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SEPARATION TECHNIQUE ON PROTEINS VIA A PH-PARAMETRIC PUMP: A THEORETICAL AND EXPERIMENTAL STUDY

New Jersey Institute o f Technology D.SC.ENG. 1982

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SEPARATION TECHNIQUE ON PROTEINS VIA A pH-PARAMETRIC PUMP:

A THEORETICAL AND EXPERIMENTAL STUDY

byUra Pancharoen

Dissertation submitted to the Faculty of the Graduate School of the New Jersey Institute of Technology in partial fulfillment

of the requirements for the degree of Doctor of Engineering Science

1982

APPROVAL SHEET

Title of Dissertation: Separation Technique on Proteins Via A pH-Parametric Pump: A Theoretical and Experimental Study

Name of Candidate: Ura Pancharoen Doctor of Engineering Science, 1982

Dissertation and Abstract Approved:

Dr. C.R. Huang Date Professor & Assistant Chrmn. Dept. of Chemical Engineering

Date

Date

Date

Date

VITA

Name: Ura Pancharoen

Degree and date to be conferred: D. Eng. Sc., 1982

Primary education: Pra-ka-nong School, Bangkok, Thailand, March 1964

Secondary education: Triam-Udom-Suksa School, Bangkok, Thailand, March 1966

Collegiate institutions attended Date Degree Date of Degree

Chulalongkorn University 66/70 B. Eng. 6/70

N. J. Institute of Technology 72/75 B.Sc. 5/75

N. J. Institute of Technology 75/77 M.Sc. 5/81

N. J. Institute of Technology 77/82 D.Sc. 5/82

Major: Chemical Engineering

Minor: Mathematics

Publications; Chen, H fT f, U f Pancharoen, W.T, Yang, C,0,Kerobo and R,J, Parisi, ''Separation of Proteins Via pH-Parametric Pumping," Separation Sci. & Tech, 15, 1377 (1980)Chen, H.T., W.T. Yang, U. Pancharoen, and R.J. Parisi, "Separation of Proteins Via Multi- Column pH-Parametric Pumping," AIChE. J., 26, 839 (1980)Chen, H.T., U. Pancharoen, C.R. Huang and C.O. Kerobo, "Analytical and Graphical Solution for Separation of Proteins Via Multi-Column pH- Parametric Pumping," in preparation.Chen, H .T ., U . Pancharoen, C.R. Huang and C.O. Kerobo, "Separation of L-Dopa & D-Dopa Via Multi-Column Parametric Pumping," in prepara­tion .Chen, H .T ., U . Pancharoen, C.R. Huang and C.O. Kerobo, "Mathematical Modeling for pH-Parame- tric Pumping based on Elementary Matrix Algebra, in preparation.

Position held:1978 - present Special Lecturer, Chemical Engineering

Department, New Jersey Institute of Technology, Newark, New Jersey.(first served as adjunct instruetor)

1975-1978 Teaching Assistant, Chemical Engineering Department, New Jersey Institute of Technology, Newark, New Jersey.

1970-1972 Process Engineering, Thai Chemicals &Fertilizers Corporation, Lumpang, Thailand.

ABSTRACT

Title of Dissertation: Separation Technique on Proteins ViaA pH-Parametric Pump: A Theoreticaland Experimental Study

Ura Pancharoen, Doctor of Engineering Science, 1982Dissertation directed by: Dr. C.R. Huang, Professor and

Assistant Chairman, Department of Chemical Engineering

The separation of protein mixtures via pH-parametric pumping was investigated both theoretically and experimental­ly. A simple system consisting of one column packed either with cation or anion exchanger was first considered. A system of parapumps was then developed with more columns which were connected in series and packed alternately with cation and anion exchangers. Various methods of operation of parapumps are discussed. Enrichment and spliting of protein mixtures were examined. In most cases, the separation factor was defined at a steady state condition and was improved by increasing the number of cycles and columns.

Computational methods for predicting both Batch and Semi- Continuous parametric pump performance, with equilibrium con­ditions described were developed. The physical system was characterized by means of interphase mass transfer rates. These methods were based on a set of exterior and interior material balances. Linear parameters were calculated for the

adsorption of the solute on the ion exchanger. A mathematical model based on elementary matrix algebra was developed as well as a graphical method. The properties of eigenvalues and eigenvectors of this formalism were studied. The subject was extended to more complex situations involving a multi-column, and the separation of multi-protein . There is good agreement between predicted and experimental results.

ACKNOWLEDGEMENT

This research was done under the direction and with the encouraging advice and guidance of Dr. H. T. Chen of the Chemical Engineering Department. After the tragic automobile accident which ended Dr. Chen’s life on April 21, 1981;Dr. C. R. Huang was instrumental to see a successful completion of this work. Heartfelt appreciation is extendedto Dr. H. T. Chen, thesis advisor, and to Dr. C. R. Huangfor their invaluable assistance.

Greatful thanks are extended to the Doctoral Committee for their suggestion and encouragement, and to M.R. Idhinand Abhakara and to Dr. R. A. George who have offerred support and guidance over the years at this College.

Special thank you to Mr. D. F. Bravender, Vice Presidentof The Chase Manhattan Bank, for prove reading thismanuscript. Financial support from the Chemical Engineering Department at New Jersey Institute of Technology, where the author is currently employed, also the typing of initial drafts and the final manuscript by Y. Pihtayanukul,T. Nimboonchaj and M. Jampathom are appreciated.

TABLE OF CONTENTS

Chapter PageACKNOWLEDGMENT iiLIST OF FIGURES viLIST OF TABLES xiI. INTRODUCTION 1

II. PROCESS DESCRIPTION 9A. The One-Column Parametric Pumping System 9B. Two-Column Parametric Pumping System 14

(1) Mode 1: Three Reservoirs With BothCation and Anion Exchangers 14

(2) Mode 2: Four Reservoirs With BothCation and Anion Exchangers 17

(3) Mode 3: Five Reservoirs With BothAnion and Cation Exchangers 20

(4) Mode 4: Two Reservoirs With An IonExchanger (Cation or Anion) 23

III. EQUILIBRIUM THEORY-GRAPHICAL SOLUTION 26A. One-Column System 26B. Two-Column System 32

IV. ANALYTICAL SOLUTION 51A. Formal Mathematical Solution 51B. Calculation of [M]n 57C. The Cyclic Steady State 59

V. EXPERIMENTAL METHOD 65A. Experimental System 65B. Description of Apparatus 66C. Solutions and Buffers 67

i i i

Chapter PageD. Gel Preparation and Packing 69E. Measurements 69F. Operation Process 70

(1) One-Column: Semi-Continuous 70(2) Two-Column System 73

VI. SEPARATION OF PROTEINS VIA MULTI-COLUMN 85A. Process Designing for Multi-Protein Separation 85B. Selection of pH Level 88C. An Addition to the Original System (Exten­

sion System) 91D. Symmetrical System 91E. Unsymmetrical System 94

VII. RESULTS AND DISCUSSION 100A. General 100B. One-Column System 101C. Two-Column System 106D. Separation of Proteins Via Multi-Column 129E. A Theoretical Study Via Mathematical

Formalism Based On Elementary Matrix Algebra 162VIII. SUMMARY OF CONCLUSIONS 168

NOMENCLATURE 170APPENDIX A. ANALYTICAL DETAILING 174APPENDIX B. EXPERIMENTAL DATA 200APPENDIX C. COMPUTER PROGRAM ON EQUILIBRIUM 263

THEORY: SEPARATION OF MULTI-COMPO­NENT VIA pH-PARAMETRIC PUMPING

i v

Chapter Page

APPENDIX D. TABLES: pH-PARAMETRIC PUMPING 314APPENDIX E. GLOSSARY 329LITERATURE CITED 330

v

LIST OF FIGURESPage

1. The Batch Parametric Pump (Rak, 1978) 32. Staged Cycling Zone Extraction System 6

(Wankat, 1973)3. Column Diagram For pH-Parametric Pumping 104. Schematic For Equilibrium Plug Flow Model 125. Effect Of n On Concentration Transients 156. Two-Column Diagram, Packing With Anion And 16

Cation Exchanger For Mode 17. Two-Column Diagram, Packing With Anion And 19

Cation Exchanger For Mode 28. Two-Column Diagram, Packing With Anion And 22

Cation Exchanger For Mode 39. Two-Column Diagram, Packing Either With 24

Anion or Cation Exchanger For Mode 410. Schematic Of One-Column System 2911. Graphical Solution For One-Column System 3112. Schematic Of Two-Column System: Mode 1 3513. Graphical Solution For Two-Column System: 36

Mode 114. Schematic Of Two-Column System: Mode 2 3815. Graphical Solution Of Two-Column System: 41

Mode 216. Schematic Of Two-Column System: Mode 3 4317. Graphical Solution Of Two-Column System: 45

Mode 318. Schematic Of Two-Column System: Mode 4 4719. Graphical Solution Of Two-Column System: 49

vi

PageMode 4

20. The pH-Parametric Pumps Diagram For 52Mathematical Approach

21. Equilibrium Constants For the Haemoglobin- 54Albumin System: Sephadex Ion Exchanger (Reference 28)

22. Graphical Solution Base On McCabe-Thiele 63Diagram23. The Experimental Apparatus Describes The 68

Three Reservoirs Batch System24. Schematic Of Single Column, Semi-Continuous 71

System25. Schematic Of Two-Column, Semi-Continuous 75System: Mode 226. Schematic Of Two-Column, Semi-Continuous 82System: Mode 427. Schematic Of Process-Designing For: 86

(a) An Original First Unit And(b) An Additional Unit

28. Graphical Solution For Process Designing, 87M-Column System29. Schematic Of Process Designing For: 93A Symmetrical Multi-Separation System30. Schematic Of Process Designing For: 97

An Unsymmetrical Multi-Separation System31. The Concentration Transients Of Haemo- 102

globin And Albumin vs. Number of Cycles32. Comparison Of Anion And Cation Column 104For Haemoglobin33. Comparison Of Anion And Cation Column 105

For Albumin34. The Concentration Transients Of Haemo- 107globin In A Single-Anion-Column System35. The Concentration Transients Of Albumin 108

vii

Ill

112

114

115

116

118

119

120

121

123

125

126

128

In A Single-Anion-Column SystemThe Concentration Transients Of Haemo­globin In A Single-Cation-Column SystemComparison Of Albumin Concentration Between One- And Two-Column SystemThe Concentration Transients Of Haemo­globin And Albumin vs. Number Of Cycles: Mode 1The Concentration Transients Of Haemo­globin And Albumin vs. Number Of Cycles: Mode 2 (Case I)The Concentration Transients Of Haemo­globin And Albumin vs. Number Of Cycles: Mode 2 (Case II)The Concentration Transients Of Haemo­globin And Albumin vs. Number Of Cycles: Mode 2 (Case III)The Concentration Transients Of Albumin vs. Number Of Cycles: Mode 2The Concentration Transients Of Haemo­globin vs. Number Of Cycles: Mode 2The Concentration Transients Of Haemo­globin vs. Number Of Cycles: Mode 2The Concentration Transients Of Albumin vs. Number Of Cycles: Mode 2The Concentration Transients Of Haemo­globin vs. Number Of Cycles: Mode 2The Concentration Transients Of Haemo- globin-Albumin vs. Number Of Cycles: Mode 3 (Case I)The Concentration Transients Of Haemo- globin-Albumin vs. Number Of Cycles: Mode 3 (Case II)The Concentration Transients Of Haemo- globin-Albumin vs. Number Of Cycles: Mode 3 (Case III)

viii

130

131

132

135

136

137

138

139

140

142

144

147

148

149

150

Separation Factor Of Haemoglobin vs. Number Of Cycles: Mode 4Separation Factor Of Albumin vs. Number Of Cycles: Mode 4Separation Factor Of Haemoglobin And Albumin vs. Number Of Cycles : Mode 4Graphical Solution Of Protein A Via Two-Column SystemGraphical Solution Of Protein B Via Two-Column SystemEffect Of "P On Concentration Transients For Protein AEffect Of p On Concentration Transients For Protein BGraphical Solution Of Protein A Via Multi-Column System, Separation From Two Components Of ProteinGraphical Solution Of Protein B Via Multi-Column System, Separation From Two Components Of ProteinSchematic Of Staircase For Predicting The Protein Steady State ConcentrationSteady State Separation Factors Of Two Proteins vs. Number Of Columns (M)Graphical Solution Of Protein A Via Multi-Column System, Separation From Multi-Component Of ProteinGraphical Solution For Protein Mixtures B, C and D Via Multi-Column SystemThe Concentration Transients Of Protein A And Protein Mixtures B, C And D vs.Number Of CyclesGraphical Solution For Protein B Via Multi-Column System, Separation From Multi-Component Of Protein

ix

Page65. The Graphical Solution For Protein

Mixtures C And D Via Multi-Column System

66. The Concentration Transients Of Protein B And Protein Mixtures C And D vs.Number Of Cycles

67. Graphical Solution Of Protein C Via Multi-Column System

68. Graphical Solution Of Protein D Via Multi-Column System

69. The Concentration Transients Of Protein C And Protein D vs. Number Of Cycles

70. Graphical Solution For Protein Mixtures A And B Via Multi-Column System

71. Graphical Solution For Protein Mixtures C And D Via Multi-Columm System72. The Concentration Transients Of Proteins

A & B And Proteins C & D vs. Number Of Cycles

73. The Concentration Transients Of Protein In The Fluid Phase vs. Number Of Cycles (Case I)

74. The Concentration Transients Of Protein In The Solid Phase vs. Number Of Cycles (Case I)

75. The Concentration Transients Of Protein In The Fluid Phase vs. Number Of Cycles (Case II)

76. The Concentration Transients Of Protein In The Solid Phase vs. Number Of Cycles (Case II)

A-l.l. The Plot Of 7% vs. Number Of Cycles

151

153

155

156

157

159

160

161

163

164

165

166

179

x

LIST OF TABLESPage

1. An Expression of Protein Charges, 89Those Which They Would Bear in The Different pH Level Solution.

A-4.1 The Elements of The Matrices And 193Vectors

A-5.1 Protein Concentration: Case I 198A-5.2 Protein Concentration: Case II 199

B-l Experimental Raw Data for One-Column 204-to B-7 System 210

Ex-B-2.1 Summary of The Experimental Results. 211-to Ex-B-2„5 One-Column: Batch Operation. 215

B-8 Experimental Raw Data for Two-Column 217-to B-13 System: Mode 1. 222

Ex-B-3.1 Summary of The Experimental Results. 223Two-Column System: Mode 1, Batch Operation.

B-14 Experimental Raw Data for Two-Column 225-to B-18 System: Mode 2 234

Ex-B-4.1 Summary of The Experimental Results. 235Two-Column System: Mode 2, Batch Operation.

Ex-B-4.2 Summary of The Experimental Results. 236-to Ex-B-4.4 Two-Column System: Mode 2, Semi- 238

Continuous Operation.B-19 Experimental Raw Data for Two-Column 240-

to B-22 System: Mode 3. 249Ex-B-5.1 Summary of The Experimental Results. 252

Two-Column System: Mode 3, Batch Operation.

B-23 Experimental Raw Data for Two-Column 254-to B-29 System: Mode 4. 260

Ex-B-6.1 Summary of The Experimental Results. 261

xi

Page

Ex-B-

to

toD

D

D

D

D

Two-Column System: Mode 4, Batch Operation.

6.2 Summary of The Experimental Results. Two-Column System: Mode 4, Semi- Continuous Operation.

C-l Nomenclature for Computer Program Input and Output

D-l Computational Results on SeparationD-6 of Protein A via Two-Column.D-7 Computational Results on SeparationD-9 of Protein B via Two-Column.-10 Computational Results on Separation

of Protein Mixtures A and B via Two-Column.

-11 Computational Results on Separation of Protein Mixtures C and D via Multi-Column.

-12 Computational Results on Separation of Protein Mixtures B, C and D via Multi-Column.

-13 Computational Results on Separation of Protein Mixtures A, B, C and D via Multi-Column.

-14 Computational Results on Separation of Protein Mixtures A, B and C, D via Mulyi-Column.

262

264

315-320321-323324

325

326

327

328

xii

1

Chapter I INTRODUCTION

A. DEFINITION

Parametric pumping is a separation technique that is based on the periodic movement of a fluid phase over a solid adsorbent bed and a coupled energy input into the system to induce the separation.

The term "Parametric Pumping" was applied to the separa­tion process in 1966 by the late R.H. Wilhelm of Princeton University, inventor of the batch pump. This separation process was a recuperative mode, which dealt with a two-phase system by means of an interphase mass transfer with an oscil­lating direction of the fluid flow. The fluid was heated in a heat exchanger before flowing up through the column and cool­ed before the flow direction had been changed as shown in Figure 1.

B. OPERATION

The basic parametric pump handles a batch operation and illustrates the coupling action. Consider the removal of component A from a fluid mixture of A and B. Assume that component A is absorbed on solid (S), packed in the column as shown in Figure 1. The column will have some void volume to allow the fluid to flow into it by means of two piston-operated fluid reservoirs at each end, which are filled with

2

the fluid mixture at a known concentration of A, (Yq )- Also assume that the condition of interphase equilibrium occurs at a high temperature. Allow the temperature of the two-phase system to change periodically through alternate heating and cooling by transferring heat energy through the media of appropriate temperature to the jacket of the column. Then, the concentration of A in the liquid (y) and the con­centration of A on the solid (x), will periodically change to new values in response to the change in the thermodynamic state of the system. Normally, A will be adsorbed on S while the system is heated.

At this step, the direction of flow of the fluid will be changed periodically and synchronized with the system tem­perature; e.g., only upward flow will occur during heating only downward during cooling. The volume of fluid in the column interstitial space will be depleted in A by adsorp­tion on S only while it moves downward and enriched in A by desorption from S while it moves upward. After the system has completed the cycle of hot upflow and cold downflow, fluid depleted in A will migrate to the bottom of the column; while fluid enriched in A migrates to the top. The result of this operation is a net displacement of component A to the top of the column after a number of synchronized tempera- ture-flow cycles. Separation of the system fluid into a fraction relatively concentrated in A at the top of the column has been achieved while the bottom contains a fraction

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4

relatively lean in A.

C. DEVELOPMENT

In 1966, Wilhelm and his co-worker had investigated the separation of NaCl from water using a mixed bed of ion- exchanger for a batch parametric pumping process in the recuperative mode. Wilhelm also expressed his idea of apply­ing the parapump principle/processes with various driving forces such as magnetic, chemical potential, etc.

Wilhelm and Sweed (1968) had modified the system by using the direct mode as shown in Figure 1 on a batch system, to separate toluene from n-heptene, using silica gel as an absorbant. This direct mode is operated by a heating and cooling source which is supplied through the water jacket during upward and downward flow respectively. The stationary bed (column with jacket) is heated before the upward flow of liquid and is cooled before the downward flow by an external source. The parametric pumping process is not limited to only temperature induced liquid/solid mass transfer systems. Jen- czewski and Myers (1970) separated the mixture of ethane and propane passing through activated carbon.

Sabadell and Sweed (1970) employed the recuperative mode to remove K+ and Na+ from water by changing pH levels. For this type of process the high pH end was opened while low pH end remained closed. HC1 was introduced to the low end to

5

maintain the pH levels. The product was withdrawn while dfresh feed was supplied for every half cycle. During theprocess, the neutralization reaction occurred in the columnand was claimed as an energy supplier for the separation.By means of this operation, the maximum separation factor(ratio of enriched product to depleted product) yield for

+ +total K + Na was obtained, although the deriving energy source by this method was not optimized.

Nor is parametric pumping limited to single adsorbant beds, one-solute systems, or oscillating flow patterns. In cycling zone extraction (see Figure 2), the mobile phase flows unidirectionally but enters successive zones of alter­nating, parameter values, e.g., hot and cold temperature, or high and low pH, both of which are utilized to separate glu­cose and fructose in an aqueous solution, which had been done by Busbice and Wankat in 1975. Chen, Jaferi, and Stokes(1972) had also used parametric pumping for sugar separation

+ +in aqueous media. The separation of Na and K in aqueous media has already been mentioned. In addition, toluene and analine can be separated from n-heptane using silica gel adsorbant in thermal parametric pumping.

In 1977, Chen and his co-workers had investigated the separation of proteins by use of a continuous pH parametric pump. Many system characteristics such as flow rate, buffer concentration, pH-level and reservoir displacement, which

6

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CYCLING

ZONE

EXTRACTION

SYSTEM

(WANKAT, 1973)

7

would affect the separation were examined. Chen considered a process which consists of a one column system packed withS.P. Sephadex (C-50) exchange resin and two reservoirs, one having a high pH level the other having a low pH level. Both buffer solutions carry protein mixtures. Chen began the pH- parametric pump process operation using the batch system (before he developed the continuous process system) and investigated the separation of haemoglobin and albumin.

Chen, et al., (1979) developed the continuous separation process using a protein mixture (haemoglobin-albumin) via pH- parametric pumping. The exchange resin, CM Sepharose, was selected for this experiment. The protein mixture was fed alternately to the top and bottom of the column at different pH levels. The top and bottom products were removed con­versely. Chen came to the conclusion that the continuous process reached the steady state faster than the batch para­metric pump. Also, when the batch system reaches a peak (optimum of steady state value) the concentration of protein in the respective reservoirs will begin to decrease due to the dilution of acid/base titrations (to maintain the pH levels) while the continuous system can be maintained as the number of cycles increases.

The results of this experiment showed that haemoglobin, with an isoelectric point less than pH" Value,-migrated:to:the higher pH end of the column while the albumin with an iso-

8

electric point greater than the pH value migrated to the low end of the column.

Chen and his co-workers (1979) also extended the parapump process to multi-column pH-parametric pumping. The system considered was a series of columns that were packed alter­nately with cation and anion exchangers. Many different types of methods and operations for single and multi-column parapump system were described.

D. DISSERTATION

This dissertation investigates both theoretical and ex­perimental methods using a single or two-column parapump, operated on batch or semi-continuous systems, and also ex­tending the method into a multi-column system. The emphasis of this work is divided into two parts the theoretical and the experimental. New methods of predicting performance are developed which include a method of mathematical approach and a graphical method. For experimental study, the separation of haemoglobin-albumin was selected. We established the neces­sary displacement, reservoir dead volume, buffer and Sodium Chloride concentration, circulation time and flow rate which would achieve the desired separation.

9

Chapter II

PROCESS DESCRIPTION

The One-Column Parametric Pumping System

The first system we will consider is shown in Figure 3.It consists of a column packed with an ion exchanger (cation or anion) and reservoirs attached to each end. The pump has dead volumes Vrj and Vg for the top and bottom reservoirs, respectively. Initially, the mixture to be separated fills the column voids, the top reservoir and the bottom dead volume. The top reservoir is maintained at a low pH level ky anautomatic titrator while a second titrator is used to keep the bottom reservoir at a high pH level (P2 K The ionic strengths of the buffer solutions in both top and bottom reser­voirs are kept at IS2 and IS^, respectively by means of two hollow fiber dialyzers manufactured by Amicon.

Two constant pH fields (P^ and P 2 ) are imposed periodical­ly to the system. During the first half-cycle, the fluid with pH = P2 in the top reservoir is pumped into the top of the column. At the same time, the solution that emerges from the column fills the bottom reservoir. On the next half-cycle, the solution with pH = P^ in the bottom reservoir flows back into the column. At the end of this half-cycle, the top reser­voir is filled with the solution that comes out of the top of

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FIGURE 3 - COLUMN DIAGRAM FOR pH-PARAMETRIC PUMPING

11

the column, and one cycle is completed. This procedure is repeated in each of the succeeding cycles until the desired number of cycles are completed.

We deduce the characteristics of the pH-parametric pump described above via a simple discrete transfer equilibrium stage model (Jenczewski and Meyer, 1970; Wankat, 1974;Grevillot and Tondeur, 1976). Let us assume that the adsorbent bed is divided into N equal segments or cells (stages) of length Z/N, where Z is the length of the pump column. Each stage is represented as (I, J), where I is the stage number and J is the transfer step (Figure 4). The system is initial­ly in equilibrium at J-l, and each cell has uniform concen­trations in both fluid and solid phases. In the transfer step, each fluid segment is displaced exactly one step ahead. Thus, the fluid y(I,J-l) originally opposite the solid section I is now opposite 1+1. After the transfer step, the phase equili­brium is immediately reestablished and the next transfer step J begins.

The mass balance for each component at I and J is,

Vy(I-l, J-l) + Vx(I, J-l) = Vy(I, J) + Vx(I, J) (1.1)

where V and V are the volumes of the fluid and the solid phases per stage, respectively, and will be assumed to be constant. Furthermore, we will make the following assumptions:

12

I+II+l

I-l

Equi l ibrium at T r a n s f e r S t e p J - l

Y / / ] So l i d p h a s e

Liquid p h a s e

D i s p l a c e m e n t of l e n g t h Z / N

I + l

I -

Equil ibrium at T r a n s f e r S t e p J

FIGURE 4 - SCHEMATIC FOR EQUILIBRIUM PLUG FLOW MODEL

13

(1) The solute will be distributed between the solidand fluid phases according to a linear form,

x = ky (1 .2 )

where k is pH dependent only.

(2) The hydrogen ion does not exchange for the exchanger'scounter ion, and therefore there is no lag of pHwave velocity behind the linear liquid velocity.

Proteins carry both negatively and positively charged groups of protein and can be bound to both anion and cation exchangers. Their net charge is dependent on pH. At low pH, the net charge is positive; at high pH it is negative. At the point of zero net charge, the isoelectric point, the substances are not bound to any type of ion exchanger.

Suppose we are concerned with the separation of a protein A from a mixture or solution, and this protein has the isoelec­tric point 1^ and P£ <C 1 ^ ^ P]_ • Thus, A will bear a negative charge at P2 and a positive charge at P£, whereupon A will be taken up by a suitable cation exchanger, R (with the counter ion S+) at P£ and released at P^:

R~S+ + A+ --------------------------- R“A+ + S+ at P£

R"A+ + S+ ------------------------► R~S+ + A" at ?1

Therefore, a parametric pump operating with levels of P^ and P2 should be capable of removing the solute A from the low

m

pH end of the column and concentrating it at the high pH end. The reverse effect will occur if an anion exchanger is selec­ted .

Concentration transients calculated by means of Equa­tions 1 and 2 are shown in Figure 5. The ordinate is the average reservoir concentration divided by the initial liquid phase concentrations. As long as a = 1, the steady state concentrations in both top and bottom reservoirs are inde­pendent of N chosen, a is defined as the quotient of the reservoir displacement and the column void volume (i.e., number of transfer steps/number of stages) . Note that when ct = 1 , N = Q(tt/oj )/V.

Two-Column Parametric Pumping SystemMode 1 : Three reservoirs with both cation and anion

exchangers

The system has two columns and three reservoirs as shown in Figure 6 . One column is packed with a cation exchanger (R“ ) and the other with an anion exchanger (R+ ). The pH level for the top and bottom reservoirs is maintained at Pi(8 ) and that for the middle reservoir is kept at P2 (6 ). Initially, the top reservoir and both columns are filled with a mixture of the concentration yQ . The R- and R+ columns are respectively in equilibrium at Pi(=8 ) and P2 (=6 ). One cycle of operation is described as follows:

(1) Transfer down:Step 1. The fluid in TR (top reservoir) is trans-

15

2.0

So l id = Cat ion i ' P 2< ^ A < p i

Vj= Vg= 0 ; kp2= 1.5 i kP)= 0 . 0 7

reservo i r d i sp lacement

co lumn void volume

25 0.8CA

No. of c e l l s (N )0 .4

0.2

3 28 16 2 4 400

n

NUMBER OF CYCLES

FIGURE 5 - EFFECT OF n ON CONCENTRATION TRANSEINTS (CHEN, 1980).

16

FIGURE 6

f T R pH=P-V ( 8 )

f B R pH=P.

- TWO COLUMN DIAGRAM, PACKING WITH ANION ANDCATION EXCHANGER FOR MODE 1

17

ferred to the R+ column, and the content in the R+ column goes to the MR (middle reservoir).Step 2. The content of the R“ column goes to the BR (bottom reservoir) and the fluid in the MR is trans­ferred to the R" column.

(2) Equilibration: The pH in the R+ column is changed from P2 to P]_, and at the same time the pH in the R- column is shifted from Pi to P2 - Thus, re-equili­brium is allowed in both columns.

(3) Transfer up: The content in the BR is brought back to the R“ column. The content in the R” is pushed through the MR and goes back to the R+ column. The content in the R+ column is transferred to the TR.

(4) Equilibration: The pH is switched from Pi to P2 for the R+ column, and from P2 to Pi for the R" column. The phase equilibrium is reestablished in both col­umns. Thus, one cycle is completed.

The procedures is repeated for each of the succeeding cycles .

Mode 2: Four reservoirs with both cation and anionexchangers

The system consists of two columns and four reservoirs as shown in Figure 7. One column is packed with a cation exchanger (R- ) and the other with anion exchanger (R+ ). The flow rate within the column is always equal to the reservoir

18

displacement rate (Q). Thus for both down and up flow, the reservoirs have the same displacement. For this mode, the system requires three different levels of pH, P^, P2 , anc P 3

where P^ ■< P2 ^ -l •

The pump has four reservoirs; one top (TR), two middle (ML and MR), and one bottom (BR), respectively, with pH = P 2 ,P^, Pg and ~?2 ' The system starts with the top reservoir (TR), one middle reservoir (MR), and both R+ and R~ columns filled with a mixture of concentration yQ. The R* and R columns are in equilibrium at P^ and P2 respectively. Flow sequences for one cycle are:

(1) Transfer down: Pump the fluid from the TR throughthe R column to the ML (P- ) > and at the same time, pump the fluid from the MR (P3 ) through the R column to the BR.

(2) Equilibration: The pH in the R+ column is changedfrom P^ to P 2 , and the pH in the R_ column is changedfrom P 2 to Pg. Then, the equilibration of both columns are reestablished

(3) Transfer up: The fluid from BR is pumped to the R~ column while the content in the R column goes through the middle reservoir (MR) to the R+ column.At the same time, the content from the R column is pumped into the TR.

(4) Equilibration: The pH in the R**" and the R columnsare changed from P2 to Pg and Pg to P 2 respectively.

19

FIGURE 7

f TR pH=P,V (6)

f BR pH=P,V( 6 )

' MR pH=P.V (A)

MLpH=Pv (8)

- TWO COLUMN DIAGRAM, PACKING WITH ANION ANDCATION EXCHANGER FOR MODE 2

20

Thus, reequilibrium is allowed in both columns.(5) Transfer down: The content in the R+ place is taken

by the fluid from the TR, and goes into the MR while the content in the R column is displaced by the fluid from the ML and transferred to the BR.

(6 ) Equilibration: The pH in the R+ and the R- columnsare changed respectively from Pg to P2 and P2 to P^• Both columns are allowed to re-equilibrate.

(7) Transfer up: The liquid in the R- column is pumpedthrough the ML to the R+ column while the fluid from the BR is transferred to the R~ column as well as the content from the R+ column goes to the TR.

(8 ) Equilibration: The pH in the R+ and the R- columnsagain are changed from P 2 to P^ and P^ to P2 respec­tively. Re-equilibration of both columns are allowed to re-establish.

Mode 3: Five reservoirs with both anion and cationexchangers

This process is consistent with two columns and five reservoirs. Both columns are packed; one with a cation ex­changer (R~) and the other with an anion exchanger (R+). The system requires two top reservoirs, one middle reservoir and two bottom reservoirs and they are connected by the columns as shown in Figure 8 . One top and one bottom reservoirs are maintained at P- (8 ) and the other top and bottom reservoirs are at ? 3 (4 ) while the middle reservoir is kept at P2 (6 ). Both

21

+the R column and the R column are in equilibrium at P2 (=6 ) and P^(=8 ) respectively. The two top reservoirs are filled with a mixture of the concentration yq at P^(8 ) and P^CA).Also one of the bottom reservoirs is filled with the same con­centration yg of a mixture at P^^A). The operation for the complete cycle is described as follows:

(1) Transfer down: The fluid from the TR(P^) is trans­ferred to the R " column, while the content in the

-I-R column (P2 ) is transferred through the MR to theR column. At the same time, the fluid in the R-column (P^) is transferred into the BR.

(2) Equilibration: The pH in the R column is changedfrom P 2 to P- while the R~ column is changed from P^ to P2 . Thus, re-equilibrium is allowed in both columns.

(3) Transfer up: The content in the BR(Pg) is pumpedinto the R~ column and at the same time, the fluidin the R~ column (P2 ) is transferred through the

+ +MR to the R column, while the content in the Rcolumn (P^) -*-s transferred into the TR.

(4) Equilibration: The re-equilibration in both the R+and R~ columns are allowed due to their changing inpH respectively from P^ to P2 and P2 to P .

(5) Transfer down: The fluid in TR (P3 ) is transferred+ + to the R column. The content in the R column (P2 )

is pushed down through the MR to the R- column while

22

FIGURE 8

BRpH=P

M RpH=P.(6 )

TRpH=P(8)

' BR pH=P

T Rp H = P(A)

R “

- TWO COLUMN DIAGRAM, PACKING WITH ANION ANDCATION EXCHANGER FOR MODE 3

23

the fluid in the R column (Pg) is transferred to the BR.

(6 ) Equilibration: The equilibration in both the R+ and R are re-established due to the pH change from P2 to and Pg to P2 respectively.

(7) Transfer up: The content from the BR(P^) is pumped to the R column, while the fluid in the R column (P2 ) is transferred through MR to the R+ column.

-I-Meanwhile, the fluid in the R (P3 ) is transferred to the TR.

(8 ) Equilibration: Again, there are some changes in pH from to P 2 and P2 to P- for the R+ and R columns respectively. So the re-equilibration is allowed.

Mode 4: Two reservoirs with an ion exchanger (cationor anion)

This mode is different from the other three modes as explained on the previous pages. The system has two columns, two reservoirs and two pH-converters (dialyzers and titrators) as shown in Figure 9. Both columns are packed with an ion exchanger (either cation or anion). The pH levels for the top and bottom reservoirs are maintained respectively at P^CS) and P2 (6 ). Between the top and the bottom columns are two pH- converters, for automatic changing the pH from P- to P2 or from P2 to Pj and also maintained the ionic strength constant. Initially, the top reservoir and both columns are filled with a mixture of the concentration yg. The equilibration of both

24

r

FIGURE 9

BRpH=P

TRpH=PJ 8 K

PCpH=Pv<6 )

- TWO COLUMN DIAGRAM, PACKING EITHER WITHANION OR CATION EXCHANGER FOR MODE 4

25

columns are at ~P^(=6). A complete cycle of operation is des­cribed as follows:

(1) Transfer down: The fluid in TR (P- ) is transferredto the top column (M = 1), and the content in thetop column (P2 ) goes through the pH-converter (P^)and transfers to the bottom column (M = 2) . At thesame time, the content in the bottom column (P2 ) i-s transferred to the BR.

(2) Equilibration: The pH in both columns are changedfrom P 2 to P-p Thus, the equilibration is allowedin both columns.

(3) Transfer up: The content in the BR (P2 ) is trans­ferred back to the bottom column (M = 2 ), while thecontent in the column goes through the pH-converter (P2 ) to the top column (M = 1). The fluid in thetop column (P^) i-s transferred to the TR.

(4) Equilibration: Again, the re-equilibration in bothcolumns are re-established due to the changing in pH from P^ to P 2 * Thus, one cycle of operation is completed.

Note: There is a minor change with a Semi-Continuous processwhich will be discussed in the next Chapter.

26

Chapter III

THEORY

Equilibrium Theory - Graphical Solution

1. One-Column System

The first system we will consider is shown in Figure 10. It consists of a column packed with an ion exchanger (cation or anion) and reservoirs attached to each end. The pump has dead volumes Vrj, and Vg for the top and bottom reservoirs res­pectively. Initially, the mixture to be separated fills the column voids, the top reservoir, and the bottom dead volume.The top reservoir is maintained at a low pH level ky anautomatic titrator, while a second titrator is used to keep the bottom reservoir at a high pH level (P- ). The ionic strengths of the buffer solutions in both top and bottom reservoirs are kept at IS2 and IS^, respectively, by means of two hollow fiber dialyzers. The flow system has four distinct stages in each cycle:

(I) The low pH (P2 ) fluid from the top reservoir enters the top of the column, while- the solution emerging from the other end enters the bottom reservoir.The displacement Qt^ is set to be the void volumeof the column Vg ; that is Qt^ = Vg .

27

(II) Circulation between the top reservoir and the column: This will ensure a complete shift of the pH and ionic strength in the column to and IS2 , respectively. Also, at the end of the stage, the concentrations in both the top reservoir and column will be iden­tical .

(Ill) The high pH (P- ) fluid from the bottom reservoir enters the bottom of the column, and the solution emerging from the other end enters the top reser­voir, with the displacement Qtjj-j- = Vg and

(IV) Circulation between the column and the bottomreservoir: This will allow the pH and ionic strengthto shift back to P^ and IS^, respectively, and at the end of the stage the concentration in the column will be the same as that in the bottom reservoir.

Note that the flow rate within the column is always equal to the reservoir displacement rate Q. The duration of circulation t ^ or t^^, which can be determined experimentally, depends on Vg and Vg (or Vg), and the pH and ionic strength in both the column and reservoir.

Figure 11 is a graphical solution for one-column system. The assumption made here are:

1. The solute will be distributed between the solid and fluid phases according to a linear form from Equation 1.2,

x = ky

28

where k is a function of pH and ionic strength.2. The duration of curculation t ^ or is long

enough so that at the end of the stage II or IV a phase equilibrium is established.

In Figure 10, the pump consists of a column packed withcation exchanger and reservoirs attached to each end. The pHvalues of the top and bottom reservoirs are maintained atgiven levels P2 (=6 ) and P^(=8 ), respectively. The operationbegins with the column filled with a mixture of concentrationYq , every where at equilibrium with solid. The initial pH inthe column is high (P^ = 8 ). Also, there is fluid of thesame initial concentration in the top reservoir. The firstfluid motion is downward, and = Vg. Let x and y be theconcentrations of A in the solid and fluid phases, respectively.Using Equation 1.2, we draw two equilibrium lines (with slopesequal to k and k ) on an x - y diagram. The initial con-

pl p 2centration in the column (yQ>xo represented by the point 0 . One cycle of the operation includes four steps, and the effect of the operation in the first cycle is as follows:

(1) Transfer down: The fluid in the TR (top reservoir)is transferred to the column, and the fluid in the column is transferred to the BR (bottom reservoir). Therefore, the bottom reservoir concentration for the first cycle is yQ.

(2) Circulation and Equilibrium at P2 : The column pH

(II)

(III)

(IV)

29

r- -✓*—N 1H 1L.... .

sx

■ O'

•O '

xXX

— _

o•r44-)cdso4-)

5

V4o4-) CM cd PM U II4-1 HJ •H (X H

(NC/3HUd)NHctf•Ho

.O'

rO ~-| Q i

i—i C/3 Hv_/UcuNr-4cd•HO

sMM

4-1o- Hl-l4-1

O•p44->cdSo4-1

}-iO«M r Hcd p-iu JL4-1 fxj•r4H v-'

fQ r"0-i ill

1 1 r-J*

FIGURE

10 -

SCHEMATIC

OF ONE

COLUMN

SYSTEM

30

is changed from P^ to P£. The two phases are then allowed to equilibrate at This leads to a newcomposition in the column (yq>;i. sx^) > represented by the point T1. The point is located at the inter­section of equilibrium line k and of the opera-p2ting line passing through (yqjXq ). The slope of the operating line is -(V,p + V)/V, and is obtained by the mass balance constraint, i.e.,

(VT + V)yT 0 + VxB 1 = <VT + V)yT 1 + VxTJ ( 2 ^

or<VT + V J y ^ . ^ + VxBn = (VT + V)7Tn + VXTn (2.2)

where n = 1 , 2 , ....Also yTQ = yQ, xBl = xQ, and V = V€ .(3) Transfer up: The solution in the column is brought

to the TR and the solution in the BR is returnedto the column. The composition in the column is now (yBi;xTi) .

(4) Circulation and Equilibration at P- : The columnpH is shifted back to P^. A phase equilibrium is re-established. The new equilibrium point (Yg2 ; XB2^’ represented by the point B2, is located at the inter­section of the equilibrium line kp and of the operating line passing through anc havinga slope of (VB + V)/V, and is obtained from the following mass balance,

31

I s t cyclei.e.----------------------1---Transfer e Transfer

down tq u i l up

— X,

_ i I U I I 9 I IEqull. down

2nd cycleTransfer _ Transfer ,,Equil. up Equll.

ye) Ki{6)\ /y0(8) y0(6) v-nce) yBI(s)

Xo TI / *TI

ys,=y0 (8 ) y8 l(s)

yT,<6)

yS2(S) XB 2 \ XB2

yB2 ts) yB2(s)

yT2<s)

yB3<8 >

XB3

CO 4->•r4

<U r-H

, where4-1 <0

T2,1.0

T3T4 I \~

<yT^n T CQ

I j_____

B a d

B3•HB20.5

1.0 1.50.50y, concentration of protein in the fluid phase, gm-mole/lit

FIGURE 11 - GRAPHICAL SOLUTION FOR ONE COLUMN SYSTEM'

32

(VB + V)yB(n-l) " (VB + V>yBn + VxBn <2’3>

where n = 2, 3...... and V = Ve .

This completes the first cycle. The second cycle will start from a transfer of the fraction yT- from the TR to the column and the fraction y ^ to the We then follow thesteps described above. (See Figure 11). If the procedure is repeated in each of the succeeding cycles, one can see that as n becomes large, the top and bottom reservoir concentrations will approach steady values, i.e., y , >oo and <yg)>«» >respectively. At steady state, the solid phase has a constant composition which is in equilibrium with both < Yt^co a n ( 3

< yB > « > i.e.,

x«» = kPl< yB >*» = kp2 < yT '>® (2'4)

and therefore, the line TgBg must be paralleled to the y axis.

Note that the graphical method described above is based on a simple discrete transfer equilibrium model (Pigford et al.,1969; Jenczewski and Myers, 1970; Wankat, 1974b; Grevillotand Tondeur, 1976; 1977).

2. Two-Column Systems

We will consider four modes of two column system shown in Figures 6 , 7, 8 , and 9. For all systems but one, Mode 4,

33

one column is packed with a cation exchanger (R~) and the other with an anion exchanger (R+). The flow rate within the column is always equal to the reservoir displacement rate Q. For both down and up flow the reservoirs have the same displacement. It is assumed that we are concerned with the separation of a two-protein system. The two proteins, A and B, have the isoelectric points 1^ and Ig, respectively, and P 3 < I B < P 2 < I A < P-p where P^ , P 2 * an<3 P^ are the pH levels in the reservoirs. Thus, both A and B will bear negative charges at P- , and positive charges at P^, while A and B will carry a positive and negative charge, respectively at P 2 . Therefore, A will be taken up by a suitable cationic exchanger at P2 or P^ and released at P^, The reverse effect will occur if an anion exchanger is selected. The steady state concen­trations in the reservoirs are graphically shown in Figures13, 15, and 17. For the purpose of simplification, it is

- + +assumed that for protein A, k = k and k = k , and forP2 . P3 p2 p3protein B, k = k and k = k However, other conditionsP Pi P 2 Pi p 2

are conceivable. Two basic separation problems will be con­sidered, i.e., enrichment and splitting:

A. Enrichment

The model to be discussed below is for an enrichment process. Our aim is to obtain a product in which the concentra­tion of a component is larger than the corresponding concentra­tion in the feed.

34

Mode 1: The system has three reservoirs as shown inFigure 12. The pH level for the top and bottom reservoirs is maintained at and that for the middle reservoir is keptat Initially, the top reservoir, the dead volumes forthe middle and bottom reservoirs, and both columns are filled

4.with a mixture of the concentration yg. The R and R columns are respectively in equilibrium at P- and 1?2 - One cycle of operation is:

(I) Pump the fluid from the top reservoir (TR) through the R+ column, the middle reservoir (MR) and the R- column to the bottom reservoir (BR), for time t^.

(II) Circulate the fluid between the TR and the R+ col­umn, and between the MR and the R" column, for time

tII'(III) Pump the fluid from the bottom reservoir through

+the R column, MR and R column to the top reser­voir, for time and

(IV) Circulate the fluid between the MR and the R+ col­umn, and between BR and the R~ column.

The graphical construction for the concentration profile (Figuresl3a andl3b) can be made in the same way as described for the one-column parametric pump. After a certain number of cycles, the concentrations of protein A in the solid phase for both R+ and R~ columns converge to two limits, x^+ and

Down

flow

Circulation

Up flo

w Circulation

Down

flow

35

FIGURE

12 - SCHEMATIC

OF TWO

COLUM

N SYSTEM:

MODE

1

, prot

ein con

centra

tion

in the solid

phase

x, pro

tein

concen

tratio

n in

the solid

phase

36

Protein A

R.0

Fig. 13a.0+R

0<’yT > oo protein concentration in the fluid phase

Protein Bx/k

.5r + /T=M+

.0

B=M

0

protein concentration in the fluid phaseFIGURE 13 - GRAPHICAL SOLUTION FOR TWO COLUMN SYSTEM: MODE 1

37

Xt,-, respectively. Thus, a two step staircase is formed.Note that at steady state, the concentration in the middle reservoir is such that it is in equilibrium with both cation and anion exchangers at P2 , i.e.,

xr + " k p 1 < y T = k p 2 ^

and

X R - = k p 2 yM ><» ( 2 - 5 )

In the R+ column, the protein A migrates from the high pH end (P^) toward the low pH end (P2 )> whereas in the R column, it moves in the opposite direction. Thus, we accu­mulate protein A at the high pH end of the R column, i.e., the bottom reservoir. By comparing Figures 11 and 13, one can see that the separation factor ( < y^ ><* / <£ y , 0 0 ) f°r the two column system is much higher than that for the one column system. Also, from the diagram on Figure 13, no sepa­ration occurs for protein B, i.e. , ( < Yg >co / ^ Y-p 0 0 ) = 1-It should be pointed out that, though B carries the same charge at P^ and P2 , there may be a difference in the k values at these pH levels (depending on the ionic strength, and some amount of separation may occur on B.

B . Splitting

Modes 2 and 3, shown in Figures 14 and 16 respectively,

38

MM>

MM>

M>

>H

MM

!5Om

op

£ot-4m

op

!3oI—I

op

£o•r44-)cdi—iPO4*r4o

!3oT“HmpP

Po•H4-1cdI—I3CJ5-)•rlu

no•H4-1 cd !—IPCJ5-l •HO

£Oi—ImPuP

£o•r44-1cdi—IPop*r4o

M

<N i—I

M

CO

CM'CM

HMCO

CM

H4-1

i—IP

\/

\/CM

P

VPQM

VCO

p

fp CMIh p

rH <N

FIGURE

14 - SCHEMATIC

OF TWO

COLUMN

SYSTEM:

MODE

2

39

are for split processes. The purpose of these inodes of oper­ation is to separate the desired proteins from each other.

Mode 2: The pump has four reservoirs; one top, two mid­dle, and one bottom reservoirs, respectively with pH = P£,

, P 3 , and ? 2 ' Flow sequences (Figure 14) for one cycle are:

(I) Pump the fluid from TR through the R+ column to the MR (P3 ), and, at the same time pump the fluid from the MR (P3 ) through the R- column to the BR, for time tj-.

(II) Circulate the fluid between the TR and the R+ col­umn, and between the MR (P3 ) and the R_ column, for time t-j--j-.

(III) Pump the fluid from the BR through the R- column,the MR (P3 ) and the R+ column to the TR, for time

tIII*(IV) Circulate the fluid between the BR and the R" col­

umn, and between the MR (P3 ) and the R+ column, for time tjy.

(V) Pump the fluid from TR through the R+ column to theMR (P3 ), and at the same time pump the fluid fromthe MR (P3 ) through the R~ column to the BR, fortime ty.

(VI) Circulate the fluid between the TR and the R+ col­umn, and between the MR (P^) and the R column, for time ty-£.

40

(VII) Pump the fluid from the BR through the column, MR (P^), and R+ column to the TR, for time and

(VIII) Circulate the fluid between the BR and the R- col­umn, and between the MR (P3 ) and the R+ column, for tzxni0 ^VXXI *

Figures 15a andl5bshow the steady state concentrations in the reservoirs. At steady state, the average concentra­tion of the middle reservoirs (MR (P3 ) and MR (P3 )) is such that it is in equilibrium with both cation and anion exchan-

*R+ = kp 2 yT = k+ yM+ (2.6)

xr- = kp2 yB>>® = k" < yM->co

and

<^yM+> « » = °-5 (yMR+ + yMR+ } = < V m “ > »P1 p3

0 ,5 (yMR" + yMR" * (2.7)pl p3

where y^^f and y ^ f are the steady state solute concentra- pl P3

tions from the R-*" column to the MR (P- ) and MR (P3 ) respec­tively, whereas y ^ - and y ^ - are those from the R column

P1 p3to the MR (P^) and MR (P3 ) , respectively.

protein

concentration

in the sol

id phase

41

xRxR

= k"

Protein A(MR)

(MR).0

Fig. 15a

(MR)

0

>oo ODX

Sx!

1 .X T

X-R

P r o t e i n B

(MR)

I / (MR) l/i

~/

Fig. 15b

0

^ ^ ooooy, protein concentration in the fluid phase

FIGURE 15 - GRAPHICAL SOLUTION OF TWO COLUMN SYSTEM: MODE 2

+ P«

42

T h e r e s u l t s in F i g u r e s 15a and 15b s h o w that, A a n d B

m o v e in t h e o p p o s i t e d i r e c t i o n s , b u t in this case, p r o t e i n

A m i g r a t e s u p w a r d to t h e top r e s e r v o i r (pH = P2) , w h i l e B

m o v e s d o w n w a r d to th e b o t t o m r e s e r v o i r (pH = P ^ )•

M o d e 3 : T h e s y s t e m c o n t a i n s f i v e r e s e r v o i r s , t o w top,

o n e m i d d l e , a n d two b o t t o m r e s e r v o i r s , r e s p e c t i v e l y w i t h

p H = P ^ , P3, P 2 , P3 a n d P3 (Figure 16). T h e f l o w s y s t e m

has e i g h t d i s t i n c t steps in e a c h cycle:

(I) P u m p the f l u i d f r o m the T R (P3) t h r o u g h the R *

c o l u m n to th e M R a n d the R~ c o l u m n to the B R (P^),

fo r t i m e t-^.

(II) C i r c u l a t e th e f l u i d b e t w e e n t h e T R (P-^) a n d R -*"

column, a n d b e t w e e n the M R a n d th e R column, for

t i m e tj-j.

(Ill) P u m p t h e f l u i d f r o m the B R (P3) t h r o u g h the R

c o l u m n to t h e M R a n d the R"1" c o l u m n to the T R (P-^),

fo r t i m e tjjj*

(IV) C i r c u l a t e the f l u i d b e t w e e n the B R (P3) a n d the R

column, a n d b e t w e e n the M R a n d the R"1- column, for

t i m e tjy.

(V) P u m p the f l u i d f r o m the T R (P3) t h r o u g h the R+

column, M R a n d R - c o l u m n to th e B R ( P 3 ) » for t ime ty.

(VI) C i r c u l a t e t h e f l u i d b e t w e e n the T R (P3) a n d th e R +

column, a n d b e t w e e n the M R a n d t h e R column, for

t i m e t y j .

(VII) P u m p the f l u i d f r o m the B R (P-^) t h r o u g h the R

column, M R a n d R c o l u m n to th e T R ( P 3 ) , f o r t ime t y i l -

43

FIGURE

16 - SCHEMATIC

OF TWO

COLUMN

SYSTEM:

MODE

44

(VIII) Circulate the fluid between the BR (Pg) and the R-column, and between the MR and the R+ column fortrine tyj *

The steady state concentrations in the reservoirs are graphically presented in Figures 17a and 17b. At steady state (n — «"<»)

x e+ = = kp^

“ kp2 yM>«°l

and

XR “ = ^ = kp3 C < 'yB'^.] P 3

= k;2 ;[<yM>«,]' (2 .8 )

By connecting the points Tp , Tp , Mp , Mp , Bp and Bp , a*1 3 2 2 3 *1

two step staircase is formed for both proteins, A and B. However, the concentration of A in the bottom reservoir BR (P^) ( Yu'>&,]] p ) is much higher than that in the TR (Pj)( yTx ] p ) » while the concentration of B in the top re­servoir TR (Pg > < [ < y ^ l p ) is much greater than that in the BR (P3) ( [<TyB V l p ). This separation phenomena can be explained as follows: The pH levels, Pg and Pg, and Pg andPg, respectively bracket the isoelectric points of A and B,i.e., P2 < IA < P.2 and P 3 Ip < Pg. Thus, in the R- column,

protein

concentration

in the

solid

phase

45x

Protein A

? 2 P3

B =MP^ - 2

Fig. 17a

p3 p2

y, protein concentration in the fluid phaseProtein B

T /= M

Fig. 17b

F

yoi l<yB>ool Pl= - k ^ c o ]1 '. 0 2.0

p 3 l< y T^ aoI p 3

FIGURE 17 - GRAPHICAL SOLUTION OF TWO COLUMN SYSTEM: MODE 3K b > 0 0 )

46

A and B respectively migrate toward the BR (P^) and the MR (P2 ), whereas in the R+ column, A and B respectively, move toward the MR (P2 ) and TR' (P3 )• In the other words, A and B migrate in opposite directions and concentrate respectively in BR (P^ and TR (P3).

The results shown in Figures 17a and 17b are very similar to those for Mode 2. Also, by comparing Figuresl5a and 15b, and Figures 17a andl7b one can see that separations by Mode 3 are better than those by Mode 2, i.e.,

For protein A: 0 ^ B > » ] Px

.. r<yT > ® ] p.>

JL —1Mode 3

For protein B : [<yT > „ ] P3

. C<yB^“ ].p3 - Mode 3

<yT>

Mode 2

(2.9)

Mode 2

Mode 4: The system has two reservoirs; one top and onebottom reservoirs, with pH = P^ and P 3 respectively. Also the pH-converters are connected to the columns as shown in Figure 18 . Flow sequences for one completed cycle are:

(I) Pump the fluid from TR (P- ) to the first column(R~) while the content from the R column (P3) Is transferred through the pH-converter (P^) to the second column (R~). At the same time, the fluid

(D (II

) (II

I) (IV

) (I)

Dow

n flo

w Circulation

Up flo

w Circulation

Down

flow

47

o o3CM CM

CMPmII VO

P - i ^

L--. 3

i-----

t-i

CM

f CM t P-) pd II vo

00, I—I/ CM N' PH Pd II MO ■PQ |X3

CM

> <f H 4-> W O OS

wHco>-<CO

MM O4-1 O

- Pm0aH1wH ffi M O

4-1 COI

CO

3gHpl

r-CM CM

CM

H4J

48

from the second column (P^) is transferred to BR, for time t ..

(II) Circulate the fluid between the TR and the firstcolumn and between the pH-converter and the second column, for time t^.

(Ill) The fluid from the BR (P£) is pumped back to the second column. Meanwhile, the fluid in the second column (P- ) is transferred through the pH-conver- ter (P2 ) to the first column. Also, the fluid from the first column transfers to the TR, for time t^j and

(IV) Circulate the fluid between the first column and the pH-converter, and between the second column and the BR.

Figuresl9 a and 19b show the steady state concentration in the reservoirs. After a certain number of cycles, the concentrations of protein A in the solid phase for both R- columns converge to two limits, x^- (at M = 1) and x^- (at M = 2). Thus, a two step staircase is formed, i.e.,

X" - ( M 1) ■ kP! p , - k; 2 £ < yM > JR

and

X r ' ( M = 2 ) = k P 2 C < y B > » l p 2 - k p x [ < % > ] ( 2 - 1 0 )

The results of this system is similar to Mode 1. The

protein

concentration

in the

solid

phase

x49

Protein A

2 ). 0

(MR )

Figure 19a

0

x

Protein B0

(MR )Figure 19b

O

0y, protein concentration in the fluid phase

FIGURE 19 - GRAPHICAL SOLUTION OF TWO-COLUMN SYSTEM: MODE 4.

50

protein A migrates from the low pH end (P2 ) toward the high pH end (P- ) , also Figure 19b shows no separation occurs for protein B.

51

Chapter IV

ANALYTICAL SOLUTION

Formal Mathematical Solution

Figure 20 shows the principle of the discrete transfersand equilibrations for a total reflux parapump, with a singletransfer per half-cycle. The system consists of N columns, which are packed with an ion exchanger (either cation or anion); and two reservoirs, top and bottom, where maintained at a high pH (P- ) and a low pH respectively. Betweenthe columns, the pH-converters are connected as shown in Figure 9.

Let y^(n) designate the protein concentration, in gramsper liter, for the fluid phase in the column (fraction stage)number j (j =0, 1, .... N, and where j =0 is a reservoir), at the low pH level, during cycle n. In the same manner,Xq(n) designates the protein concentration in the solid phase, at the high pH level, in the column or stage q (q = 1, 2, ..... N), during cycle n. N is defined as the total number of columns or stages; the number of protein fraction is thus N + 1. With these notations, at the beginning of cycle n (See Figure 20), Yq (h ) is the concentration in the high pH product reservoir; and in stage q, yq(n) is in equilibrium at low pH with x^(n). Let V be the volume of the fluid phase in each

52

Col. 1

Col. q-1

Col. q

Col. N

R+

”0 : 0.pH=PgJ '

r —C 1

P C „ 9 i6PH = £j

mrl-

PC

R+

V 2

SH=Pt C - - 1

p5lp2io 0.py V Hr pi

PCqPH=P^

—i

.0R+

PCN-pH=P

( 3 :

i---“Cq

i S r h

R

0 " 1VpH=Pn

ColPC

= Column #= pH-Converter

FIGURE 20 - THE pH-PARAMETRIC PUMPS DIAGRAM FOR MATHEMATICAL APPROACH.

53

column while v is the volume of the solid phase in each column. It is also assumed both are constant.

We shall define a relation between the concentrations in cycle n and in cycle n + 1. By using the material balancesand the equilibrium relation within cycle n, the index (n)of the cycle being omitted for simplicity. After a forward transfer, and before any equilibration, stage q contains V liter of liquid phase at concentration an-d V liter ofsolid phase at concentration s". After re-equilibration at high pH (P- ) , these concentrations become respectively yq_j and Xq. Conservation of protein implies:

xq + P y q - 1 " xq + ? y j - l ! <3-1)

(q = 1, 2, ... N)where £> is the ratio of fluid to solid phase volumes:

9 = V/V (3.2)

The low pH equilibration at the start of the cycle and thehigh pH equilibration after transfer are expressed by:

xj = k V ; (q = 1 , 2 , . . . N) (3.3)4 4

x^ = khyq_i ; (q = 1, 2, ... N) (3.4)1 Viwhere k and k are the linear (See Figure 21) equilibrium

constants for low pH and high pH respectively. Equations 3.3and 3.4 are substituted into Equation 3.1 and simplify it.Then we shall obtain:

protein

concentration

in the

solid

phase

54

x

o

□

Albumin in Anion Column (R ) Albumin in Cation Column (R_) Haemoglobin in Anion Column (R‘) Haemoglobin in Cation Column (R ) Solute at pH = 8.5 Solute at pH = 6.2 )Calculated Values

0.10 -

Region of Interest

0.05 - #

m0.05 0.10

y, protein concentration in the fluid phaseFIGURE 21 - EQUILIBRIUM CONSTANTS FOR THE HAEMOGLOBIN-

ALBUMIN SYSTEM: SEPHADEX ION EXCHANGER (REFERENCE 28).

55

9 + kr•y1 i +Q-l

9 + kr

(3.5)

(q = 1, 2 , N)

Since the last protein fraction is in the low pH reservoir during the high pH equilibration, it undergoes no exchange, and also no concentration change; thus:

(3.6)

Equation 3.5 and 3.6 from a system of N+l linear difference1 . -Iequations relating the y 's to the y 's in the matrix form

and be expressed by:

Yh(n) (n) (3.7)

1_ *1where Y and Y are the column vectors of the protein frac-/V /V *•tion concentrations, and [©, ] is the N+l dimensional bi- diagonal matrix:

I © h i§ +k

0 . (s + kh)

(3.8)

In the same manner, the analysis for the backward half-cycle

56

hleads to a symmetrical relationship between Y (n) and the concentration vector Y (n+1) which represents the conditions after the low pH re-equilibration, thus at the beginning of cycle n+ 1 :

Y (n+1 ) [©,] • Yh (n) (3.9)

where

[01 ~ 1

(5 >+ k1) 0

.0 ' '

%

0 . . . -,hk f

(3.10)

Then, we combine both Equations 3.7 and 3.9 to yield a com­plete cycle:

Y 1 (n+1) = [M 1 . Y 1 (n) (3.11)

where [m ) is the tridiagonal Jacobi matrix of dimension N+1:

d e 0 0 . .a b c 0 .0 a b c 0 .

a ’ a+b

(3.12)

57

where: a = ; b = £2+ k^k*1 ; c = yk^

d = ?(£ + k1) ; e = k^CyH- k^) and (3,13)

p = ( p+ k^)(9 + k*1) = a + b + c

Equation 3.11 is in a form of a linear first order difference equation, so we can solve this equation by recursion

Y 1 (n) = [MlY^n-l) = [M]2 Y 1 (n-2) = ........

= [MjnY 1 (0) (3.14)

From Equation 3.14 the concentration vector for any cycle can be obtained in terms of the initial concentration vector Y^(0) . Thus, it can be called "A Solution of the Conservation Equations", and this formal solution is very simple. However,

x.'tthe calculation of the n power of the matrix (M) is not a trivial matter if its dimension and n are large. Therefore, the next section covers the calculation of this matter which will lead us into the physical problem.

Calculation of [l?)n

The calculation of the n *’*1 power of a matrix by succes­sive multiplication is numerically straight forward, although it may require much time and give little qualitative informa­tion. So another method is introduced by the calculation of

58

the eigenvalues of [ Ml for which standard numericalmethods exist. In this case, much more information can be obtained on the eigenvalues by algebraic means, and a simple rapidly converging numerical method can be used, (See Appen­dix A) owing to the fact that the matrix is of the Jacob.i type (tridiagonal matrix). Once the eigenvalues ( \ ) are known, the elements of the corresponding eigenvectors are calculated directly by:

yiq - - I <d - p y0q

y2q = - I <b - p \ > yiq + ay0q

yjq ‘ ' § (b ' p V yj - i .q + ayj-2.q <3' 15)

yNq - - I <b - p \ > yN-i>q + ayN-2,q

q = 0, 1, ---------N

where a, b, c, d, e and p are given by Equation 3.13. Asusual, the elements of the eigenvectors are defined up to a .multiplicative factor, y 0 . Designating, by CSl the matrixu4of column eigenvectors of elements Yjq> the matrix tM] may be re-written in a diagonalized form:

[M] = IS3 [ b i t s ' } " 1 (3.16)~ w

where [D] is the diagonal matrix of the eigenvalues. Then:

59

\M\n = [S }lD]n . [ S} />* ^-1 (3.17)

where

[Dl n

IXq 0 0 0o 0 0

0 . \ iaN

(3.18)

An equivalent approach is the use of Sylvester's Theorem Expression and gives:

N[M ln

where:

x ? I a . )j- 0 3 l~J

adj ( “X . I - M)

T). ( x . - x . >J l'

(3.19)

(3.20)

and adj ( 'X •I - M) is the transposed matrix of cofactors of J/”1 ^ . 1 - M ] , independent of n. It is seen that the number of

3 ~ ~cycles (n) appears only as the powers of the eigenvalues, and this allows a quick qualitative look on how the system con­verges toward its steady state. Here, we shall first try to characterize this steady state.

The Cyclic Steady State

60

The behavior of the system when the number of cycles (n) becomes large, can be deduced from a close examination of Equations 3.16 to 3.20 and of the eigenvalues. It also can be deduced by physical reasoning. In Appendix A, we demonstrate that all eigenvalues of Cm 3 are real, positive and smaller than or equal to 1. These conclusions may also be reached by the following considerations:

1. Any negative eigenvalue would bring a contribution to [M)n , that changes sign every cycle, leading to an oscillatory behavior of certain concentrations.

2. Any eigenvalue larger than one,.would lead to an ever increasing contribution to [Mln , and to infinite concentrations for certain initial conditions.

3. Any positive eigenvalue, smaller than one, has an ever decreasing contribution as n becomes large; if there were no eigenvalue equal to one, (M)n would tend toward the zero matrix, and all final concentrations would be zero.

We thus have:

61

0 (3.21)

From Equations 3.14, 3.19, and 3.20, when n becomes large, the contribution of all eigenvalues different from one dis­appear and the cyclic steady state is given by:

i ™ i ladJ - M)1 v l , n.Y (oo) = [M] Y1( O ) = -----— - I (0) (3.22)~ 'TT *

i « ( 1 - V

More explicit information is obtained by noting that, in the steady state, we will have:

Y 1 (n+1) = Y 1 (n) = Y 1 (0 O )rv ^ (3.23)

and that this equality is compatible with Equation 3.11 only if Y1( oo ) is an eigenvector of matrix [ M3- From the dis­cussion above, it must be the eigenvector corresponding to X = 1. Thus, the components y* of Y^(oo ) are calculated byi ~letting Xq = = d dn t ie set Equation 3.15. It mayeasily be verified that the following relations hold between the concentrations y* thus calculate:

** 1

*Yi y2

I±

yj+i

*?n -i* (3.24)

which implies:*

1 ° = •bn*%

(3.25)

62

This is the equivalent of Fenske's equation. The steady state composition vector, then may be written in terms of y^, for example:

Y ( Oo ) =

*^ 0 1

*y i p - 1

•fc CM

*= p~2

*%

(3.26)

An interesting property of this vector is that, it is invari­ant upon multiplication on the left by [0 ^ , 3 > which from Equation 3.7, implies that:

Yh (oo) = Y 1 (oo) (3.27)

This means that the compositions of the protein fractions are the same after an equilibration at high pH and low pH. In other words, in the cyclic steady state, all compositions are constant, and no protein transfer occurs between phases.

The geometric interpretation from Equations 3.24 to 3.27 is like the relations in the McCabe-Thiele diagram which is a staircase construction between two straight lines as shown in Figure 22, and is consistent with the graphical method from the previous chapter. The steady state composition vector, in Equation 3.26, is defined up to the value of yQ. This

protein

concentration

in the

hig

h pH

buffer.

63

V

2.0

1.0

2.01.00

protein concentration in the low pH buffer

FIGURE 22 - GRAPHICAL SOLUTION BASED ON McCABE-THIELE DIAGRAM.

64

parameter is calculated from an overall material balance over the system, and give (see Appendix A)

* w/vN (3.28)

? + ( ? + 1 0 2 1 Ti=l-r

This result is seen to be an independent of the initial distribution, but to depend only on W, the total mass of protein present in the system.

The knowledge of this steady state allows us in turn to determine the structure of [M]n when n becomes large, as illustrated in Appendix A.

65

Chapter V

EXPERMENTAL METHOD

A. The Experimental System

The system of separation is considered for removing either Hemoglobin or Albumin from its aqueous solution or their mixture by pumping through a suitable solid phase (absorbant bed) i.e., an ion exchanger (anion or cation). The ion ex­changer will attract a protein (absorption) which carries an opposite charge to one in a pH buffer solution, and the pro­tein will be released (desorption) when its charge is changed back (to the same as an ion exchanger) in the other pH buffer solution, in such a way that both fluid and solid phases, in the absorbant bed, are in equilibrium.

Equation 1.1 shows the material balance of protein in both fluid and solid phases. The relationship ratio of the concentration of the solute in the solid to a fluid phase is a function of solute concentration, pH buffer and ionic strength and also expressed in Equation 1.2:

x = ky (1 .2 )

where k is called as "an equilibrium constant". The experi­mental and calculated the equilibrium constant are pictured on Figure 21, where the specific region of interest treated

66

in this work is marked. The linearlity of the adsorption equilibrium constant in this region is apparent.

B . Description of Apparatus

The system consists of one or two chromatographic columns manufactured by Phamarcia Fine Chemicals. The column(s) was packed either with DEAE-Sepharose (anion exchanger) or with CM-Sepharose (cation exchanger) for a one column system other­wise the top and the bottom columns were packed alternately with anion and cation exchangers. The reservoirs (50 cc Pyrex beakers) were connected to the column(s) as the system required. Reciprocating flow was introduced into the system by a four channel Multi-Staltic Pump # 2-6200 manufactured by Buchler Instruments. The tubing used in the pump was 1/16" I.D. Tygon tubing manufactured by Norton Plastics. The pump was set up according to manufacturer's specifications and the flow rates of all four channels were adjusted to 1 cc/minute.

The pH levels in the reservoirs were maintained by using three PHM61 meters and two TTT60 automatic titrators, all manufactured by Radiometer/Copenhagen. The pH 8.5 (P- ) an(i the pH 4.0 (P3 ) reservoirs were monitored by the automatic titrating the solution manually. The acid and base solution used were Hydrochloric acid (0.5N) and Sodium Hydroxide (0.5N). Magnetic stirrers were used to ensure perfect mixing in the reservoirs. The reservoirs were placed in the jacketed Pyrex

67

beakers. Both the reservoirs and the columns were maintained at 5°C by the use of circulation bath. An electrically con­trolled timer was connected to the system for the purpose of starting and ending the process automatically. To maintain the ionic strength, a hollow fiber dialyzer manufactured by Harvard Apparatus Company, was introduced. The experimen­tal apparatus for the three reservoirs batch system is shown in Figure 23.

C. Solutions and Buffers

Three types of buffers were used. For pH value of 8.5, a buffer of tris (Hydroxy-Methyl) Aminomethane and HC1 was used. For pH value of 6.2, the buffer was tris (Hydroxy-Methyl) Aminomethane, Malaic Acid and NaOH was used. For pH value of 4.0, a buffer of Acetic Acid and Sodium was used.

The concentration of the above buffer solutions was 0.2 M. Sodium Chloride in calculated amounts was added to each of them. Dilution of the buffers were made according to the experimental parameters.

The two proteins were selected to investigate the separa­tion were Haemoglobin and Albumin; both are manufactured by Worthington Biochemicals.

ComponentA

ProteinMolecular Weight Isoelectric Point

Haemo. 63,000 6.7B Alb. 69,000 4.7

68

NaOH SolutionPeristal­tic pump

AutomaticTitratorAnion '

Exchanger packed Bed

High dH(P1) 3uffer

HC1 Solution

AutomaticTitrator—txh

Dialyzer

Low>h <p 2 •Buf fe::

NaOH SolutionCationExchangerpackedBed

AutomaticTitrator

Dialyzer

Peristal­tic pump H i g h

p H (P 1 ) Luf f ei

— *- down flow up flow

FIGURE 23 - THE EXPERIMENTAL APPARATUS DESCRIBES THE THREE RESERVOIRS BATCH SYSTEM.

69

The concentration of protein in the feed solution was0 . 0 2 weight percent (i.e.,0 . 0 2 gram protein/ 1 0 0 cc. buffer).

D. Gel Preparation and Packing

Both the CM and the DEAE-Sepharose exchangers were washed and stored for 24 hours in their respective initial buffer solutions. This ensured that the gels would be at their respected pH. The gels were then loaded into the vertical columns and were allowed to settle to a volume of 1 2 cc.

The columns were next connected to the pump. The next step involves the saturating of gel with the specific feed or buffer solution. This step is a function of the system under investigation. The solutions were pumped into the respective columns for a period of 90 minutes to ensure that solid and the liquid phases were in equilibrium.(NOTE: Pump flow rate = 1.0 cc/min).

E. Measurements

A sample was taken at the end of each cycle from each reservoir, with the Batch System, or at the end of each step, with the Semi-Continuous System. The sample was analyzed on a Bausch and Lomb Spectrophotometer. Past work shows that the absorbance obtained from the spectrophotometer can be related to the relative amounts of protein in the solution. The wave lengths used, were 430/**, 560/**, 576/**, 595/** and

70

630/*.

A dye reagent was used to measure the total amount of protein at 59/*. The dye is manufactured by Bio-Rad Labora­tories and was prepared and stored according to the manufac­turer1 s specification. The sample/dye ratio varied, but re­mained constant for any given experiment. The ratio was some­times changed to acquire more accurate readings. The reac­tion time for all samples which required the use of the dye reagent was 5 minutes. This procedure is described in the analysis of the experimental data (see Appendix B for sample of calculation).

F. Operation Processes

One-Column: Semi-ContinuousWe first consider two types of systems. In one the column

was packed with an anion where the other packed with a cation exchanger. The equipment and the column preparation for the two reservoirs, Semi-Continuous single column (anion) is al­ready explained in Section B and D, respectively. This sys­tem consists of an anion exchanger and two reservoirs; 6 . 2

top (P2 ) and 8.5 bottom (Pj). The pumping flow diagram is shown in Figure 24.

Procedure. The reservoirs's specifications were:

71

<D 4-1OP

O|MC U

/ P m L O

i 6 (pi II •I ° \ p q p d o oI 4-1

J 4-1t r °f p Q

I—I >

4-1

>4-1

4-1

l-l

1 - 1

■U

f CM>\ ' Pm CMpi II

cn^ Pm (N:iPd MD Pm

FIGURE

24 - SCHEMATIC

OF SINGLE

COLUMN,

SEMI-CONTINUOUS

SYSTEM.

72

6.2 TR(P2) 8.5 BR(P1)

Dead Volume 30 cc 30 ccDisplacement 12 cc 0 cc

(NOTE: In some experiments the dead volume was eitherincreased or decreased).

(I) Pump the fluid from 6.2 TR through the R+ columnto the 8.5 BR, for a time period t^ (t^ = 12 min).

(II) Circulate the fluid between the 6.2 TR and the R*column, for a period of t ^ (tjj = 24 min) .

(Ill) Fresh 6.2 (P2) feed enters the R+ column from the bottom, for a time period of = 8 min).At the same time, the top product was withdrawn for analysis.

(IV) The fluid from the 8.5 BR is pumped through the R+ column to the 6.2 TR for a period of t -y (t^y = 12 min) .

(V) Circulate the fluid between the 8.5 BR and the R+column, for a period of ty (ty = 24 min).

(VI) Fresh 8.5 (P- ) feed enters the R column from thetop, for a period of tyj. (ty-j- = 8 min). The bottom product was withdrawn and analyzed.

The completion of step VI is the end of one cycle. All of the products were analyzed on a Bausch and Lomb Spectro­photometer (BLS) at 403^, 595^, 560y*, and 6 3 0 ^ .

73

The purpose of using 560 y, 576y and 630y is to determine the concentration of haemoglobin. It was determined that the type of buffer will affect the absorbance, thus leading to an error in calculating the relative amount of protein. The 403y reading was not versatile enough to detect the protein con­centration. The procedure for analyzing the samples is described in Section E.

NOTE: For the cation column, the equipment and the opera­tion steps are exactly the same as the operation on an anion column as explained above. Also the Batch System operation for the experiment was described earlier in Chapter II.

Two-Column System

Mode 1 : Three Reservoirs Batch System

The apparatus and the preparation of the columns for this system has already been explained previously in this chapter. The pump flow diagram can be seen on Figure 12.

Procedure. The reservoirs were started with the fol­lowing dead volume:

8.5 TR(=Pi) 6.2 MR(=P2 ) 8.5 B R (= P!)

Dead Volume 30 cc 30 cc 30 ccDisplacement 12 cc 0 cc 0 cc

74

NOTE: In some experiments the dead volume was eitherincreased or decreased.

The four operational steps were explained in Chapter II, where t-j- = = 12 min and tjj = t-^ = 24 min.

At the end of each cycle, a 3.0 cc sample was removed from each reservoir, TR, MR and BR. The samples were analyzed on a BLS at 403J*- and 595yA£. The procedure for sample analysis, is described in the earlier pages of this chapter.

NOTE: For the Semi-Continuous or Continuous Process, theresults were not consistent and omitted from discussion (see Reference 48 for detail).

Mode 2: Four reservoirs Semi-Continuous System

The equipment and the column preparation in the operation of the four reservoirs Semi-Continuous process is the same as described at the beginning of this chapter. This system requires the introduction of fresh feed after each circulation step. The pump flow diagram is shown in Figure 25.

Procedure. The reservoirs were started with the following dead volume:

6.2TR(P2) 8.5MR(P1) 4.0MR(P3) 6.2BR(P2)Dead Volumes 30 cc 30 cc 30 cc 30 ccDisplacements 12 cc 0 cc 12 cc 0 cc

(I)

(II)

(III)

(IV)

(V)

(VI)

(VII)

Down

flow

Circulation

Up fee

d Up

flow

Circulation

Down

feed

Down

flow

75

FIGURE

25 - SCHEMATIC

OF TWO-COLUMN,

SEMI-CONTINUOUS

SYSTEM:

MODE

(VII)

(VIII)

(IX)

(X)

(XI)

(XII)

(I)

Down

flow

Circulation

Up fee

d Up

flow

Circulation

Down

feed

Down

flow

76

FIGURE

25 -

CONTINUED.

77

(NOTE: ased or

(I)

(II)

(III)

(IV)

(V)

(VI)

(VII)

In some experiments the dead volume was either incre- decreased).

Pump the fluid from 6 .2TR through the R+ column to the 8.5MR, and at the same time pump the fluid from the 4.OMR through the R" column to the 6.2BR, for a time period of t^ (t-j- = 1 2 min)The fluid between the 6.2TR and the R+ column, and the 4.OMR and the R~ column were circulated, for a period of t ^ (NOTE: t^j depended on the experiment;see the experiment data for the correct value)Fresh 6 .2 ^ 2 ) feed enters the R+ column from the bottom and fresh 4.0(Pg) feed enters the R- column from the bottom, for a perid of = ® min) ,Both top products were analyzed.The fluid from the 6.2BR is pumped through the Rcolumn, the 4.OMR and the R column to the 6.2TR,for a period of t ^ = 1 2 min) .The fluid from the 6.2BR and the R~ column, and the 4.OMR and R+ column were circulated for a period oft vFresh 4.0(P^) feed enters the R+ column from the top and fresh 6 .2 ^ 2 ) feed enters the R~ column from the top, for a period of ty^ ^vi = ® min), while the bottom product were withdrawn and analyzed. The fluid from the 6 .2TR is pumped through the R+

78

column to the 4.OMR , and simultaneously, pump the fluid from the 8 .5MR through the R- column to the 6.2BR, for a period t ^ ^ ^vil = ^ •

(VIII) The fluid between the 6.2TR and the R+ column,.andthe 8.5MR and the R- column were circulated, for aperiod of

(IX) Fresh 6 .2 ^ 2 ) feed enters the R+ column from thebottom and fresh 8.5(P-^) feed enters the R- column from the bottom, for a period of t^x = ® ^in) •Both of the top products obtained were analyzed.

(X) The fluid from the 6.2BR is pumped through the R-column, 8.5MR and R column to the 6.2TR, for a period t- (t^ = 1 2 min).

(XI) The fluids between the 6 .2BR and the R- column, andthe 8.5MR and the R column were circulated, for aa period of t^.

(XII) Fresh 6.2 (I^) feed enters the R column from the top and fresh 8.5 (P^) feed enters the R+ column from the top, for a period of tXII (tXII = 8 min). Both of emerging bottom products were analyed.

The completion of step XII is the end of one cycle. All of the products were analyzed on a BLS at 403^*, 595/**, 560y*t, 51§yA and 630^*. As mentioned before that, the purpose of using 560yt(, 576 /t* and 6 3 0 is to determine the concentration of haemoglobin. It was determined that the type of buffer will affect the absorbance, thus leading to an error in cal-

79

culating the relative amount of protein. The procedure to analyze the sample is already described in the earlier pages of this chapter.

Mode 2: Four reservoirs Batch SystemThe apparatus and the preparation of the column for this

system is the same as the Semi-Continuous System as explained in the above paragraph. Figure 14 is shown the flow diagram of the system.

Procedure. The reservoirs were started with the follow­ing dead volumes:

6.2TR(P2) 8.5MR(P1) 4.0MR(P3) 6.2BR(P2)

Dead volumes 30 cc 30 cc 30 cc 30 ccDisplacements 12 cc 0 cc 12 cc 0 cc

(NOTE: In some experiments the dead volume was either incre­ased or decreased).

The steps of operation were explained in the Chapter II, page where t^ = = ty = ty^j = 1 2 min and t ^ = t-j-y =

^ 1 = ^III = ^ min.

At the end of each cycle, a 3 cc sample was removed fromeach reservoir. The sample was then analyzed on a BLS (Bausch and Lomb Spectrophotometer) at 403yM-and 595yU. The procedure for the analysis of each sample was described as the same as the other Modes from the previous section.

80

Mode 3: Five Reservoirs Batch System

The equipment and the column were prepared for a system of five reservoirs Batch Operation as was described in the earlier pages of this chapter. The flow diagram of this operation is shown in Figure 16.

Procedure. The reservoirs' dead volume and the displacements were as follows:

8.5TR(P1) 4.0TR(P3) 6.2MR(P2) 8.5BR(P1) 4.0BR(P3)

Dead Volumes 30 cc 30 cc 30 cc 30 cc 30 ccDisplacements 12 cc 12 cc 0 cc 0 cc 12 cc

NOTE: In some experiments the dead volume was eitherincreased or decreased.

The operation steps of this type of system, can be found in Chapter II. Allow t^ = t-j-j-j- = ty = tVII = minuteswhile tjj = t^y = t^j = tyjjj = 24 minutes.

A complete cycle is ended by step VIII and 3.0 cc samplewas taken from each reservoir. The samples were thenanalyzed according to the procedure described, and used, for other different mode(s) as mentioned before.

NOTE: For the Semi-Continuous process, the system had beeninvestigated and the results were very poor. The detail of this explanation is in the Reference 48.

81

Mode 4: Two Reservoirs Semi-Continuous System

The apparatus and the column preparation for the system have been explained in the earlier pages of this chapter. First of all, the system was packed with anion exchanger in both columns. The system is supplied the fresh feed of both at P^ = 8.5 and P 2 = 6.2 after each circulation step.Figure 26 shows the diagram of flow sequences.

Procedure. The reservoirs and pH-Converters (PC) were started with the following dead volumes:

8.5TRCPP 8.5PCCPJ) 6.2PC(P2) 6.2BR(P2)

Dead Volume 30 cc 30 cc 30 cc 30 ccDisplacements 12 cc 0 cc 0 cc 0 cc

NOTE: In some case of the experimental, the dead volume waseither increased or decreased.

(I) Pump the fluid from 8.5TR through the first column and also through the 8.5PC to the second column, while the fluid from the second column is trans­ferred the 6.2BR, for a time period of t-j. (t-j- = 12 min) .

(II) The fluid between the 8.5TR and the first column, and the 8.5PC and the sedcond column were circu­lated, for a period of t ^ (NOTE: t ^ = 24 min,otherwise see the table for the correct value).

Down

flow

Down

feed

Up flo

w Up

feed

Down

flow

Circulation

Circulation

82

FIGURE

26

- SCHEMATIC

OF TWO-COLUMN,

SEMI-CONTINUOUS

SYSTEM:

MODE

83

(III) Fresh 8.5TR is fed from the top of the first column through 8.5PC and through the second column, for a period of (tj-j-j- = 8 min) . The bottom productwas collected at pH = 8.5 and analyzed.

(IV) Pump the fluid from 6 .2BR through the second column and through the 6.2PC to the first column, while the content in the first column goes back to the 8.5TR, for a time t ^ ^xv = ^ min).

(V) The fluid from the first column and 6.2PC, and the 6.2BR and the second column were circulated for a period of t^ (t^ = 24 min).

(VI) Fresh 6.2BR feed enters the bottom of the secondcolumn through 6 .2PC and first column, and at the same time, the top product (pH = 6.2) was collected for a period of t ^ (t^ = 8 min) .

Each cycle is ended at step VI. Then, all the products(top and bottom) were analyzed on a Bausch and Lomb Spectro­photometer at each different wave length as mentioned in the previous section.

NOTE: We repeated the process by replacing the cationexchanger instead of an anion exchanger. The prepara­tion of the apparatus, the operation steps and also the analysis of the sample are exactly the same as we operated on an anion exchanger system. Any minor changes either increasing or decreasing the time

84

period (t) are indicated in Appendix B.

Mode 4: Two Reservoirs Batch System

The apparatus and the preparation of the column are the same as the Semi-Continuous System. The flow diagram and the procedures were shown in Figure 18 and described in Chapter II. Any minor changes will be explained in Appendix B.

85

Chapter VI

SEPARATION OF PROTEINS VIA MULTI-COLUMN

This chapter extends the work theoretically from the separation of two proteins via two columns into multi-protein via multi-column. The system is developed and established base on Mode 2 as described in the Chapter I.

Examine any multi-unit system where M columns are con­sidered. Each unit consists of two columns, one which is packed with a cation exchanger (R~) and the other with an anion exchanger (R ). For the first unit, we need four reservoirs, while each additional unit requires three reservoirs as shown in Figure 27. We will follow the operational steps as mention in Mode 2 Chapter I. Therefore, the steady state concentration of protein A will reach the top reservoir of the first unit, while the steady state con­centration of protein B will be found in the bottom reservoir of the last unit. As we explained for the two columns system (see Chapters I, II and IV on Mode 2), proteins A and B will move in opposite directions. The movement of both proteins A and B is shown in Figure 28 and the operational steps, which are exactly the same as Mode 2 system, is shown in Figure 14.

Process Designing for Multi-Protein Separation.

86

C O

CM

00

CMCM

FIGURE

27 - SCHEMATIC

OF PROCESS-DESIGNING

FOR: (a) AN

ORIGINAL FIR

ST UNI

T AND

(b) AN

ADDITIONAL

UNIT.

protein

concentration

in the

solid

phase

- /

Protein A

< P

3.______ __0

Protein B

y, protein concentration in the fluid phaseFIGURE 28 - GRAPHICAL SOLUTION FOR PROCESS DESIGNING,

M-COLUMN SYSTEM

88

This process is quite similar to the separation in the two proteins system; the differences which we have to considered are:

I. Selection of pH level in the reservoirs.II. Adding the extension system(s) to the original

system.

Selection of pH Level:

To commence we choose any four proteins A, B, C and D which have the isoelectric points 1 ^, Ig, I^ and Ig respec­tively and

P5 * XD P4 ^ *<;< P3 * *B < P2 < PA P1

where P^ , Pg, Pg, ^ 4 anc* ^ 5 are t rie levels in the reser­voirs. Thus, all proteins (A, B, C and D) will bare a negative charge at P^ and positive charge at P^. Of course, at a different pH levels P2 , Pg and P^, proteins A, B, C and D will carry a different charge as shown in Table 1.

To select the pH level for the reservoirs, the first necessity is to choose three pH levels. One will be locatedin TR, R 2 , 2 and BR, the other two will belocated in ML^, MLg, ....... ML^^, on the same level of pH,while MR^, MRg, ....... MRM _^, will be on the other levelof pH.

Case I. If we consider P 2 for reservoirs R^, R 2 , ••••

89

TABLE 1

An expression of protein charges, those which they would bear in the different pH level solutions.

P5 4 rD P4 < PC < P3 < H < P2 < PA < P1

pH Level Protein Protein Protein ProteinA B C D

P 1

P2 +P 3 + +

P4 + + +

P5 + + +

90

.... Rjyj+ > then proteins will be grouped where B, C and D are in the first group while A is in the other, thus

ID ’ IC and IB ^ P2'< ZA

In the next step we have to evaluate the lowest and the highest pH levels for the middle reservoirs ML and MR. Rewritten, the isoelectric points of these four proteins, will reduce to:

P5 ^ X D , Ic and IB < P 2 < XA < Px

Then, ML^ , MLg, ....... MLM_^, will have the pH level P^while MR^, MR^, ....... MRM_^, carry the pH level at .

Case II. If P^ be selected for reservoirs TR, R 2 , ....... 2 and BR, then groups of proteins will be as:

XD and IC ^ P3 ^ rB and XA

Similar to Case I, P^ and P^ must be selected for ML^, MLg, ....... ML^ and MR^, MR^.......... MR^_^, respectively.The isoelectric point can be written as:

P^ < 1 IQ and I P 3 < Ig and 1 ^

Case III. If P^ be desired for TR, R 2 ...........®M-2and BR then groups of proteins will be different than the other two cases mentioned before. Also, we will have:

■D P4 ^ IC ’ IB and XA

91

Then and are selected for ML and MR, the same as the first two cases. The isoelectric points now can be stated as

P5 •<£ Ir P4 ■*■(]» ^3 an< ^ ^1

An Addition to the Original System (Extension System):

The new system of multi-separation via multi-column will be developed into two type of systems, one called "SYMMETRICAL SYSTEM" and the other called "UNSYMMETRICAL SYSTEM". To decide which system will be used depends on the way we choose the pH level. If the pH level is selected as in Case I or Case III, then the system developes into an "UNSYMMETRICAL SYSTEM". If Case II is selected then the system will be the "SYMMETRICAL SYSTEM".

Symmetrical System:

We consider A and B which are in one group where iso­electric points (1^ and Ig) fall in between Pg and P^. Where as in the other two, proteins C and D, are in the other group where isoelectric points (1 and 1 ^) fall in between Pg and Pg. At the outset, we will separate these two groups of proteins by using the same system as shown in Figure 14. Weselect pH level Pg in TR., Rg...........^M-2 anc* reservoirsand take P- in the middle reservoirs, MLg, MLg, .......

^M-l while Pg will be in the reservoirs MR^, MRg, .......

m r m -i -

92

Then both proteins A and B will move upward together, and the steady state value of both concentrations, A and B, will locate together at the top reservoir (pH = P3 ), while the other two proteins C and D will move in the opposite direction into the bottom reservoir (as the same pH level Pg)

The next step is to separate A from B and C from D. We need two more extension system to connect with the top reservoir and the bottom reservoir.

Let us consider the separation of A and B first, the isoelectric points of A and B can be written as:

P 3 ,£ Ib < p 2 <r IA C Pj

So we select as a pH level in TR, R 2 , ....... ^M-2 an<BR of the next extension system. However we choose Pg forthe left hand side middle reservoirs MLg, MLg, .......ML^_i and Pg for the right hand side middle reservoirs MRg ,MRg, ....... 1 to ke used in the new extension system.Protein A will move to the top of the extension system which is on the right of the original system, while protein B will migrate to the bottom of the extension system as shown in Figure 29. The steady state concentrations of A and B will be collected at the top and bottom reservoir respectively on this extension system and locate to the right of the original system.

Separation of protein C and D is similar to the

93

i=!•HCD+JOdPm

+P

IPi 0 a ) cd4-1 4-1 X co W

CO4-1

Pd.

I p y

do•HCO

rcti

pqUS

d•r4CD4-1od

p-l

r

PM

PM

i

d 0 d <d•H 4-> bO co •Hd co o

i / c d c ? \ [ +- • pci —t o pm j— p^ , +Pen “

i

PM

<-S

Ud

•Ha)4-1Od

PM

_/

'p4

© ■CJd•HCD4-4odPm

+PS

mlPM

PM

dCD E4-1 a>X 4-1w CO

aSM TJ COdo do o0) •r4CO CO

FIGURE

29 - SCHEMATIC

OF PROCESS

DESIGNING

FOR:

A SYMMETRICAL

MULT

I-SE

PARA

TION

SYSTEM.

94

separation of A and B. Thus the isoelectric points of proteins C and D are stated as:

So we need pH level for reservoir TR, R£, ^ M -2 andBR in the second extension system at P^, while the middle

MR^_2 > are P^ , for the second extension system.Protein C will migrate to the top reservoir on this second extension system which locate to the left of the original system and protein D will migrate downward to the bottom reservoir on the second extension unit as shown in Figure 29.

Unsymmetrical System:

The method of separation with this system is basically the same as the "Symmetrical System". This system is depen­dent on the way we decide to use the pH level as explained in the previous discourse. In this type of process, Case I and Case III, the separation method will become an unsym­metrical separation process system. Either Case I or Case III will have exactly the same process. So in the following paragraphs we will consider only Case I as an example.

We have two groups of proteins, one is protein A and the other are B, C and D, the isoelectric points of these proteins can be expressed as:

reservoirs ML-^, ML^ , MLm _i , are P^ and MR^, MR^, ...

95

P5 ID ’ IC and IB^' P2 IA^' P1

As we proceed with the method, we select pH level for thereservoirs TR, R2 , ....... 2 and ‘P’’ P1 ^or t*ie m:*-ddlereservoirs ML^, ML^.........^ M - l ’ and P 5 ^or » ^ 3 ’ ^®M-1 as dn t*le or^Sina - system. Then protein A willmigrate upward to the top while the rest of proteins B, C andD migrate in the opposite direction to the bottom of thesystem. At steady state condition, the high concentration of protein A will be found in the top reservoir of the system. But the high concentration of all the rest of proteins B, C and D will be discovered in the bottom reservoir of the system. At this point we see that protein A is separated first, and the others are the mixture of proteins B, C and Dwhich need more extension system to separate.

Isoelectric points of proteins B, C and D are

P5 ^ XD ^ P4 ^ ^ P3 ^ IB < P2

We set up the second separation unit by selecting the pH level on either Pg or P^. If we choose Pg then proteins can be grouped and their isoelectric points can be expressed as:

P 5 PD and P3 XB ^ P2

while the other P^, the isoelectric points of proteins will be:

p 5 ID «d. P^ Ic and Ig < P 2

96

For this explanation, we use P^ for reservoirs TR, R 2 , ....... 2 and BR on this first extension system, and allow P 2

for ML^, ^M-l wkile ^®M- 1

will carry the pH level P^. As explained in the previous cases, protein B will migrate toward to the top reservoir on this extension system, while proteins C and D will migrate downward in the opposite direction of B or toward the other end of the system where the last column carries a cation exchanger R . At steady state, a high concentration of B will be found at the top reservoir of the unit while the bottom reservoir contains a high concentration of the protein mixtures C and D which their isoelectric points stated as:

P5 ^ ID P 4 Ic P 3

Once again, we need another extension unit to complete the separation. This extension will separate C from D. First ofall, we choose P^ for reservoirs TR, R2 , ........ ^M-2 ancBR, while P^ and P^ will be carried by ML^, ML^, ........MLm_1, and MR^, MR3, ....... MRM _1, respectively.

In the same manner, the protein C will migrate to the top reservoir of this second extension system, while protein D migrates in the opposite direction of C and reaches the bottom reservoir as shown in Figure 30.

For the separation of "K" components of protein mixtures where their isoelectric points are 1 , I3 , ....... ^K-l anc*

97

O (U 4-1 O 4-1 CO

r*H

,FQ PMrH

TCO <U 4-1 M 4-> W

cvj onPM

rH

i— I

■r4 4-J 5 0 m 'iH}H CO

•tI

FIGURE

30 - SCHEMATIC

OF PROCESS

DESIGNING

FOR AN

UNSYMMETRICAL

MULTI-SEPARATION

SYSTEM.

98

I„, the correlation between pH levels and isoelectric points K.can be expressed as:

P Z T P K+l I< K X2 <C P2 Ii < P2

Assuming that, I^, I^q and 1^ are selected as a majorproducts. To begin with, the process will have to repeat the steps as mentioned above in the previous case. First, restate the isoelectric points and the coeeesponding pH level of these proteins in terms of:

where I- q and 1 are grouped together. Pj, is selected forreservoirs TR, R2 , ....... BR, choosing P^ for the middlereservoirs ML^, ML^, ........... whereas -*-s selectedfo MR-,, MRg, ....... MRj^_2 * This is called the originalsystem. Then protein 1^ will move upward and be collected as one of the major products from the top reservoir of the system while the mixture of proteins Ig_2 > ^k-2 * •••• ^ 1 0 *’* .. 1 will move downward to the bottom reservoir.

The following step is decided upon to separate 1^ out of the mixture. The isoelectric points and pH levels must be written as:

p / T IK ^ K-l’ K-2 ’ * *

P2 , Pjr and P^ are chosen for reservoirs R- , R 2 ,

99

, middle reservoirs MR^, MR^, ....... ^®M- 1 and ^ 1 ’ML^........... ^M-l ’ resPectively. This new process will becalled a first extension unit. Then 1^ is found at the bottom reservoir of this first extension system while the rest of proteins will move upward to the top of the column.

Again, the protein I^q can be separated from the mixture

of IK-1 ’ PK-2 ’ ....... I10’ I9’ ....... and I2 by SrouPingthese proteins as:

PK ^ IK-1 I11 P11 ^ I10’ ' ' - ' I2 ^ P2

for the beginning step and selecting P^, P ^ and P 2 as a pH levels for use in the second extension unit. Next, proteins are grouped as:

P11 I10 P10 ^ I9’ I8 ’ ....... and I2 P2

where P-q > P- q and P2 are chosen for the third extension unit. At the end of this step I^q is separated and the system is now completed. Altogether we required 4 units of these multi-column systems (one original unit plus three extension units) and these will be connected in series.

100

Chapter VII

RESULTS AND DISCUSSION

A. General

The experimental, analytical and computer solutions for pH-parametric pumps were used to generate concentration curves for both Batch and Semi-Continuous parametric pump at the various values of the operating parameters. These curves give the variation in solute separation, i.e., top and bottom product concentrations, with the change in number of cycles.

Once the experimental process had been established, the internal operation of the pH parametric pump was investigated using Equations 1.1 and 1.2 via graphical and mathematical base on elementary matrix algebra methods. Both fluid and solid phase concentrations were calculated by means of equi­librium theory with linear relationships (for dilute protein concentration) and simple material balances. Each movement of the two pistons push the liquid from top and bottom reservoirs alternately through the column(s), generating varoius concentration curves for any set of operating conditions.

The major variables affecting the shape of both Batch and Semi-Continuous pH-parametric pump concentration curves

101

are the number of cycles, dead volume, displacement volume and of course the parameter , where is defined as the ratio of the equilibrium constant for a low pH to the equi­librium constant for a high pH (See Equation 3.24).

B . One-Column System

First of all, we are concerned with the Batch operation system. Figure 31 illustrates the separation factor (S.F.)( y ”> n/ < yg vs. n for a one column pH parametricpump. Initially, the feed solution containing a solute (haemoglobin or albumin) was present in the top reservoirs only. The column and the bottom reservoir dead volume were filled with the buffer solution pH = i-s varied from 8.0to 8.5). The buffer solutions were made from monobasic and dibasic sodium phosphate. The top and bottom reservoir were respectively maintained at pH = 6 (?2 anc = ® ^1^ so that the isoelectric point of haemoglobin would lie between the two pH levels. As a result of a change in the column pH, haemoglobin experiences a change in net charge, and migrates toward the high pH end on the bottom reservoir. Thus, the separation factor (S.F.) for haemoglobin increases with n and approaches a limiting value. For the case of albumin,■'’albumin = ^ ^ P 2 ’ ant* t *1 0 net c^arSe always negative during upflow and downflow. As a result, the albumin concentration is unaffected by the parametric pumping operation and remains at zero.

102

<y>n< ? 0 >in

uo4-3ostf<4-3

CJO•H4-3nJUctieua)«3

Exp. Bottom Top

1. Haemoglobin ® O2. Albumin Jk A

Calc.BottomTop

.,2

.1

.0

.9

.8

.7

. 6

8642 n0

number of cyclesFIGURE 31 - THE CONCENTRATION TRANSIENTS OF HAEMOGLOBIN AND

ALBUMIN vs. NUMBER OF CYCLES.

103

Figures 32 and 33 show the comparison of anion and cation exchanger column for haemoglobin and albumin respec­tively. As we know the isoelectric point of albumin is 4.7. The experimental results are shown in Figure 31. Instead of using pH = 8 , pH = 4 was selected. The buffers used for this part of the experiments were mixtures of acetic acid, sodium acetate and sodium chloride. As the theory predicts, albumin is concentrated at the low pH end of R+ column and at the high pH end of the R column which are opposite from the result for haemoglobin.

For the Semi-Continuous system the analysis of a few experiments using anion and cation exchangers and feed of single components only are involved. The operating parameters for these experimental runs can be found on Exhibit B-2 in Appendix B.

The purpose of these experiments was to investigate the flow migration of the individual components by varying the buffer conditions and also verify the equilibrium constants at the different pH level. The results, shown in Figure 21, not only explained how the equilibrium constant varies due to both the pH change and the ion exchanger, but give us more confidence by confirming the equilibrium theory at a low concentration of the solute (region of interest).

The first set of experiments investigates the anion column using a feed of pure haemoglobin. The ideal conditions

104

Haemoglobin-BufferpH= 8 > I, , , . = 6 .7 > pH= 6r haemoglobin ^

One Column (DEAE-Sepharose), R One Column (CM-Sepharose), R

10

8

6

44-J

•H2

eu

4 51 2 30 nnumber of cycles

FIGURE 32 - COMPARISON OF ANION AND CATION COLUMN FOR HAEMOGLOBIN.

separation

factor

105

Albumin-Buffer

PH - 6 > Albumin- 4 ' 7 > PH = 4

One Column (DEAE-Sepharose) , R One Column (CM-Sepharose), R

10

8^n

4

2

42 5310 nnumber of cycles

FIGURE 33 - COMPARISON OF ANION AND CATION COLUMN FOR ALBUMIN.

106

were to have a large concentration of haemoglobin in the 6 . 2

BR product stream. It was found that the experimental delivered the best results, which is shown in Figure 34.

The next group of experiments involved the use of an anion exchanger and a feed of pure albumin. The ideal condi­tion were to have the concentration of albumin in the 6 . 2 top product stream low. The experimental results can be seen in Figure 35.

It should be noted that the buffer and sodium chloride concentrations were equal to 0.10 M and 0.05 M, respectively for all reservoirs and feeds.

The last group of experiments were conducted using the cation exchanger and a feed of pure haemoglobin. The ideal conditions were to have the concentration of haemoglobin in the 6.2 bottom product stream low. The results are shown in Figure 36.

C . Two-Column System

Mode 1: Three reservoirs Batch operation

This section is a combination of a two single column system connecting in series and they were packed alternately with an anion and a cation exchanger.

Before we discuss the results of this mode, we have to to understand the flow movement of the individual components

separation

factor

107

Haemoglobin - Anion Column

8 .0 and P8 .5 and P

1.4 —Pi buffer

Calc.P 9 buffer,

84 620 nnumber of cycles

FIGURE 34 - THE CONCENTRATION TRANSIENTS OF HAEMOGLOBININ A SINGLE-ANION-COLUMN SYSTEM.

separation

factor

< yA>

< y 0>

108

Albumin - Anion Column

6 .2 and P

1.8 -

P 0 bufferP 0 bufferCalc.

84 62 nnumber of cycles

FIGURE 35 - THE CONCENTRATION TRANSIENTS OF ALBUMININ A SINGLE-ANION-COLUMN SYSTEM.

109

uo4-JOcamPSo•H4->COn«acua)CO

Haemoglobin - Cation Column8 .0 and P8 .5 and P

Calc.

6

.21 0 n84 62

FIGURE 36number of cycles

THE CONCENTRATION TRANSIENTS OF HAEMOGLOBIN IN A SINGLE-CATION-COLUMN SYSTEM.

110

in the system. The haemoglobin having the higher isoelectric point (= 6.7), will migrate the 8.5 (P- ) reservoir through

-I-the anion (R ) column to the 6.2 reservoir. Albuminhaving a lower isoelectric point (= 4.7), compare with P^ and ?2 , then the system will have no mass transfer on albumin.

In the same manner, if the column was packed with cation (R) the haemoglobin will migrate from 6.2 reservoir through R column to 8.5 reservoir, while no change for the concen­tration of albumin occur in any reservoirs.

Figures 37 and 38 show the results of running pure haemoglobin and pure albumin. We also found that, for the two column system, a better result on haemoglobin is occured, where there is no change in albumin concentration

Mode 2: Four Reservoirs Batch Operation

A general understanding of the flow movement of the individual component of the four reservoirs system must be explained before we can discuss the results. The haemoglobin having the higher isoelectric point (I.P.), will migrate from the 6 . 2 bottom reservoir, through the cation column to the 8.5 middle reservoir; and from the 8.5 middle reservoir, through the anion column to the 6.2 top reservoir. The albumin, having the lower isoelectric point (I.P.), will migrate from the 6 . 2 top reservoir, through the anion column to the 4.0 middle reservoir; and from the 4.0 middle reser-

Ill

Albumin

pH = 6.2 > Ialbumin= 4.7 > pH - 4.0

< yB > n < yT > n

uouoCDmao•H4Ja)ucdPuCDcn

One Anion Column Two Anion Columns Calc.

10 -

8 -

6 -

2 -

number of cycles FIGURE 37 - COMPARISON OF ALBUMIN CONCENTRATION BETWEEN

ONE- AND TWO-COLUMN SYSTEM.

112

Haemoglobin - Albumin

< yT > n < yB > n

uo•uocti<4-1ao•H4-1J-4

<uco

=6 . 7 > pH= 6 . 2 > I =4.7haemoglobin

O Haemoglobin [~!~1 Albumin Calc.

12

10

8

6

4

2

1

4 52 310 nnumber of cycles

FIGURE 38 - THE CONCENTRATION TRANSIENTS OF HAEMOGLOBIN AND ALBUMIN vs. NUMBER OF CYCLES: MODE 1.

113

voir through the cation column to the 6 . 2 bottom reservoir. Thus, the 6.2 top and the 6.2 bottom reservoir are examined.

Experimental parameters are tabulated in Exhibit B-4 which were conducted by initially having a feed mixture of haemoglobin and albumin in the 4.0 and 8.5 middle reservoirs, and having a pure buffer solution in the 6 . 2 top and 6 . 2

bottom reservoirs. This was done to examine the flow migration of haemoglobin and albumin in the system. The 6.2 top and bottom reservoirs buffer and sodium chloride concen­tration in the 4.0 and 8.5 middle reservoirs varied to aid in the protein migration.

The main objective of these experiments was to have the concentration of haemoglobin greater to that of albumin in the 6 . 2 top reservoir and to have the concentration of albumin greater to that of haemoglobin in the 6 . 2 bottom reservoir. By examining Figures 39, 40 and 41, we can see that the concentration of albumin is greater than the concentration of haemoglobin in the 6 . 2 bottom reservoir.We can also see from the figures that the concentration of haemoglobin is less than the concentration of albumin in the6.2 top reservoir. This result proved to be negative for the 6 . 2 top reservoir.

The next set of experiments were designed to investigate the migration of the individual components in the Four Reser­voir Batch System.

separation

factor

114

Haemoglobin - Albumin

^ 1 ^ ^"haemoglobin ^ 2 ^"albumin ^ ^3

o Haemoglobin in the top reservoir □ Haemoglobin in the bottom reservoir

Albumin in the top reservoir Albumin in the bottom reservoir

.0 2 and P CASE I

0.8

0.6

0.4

0.2

0

106 8420 nnumber of cycles

FIGURE 39 - THE CONCENTRATION TRANSIENTS OF HAEMOGLOBINAND ALBUMIN vs. NUMBER OF CYCLES: MODE 2.(CASE I)

separation

factor115

<yn>

Haemoglobin - Albumin

^ 1 ^ ^haemoglobin ^ 2 ** ^"albumin ^3

o Haemoglobin in the top reservoir□ Haemoglobin in the bottom reservoir® Albumin in the top reservoir

Albumin in the bottom reservoir.0

6 . 0 and P CASE II

.8

. 6

.4

.2

0

4 60 2 nnumber of cycles

FIGURE 40 - THE CONCENTRATION TRANSIENTS OF HAEMOGLOBINAND ALBUMIN vs. NUMBER OF CYCLES: MODE 2.(CASE II)

116

Haemoglobin - Albumin

^ 1 ‘'‘haemoglobin ^ 2 ^albumin ^3

o Haemoglobin in the top reservoir

1.2

1.0

0.8<yn>

^ 0

0.6

o4Jocflmao•H■l-JftiMCTJfta)03

0.4

0.2

Haemoglobin in the bottom reservoir Albumin in the top reservoir Albumin in the bottom reservoir

6 .2 and P CASE III.

>4 6 80 2 nnumber of cycles

FIGURE 41 - THE CONCENTRATION TRANSIENTS OF HAEMOGLOBINAND ALBUMIN vs. NUMBER OF CYCLES: MODE 2.(CASE III)

117

This experiment had pure albumin feed in the 4.0 and the 8.5 middle reservoirs and pure buffer in the 6.2 bottom and top reservoirs. The results of using this experiment proved to be positive (i.e. y^ 6 . 2 bottom > 6 . 2 top).See Figure 42. The next logical step was to use the same buffer conditions and run the same experiment with pure haemoglobin.

Mode 2: Four Reservoirs Semi-Continuous Operation.

A general understanding of the flow movement of the individual components of the Four Reservoirs Semi-Continuous System. The haemoglobin having the higher isoelectric point (I.P.), will emerge from the 6.2 top product where albumin having the lower isoelectric point (I.P.) will emerge from6.2 bottom product. The other intermediat steps were analyzed for protein concentration.

Experimental results, see Figures 43 and 44, were identical with respect to the operating parameters. These experiments were conducted with a feed of pure haemoglobin. The results that were obtained were positive. The concen­tration of haemoglobin was greater in the 6 . 2 top product stream than in the 6.2 bottom product stream. The next step was to run another experiment with pure albumin to observe how the albumin migrates.

Figure 45 shows the results which were operated under

118

^ ? > n

o•uocdM-lO•rH•PcdUcdft<Dco

Albumin

2 albumin

@ Bottom product O Top product

0

8

6

O

00 4 6

number of cycles8 1 0 n

FIGURE 42 - THE CONCENTRATION TRANSIENTS OF ALBUMINvs. NUMBER OF CYCLES: MODE 2.

119

Haemoglobin

^ 1 ^ ^haemoglobin ^ ^ 2

1.2 -

1.0

< y > n

0.8

no•Ui h 0.6ao•r*l4-1cO}-lCO

& 0 .4CO

0.2 -

O — □

Case I

4 6number of cycles

Top product Bottom product

= 8 . 0 and P 2 = 6 . 0

= 8 . 0 and P 2 = 6 . 2

FIGURE 43 - THE CONCENTRATION TRANSIENTS OF HAEMOGLOBINvs. NUMBER OF CYCLES: MODE 2 (CASE I).

separation

factor

120

O Haemoglobin

< y > n

.4

haemoglobin. 2

o — o Top product & --■ Bottom Product

. 0

.8

Case II.. 6

.4

. 2

0 1086420 nnumber of cycles

FIGURE 44 - THE CONCENTRATION TRANSIENTS OF HAEMOGLOBINvs. NUMBER OF CYCLES: MODE 2 (CASE II).

separation

factor

121

Albumin

1.

1 .

1 .

< y > n

i.

0 .

0 .

0 .

albumin

0 H Top productQ — □ Bottom product

42 6 8 100 nnumber of cycles

FIGURE 45 - THE CONCENTRATION TRANSIENTS OF ALBUMINvs. NUMBER OF CYCLES: MODE 2.

122

the same buffer and sodium chloride conditions as the in the previous paragraph. The feed was a pure albumin. The results that were obtained were positive. The concentration of albumin was greater in the 6 . 2 bottom product stream thanin the 6.2 top product stream. The next step was to run torun the mixture of haemoglobin and albumin by using the same buffer conditions that were used for the individual run.

The experiment (Figure 4-6) was conducted with a mixture of haemoglobin and albumin. The results that were obtained were positive. The concentration of haemoglobin in the 6.2 top product stream was greater than the concentration of albumin in the 6.2 top product stream. The y^, ’values for the 6.2 top product streams were 1.42 and 1.61respectively. The y^, (yA/yAo)’ values were in the order of 0.19 and 0.09 for the 6.2 top product streams. The concen­tration of albumin in 6 . 2 bottom product stream was greater than the concentration of haemoglobin in the bottom product stream. The yA> (yA /yAQ) * yn and val-ues were 1-58,1.39, 0.15 and 0.31 respectively in the 6.2 bottom product stream. The buffer concentration for this experiment was 0.10 M and the sodium chloride concentration was 0.05 M for all reservoirs and feed streams. Thus, the experimental parameters that were used in this experiment and calculation were considered acceptable.

Mode 3: Five Reservoirs Batch Operation.

□ 123

1.4 -

1.2

1.0<y> n

0.8

uo■uotfl 0mao•H4->nPu 0Q) U 'CO

.6

4 -

0.2 -

0

0

®

u

- 2

— 1

Haemoglobin-Albumin

P 1 ^ ^haemoglobin ^ P 2 ^albumin ^ 3

HaemoglobinAlbuminTop product Bottom product

0, ~ 6.0 and = 4.0.5, P 9 = 6.2 and P 9 - 4.0

1

22

4 6

number of cycles8 1 0 n

FIGURE 46 - THE CONCENTRATION TRANSIENTS OF HAEMOGLOBIN-ALBUMIN vs. NUMBER OF CYCLES: MODE 2.

124

Before we can discuss the various results of this system, we have to understand the flow movement of the individual components in the system. The haemoglobin having the higher isoelectric point (I.P.), will migrate from the 8.5 top reservoir through the anion column to the 6 . 2 middle reser­voir; it will then move from the 6 . 2 middle reservoir through the cation column and into the 8.5 bottom reservoir. The albumin having the lower isoelectric point, will migrate fromthe 4.0 bottom reservoir through the cation column and to the6 . 2 middle reservoir; then from the 6 . 2 middle reservoir, it will migrate through the anion column and into the 4.0 top reservoir.

Figure 47 can be explained that the haemoglobin didmigrate to the 8.5 bottom reservoir, and the albumin alsomoved to this reservoir. This phenomenon implies that the buffer strength of the 8.5 bottom reservoir will remove not only the haemoglobin but also the albumin from the cation exchanger. By examining the 4.0 top reservoir, we found that the albumin migrated to the 4.0 top reservoir; yet, the buffer strength of the 4.0 top reservoir did not allow the removal of the haemoglobin from the solid phase of the anion exchanger. This type of result was obtained when the the buffer strength was 0.15 M and 0.20 M, and for a sodium chloride of 0.05 M and 0.05 M for experimental results shown in Figures 47 and 48 respectively. The yH value (equivalent to 4 y ^ j / y t ,e Prev^ous pages) refers to the feed

125

<y>

0.2

9 - "O'

Haemoglobin-Albumin

CASE I ..

HaemoglobinAlbuminBottom productTop productDead Volume = 0 cc

^ 1 ^ ‘'"haemoglobin ^2 ^ ‘'"albumin ^3

_L _L

4 6 8number of cycles

10 n

FIGURE 47 - THE CONCENTRATION TRANSIENTS OF HAEMOGLOBIN- ALBUMIN vs. NUMBER OF CYCLES: MODE 3 (CASE I)

126

Haemoglobin-Albumin

''haemoglobinO ^ 1 ^ ’''haemoglobin'^ ^ 2 ^ "'"albumin^3

< y >

o — ® Haemoglobin Albumin Bottom product Top product• CASE II Dead Volume = 30 cc

4 6number of cycles

8 10 n

FIGURE 48 - THE CONCENTRATION TRANSIENTS OF HAEMOGLOBIN-ALBUMIN vs. NUMBER OF CYCLES: MODE 3-(CASE II)

127

concentration. If this value is equal to 1.0, this indicates that the haemoglobin is at the initial condition (assuming the buffer solution has haemoglobin present). The same explanation is true for albumin (y^)•

The results, shown in Figure 49, were conducted using the same buffer and sodium chloride conditions as mentioned before in the previous page. The major difference was in the 4.0 top reservoir and 8.5 bottom reservoir. The 4.0 top reservoir had only albumin while the 8.5 bottom reservoir had only haemoglobin. This was done to see to what extent the haemoglobin would enter the 4.0 top reservoir and albumin would enter the 8.5 bottom reservoir. The results of this experiment is also confirmed the previous results as discussed in the earlier pages.

Mode 4: Two Reservoirs Batch Operation.

This section is included a few experiments to confirm the mathematical model. The experiments were investigated by running individual components. First of all, with pure haemoglobin where pH = 6.2 (P^ an< = 8 .5 (P^) were used. Later on, we performed the experiment on pure albumin where pH = 6.2 (P2) and pH = 4.0 (P^) were designed.

The haemoglobin having a higher isoelectric point (I.P.), will migrate from the 6 . 2 bootom reservoir through the cation column, and through the pH-Converter, then it migrate from

128

<y>n

No■MacdINGO•N•NcdNcdCXa)CO

fl

Haemoglobin-Albumm

o — ® Haemoglobin Albumin Bottom product Top product

^ 1 ^ "'"haemoglobin ^ 2 ^ "'"albumin ^3

CASE III .. Dead Volume = 40 cc

4 6 8

number of cycles1 0 n

FIGURE 49 - THE CONCENTRATION TRANSIENTS OF HAEMOGLOBIN-ALBUMIN vs. NUMBER OF CYCLES: MODE 3.(CASE III)

129

the pH-Converter through another cation column into the 8.5 top reservoir. In the same manner, albumin will migrate from the 4.0 bottom reservoir through the cation column into the pH-Converter and go through another cation column into the 6 . 2 top reservoir.

Figures 50 and 51 show how the separation factor of haemoglobin and albumin respectively, were developed as the number of cycles were increased. The experimental results are agree well with the calculation value for both haemo­globin and albumin.

Mode 4: Two Reservoirs Semi-Continuous Operation.

The experiment were performed by running a mixture of haemoglobin and albumin by using pH = 8.5 (P^) and pH = 6.2 (P2 )• The isoelectric point of haemoglobin are in the range of 6 . 2 to 8 .5 , then the separation of haemoglobin was occured. The flow movement of haemoglobin is the same as we mentioned in the previous paragraph. The isoelectric point of albumin is 4.7 and lower than either P^ or P2 , then there is no separation on albumin. Figure 52 shows the separation factor vs. n (number of cycles) for both haemoglobin and albumin.

D . Separation Of Proteins Via Multi-Column

This section is atheoretical study which extend our study from two column system into a multi-column system.We established that, Mode 2: Four reservoirs Batch Operation,

130

< y T>^ y B>

nn

uoportpao•pHPftPL,a)CO

Haemoglobin13

11

9

7haemoglobin

5

3

14 50 1 2 3 n

number of cycles

FIGURE 50 - SEPARATION FACTOR OF HAEMOGLOBIN vs. NUMBER OF CYCLES: MODE 4.

131

Albumin13

albuminuopocd

ao•rHPcdUcdPha)CO

4 5 n31 20

number of cycles

FIGURE 51 - SEPARATION FACTOR OF ALBUMIN vs. NUMBER OFCYCLES: MODE 4.

132

< ? T > n* y B > n

o•MOccJmso•H4->cdnctipu<Uco

Haemoglobin-Albumin

14

12

Haemoglobin

10

8

haemoglobin ^2 ’'"albumin6

4

2

1

42 3 510 nnumber of cycles

FIGURE 52 - SEPARATION FACTOR OF HAEMOGLOBIN ANDALBUMIN vs. NUMBER OF CYCLES: MODE 4.

133

can extend well to a multi-column system and be able to explained by using a graphical method. Our discussion will begin from a simple case and introduce a new symbols of proteins as A, B, C etc., just for our convenience for this explanation as well as the pH levels i.e., P- , > P 3 andso on.

Two Proteins - Two Columns:

Since the graphical method can predict the steady state concentrations of both top and bottom products for a single column system well, we are able to extend this concept of the graphical method to the tx o column system where the process description has been described in Chapter II.

To understand the flow movement of individual protein component, we consider the expression of isoelectric point and the pH level. Protein A having the higher isoelectric point (I.P.), will migrate from the P 2 bottom reservoir, through the cation column to the P^ middle reservoir; from the P^ middle reservoir, through the anion column to the P2

top reservoir. The protein B having the lower isoelectric point(I.P.) will migrate from the P 2 top reservoir, through the anion column to the P^ middle reservoir; and from the P^ middle reservoir through the cation column to the P2 bottom reservoir. Thus the enriched concentration of protein A and protein B will be found from the P2 top reservoir and the P2

bottom reservoir respectively.

134

Once the system operates for anumber of cycles, the steady state values of protein A and B reached, the results shown in Figures 53 and 54 as protein A and B are moved in the opposite direction indicate, that where protein A migrates upward to the top reservoir (pH = P 2 )> protein B moves downward to the bottom reservoir (pH = P 2 )•

The separation factor of protein is defined asyT >a>/ £ Yg > 0 0 • For any protein mixture, to which this

process can be applied, the S.F. (separation factor) will behigh or low depending upon the value of the equilibriumconstants for anion and cation exchanger which correspond tothe pH in the top and bottom reservoirs, kp and kp

* 2 * 2respectively.

Figures 55 and 56 show the plot of S.F. versus the number of cycles at a different value of p for the protein A and B respectively. As increases the S.F. is also increases. Figures 53 and 54 also show the results where both top product, < y^^oo and bottom product, <yg>oo°f t*1 6

proteins A and B are located.

Two Proteins - Multi Column:

This section investigates how the S.F. is effected if the number of columns is increased. Figures 57 and 58 show that as we increase the number of columns, the top and the bottom products of protein A are increasing and decreasing

135

CO!-)CM

■+

CM

oCM

CO

rH+ P-<

i—IOOCM i—I

+ P-l

•HCOm

oo

asBqd p-pxos a q. uf uofq.aj 'uaoxioo trcaqoad ‘x

136

t—I CO

MCM

Oco

CM+ cm

+ PMoo

CO

CO

oo

aseqd ppjos aqq ux uof^aa^uaouoo uxaaoxd ‘x

y, protein

concentration

in the flu

id phase

FIGURE

54 - GRAPHICAL

SOLUTION

OF PROTEIN

B VIA

TWO-COLUMN

SYSTEM.

137

=5.67Protein A

13

11

9

77® =3.2

5

3p =2.14

1

2520151050

n, number of cycles

FIGURE 55 - EFFECT O F ^ ON CONCENTRATION TRANSIENTS FORPROTEIN A'

138

Protein B

.0

.8•H

.6

.4

.2

7* = 0.18

.0

2520151050n, number of cycles

FIGURE 56 - EFFECT OF yB ON CONCENTRATION TRANSIENTS FORPROTEIN B

139

m<1) >-»

pH

CMCM

m

pH

•H

x— \+ PH

CO

CM

pHCO

MCM

•HMCO

O

A8HKl'lV

<ucocdxip*

•r43r-4m<urP4JP•HCo•H4-1Cd4->PiQ>OCOOPi•H<U4JOUPu

8Apq>>V

aseqd PTios sip uj u o t^bjpusouoo uxa^oad ‘x

r-~in

sBMpH

14©

CO + Ph

1-I

CN

ln

corH

•H

CO

in

ooHCO

O

A8wV

wHco>-<CO

l-Jo

CD ow 1P M iS

43 H MP h J M

3 HX) S o

P hP < ! PhI—1 Mm > Pen

O<u CP

43 CO■u i s H

M ISP W H■H H !S

O OP pH PhO Ph S•H OU Ph Ucd OP O■M JS £5P O HCD HO H SP B <3O iJ p3y O Ph

COp i s•H i J O<d < M•u O E-h-o M <lju P3 3P h Ph ^

<d Ph•» p3 WO CO 11CO

IK*1V

LO

iqoMph

asaqd pTios aqq. ux uoxqexquaouoo uxarioxd ‘x

141

respectively compare with the two-column system as shown in Figures 53 and 54. Bottom product of protein B is also increasing while the top product is decreasing as we increase the number of columns. Figures 57 and 58 show that where the top and bottom products of both proteins A and B are located, and also locates the concentrations of protein A and protein B for each correspondind column.

Figures 53 and 54 show the straight lines which are+ +connected from a point T to a point M , from M to M and

from a point M~ to a point B. Then, the line which connects-f-the point T and M , represents the anion exchanger column

while the other line which connects the point M~ and B,represents the cation exchanger column. From this step, thetwo "Assymtotic lines" can be drawn by conecting the origin

+to the point M and the origin to the point M where their slopes are k" and k+ respectively.

If we fix all those parameters except the number ofcolumns, then the two assymtotic lines are drawn at a slopesof k" and k"** (see Figures 57 and 58). Once either top orbottom product is known, then we are able to graph andpredict the other product. The example of this graphicalmethod, to predict the bottom product where top product isknown, is shown in Figure 59 for a six-column system. Theknown top product is located at point T on the equilibrium

+ +line, slope is equal to kp (= kp ). The horizontal line

142

CO

i—i

pH

CN

CN O

CN <rt-tCN

1 1HCO O

a s a q d p T j o s aqq. ux uoxrjaxruiaouoo uxarjoad *x

A8EHpH

V

0 Q)* W01 cO XPT3•H<—I UHcuX+Ja•Hao

• r - l■uCCJn° fi- saoo

ti•H<u•Uo}H04

PQto

wEh§PWwHOHHaMPPPpci S O O P M H W <J C/3 P<ti EHq S pci WH UC S EH O C/3 UP W ° % O EH H CO H i*M . Ed w U H CO COI

cr> in3 gH P

fed - P +P

P

p;p p

r O i

p

143

T(MR^) represents the column 1 (R+) where the point X^indicates the solute concentration in the solid phase. The

+ — + —vertical line (MR^) (MR^) is drawn where MR^ and MR- are theaverage concentrations of the middle reservoirs as mentionedpreviously. Next, we draw the horizontal line (MR^)-(MR2 )~which represents column 2 (R-) while is the concentrationof protein in the solid phase. The concentration of proteinin MR2 reservoir be located at Y 2 by drawing a vertical linefrom the point (MR2 ) to the y-axis, the intersection of this

+ + + vertical line and the line kp = kp is (MR2 ) . In the samewe can draw the lines (MR2 )+ (MRg)+ , (MR^^MR^) " , (MR^) ~ (MR^) ~and so on until the last line (MR^)-B is drawn. Once B isknown then the bottom product y-g Pbo can located.Clearly shown in Figure 60, the plot of S.F. versus M(number of columns) on semi-log scale. As the number ofcolumns is increasing, the S.F. intends to increase a greatdeal.

Four Proteins - Multi Column:

This process operates similar to the separation of twoproteins as described in the previous section, the different is the number of proteins, which is increased to four components: A, B, C and D. If the system considers the separation of these four proteins individually as the major products, then the separation process can operate based on the selection of pH levels as explained in Chapter V.

144

100

3 ; Dead Volume = 10

10

D

S.F.

1

.010 2 4 6

M

FIGURE 60 - STEADY STATE SEPARATION FACTORS OF TWO PROTEINSvs. NUMBER OF COLUMNS <M).

145

Case I The isoelectric points of this protein mixture can stated as:

P5 ^ *D- ZC and h * P2 < IA < P1

where we let B, C and D be the group of proteins with their isoelectric points (Ig, Iq and I^) in between P^ and P2 .The pH levels P^ , P2 and P^ are chosen for this first separa­tion process. As the protein A having the higher isoelectric compared with the rest, A will migrate from the P2 bottom reservoir (BR) , through the cation coliimn (M) to the P^ middle reservoir (MR^ _ 1 ) . Again from reservoir, protein A will migrate through the anion column (M-l) to the P 2 reservoir ( ^ . 2 anc keep repeating the flow step by- migrating up through cation column (M-2) to the P^ middle reservoir (MR^^) and so on until protein A reaches the top reservoir. As A is moving upward, proteins B, C and D having the lower isoelectric point s, compared with protein A, will migrate down from the P 2 top reservoir through anion column (M = 1) to the P^ middle reservoir (ML^). Then from the reservoir ML^, protein mixture B, C and D migrate through cation column (M = 2 ) to the P 2 reservoir (R2 )• ln the same manner as protein A, the mixture of B, C and D will migrate down through anion column (M = 3) to P^ reservoir (ML^) and through cation column (M = 4) to P2 reservoir (R^) and so on until these protein mixtures reach the P 2 bottom reservoir. Graphical solution of both protein A and the mixture of B, C

146

and D are shown in the Figures 61 and 62 respectively. At the steady state condition, the enriched concentration of protein A will be found in the top reservoir while the bottom reservoir will obtain the enriched concentration of proteins B, C and D. The separation factor of protein A and the mixtures of B, C and D are plotted and shown in Figure 63.Up to this point, protein A is separated while protein B, Cand D still mixed together and are ready to be separated onthe first extension unit.

The isoelectric points of protein mixtures can be expressed and related to the pH level in terms of:

P5 ^ ID and -C P3 IB P2

For this first extension unit, the P 2 , Pg and Pg to be used,are selected as explained earlier in this chapter. ProteinB having a higher isoelectric point, it will migrate from the Pg bottom reservoir through cation column (M) to the Pg middle reservoir (MR^ and through anion column (M-l) to the Pg reservoir an< continue flowing until theprotein B reaches the Pg top reservoir. Protein mixtures C and D having a lower isoelectric points, will migrate down from the Pg top reservoir through anion column (M = 1) to the Pg middle reservoir (ML- ) and through cation column(M = 2) to the Pg reservoir which locates toward to thebottom of this extension unit, until the movement reaches the Pg bottom reservoir. Figures 64 and 65 show clearly the

147

H CM

OMMm

mCO

i—i

m

co

\ \N

oasaqd pTIos aq:* ui uox^BJi^uaouoo UTa^o^d ‘x

9AHV

a)cocdrPp.T3•Hpr-Hma)

rP■PP■HpO•rl4->cdp4->P0)OPoop•P(U+JopPh

A8pq150V

FIGURE

61 - GRAPHICAL

SOLUTION

OF PROTEIN

A VIA MULTI-COLUMN

SYSTEM,

SEPARATION

FROM

MULTI-COMPONENT

OF PROTEIN.

148

m+ PMCN

CN

m

+ PM m

in

CN

M

O

8APQX.\J

a)COcd&PM•HP»rMIH<UrP*P5•Hao•rlPcdPp§oP!OOPI•Ha)popPM

aAh

<3M>P3P5sU

PQco§t=>HX!MESMwH§PMPiO

s wO H M CO H >-• to CO■Jo g co go uM I ffi H P-i H

O SCNCO

s8HP4

asaqd pxxos aqq. ut uoT^aa^uaouoo uxa^oad ‘x

149

12.0(2) Protein B

C and D

10.0

m•H

0 105 15 20 25 nnumber of cycles

FIGURE 63- THE CONCENTRATION TRANSIENTS OF PROTEIN A ANDPROTEIN MIXTURES B, C AND D vs. NUMBER OF CYCLES.

150

LO+ Ph P£!

+ 1ucu

-9/-N E•H •H p

% § p

P

II IIX)o

+ CN] I CN]/-N

•H •Hg g tnV-/

II IICO

+ l!—1

/-s II•H •Hss-/ ss-/

•H

+ Ph8%M

0)COcO

,PPh

*HPi—Im<u

rP■U)P•HPO•H4-1COP4-1P0)OPoop•H(U4-1opp.

8APP!>»

VX o

asnqd pfxos aq:j. up uoTa^jquaouoo uxaqoxd ‘x

FIGURE

64 - GRAPHICAL

SOLUTION

FOR PROTEIN

B VIA

MULTI-COLUMN

SYSTEM,

SEPARATION

FROM

MULTI-COMPONENT

OF PROTEIN.

151

LTlCO

CN

mCO

1—I

CN

mCN co

CO

ow

VO

M

oaseqd pTios aqq. up uoxpBjpuaouoo uxapoxd ‘x

8AFQV

<ucocd43ftX)•H3r— 1QJ43■U

•H

co•H4-1cdn4-1&(UoS3oo13

•H<U4-1OHft

8AHN/

FIGURE

65 - GRAPHICAL

SOLUTION FOR

PROTEIN

MIXTURES C AND

D

VIA

MULTI-COLUMN

SYSTEM.

152

graphical analysis and predict the top and the bottom products for both proteins B and mixtures of C and D. Once again, when the steady atate is reached the enriched concen­tration of protein B will be obtained from the top reservoir while the enriched concentration of protein mixtures C and D is found from the bottom reservoir and another extension unit is need to separate C and D. The transient concentrations of protein B and a mixture of C and D are shown in Figure 6 6 .

For this second extension unit, the unit will be the last which is added into the system due to the number of solutes which remain (protein C and D). The isoelectric points of C and D can correlate with the pH level and be stated as:

P5 IC < P3

The pH levels Pg , P^ and Pg are chosen for this second extension unit. As we explained in the earlier part of the chapter, protein having a higher isoelectric point will migrate from the P^ bottom reservoir through cation column (M) to the P^ middle reservoir anc* through anioncolumn (M-l) to the P^ reservoir (R^ g) until this flow movement reaches the P^ top reservoir. However, while protein C is moving, protein D which has a lower isoelectric point will migrate from the P^ top reservoir through anion column (M = 1) to the Pg middle reservoir (ML^) and migrate

153

(1) Protein

12.0(2) Protein

and D :

210.0

(1)•H

2520151050 nnumber of cycles

FIGURE 6 6 - THE CONCENTRATION TRANSIENTS OF PROTEIN B AND PROTEIN MIXTURES C AND D vs. NUMBER OF CYCLES.

154

through cation column (M = 2) to the reservoir toward to the bottom of the unit until the movement of flow reaches the P^ bottom reservoir. Figures 67 and 6 8 show the graphical solution of both proteins C and D respectively.Also the transient concentration of proteins C and D are plotted versus the number of cycles and shown in Figure 69

Case II In this case, P^ is selected for reservoirs TR,and BR. Then the P^ will split the

proteins into two groups; A, B and C, D. The isoelectric point can express as:

P5 < ID and Ic < P 3 < IB and IA < P1

The pH level P^ is chosen for the middle reservoirs ML^, ML^....... and the P^ is chosen for MR^, MR^ .......MR^_^. The protein mixtures A and B having the higher iso­electric points than the P^ and protein C and D, will migrate from the P^ bottom reservoir (BR), through the cation column (M) to the P^ middle reservoir (MLM_^). From this middle reservoir, protein mixtures A and B will continue migrating through the anion column (M-l) to the P^ reservoir ( ^ _ 2 and migrating further in the same manner until the mixture of A and B reach the P^, top reservoir (TR). As proteins A and B are moving upward, the mixture of proteins C and D will migrate in the opposite direction of A and B due to the fact that, their isoelectric points are lower than the P^ and

R, *M-

155

m

L-<f

co

co

LO

co

M<r

LO

o

asaqd ptxos aq^ trt uoxqaaquaouoo uxa^oad ‘x

FIGURE

67 - GRAPHICAL

SOLUTION

OF PROTEIN

C VIA MULTI-COLUMN

SYSTEM.

156

m

co

<r

mo

asaqd ptxos aqri ux u o x^bj^usouoo uxaqoad ‘x

FIGURE

68 - GRAPHICAL

SOLUTION

OF PROTEIN

D VIA MULTI-COLUMN

SYSTEM.

157

(1) Protein C: k.

12.0

10.0

(1)

(2)0

0 5 10 15 20 25number of cycles

FIGURE 69 - THE CONCENTRATION TRANSIENTS OF PROTEIN C ANDPROTEIN D vs. NUMBER OF CYCLES.

158

proteins A and B. The proteins C and D will migrate down from the Pg top reservoir (TR) through anion column (M = 1) to the Pg middle reservoir (MR^). Then from reservoir MR^ , proteins C and D migrate through cation column (M = 2) to the Pg reservoir anc* so on until this flow movement of theprotein mixture reaches the Pg bottom reservoir. Figure 70 shows the graphical solution for protein mixtures A and B, where the graphical solution for proteins C and D is clearly- shown in Figure 71. As the steady state condition is reached, the enriched concentration of proteins A and B will be obtained from the top reservoir while the bottom reservoir collects the enriched concentration of the mixture of proteins C and D. The concentration transients of the mixture A and B, and the mixture C and D are plotted versus the number of cycles and show in the Figure 72.

The next step is the separation of the mixture A and B or C and D. At the beginning we had a mixture of four proteins for separation ; up to this point the mixture of proteins is reduced down to two components, either A and B or C and D. The separation of two proteins via multi column has been explained, also the graphical solution of proteins A and B, and proteins C and D are shown and discussed earlier in this chapter.

For mixtures of proteins of more than four components, the separation process begins in the same manner as for the

159

p-iVc m + Ph

Mon

M(N m

on

i—iin

I

+ P-I

m

sn on2S.

0 PQ •H<U Td ■U Gvo

X «<#o

asaxjd ptios atp up uoTpaa^uaouoo upaaoxd ‘x

FIGURE

70 - GRAPHICAL

SOLUTION

FOR

PROTEIN

MIXTURES A AND

B VIA MULT

I-COLUMN

SYSTEM.

160

CO m+ Pt

tNCO

i—I

co uo

i—I

CO CO'

oHCO

p

S O•rHCL) T3 4-> C o coP-i u

<3M>p

p

CJ2 wPi

p H X!

HOP5P<PiO^ a s wO H H coEh >-i !=> COPO gCOgd <1 o c_> oM I

PoMflH

Oaseqd pTIos aq:} ut uo-jp^JiquaouoD ujaqoad ‘x

161

(1) Proteins A & B:

12.0 (2) Proteins C & D:

10.0

M-l•H

o

2510 15 2050 nnumber of cycles

FIGURE 72 - THE CONCENTRATION TRANSIENTS OF PROTEINS A & BAND PROTEINS C & D vs. NUMBER OF CYCLES.

162

four components of proteins mixture. First of all, we are grouping the mixture into two groups of proteins by selecting the pH level, one is the highest (higher than the highest isoelectric point of protein component), one is the lowest (lower than the lowest isoelectric point of the protein component) and the last one is the middle one (the one which separates proteins into two groups). Once the process is completed, both top and bottom products are obtained and then we repeat the same step again, by taking either top or bottom product to separate until the separation of the desired product(s) is reached.

E . A Theoretical Study Via Mathematical Farmalism Based On Elementary Matrix Algebra

This work can not complete without discussion on this title. After we have been investigated on the subject for a length of time. The experiment was performed and dicussed in the earlier part of this chapter for Mode 4. Figures 73 and 74 show the calculation curves of protein concentrations in the six sections of liquid phase (five columns and one top reservoir), and five sections (columns) of solid phase respectively. The calculations were made at the beginning of the cycles, after equilibration at the low pH. The parameters used, were given in the Appendix A and also shown on the figures. Similarly, Figures 75 and 76 show the results of a different parameters used. As expected from the smaller

163

o<r

oon

mono

oCM

o

inCM

mo

L 1S'.

CO

g3H

■asaqd ppnpp sqd up uoppBJpuaouoo upapo-id ‘A.

164

ir>,on <rCM

00OCM

Oun

o-3"

01 0) rH O >■» O °on m oM(U

!

oCM

rH i—I O O O

a s a q d P T I os U T u o t ; h i ^ u 3 D u o d uxa^ojid ‘x

FIGURE

74 - THE CONCENTRATION

TRANSIENTS OF

PROTEIN

IN THE

SOLID

PHASE

vs. N

UMBER

OF CYCLES

(CASE

I).

165

o< 1-

< 1COCMo'

oCO

oCM

o

oo

CO(DI—Io>■>Om05-1<D1

$

LOt-"9pd!=>OHPn

CM

asaqd p-tnxj sqd ui uoj^aarjuaouoo ujapoad ‘A

166

oLT>

Ocn <f ir

ocn

oCM

o

0 0oCM• • • • •

«—I i—1 CD ^D ^D

•3SBqd PTI°S UT uoj^ejquaouoo UTaq.o.xd ‘x

number

of cycles

FIGURE

76 - THE

CONCENTRATION

TRANSIENTS OF

PROTEIN

IN THE

SOLID

PHASE

vs. NUMBER

OF CYCLES-(CASE

II).

167

value of y S , the maximal separation (see Figures 75 and 76) are smaller than the results show on Figures 73 and 74. More detail of extending the stxxdy of this subject is explained and discussed in Appendix A.

The technique of separation of protein via a pH-para- metric pumps seem to work well as discussed in this chapter from Mode 1 through Mode 4. We also established that, Mode 2 and Mode 4 are able to extend the model into a multi-column system. The advantage of Mode 2 is, unlimit on the number of protein components for the separation process. This work is only study on the Batch operation basis and also found the difficulty of extending this work into either Semi- Continuous or Continuous process. Mode 4 is able to run either Batch or Semi-Continuous for a multi-column system. The limitation of work is the pH level. As we observed, the pH level used for this mode is two (either P^ and P2 or P2

and F 3 )> the protein can purify, must has its isoelectric point fall in the range of P^ and P 2 . But some how, this process is work well for recovery any protein component.

The extendind of this work still carry on both experi­mental study and theoretical study by Chen and his students.

168

Chapter VIII

SUMMARY OF CONCLUSIONS

This work establishes the reliability of the model equations for predicting the behavior of batch and semi- continuous equilibrium via a pH-parametric pumps. We have examined one-, two- and multi-column system by both experi­mental and theoretical study. The model is based on the linear equations of change for the liquid -solid system with the diffusion term of negligible importance, a liquid-film controlling mass transfer rate expression, and a linear equilibrium relation between the liquid and solid phases.

This work further establishes the reliability of the method of graphical and the method of using the elementary matrix algebra to predict the concentration curve on protein separation.

There is little to choose between this two computational schemes. The graphical method is more fundamental and more efficient on predicting the steady state value while the matrix algebra method can give us more detail in a transient state.

The agreement between the experimental results and the behavior predicted by computational methods is good. The

169

qualitative differences between separations achieved under varying operating conditions is correctly predicted by both experiments and calculations.

For the process designning on both batch and semi- continuous pH-parametric pumps, the following were noted:

1. Any separation process in this paper, the process is worked on either one component or two components of solute.

2. The separation system is required to use either two or three pH levels at a time.

3. Literally, scaling up column parameters results in no improved separation.

4. Decreasing the reservoir dead volume, decreases the time of operating to reach the steady state condition

170

NOMENCLATURE

a, b, c, d, e, p coefficients in material balanceequations, defined by Eqn. 3.13 (dimensionless)

A, B, ... protein componentI stage number1^ isoelectric point of iIS^ ionic strength in the bottom

reservoirIS2 ionic strength in the top reservoirJ transfer stepk x/y, equilibrium constantkp equilibrium constant at pH = P^

iM number of columnsn number of cycles of pump operationN number of stages or cellsP^ pH level i and higher than pH

level i+1 (i = 1, is the highest)Q reservoir displacement rate,

3/cm /sect^ duration i, secV volume of fluid phase per stage,

cm3-V- volume of solid phase per stages,

cm3

171

3Vr, bottom reservoir dead volume, cmD3middle reservoir dead volume, cm

3Viji top reservoir dead volume, cmW total mass of protein present in

the system, gmx concentration of solute in the

3solid phase, gm mole/cmy concentration of solute in the

3fluid phase, gm mole/cm concentration of solute in the feed, gm mole/cm^

yo

n average concentration of solute intilthe bottom reservoir at n cycle,

gm mole/cm^< yT> n average concentration of solute in

tilthe top reservoir at n cycle, gm mole/cm^

■^yg><» steady state concentration ofsolute in the bottom reservoir, gm mole/cm^

<yT> co steady state concentration ofsolute in the top reservoir, gm mole/cm^

172

Greek Letters

oC ( reservoir displacement)/(columnvoid volume)k” / kp (dimensionless)

i i‘TT/<& duration of upflow or down flow,

seceigenvalues of matrix [m "\ (dimensionless)

^ ratio of volumes of liquid phaseto solid phase (dimensionless)

^ dead volume ratio, defined byEqn. A-4.1 (dimensionless)

Vector and matrix quantities

[A.] matrice defined by Eqn. 3.20~ JC column vector defined by Eqn. A-3.1F^, feed vectors in open parapump,

defined by Eqns. A-4.3 and A-4.4 [i] unity matrix[Ml, te] matrices of coefficients in

material balance equations, defined by Eqns. 3.8, 3.10 and 3.12

fS1, [S matrix of column eigenvectors of[Ml, and inverse

[ d ] diagonal matrix of eigenvalues/v

Indices, Subscripts and Superscripts

+ anion exchangercation exchanger

R+ anion exchangerR cation exchanger*» (00) define the cyclic steady statel,h designate variables defined at the

low pH and at the high pH respec­tively

174

APPENDIX A

ANALYTICAL DETAILING

The following material is the information and detailing for a mathematical formalism based on elementary matrix alge­bra which explained in Chapter III. There follow, in order,

Exhibit A-l, Calculation of Eigenvalues of lM 1 •Exhibit A-2, The structure of [M^00 .Exhibit A-3, Example of analysis of transient region.Exhibit A-4, Extension of the theoretical approach.Exhibit A-5, Tables of the computational results for

Five-Column system

175

Exhibit A-l

CALCULATION OF EIGENVALUES OF [m "\«s/

The eigenvalues of M are calculated from the equation

d-pX e 0 a b-pX c

a 0

0000

00

0 00 0

b-pX c 0a b-pX c 0 a0 0

0000

b-pX c 0 a+b-pX

= 0 (A-l.l)

Since the determinant is tridiagonal, it may be expanded easi­ly, by elements of the last column for example. Let PN-1(^0 be the determinant obtained by deleting the last row and the last column, and let ( X) be the determinant obtained bydeleting the j last rows and columns. We then have (with N = 6):

v x > = (a+b-pX) P ( X) - ac P4( X )p5(A) (b-pX) P4( X) - ac P3(X )

= (b-pX) P3( X) - ac P2(X)p3a > (b-pX) P2(X) - ac P ( X ) (A-l

176

P2(>) = (b-pX) P1('X) - ae Pq('X)P1('X) = <d-p>) PQ(>0Pg('X) = 1

A trial value of X is assumed and the successive expressions P^(i = 1 to N) are calculated. An eigenvalue is found when PN( >v) = 0 .

The localsation of the eigenvalues, and thus the trial values, is facilitated by the fact that the expressions P^ form a series, which permits the following test:

Assume a value and calculate the sequence Pq ....... P j. Let V(X) be the number of sign changes in this series. Assume an other trial value V ' and determine in the same way the number of sign changes in the sequence V(7v!). The diffe­rence V( X) ~ V( X) gives the number of real eigenvalues in the interval ( X', X")* This property may be used to show that all eigenvalues are real. We assume X' very large and positive and x" very large and negative. It is then easy to see that

V > > o X' < < op 0 = 1 > ° p 0 = l > o

P. = d-p^ < 0 Pj = d-pC\ > 0

P2 - <b-p>) Pj- ac > 0 P2 - (b-p'X) Pj- ac ,> 0

P 3 < 0 P 3 > 0

177

? „ > 0 > 0P5 < 0 P5 > 0

V o p6 > °

The numbers of sign changes are V( X) = N and VC^1) = 0 and the number of real eigenvalues, positive or negative, is N. Thus all eigenvalues are real.

The sturm sequence A-l.2 may also conveniently be used to show that X = 1 is an eigenvalue. For *X = 1, we have

PQ = 1 > 0

?1 = d - p = -kh ( S + k1)< 0

? 2 ~ (b-p) P^ - ac = -aP^

P^ = (b-p) ~ acP^ = -£d?2 ~ ~ acPi = -aP2

Pj = (b-p) Pj_j " acPj _2 = "aPj-l “ cPj-l “ acPj-2and since P. =-aP. 9

we have

Pj = _aPj-l

For the last polynomial P^, which represents the character­istic equation, we have:

PN = (a+b“P) pN_i - ac pN-2

with a + b - p = - c

and pn _i = “ aPN-2

178

thus Pjjj = 0

and X = 1 satisfies the characteristic equation and is thus eigenvalue, independently of the values of the parameters. Incidentally, this calculation shows that V ( V = 1) = N-l. Since V ('yi > 0) = N, there is a single real root in the interval (+1, +oo) which is precisely X= 1. No eigenvalues can thus have a value larger than one. A somewhat more tedious calculation can be made for •X" = 0, showing that V(^' = 0) = 0. This ensures that all eigenvalues are positive, and finally, we must have

0 * *0 * \ * .... * * * ■ 1

Figure A-l.l shows the plot of ^ as a function of the number of cycles (n) on the Semi-Logarithmic ordinate.

eigenvalue

179

10

0.0011 5 10 15 20 25

n, number of cycles FIGURE A-1.1 - THE PLOT OF'V? vs. NUMBER OF CYCLES.

180

Exhibit A-2

THE STRUCTURE OF [ Ml00

For large values of n, that is at cyclic steady state,M n must satisfy for N+l equations

limit [Mln Y(0) = Y(oo) (A-2.1)n-^00

independently of the initial distribution (0). The concen­trations (Wq , w^, w^) of Y(0) , and the concentration(y*, y*,..... .. y^) of Y(oo) are related only by the condi­tion of conservation of mass of solute in the whole system.This condition is expressed by:

N -iW = V ( ?wn + T ( f + k1) w.)J U i=l 1

= v (Jyg + 2: (?+ k1) y!) (A-2.2)

^ ^ — T_ ^Replacing y^ by yg p , from Equation 3.24, factoring out yqin the right hand side and re-managing, we obtain

* N yQ = Aw q + B Z Wj (A-2. 3)

where:

A = ? j B = T + k 1 A (A-2.4)i JL? + (?+ ki) Z p " qq=l

181

Cleary the N+2 equations A-2.1 and A-2.3 may hold for any setof w. only if they are redundant: we may thus identify, for

tinexample Equation A-2.3 with the i equation of A-2.1, whichwe write (i = 0, 1, N)

“in m n ■ = y o ? ’1 (A-2.5)

and we obtainA for j = 0

B for j =1,2,(A-2.6)

N

The elements tn^ of Jm} are thus completely identified by Equation A-2.6, together with A-2.4. [ M)n may be visualizedas:

[m ]GO

A B B .............. . B

A p 1 B p-1 Bp-1 B p 1A p 2 B p 2 Bp“2 B p 2

AprN B P '1* B p N B p N

(A-2.7)

It may be verified that this matrix is invariant on multipli­cation on the left or on the right by [m ].

It is interesting to look at the other possible approach starting from Equation 3.17

182

fm "J°° = Is M d ^ s V 1 (A-2.8)

Clearly 1®}°° reduces to the single element 1 in the last rowand last column, all other element being zero. The product[S\ lDl00 is a matrix with the first N columns of zeroes, thelast column being the last column of [S ] , that is the eigen-vector belong to A = 1, Multiplying this matrix by weshould recover the result of Equation A-2.7. It is easy to

_ *1show that the only elements of that appear in the pro­duct are the elements of the last row, which are the cofactors of the above mentioned eigenvector in Is}. Identifying with Equation A-2.7, we conclude that the last row of [S1— is-■“V

( A B B B ...... B ).

183

Exhibit A-3

EXAMPLE OF ANALYSIS OF TRANSIENT REGIME

The equilibrium constants (Figure 21) are charaterizedfollowing values of the slopes

at Low pH: k1 - 0.70at H4 gh pH: kh = 0.52

k1P -

1.346

This corresponds to the experimental conditions of Run We also have:

V 26 cc fluido = = = iV 26 cc solid

and N = 5 since there are five stages. With these values,

f M ] =

1 is written (Equations 3.12 and 3.13)

1.70 1.19 0 0 0 00.52 1.364 0.70 0 0 0

1 0 0.52 1.364 0.70 0 0

.584 0 0 0.52 1.364 0.70 00 0 0 0.52 1.364 0.700 0 0 0 0.52 1.884

The eigenvalues, calculated as outlined in Chapter III, are:

184

*0 = 0.1050 >3 = 0.7336

= 0.2522 ^4 = 0.9239

= 0.4838 ^5 = 1.0000

(NOTE: Calculations were performed with 8 significant figures)

In Run , the initial condition is that all fluid fractions are identical, and in equilibrium with the solid phase frac­tions with the following protein concentrations (i = 0, 1, N) :

w = y^(0) = 1.18 gm/liter "j equilibrium at Low pHx^(0) = 0.826 gm/liter

so that the total amount of protein is:

W = 0.290 gm of protein

then from Equation 3.28, we calculate

y-Q = 2.324 gm protein/liter

The final steady state is then given by Equation 3.26*

Y1(oo)

^0*?1*^2*^3**

= 2.324 = 1.726 = 1.282 = 0.953 = 0.708 = 0.526

185

New, we should like to know the composition at an arbitrarycycle n. In principle, we would have to calculate inorder to use Equations 3.17 and 3.18, or calculate the [A^Iinorder to use Equations 3.19 and 3.20. We shall see that thesetedious calculations may be partly avoided if only estimations are sought, and for n sufficiently large. Equation 3.17 or 3.19, when developed, lead to expressions of the form:

Y (n) =

a0 0 ^ + a01^1 + a02^2 + a03^3 + a04^4 + y0

a 1 0 0 + all 1 +

a2 0 ^ 0 +

yl*

y 2

a3o'Xoa \ n 40 0

\ n50 A o ------------------------------------ + y5

the last column corresponds to Y (oo) . The examination of the successive powers of the X ’s shows that the contribution of the smallest eigenvalues becomes rapidly negligible. This is illustrated on Figure A-l where In W? is plotted against n. We observe that Xq becomes neligible with respect to 1 (Xq .< 1 0 - ) as early as the third cycle, X ^ around the fifth cy­cle, X 2 around the tenth cycle. The contribution of X 3 per­sists until the 2 0 ^ cycle, and that of X^ until the 90t*'1 cy­cle. These contributions are somewhat modified by the factors a ^ , but these actually reinforce the importance of the larg­est eigenvalues. Figure A-2 shows a comparison between the

186

rigorous curve (full line) and the approximation obtained by- neglecting the contributions of X-^, 'V,, This relation isexpressed by:

Y(n) - Y(oo)fsJ

with

C

=

- 1.024- 0.563- 0.090 + 0.339 + 0.540 + 0.615

(A-3.1)

and w = 1.18 gm/liter

It is seen that this approximation, besides showing the cor­rect trend; gives an estimate better than 1 0 % for n >3, bet­ter than 5% for n ^.10, and better than 1% for n ^20. For all practical purposes, it seems thus sufficient to calculate the matrix corresponding to Xj = 4 in Equation 3.19, orin other terms, to calculate the two lines in Is}- that cor- respond to the two largest eigenvalues.

Note that Equation A-3.1 is comparable to a result estab­lished by Pigford et al (1969) for linear packed bed parapumps after a certain start-up period. Using their notation, their Equations 3.16 and 3.17 may be put in the form:

1 -b n(yT )n - - <yB )n - = (-J+5) y0

which expresses, that the "distance" from the steady state

187

for top and bottom reservoir concentrations is a power func­tion of the number of cycles.

188

Exhibit A-4

EXTENSION OF THE THEORETICAL APPROACH

The discussion illustrates that in any experiment, we would be faced with imperfect phase transfer, volume varia­tions of the fractions, volume differences in the stages, and so forth. In addition, the mode of parametric pumping consi­dered here is restrictive: it ignores partial reflux and mul­tiple transfers per half-cycle, situations studied elsewhere (Grevillot, G., and Tondeur D. 1977, 1980) from the point of view of the cyclic steady state. We should like to give a hint on how the present approach can be extended, without major difficulty, to account for some of the situations men­tioned above. For this purpose, we shall examine how the basic equations are altered separately by the different eff­ects .

Existence of a dead volume

In the experiments presented, we mentioned that some of solute (protein) was not transferred when the apparatus was connected to the reservoirs and pH-converters. Let us charac­terize this "dead volume" V,p or Vg, by its ratio V to the volume of the solid phase fractions.

= VT/V = Vfi/V (A-4.1)

189

and we assume this ratio is constant and equal for all stages, in transfer up and transfer down. When the material balances (Equation 3.1) are re-written, taking this hold up into acc­ount, one obtains the same form as Equation 3.5, but with p

replaced by <g - V, by and k*1 by k*1 + V; (so thattlthe denominator p + k in Equation 3.5 is unchanged). A sim­

ilar property holds for the transfer up half-cycle, and final­ly the whole approach outlined so far remains valid providing the substitutions indicated above are made in the elements of matrix [m]. The discontinuous lines on Figure A-4.1 show the resultof such a calcultion, made with a 10% dead volume of solvent (.'6= 0.1) which slightly overestimates the reality.

Intuitively, the effect of V can be foreseen by consider­ing the system as having a lower p , and higher k's, but a lower effective ^ . The effect on the cyclic steady state is seen immediately from Fenske's equation (Equation 3.25), with data given:

*y0 _■ r <%

' k 1*5 •

L k h + * .

= 3.29 for 0

The effect of a smaller p and larger k's is favorable to speed of convergence but may be offset by the decrease in yB .

Unequal volume of fractions

A simple modification accounts for the volume of solid phase being different in each stage, and the volumes of each

190

fluid phase fraction being different, providing these volumes are constant (same volume transferred up and down). It suf­fices to take a different ^ for each stage and for equilibra­tions at different pH levels. In the transfer down matrix [@^1 (Equation 3.8), the unique will be replaced by dif­ferent in each line, and similarly, in matix [0-jl , q will be introduced. The product matrix [Ml remains tridiagonal, and the methods for eigenvalues and eigenvector calculations are unchanged. All the other properties mentionned still hold.

Volume variations of phases

As discussed earlier, important variations of the volume of the fluid fractions may be caused by geometric dissymmetry of the apparatus in transferdown versus transfer up, and by dilatation of the solid phase. These effects can be quanti­fied and accounted for in writing the material balances. Un­fortunately, they will cause the value of f to change each stage and at each cycle. Therefore, there is no unique mat­rix [M ] and the approach presented fails to apply.

Several transfers per half-cycle

Suppose the apparatus used in the present work was equip­ped with an additional reservoir in series at each end. Then seven fluid phase fractions would be used, and there would be two successive transfers in the same direction at each pH lev­el. The cyclic steady state of such system has been exten­sively studied (Chen, H. T., et al 1980). The matrix formal-

191

ism can be used conveniently by noting that each transfer of fluid, phase follwed by an equilibration is described by a bi­diagonal matrix similar to[0..) or Let us consider-v J- ftfor example a parapump with two stages and four fluid phase fractions thus two transfers per half cycle. The matrix describing the complete cycle is the product of successive bi­diagonal matrices describing each transfer;

^ 1 2 ^ ( ?+ k l) (? +kh) l © h 2l <? '|-kh) (? +kl>

'j+k^-o 0 0 ftkh 0 0 0 k1 0 0

1—1 0 0 0

0 ^ k 1 0 0 kh ? 0 0 0 f k1 0 0 5 k1 0

0 kh £ 0 0 kh ? 0 0 0 §+kh 0 0 0 S k10 0 kh ? 0 70 0£+kh 0 0 0 5M-kh 0 0 0

t—1 •

a n d [ M l . i Q lJ t a j i e h2\ t o h l i~ 1 9 h 9(J + k1) ( 5 + k )

{M]is no longer tridiagonal, but in the present case, compri-/v

ses 5 diagonals. The simple numerical methods for calculating eigenvalues and eigenvectors of tridiagonal matrices no long­er apply, but otherwise the general method is unchanged.Also notice that different definitions of £M] may be introdu­ced, depending on how the beginning of the cycle is defined. These various forms differ from each other by a circular per­mutation on the bidiagonal matrices 10).

Partial reflux parapump

192

We adopt the description given by Ghen:rH.Tt,et al (1980) for one transfer per half-cycle, in a pump where fresh feed is added at each half-cycle in an intermediat stage, and with a different reflux ratio at each end. The operating scheme of such a pump is summarized on Figure A-4.1. The equations describing the operation of the lower section during the low pH half-cycle, and the upper section during the high pH half­cycle are that of the simplest case, that is, Equation 3.1 to 3.10. The other equations are that for a holdup in each stage, as explained in a previous paragraph (p replaced by 9-Y, k by k + K). Special material balances must be writt­en for the feed stage. The result may be written in the fol­lowing form:

column vectors representing the feed contribution. Table A-4.1 give the elements of these matrices and vectors, as cor­responding to the stages in which the conservation and equili­brium relations are written. All other elements are zero, yp is the feed composition, assumed constant. The feed vec-

Yh (n) = IB ] Y1 (n) + F,~ n — n (A-4.3)

andY1 (n+1 )= [0. J Yh (n) + F-,

= ISi1 [§>hJ r (n) + L®iLFh + Ji

where tf*h> and \Q } are bidiagonal matrices and F^ and F^ are

Table

A-4.1

193

H

<y\o O

pnt*.i—i

> 0

0

j—iS '✓>—'■*I—1+S ?

Lower

diagonal

& +Main

diagonal rH

+Q o

1—1 >o1 : Q*

1—1 1

Q/~>

rCfo,

o*v-/o 0 O

*^cSS . *

1 * .<y>

Upper

diagonal

+ i—H

t—1 t-HA5

Main

diagonal &>i

O v

>0^1Qr\

0 ^+Q o

jSta

ge or

reservoir

1Top

reservoir

Stage

in

top

section

Feed

stage

Stage

in

bottom

section

Bottom

reservoir

Index

of

stage

1, 2,..f-1

f(feed)

f+1,

f+2,

......

N

194

tors F, and Fi have each a single non-zero element, owing to the fact that the feed is added in a given single stage. The non-zero element is not on the line in the two vectors because the feed is mixed with a different mobile phase fraction, in the high pH and low pH steps. Note that a feed distributed over several stages can be accounted for by the same Equations A-4.3 and A-4.4, but different elements in the matrices andj©^^, and additional non-zero elements in F^ and F^.

The general solution of the first-order recurrence of Equations A-4.3 and A-4.4, relating Y^(n+1) to Y^(n), is easi- ly seen to be:

Equations). The matrix [m 3 is still tridiagonal and the met­hods for calculating the eigenvalues remain valid. The geo­

written by applying Sylvester's theorem (Equations 3.19 and 3.20) to each term, so that a scalar geometric series appears on each eigenvalue. If all 's are different from 1, Equation A-4.5 becomes

(A-4.5)where |m ] Equation A-4.5 is to be compared toEquation 3.14 (Note: that [m ] is not the same in these two

A.J(A-4.6)

195

where [A.] are matrices obtained from Trilby applying Equa-/V J ' #-*tion 3.20, and F is the overall feed vector, given by:

0 0

?*hV ^ S + k 11) + Vhkh

o o

the two non-zero elements of F are on lines f and f+1.

If any eigenvalue was larger than or equal to one, theO Tseries Li + M + M + Mn“ J would not converge and no** ***

steady state would be reached. On physical grounds, we may thus state that all eigenvalues are smaller than 1. Under these conditions, the cyclic steady-state is not obtained di­rectly as an eigenvector of Tm ], but by letting Y(n+1) = Y(n)*vin Equation A-A.A, or n — >oo in Equation A-A.6:

Y (co) = [i-M) *F = J ‘F (A-A.7)j=o 1-X

We know that the cyclic steady state can be geometrically re­presented by a Me Cabe-Thiele diagram somewhat more complica­ted than that of total reflux, and that the analytical expres­sions for the separation factor are quite involved. There is thus little hope to bring Equation A-A.7 to a more analytical

^FF = F. + IG.If. = T—i (2+k1) (f+lO

196

form by simple manipulations.

197

Exhibit A-5

Conditions for Computational the Results with variable parameter:

Operating Variable Cases I Case II3 1Volume of Fluid Phase per Column 26.0 cm 30.0 cm3 3Volume of Solid Phase per Column 26.0 cm 30.0 cm

Equilibrium Constant at Low pH 0.70 0.75Equilibrium Constant at High pH 0.52 0.60

p 1.346 1.250p 1.0 1.0

Table

A-5.1

198

o o O mm o in <r O r".

X VO in <r ~d" CO■ • • • •o o o o o

o CM i— i o- 1— 1-cr o VO r'- CM o

X r'- VO m m m• • • • •

o o o o o

o co VO CMoo o VO o oo r".!x! oo r-« VO vo

* • • • •o o o o o

o CO <r CM 00CM in VO i". 00 00

X oo 00 00 00 oo• a ■ • a

o o o o o

o CO CM I"-.1— 1 o I— 1 i— 1 m r"-

X o o i— 1 t-H *— i■ • • * •1— 1 1— 1 i— 1 t— i i— i

o m -d" o *— im oo 00 o r»1— 1 r- VO VO m• • • a «1— 1 o o o oo m CO i— i00 in CM VO CM

kO 1— 1 Ov 00 I''-a • • ■ •

1— 1 o o o O

o m rH CM r-~CO oo cn CM 00 votn 1— 1 o O CTi o\

• • • ■ •rH i— i rH o o

o oo -d" m n*CM 00 I— 1 VO r"- r".K~> 1— 1 CM CM CM CM• • • • «

I— 1 i— 1 i— 1 i— i rH

o i— 1 CM CM m1— 1 00 m Ov m oo>> 1— 1 CO m vO VO

• « • • •I— 1 i— i i— i i— i 1— 1

o <r VO <ro oo CM OV *— i VO!>> 1— 1 00 o CM <N• • a • *

MMOj-i m

I— 1 i— 1 CM CM CNl

OJ QJ I— 1 i— 1 i— 1 O O-s6 o 3 >> S o

i— 1 CM oo

Table

A-5.2

199

wCO<3uSOMHsHSWOSOO

WH§P-i

o CNJ in. CO I—1m o in r-» o m CO rHX 00 VO m in NT <r <r• • • * « • •o o o o o o o

o in r-N oo CO CO CNJ<r o CO in. o VO COoo in. VO vo in in ma • • • • • •o o o o o o oo o 1—1 in COCO o 00 in i—i <ys 00 r.fxj 00 r-» in. in. VO VO voo o o o o o o

o CO in <r vo rHOH o o i—i co <3* -<r infx* oo 00 00 00 00 00 00• • • • • • ■o o o o o o o

o <r CO o VO in rHrH o in CNJ o vo r-X 00 00 ON o o o o• • • a • « •o o o rH rH rH rH

o in CN] 1—1 CN <3*in o r" IN. 00 O 1>-> CNl ON oo IN. VO 1« ■ • • • • 1•-1 o o o o oCO 00 <r VO CNJ in<r o I—1 co n J- 00 <3* 1CNJ I—I o O n 00 00 1i1—1 I—1 i—j o o o t

<r <J" in CNl m inco o 00 co i—1 m <o 1fn CNJ rH *—i i— 1 o o 1

a ■ • • • • 11—1 i—1 i—i i—1 rH i—i

I—1 in. 00 CNJ 00CNJ o i—i CO JN. 00 Ch 1►n CNJ CNJ CNJ CNJ CNJ CNJ 1• • • • • • 11—I I—1 rH rH tH rHCNJ o l—l CNJ coi—i o o O CNJ 00 i—i 1rH CNJ CO <r in in VO 1I1—1 I—1 i—i 1—1 i—i tH i

o ON CO <3- o vOo o rH oo r-N tH 1CNJ in vo oo O O 1■1—I I—1 i—j i—i CNl CNJ i

QJ 0)

S O

VO O<N OCO o■<r om

200

APPENDIX B

EXPERIMENTAL DATA

Information and Condition of the experimental results are as follow.

Exhibit B-l Exhibit B-2 Exhibit B-3 Exhibit B-4 Exhibit B-5

Sample of Calculation Single Column System Two Column System: Mode 1Two Column System: Mode 2Two Column System: Mode 3

Exhibit B-6, Two Column System: Mode 4

201

Exhibit B-l

Sample Calculation:

1. To calculate the concentration of Haemoglobin, (using a 0.02 weight percent solution)

a). Via 403/* Reading: (Any pH Value)

Reading of Sample at 403 Rg 403Initial Reading of Feed at 403/°* Rp 403

= Concentration of Haemoglobin

b). Via 560 /*, 576/<and 630/'*- (A^, A2 and A^ respectively)

Concentration of Haemoglobin = ^ C Sample.e^ C Initial

pH = P3(4.0);C4 0 = (2.593x 10"3)A1 + (4.483x 10_5)A2 + (1.741xlO"4)A3

pH = P2(6.2);C6 2 = (2.505x 10"5)A1 + (4.525xlO"5)A2 + (1.808xl0"4)A3

pH = P1(8.5)Cg 5 = (1.958xl0"5)A1 + (4.789x 10"5)A2 + (2.214xlO"4)A3

Thus, the concentration of Haemoglobin (y^) can express as:Cp^ of Sample at 560/4, 576y«and 630yU______________

% Cpjj of Initial Feed Reading of 560/* , 576^//and 630/*

202

2. To calculate the concentration of Albumin, (using a 0.02 weight percent solution)

Reading at 595J*

Thus:

Total Protein Concentration (y^) Albumin Concentration (y^) + Haemoglobin Concentration (yjj)

yA yAH yH

Let, RS595RB595^595RS403RF4030.04

0.02

Reading of Sample at 595J*- Dye Reading at 595y**Reading of Feed at 595/J

*Reading of Sample at 403y**Reading of Feed at 403 y*

Total weight percent of Haemoglobin and AlbuminComponent weight percent

A

RS595 ~ RB595 RF595 “ RB595

(0.04) - RS403 (0.02)RF403

(0.02)

* NOTE: One can use the calculated value of Haemoglobin via560y , 576 A and 630/< also.>0 M , 576 /* and 630/<

20354Pu 01o v a) s h v

PO !>i PPO 4-)

"H O 54•H cd i—Ipj i—i ao o cdH 0 0 so

4-14->OPP 54

Q) 44<44

FP

mo mo ino mo mo 05 ino 05 025 mo ino 05

mCMo• • • • • • • • • • • • •o o o o o o o o o o o o o

t—i i—i i—i i—i 1—1 r—4 1—1 mvO inCM 1—1 1—1• • » • • • • « • • •o o o o o O o o O o o

04 04 04 CM CN] CM CM mo mCM mo CM CM mCM• • • • • • ■ • • • • • •o o o o o O o o o o o o o

i— ioo

01CM rH1 bO

PP G•r4

44 CO•r4P 54»|4 OP PfxJw CO

54ai4401

54cdp

cd■U

s$

*Jtx!

W

4-1

sIo cd 0) t-4

CO pa) to

P t4 p

54•HoB

MM1-4

4-1O '

4-1O '

CO in m in• m in in in in m in ms CM CM CM CM CM CM CM 04 CM CM m o 04o CM CM CM CM CM CM CM CM CM CM CO 1—1 CM

CO0 P0 oW H01

4-1O '

4-1

i—i B0 o> 4-1

4-1”d o o01 PP 0)

P

4-1Sai0 otu -o 01td 4-i

r—i td P 5-4to•r4P

o o

to

CO

o o o o o o oi—I i—1 f—I i—I i—I i—I i—! o o o o

m m o o04 i-H o o i n m i n o o i n

§

•S

P/—N 1 IEr-S <1•y gV Poai wj a) o P 0

0) tdtx

ro CO CO CO CO CO CO CO CO1oCO CO CO CO1o 1o 1o 1o 1o 1o 1o 1o 1o 1o 1o 1o1—1 i—H 1—4 I—1 1—4 I—I 1—4 i— 4 1—1 1—1 1—1 i— 4 rHX X fx! K X X !*! *xj !* 1*! X !*: XCO CO CO CO CO r>- o CO CO CO CO COCO CO CO CO CO VO o CO CO CO vO CO CO• • • • • • • • • • • • •00 oo 00 00 00 VOI— 1 25 00 00 00 VO 1—1 00 00

CM CM CM CM CM CM CM CM CM CM CM CM I— io o o o o o o o o o o o o• • • • • • • • • • • • •o o o o o o o o o o o o o

CM CM CM CM CM CM CM CM CM CM CM CM I—io o o o o o o o o o o o o■ • • « ■ • • • • • • • •o o o o o o o o o o o o o

04

vOII04

P

njsinooIIi—iP

I i - l 0 4 COc M c o - d - i n v o i ^ o o a v i - i

TABLE

B-l

204

i lo O <r 00 o n <r 00 v O VO mo OO 00 1— 1 rH CN rH rH o n o o• • • • • • • • • • •

rH o o rH rH rH rH rH o rH rH

*

CM

Pi

Pi•HrO i— !<3

CM

VOII

.— vCMCHpico

*smcr>m

Cl>•» I

■ Ain•V m <T>

1 oo in

1— 1 O

IIO Pii—i •»Pi P-t a)o rH•H aa Pi roc H CJ

CTv 1—I O o in 00 vO ■<r vO rHm o VO in m CN O i—I e'­ CO CNo CT\ OV CM Csl in CN CM er! rH rH• • • • • • • • • • •rH o O rH i— 1 rH rH tH o i—1 i—1

o CM iH CN i—1 00 ON CO vO VO VOo vO OV O i— 1 rH CN CO CM rH rH■ • • • ■ • • ■ • • •rH o o rH i—1l— 1 i—I p H i—1 i— I i— 1

OO m CO i— I ON ON OV O'. OV ON mCTv in o 00 1—1 CO m CO 00 r-'OV r-~. o n ON ON O o O o O N O'i• • • • • • • • • • •o o o O o rH 1— 1 I--1 1— 1 o o

o• rH CN co <r in VO r-. oo ON o

a>!>v«ooocnCDT-ICOCJo

O'!m

W|>> Io CO 00 CO 00 VO C O nr in COo m CO CM rH o o o CM o o• • • • • • • • ■ • •

1—1 o o o O o o o O o o

CMVO

COo<r

Pi

Pi II•r-i40 /— * fflO CMrH cn00oB Pi<u pqw *> COin o

• <rpj

rH

00

IIoo Pi1—1 *v

pi cn CDo rH•rH oa Pi !>.< EH O

co CO VO r-» oo co -d" in CM coCO 00 VO pH in CO CM i—1 o CM rHCM pH i—1o o O O rH O O• • • • • • • • • • •o o O O o o o o O o O

o rH OV VO CO <3* in ov oo CM CO CO <r <r <r <r CO ~cr• ■ * • • • • • • • •o o o o o o o o o o o

CO 1—1 pH r-~- OV 00 <i* rH in av pHo av VO VO 00 av 00 ON ON voo o pH i—i 1—1 i—i rH 1—1 rH pH t—i• • • • • • • • • • •o o O o o o O O o O o

o• i— i CM CO in VO r*- oo av oM

TABLE

B-2

205

mo 1-"- CO CN cn co m m in p". r-»o m CO oo oo oo oo 00 p-• • • • • • • • • • •o o o o o o o o o o o

CN CO

•H II•s ~i—I CNbO PM O§ Phcd pqm

cno'CP

mi tn I

9s o

i— iinCO

<P

oo II/— V a

Pi 1—Io PM a)•rl c_/ rH4-1 acd Ptfu H a

OC o cr\ cn 00 o rH <P 00 COo o CN •<p r- m CO ~d- <T> CTco VO CO CO CO CO CD CO in m• • • • • • • • • • •o o o o o o o O o o o

o 00 <r i—1 !—1 co CN o 00 r- COo CO m <p CN i—i i—i 1—1 o o o- • • • • • • « • • •1—I o o o O o o o o o o

00 in o i—i cO cn CO CO CN 00 or-- CN CN CN CD CN cn CO m COm -<r cn rH i—! o o O o o• • • • • • • « « • •o o o o O O o o o o o

o• 1—1 CN cn <r in co p- 00 cn o

miK> Io CN n- 00 o cn i". in < p m < po CO cn CN CN i— i o o o o o

• • • • • ■ • • • • •1—1 o o o o o o o o o o

cn

m

a•Hmoi—i bO Ocdm

CNcOIICN

PM

mpq

cno-d-

(?l

5cm cno• <r

1—100

IIou Pil— 1pi PM a)o c/ *—I

•rl od m kO<3 Eh CJ

oo ~d" CN OO o CN o CN r-- oc 00o in in oc 00 m cn CN rH 1—1 1—1<r CN i—i o o o o O O o o• • • • • • • • • • •o o o o o o o o o o o

o CO o CO cn cn cn CO o cno i—1 <p m m <p <r >d- <r cn• • • • • • • • » • •o o o o o o o o o o o

CN in CN n- cn m cn o •o- 'CP cnO co CO 00 i—i i—! cn o r-» CO mO o i—I rH CN CN rH CN rH i—1 rH• • • • • • • • • • •o o o O o O O o o o O

o• 1—1 CN cn •<r m CO 00 Oc o

206

o CO vo t—1 CN cn CN in -3" rH rHo in <r CO CO i—I i—1 o O O O• • • • • • ■ • • • •rH o o o o o o o o O o

*

COIPQW9H

vo

Pi

o<3"IICOPhPiPQ

CNCDIICN

Ph

piH

in VO CD in o ~3- m CN IN. cn IN.m rH o CO CO CO CO CN O CO IN fNO'. rH cn IN CD CO m m m <r <rm • • • • • • • ■ • • •i—1 o o o o o o o o o o

O o in -3- 1—1 CO CO CO m cn 00< o m 00 00 o CN CO CN *—i o oPo • • • • • • • • • • •o o o o 1—1 i—1 1—I rH *—i rH 1—1

r^ 00 in 00 o rH CN cn rH rH |Nm 00 r- in 00 in m IN CO 00 m <rcn <3- cO 00 00 cn o o O cn cn cnm • • • • • « • • • • •o o o o o 1—1 I—1 i—1 o o o

P<u a

l” 1 • 1—1 CN 00 *d" m CD in 00 cn oo H I—1

o

O cn 00 CN cn 00 t—1 CO |N 00 CO<J o <r cn 00 cn cn cn cn 00 00 00>n • • • • • • • • • • •o o o o o o o o o o o

in

pi

.5rQH<s

o oC o•rl•UnJ pd O JH

in'* i—i o i—i CO IN IN CO CO <1- m cuI-N CN CO rH oo 00 in cO -3- CN rH t=Ncn Hf cn o O o o o O O O O Qo m • • • • • • • • • • ■-na­il

o o rH rH I—1 t—1 i—i i—1 rH 1-1 i—1 oao

r—\ o r • 00 P". IN o CN cn CO cn Hj- COCO <i o l-N co <r CN CN CN i—i i—1 rH CN NPh Po • • • • • • • • • • • 0)-—/piPQ

I—1 o o o o o O o O O O 1—1 1

iH <r co CN CO <r rH cn CN O cn C/3•» m hT m in CO CN 00 00 m CO m co OCN cn t—1 cn 00 IN VO in m m in m in O• in • • k • • • • • • • •COII

i—1 o o o o o o o o o o

0.1

CNPhaCDi—IOfnO

O c N c o < r m c o i N o o c n o *mO'!m

TABLE

B-

207

*?\o CM CM m <J\ m CO <r 00 CO LOo LO O rH CM CM 1— 1 x—! CM CM CM• • • • • • • • • • •o o rH rH rH rH 1—1 t— I rH rH rH

rHO

O

oo Pi— O

•HPi 4->2 nj

P i U

o< 1-

a oo•rj P h

rO P3r-1 FQ < 1Pi <N |1 CO

IICM

P h

AinCT>m

*

<urHoPnu

OO m rH o cn CO cn 1—1 cn co 00CM r-. cn 00 co CM e'­ m m 0)<r r- 00 ac CTi oc OC Ov er! o> oc |5n• • • • • • • • • • • no o o o o o o o o o o CJooo 00 CM i—i o o o o o o o •o in CM o o o o o o o o cn. • • . • • • • • • •1—1 o O o o o o o o o o a)i—i

o 00 Ht rH m -d- i—i o -ci- cn ac COin oc 00 00 oo in CO m in m -cr oCT\ o m -d- <d- <r <r <r <r -d- -d- om • • • • • • • • • • •rH o o o o o o o o o o

0.1

oc M c n - d - i n c D r - o o a c o Ain 'inONin

CM

CO

5 iirOO /-v i— i c mbO Ph O

§ Pi tti P3

«

W|I

ono

o rH CO r- r- CO cn CD m <ro CM CM cn cn co cn cn cn cn cn• • • . . . • . • • •o O o o a o o o o o o

o CO I"- co 00 i—i oo <y> in *— io o\ CM m vo CO m <r m m mo o i—1 i— i i— i i—1 rH i—i i—i i—i r-H• • • ■ • . . • • . *o o o o o o O o o o O

o CO 00 CO <r cn cn cn cn cno <r rH o o o o o o o o• • • . • . . • • . •rH o O o o o o o o o o

'S ac CT\ 00 CO 00 <r I'- m m cn -d-on cn 00 r-- CM 1— 1 i— i rH l— i rH i—i i—im o <r i—1 o O o o O o O o o

• « • • • • . . • • * •o o o o o o o o O o o o o

I

o oa o•rl4-1nJ pi O H

Ph CDi—I O Pn O

uc M c n < f - i n c o r ^ o o a > o

TABLE

B-5

208

s•H3rHC

o<r11coPh

Pipp

!?l

LOCTLLO

o o co m uo CM tn CM m 00o LO CO O'! o O o O o o O• • • • ■ • • • • • •

I—1 o o o o o o o o o o

I-'- t-l CM ON 00 r o LO cnco CO r. CM o 00 o\ o> cn cn1—I CO LO vo in <3" <r <U• • • • • • • • • • • tot— 1 o o O o o o o o o o 1=1

Ooo m cn m 00 CM o o r- <1- CO oo o cn CO CM co CM CM o o •• • • • • • • • • • • ooo rH o T— H i—I rH rH rH i—i rH rH (U I—IS'

* > a\ LO O'v CM CM O in 00 00 LO cn C/3m in oo CT> CO m CM CM CM cn i—i

CM cy\ CT\ o CM CM CM CM CM CM rH rH O• LO • • • • • • • • • • • aVO o o \—f i—1 rH rH rH rH rH l—1 rH

I

1—I OcoPJo•H%

OiPhPiH

Cm,CDrHou

CJM cnro-ct-mLor-cocn ■itLOcn

LO

K oo cn~d- incncno cncn oocn mo LOO r--cn cncn i—icn

o O o rH o o i—! i—1 o o o

cn

Pi

CSl

LO •H IIrQOi—1 cnbO Ph O§ Pi td pq Cd

coo<r

Cdl>%

- cnm o§ • <}•i—1O

ooIIC_>

£G l—1 *o Ph cu•H rH4-J ocd Pi tno H o

cn in CM rH VO CM in t". cn cn cno o OO O rH i—1 LO r-~ o m <ro <r r o\ 00 00 00 oo oo r-'• • • • • • • • • • •o o o o o o o o o o o

o m i—! CO t—1 r- LO m m <ro CO CM 1—\ o o o o o• • • • • • • • • • •rH o O o o o o o o o o

m VO CO 00 LO 00 cn CO oCM o in O'* oo m co CO cn CO00 <)• CM rH o o o o o o o• • • • • • • • • • •o o o O o o o o o o o

o• rH CM CO <r m LO r-~ 00 cn o

TABLE

B-6

*Vcnm

o

-3-II

•H c_r

< •> m- 03 cnincoT— 1 11O

CM u .**■>*» dt— 1 CM ■s

d PM CU0 r— 1g •rH O9 d Pi >nC3Pj <! H O

o-3*CMCO

Ml PM O§ p icd PQa a- O'V

m o

00rHO II0

1—I di—I d r—1rrS 0 P-l cu•rH __' 1—1g 4-1 09 cd pd >cpci O H CJ

O r-~ cn <r t"- CMO 00 CM CM rH O• • • • • •

1-1 0 0 O O O

CO r-~ in OO in cnrH n cn 00 CM CTirH vO m m -3‘■ ■ • • • •1— ! 0 0 0 0 O

O m <r 1—1 CO cn.O CM m CO CO co• • • • • •

O 0 0 0 O 0

vO 00 CM CM CM COCO cn CM m CO I-'-m I-'- n- r- r-• • • • • •

0 0 O 0 0 0

0 • r— 1 CM on -3- mH

O in m r- m COO 1—1 CM CM CM CM• • • • • •O 0 0 0 0 0

CM oo CO 1— 1 m 00O CO 0 rH 0 0O 0 I—1 i—1 1—1 rH• ■ . • • ■O 0 0 O 0 O

O CM CM oo 00 VOO <r CM r—1 0 O• » . . • .rH 0 O O 0 O

m CM CM cn CM cnI—1 r'- O'v m cn CM1—1 O 0 0 0• • • . • •

0 0 O 0 0 0

0• r—1 CM cn ■3- in

209

cn 1— 1 0 0 00 O 0 0 0• • • ■ •0 O 0 0 0

m cn cn CM t-"cn 00 00 cn 00-3- -3" -3- -3- <r cu• • • • • rn0 O 0 O 0 PQ

OOcn r". m 00 CO Oco 00 r— 1 cn cn •• • • • • cn0 0 rH 0 0 <u1— i

i*cn CO CM CO cn COcn CM cn C O r-

O O cn 00 00 0• • • • • 00 O 0 0 0

: 0.1

C O 00 cn

10 ■ Aincn

m

1— 1 <r cn C O r**-CM CM CM CM CM• • • • •O O O 0 0

00 00 O V O CM00 cn CM 0 rH0 0 1— 1 1—1 rH■ • • • •0 0 O 0 O

■3" CD 00O 0 O 0 0• • • • •

O 0 O 0 0

00 in <r CM o\1— 1 rH CM cn CMO O 0 0 O• • • . •O O 0 0 0

CO 00 cn

10

210

TABLE B-7

Run #13Cation Column, Haemoglobin TR (P1) = 8.5, BR (P2) = 6.2

Cycle, n 403/* y^ 403/*

I.e. 0.871 1.00 0.0031 0.584 0.67 0.4752 0.432 0.50 0.7983 0.336 0.39 0.9064 0.264 0.30 0.8905 0.200 0.23 0.8896 0.167 0.19 0.8297 0.111 0.13 0.8268 0. 078 0.09 0.8539 0.056 0.06 0.780

10 0.041 0.05 0.769

Z5

0.00 0.55 0. 92 1.04 1.02 1.02 0. 95 0.95 0.98 0. 90 0.88

211

Table Ex-B-2.1 SUMMARY OF THE EXPERIMENTAL RESULTS

ONE-COLUMN: BATCH OPERATION

Haemoglobin-Albumin System

Haemoglobin Albumin

Number of Top Bottom Top BottomCycles, n yR yR yA yA

1 0.881 1.0532 0.840 1.1223 0.797 1.1314 0.775 1.1405 0.763 1.165 0.9966 0.754 1.145 0.998 0.9557 0.744 1.160

Table

Ex-B-2.2

212

faoMR

WROffloPQ

G0)RRPPQIg•HrQ I—Ic

G(URrPmiG•HrQOi—Ioqo§cdw

0 o1Go

•H•Gcdo

G

PQ

G

%>/

GAPQ

>■>V

GARV

G GA AR PQ

P PnV V

GARPnV

GAPQPnV

i-'- r . rH oo 00cn <*• 00 m orH CM o CM rH• • • • •

co VO 00 CT>

CM LO CM CM COc o OO rH corH as VO CM CM

• • • • •rH rH CM CO <1*

< r O O VO com CO CM rHC O lO 00

• • • • •rH CM co <r

r H O CM COm CM CO r^ <3-as CM 00 as CM

• ■ • • •CM VO 00 as rH

rH

R G OG 03cu curO I—I§ G Pla o

CN on LO

Table

Ex-

213

cncniPQ

ISOMH3WPiOCOP30PP>ISHHISOO1HSwco

CNCDI!CMPM

§m•ooIIrH

PM

MHaiCOg cd

s o1—1oo1ao•Hc<1 o1s VO•H& IIOt~H CMM P mOg T3ai Picd cdtd o

00II

PM

H<1>COcxJa

CNPM

4-j ecda) pd■U >-> PJi—IO

CO

PM

4-1ctf0)4-1P>rHOCO

O

PC o

CNPm4-1cd

£ai4-1Pii—IOco

P m

4J acdai W4-i tnpJi—iOCO

o>v

o

o rH00 cn00 I"'-o O o

oo VO rHcn O'! 00CN i—! CNi—i rH i—1

Hj* oo r-o VO cnOV OV <T\. . •o o o

oo i—i cnm i"- oo O i-H

ai a> CN cn

.076

0.93

8 1.

182

0.60

2

Table

Ex-B-2.

214

oo

COHCO

53

sOM§wPhOCO!3O!=>SMH!ZOOiMgwCO

o PhP £ acd A vo 00 CM CMII /' A o CT* CM <ra) <3 o CT\ vD ooOO P kO • • • •

Ph 0rH V V o o O O03 o0 COcdCMVO CMII PhCM P a PiPh cd A A o o i—1 O/\ /v CM r-. LO rHcu < o VO 00 vD 00p • • • •• p t J i— ! I— 1 i— 1 rHW rH V VH oCOCUCOcdu

o~crIIooPh■nsovo

IICMPh

0)COcdo

ooPhPcda)p01-Hoco

PiA£V

aAo~>V

rH CM LO o<fr <r CM r^O'* a* ON <r• • • •o o o rH

CMPhPcdCU P 0 i—IOCO

PiA LO O o oA A vo LO <T><3 o CM OO <r{>. rN • • • •V V rH i— j i—i rH

215

Number of Cycles , n

12345678 9

Table Ex-B-2.5 SUMMARY OF THE EXPERIMENTAL RESULTS

ONE-COLUMN: SEMI-CONTINUOUS OPERATION

Haemoglobin-Cation-Column

1. P1= 8.0, P2= 6.0

< yT > n ^ yB > n

0.852

0.7640.6310.586

0.4950.5020.514

2. P^= 8.5, P2= 6.2

^ yT > n < y B > n

0.2450.3140.3230.3100.312

0.267

Experimental Parameters For

Two-Column

System:

Mode

216

rH to m mCJ o o ocd • • •S 53 o o oo4->4-1oPQ !h0) rH rH i—imh « • •MH o O oPPQ£

Ph4-1 rH m m m•H CJ o o oM cd • • •cd <u a o o o1—1 t—IOa •H•S uo cu i—i i—i i—id mh • • •O MH o o oo 53PQo■iH53O rHM CJ i—! I—1 rHcd • • •

3 O o oPhOEH MCU CM CM CMMH • • •MH O o o

53PQ

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4-1 d15 -H'-'rQOTd rH CM rH 1—1CU bO O O oCU O • • •ph e o O ocucdw

d m vo53 i—1 i—i 1—1Pi

d•r)

Oom m m rHo o o• . • CUo o o 4->cdpi

rH rH i—I rH• • pHo o o

ooCMin in m rHo o o

• • • 4Jo o ovDacuo •cd d

I— 1 rH i— i rH •H• • • P h ao O o CO

•H < ra CM

CU- a

CJ •H1— 1 rH 1— 1 o 4->

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•rHPQ

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rH ao •r)> 4-1

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TE:

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18 and

19 are

Semi-Continuous

Process

TABLE

B-8

217

LO

OOII/-s

1— FMpiFQ

mooII

pq EHA A< <J>* toV V

H ( : PQA Atd tdtn toV V

&O'vm

3 sO

wi >» I

•3c2 s01m

2 so<r

o o CM o m m VO CMo vO O o O'v 00 O'v cr\• • • • • • • •1—Io i—1 rH o o o o

o oo 00 rH o VO 00 O'vo OV rH O'v 00 00 00• • • • « • • •1—1o o i—1 o O o o

o o 00 eg O'V i—1vO O'Vo o <r <r VO r. vo n-• • • • • • • •rH 1—1 o o o o o o

O CM OV eg <1- eg CM rHo in CM T—I<}■ <1* <r <r• • • • • • • •i—i rH rH 1—1 I—1 rH rH i—i

m vo CO 00 O'v ON vOVO 00 <!• CO t"- CO r-' <r00 CSV 00 00 00 ON O'v O'.■ • • • • • • •o o o o o o o o

00 in CO CO m ON inVO i—i rH e- in CO CO CM00 CO rH ON CM CM eg CM• « • • ■ • • •o 1—Ii—1o i—1 t—1 rH 1—1

o VO r^ CM CO <r O'v VOo VO <r 00 VO oo1-1 I—1o o o o o o

o rH VO <r o CM m VOo rH eg CM co CM CM CM• • • • • • • •1—1 rH i—irH i—i 1-1i—irH

m CM CA r-- CM OO CO Ovo CM o CTv r~- n- m O'!00 O oo I''- 00 00 00 00• • • • • • • •o rH o O o o o o

00 CM <r cr\ ON o vO voVO VO ON r"- eg VO OO O'V00 OV o o rH o o o• • • • • • • •o o rH i—irH rH 1—I1—1

<r ,— . fdrH i— i •=S= CU aT o

i— i ■a CJ Hd PiPi H O

cm co <j- m vo

cuoooomcui—i| . COoorHO

•3c Ovin

TABLE

B-

218

CT\

moo

P-i

ctfpp

PP EH

A A<3 <3

Ph PhM V

H PPA A

KPh

V V

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S .cnoh p

PPI Ph I

moo

mCPii n

3Soh p

o o Hp CO cn iH CM cno r—1 CO O 00 CO o• • • • ■ • » •1— 1 i—i o i— 1 o O i— I rH

o I-- cn h p i—1 CM CDo in CM cn CN 00 HP• * * • • • • •

1—1 CM rH rH t— 1 i— I o rH

o CM 00 m PH m m O'!o CM CM cn CM cn in cnrH O o o O o o o

O m CO rH CM HP r-» COO CTn CM H P CM CM i—i O'!• ■ • • • • • •i— 1 o 1—1 1— 1 i— 1 I-1 i—i o

i— 1 00 1— 1 O'! O <1* COH P CO co 00 m r*- in 00CD co CO m m LT) m m• • • • • • • •o o o o o O o o

CM in co i"- cn m cn oCM 00 o rH 00 <j\ h p c\

CO O'! O 00 00 00 CO• • • • • • • •o o o I-1 o o o o

o o HP cn r-'. cn HP 00o CM h p cn cn <? cn cn• » » • • • • •rH o o o o o o o

O cn 00 H P HP o rH oO CO O'! P-~ cO in Hp HP• • • • • • • •rH CM I—1 !-1 i— 1 i—i !—1 1—1

t—1 in CO I''- t". Oc CM 00HP CM CO 1-1 Ph rH O 1— 1CO 00 r-- r-- cO CO CO CO• • • • • • • •O o o o o O o o

CM CT\ o H P r-~ CM o CMCM CSC cn m 00 00 CM i—100 Hp CM i—i O O o• • • • • ■ • •o rH i— i I— 1 rH rH rH rH

<uPhooo0 in a>i—i1cooo

m

I

P-i

PiIH

c

CD .iH oo •Ph H

O

i-h cm cn hp m coincr\i n

TABLE

B-10

219

pqA

ifN)

HA<1Ph

o VO <r CN 00 VO o Oo CN) m O O o\ r-' <r• • • • • » • •rH tH iH CN rH o iH rH

EHA

pqAW>nV

o LO ON NO CO O fN.o m rH 00 <r VO m 1-1• • • • • » • •1—1 rH CN rH CN CM <r CO

p?o 00 co ON 00 CO <r ooo <r cn CN) CM CO CM

rH o o o o o o o

o Os -d" 1— 1 i— 1 m CM ono I-" in VD <r CO CM CM. • . . . . • •1—1 o o O o o o o

VD

I

in00II/■-sr-P-.pipq

mooIIr-PHPiH

inOsm

*o-d-

£

ffil Ph I

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o<r

curHCJPHu

o VO rH VO CO i—iCO 00•d- cn -d' VO rH o r~- OOVO in m m m in -d- ~d-. . . . • . . .o o o o o o o o

o oo o 1— 1 rH o - 00 ONon -d- rH as O as r . C"CO i—i i—1 i—i i—Io o o. . . . . . • .o o O o o o o o

o OO 00 cn VO <r o oo CO CM <r CM CM (N CM. . . . . . . •1—1 o o o o o o o

o CM vD m 1—1 CM cn CMo CM i—! rH o ON ON ON. . . . . . . .1—1 i—1 i— 1 i—I rH o o o

•d- <r 00 -d" 00 m r-' CM1"- 00 as i—I VO VO 00 CMVD r~- r . r-~ 00 vo vo. • • . . • . .o o o o o o o o

00 rH o r"- CO r-. 00 i— i00 OS <—1o as CM CMr-N VO cn cn r- r- n-. • . • . . . •o O o o o o o o

CJ. i—1 CM CO in VO r-~

595j*-

: 0.1 cc

Sample/5. 0 cc

Dye

TABLE

B-ll

220

inooII/—SCU

piPQ

in00II

i"* <rv*—i 1—1CU•—s§ PiPi H

M HA A<! <1Pn !>■>'V y

Eh PQA AEC ECPn

S/

Ain'<nm

O

wi Pn I

in<nm

COo<p

a)rHot=Ho

o in o> o CO m m cn o oo i—i cn o vo oo vO VO *—i CN CN• . . • • a . . . • aI—1 i—i o rH rH o o o o !—1 I—1

ino cn CTV m CO rH 1—1 o VO CNo O'N cn rH r*- CO cn m 00 vo a• • . a • a a . . . <ro o i—i CN CO m VO VO cn cn rH

o in o CO m o i—1 cn cn CN CNo m cn CN rH rH i—1 rH o rH rH• • . • • a a . . . aI—1 o o O O o o O o O o

o r'- i—i CO CN VO CO CN p- VO <ro m CO CN rH rH i—I o o o• . . • • a a . . . aI—1 o o o O o o O o o o

CN m cn CN i—I vO CO vO VO cn COon m o 00 ON 00 ON cn <p cn CO!—1 00 cn VO m LO in m m m m• . . • • a a . . • a1—1 o o O o o o o o o o

on VO <r CO CO vo 1—I cn <p cn 1—i00 o vO ON ON CN o VO -S' CO00 m cn CN 1—1 rH rH rH o o o• . . • a a a . . . ao o o O o o o O o o o

o 00 vo CO ON CN o o o oo <r p" CN o rH rH CN I—I 1—I rH• . a • • a a » a . a1—1 o o o o o o o o o o

o cn p 1—I CM in CN CO cn 00 r-o m m OO oo OO p~- VO m m• • ■> • • . a . . a ao o o o o o o o o o o

CN i—i CN o o cn r. cn oo VO 00r-. o VO vO o CN rH p- p-' cn r<r O'v O o CN CN CN CN 1—I o o■ . . • a . a . a a ao o rH rH 1—1 t-H rH i—i 1—1 rH 1—1

co in VO ON VO cn VD o CN COo p~- O CN CN m CN Cn rH rH oo •<r in vO p" r-. VO VO m m• • • • a . a . . • ao o o O o o o o O o o

o c N c n < r m v o r ' ~ o o c n -3<

595/- : 0.1 cc

Sample/5.0 cc

Dye

TABLE

B-12

221

PQ H o CA vOo in CSVA A • ■

<1 <J t—i 1—1 O!>v !>v\ V

H FP o CMA A o in CMES w t—! cn r-~Eo 1V N/

o CM iH<3 o O otn • •

1—1 i—Ii—i

<r VO !—1oo CM I—1~d- r-'.o VO oo VO OV 00. • . « • • • •t-H o o o o o o o

o o r-~ o r» o o min m vO m cn o m CM• . • . . . . •in m 00 in cn CO CO CO

i—i i—i 1—1 CM *— i I—1 i—i 1—1

m 00 r-. cn CTv OV in inCT\ r-- oo o 00 00 Ov OVo o o rH O O o o

o co rH CO CM <r -d* <ro CN] rH o o o O o o o o« • • • • • • • • . .l—l o O o o o o o o o o

m* \ i—i o co I—I iH VO 00 -d- m co• iH CO VO CM ON m 00 CN] CM o Ov00 in <1* 00 VO in <r m m in <rcn • • • • • • • • • • •II m rH o o o O o o o o o o

/—\1—1 Ph \o> oc -d- m NO m CO -<r VO i—iN—r 00 co VO CM <N rH rH CN] CM CM CM

piCO LO rH O o o O O o o O Oo • « . • • • • • • • •

pq <r o o o o o o O o o o o

oo

I

mooII#*—s

T—PhpiH

>f\

ESII

toovm

\co 'o -d*

PS•sa)i—ioCJ

o m i—i Ov CO <r -d* in rH ONo VO o CTv rH CN] CN ««d* CM O o. • . . • • • • » • •o o iH O rH rH rH rH I--1 rH 1—1

o iH O CM CN] VO i—1 m CM <r COo 00 CXD vO vD m m m m tn in• • • . • • • • . • •1—1o o o O o o o o o o

CN] o 00 CM i—1 m CO VO 00 00ON CM o VO rH in CN m vo m OV<r m m <r <r co «<]■ ~d“ i—i CO CM• . • . • • • . • • .i—i i-H rH rH i—1 1—1 i—I rH 1—1 iH i—1

i—1 00 CT\ oo CN o OV m CT\co m <r VO NO <r CN CO CN CO CMco co CM CN CN CN CM CN CN CM• . . • • • • • • • .o o o O O O o o o o O

CJ cm cn <t in vo oo O'i •3<

595/U.

: 0.1 cc

Sample/5.0 cc

Dye

TABLE

B-13

222

PQ H o ON LO OV i—1 ovo ON i I". 1 in CM cnA A • . « •1—1 o NO o i—I i—irnV/ K»

M

H PQ o CN) NO CTt ONA A o• l"- O0 OO• in !—1 • cn 00W W 1—1 LO on -3* in in cn

>. >nVJ

o o vo 1— 1 vO cn <Sr CM<1 o LO o 00 rH cn cn>n • ■ • • • • • *

1— 1 i—i i"H o o O o o

o i—i in VO CT\ rHo CO cn CM i—1 rH rH CM

*1 • • • • • • • •*—1 o o o O O O O

LO o o VO vO i—1 rH cn vO• * <r I—1 m CTi rH00 LO 00 r-» r^ C7\ 00 00on • • • • • • « •

II LO o o o O o o O o1—1

Ph Cn) m ■<r cr> o rH'—^ \ r^ cn VO r- r- O CMoo o cn cn CM rH rH CM CM

Pi o • • • • • • • •PQ -<r 1—I o o o O O O o

o rH O CM O CM 00 cno n o rH O CM CM CM>N 1 • • • • • • « •1—1 !—1 o O O o o o

cno CTt o cr» in cn oo rHo r cn o o*\ 00 oo O0>N 1 • • • • • • • •

rH rH rH rH o o o o

o 00 00 i—1 NO ON CM CO<(■ 00 o CM CM CO ON r".m oo o ON 00 f-'. NO NO NOON • . • . • • ■ •LO o 1—1 o o o o o o

CM 00 CM 1—1 ON NO ON CMrH ON r» 1—1 00 00m CO o ON CO rH o OO oo 00. o . . . . . . • •00

iti—i i—1 I—1 I—1 rH o o o

ONii

dI—1 i—iPh 0) •N rH od o • i—1 CM OO -Ct- LO NO I"''

595/*-

: 0.1 cc

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Table

Ex-

223

o<rIIco d CJ d* S A A* P H pqCM ^ >»• i—1 \co <3 VIICMP h

cn o r - COo o o r-« < ro o a \ 0 0 CM• • • •rH cn m CD

cniPQ

d•H

s rQo 1—1H <3

TOP4 dw cdPhO pp•HW &O OH rM<3 orpq o

0cucdtd

6.2

iiCM d d dPH •H A A•> H pqLO rP >>00

rH< s V V

Ph

i—i 00 LOi—i o 00 COo CM cr> I''-. . . .i—i 1—1 o o

CMCO dII *H CM ,0 PM O

LOoo

Ph

1— I AbO i* Vtd

CM <r cn oA CM i—i co cnpq i—1 m i—i O'!. . • .V CM <r oo

10

CM c n LO

12.281

1.302

10.355

224

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cuTdog

0cu4-1CO

CO

rHoCJ1

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1 Pdpq o

Ph4-1•H IhrQ o•rl Ph

X COw Pi

CU4-1CU

PicdP-I

cd4-1fiCU0

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4-1•HM cd 1—Iogc*p{PiO

•H

rH LO LO LO LO LO •rlCN CJ O o o o oPH cd • • • • •

o o o o o CJ

1 M4-1 CU o o o o o

CJ 1—1

4-1 C4H rH 1—1 1—1 1—1 1—1 CUO <4H • • . • • 4-1pq p) O o o o o cdpq

> ' i—i LO LO LO LO LO

Pi

% I—1CO CJ o o o o o PnPH cd • • • . •

S o o o o ccurH Pi Td <U o o o o o c

c,

Td <4H 1— 1 1—1 1— 1 1— 1 rH 04•Hg mpjpq

4-1 PH cdrH CJ

cd

u4-1

goPiOCJo•rlPioM

CUrHTd IH

CUT d «4H•h m g P* pq

CJ/~n cd

c n S PhH

PX (U O <4H

H *4H p)pq

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1

o o o o o

UT UT LO LO COo o o o o• • « * »o o o o o

o o o o orH rH rH rH rH

O O O O O

LO in LO LO LOo o o o oI » • « •o o o o o

o o o o oI—I I—I I—I I—I I—Io o o o o

CN OH i— I CN t— Io o o o o• • • • •o o o o o

CN 04o o CNoo o o• • • •o o o o

o04

rH CN CO <r CN CN CN CN

4-1

s@ocd tdi— I «rHPX 0 co•rl '-Lf Q CN

cu - 0 CJ -rlO 4-1

OCOII

PiO• r l4-1cdg>

> PdoII Pi •Hpq CJ>II

PiEh -H > 0CU 0 0

o>cuI4-1

Td Tdcd Q) <U CU Q Ph

8uI—I I—Icd

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Run

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24

are

Semi-Continuous

Process.

TABLE

B-14

225

CslM3

CMPm *—-*PiPP

CMVOII

oCM CM

Pm—"§ PiPi EH

PP EHA A<J CV V

Eh PPA Affi WV V

to

u-i ' O'm

« 5 sO

►?

inO'in

O

Gd)i—io>vCJ

11 O' CM o rH p- 00 VO 00 00 in1 CM i—1 r- rH o 00 00 o o o1 • . . • • • « • . •1 I-1 O cM CM I—1 rH CM CM CM

1 o o O'v CO o in CO r-'-1 00 CM CM CO rH rH O' CM <p vo1 • • . « • • • . . .1 CM CO CM 1—I CM CM CO i—i 1—1 rH

o o\ o CM 00 O o O' 1—1 00o <T vO p-. VO vD oo 1 00 P• • • * . . • • . . .o o t—1 o o o o o o o O

o m m 1"- O'v p". p-. <r oo P-- voo o o o o o o o o o o• . • . • . • . . . •o o o o o o o o o o o

1—1 in CO O'V I-'' CM m m O' rH 00LO vo CO 1—1 oo rH CM r-' 00 O' r-'.vo rH r-- p-* P'. r-' p- p> p* r-"• • . • • • • • . • •o o rH o o O o o o o o

cn m rH r-> o CM oo oo oo 1—1 oo VD r-' O'v CM O' 00 <r o O' 00o o o o i—1 o o o i—i o o. * ■ . * * . • * • •o o o o o o o o o o o

o oo i—i CO O'v O' <r CO 00 O' 00o CO CM CM i—1 CM CO CO CO CO. • . . . • . . • • •o o o o o o o O o o o

o VO VO CM in in o* o o oo rH rH 1—1 i—1 i—i rH rH 1—1 1—1 I—1. . . • . . . . . . •o O O o o o O O o o o

I—1 CM m o CO CM O O' p". o r-~m m O' o p- CM <r VO CO <r CO<r vo in VO m vO vo VO VO vo VD. . • • . . • • . . •o o o o o O o o o o o

CO <r O'v CM VO in <r CM in o CMo 00 t—1 rH VO o o oo co CO COo rH CM CM i—1 CM CM i—1 i—i 1—1 rH. . . • • . • . . . •o O O O o o o o o o o

o N c o < r m i D i v o o ^ o

595A

: 0.1 cc

Sample/3.0 cc

Dye

TABLE

B-14

(Cont'd)

226

o CTV CTv o o o VO <r CM CTvo CO Cfv 00 o m 00 < r cn cn. • . » • . • . • • .

1— 1 i-H o o o o o o o o o

o CM r-'. VO rH ov n- vO VO VOo LO CM 1— ) VO o o o O o. . . • . • • . . . .

1— t O o o o o o o o o o

o<!* Ain

crvm

LO 00 oo vo CM r"'. VO oo m CM i-Ho cn VO VO i—1 o- o i— ! 00 CTv OO1— 1 CM oo n- vo VO Ov VO m m m• • • • . • . • • . .i—i rH o o o o o o o o o

cnPh iscnoi—iVO cn vO 00 ov CTV m rH00 o t—1■o- VO CM o -cr <r <rr-. cn CM rH <r o cn o o o oo o o O o o o o o o o

LOOO

£ * 1

Am 'cr\m

o•vT

o vO <r VD i— i rH 00 m rH cno Ov <r i— 1 vO m in o OO 00 CTV• . . . . . . . . . .I— 1 o i— i i— i o o rH i— i o o o

o o o r-~ CTV OO i— i in cno 00 00 t'- in I— 1 CM CM CM CM. . . . . . . . . . .r-l o o o O o O O o o o

cn VO vo CM i— i o VO CM CMo cn vO 00 CM m VO CTV <r m t''.o CTV o CTV m r-. O r-- r-« r- n.. . . . c . . . . . .rH o 1— 1 O o o i— 1 o o o o

cn 1— 1 I— 1 cn 00 r-'. m 00 o i—i cnm o o 00 vo CM cn in CTV 00

VO VO in cn rH rH !—1 *—i rH. . . . . . . • . . .o o o o o o o o o o

oCM

lPh

dCL) i—IOvCJ

CJ c M c n < r m v o n - o o o v o

595>

: 0.1 cc

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cc Dye

TABLE

B-15

227

CMVO

CMPh

PQ HA A<3 <3toV V

H PQA A

ffitoV V

*1to

PiPQ

LOcrto

o<r

oo <r LO rH <rCTv m CM• • • • •CO rH rH rH rH

oo

<T\m

CMoo

O CM CM r-' oON CTv CT r-'- rH• • • • •i—1 rH rH i—i CM

LO O O o VOLO <r <r O' •<r• • • • •o o o o o

o CM CM OO o|H i—t i—1 1— 1 1—I• • • • ■o o O o o

OO oo CTv VO -d"o CTv 00 O' oCD LO LO vo VO• • • • •o o o o o

I— 1 LO CTv o ooCTv I—1 O CM CTvO 1—1 rH 1— 1 O

o o o o o o

.<1Po

mm

O ~cr VO CM I—1 CMO i—i OO 00 <r CO• • • • • •o o o o o oCDtoo CTv OO oo oo I—1 Qo rH CM CM CM CM• • • • • • oo O o o o o o

CTv rH I—1 o <T CMLO <r 00 o CM CTv

LO LO vo VD LO• • • • • *o o o o o O

ooo0)rH&

CMOCM 00 ’ o« o •vO Hi- oII

rH /—s fiCM CMPh CU •'-' iH aO CJ •3 Pi to M

pi H o

00

cm oo <r lo

coVO o CM CMO CM rH ON oCM CM CM rH CJ• • • •o o O o rH

!<\LOCTvLO

TABLE

B-15

(Cont'd)

228

0 10 CM CO in <r< 0 o\ t-"- <r <1-. . . . . •rH 0 0 0 0 0

O vO 10 CM CM 00O CM t—i 1—1 1—1 0• • . • • •I-1 O 0 O O 0

0 00 Os o> VO 1—1 1—1• * \ OO 00 os O Ov<r in CTi r-- VO in vO inOS . . . . . .II in O 0 0 0 O 0

\00PM2 s

r-« r» O'! <r CM 1—10 tn os r-~ r in10 1—1 0 0 0 0

rA 0 • • • . • .0 0 0 0 0 0

0 <r ov CO 00 10<n 0 00 10 in 10. • . . • •1—1 0 0 0 0 0

0 r. CM CO in CMtd 0 00 10 <r1=0 . . • . . .1—1 0 0 0 0 0

CM

l

moollV—s T—P-i

LOo>n

COo<r

dcu1— 1oo

0 r» in 00 COCM 00 i—1 -3- VOO O'! 00 00 h-. . . . . .1—1 O 0 0 0 O

CM O ~d" O'! CM CM1—1 CM 1—1 CM Ol"- VO in CO CO. . . . . .O O 0 O O O

u1—t cm co uo *

595y*:

0.1 cc

Sample/3.0 cc

Dye

TABLE

B-16

229

PQ HA AC <J>o >v

V V

PQA A

W>»V

o o I—1 00 m O o CO o m Oo CTv CM 00 CO in <r <r vo• • • . • • • • . • •1—1 CM <r oo rH m vO o o CO <rCM CO i—1 i—i i—i rH rH

O 00 00 «—1 o m CM r- 00 rH <rO LO rH rH i—! oo CO VO vo• • • • • • • • • > •rH rH CM 00 CO 00 00 CO CM CM

CMV O

CMPHPdPQ

►fl

Pdl >V I

•3C\mct>mCOo-<r

O CTV 00 00 o CTV CO oo VO 00 VOO oo vo vO vo m m <r• . . . . . . . . • »rH i—1 *—i rH rH rH 1— 1 *—i rH i— i rH

O P- 00 m O <r Ov CTv rH oo CMo 00 VO <r <r CO CM rH CM CM CM• . • . . . . ■ . • •1—1 o o o o o o O O o o

o OO 00 vo o CTV -CT OV O 00 inCM I—1 p'- in 00 O VO 00 o 00 CM•vt* oo 1— 1 CTv CTV CTV OO p-~ CTV CTv. . . . . . . . • • •i—i 1— 1 rH o o O o o o o o

~d" VO m <p p" i—i 00 oo t—1 CM p^CTV 1"- o o m o m o n O CTv00 r-' vo <r oo CO CM i—i i— i CM i—1o o o o o o o o o O o

<t*l> v I

o 00 CO m o in m rH oo m 00 rH o o rH rH T—1 rH rH. • • • • • • • • • •1—1 o o O o o O o o O O

* 1 >v IO CO m O VO r>- 00 CO rH o 00o OO <r OO o o 00 I"' VO m• • • ■ « . . . . . .rH rH rH i—1 rH i—i 1— 1 o o o o

CMVOII

CM /*>CM CMTrS PHs—/B pcj

H

inOvm

o<r

dQ)rHoPou

o 00 <r CM r-- m P-- O CTV 00 ON<p m CTv r- CTV CO CM CM <P inm VO VO vo m m in CO CM CM. . . . . . . . . ■ •t—i i— i t— 1 t—i t— i i—i t—i i—1 i—1 1— 1 I—I

00 i—i 00 CM o CO CTv CM CTv VO -d-p- CO CM CTv vo CO CO <P ~d- vo mi"- o i—1 O o oo 00 vo m -d* -d*• a . . • . • . • • •o I--1 i—1 i— 1 rH o CTV o o o o

oH i—i cm co ~ct in vo 00 OV O

*

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PtJooVO i—I IPQWPQ$

o<rIICOPQ

s?l

AmCTvin

COo<r

o i— i CO n- 00 CO rH uo <r oo av 00 00 CTt ON on ON CM 00• • • • • • • • • • •!—1 o o o o o O o O i—1 o

o o <r ~cr i— i CTv VO LO CO oo COo VO in in n• • • • • • « • ■ « •I—1 o o o o o O o o o o

CM r~- in OV CM CM i—1 CO o <r130 r-- in <r r-- o CM ON OO vo mCM CM CO CO CO <r CO CM CM CM CM• • • • • • • • • ■ •i— 1 i—1 i— i i— i 1—1 T— I rH rH i— I i— i rH

vO r-~ VO r-- VO o UO o VO ON•<r o 00 oo m LO m VOco CM• 1—1 i— ! i— I *— i i— i rH i— i 1—1 i—1o o o o o o o o o o o

CMCM

l

inoolli—FQ

a\

AinCJVin

2So <r

Ca)r—Iotou

o rH CO CM CM LO VO CM i-Ho rH rH O rH rH I—1 ov OV O av• • • • • • • • • • »1—1 i— 1 i—1 rH i—1 i—1 1—1 o o t-H o

o VO CO <1* CO VO in in CO COo m VO <r <r CO CO CM CM CM CM• • • • • • • • • • •I— 1 o O o o o o o o O o

in CM CO CM 1—1 vo 1—1 o ovvo 00 CO n*. rH 00 CO CM o CO i—im CO <r CO CO CM CM t—1 1—1 1—1 rH• • • • • • • • • • •rH rH rH 1—1 i—1 rH i—1 i—1 rH I—1 rH

VO CO CO 1— 1 CM 00 CO o VOCO o 00 00 vo Ov vO vo m t-crO VO VO <r <lr CO CO CM CM CM CM• • • • • • • • • • ■rH o O o Q O o o o o O

oM

i - H C N i o O ' c r i n i o r ^ - o o c r i o

a)toOoooCO<u1—Ie-COooCMo

u-Aavin

TABLE

B-17

231

pqA

HA

00 02 22 CS1O tnCO m»n 26 46 03

<ri— i

h TCM• • • • • • • • • . .

V/I— 1 i—I i— 1 rH i—i *— i I— 1 i— 1 CM CM CM

EH ppA A o CO ov o VO 00 VO VO VO o 00r V /v o CM <3- o m I—1 in m in 00 r-'. • • . . . . • . • •K*V >v o o o iH i—i CM CM CM CM I—I !-1V V

o I—1 CO O o CM CO i—1 i—I r-. VOo ov 00 VO [•"- VO in in f" r-'>v . . . • . . • • • . .rH o o o o O o o O o o

O VO lO OO vO i— 1 Ov ON O' O O' ffil O lO CO CM i—) i—I O O O i—J O I . . . . . . . . . . .

i H O O O O O O O O O O

CMvoII

movmco <d- vo mLO rH ov

voVOI-- oo CM

VO VOr"-ovo

o o o

vo <r ov o m vorH 00 CM rH VO VO

O O OCM

PdMi sCOo

CO CM OV

ovCOCO CM rH

CM i— I <3*OV VO <fo o o

VOCOor-» <rCO CO o o

oo inCO CO o oo o o o o o o o

oo o v o o o v c M o v o m m v o - c i -o o v o i n i n < t < a - c o < o c o e oo o o o o o o

Oo CO co in <r cl d ci oo i H C M C M C M C M C M C M r H

V O

O O O O O O O O O O

movin

oo vo oo o <r r"- • • o o

rH CM CO O 0 0 O

oo cm oo o <r n oo <r oo cm <r coov ov ov oo oo r»

• • • • • • •o o o o o o o

CM CO V o. o •VO oIIco

CM ,— \ aCM •vPh a) •*—/ i— i ort o .

H Pi >v Hpi EH U

CMOOCMr^-d-CMCMvO m v o o v o v o v o v o v o o o ooo

oo

oo o o

oo

oo

oo

O Hf !''■ VO o o • • o o

• i—11 cm i co <j- in vo r-oo ov o *

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>?\o oo 1"- CO o CM CM CM o oo CM *d- VO r-» lO lO <r CO CO• • • • • • • • • • •o o o o o o o o o o o

o VO ov VO n* VO 00 CO r-'- CO COo OO I"- vO in -d- CO CO CM CM CM• ■ • » • • • • ■ • •t-H o o o o o o o O o o

4-1Oo

Ipqwg$

o-d-IICO

P-I

*Vmcr\LO

o<c

CO m rH d" m ov -d- r"» r"- VO CMo VO rH 00 ov VO in vo vO 1—1 OVO •d- CO rH o ov OV oo 00 00 00• • • • • » • • • • •1— 1 rH i—) H i—i o o o o o o

CO <f* CO CM VO VO o p'- CM 1— 1 ovCM OS CO rH CM CM in o m rH oov r- l-» VO in «d- CO CO CM CM CM• • • ■ • • • • • • •o o o O o o o o o o o

COCM

Pi

LOCOIII—

PH

l>s

mCTlm

i sCOo-d-

£oTpHO>■>O

oo

m00

V OV O

0 0in

COLO

vom

I"--d'

om 1

vo-d"

in< r

• • « • • • • • 1 • •1—1 o o o o o o o 1 o o

o 1— 1 in o 1". m 00 VO in CO COoto

o CM CM rH rH 1— 1 1— 1 i—i 1— 1 rH Q• • • • • • • • • a •1— 1 o o o O o o o o o O O

OS m VO 0 0 l— 1 OV o CO m i— 1

O

o

0 0 rH o CO OV ov V O vo i CM CM COm CM o ov 00 00 0 0 oo i 0 0 00

<u• • • • « • • • i • •!— 1 i— 1 I— 1 o o o o o o o 1— 1

1— 1 Os CM in OV in in i—! -d- oo -d-toCO

m O O <r o 00 i-: OV 00 i n mrH LO CO CM CM I—1 CM 1—1 rH i— i i— i o• • • • • • • • • • • CjrH o o O o o o o o o o

uM i H c M c o < r m v o r - - o o a v m

O'!m

TABLE

B-18

233

PQ HA A£VH PQA A

.£?V

1 CTv <r CO i—1 VO in oo o oo1 VO o oo kT vo KJ- <t- in 001 • • * . • • . • •1 rH CM CM OO <r VO LO oo CM 1—1

Ij CO m O 00 oo 00 CO m CO oi <r Ov VO KT ov OO VO ov to KTi • • « . • • • • •i; rH rH CM CO OO <r Kir to r-~ r-'

o to CM CM to o Kp o 00 o oo 1—i ov 00 o. O' 00 vo KT Kf CO<tj • • • • • . • • • •Po rH rH o o o o o o o o o

O rH Ki­ 00 00 I—! CO O' 1—1 in mO OV p'' m Kt- Kf oo CM CM 1—1 *—iEd • . • • • • • • « • ato rH O o o o o o o o o o

CM O Ov OV r-' o- CM CM OV CM CM oo. * \ rH CM OO o rH to VO CM 0O VO oVO to m to CO CM i—1 o o OV 00 O' O'Ov • • . . . • * • . • •II to rH 1-1 I—1 *—i i—1 1—1 1—1 o o o o<—\CMPm O o O' CO o- 1—1 00 VO OV CO'—' % cr» to oo Ki­ KT oo o to Ov <1* ooOO 00 00 vo rn KT oo CO CM rH rH rHPi o • • . • • • • • • • •PQ <r o o o o O o o o O O O

o 00 in ov CM m CO rH <r VO VDo VO CM CM rH rH rH rH rH rH

<3 • • • • • • • • • »to 1— 1 o o O O O O O O O O

o o i— I r-' rH CO m m CO *— io CO m VO VO CM CM rH rH

Ed • . • • • • • • • • •to rH I— 1 t— i i— ( 1-1 i— 1 rH *— i rH i—1 i—i

* * NO OV CTn CM vO 00 i— i 00 i— 1 CMl— 1 r-' <r to CM 00 lOto m vo r*-". O' r^ r*. to in m

Ov • • • • • • * • • • •LO I—1 i— ! x—1 i— i rH rH i— i i—i i—1 rH rH

< o CM O as rH CM m rH t-' -■3*OV i—! o VO O CO ON to CO

CM OO' 00 CM CO <r m m CO CM rH o O• o ■ • • • • • • • • • •

VO <P o i—1 rH i—i *—i rH I—1 i—i rH I—1 i—!

(N

I

C MPmPiH

GClTi—I CJ i>v CJ

CJH H N r O < f i n v O N O O f f i *

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cc Sample/3.0 cc

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TABLE

B-18

(Cont'd)

234

o vD CM mo CTv LO coC 1 • • •>s rH o O o

o rH t—1 CTio LO CO H

K • • •1—1 O o o

o CM i—t VO• <J\ r- vO CM<r lO <1* r-H 00CTv • • • •1! LO rH rH o o

—sCO

Ph 4 CM •<r CMco CM co 00CO <r CM rH o

erf o • • • •PQ <T o O o o

o CM 00 *—!o CM VO

c • • • •!-1 i—1 o o

o vO rH LOo <1* CJ 1— 1

w • • • •i-H O O o

O f - o•ic \ o in 00LO vO CTv (TvCTv • • • •LO I—1 i—i o o

s o vD LO CMo O r-> O

co CO VD CM CMlO o • • • •

. O ' 1—1 O o O00IIt—s c1—1 •Vpx< Q) •s—' i—! CJ

a • i—i CM COprf HH a

CO i—! CTv VO o COI—1 r—• O o 1—1 o o• • • • • • •o O O o o o o

CTv r-" vo LO r'- vO VOO o o o o o o• • • • ■ • •o o o o o o o

co CM !"■' oo oo CTv 1—1r-- LO CO 1—1 <T o CMlO LO LO lO LO LO LO• » • • • • •o o o o o o o

co !—1 l"~ CO CM VO <rCO CM CM CO CM CMo o O o O o o• • • • • * •o o o o o o o

r--~ ' r~- LO o -T 1—1 OVVO -<r LO VO <r LO <r• • • ■ • • •o o o o o o o

CO CO <r CO CO CM i—i CD1—I rH v—1 v—1 1— 1 rH *— i. « • • • • • !>ro O O o o o o Q

Oa

o LO CTv C'' CTv CM LO oCO rH VO CTv CTv CO I—1 •CTv OO OO 00 00 oo co• • • • « • •

o o o o o o o CDi— 1

CTv 00 o CO VO p- cdVO VO CO I"' LO COi—1 1—I 1— 1 I—1 1—1 rH rH• » • • • • • ao o o o o O O o

CJo

o ■jc'v< r m v o r ^ o o < T i i - H 10

cr>LO

SUMMARY

OF THE

EXPERIMENTAL

RESULTS

od- CNII 6 <3 o inco O Po Pn rHPh +J •+J o#» O• CN PQ -d-M • Pd o VOM vD Po Po ooM II •CM oCU PhCO 1—1CCS <3 0 oU m Po Po vo• P. •oo O o11 Ehi—i CNPh Pd o d->v v 0 0

S3 ooM oH •d- 0 0II B <3 o oM 00 O Ph Po 1—1pH Ph +J •O P o•> oPd • O PQ 1—1o pi M • Pd o d"H •rl M VO >V !>h rH<3 g II •PQ p CU CN o

£1 CO PhCN !-l Qj 1—1<3 o < o mw i o kH Pn CNo PI • Ph •o •rH 0 0 o os rQ II E-HO 1—1 d"• • 1—1 Ph Pd o ms PC Po Po mw o •H 0 ocn CUP* nScn tn o• *—id- <3 o m§ II s Po Po ooo o •Ph p oO • po M o CN1 CN PQ Pd o OOo CU • Pn !>h i—1CO VO •CCS II oCJ) cNPh d"<3 o r*'Po Ph , 0 0o •• Pin ooo oII EH ooi—i Pd 1o ooPh >V Po d"

o

m P0Ph COCU 0)rg rHOP Po13 u

235

d- t—1 CNm 1 1 d" i 1 m i 100 1 1 00 i 1 00 i 1• 1 1 • i 1 • i 1o o oCN CN 00d- 1 1 00 i 1 r-- \ 1

1 1 OO i 1 d- i 1• 1 1 • i 1 • i 1o o O<r 00 o00 1 1 o i 1 oof'- 1 1 00 i 1 OV• 1 1 • i 1 •o o o<r oo 00o 1 1 d* i 1 d i 1oo 1 1 OV i 1 OV i 1• 1 1 • i r • i 1o o o

o m 00 O'oo CN CN o i i 1 i 11—1 1—1 i—1 1—1 i■ i* 11 i■ 11o o o o 1 i 1 i 1

r-' o m invo m d- o 1 i 1 i 1rH i—i 1—1 CN 1I i■ 11 i■ 11O o o o

1 i 1 i 1

CN oo CN d-VO OV o co 1 i 1 i 1CN oo •d- d- 1■ i■ II i■ 11O O o o 1 i 1 ■ 1

00 -d- CO 00OV 0o VO m 1 i 1 i 1OO d" ~d" d- 1■ i■ 11 i■ 11O o o o 1 i 1 i 1

00 CN o in cn r-~ 00 vO CM•d- in rH 00 00 r-< 0 00o rH i—1 o rH i—i o o O• • • • • • • • •o O O o O o o o o

1—1 CN r-- m O CN min in ov d" r- rH O rH CMi—i rH rH i—1 rH CN rH CM CM• • • • • • • • •o O o O O o O O o

!—1 CO vO CN i—1 o 1—1i in 1—1 1 a\ OV o r*- ri i-- vo 1 r-s VO oo ri • • 1 • • • « •o o o o o o o

00 d- CO i—i m d" to LOOV o 1 LO CN r-* rHf'- vo 1 00 00 00 o\• • • 1 • » ■ • •o o o o o o o O

CN oo d- in vo r-- 00 O'* o

236

s0 w%wPhOCOP>OP>!SMHSoCJ1Mswcocm

P•r lrOOrHOCOgcOW

<UcocdO

CM

VOIICMP-l

•%LO

0o4-)•POpq

PA>•>V

oK*V

0 0II p1—1 P h AP-l O

H >v• VCM

O• 0 pVO o

II 4-> ACM 4-4 rO

PH o \lPQ V—LO

H 0 0H II P

l—1 P h lCU P h O ACO H >vcti • vCJ 1—1

o

o>v

o!>v

CMvO 0 PoII 4-> ACM 4J >vP-l O vPQ—

O

0 0II pr-H P h AP-l O AH Po• VCM

O• 0 PVO OII 4-J ACM 4-> p0Pi O VPQO00II pi—1 P .P h O AH Po• V

ot-O

o>v

o>>

oKl

•4-1 dop co <U aj’Q0 P>P K»3 o

to O CO LO LOto to CM 1—1 <r 00to <r CO 1—1 I—1 i—i• . . • . •o o o o o o

o I—1 -Cl­ CO LO1 r- CO io rH CM1 <r vo CO CO CO1 . . • . .i—i rH 1—1 1—1 i—1

<f i—i e'­ to to CMLO CM er! o CM r-r- LO <r CO CO i—i. . . . . •o o o o o o

LO CM to CO <r LOCM <!• VO CO o r-HO 00 r-H 00 00T—1 t—1 o rH o o

LO rH LOo O rHco CO l—1. . oo o O

CM

o i—1 LOo o COCM CM i—1. . .i—1 r-H i—1

O to CMVO CO OLO CM CM. . •o o O

to to o00 <r 1—1 1Ov ov 00 1. . . 1o o o

CO LO vo

0.741

---

1.010

0.023

237

Table Ex-B-4.3 SUMMARY OF THE EXPERIMENTAL RESULTS

TWO-COLUMN SYSTEM: MODE 2 SEMI-CONTINUOUS OPERATION

Albumin

1. P2= 6.0, P3= 4.0 2. P2= 6.2, P3= 4.0Top Bottom Top Bottom

Number of <Y> n <Y > n > n <Y> nCycles, n yQ yQ yQ yQ

1 0.955 1.144 1.210 1.3352 0.987 1.530 0.685 1.6503 0.835 1.734 0.716 1.6434 0.940 1.835 0.740 1.8715 0.624 1.510 0.501 1.4426 0.774 1.614 0.451 1.1167 0.671 1.533 0.450 1.1758 0.698 1.555 0.482

238

<riPQIXwa)i—i rQcdH

o 6• o-d" 4-JII ■PCO OPM PQ13CcdCMVOIICMPM„

m• PM00 OII HrHPM

CM

eo4-J■PO O• PQ<rIIcnPM13P3cdoVOIICMPM PM•> Oo H00II1—iPM

<31to

ffll!>» I

m\ tn I

<31I

tni >n I

<31 >n I

Wl!>» I

CM o CM ~d- COO i—I cn 1 i CO o r-.

co Hi" 1 i -d- m VO• • 1 i ■ • •rH 1—1 i— 1 rH i— i

O m I—1 00 O* r—io Hf rH o t''. 1 m i—i-d- -3- CM CM 1 t—i CMo O o O o O

m m CM t—1 m o- o-o cn 00 CM cn n-kH m co CM CM o i— i i—)

o o O o o o o

m m CM m cn CMO CT\ VO O 1 00 00 CO!>. -d" m VD 11 -d- m r-'-

i—i rH i—1 1 i—i rH rH

OV m m CO CM i—1 i—1o r-. vo vo r"> VO Oi— i tH CO CO CO CO mi—i »— i i— i I—1 i— i i—1 tH

CO CO o cn m i—I COo i—i CO CO 00 i—i m <r>v Hf CO CO COo o o o o o o

m m CM cn r-N mo vo 00 r~- cn o mrH r- r-~ m o- CO CO CM> • • • • • •

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Table Ex-B-6.1 SUMMARY OF THE EXPERIMENTAL RESULTS

TWO-COLUMN SYSTEM: MODE 4 BATCH OPERATION

Haemoglobin and Albumin

Haemoglobin AlbuminP^= 8.5, ^2= ^2~ 6.2, P^= 4.0

Number of < yT > n ^ yT> nCycles, n ^ ^B> n < yB> n

1 3.817 3.0512 8.779 7.2243 13.258 11.2584 14.269 11.6505 14.901 12.572

2 6 2

Table Ex-B-6.2 SUMMARY OF THE EXPERIMENTAL RESULTS

TWO-COLUMN SYSTEM: MODE 4 SEMI-CONTINUOUS OPERATION

Haemoglobin and Albtimin= 8.5 and ~ 6.2

Number ofHaemoglobin

< yT > nAlbumin< y T > n

Cycles, n < yB> n < yB> n

1 3.452 1.0222 8.320 1.7343 13.214 0.3474 14.904 0.5105 15.153 0.908

2 6 3

APPENDIX C

COMPUTER PROGRAM ON EQUILIBRIUM THEORY:SEPARATION OF MULTI-COMPONENT VIA

pH-PARAMETRIC PUMPING

The following material is appended to this work to deta­il the computational operations discussed in Chapters II and V. There follow, in order,

Table C-l, Nomenclature for Computer Program Input and Output

Exhibit C-l, The Computer ProgramExhibit C-2, Sample InputExhibit C-3, Sample Output, First 5 Cycles of Operation

2 6 4

TABLE C - l

NOMENCLATURE FOR COMPUTER PROGRAM INPUT AND OUTPUT

ProgramSymbolYHCOL1

YACOL2

YHRS3

YARS4

YHRSL5

YARSL6

YHRSR7

YARSR8

YHAO

YAAO

YHCO

TextSymbol

y ML

yML

yMR

yMR

y 0

y 0

y 0

Destinationaverage solute concentration of a higher isoelectric point in the flu­id phase for a column, duration t^average solute concentration of a lower isoelectric point in the flu­id phase for a column, duration t-j-javerage solute concentration of a higher isoelectric point in the reservoir, durationaverage solute concentration of a lower isoelectric point in the reservoir, duration t^yaverage solute concentration of a higher isoelectric point in the middle reservoir, ML, duration tyaverage solute concentration of a lower isoelectric point in the middle reservoir, ML, duration ty^average solute concentration of a higher isoelectric point in the middle reservoir, MR, duration ty^^average solute concentration of a lower isoelectric point in the middle reservoir, MR, durationinitial solute concentration of a higher .isoelectric point in an anion exchanger columninitial solute concentration of a lower isoelectric point in an anion exchanger columninitial solute concentration of a higher isoelectric point in a cation exchanger column

2 6 5

ProgramSymbolYACO

YHO

YAO

VVDEAD

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HCKP1

.AAKP2

ACKP3

YHOO

YAOO

YHRS1(1=1) YARS1(1=1) YHRS1(I=M) YARS1(I=M)

TABLE C-l (Cont'd)

Text ........-Symbol __ Designation

yo

yo

yo

yo

initial solute concentration of a lower isoelectric point in a cation exchanger column

y« solute concentration of a higherisoelectric point in the feedsolute concentration of a lower isoelectric point in the feed

V volume of fluid phase in the columnVg, Vrp reservoir dead volume

V volume of solid phase in the columnk” anion exchanger equilibrium constant^1 for a higher isoelectric point solute

at pH = P^ (high pH level)cation exchanger equilibrium constant

*± for a higher isoelectric point soluteat pH = P^ (high pH level)

k- anion exchanger equilibrium constant^2 for a lower isoelectric point soluteat pH = P2 (middle pH level)

k"1" cation exchanger equilibrium constant^3 for a lower isoelectric point soluteat pH = Pg (low pH level)initial solute concentration of a higher isoelectric point in the middle reservoir, MRinitial solute concentration of a lower isoelectric point in the middle reservoir, MR

^ ^ yT n t*le Prochict(s) in top reservoir| < y B> n the product(s) in the bottom reser­

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2 6 6

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YHAO YAAO YHCO YACO YHO YAO V VDEAD VB1.000 1.000 0.497 0.660 0.692 0.941 30.000 30.000 20.000

HAICP1 HCKPl AAKP1 ACKPl2.500 1.500 4.000 1.300

HAKP2 HCKP2 AAKP2 ACKP20.600 3.000 4.000 1.500

HAKP3 HCKP3 AAKP30.300 4.000 2.000

ACKP34.500

278

SENTKY

283

YHHS

H6=

0.10

139E

01

YARS

Kb=

0.10

357E

Ul

YHRS

Lbs

O.lO

OOOb

01

YARS

L6=

0.10

000E

01

284

Y H K S

k 3 -

0.98

285E

OU

YARS

R3=

0.89

389E

00

YHRS

L3=

0.99

909E

00

YAH5

L3

s 0.

9785

1E

00

288

YHKSL2

= 0.9

0374E OOY

ARS|_2

= 0.9

0617E

00YHKSR2=

0.9737

5E 00

YARSR2

= 0.1

0220E

01

2 8 9

tHkSLH

= 0.1

047 If 01

Y AR 5L 8 =

0.9564

7E

OOYH

RSRB

s 0.9

5589t

OOYARSRSs

0.1009

3E 01

SENTRY

YHWSi.l:

Q.10

665E

01YARSLl=

0.9375

0E OOYHKSRls

0.J0316E OlYARSRl=

0.10250E

0.1295

yhhSHS

s O.lOhHOt 01Y

APSWb>

= U.S

S237E UUYHRSLbs

O.lObbbE

01YARSLS=

0.9375

0E 00

YHKSLl

= 0.96908E 00 Y ARSL1=

0.9272IE

OOYHRSR

ls Q.9

9155E

OOYARSRla

0.1030

0E 01

297

YHKSR5

= 0.1

1190E

01YAR3R5=

0.95019E

00YHRSL5=

0.1U88E

01YARSL5a

0.8897

1E 00

3 0 1

TM

Khn

a=

li.H

hbH

iE

tiu»

AK

bW4=

0.

M2

969E

U

OY

HK

SIA

: 0.8

9083E

00 Y

AHSL

0*

0.8

5330E

00

310

312

314

APPENDIX D

TABLES: pH-PARAMETRIC PIMPING

Conditions for Computational the Results with variable parameters:

Operating Variable ValueVolume of Fluid Phase per Column Volume of Solid Phase per Column

30.0 cm^2 0 . 0 cm^

Initial Solute Concentration (Normalized) Dead Volume of Top Reservoir Dead Volume of Middle Reservoir

1 . 0 kg mole/cm^

Dead Volume of Bottom Reservoir

30.0 cm^30.0 cm^30.0 cm^

Number of Cycles 30

315

TABLE D-l

SEPARATION OF PROTEIN A Via TWO-COLUMNSP = 2.14

k" = 0 .6 , k-p = 1 .2 , k" = kp = 1.5, kt = kj = 0.7 2 V3

Number of Cycles, n

12345678 9

1011121314151617181920

Top Product^ y T > n

1.07831.14891.21001.26151.30431.33921.36751.39021.40381.42271.43401.44291.44981.45531.45951.46271.46531.46721.46871.4699

Bottom Product< y B > n

0.76390.72130.68820.66210.64160.62530.61250.60240.59450.58820.58340.57960.57670.57440.57270.57130.57030.56950.56890.5684

< y B > n

1.40071.59281.75831.90532.03302.14172.23272.30792.36912.41862.45802.48942.51392.53342.54852.56022.56942.57632.58172.5860

25 1.4726 0.5673 2.595930 1.4734 0.5670 2.5987

316

TABLE D-2

SEPARATION OE PROTEIN A Via TWO-COLUMNSZ3 - 3.00

k-o - 0 .6 , k1 = 1 .2 , k“ = k" = 1.5, kp = kp = 0.5

Number of Cycles, n

12345678 9

10 1 1

1 21314151617181920

Top Product

1.1539 1.2827 1.3873 1.4706 1.5363 1.5378 1.6279 1.6590 1.6831 1.7017 1 .7 16 1 1.7272 1.7358 1.7424 1.7474 1.7513 1.7543 1.7566 1.7584 1.7598

Bottom Producy

0.8691 0.7834 0.7247 0.6832 0.6529 0.6304 0.6135 0.6007 0.5909 0.5834 0.5777 0.5732 0.5699 0.5673 0.5653 0.5637 0 .5625 0.5616 0.5609 0.5604

< yT > n ^ B >n

1.3278 1.6375 1.9142 2.1526 2.3530 2.5187 2.6535 2.7619 2.8485 2.9170 2.9708 3.0131 3.0461 3.0717 3.0914 3.1067 3.1185 3.1277 3.1347 3.1403

25 1.7630 0.5591 3.153230 1.7638 0.5588 3.1564

317

TABLE D-3

V 1

NumberCycles

SEPARATION OF PROTEIN A Via TWO-COLUMNS

^ yT> n^ -^B^ n

.o, ki = 1 .

of

Z3 = 3.

2 » k.p = kp =2

Top Product ^ yT ^ n

2 0

1 .6 , ki = kt = 0 .5 2 3

Bottom Product yB > n

1 1.1539 0.8691 1 .32782 1.2907 0.7834 1.64773 1.4192 0.7242 1.95984 1.5441 0.6812 2.26675 1.6673 0 . 6 4 8 8 2.56996 1.7895 0.6234 2.87067 1.9103 0.6029 3 . 1 6 8 6

8 2 . 0 2 9 0 0.5859 3.46299 2.1448 0.5716 3.7523

1 0 2.2571 0.5592 • 4.03621 1 2.3653 0.5483 4.31361 2 2 . 4 6 8 8 0.5386 4.58361 3 2.5673 0.5298 4.845514 2•6606 0.5218 5.099215 2.7486 0.5143 5.344416 2 . 8 3 1 2 0.5073 5.580717 2 . 9 0 8 6 0.5007 5.808718 2.9807 0.4945 6.027819 3.0479 0.4885 6.23892 0 3 . 1 1 0 1 0 . 4 8 2 8 6.441525 3.3545 0.4571 7.338030 3.3546 0.4570 7.3400

318

TABLE D-4

k; = or i

NumberCycles

SEPARATION OF PROTEIN A Via TWO-COLUMNS

«£. yT> n^ yB > n

.8 , kp = 1 . r 1

of , n

2 , kp = kp =2 3

Top Product yT> n

50

1.4, kp = kp = 0.4 2 3

Bottom Product ^ yB > n

1 1 .1250 0.8214 1.36972 1.2421 0.7691 1.61513 1.3528 0.7105 1.90404 1.4576 0.6534 2 . 2 3 1 0

5 1.5568 0.6009 2.59096 1 . 6 5 0 0 0.5542 2.97737 1.7375 0.5133 3.38488 1 . 8 1 9 0 0.4779 3.80669 1.8948 0.4472 4.2367

1 0 1 . 9 6 5 0 0.4208 4.66921 1 2.0297 0.3981 5.09861 2 2.0893 ' 0.3785 5.52031 3 2.1440 0 . 3 6 1 5 5.93021 4 2.1940 0.3469 6.32461 5 2.2398 0.3342 6.70161 6 2.2815 0.3232 7.058717 2.3195 0.3137 7.3952

' 18 2.3541 0.3053 7.710319 2.3855 0 .2 9 8 1 - 8.00342 0 2.4140 0.2917 8.275325 2.5209 0.2699 9.339830 2.5853 0.2583 10.0093

319

TABLE D-5

SEPARATION OF PROTEIN A Via TWO-COLUMNS

^ y T> n<^yB > n

k; = o.s, k+ =1 .

Number of Cycles, n

Z3 . = 4..

0 , k" = k" = 1 2 3

Top Product< yT> n

0 0

.6 , ki = kp = 0.4 2 *3

Bottom Product < ^ yB > n

1 1.1860 0.8214 1.44402 1.3548 0.7634 1.77463 1 .5100 0.6978 2.16404 1.6534 0.6339 2.60855 1.7855 0.5755 3.10236 1 . 9 0 7 0 0.5240 3.63907 2.0182 0.4793 4.21048 2 . 1 1 9 6 0.4409 4.80739 2 . 2 1 1 6 0 . 4 0 8 0 5.4203

1 0 2.2949 0.3799 6.04051 1 2.3700 0.3559 6 . 6 5 8 8

1 2 2.4375 0.3354 7 . 2 6 6 8

13 2.4981 0.3179 7.857914 2.5523 0.3029 8.425915 2.6007 0 . 2 9 0 1 8 . 9 6 6 1

16 2.6439 0.2790 9.475317 2.6823 0.2695 9.951418 2.7165 0.2614 10.392919 2.7468 0.2543 10.79972 0 2.7737 0.2483 11.172125 2.8683 0.2282 12.570330 2.9191 0.2183 13.3738

320

TABLE D-6

SEPARATION OP PROTEIN A Via TWO- COLUMNS

3

^ yT> q^ yB > n

k-p = 0 .6 , kp = 1 •-M

Number of Cycles, n

Z 3 - 5-0 , kp — kp —

2 3

Top Product < yT ^ n

67

1 *7 , ki = kp = 0 .2 3

Bottom Product < ^ B > n

1 1.2746 0.8214 1 . 5 5 1 8

2 1.5133 0.7556 2.00273 1.7248 0.6806 2.53434 1.9136 0.6081 3.14715 2.0821 0.5427 3 . 8 3 6 8

6 2 . 2 3 2 1 0.4857 4.59567 2.3653 0.4369 5.41338 2.4831 0.3956 6 . 2 7 6 8

9 2.5869 0.3607 7.17151 0 2 . 6 7 8 0 0.3314 8.08181 1 2.7577 0.3067 8.99241 2 2 . 8 2 7 2 "0.2859 9 . 8 8 8 8

13 2 . 8 8 7 8 0.2684 10.758514 2.9404 0.2537 11.59051 5 2 . 9 8 6 0 0.2413 12.375716 3.0255 0 . 2 3 0 8 1 3 . 1 0 8 2

17 3.0596 0 . 2 2 2 0 13.783818 3 . 0 8 9 0 0.2145 1 4 . 4 0 1 6

19 3.1144 0.2082-' 14.96092 0 3.1363 0.2028 15.463525 3.2073 0.1861 17.238030 3.2403 0.1787 18.1367

321

TABLE D—7

SEPARATION OF PROTEIN B Via TWO-COLUMNS

A -

k” = kl = 0.3, kp = kp = 1.7 * 1 2 1 2

Number of Top ProductCycles, n ^ yT > n

1 1.08032 1.10853 1.11034 1.09945 1.08326 1.06567 1.04848 1.03269 1.0184

1 0 1.006011 0.99521 2 0.985913 0.977914 0.971015 0.965116 0 .9 6 0 117 0.955918 0.952219 0.94912 0 0.946525 0 . 9 3 8 1

0.18

kp = 2 .0 , kp = 0.3 3 3

Bottom Product ^Ty-Q^ n y-Q> n

1 . 3 3 6 1 0.80861.4436 0.76791.5155 0 .73261 . 5 6 6 2 0 . 7 0 2 0

1.6037 0.67541 .6327 0.65271.6558 0.63321 . 6 7 4 8 0 . 6 1 6 61 . 6 9 0 6 0.60241.7039 0.59041.7152 0 . 5 8 0 21.7248 0.57161.7330 0.56431 . 7 4 0 0 0.55801.7459 0 . 5 5 2 81.7510 0.54831.7554 0.54451.7591 0.54131 . 7 6 2 2 0 . 5 3 8 6

1.7649 0.53631.7735 0 . 5 2 9 0

30 0.9343 1.7773 0.5257

322

TABLE D-8

V

SEPARATION OB PROTEIN B Via TWO-COLUMNS= 0.53

= 0.5, kp = kp ='1.5, kp = 1.6, kp = 0.4

Number of Cycles, n

12345678 9

10 1 1

1213141516171819202530

Top Product< yT> n

Bottom Product < ^ B > n

* yT > n ^ yB > n

0.8709 1.0788 0.80730.7807 1.1689 0.66790.7163 1.2492 0.57340.6693 1.3194 0.50730.6342 1.3798 0.45970.6075 1.4312 0.42450.5869 1.4747 0.39800.5706 1.5113 0.37760.5577 1.5420 0.36170.5472 1.5676 0.34910.5388 1.5891 0.33910.5319 1.6070 0.33100.5263 1.6219 0.32450.5216 1.6343 0.31920.5178 1.6447 0.31480.5146 1.6533 0.31130.5120 1.6605 0.30830.5098 1.6665 0.30590.5080 1.6714/ 0.30390.5064 1.6756 0.30220.5019 1.6879 0.29740.5001 1.6929 0.2954

323

TABLE D-9

SEPARAT ION OF PROTEIN 3 Via TWO-COLUMNS

c y T> n< ^ > 7 1

k“ = kZ = 0 . 6

1 2

NumBer of Cycles, n

;s = 0 .

, kp = kp = 1 .5, * 1 2

Top Product^ y T > n

40

k” = 1.5, kp = 0.5 3 3

Bottom Product < ^ > 1 1

1 0.8597 1 . 1 2 0 9 0 . 7 6 7 0

2 0.7698 1 . 2 3 0 2 0 . 6 2 5 8

3 0.7092 1.3233 0.53594 0.6665 1.4002 0.47605 0.6355 1.4625 0.43456 0.6123 1.5123 0.40497 0.5948 1.5519 0.38338 0.5815 1 .5831 0.36739 0.5712 1.6076 0.3553

1 0 0.5633 1 . 6 2 6 8 0.34621 1 0.5571 1 . 6 4 1 8 0.33931 2 0.5524 1.6535 0.334013 0.5487 1 . 6 6 2 6 0.330014 0.5459 1 . 6 6 9 6 0.327015 0.5437 1.6751 0.324616 0.5420 1.6793 0 . 3 2 2 8

17 0.5407 1 . 6 8 2 6 0.321318 0.5397 1 .6851 0.320319 0.5389 1 .6871 0.31942 0 0.5383 1 . 6 8 8 6 0 . 3 1 8 8

25 0.5368 1.6923 0.317230 0.5365 1.6932 0 . 3 1 6 8

SEPARATION

OP PROTEIN

MIXTURE

A AND

B Via

TW

O-CO

LUMN

S

32.4

cqgApq o >> uv

e'­ te­ CO CM ■«d- 'd"en eni cn CM c— inO in ■'3- T— C cn cnCD ■sf cn cn tn CM CMs • • • • • •o O o O o o o

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X

oncn

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•ftM3

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CM

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oc O O '3* cn CM •*3*C— m c— T- O cn MDCM in T— cn -si* in intn, tn <n o T— T— r—• • « • • • •«T- CM CM tn tn tn tn

pq

PM

C £ CO 00 M3 c— M3 cn cnin in * A 00 cn C— 'd ' in c- CM• • c- c— MD '3' c— 00 cnT— o -p pq o cn in M3 M3 M3 M3o >> • 9 • • • • •II n £ . , V ■*— T— T”

pq

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<n CM CM 0 0 -a- cn T—o C— c— M3 T"” oc— tn T— O o o0 0 M3 in in in in in• m • • • • •o o O o O o O

M3•0II

1 PM X

in0 ii1 PM X

£•HCD-POPhPM

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T— cn cn *st" T- 00cn CM cn in o <n COMD in 00 M D M3 in in00 M D in in tn in in• • • • • • •o o o o o o o

g•HCD-POPhPM

pn£•HCD

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cn m C— •'fr cc o 00tn M3 H— c— cn tn cnin cn o in M3 MDT— in c— c— c— c— c—• • • ■ • • •T— T— H— T— T— T—

cm C oPh m <D 0>n= oC3 >■.

in in OCJ inCM

ccn

SEPARATION

OF PROTEIN

MIXTURE

C AND

I) Via

MU

LTI-

COLU

MN

325

c c "PA A • O CM n c- CM C—A 43 C- n n M3 CME- PC O MD T— c— O VO

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n■<3- • + Ph X

in

ii in I Ph XII

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CM

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mM3

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in

ii

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m 11M3

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c 0 CO <T> CM in OA A • c—CM

CT.M3

M3tn 1- 00tnEh PC 43 tn n 0 m tn>> >5 0 • • • • • •V V PhPh

CM 1" in M3 c—

nfi•HCD+3oShPh

aAEH

C•H03■POfH

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PQ

e'­ M3 tn 00 COen c- 00 M3 CM CMin O •d* 0000 M3 ■'d- tn CM CM• • • • • •

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P-H C OPh CO 0) 03-a (—1 5 C3c;

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3.3548

0.4570

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'H P OP cn <u <uR rHE a 3

LTv in OOJ

incm

C

329

APPENDIX D

GLOSSARY

batch

continuous

cycling zone adsorption

parametric pumping

parapump, PP

recuperative mode

semi-batch

separation factor

a parametric pump with no feed input or product withdrawalsoperation with feed during all parts of the cyclea cyclic separation processes with unidirectional flow of fluid and one or more beds in series. The bed temperatures or the inlet flu­id temperatures to each bed are varied periodically and are out of phase with the adjoining beda cyclic separation with periodic reversal of fluid flow direction utilizing fluid stored in reser­voirs. The bed or fluid tempera­ture (or other cyclic variable) are varied periodically to force the separationabbreviations for parametric pump­ingparametric pumping operation where the fluid flowing into the column is heated or cooled and the column itself is adiabatic. In general applies to operation where cyclic variable is changed in fluid flowing into the columnoperation of open parametric pump with product withdrawal at one end of column only. Concentration in reservoir at other end increases(Solute concentration in concen­trated product)/(Solute concen­tration in dilute product)

semi-continuous operation with feed during part of a cycle but not all of the cycle

330

1 .

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

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