Falling Drop Experiment

A study on liquid-liquid extraction

using a single drop

Team Leader: Thomas Salerno

Group Members: Gregory Rothsching

An Du

Presentation Agenda

Introduction – What is LLE and single drop extraction?

Theory – How do we analyze and model LLE?

Equipment and Procedure – What did we use?

Results and Discussions – What did we find?

Conclusions – How can we use these results?

Questions – What parts did I go too fast on?

Introduction

What is LLE?– One or more solutes are removed from one liquid

phase to another, immiscible phase which has a greater affinity for the solute

Why use LLE over distillation?– LLE requires no vaporization– Less expensive, no condenser nor reboiler

Introduction

Where is LLE used?– Penicillin manufacture– Petroleum Processing

Why is this experiment important?– Many of the predictive equations require

experimental measurements– Using single drop allows quick measurements on

lab scale instead of designing on a pilot plant scale

Theory - Experimental

Initial Measurements– Volume of Drop

– Terminal Velocity

T

Distancev

Time

50

50Drop

Volume of DropsVolume

Theory - Experimental

Mass Transfer Measurements– Mass Transfer Rate

– Overall Mass Transfer Coefficient

– Equilibrium Distribution Coefficient

HAc

moles of HAc extractedN

Time needed for extraction

,

,

HAc Wat

HAc Tol

Cm

C

*,* *HAc HAc WatN K A C C

Theory - Predictive

Terminal Velocity– Force Balance on Falling Drop

– Using the definition of terminal velocity

– Coefficient of Drag Correlation?

FGravity

FDrag FDrag FBouyancy

Velocity

* *2

D drop projectedgravity surrounding fluid gravity

drop

C v v Adv MM M a a

dt

.6

24Re 2

Re18.5

2 Re 500Re.44 Re 500

D

D

D

C for

C for

C for

2

2*

.44* *gravity Wat Tol

Wat Wat drop

a Mv

r

Theory - Predictive

Overall Mass Transfer Coefficient– Three mass transfer mechanisms

– Create one model to account for all?

Theory - Predictive

Outside Mass Transfer Coefficient– Apply regular boundary layer equations

Continuity:

Momentum:

Mass:

– Final Result:

2

2

u u uu

x y y

0u

x y

2

2A A A

x y AB

C C Cv v D

x y y

1/ 2 1/ 2

1/ 21.132

T HAcoutside

drop

v Dk

r

Theory - Predictive

Inside Mass Transfer Coefficient– Oscillating Drop

– Develop probability distribution

– Final Result:.00375

1

Ti

i

o

vk

Theory - Predictive

Overall Mass Transfer Coefficient– Two resistance theory:– Graphically relate driving force

– Result:

, ,A in A Wat Ai out Ai A TolN k y y k x x

"

'

*

*

mxx

yy

mxx

yy

AiA

AiAG

ALAi

AAi

1 1

in out

m

K k k

Equipment and Procedure

Week 1: Experimental Measurements

Volumetric Flow: mL per Minute

Volumetric Flow: mL per Hour

Equipment and Procedure

Week 2: Titrations

Results and Discussions

Terminal VelocityTerminal Velocity of Drop as a Function of Drop Diameter

y = 1.8303x - 0.0327

R2 = 0.9754

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.07 0.075 0.08 0.085 0.09 0.095 0.1 0.105 0.11

Square Root of Drop Diameter (m^.5)

Ter

min

al V

elo

city

(m

/s)

Experimental Velocity

Predicted Velocity

Linear (Predicted Velocity)

Results and Discussions

Distribution Coefficient

Results and Discussions

Overall Mass Transfer Coefficient– Experimental vs Theory:

Overall Mass Transfer Coefficient as a Function of Drop Diameter

-5

45

95

145

195

245

295

0.003 0.0035 0.004 0.0045 0.005 0.0055 0.006

Diameter of Drop (m)

Ove

rall

Mas

s T

ran

sfer

Co

effi

cien

t (1

0^-7

m/s

))

K Exp

K Pred

Linear (K Pred)

Results and Discussions

Overall Mass Transfer Coefficient– The Major Factors:

Individual Mass Transfer Coefficient as a Function of Drop Diameter

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

0.003 0.0035 0.004 0.0045 0.005 0.0055

Diameter of Drop (m)

Ind

ivid

ual

Mas

s T

ran

sfer

Co

effi

cien

t (1

0^-4

m/s

))

K inside drop

K outside drop

Linear (K outside drop)

Linear (K inside drop)

Results and Discussions

Overall Mass Transfer Coefficient– Instability Factor:

Accounts for non-idealities of the system Constant with diameter and scale-up

.00375

1inside

iIP

o

PeSh

C

1/ 221.13 T drop

outsideIP HAc

v rSh

C D

Results and Discussions

Overall Mass Transfer Coefficient– Experimental vs Predicted with

Overall Mass Transfer Coefficient as a Function of Drop DiameterExperimental versus Predicted with Fudge Factor

1.5

1.6

1.7

1.8

1.9

2

2.1

2.2

2.3

2.4

2.5

0.003 0.0035 0.004 0.0045 0.005 0.0055

Diameter of Drop (m)

Ove

rall

Mas

s T

ran

sfer

Co

effi

cien

t (1

0^-7

m/s

))

K Exp

K Pred FF

Linear (K Pred FF)

113.3IPC

Results and Discussions

Mass Transfer Rate– Two Factors: Surface Area and Mass Transfer Coefficient

Molar Transfer Rate as a function of Drop Diameter

y = 4058.2x - 8.0895

R2 = 0.9984

5

6

7

8

9

10

11

12

13

14

15

0.003 0.0035 0.004 0.0045 0.005 0.0055

Diameter of Drop (m)

Mo

lar

Tra

nsf

er R

ate

(m

ol p

er s

eco

nd

*10

^-8

)

Conclusions

Mass transfer coefficient decreases with increasing diameter

– Toluene Phase is the controlling resistance.

Mass transfer rate increases with increasing diameter

– The surface area is the controlling factor.

Trends were predicted by theory, however, experimental data is needed to get exact numbers

– Non-idealities in system: Surface tension, coalescence– Oscillations in drop.

Questions?