# Counter-Current Extraction

## 1st Edition

### An Introduction to the Design and Operation of Counter-Current Extractors

**Authors:**Stanley Hartland

**eBook ISBN:**9781483160641

**Imprint:**Pergamon

**Published Date:**1st January 1970

**Page Count:**280

## Description

Counter-Current Extraction: An Introduction to the Design and Operation of Counter-Current Extractors provide useful conclusions and results pertaining to counter-current extraction. This book aims to present illustrations of the various mathematical techniques as tools as well as means to an end. Organized into eight chapters, this book begins with an overview of the various aspects of the transfer of a single solute between two immiscible phases in counter-current flow. This text then describes all possible factors and obtains their relationship to the extraction factor and number of stages or transfer units. Other chapters consider the flows and concentrations in counter-current forward and back extraction. This book discusses as well the optimization of forward and back extraction using counter-current flow in differential and stagewise extractors. The final chapter deals with further applications of counter-current extractions. Undergraduates and researchers involved in the design and operation of counter-current extractors will find this book useful.

## Table of Contents

Preface

Glossary

Notation

1. Introduction

1.1. Basic Equations

1.2. Inverse Separation Factors

1.3. Graphical Representation

1.4. Absorption and Stripping

1.5. Concentration Profiles

Stagewise

Differential

1.6. Application of the Equations

1.7. Units and Dimensions

1.8. Straight Equilibrium Lines

1.9. Comparison with Cross-current Extraction

1.10. A General Survey

Notation

References

Appendices

1a. Stagewise Concentration Profiles

1b. Differential Concentration Profiles

1c. Cross-current Extraction

2. Formulae Relating N and J to the Different Separation Factors Q

2.1. Introduction

2.2. Separation Factors

2.3. Inversion

2.4. Formulae Relating N, J and Q

2.5. Comparison with Other Formulae

2.6. Analogy with Heat Transfer

2.7. Discussion

Example 2.1

Example 2.2

Notation

References

Appendices

2a. Inversion of Formulae Relating N, J and Q

2b. Derivation of Formulae Relating N, J and Q from Basic Principles

2c. Examples of the Use of Formulae Relating N, J and Q

2d. Numerical Examples of Heat Transfer Using NT (1 — J ) = ln Q

3. Errors in the Calculation of Numbers of Stages and Transfer Units

3.1. Introduction

3.2. Theory

3.3. Discussion

Example 3.1

Notation

References

4. The Optimisation of Counter-current Forward and Back Extraction

4.1. Introduction

4.2. Equations Governing the Optimisation of Forward and Back Extraction

Basic Equations

Overall Separation Factor

Optimisation

Inversion

Second-order Derivatives

4.3. Solution of the Equations

Differential Case

Stagewise Case

4.4. Comparison with Ordinary Counter-current Extraction

Differential Case

Stagewise Case

Example 4.1

Example 4.2

4.5. Operation of an Existing Contactor

Differential Case

Stagewise Case

Example 4.3

Example 4.4

Notation

References

Appendices

4a. The Relationship between Overall and Individual Separation Factors

4b. Comparison with Other Formulae for Forward and Back Extraction

4c. Use of Other Separation Factors in Forward and Back Extraction

4d. Derivation of (∂Q0\∂N1) and (∂Q0\∂J1)N1

4e. Derivation of (∂2Q0\∂N21) and ∂2Q0\∂N1∂J11

4f. Derivation of (∂2Q0\∂J21) and ∂2Q0\∂J1∂N1

4g. Derivation of (∂P\∂N1)J1 and (∂P\∂J1)N1

4h. Solution of the Equations Governing the Optimisation in a Stagewise Contactor

4i. Limiting Cases of the Equations a Stagewise Contactor

4j. The Optimum Operating Conditions in an Existing Differential Extractor

4k. Solution of the Equations Governing the Optimum Operating Conditions in an Existing Stagewise Extractor

4l. The Optimum Operating Conditions in an Existing Stagewise Extractor

4m. Computer Program 4.1. Newton-Raphson Technique for the Optimum Design of a Stagewise Extractor

4n. Computer Program 4.2. Random Search Technique for the Optimum Design of a Stagewise Extractor

4o. Computer Program 4.3. Newton's Method for the Optimum Operating Conditions in an Existing Stagewise Extractor

4p. Computer Program 4.4. Random Search Technique for the Optimum Operating Conditions in an Existing Stagewise Extractor

5. Forward and Back Extraction Using Cross-current Flow with Recirculation

5.1. Introduction

5.2. Theory of Cross-current Extraction with Recirculation

5.3. Comparison with Counter-current Forward and Back Extraction

5.4. Comparison with Ordinary Counter-current Extraction

Example 5.1

Notation

References

Appendix

5a. Design and Operation of a Cross-current Forward and Back Extractor

6. Linear Equilibrium Data

6.1. Introduction

6.2. Theory

6.3. Experimental Data

1. Sources of Data

2. Analysis of Data

6.4. Results and Discussion

Least Squares Criteria

Tabulation

Extraction Studies

Physical Properties

Notation

References

Appendices

6a. To Fit a Straight Line to Data by the Method of Least Squares—The Regression of y on x

6b. To Fit a Straight Line to Data by the Method of Least Squares—The Regression of x on y

6c. To Fit a Straight Line through the Origin by the Method of Least Squares—The Regression of y on x

6d. To Fit a Straight Line through the Origin by the Method of Least Squares—The Regression of x on y

6e. Reduction of Functional Relationship to the Two Regressions

6f. Computer Program 6.1. Functional Relationships and Least Squares Regressions for Equilibrium Data

6g. List of Systems Investigated

6h. Slopes and Errors of Lines through Origin

6i. Parameters of Lines through Mean Values x and y

6j. Physical Properties of Solvents and Solutes

7. Conclusions 9 7.1. Generalised Form of Equation

7.1. Generalised Form of Equation

1. Differential Formula

2. Stagewise Formula

7.2. Introduction

1. Absorption and Stripping

2. Concentration Profiles

3. Cross-current Extraction

7.3. Separation Factors and Basic Formulae

1. Separation Factors

2. Inversion

3. Basic Formulae

4. Particular Formula

5. Recommended Formula

6. Straight-line Plots

7. Graphical Representation

8. Inaccuracies

9. Heat Transfer

7.4. Errors in N, J and Q

1. Effect of Errors in J

2. Effect of Errors in Q

3. Magnitude of Errors in J and Q

4. Effect of Errors in N

7.5. Forward and Back Extraction Using Counter-current Flow

1. Optimisation

2. Differential Extractor

3. Alternative Formulae

4. Stagewise Extractor

5. Approximate Solution

6. Alternative Formulae

7. Comparison with Ordinary Counter-current Extraction

8. Operation of Existing Differential Extractor

9. Operation of Existing Stagewise Extractor

7.6. Forward and Back Extraction Using Cross-current Flow with Recirculation

1. Recommended Formula

2. Alternative Formulae

3. Minimum Number of Stages

4. Comparison with Counter-current Forward and Back Extraction

5. Comparison with Ordinary Counter-current Extraction

7.7. Linear Equilibrium Data

1. Systems Investigated

2. Tabulation of Slopes

3. Systems with Error in Slope of less than 1%

4. Systems with Error in Slope of less than 2%

Notation

8. Further Applications

General Applications

8.1. Form of Presentation

8.2. Errors

8.3. Optimisation

Forward and Back Extraction

8.4. Effect of Solvent Washing

8.5. Minimum Capital Cost

8.6. Economic Optimisation

8.7. Empirical Correlations

8.8. Curved Equilibrium and Operating Lines

8.9. Non-equilibrium Stages

8.10. Cross-current Extraction

Linear Equilibrium Data

8.11. Effect of Concentration Units

8.12. Effect of Concentration Range

Notation

References

Index

## Details

- No. of pages:
- 280

- Language:
- English

- Copyright:
- © Pergamon 1970

- Published:
- 1st January 1970

- Imprint:
- Pergamon

- eBook ISBN:
- 9781483160641