (min.)

c = g0 = reduced concentration

[10]

Zweitering went further to show that the life expectation function in terms of 'A. is the same as

the age distribution in terms oft,. This means that

/{y) = £(0)

and

F(y) = siE(0)d0

where;

0 = = ..L = reduced time V -r

t = time (min.)

v= inlet flow rate (ml/min.)

V = volume of the reactor (ml)

't = = space time (min.)

[11]

[12]

By obtaining the E-curve experimentally for a vessel we can predict the conversion ratio of a

reaction with known rate-equation using the non-segregated flow model.


The segregated flow model describes a fluid with a maximum degree of segregation while the

maximum mixedness flow model describes a fluid with a minimum degree of segregation.

Therefore, these two models set the upper and lower limiting values of convarsion for a re-

actor vessel. As for which model sets the upper limiting conversion value depends on the

kinetics of the reaction.

Other mixing models are mainly proposed to describe the intermediate degree of segregation

between the two limiting cases mentioned previously and serve to describe the reaction con-

version when the two limiting flow models fall short. In order to characterize micromixing

Danckwerts < 13 > proposed a parameter called the degree of segregation (J) which was

defined as follows

f(X)( - 2 JO a - a) l(a)da

where

var a= Total variance in age within a system

var aP = Variance in age between points in a system

a= Mean age of molecules in a system, time

/(u) = Internal age distribution of molecules in a system, time- 1

V = Total volume of the reactor system, L 3

v= Volume element, L3


The volume integral Jv represents the sum over all points. The term point is a volume element

small compared with the size of the whole reacting volume but large enough to contain many

molecules ( say, 1012 ). In finding the J parameter, the total variance in age within a system (

var a) depends only on the residence time distribution whereas the variance in age between

the points (var ap) changes from a maximum value equal to the total variance when the system

is completely segregated to a minimum value characteristic of the residence time distribution

when the system is in the state of maximum mixedness. This minimum v~lue is equal to zero

for the RTD of a perfectly-mixed vessel and is greater than zero for all other residence time

distributions. Because of the difficulties, of a mathematical nature, involved in calculating

var aP for a system, mixing models are proposed in such ways as to utilize the simplicities, in

terms of the age distribution within a point, of the two limiting micromixing cases (i.e. com-

pletely segregated and maximum mixedness). For the case of completely segregated flow,

the mean age of a point is the same as the age of every molecule within the point. In maxi-

mum mixedness flow, it is characteristic that all elements within a point have the same life

expectation and elements of the same life expectation have identical age distributions < 19 >.

However it should be noted that for vessel systems having the same residence time distrib-

ution and the same degree of segregation may nevertheless produce different degrees of

conversion < 15 >.

The two-environment model: Ng and Rippin proposed a two-environment model < 11,27,28 >

to simulate the intermediate degree of segregation for an arbitrary RTD by considering the

reactor to consist of two environments which correspond to the extreme cases of mixing, i.e.

complete segregation and maximum mixedness. As shown in Figure 3, the reactor feed is

assumed to enter the segregated environment first. Material from the segregated environ-

ment either leaves the reactor or is transferred to the maximum mixedness environment. The

output from the reactor is then a combination of the flows from the two environments.


age a=O a= oo

segregation environment feed

product

maximum mixedness environment-----

A= oo

life expectation

Figure 3. Two-environment model: Rao, D. P. & Louis L. Edwards, ·Mixing effects in stirred tank reactors: a comparison of models·, Chemical Engineering Science 28 1179, 1973


An innumerably large number of laws governing the material transfer from the entering to the

leaving environment would be possible. Ng & Rippin have proposed the following three :

<27>

1. Every point spends the same fraction of its residence time in each environment.

2. The rate of transfer of material from the entering to the leaving environment is propor-

tional to the amount of material remaining in the entering environment.

3. The rate of transfer of material from the entering to the leaving environment is propor-

tional to the concentration difference between the two environments.

The second governing rule above was considered to be most reasonable and worked out in

detail by Ng & Rippin.

If the second governing rule for material transfer between the entering and leaving environ-

ment applies then the material transfer between these two environments can be derived as

follows:

dm = -m x R1 dt

where

m = units of a particular material are in the entering environment at any time, t

R, = transfer parameter

If at t= 0, m=m 0

Literature Review

[13)

19

In ratio of m and m0

Then

Where:

FE(a) = fraction of m of age a remaining in the entering environment

FL(a) = fraction of m of age a remaining in the leaving environment

a= age (time)

Now, the following can be derived for the average concentration in the exit stream after a

rather lengthy mathematical manipulation

[14]

Where


C = average exit concentration

CL= Cone. of reactant in the leaving environment

C0 = Initial cone. of reactant in the entering environment

C(u) = Cone. of reactant at age a in the entering environment

'f = Mean residence time

To use this model an arbitrary RTD and an arbitrary reaction kinetics are needed. The feed

is assumed to be premixed.

Micro- and Macro-mixed model: Manning and coworkers studied the turbulence inside a agi-

tated vessel and found that the turbine impeller can completely mix two different streams in

the time they take to pass the physical confines of the impeller, that is within a fraction of a

second. However, outside the impeller the mixing is by no means so intense < 21 >. Based

upon this finding they proposed that a physical model, see Figure 4 on page 24, which divided

a agitated vessel into two zones

1. A small micro-mixer surrounding the impeller. The volume of this zone is negligibly

small.

2. A large macro-mixer, which occupies the remaining tank volume.


Two feed conditions were considered by Manning, one was the macro-mixed feed while the

other was the micro-mixed feed < 29 >. Only the micro-mixed feed will be considered here.

Figure 4a on page 24 shows a typical stirred, baffled vesssl in which the feed is assumed to

be completely micro-mixed with the recirculating stream at the impeller before it reacts.

Figure 4b on page 24 presents the model flow and mixing patterns. The vessel is assumed

to be composed of a micro-mixed area near the impeller and a macro-mixed area which in-

cludes the rest of the vessel volume. Aggregates in the macromixed area are circulated into

the micro-mixed area and get micro-mixed with the feed then discharged into the macro-

mixedarea. The output concentration C0 of the reactor vessel can be written as < 29 >

[15]

where

C0 = Output stream concentration.

c0 = ((Q - F)~ 0 + FCF) - Impeller discharge concentration when it leaves impeller.

Cq(t)batch = Impeller discharge concentration variation with time in a completely micro-

mixed, constant volume, batch reactor when it leaves the vessel.

CF= Feed concentration when it enters vessel.

E(t) = Residence time distribution function.

Q = Impeller pumping capacity.


F = Feed rate.

t= Time.

Concentration variation with time in a perfectly micro-mixed batch reactor, Cq(t)batch• depends

on the reaction rate order and stoichometry. E(t) can be any arbitrary RTD. C0 can then be

solved if the vessel operating conditions are known.


output

(A) Physical picture

recirculation .

duct I - - -----;------ --I pro

I I input feed . I I - --, macro-mixer

I I I I

- - - - - __ J discharge

micro-mixer

(8) Flow and Mixing pattern

Figure 4. Micro- and macro-mixed model: Manning F. S., David Wolf, and D. L. Keairns, #Model simulation of stirred tank reactors#, AICHE J. 11 723, 1965


Partial segregation model: In 1979 Valderrama and co-workers < 30 > proposed this partial

segregation model for simulating the intermediate degree of segregation for a flow reactor.

Readers are referred to Figure 5 for the following discussion. This model assumes that all

entering fluid (V,1) remains segregated up to an age a,. The portions of the flow with residence

time less than a, leave the reactor, having experienced only uegregated flow. The fluid leav-

ing V,1 with an age a, is distributed into a system of two environments formed by one segre-

gated environment (V,2) and one of maximum mixedness environment Wm) which are assumed

to be connected together, no transfer between these two environments, in parallel. A pa-

rameter called " micromixing parameter" (co1) is used to define the flow ratio between Vm and

V,2 environment.


~Q,f, --II\ ,11, I" '~ I\

co,Q microfluid f,,, ... , v,,, Q, j

macrofluid

- - -, , r

Q V,1 f,(a) fc

W2Q macrofluid

-r

V,z f,2

Figure 5. Partial segregated model: Valderrama, Jose 0. and Alfredo L.Gordon, "Mixing effects on homogeneous p-order reactions. A two-parameter model for partial segregation•, Chemical Engineering Science 34 1097, 1979


The total flow which leaves the reactor with an age less than as ,

[16]

Where

E(a) = Residence time distribution

p = Auxiliary distribution parameter

with a conversion fs

[17]

the coefficient as then is,

[18]

where

fe{a) = Conversion from a single aggregate

f= Conversion

rA = Rate of reaction for the limiting reactant A

CAo = Initial concentration of A


f,(a,) = Conversion of flow with age= a, that leave V,1

the conversion f,2 from the segregated environment V,2 is,

dy _ ( ) + E (A) ( _ ) dx - r A y 1 - F(A.) y Yo

with

dy -(A. -+ 00) = 0 dA.

where

C y = _A_

CAO

E(A.) = Residence time distribution

CA= Concentration of A

The global conversion fc at the output of the two -environment section is written as

where

Literature Review

[19)

[20)

[21 I

28

co, µ=---

1 -

co1 = Micromixing coefficient

At the exit of the reactor, the actual conversion is expressed as

[22]

To use this model a reaction kinectics and a RTD are needed to determine the various con-

versions and parameters for this model. One important restriction on the validity of this model

is that the feed of reactants must be premixed.

Data acquisition techniques

This section of literature review will cover the techniques required to detect the exit stream

tracer response in a stimulus-response type experiment and to transmit this response into a

digital computer system for ease of data processing.

Generally, a certain physical property of the exit stream will change in accordance with the

tracer concentration in the exit stream in a mathematically related manner. These changes

in the selected physical property of the exit stream will in turn be detected by a transducer

which will again convert these changes to a continuous analog signal electrically in a math-

ematically related manner. An analog signal can thus be generated to monitor the exit stream

tracer concentration response as a function of time in a stimulus-response type experiment.


For example, a tracer can be selected such that changes in its concentration in the exit stream

will vary the electrical conductivity of the exit stream of flow accordingly. Then, the variation

in conductivity of the exit stream can be picked up in turn by a conductivity probe which should

have adequate sensitivity, range, and frequency response as the situation calls for. As a re-

sult, an analog signal will be provided at the output of the conductivity probe.

One such probe < 20,21 > was reported to be capable of measuring concentration variations

in volume elements of the order of 3.00 x 10- 5 ml over a concentration range of six orders

of magnitude and frequency response bandwidth of the probe was reported to be 8 kHz. A

block diagram in Figure 6 shows how this probe can be implemented as a transducer in a

stimulus-response type experiment.


probe AC 1-------~cmodulator

amplifier

carrier

wave

analyzer

squaring

circuit

averaging averaging

mean square mean circuit circuit

Figure 6. Block diagram of a typical conductivity measurement system: Lamb, D. E., F. S. Man-ning and R. H. Wilhelm, 'Measurement of concentration fluctuations with an electrical conductivity probe', AICHE J. vol 6, pp. 682, 1960


The essential elements in that block diagram are the signal conditioning blocks. These func-

tion blocks can usually be accomplish by integrated-circuit operational amplifier based cir-

cuits. Functions like amplifying, summing, integrating, differentiating, rectifying, function

generating, and filtering are the most common ones. In situations where real time data

processing are essential, VLSI (Very Large Scale Integration) signal processors can be used.

These processors usually offer a basic set of arithmetic operations which can be accessed

by programming. These arithmetic operations are then combined to implement a specific

processing requirement on the data input to the processor. Applications like real time FFT (

Fast Fourier Transformation ) can be implemented this way.

Taking advantage of the computational power offered by digital computers nowadays, the

appropriately conditioned analog signal from the conductivity probe can be converted into

digital form easily by using one of the many LSI (Large Scale Integration) integrated circuits

made for that purpose. These LSI circuits are referred to appropriately enough as A/D (analog

to digital) converters.

An analog-to-digital converter (A/D converter or ADC) takes an unknown continuous analog

input signal, most often a voltage, and converts it into an n-bit binary number which can then

be manipulated by a digital computer system. The n-bit number is a binary fraction repres-

enting the ratio between the unknown input voltage and the converter's full scale voltage (the

maximum voltage that can be converted by an A/D converter.) For example, an ideal 3-bit

A/D converter which accepts a full scale voltage of v,. as the analog input will convert the

analog signal into 23 (8) discrete binary numbers. The resolution of the converter, in this case,

is said to be ~• which is the finest detail it can resolve the applied analog input voltage into.

Figure 7 shows the transfer function (input-output relation) and the error function (errors due

to quantization of an analog signal) for this 3-bit ideal A/D converter < 22-25 >.


111 /

110 /

/ "Cl 101 0 (.) - / :, P.. 100 / -:, 0 / u / Q 011 <

/ 010

/ 001

/ /

000 1 2 3 ..i 5 6 7 1 8 8 8 8 8 8 8

analog input voltage ( x V1,)

a. Transfer functio~ for an ideal 3-bit A/D converter. 1 LSB

.l LSB 2

- _l LSB 2 -1 LSB

b. Error function for the same converter.

Figure 7. Transfer and Error function for an Ideal 3-bit A/D converter: Jaeger, Richard C., "Tu-torial: analog data acquisition technology-t, IEEE-Micro, pp. 20, May 1982


After acquiring these binary numbers into the digital computer system, a transfer function can

be found which will relate these binary numbers to the physical property being monitored by

the transducer. The digital computer system can then treat the variations of the physical

property as a function of time and analyze this function in a number of ways: curve fitting, in-

tegrating, smoothing, and frequency spectrum analysis being the most popular, but the pos-

sibilities are only limited by our imagination.


Experimental

This section contains the following:

• Purpose of investigation

• Plan of experimentation

• Results

Purpose of investigation

Traditionally, the tracer response data obtained from a stimulus-response type experiment for

a reactor is used to calculate an exit-age distribution curve. The variance and mean value

of this curve can be used to characterize the curve and these values can in turn be used to

describe the over-all now pattern of the reactor. A family of curves based upon a certain se-

lected mixing model could then be used to match the curve obtained experimentally. There-

fore various physical models using different regions of plug now, mixed now, dispersed now,

Experimental 35

and deadwater could be interconnected by means of bypass, recycle or crossflow to simulate

the behavior of the actual reactor under test in terms of both the velocity variations and the

extent of micromixing in the vessel.

The purpose of this investigation was to determine the possibility of analyzing the tracer re-

sponse information collected at the exit stream of a CSTR reactor during a stimulus-response

type experiment in terms of the fluctuations around the instantaneous mean of the exit con-

centration record during the lifetime of the tracer effluent flow in order to find a unique and

meaningful parameter which could distinguish the completeness of mixing within the vessel.

In this investigation no attempt was made to fit the resulting RTD curves of our tests into a

mixing model which would usually impose some assumptions on the extent of local mixing in

the reactor vessel, but rather we felt that the fluctuation in the exit stream concentration re-

cord itself would reveal information beyond that contained in the shape of the mean concen-

tration curve. Therefore, an effort was made to process the unsmoothed time record of the

tracer concentration response collected at the reactor exit stream in order to obtain more in-

formation about the reactor. This information, in addition to the gross flow pattern information

obtained from the shape of the residence time distribution, was used to define a new param-

eter describing the completeness of mixing in a CSTR reactor. Any additional parameter so

obtained must be reproducible, consistent and relate to the controlled operating conditions

imposed upon the reactor system.

Experimental 36

Plan of experimentation

The experimental plan for this investigation consisted of the following operations:

• Design and construction of the experimental apparatus.

• Calibration of the apparatus.

• Determination of exit tracer response.

• Determination of fluctuations of the exit tracer response.

• Determination of standard deviation of fluctuations.

• Determination of frequency of occurrence.

• Determination of FFT spectrum.

Design and construction of the experimental apparatus.

The experimental apparatus can be divided into four parts as follows

• Reactor flow system.

• Conductivity probe.

• Data acquisition section.

Experimental 37

• Motor speed sensing section.

Each of these will be described in the following paragraphs in that sequence.


A schematic flow diagram for the reactor flow system can be found in Figure 8. As can be

seen from the schematic, this portion of the apparatus includes a vessel which can serve as

a reactor, a holding tank, a rotameter, a tracer pulsing port, and a conductivity probe port.

There was also a constant temperature bath built around the vessel but never used in this

investigation since all the tests were conducted at ambient temperature. Only one of the two

flow lines was used in this investigation. The constant temperature bath and the second flow

line were intended for further study but were built as part of the reactor flow system in this

investigation.

In order to introduce tracer into the flow stream, a tracer pulsing port was installed 177.8mm

upstream of the vessel bottom entrance. The conductivity probe which was used to measure

the tracer response was installed through the wall, using a three way tube fitting, 101.6mm

downstream of the vessel exit at the top of the vessel. Detailed information about the reactor

flow system, including dimensions of the baffle and agitator, can be found in Appendix A, page

117.

Experimental 38

~holding tank

~motor constant temperature bath

agitator

drains rotametcr

pulsing port

L

Figure 8. Schematic flow diagram.: flow diagram for the reactor system.

Experimental

1' probe

39

Conductivity probe.

The conductivity probe used in this investigation was constructed following the design of D.

E. Lamb, F. S. Manning and R. H. Wilhelm < 12 >. The probe was made from a pair of

platinum wires inserted through a tenon slug and installed in apiece of stainless steel tube.

Detailed information on the construction of the conductivity probe can be found in Appendix

A, page 126.

The signal from the probe was fed to a signal conditioning circuit, the block diagram of the

circuit is shown in Figure 9. A complete schematic of the circuit used is shown in Appendix

A, page 129. This conditioned signal was referred to as the probe output which was then fed

to the input circutry of the data acquisition section which we are going to discuss in the fol-

lowing section.

Experimental 40

probe

0.8v p-p 15khz sme wave

span control

offset control

gain &

rectifier

~--- inverter

r-c filter

summer &

filter

Figure 9. Block diagram of probe circuitry.: this figure showed the block diagram for the probe signal conditioning circuitry.

Experimental 41

Data acquisition section

This section of the apparatus took a continuous analog signal from the conductivity probe and

converted it into an 8-bit binary code fed to a digital computer system. The major component

in this section of the apparatus was an integrated-circuit AID converter (ADC0808). A block

diagram of the data acquisition circuit is shown in Figure 10. Readers are referred to Ap-

pendix A, page 130 for detailed information, including circuit schematic, on construction of this

section of apparatus.

Experimental 42

voltage reference

programmable i/o port

address decoder

analog input

ADC converter

rmcroprocessor

Figure 10. Block diagram of data acquisition circuit.: this figure showed the block diagram for the A/D converter.

Experimental 43

Motor speed sensing section

The major component of this section of the apparatus was an integrated-circuit programmable

timer/counter module (MC6840). This IC was used to measure the rotating frequency of the

motor which was used to drive the agitator used in this investigation. A block diagram of the

motor speed sensing circuit is shown in Figure 11. A detailed description, including circuit

schematic, of this section of apparatus can be found in Appendix A, page 132.

This completes the design and construction of the experimental apparatus section.

Experimental 44

pulse width counter

opto sensor

signal conditioner t

-1,

address decoder~

bus transceiver

1' microprocessor

Figure 11. Block diagram of motor speed sensing circuit.: this figure showed the block diagram for the motor speed sensing circuitry.

Experimental 45

Calibration of the apparatus.

The calibration procedures used in this investigation were as follows;

• Calibration of the rotameter.

• Calibration of the conductivity probe.

• Calibration of the motor agitation speed.

Calibration of the rotameter.

The rotameter was calibrated with stream of water flow. The resulting calibration curve for

the rotameter is shown in Figure 12. The detailed procedures used and the resulting cali-

bration data for the rotameter can be found in Appendix B, page 138.

Experimental 46

Rota.Meter- calihr-ation curve 24.....,_ ______________________________ ..,

! flow rate (Mlhiin)

200

160

120

...... 80 C .... :E ...... -:E ..... <II ... ni

40 :a 0 -...

"'Cl .... :::J -

12 1

Scale on rotaMet~r

Figure 12. Rotameter calibration curve.: this was the rotameter calibration curve.

Experimental 47

Calibration of the conductivity probe.

The conductivity probe was calibrated with a standard solution made from 0.218g of pure

sodium chloride and 250ml of clean water. A calibration curve which gave the input-output

relation between the concentration of the solution and the 8-bit binary code output by the A/D

converter is shown in Figure 13. Detailed calibration procedures used and the calibration data

obtained for the conductivity probe can be found in Appendix B, page 139.

Experimental 48

Conductivitg p:rohe calih~ation Clll'lle 1

/J. saMpled at :rooR teMpe~att.lN!, .9

.8

.7

.6

.5 / ..... -' i' ,3 ..... C 0 .... .... .,, . 2 .... C QI

C .1 0 -.... 0

29 49 69 89 1 9 1 0 1 0 1 0 1 9 2 9 2 0 2 925

ADC conve~te~ Nading

Figure 13. Conductivity probe calibration curve.: this was the probe calibration curve.

Experimental 49

Calibration of the motor speed sensing section

The motor speed sensing section was calibrated with a stroboscope, strobe light. The detailed

procedures used, including the software subroutine used, can be found in Appendix B, page

144.

Determination of the exit tracer response.

The exit tracer response was determined by continuously sampling, at a fixed frequency

(samples per second), the A/D converter's 8-bit binary output which was in turn converted

from the analog input of the conductivity probe section of the apparatus. The information thus

collected were converted to concentration information and stored on floppy disks as the exit

tracer response in terms of concentration for further processing. More information on the exit

tracer response can be found in the section "Discussion of procedures", page 103.

Determination of fluctuations of exit tracer response.

The fluctuations of the exit tracer response in terms of concentration were determined using

the procedures as described in the following paragraph.

The exit tracer response concentration data were fed to a five point moving window filter

software routine. The arithmetic mean of the five data points was taken to be the instanta-

neous mean for the mid-point. The measured mid-point was subtracted from this instantane-

ous mean value and the difference was saved as the fluctuation around the instantaneous

mean at the mid-point, then the filter window was moved up one data point and the filtering

process repeated itself until all the data points had been processed.

Experimental 50

More information on the fluctuations of exit tracer response can be found in the section "Dis-

cussion of procedures", page 105. For a sample calculation, please refer to the section

"Sample Calculation", page 145.

Determination of standard deviation of fluctuations

The fluctuations data of exit tracer response in terms of concentration obtained previously

were fed into a traditional statistical equation for calculating the standard deviation of a set

of samples. This procedure was quite straight forward, all the fluctuation data for a particular

test run were used to calculate a standard deviation of fluctuations for that test run. For a

typical sample calculation of the standard deviation of fluctuation, please refer to the section

"Sample Calculation", page 157.

Determination of frequency of occurrence

The frequency of occurrence for the fluctuations was determined by setting a base bandwidth,

i.e. a certain fluctuation range was chosen and all the fluctuation values which fell in that

range were all considered to have the lowest value of that range, for the fluctuations and di-

viding the extent of fluctuations into several subranges in multiple of the bandwidth and ex-

tended to both positive and negative sides around the mean value. Then the fluctuation data

were grouped to each subrange according to the base bandwidth. For exam;-le, if the band-

width was set to 2 ( ~g) then fluctuations between ± 2 ( ~g) and O ( ~g) exclusively were

considered zero and therefore grouped accordingly, in this case they would be grouped to the

mean value and did not contribute to any fluctuations at all.Similarly, fluctuations between

± 4 ( ~g) and ± 2 ( ~g) were considered to have a ± 2 ( ~g) fluctuation and so on. During

Experimental 51

the process of grouping, the number of fluctuation occurrences which fell into each particular

subranges were counted and a distribution of frequency of occurrence curve was generated.

Determination of FFT spectrum

An FFT test routine was developed to convert the tracer time domain record into a frequency

domain record. A total of 512 data points from the tracer response were processed as a batch

at one time, a spectrum of the frequency components was obtained.

This completes the description of the procedures used in this investigation.

Results

The results of this investigation were divided into the following groups;

• Group 1 - A total of 65 experiments were made which were all used to determine the

standard deviation of fluctuations under different reactor operating conditions.

• Group 2 - A total of 30 experiments were made using same tracer pulse width under dif-

ferent flow rates and agitation speeds. The tracer concentration was different for each

test. This testing was done in order to determine the effects of different tracer concen-

trations on the calculated value of the standard deviation of fluctuations.

• Group 3 - Two experiments were made, they both used the same amount of tracer, but

one tracer was a 2 ml pulse and the other was a 2 ml pulse diluted to a 4 ml tracer pulse.

These two experiments were made using the same motor agitation speed and inlet flow

Experimental 52

rate in order to determine the effect that tracer pulse width had on the calculated values

of standard deviation of fluctuations.

• Group 4 - Three sample exit tracer responses and their corresponding fluctuation re-

sponses were presented in this group.

• Group 5 - One each of the frequency of occurrence distribution and FFT spectrum analysis

was presented in this group.

8.oth group 1 and 2 used 2 ml of 2.4 tracer pulse, while group 3 used one 2 ml of 2.4

tracer pulse and one 4 ml of 1.2 tracer pulse. The injection time for all the 2 ml tracer

pulses was 1.5 second and was 3.0 second for the 4 ml tracer pulse.

Results for group 1: This group of 65 experiments was conducted using five different now

rates. At each now rate several different motor agitation speeds were used. The different

agitation speeds used at each particular now rate were slightly different among the five now

rates used for this group of tests. This variation was due to the inherent unrepeatability in

readjusting the motor agitation speed after each test.

The total number of points sampled for each test depended on the particular now rate and

motor agitation speed used for that test. However, the sampling was stopped after a complete

wash-out condition was confirmed, by monitoring the A/D converter reading until it gave zero

continuously for a period of one fifth of the total sampling time which was the time period

between the starting time of the test and the starting time of the continuous zero period, then

the extra trailing zeros were dropped and the data points were ready for further processing.

The raw data which contained the binary code for the corresponding tracer response con-

centration was fed to the probe calibration equation and converted to concentration informa-

tion. The concentration data were then processed digitally by a five-point moving window

Experimental 53

filter. This method would calculate the least square fit for a straight line from the five data

points being processed, then the fluctuations around instantaneous mean value at each point

was calculated by subtracting the raw data from the corresponding point on the fitted straight

line at each particular instant along the life time of the tracer response. The resulting fluctu-

ations data were further used to calculate the standard deviation of fluctuations of the tracer

response.

The standard deviation for each test was calculated using the traditional statistic equation for

that purpose. The inputs to the equation were the fluctuations data described in the previous

paragraph.

The standard deviation of fluctuations for each test was grouped according to the flow rates,

each group had the same flow rate but were run under different motor agitation speeds. All

the calculated standard deviation of fluctuations for each group were tabulated in Table 1 Ta-

ble 1 on page 55 through Table 5 on page 59 and plotted using both linear and logarithmic

scales. Figure 14 on page 60 through Figure 18 on page 64 were the x-y linear scale plots

at flow rate 213 ml/min, 184 ml/min, 147 ml/min, 103 ml/min and 52 ml/min respectively,

Figure 19 on page 65 through Figure 23 on page 69 were the log-log scale plots in that same

order.

Experimental 54

Table 1. Standard deviation of fluctuation: flow rate=213 ml/min.

MOTOR AGITATION SPEED STANDARD DEVIATION

0.0 rpm 29.66 mg/1

5.84 17. 11

9.49 15.32

10.91 13.97

15. 18 11. 89

19.88 12.23

30.26 8. 76

44.26 7. 18

62. 17 7.58

73.69 6.89

90.01 6.96

108.85 6.42

130.32 5.60

179.47 4.89

Table 1. Standard deviation of fluctuations; flow rate= 213ml/min

Experimental 55

Table 2. Standard deviation of fluctuation: flow rate= 184 ml/min.


0.0 rpm 40.61 mg/1

5.99 26.68

9. 78 16.48

15. 93 12.85

20.09 15.07

30.57 10.56

42. 10 10.83

60.04 9. 12

74. 74 9.37

92.66 7. 93

109.84 7.94

128.38 7.21

181. 04 6.01

Table 2. Standard deviation of fluctuations; flow rate= 184 ml/min

Experimental 56

Table 3. Standard deviation of fluctuation: flow rate=l47 ml/min.


0.0 rpm 53.25 mg/1

5.89 22. 74

9.65 24.56

13.99 17.65

31. 82 11. 88

45.60 11. 93

70. 10 8.97

74.96 9.66

98. 10 8.38

111. 72 8.04

135.09 6.99

176.44 5.65


Experimental 57

Table 4. Standard deviation of fluctuation: flow rate=l03 ml/min.


0.0 rpm 65.24 mg/1

5.55 23.93

8.22 25. 71

14.53 20.41

33.82 15. 15

45.92 10.45

72.67 9.36

78.33 8.85

97.71 7.48

121. 87 6.97

136.59 6. 73

181. 64 5.54


Experimental 58

Table 5. Standard deviation of fluctuation: flow rate=52 ml/min.


0.0 rpm 80.32 mg/1

5.65 40.93

9.82 31. 09

11. 27 17.49

15.85 16. 10

20.37 19.43

35.94 10.68

45.48 13. 12

70.88 10.66

74.21 7.41

88. 76 7.62

111. 05 7.26

132.29 6. 19

159.49 6.02


Experimental 59

Standai-d devi1tion of fluctuation plot 1B0r---------------------------,

.... -

90

80

, 70 ..... C 0 .... .... 60 .... -... 58 ... 0

C 0 .... .... "' .... :>

l ij .... ""

40

3U,

20

18

/J. flow Rate= 213 11l/11in

/).

20 40 60 80 1 0 1 9 1 1 0 1 0 2 Moto~ agitation speed in ~PM

Figure 14. Standard deviation of fluctuations; 213 ml/min: x-y linear plot; flow~213ml/min; pulse-2 ml;

Experimental 60

StandaJ'd deviation or fluctuation plot 100,----------------------------,

90

80 ..... i 70 ..... C 0 ... ... 60 : ... ... 0

C 0 ... ... "' ... =-

40

30

20

18

0

A

/J. AA

20

'3 f1011 Rate= 184 Ml/Nin

A /). /). /J.

40 69 80 1 1 e 1 0 1 e 1 e 2 Moto~ agitation speed in ~PM

Figure 15. Standard deviation of fluctuations; 184 ml/min: x-y linear plot; flow-184ml/min; pulse=2 m;

Experimental 61

StandaN deviation or fluctuation plot 1n-,- __________________________ _

.... -

99

89

, 10 .... C 0 .... ... 69 :I ... -.., 50 ... 0

40

39

ze

19

0

/J./).

I::. /J. I::.

29 49

/J. F10111 Rate: 147 1dh1in

/J. I::. /J. /J.

69 89 1 9 1 0 1 9 1 0 1 0 2 Moto~ agitation speed in ~PM

Figure 16. Standard deviation of fluctuations; 147 ml/min: x-y linear plot; flow-147ml/min; pulse=-2 ml;

Experimental 62

Standcll'cl deviation or fluctuation plot 100,-----------------------------,

.... i .... C 0 ... ... = ... -... ... 0 C 0 ... ... "' ... ::>

90

80

70

60

50

40

30

1/). 20 A

10

e 29

Flo111 Rate = Hl3 Ml/111in

A A /l A /J. 1l 1l

60 80 1 1 0 1 0 1 0 1 0 2 Moto~ agitation speed in ~PM

Figure 17. Standard deviation of fluctuations; 103 ml/min: x-y linear plot; flow-103ml/min; pulse=2 ml;

Experimental 63

StandaJ'cl deviation of fluctuation plot 100,,------------------------------,

t:. flow Rate= 52 111/Min 90

80 .... -r 70 .... C: 0 .... ... 60 ... u =i -... 58 ... 0 C: 0 ....

40 /J. ... "' .... ..

"'1:1

] 30 !::.

::a ... f,o'J Z0 !::. bt

A !::.

10 A /J. /J.

0 20 40 60 89 1 lit 1 e 1 0 1 0 1 0 2

Noto~ agitation speed in ~PM

Figure 18. Standard deviation of fluctuations; 52 ml/min: x-y linear plot; flow-52ml/min; pulse-2 ml;

Experimental 64

..... 'i .... C 0 ..... ... :g ... u = -... ... 0 C 0 .... ... .. .... :>

Standal'd deviation of fluctuation plot 100

fl F10111 Rate= 213 Ml/Nin

50

10

Log. of 1110to~ agitation speed in ~PM

Figure 19. Standard deviation of fluctuations; 213 ml/min: log-log plot; flow-213ml/min; tracer pulse=2 ml

Experimental 65

.... } ..... C 0 .... -:: -g -... ... 0 C 0 .... -,., .... :> -%

100

50

10

] 5

-Ill ... 0 .,, .s

Standal'd deviation of fluctuation plot

fJ F1011 Rate: 184 Ml/Nin

1 r---.--~-.--.-.-rrrr----.---r---r--r-,--.-rr-.---=---~ 1 S 10 50 100 200

Log. of MOtor agitation speed in rpN


Experimental 66

C: 0 ..... -I'll ::I -u ::I -... ... 0 C: 0 .... -I'll .... :>

Standa?'d deviation of fluctuation plot 1eer--------------------------,

/). Flo111 Rate= 147 111/1dn

50

10

5

1 5 10 50 100 200 Log. of MOtor agitation speea in rPM


Experimental 67

Standai-d deviation of fluctuation plot 100

!J flow Rate = 103 Ml/Min

50 .... -r .... C Cl .... fl -"' :, - /). u :, -... ... Cl 10 C Cl .... -"' .... =-QI

"'U

l 5 "U ; -"' ... Cl

"' .s

1 t----.-.--,--,-.-r-rTT"----r---,---r--r-,-,.-,--.~.-----J 1 5 10 50 100 200

Log, of Noto~ agitation speea in ~PM


Experimental 68

..... -r ..... C 0 ..... --g -...

100

50

10 C 0 .... -.. .... =>

l .,, ; -Ill ... 0 i:,,

.!3

5

Standa~d deviation or fluctuation plot

/). Flow Rate= 52 Ml/Min

5 10 50 100 200 Log. or 1111to~ agitation speed in ~PM

Figure 23. Standard deviation of fluctuations; 52 ml/min: log-log plot; flow .. 52ml/min; tracer pulse-2 ml

Experimental 69

Looking at the log-log plots for these tests, straight lines could be used to fit •hese tests rea-

sonably. After converting the standard deviation of fluctuations to the logarithm scale, these

values were fitted using a first order linear regression routine. The resulting equations were

shown below and their corresponding log-log plots were shown in Figure 19 on page 65

through Figure 23 on page 69

Flowrate = 213m//min; Y = - 3.617 x 10- 1 x log( 2i0 ) + 1.516 (23]

F/owrate = 184mllmin; Y = - 4.133 x 10- 1 x log( 2i0 ) + 1.730 (24]

Flowrate = 147ml/min·, Y = - 3.702 x 10- 1 x log( X ) + 1 629 200 . (25]

F/owrate = 103mllmin; Y = - 4.529 x 10- 1 x log( 2i0 ) + 1.797 [26]

Flowrate = 52mllmin,· Y = - 5.367 x 10- 1 x log( X ) + 1 941 200 . [27]

where;

X= Motor agitation speed in rpm.

Y = Natural Log of standard deviation of fluctuation in ~g .

In Figure 24 we have combined all the log-log plots for these tests together in one graph. This

was done to better demonstrate the test results.

It would be useful to be able to predict the standard deviation of fluctuations for those oper-

ating conditions of the reactor that were not covered in these tests.

Experimental 70

Stanclal'd deviation ot fluctuation plot 100-r------------------------------,

..... i ..... c:: 0 .... -fll :, -g -... ... 0

50

; 10 .... -fll .... :>

5 /). Flow Rate= 213 Ml/Min

D Flow :rate= 147 111/Min O Flow :rate= 52 11l/11in

.A Flow :rate= 184 111/Min

I Flow 11ate= 193 Ml/Min

1 +-----,---,r--r--r-,--,--r-r-r-------r-----r--.--,--,--r-,.-,-~--~

1 5 10 50 100 200 Log, of MOto:r agitation speed in l'PN

Figure 24. Standard deviation of fluctuations.: log-log plot; flow=213, 184, 147, 103, 52 ml/min; pulse=2 ml

Experimental 71

The intercepts of these five lines were tabulated in Table 6 and fitted using a first order

polynominal on a x-y linear plot. The resulting curve is shown in Figure 25 on page 75 and the

fitted equation is shown below

Y = ( -2.503 x 10- 3) x X +2.073

where;

X = Flow rate ( rn_J ) mm

Y= Intercept of log standard deviation line ( ~g)

[28)

The slopes of these five lines were tabulated in Table 7 on page 74 and fitted using a second

order polynominal on a x-y linear scale, the resulting line was plotted in Figure 23 on page

69 and shown below

y = (3.9 x 10-6) x x 2 + (1.369 x 10- 3) xx - 5.393 x 10- 1

where;

X = Flow rate (~) mm

Y = Slope of log standard deviation line ( 1 mg ) x rpm

[29)

This information would enable us to predict the standard deviation of fluctuations for a par-

ticular reactor operating condition of interest by finding the corresponding intercept and slope

of that particular operating condition and thus the operating line of the standard deviation of

fluctuations which the particular operating condition fell in could be drawn.

Experimental 72

Table 6. Intercept corelation data.

FLOW RATE INTERCEPT

213 ml/min 1. 156 mg/1

184 1. 629

147 1. 730

103 1. 797

52 1. 941

Table 6. Intercept data.

Experimental 73

Table 7. Slope corelation data.

Experimental

FLOW RATE SLOPE

213 ml/min -.362 mg/(l*rpm)

184 -.370

147 -.413

103

52

-.453

-.537

74

Correlation or· intercepts 2.,----~=---------------------------,

II C: :: 1.75 C: 0 .... -"' .... :> .g

] ! 1.5 Ill b'I· 0 -'; Agitation speed:9.09 l'PM -De II f II

1.25 -

11------,------.-------r-----..--------l 59 1 1 a 2 25

Flo• !'ate in Ml/Min

Figure 25. Corelation of intercepts.: the intercepts of the five lines in Figure 24 were fitted and plotted in this figure.

Experimental 75

CoPHlation or slopes -,3..-----------------------------,

., C .... -C -0 .... .... .. .... ., .,, 1 .,, ; .... Ill 1111 0 -.... -.5 0

t 0 -

.ReactoP Flow Rate (Ml/Nin)

Figure 26. Corelatlon of slopes.: the slopes of the five lines in Figure 24 were fitted and plotted in this figure.

Experimental 76

In order to test the validity of this method, two tests were made to assess the accuracy of

prediction using this method. A new inlet flow rate of 196 ml/min was set up and two different

motor agitation speeds of 16.74 rpm and 106.32 rpm were used to check the accuracy of the

predictions. The predicted line was determined by using the two fitted equations for intercept

and slope in Figure 25 on page 75 and Figure 26 on page 76 respectively, then the calculated

standard deviation of fluctuations for the two new tests were checked against this predicted

line at the two agitation speeds. The accurracies were found to be within ± 10% in both

cases.

Results for group 2: This group of tests was performed to observe the effects that different

tracer concentrations had on the calculated standard deviation of fluctuations for the exit

tracer response.

Thirty tests were made, all at no agitation condition i.e. 0.00 rpm. The concentration of the

tracer was increased gradually for each test from 1.00 to 2.8 . A steady flow rate was

set up and a set of ten tests were made under this flow rate using ten different tracer pulse

concentrations but the tracer pulse width stayed the same at 2 ml, necessary procedures were

gone through and the ten standard deviation of fluctuations were calculated.

The above procedures were repeated three times using now rates of 213 ml/min, 147 ml/min

and 52 ml/min. Therefore; a total of thirty tests were taken with ten tests for each flow rate.

The resulting thirty standard deviation of fluctuations were tabulated in Table 8 through

Table 10 on page 80 and plotted in Figure 27 on page 81.

Experimental 77

Table 8. Tracer concentration effects: flow rate= 52 ml/min; agitation= 0.00 rpm

TRACER CONCENTRATION STANDARD DEVIATION

1. 00 g/1 11. 23 mg/1

1. 20 16.67

1. 40 29.48

1. 60 31. 17

1. 80 47.81

2.00 55.49

2.20 70.05

2.40 81. 35

2.60 89. 14

2.80 95.44

Experimental 78



1. 00 g/1 7.64 mg/1

1. 20 15. 73

1. 40 20. 17

1. 60 26.03

1. 80 38.96

2.00 45. 79

2.20 50. 11

2.40 56.03

2.60 61. 63

2.80 64.40

Experimental 79



1. 00 g/1 4.03 mg/1

1.20 7.09

1. 40 15.22

1. 60 18.47

1. 80 19.68

2.00 25.84

2.20 26.98

2.40 29.98

2.60 31. 77

2.80 34.49

Experimental 80

--r .... C 0 ... ---.... .... 0 C 0 ... -"' ... :>

] Ii -c.,

T..ace:r concent!'ation ettects plot 100-.------------------------------,

90

80

78

60

58

40

30

20

18

a F1011 Rate= 52 Ml/Nin fl Flow Rate= 147 111/11in A rlo11 Rate= 213 111/Min

B+-----.------.---...----,-----,----..----,---~-----1 1.2 1.4 1.6 1.8 2.2 2.4 2.6 2.

T:race:r Concent:ration (g/1)

Figure 27. Effects of tracer concentration.: this figure showed the effects of the tracer concen-tration on the calculated value of standard deviation of fluctuations.

Experimental 81

Results for group 3: The purpose for this group of tests was to determine the effect that un-

certain tracer pulse width had on the calculated value of standard deviation of fluctuations

from the time record of the tracer response.

One test used 2 ml of 2.4 f tracer pulse while the other used 4 ml of 1.2 tracer pulse. The

injection times for the 2 ml and 4 ml pulse were 1.5 second and 3.0 second respectively.

Both tests in this group were made at a flow rate of 147 m_J and an agitation speed of 0.00 min

rpm. The resulting exit stream tracer responses are plotted in Figure 28 and Figure 29 on

page 84 respectively and the fluctuations plots were plotted in Figure 30 on page 85 and

Figure 31 on page 86 respectively. Finally the calculated standard deviation of fluctuations

are tabulated in Table 11 on page 87.

Experimental 82

j_. 5

X-residence tiMe (Min.> Y-exit tracer concentration (g/].)

Figure 28. Effects of tracer width; 4ml tracer: this figure showed the effects of the tracer pulse width had on the exit tracer response. now= 147ml/min; agitation =0 rpm; pulse =4 ml

Experimental 83

.I. • 5

X-residence tiMe (Min.) Y-exit tracer concentration

4.1.

(g/1)

Figure 29. Effects of tracer width; 2ml tracer: this figure showed the effects of the tracer pulse width had on the exit tracer response. flow - 147ml/min; agitation -o rpm; pulse.., 2 ml

Experimental 84

fluctuation plot

y+=+0.35 g/1 y-=-0.35 g/l.

y-r-~-.--,---.--r--,--..----r-,-~--,--,--r--r---r-0

x-Residence tiMe CM1n.) y-Fl.uctuation around Mean

4.J.

< g/J.)

Figure 30. Tracer fluctuation plot; 4ml tracer: this figure showed the effects of the tracer pulse width had on the exit tracer fluctuations response. flow= 147 ml/min; agitation= 0 rpm ; pulse=4 ml

Experimental 85

fluctuation plot

y+=+0.35 y-=-0.35

g/1 g/1

y--r-......,r---r--r--,r---r--y---,,........;--r--r--,r--.---.--,r--,---r--0

x-Residence tiMe (Min.> y-Fiuctuation around Mean

4.i.

(g/1)

Figure 31. Tracer fluctuation plot; 2ml tracer: this figure showed the effects of the tracer pulse width had on the exit tracer fluctuations response. flow-147 ml/min; agitation-= 0 rpm ; pulse=2 ml

Experimental 86

Table 11. Effects of tracer pulse width: Flow rate= 147 ml/min; agitation= 0.00 rpm

TRACER PULSE WIDTH

2.00 ml

4.00

Experimental

STANDARD DEVIATION

55.225 mg/1

52. 142

87

Results for group 4: Three tests made with 2 ml tracer pulse at a flow rate of 147 ml/min with

agitation speed of 0, 28.7, and 129.31 rpm respectively are presented here to serve the pur-

pose of demonstration.

The tracer responses for these tests are plotted in Figure 32 through Figure 34 on page 91 and

the corresponding fluctuation responses are plotted in Figure 35 on page 92 through

Figure 37 on page 94

Experimental 88

.i. • 5

0 4.1. X-residence tiMe (Min.> Y-exit tracer concentration (g/i)

Figure 32. Sample test 1.: this was the exit tracer response for the 1st sample test. pulse- 2 ml; flow- 213ml/min; agitation- 0 rpm

Experimental 89

.1. • 5

0 X-residence tiMe (Min.) Y-exit tracer concentration < g/].)

Figure 33. Sample test 2.: this was the exit tracer response for the 2nd sample test. pulse - 2 ml; flow- 213ml/min; agitation= 28.7 rpm

Experimental 90

.1. . 5

0 4.1. X-residence tiMe (Min.> Y-exit tracer concentration (g/1)

Figure 34. Sample test 3.: this was the exit tracer response for the 3rd sample test. pulse- 2 ml; flow= 213ml/min; agitation= 129.31 rpm

Experimental 91

---

-~••···

---

fluctuation pl.ot

•• I !

!,111+=+0. 3'5 !,11-=-0. 3'5

g/1 g/1

!,Ill - .--r---.,---.---.---,.-----,.---..--4 J.. o 0 x-Residence tiMe <~in.>

!,Ill-Fluctuation around Mean (g/l.)

Figure 35. Fluctuation plot for sample test 1: this was the fluctuations plot of the tracer response plot for sample test 1 in Figure 32.

Experimental 92

-----

n . ~.: ~-----

0

f1uctuation piot

y+=+0.35 g./1 y-=-0.35 g./l.

. . . . x-Residence tiMe (Min.> y-Fluctuation around Mean

. ' 4J..00

(g./1)


Experimental 93

y+ -

.

. A

.

.

.

. .

0

f1uctuation p1ot

y+=+0.35 g/1. !l-=-0.35 g/1.

. I . I

x-Residence tiMe- (Min.> y-Fiuc~ua~ion around Mean

. 4.1..00


Experimental 94

Results for group 5: One typical result of the frequency of occurrence analysis and one typical

result of the FFT spectrum analysis are presented in this group. The frequency of occurrence

distribution is plotted in Figure 38 while the FFT spectrum taken from the 1536th to the 2047th

data point for a typical tracer response is plotted in Figure 39 on page 97.

Experimental 95

.i.OO%

+50 . . . . .

0

X-Fluctuation; mg/1 Y-Frequency of occurrence

-50

Figure 38. Frequency of occurrence distribution.: this figure showed the distribution of the fluc-tuations in terms of the frequency of occurrence.

Experimental 96

1

X-Frequency spectrum; Hz Y-Gain; ratio

25

Figure 39. FFT spectrum analysis of tracer response.: this figure showed the distribution of the tracer response in the frequency domain for a typical test.

Experimental 97

Discussion

This discussion is divided into five parts as follows;

• Discussion of literature.

• Discussion of procedures.

• Discussion of results.

• Recommendations.

• Limitations.

Discussion of literature.

The literature treating the experimental procedure for obtaining the RTD tracer response is

quite complete, especially for homogeneous continuous flow reactor systems. The tracer

Discussion 98

measurement and injection method used in this investigation were consistent with

Leven spiel's articles < 32,33 > which described the essential considerations in correct tracer

'injection and response measurement.

Tap water has been used to conduct the tracer experiments by other workers < 21,34 >, the

essential consideration reported by these workers was the null position of the tracer response

not the purity of the tap water.

The RTD fluctuations measured at the downstream of a vessel are generally believed to be

statistically random < 10> and provide no useful information. In fact, RTD measurements are

usually made and processed in such ways to minimize the effects of fluctuations on the ob-

tained shape of the RTD.

Hanley < 35 > measured the mean and variance of the concentration fluctuations in the exit

stream for RTD with an analog computer and found that the variance was not random and that

the variance was consistent at several reproducible mixing patterns but was unable to relate

the variance output voltage from the analog computer to the concentration of the tracer be-

cause of the analog noise-suppression integrator used. Hanley suggested that these fluctu-

ations could be explained by the fact that during the greater portion of the test, no steady state

condition was obtained. Therefore globs of fluid, aggregates, exiting the vessel at random

times would cause these peaks and drops effect. This thesis was basically a follow-up of

Hanley's work by updating the measuring techniques and taking advantage of the digital

processing techniques made available nowadays to provide a quantitive description of the

RTD fluctuations in terms of concentration.

Other methods of experimental measurement of segregation have also been developed. For

example, Spencer and coworkers < 36 > employed a double impulse experiment to measure

the presence of segregation. If a reactive tracer A1 is injected into a flow system at t =O and

another reactive tracer A2 is injected at some later time. The reaction between A1 and A2 is

Discussion 99

A1 + A2 = A3 with rate KC,C2 Then in the case of complete segregation A, and A2 will not be

mixed for a finite time on a molecular basis, and therefore no A3 will be produced. On the

other hand if maximum mixedness obtains, A, and A2 will mix to some extent before leaving

the reactor, and some product A3 will be observed. It was reported < 36 > that this method

was very sensitive to the presence of segregation.

Standard deviation has also been employed by other workers < 37 > to characterize the

concentration fluctuations in a continuous flow stirred tank reactor.

Discussion of procedures.

This section includes a discussion of the following experimental procedures used in this in-

vestigation;

• Determination of the exit tracer response.

• Determination of the fluctuations of the exit tracer response.

• Determination of the standard deviation of the fluctuations.

• Determination of the frequency of occurrence.

• Determination of the FFT spectrum.

Discussion 100

Determination of exit tracer response.

The major consideration for sampling the exit stream tracer concentration response in terms

of fluctuation analysis was to select a sampling frequency which would be adequately high to

record the short term fluctuations of the tracer response in detail, say for example no fluctu-

ation that is greater than ± 2 of the AID converter reading than its previous reading will be

left out. Though it was not necessary to reconstruct the tracer concentration response exactly,

the sampling frequency of the AID converter had to be high enough to record the variations

of the exit tracer concentration fluctuations in sufficient detail to make the analysis of fluctu-

ations meaningful.

The appropriate sampling frequency was determined by first looking at the signal output from

the probe on an oscilloscope and the maximum frequency of these signals was determined

to be on the order of 8 Hz under the least extensive mixing condition for the particular vessel

we intended to use in this investigation. The frequency of this signal would die out as we in-

creased the mixing power input to the vessel and eventually it will become a DC signal when

the tracer was nearly all washed out by the now stream. Anyway, the sampling frequency

was set at 16 Hz which was twice the maximun frequency we observed. A test was made

using the lowest agitation speed and now rate we intended to use for this investigation, then

the standard deviation of fluctuation of the exit tracer response under this vessel operating

condition was calculated. The sampling frequency was decreased a little and the above pro-

cedure was repeated under the same test condition. The resulting standard deviation of

fluctuation was compared with the one obtained using the highest sampling frequency. This

process was repeated until a noticeable change in standard deviation of fluctuation of greater

than 5% had resulted. This change would indicate that the sampling frequency was not high

enough to record the exit tracer concentration fluctuation in sufficient detail. The sampling

frequency just higher than the one that resulted in a 5% change was used as the sampling

frequency for all the tests.

Discussion 101

Using the procedures described above it was determined that a sampling frequency of 3 Hz

was sufficient for our purposes.

For each test, the whole wash-out, determined by over sampling the wash-out process for a

period of one mean residence time after the first occurrence of 20 consecutive zero AID con-

verter readings at the trailing part of the RTD, process was recorded until the tracer was

completely washed out and the AID converter readings gave zeros. Then this recorded data

file was edited to leave only ten appending zeros and the file was saved for further processing.

The entire vessel flow system, excluding the motor, plus the conductivity probe and the elec-

tronics associated with it were tied to a common ground. The stirrer, which was the only link

between the motor and the flow system, was insulated with tape at the motor joint. A large

60 Hz hum was observed if the motor joint was not well insulated. A 60 Hz second order unity

gain active low pass filter of the Butterworth type was used to attenuate the weak power line

hum. All signal transmission cables were shielded. Temperature driftings of the probe null

position and the AID converter voltage reference were within ± 2% and ± 0.1% per hour

respectively. These drifts were adjusted before each test which never took longer than 40

minutes, excluding the over sampling time for the determination of the state of complete

wash-out. Material balances were carried out to check the validity of the measurement sys-

tem, in all cases a maximum of ± 2% total mass unbalance was observed. This mismatch

in mass balance included the error of integrating the area under the tracer response curve

using the Simpson's rule. The sampling was started as soon as the tracer had been injected

into the flow stream.

A final note on adjusting the null position of the tracer response is in order. Before each test

the null position was first adjusted back to the original null position that the calibration curve

of the conductivity probe was based upon, the null position was then adjusted to compensate

for the small variation in the quality of the tap water used. This variation was of an order of

Discussion 102

10- 2 V. As long as it is within ± 0.3V of the original probe null position, the probe calibration

curve will make a parallel shift with a maximum of ± 1 % error.

Determination of fluctuations of the exit tracer response.

The information from the time record of the tracer exit concentration response was processed

using a five points least square fit routine and progressed successively through all data points.

It should be noted that as a result of this process, the identity of time, therefore the residence

time distribution was lost. By this we mean that since at each point the concentration was

smoothed and the original exit concentration was subtracted from the smoothed value, we

were essentially demodulating the RTD and only the ripplings that rode upon it were kept.

This would also imply, theoretically, that any shape of RTD could give the same set of fluctu-

ations and therefore the fluctuations were independent of the RTD.

The reason why the least square fit method was used instead of a simple arithmetic average

to obtain the midpoint of each set of "window" was that in the early stage of this investigation

various smoothing techniques were tried and the least square fit method simplified this trial

and error process. For example, it was found that fitting five points with a straight line and

calculate the fluctuation at each point then move down five points at a time would create a

sudden jump of fluctuation in some cases and produced less consistency between tests made

under the same test conditions.

Because of the sequential nature of the smoothing process, it, in general, made a difference

that which data point was the first to be processed. Originally, the smoothing process was

started at the first point of the tracer response data which was always zero since the tracer

took a finite amount of time to flow through the system. Later, it was found that taking the first

non-zero occurrence of the tracer response as the midpoint of the first window to be proc-

Discussion 103

essed produced better consistency between tests made under the same conditions. However,

the fluctuation plots in Figure 35 on page 92 through Figure 37 on page 94 were shown with

leading zeros to make the proportion of the fluctuation response correct.

Determination of standard deviation of fluctuations.

No major problem was involved in this procedure. The fluctuation data were simply fed to a

classic statistical equation for calculating the standard deviation. The total data points proc-

essed depended on the particular test being processed.

Determination of frequency of occurrence.

No major problem was noted in the processing of the frequency of occurre:-:ce distribution

from the tracer response fluctuations.

Determination of FFT spectrum.

No major problem was noted in this procedure also because of the fact that this analysis is

such a common practice. The only thing worth noting is that it took a long time to perform the

512 point FFT on the microcomputer system used in this investigation.

Discussion 104

Discussion of results.

This section includes a discussion of the results obtained for this investigation.

Exit tracer response: Generally, the tracer responses of the tests made in this investigation

showed a dead space in the gross flow pattern. However as can be seen in Figure 32 on page

89 through Figure 34 on page 91, increasing the agitation speed eliminated the dead space

accordingly, the shifting of the tracer response curve towards the Y-axis indicated this. At low

flow rate, 52 ml/min, and no agitation condition, recirculating of fluid might happen. Also at

high flow rate, 213 ml/min, and high agitation speed , i.e. > 170 rpm, by-passing of fluid might

happen. In going from low to high agitation speed, an obvious increase in mixing rate was

obtained. This increase can be visualized by looking at the attack, sustain, decay, and release

time of the tracer response or simply, the slope of the rising and falling edge of the response.

Therefore, it can be seen that the macromixing state of the fluid changed considerably over

the various test flow and agitation conditions. At low agitation speed, i.e. < 20 rpm, RTD re-

sponses were reproducible only within ± 15% , characterized by mean and second moment

of the RTD, mainly because of the variations at the tail part of the RTD. This variation can be

explained by the fact that the no-mixing condition is the most unstable condition of operation.

However,, the RTD responses were reproducible within± 5% at agitation speeds higher than

20 rpm.

Exit tracer fluctuation response: The occurrence of concentration fluctuations can be ex-

plained by the fact that there are concentration gradients among lumps of neighboring ag-

gregates within a fluid. More aggregates exiting in a fluid will have a higher possibility to

produce more concentration gradients among them, thus increasing the possibility of abrupt

changes in concentration at the downstream tracer measurement plane. The aggregates are

Discussion 105

usually assumed to be randomly dispersed in fluid < 10 >, therefore the condition at the tracer

measurement plane is, in general, an average of the condition to be expected at all regions

within a fluid. This leads one to believe that the fluctuations of a tracer response are related

directly to the degree of segregation within a fluid.

Looking at the fluctuation plot in Figure 35 on page 92 through Figure 37 on page 94, the

amount of fluctuation a certain tracer response experienced depended heavily on the pumping

capacity provided by the impeller. A state of almost no fluctuation existing in the tracer re-

sponse can be acheived if adequate agitation was provided while low agitation speed

produced a tremendous amount of fluctuation in the exit tracer response.

A final note on this section of the results is in order. It is also possible to deduce the mixing

rate from the fluctuation plot of the tracer response. For example, an arbitrary final fluctuation

value can be defined as ± 5% around the mean and the time it took to reach this final value

can be used as a measurement for the rate of mixing.

Standard deviation of fluctuation: Standard deviation was used to characterize the fluctuations

for a particular tracer response. Generally, the relation between the log of the standard de-

viation of fluctuation and the log of the agitation speed was found to be linear.

At low agitation speed, the standard deviation of fluctuation was found to be very sensitive to

factors like the amount of tracer material injected, and the tracer injection time but was less

sensitive to the flow rate variations. Also the standard deviation was less stable at low agi-

tation speed, and this was probably due to the fact that at a low agitation speed the weighting

of the motor speed variations Is larger than at •a higher agitation speed and therefore caused

more instability at lower agitation speed. The standard deviation of fluctuation was repro-

ducible within ± 8%. Experimental errors and the fact that we were trying to characterize a

complex mixing process by a single parameter are the two most probable ~auses for this

± 8% variation.

Discussion 106

Frequency of occurrence: The only purpose of this analysis was to see if it was feasible to

characterize the fluctuation of concentration for a tracer response by a single parameter that

is common for Gaussian-type curves.

The reason why a certain range of fluctuation was selected to divide the fluctuation occur-

rences into several subranges was that the uncertainty of the A/D converter reading and the

unc~rtainty introduced during the process of generating the fluctuation information suggested

that it would not be too meaningful to carry out the analysis on a point-to-point basis.

FFT spectrum: The only information deduced from this analysis was that most spectrum en-

ergy appeared at the low frequency end and that the spectrum distribution was basically

similar to a fractional noise response of the (+) type.

Recommendations

This section contains recommendations for follow-up study of this investigation.

• Reactors of other types (i.e. packed bed, tubular, etc.) can be set up to generalize as well

as verify the results obtained in this thesis.

• This investigation is rather priliminary, it provides only a fundamental description as re-

gards the nature of the concentration fluctuations for a RTD. Therefore, the practical use

and implementation of this information must be the subject of further studies.

Discussion 107

Limitations

The limitations of the results obtained in this thesis are as follows

• Geometry of the vessel- The results of the RTD, tracer response fluctuation, and standard

deviation of fluctuation are valid for a reactor of similar dimensions and configuration.

However, the methods used for deducing the tracer response fluctuation, and the stand-

ard deviation of fluctuation should be applicable to other reactor systems.

• Operating conditions- The results obtained are only valid within a fiow range of 52 J!J/-. mm to 213 J!J/-and agitation speeds from 0.00 rpm to 200 rpm.

mm

• Temperature- All testings were conducted at room temperature (25 degree C ).

Discussion 108

Conclusions

The following conclusions are valid only when the limitations noted in the section "Limitations"

of this thesis are satisfied. The conclusions of this investigation are as follows,

• At agitation speeds higher than 20 rpm, the RTD responses were reproducible to within

± 5%.

• The standard deviation of fluctuation was reproducible to within ± 8 % for all agitation

speeds (0 to 200 rpm) and flow rates (52 _I!!/-to 213 mlovre min). min

• The concentration fluctuations for a RTD are not statistically random and can be charac-

terized by their standard deviation.

• The relationship between log of standard deviation of fluctuation and log of impeller agi-

tation speed was, in general, linear.

• The FFT spectrum response of a RTD was, in general, of a f fractional noise type.

• The maximum frequency of concentration fluctuations for a RTD was around 8 Hz.

Conclusions 109

• The higher the mixing rate the lower the frequency of concentration fluctuations for a RTD.

Conclusions 110

Summary

The purpose of this study was to determine whether the fluctuations of concentration in the

exit stream for a RTD were statistically random.

Concentrated sodium chloride was used as the tracer pulse, the tracer output response was

monitored with a electrical conductivity probe in the exit flow line. A broad range of mixing

patterns were studied. The RTD responses were studied in terms of frequency spectrum and

were found to be mainly composed of low frequency hum which constituted large portion of

the energy spectrum. However, the fluctuations of concentration for these RTD were demod-

ulated from the RTD responses and an attempt was made to characterize this fluctuation in-

formation by a single parameter.

It was found that these fluctuations of concentration for a RTD response were not statistically

random and could be characterized by their standard deviation. The relationship between log

of the standard deviation of fluctuation and log of the impeller agitation speed was, in general,

linear. The standard deviation of fluctuation was reproducible within ± 8% over a broad

range of mixing conditions.

Summary 111

It was concluded that the tracer RTD response for a continuous flow stirred vessel could pro-

vide additional information about the mixing state of fluid flowing through a vessel if the fluc-

tuations of concentration for the RTD were not ignored.

Summary 112

Bibliography.

1. Nauman, Buffham, "Mixing in continuous flow systems", pp. 4-8, John Wiley & Sons, 1983

2. Levenspiel, 0. & K. B. Bischoff, "Patterns of flow in chemical process vessels", pp. 95-198,

Advances in Chemical Engineering, 4 95-198, 1962.

3. Maria, Francesco De & Robert R. White, "Transient response study of gas flowing through

irrigated packing", AICHE J. 6 473, 1960

4. Porcelli, J. V. & G. R. Marr, "Propeller pumping and solids fluidization in stirred tanks",

Industrial and Engineering Chemistry Fundamental, 1172, 1962

5. Cutter, L.A., "Flow and turbulence in a stirred tank", AICHE J. 12 35, 1966

6. Rao, M. A. & R. S. Brodkey, "Continuous flow stirred tank turbulence patterns in the

impeller stream", Chemical Engineering Science 27 137, 1972

7. Rietk Van't & J. M. Smith, "The trailing vortex system produced by rushton turbine

agitators", Chemical Engineering Science 30 1093, 1975

Bibliography. 113

8. Chang, T. P. K., A. T. Watson & G. B. Tatterson, "Image processing of tracer particle

motions as applied to mixing and turbulence flow- I", Chemical Engineering Science 40

269, 1985

9. ibid., "Image processing of tracer particle motions as applied to mixing and turbulence

flow- 11", Chemical Engineering Science 40 277, 1985

10. Danckwerts, P. V., "Continuous flow systems- Distribution of residence times", Chemical

Engineering Science 2 1, 1953

11. Rao, D. P. & Louis L. Edwards, 11Mixing effects in stirred tank reactors: a comparison of

models", Chemical Engineering Science 28 1179, 1973

12. Bourne, J. R., "Mixing on the molecular scale {micromixing)", Chemical Engineering Sci-

ence 38 5, 1983

13. Danckwerts, P. V., "The effects of incomplete mixing on homogeneous reactions", Chem-

ical Engineering Science 9 93, 1958

14. Weinstein, H. & R. J. Adler, "Micromixing effects in continuous chemical reactor", Chem-

ical Engineering Science 22 65, 1967

15. Rippin, D. W. T., "Segregation in a two-environment model of a partially mixed chemical

reactor", Chemical Engineering Science 22 247, 1967

16. Douglas, J. M., "The effects of mixing on reactor design", Chemical Engineering progress

symposium series", 60 1, 1964

17. Bischoff, K. B. & E. A. Mccracker, "Tracer test in flow system", Industrial and Engineering

Chemistry 58 18, 1966

Bibliography. 114

18. Levenspiel, 0., "Chemical Reaction Engineeringn, pp. 253-265, John Wiley & Sons, 1972

19. Zweitering, T. N., "The degree of mixing in continuous flow systemsn, Chemical Engi-

neering Science 111, 1959

20. Lamb, D. E., F. S. Manning & R. H. Wilhelm, "Measurement of concentration fluctuations

with an electrical conductivity probe", AICHE J. 6 682, 1960

21. Manning, F. S. & R. H. Wilhelm, "Concentration fluctuations in a stirred baffled vessel",

AICHE J. 9 12, 1963

22. Jaeger, Richard C., "Tutorial: Analog data acquisition technology-I", IEEE-Micro, pp. 20,

May 1982

23. ibid., "Tutorial: Analog data acquisition technology-II", ibid, pp. 46, Aug. 1982

24. ibid, "Tutorial: Analog data acquisition technology-Ill", ibid, pp. 20, Nov. 1982

25. ibid, nTutorial: Analog data acquisition technology-IV", ibid, pp. 52, Feb. 1983

26. Fan, L. T., B. I. Tsai and L. E. Erichson, "Simultaneous effect of macromixing and

micromixing on growth processes", AICHE J. 17 689, 1971

27. Ng, D. Y. C. & D. W. T. Rippin, nThe effect of incomplete mixing on conversion in homo-

geneous reactions", Third European Symposium on Chemical Reaction Engineering, pp.

161. Amsterdam. Sept. 1964. Pergamon press 1965

28. Nishimura, Y. and M. Matsubara, "Micromixing theory via the two-environment model",

Chemical Engineering Science 25 1785, 1970

Bibliography. 115

29. Manning, F. S., David Wolf, and D. L. Keairns, "Model simulation of stirred tank reactors",

AICHE J. 11 723, 1965

30. Valderrama, Jose 0. and Alfredo L. Gordon, "Mixing effects on homogeneous p-order

reactions. A two-parameter model for partial segregation", Chemical Engineering Sci-

ence 34 1097, 1979

31. Levenspiel, O.,"The coming-age-of Chemical Reaction Engineering", Chemical Engineer-

ing Science 35 1821, 1980

32. Levenspiel, 0. and J. C. R. Turner, "The interpretation of residence-time experiments",

Chemical Engineering Science 25 1605, 1970

33. Levenspiel, 0. and B. W. Lai and C. Y. Chatlynne, "Tracer curves and the residence time

distribution", Chemical Engineering Science 25 1611, 1970

34. Biggs, R. 8., "Mixing rates in stirred tanks", AICHE J. 9 636, 1963

35. Hanley, T. H., "A mixing model for a continuous flow stirred tank reactor", pp. 33-109, un-

published PHO thesis, library, VPISU, Blacksburg, Va. 1972

36. Spencer, Jordan L., Richard R. Lunt and Stanley A. Lesh aw, "Identification of micromixing

mechanisms in flow reactors: transient inputs of reactive tracer", Industrial and Engi-

neering Chemistry Fundamental 19 135, 1980

37. Lee, Young Y., and Sydney Luk, "Characterization of concentration boundary layer in ox-

ygen absorption", Industrial and Engineering Chemistry Fundamental 21 428, 1982

Bibliography. 116

Appendices

A. Design of apparatus.

This part of the Appendices includes detailed design for the following apparatus;

• Reactor flow system.

• Conductivity probe.

• Circuitry for data acquisition.

• Circuitry for motor speed sensing.


The dimensions of the reactor vessel can be found in Figure 40 on page 119. The reactor

vessel was of a round cylinder shape and was made from stainless steel. All the tubing

Appendices 117

coming out of the vessel was ! inch copper tubing. The vessel had a bottom inlet and a side

outlet. The dimensions of the baffle can be found in Figure 41 on page 120. The baffle was

used to improve the quality of mixing in the vessel. The dimensions of the agitator used in this

investigation can be found in Figure 42 on page 121. The agitator was built to make the fluid

in the vessel circulate upward. Both the baffle and the agitator were made from copper.

A construction diagram of the tracer pulsing port can be found in Figure 43 on page 122. The

tracer pulsing port was located 177.8mm upstream the bottom inlet of the vessel. It was made

from a three way copper tube fitting, two rubber stoppers, and a 4.00ml syringe. A con-

struction diagram of the conductivity probe port can be found in Figure 44 on page 123. The

conductivity probe port was located 101.6mm downstream of the vessel outlet. It was con-

structed from a three way copper tube fitting, a plastic ring, a screw-off cap, and the

conductivity probe itself. The probe port was constructed so that the conductivity probe could

be take out of the flow system easily for the purpose of calibration.

Appendices 118

0.81mm

inlet

75mm

104.77mm

19mm

I'- 76.2mm

.t puls1ng port

t

101.6mm

Tr----~__. prbbe

101.6mm~

102.66mm

reactor drain

inlet

Figure 40. Dimensions of the reactor.: detailed dimensions of the reactor, all units in mm.

Appendices 119

114.3mm

Figure 41. Baffle dimensions.: this figure showed the dimensions of the bafne.

Appendices 120

171.45mm

6'.35mm

Figure 42. Agitator dimensions.: detailed dimensions of the agitator.

Appendices 121

/syringe rubber stopper

H LJJ.4------ring fitting

'------~I rubber stopper

3-way fitting, 3/8" schedule 80

Figure 43. Pulsing port construction.: this figure showed the construction of the pulsing port.

Appendices 122

·probe ---

_____ .......,/ screw-off cap

B~--- plastic ring

3-way fitting, 3/8 " schedule 80

Figure 44. Probe port construction.: this figure showed the construction of the conductivity probe port.

Appendices 123

Conductivity probe.

A construction schematic for the conductivity probe, including dimensions, can be found in

Figure 45. The conductivity probe was made from a tip point electrode surrounded by a ring

electrode placed approximately 2.54mm apart. Both electrodes were made out of 24 gage

platinum wire. The platinum wires were soldered to leadwires and housed in a 12.7mm OD

stainless steel tubing. The assembly were filled with teflon and the probe end was coated

with plexiglass. The probe was approximately 203.2mm long.

Appendices 124

teflon filling

plexiglass

/stainless steel tubing 0.5'"od

24 gage platinum wire

Figure 45. Conductivity probe assembly.: this figure showed the construction of the conductivity probe.

Appendices 125

A schematic for the conductivity probe signal conditioning circuit is shown in Figure 46. A 15

kHz sine wave was used to modulate the signal taken directly from the tip and ring of the

probe head assembly; then, this modulated signal was amplified, demodulated, buffered, fil-

tered and finally fed to the A/D converter. As can be seen in the schematic for the probe

signal conditioning circuit, the probe signal was amplified first then passed to a precision

rectifier. The rectified signal was then summed and the 15 kHz carrier signal was attenuated.

Offset and span control for the conditioned signal were provided. Finally, a buffer stage was

provided to provide better impedance matching.

Appendices 126

0.8V p-p 15khz

sine wave

conductivity probe

40

offset

100k

12k

5.lv zener

out

Figure 46. Probe signal conditioning circuit schematic.: this figure showed the circuit used to condition the conductivity probe signal output; all resistors in ohms; all capacitors in microfarads.

Appendices 127

Circuitry for data acquisition.

A schematic of this portion of circuit can be found in Figure 47. The major component of the

data acquisition system as used in this investigation was a analog to digital converter IC. The

probe output was fed to this converter and converted to a straight binary code which then in-

put to a microcomputer based labratory station. The resolution of the converter was 8-bit,

while the sampling rate was 3 Hz as used in this investigation. Therefore, the design of this

section was not critical. A buffered voltage reference was found to be sufficient, the input to

the particular converter IC used in this investigation was single ended and therefore always

referenced to the analog ground which was tied down to the digital ground. A simple diode

over-voltage protection was provided for the analog input signal just before input to the con-

verter IC.

The design of this part of circuitry was quite straightforward. An ADC0808 analog to digital

converter from National Semiconductor was at the heart of the data acquisition setion. A

5.00V op-amp (operational amplifier) based buffered voltage reference provided the reference

voltage required by the AID converter. A 6821 PIA programmable 1/0 adaptor from Motorola

Semiconductor provided the 1/0 channels needed for the microcomputer to communicate with

the ADC0808. Anyway, the rest of the circuit were just some standard TTL logic used to pro-

vide decoding and repowering of the system bus.

Appendices 128

+5V RSi---

...... -----PA7 DO --~ Vee Vss 1-----,

+SV 6821 PIA

D7--~ PAO 23 25 OE

A8 CSO

A0---1RSl

PBO t:=====1=t:===::lD024 Vee INO r------<

Al3 CSl AI RSO

CS2

I PB7 ~=====~t===:::::lo7

E

ADC0808 -----1EOC

,.._-~ START ALE

R/W --+----' ~2 _T ___ ,.___ ___ ~L!E~_.JG~N~D-!.._.--l

A9-- ..... , __ Al2---' Al4-~ Al5_~

REF(-)

74LS30

lK

analog input

330

+ 12V

5.6V ZENER

Figure 47. Analog to digital converter circuit schematic.: this figure showed the circuit used to interface the analog probe signal to the digital system; all resistors in ohms; all capacitors in microfarads.

Appendices 129

Circuitry for motor speed sensing.

A schematic of the motor speed sensing circuit is shown in Figure 48 on page 132. Readers

are referred to it for the following discussion. While in this investigation a separate AC motor

controller was used to control the speed of the 120V AC agitator motor, the motor controller

used was not able to provide at the same time a visual indication of the rotating speed of

agitator. In order to establish the desired operating agitation speed, a separate motor speed

sensing line was used.

A thin transparent plastic ring with one narrow strip of black tape was mounted to the motor

shaft 90 degree vertically. The narrow strip of black tape was used to interrupt a pair of

photo-interrupter module, the result was a voltage pulse train whose frequency was directly

propotional to the rotating speed of the motor shaft. This pulse train was fed to the input of

a programmable timer/counter IC and it's period was measured using a software subroutine

residing within the microcomputer based laboratory station. Therefore, this section of the

apparatus was constructed to monitor the rotatior speed of the agitator which was regulated

by a separate AC motor-controller.

An MC6840 PTM, programmable timer module, was interfaced to the laboratory microcom-

puter and provided the microcomputer with the ability to measure the frequency generated

from the opto-interrupter module. The PTM was set up such that timer #3 would count the 1

MHz master clock of the microcomputer with the modula 8 prescaler enabled and the output

of timer #3 was cascaded to the clock input of timer #2 and timer #2 was set up to count this

external clock source while operated in the frequency measurement mode to measure the

signal frequency fed into the gate #2 input pin. A high to low signal transition on gate #2 input

pin would triger the timer #2 counter to start the count down process, a subsequent high to

low signal transition on gate #2 input pin would stop the timer #2 counter and issue an inter-

rupt service request to the CPU which would calculate the signal frequency by taking the dif-

Appendices 130

ference between the initial count and the final count in the timer #2 counter and dividing this

value by the clock frequency presented in clock2 input pin on the PTM.

A flow chart of the software used to implement the hardware to measure the frequency of the

agitation motor was shown in Figure 49 on page 133.

Appendices 131

D0-D7

AO A 1--:-=-_-_-_-_-_-_-_-_-:..-:..-:..-:.-:.-:.::t A2

+Sv

Vee

clk.3

03 RST-------t 02 R/W---------1 IRQ------

6840 PTM

Al3

A8 A9 ---1

AlQ--l---All_--i Al2 __ A 14 ---l~-Al 5

5.lv zener

-- cso g3 gl

GND

clk2

gate2

opto-intcrrupter

+ 5V module opb81S

tic encoder

4.7K

Figure 48. Motor speed sensing circuitry.: this figure showed the circuit used to monitor the motor agitation speed; all resistors in ohms; all capacitors in microfarads.

Appendices 132

( START

\V I STORE INITIAL COUNT TO TIMER #3 LATCH l

,1 CONfIGURE TIMER #3 AS INTERNAL CLOCKED; MODULA 8 PRESCALER ENABLE; 16 0IT CONTINUOUS WAVEPORM GENERATION W/ 50% DUTY CYCLE

\I CONFIGURE TIMER #2 IN PERIOD MEASUREMENT MODE; INTERRUPT ENABLE

..... "\LI

START TIMER OPERATION; WAIT FOR INTERRUPT REQUEST l

\/ READ STATUS; READ TIMER #2 COUNTER REGISTER I

,11 DO WAVEFORM FREQUENCY CALCULATION l

Figure 49. Motor speed sensing subroutine.: this figure showed the flow chart of the software subroutine used to measure the rotation frequency of the agitation motor.

Appendices 133

B. Notes on calibration.

The detailed calibration procedures used in this investigation are presented in this section

which includes the following;

• Calibration of the rota meter.

• Calibration of the conductivity probe.

• Calibration of the AID converter.

• Calibration of the motor rotation speed.

Calibration of the rotameter.

There were fifteen divisions on the rotameter used in this investigation, the rotameter was

calibrated with stream of water flow on every other three divisions on the rota meter by setting

the rotameter at the desired point of calibration and letting the water flow through it for five

minutes while keeping the rotameter on scale, the exiting fluid was collected and its volume

was measured and finally, the flow rate was calculated by dividing this total volume by time,

5 minutes, and expressed in --1[!L mm.

The exact operations took are described in the following list;

1. Set the scale on rotameter for calibration.

2. Start timer and collect exiting fluid from rotameter outlet.

Appendices 134

3. Wait 5 minutes.

4. Remove fluid collecting container.

5. Stop timer.

6. Measure collected fluid volume with graduated cylinders.

These same procedures were repeated three times for each selected calibration point. The

final calibration data at each calibration point was taken as the average of the three cali-

bration data for that particular point. The recorded rotameter calibration data is tabulated in

Table 12 on page 136 and plotted in Figure 12 on page 47. The rotameter was found to be

stable within ± 2%.

Appendices 135

Table 12. Rotameter calibration data

METER SCALE FLOW RATE

15 213.43 ml/min

12 184. 75

9 147.27

6 103. 14

3 52.61

136 Appendices

Calibration of the conductivity probe.

The tracer used in this investigation was pure sodium chloride because it was safe, easy to

handle, easy to obtain and its solution processed a relatively high conductivity which was

essential because of the nature of this experiment. The stream of fluid flow used was water.

A standard sodium chloride solution of 0.872 g/1 was used to calibrate the conductivity probe

and therefore it also served to set the upper range of concentration that the probe could

handle for all the tests that were conducted. The calibration procedure is described in the

following paragraph.

The conductivity probe was immersed in tap water and agitated, the offset control

potentiometer on the analog to digital converter circuit board was adjusted until the reading

from the analog to digital converter gave zero. Then, the conductivity probe was washed with

the standard sodium chloride solution and immersed in a different sample of the standard

sodium chloride solution and agitated, the span control potentiometer on the analog to digital

converter circuit board was again adjusted until the converter reading became 255 which was

the upper limit that an 8-bit converter could give, then the standard solution of sodium chloride

that the probe was in was diluted to various concentration by adding 50 ml of tab water to it

successively until the total volume of the solution reached 950 ml. For each addition of the tap

water, the diluted solution was agitated and the probe reading from the A/D converter was

recorded. The exact operations took are described in the following list;

1. An electrical balance was used to determine a 0.218 g of pure dried sodium chloride

sample.

2. Tap water was used to make a 250ml of standard sample sodium chloride solution.

3. The voltage reference on the AID converter board was checked and adjusted to 5.00V.

Appendices 137

4. The probe was immersed in tap water and agitated for two minutes.

5. The offset control knot on the probe signal conditioning circuit, refer to Figure 46 on page

127, was adjusted to give a A/0 converter reading of 00000000.

6. The probe was taken out of the tap water and washed with standard sodium chloride

solution.

7. The probe was immersed in 250ml of standard sodium chloride solution and agitated for

2 minutes.

8. The span control on the probe signal conditioning circuit, refer to Figure 46 on page 127,

was was adjusted to give a A/0 converter reading of binary 11111111.

9. The 250ml of standard sodium chloride solution which the probe was immersed in was

diluted with 50ml of tap water and agitated for 2 minute then the A/0 converter reading

was taken.

10. The last step were repeated until the total volume of the solution reached 950ml.

The sequences listed above were repeated three times, an average was taken for each cali-

bration point by summing all three data points for that calibration point and dividing the sum

by three. The conductivity probe calibration data thus recorded were tabulated in Table 13

on page 141 and plotted in Figure 13 on page 49. The data points in Table 13 on page 141

were fitted against a fourth order polynominal and a probe calibration equation was obtained

as follows;

_ 2 3 4 Yn - a+ bx Xn + c x Xn + d x Xn +ex Xn [30)

where;

Appendices 138

a= 0.037 ; b = 2.422

c = 1.468E-03 ; d = 8. 79E-06

e = 3.583E-09

Yn = Exit tracer response; in ~g

xn = Exit tracer response; in binary code.

During the probe calibration process, the probe was placed inside and in contact with' the wall

of a stainless steel beaker which was grounded to the common ground of the vessel flow

system. This grounding procedure was found necessary in order to balance the ground noise

when the probe was placed inside the flow system. After the probe was calibrated, the posi-

tions of the offset and span control potentiometer were noted and referred to as the original

null positions for the conductivity probe.

The tolerance of the offset null position for the probe, i.e. how far the probe null position can

drift away from the original null position before the probe calibration equation become invalid,

was obtained by adjusting the offset control slightly and carrying out the probe calibration

procedures to check against the validity of the probe calibration equation. Using this proce-

dure it was determined that the probe response would make a parallel shift with a maximum

of± 1% error within a ± 0.3V null position variations.

The tolerance of the graduated cylinder, 50 ml, used to measure the volume of tap water was

± 0.5% and the electrical balance used was accurate down to four digits after the decimal

point. The sodium chloride used was a 98% laboratory grade sodium chloride.

Appendices 139

The probe was fairly stable within ± 1 LSB (least significant bit) of the A/D converter reading

if proper signal transmission line shielding and by-passing of the power supply rippling were

attended.

Appendices 140

Table 13. Conductivity probe calibratio'n data

ADC READING TRACER CONC.

255 Decimal 0.87 g/1

225 o. 725

201 0.621

182 0.544

152 0.435

130 0.362

115 0.31

102 0.271

91 0.241

83 0.216

77 0. 197

70 0. 18

65 0. 166

60 o. 154

43 0. 11

22 0.054

15 0.039

0 0.00

Appendices 141

Calibration of the A/D converter.

Because of the particular AID converter (ADC0808) used in this investigation, no offset and

span adjustment for the AID converter itself was necessary. However, before each test run

the voltage reference on the AID converter board was checked for 5.00V with a 3-½ digit DMM

(digital multimeter). The rippling of the reference was found to be less than 0.1 %. The total

unadjustable error, digitization error, of the AID converter itself is ± f LSB.

Calibration of the motor agitation speed.

The motor speed was calibrated with a stroboscope, strobe light. The frequency that the light

was strobing was checked against the calculated value obtained from the motor speed sens-

ing circuitry. Three arbitrary settings, within our intended operating range, on the AC motor

controller were selected and the calculated rotating frequencies were checked against the

strobe light frequencies.

The maximum motor agitation speed used in this investigation was relatively slow compared

to the 1MHz master clock of the microprocessor. This fact will help improve the accurracy of

the motor speed sensing circuitry.

The exact sequence of operation took in calibrating the motor speed sensing circuitry is

shown as follows;

• A motor speed setting was selected.

• The strobe light was adjusted to synchronize the black tape on the motor shaft encoding

plastic ring.

Appendices 142

• The strobe light frequency and the calculated rotating frequency were recorded.

The above sequence of operations were repeated three times. The calculated rotating fre-

quency was displayed on a CRT (cathode ray tube) screen, it was actually an average of ten

consecutive samples of the rotating frequency sampled by the speed sensing circuitry, to

provide a visual feedback for the motor speed sensing line. During actual test runs, this visual

feedback was used to set the control knot on the AC motor speed controller and therefore

provided a method to establish the desired agitator operating condition. The motor speed

sensing section was found to be fairly stable with a maximum of± 5 % ripplings over a period

of one hour for all rotating speeds within the range used in this investigation.

C. Sample calculations

This section contains the sample calculation for t~e following two procedures:

• Fluctuations of exit tracer response.

• Standard deviation of fluctuation.

A set of data of a total of 30 points, which were taken from the 2100th to the 2129th data point

from the initial test 3, is used to go through the various calculation sequence performed in this

investigation for the purpose of demonstration. These data points were tabulated in Table 14

on page 145 and Table 15 on page 146 for reference. These data points, taken directly from

the AID converter, were converted to concentration ( ~g) data using the following equation;

[31]

Appendices 143

where;

a=0.037 ; b=2.422

c=1.468 E-03 ; d=8.79 E-06

e = 3.583 E-09

Yn= Data points in Table 16 on page 147 and Table 17 on page 148

xn= Data points in Table 14 on page 145 and Table 15 on page 146

The resulting concentration data were tabulated in Table 16 on page 147 and Table 17 on

page 148. We will use the data in this table for the discussion of the sample calculation pro-

cedures used in this investigation.

Appendices 144

Table 14. ADC readings of sample data

DATA NUMBER ADC READING

1 40 Decimal

2 38

3 35

4 33

5 31

6 30

7 28

8 27

9 26

10 25

11 26

12 29

13 31

14 31

15 31

Appendices 145

Table 15. ADC readings of sample data

DATA NUMBER ADC READING

16 30 Decimal

17 31

18 33

19 34

20 34

21 34

22 35

23 36

24 37

25 38

26 39

27 40

28 41

29 42

30 42

Appendices 146

Table 16. Concentrations of sample data

DATA NUMBER CONCENTRATION

1 99.83 mg/1

2 94.68

3 86.98

4 81. 88

5 76. 79

6 74.25

7 69. 19

8 66.67

9 64. 15

10 61. 64

11 64. 15

12 71. 72

13 76. 79

14 76. 79

15 76. 79

Appendices 147

Table 17. Concentrations of sample data

DATA NUMBER CONCENTRATION

16 74.25 mg/1

17 76. 79

18 81. 88

19 84.43

20 84.43

21 84.43

22 86. 98

23 89.54

24 92. 11

25 94. 68

26 97.75

27 99.83

28 102.42

29 105.01

30 105.01

Appendices 148

Fluctuation of exit tracer response.: The first five data points in Table 16 on page 147 were

processed through a five-point least square fit procedure as follows;

n=S L Xn = 3.33

n=1

n=S L Yn = 440.16

n=1

n=S L XnYn = 273.66

n=1

n=S L x~ = 3.33

n=1

m = N x LXnYn - LXn x LYn = -17.669 N x LX~ - (LXn) 2

Where;

N = the number of samples in each pass= 5

Xn = time interval; equally spaced at 0.333 sec.

Yn = conc.(in mg/I) from tracer exit stream.

m = slope of the fitted line

c = intercept of the fitted line

Appendices

[32)

(33)

149

The instantaneous mean (Yn) for the first five data points were taken as the points fell on the

straight line that had a slope of m and an intercept of c at an interval of X" starting from

Xn=O, or

Yn = m x Xn + c [34]

Where;

Yn = Instantaneous mean value of exit tracer response

The instantaneous mean values for the first five data points in Table 16 on page 147 thus

calculated were as follows;

y, =99.8

The fluctuations Fn for the first five data points in Table 16 on page 147 were simply taken as

the differences between each pair of the corresponding Yn and Yn as follows;

F, = Y1 - y, = 99.83 - 99.80 = 0.03

Appendices 150

F3 = Y3 - y3 = 86.98 - 88.04 = -1.06

F5 = Y5 - Ys = 76. 79 - 76.25 = 0.54

For any set of five data points, the calculated instantaneous fluctuation of the third data point,

the center point of this set of five data points, was recorded and the other four were simply

discarded. This procedure for calculating the fluctuation of the exit tracer response moved

on to the next set of five data points by advancing one data point at a time, for example if the

set of data being processed was the first to the fifth data point then the next set of five data

point to be processed would be the second to the sixth data point in sequence, through the

entire tracer response data file. For each set of data, only the fluctuation of the center point

was recognized. As a result of this method, the first two data points and the last two data

points in an entire tracer response file did not contribute to the fluctuation information at all.

However; in an actual test run, this was of no influence since the very beginning and the very

end of any tracer response always gave zeros.

Anyway, these procedures for calculating the F" were repeated for the next set of five data

points in sequence, in this case Y2 through Y8 in Table 16 on page 147, until all the data points

had been processed. The values of X" in each pass of the processing always started from

zero, thus the name moving window, and increased by an amount of 0.333 second for each

step size.

All the data points in Table 16 on page 147 and Table 17 on page 148 were processed using

the method described above for obtaining the fluctuation information and the results were

Appendices 151

tabulated in Table 18 on page 153 and Table 19 on page 154 for reference. Readers may

notice that 1st, 2nd, 28th, and the 29th data points did not contribute to the fluctuation infor-

mation as in this case.

Appendices 152

Table 18. Fluctuations of sample data

DATA NUMBER FLUCTUATION

3 -1. 06 mg/1

4 -1. 04

5 -1. 03

6 0.49

7 -1. 02

8 -0.51

9 -1. 01

10 -4.02

11 -3.54

12 1. 50

13 3.54

14 1. 50

15 0. 51

Appendices 153

Table 19. Fluctuations of sample data

DATA NUMBER FLUCTUATION

16 -3.05 mg/1

17 -2.03

18 1. 53

19 2.04

20 0.00

21 -1. 53

22 -0.52

23 0.00

24 -0. 10

25 -0. 10

26 0.39

27 -0.11

28 0.42

Appendices 154

Standard deviation of fluctuation.: The standard deviation of fluctuations for the sample data

was calculated using the following equation;

2 I,F2 - (I,F n)

so,= .J n N N

Where;

SD,= Standard deviation of fluctuations; ~g

Fn = Instantaneous fluctuation; ~g

N = Total number of samples.

From Table 16 on page 147 we have

I-F2= 74 86 ( mg )2 n . I

""' mg ""'Fn = -8. 73 (- 1-)

N= 26

therefore

mg so,= 1.66 (-,-)

[35]

Of course, the values obtained for the above calculation examples do not reflect the true

property of the fluctuations for initial test 9, there were approximately 5300 data points in initial

test 9, since they were calculated from a small portion of the entire response file.

Appendices 155

D. Materials and apparatus

This section contains the materials and apparatus used in this investigation.

• Glassware; 250ml glass holding tank; 10ml, 25ml, 50ml, 250ml flasks; obtained from De-

partment of Chemical Engineering, VPISU Blacksburg VA.

• 10ml, 25ml, 50ml graduated cylinder, ± 0.5% at 20°C; obtained from center stores, VPISU

Blacksburg VA.

• 50ml stainless steel beaker; obtained from center stores, VPISU Blacksburg VA.

• Magnetic stirrer; Corning PC 351; obtained from Department of Chemical Engineering,

VPISU Blacksburg VA.

• Plastic tubing; TYGON R-3603; obtained from center stores, VPISU Blacksburg VA.

• Copper tubing; 3/8" schedule 80; obtained from center stores, VPISU Blacksburg VA.

• Motor controller; GT-21 Motor controller, obtained from G.H. Heller Corp., Floral Park.

N.Y., U.S.A.

• Motor; GT21-18 Heavy-duty laboratory stirrer, obtained from G.K. Heller Corp., Floral

Park, N.Y., U.S.A.

• Sodium Chloride; 99% laboratory graded S-271 Sodium Chloride, Fisher Scientific; ob-

tained from center stores, VPISU Blacksburg VA.

Appendices 156

• Electrial balance; Mettler H20; Mettler Instrument Corp. Hightstown NJ.; obtained from

Department of Chemical Engineering, VPISU Blacksburg VA.

• Electrical conductivity probe; obtained from machine shop; Department of Chemical En-

gineering, VPISU Blacksburg VA.

• Rotameter; Type 1355-01A1FZZ40, Brooks Instrument Division, Emerson Electric Co.,

Hatfield Penn., U.S.A.; obtained from Department of Chemical Engineering, VPISU

Blacksburg VA.

• AID converter; ADC0808, National Semiconductor; obtained from Jameco Electronics;

Belmont CA.

• Programmable Timer; MC6840, Motorola Semiconductor; obtained from Jameco Elec-

tronics; Belmont CA.

• Programmable 1/0; MC6821, Motorola Semiconductor. obtained from Jameco Electronics;

Belmont CA.

• TTL Logic gates; 74LS154, 74LS244, 74LS245, 74LS11 obtained from Jameco Electronics;

Belmont CA.

• Operational Amplifiers; CA3140A obtained from Jameco Electronics; Belmont CA.

• Bread-board. obtained from Jameco Electronics; Belmont CA.

• Oscilloscope; Tektronix T912; Tektronix Portland Oregan; obtained from Department of

Chemical Engineering, VPISU Blacksburg VA.

• Stroboscope; General Radio 1531-A; General Radio Co. Concord Mass. obtained from

Department of Chemical Engineering, VPISU Blacksburg VA.

Appendices 157

• Digital multimeter; Fluke 08FLU8026B 3T digits ± 0.1%; obtained from priority one elec-

tronics; Chatsworth, CA.

• 25 conductor flat cables; obtained from Scotty's radio; Blacksburg VA.

• Resistors, Capacitors; an assortment of different values of resistors and capacitors; ob-

tained from Scotty's radio; Blacksburg VA.

Appendices 158

The vita has been removed from the scanned document

study of the c-curve fluctuation analysis for a cstr reactor

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