By Stanley Hartland

Counter-Current Extraction: An creation to the layout and Operation of Counter-Current Extractors supply necessary conclusions and effects touching on counter-current extraction. This e-book goals to give illustrations of a few of the mathematical options as instruments in addition to skill to an finish.

Organized into 8 chapters, this publication starts with an summary of many of the features of the move of a unmarried solute among immiscible levels in counter-current movement. this article then describes all attainable components and obtains their courting to the extraction issue and variety of phases or move devices. different chapters contemplate the flows and concentrations in counter-current ahead and again extraction. This publication discusses besides the optimization of ahead and again extraction utilizing counter-current circulate in differential and stagewise extractors. the ultimate bankruptcy offers with extra purposes of counter-current extractions.

Undergraduates and researchers fascinated by the layout and operation of counter-current extractors will locate this booklet beneficial.

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**Example text**

L. The direction in which the stages are numbered may be used to introduce the inverse relationships. Deriving the equation in terms of χ rather than y merely replaces each concentration by its equilibrium value. n L &2 x n+1 G g τ yζ I yn I Lxn G y n +i Lx2 û Lxi yN k (B) FIG. l. Flows and concentrations in a stagewise contactor. Numbering stages (A) from y inlet and (B) from χ inlet. 1 to Ν and / or / * . However, the expressions involving / * are the inverses of the corresponding expressions involving / .

I) + y,n(J 2(1) - 1 N+1 Qlj2. 3. 3. 3. The fourth edition of the Chemical Engineers' Handbook™ quotes _q _ Xin x out ~ x(y0ut) x(yout) _ J — I j n +1 2(5) ι ^s = ' " t t i - ^ g y ^ * ] 2) ( In 1//* which are not self-consistent. 3. 3 n d 6 34 COUNTER-CURRENT EXTRACTION The former gives negative values of Ns as may be seen by comparison with formula VIII. ( x ut x ut Ο* = ° ~ ^y° ' 2(7) 2(8) and this also leads to negative values of N. Examples of the use of these latter formulae are given in Appendix2c.

When the full concentrations range is considered the corresponding figures are 16%, 2% and 31 %. Finally Chapter 7 reviews the conclusions which have been reached throughout the book. Using these foundations Chapter 8 suggests how the work may be extended to more complicated cases and applied to other fields. Some of the material in the book is summarised in references 8-13. Notation for Chapter 1 a interfacial area per unit volume A total area of contact between phases L and G «s/, £ß integration constants c intercept of equilibrium line on j>-axis Ε overall stage efficiency G flowrate of phase in which solute concentration is y h distance along differential contactor H total length of a differential contactor Htu height of overall transfer unit J extraction factor ( / = mG/L) J* inverse extraction factor (J* = LjmG) kg individual mass transfer coefficient for phase G ki individual mass transfer coefficient for phase L kG overall mass transfer coefficient based on G phase overall mass transfer coefficient based on L phase kL L flowrate of phase in which solute concentration is χ m slope of equilibrium line (equation y = mx + c) η number of a typical stage 19 INTRODUCTION N number of theoretical stages or transfer units NA number of actual stages NG number of overall transfer units based on phase of flowrate G NL number of overall transfer units based on phase of flowrate L number of theoretical stages Ns NT number of transfer units Q separation factor (defined by equation 1 (3)) Q* inverse separation factor (defined by equation 1 (6)) s cross-sectional area of contactor S flowrate of intermediate solvent u superficial velocity of L phase ν superficial velocity of G phase χ solute concentration in phase of flowrate L x(y) χ concentration in equilibrium with concentration y (x(y) = (y - c)lm) y Solute concentration in phase of flowrate G y(x) y concentration in equilibrium with concentration χ (y(x) = mx + c) Greek symbols λ ξ φ χ ψ overall extraction factor in cross-current (λ = 7/(1 + / ) ) dimensionless χ concentration based on and yin dimensionless y concentration based on and yia dimensionless x concentration based on and xout dimensionless y concentration based on and yout Subscripts in out C G L 2a H-CC refers refers refers refers refers to inlet of contactor to outlet of contactor to cross-current extraction to phase of flowrate G to phase of flowrate L extraction concentrations xln concentrations χΐΛ concentrations xin concentrations yin 20 COUNTER-CURRENT EXTRACTION Superscript * denotes inversion The above quantities may be expressed in any set of consistent units in which force and mass are not defined independently.