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Applications of Reaction Calorimetry in the Chemical Process Industry

Reinaldo M. Machado

20 May 2105

ppt00 2

fundamentals of scale-up

© R.M.Machado, 2015

Numerous physical and chemical processes interact during a manufacturing or synthesis process. New manufacturing processes require fundamental information for scale-up and safety analysis

Kinetics

Heat

transfer

Thermodynamics;

Equilibrium

Mass transfer

Mixing

Physical property

changes

ppt00 3



Heat is Evolved or Consumed by Most Chemical Reaction Processes

Chemical reactions

Phase changes – Crystallization

– Vaporization/Condensation

Sensible changes

Mixing, solution

Viscous dissipation Friction of fluid elements “rubbing” together

ppt00 4


Heat Generation and Heat Removal Form the Basis of Reactor Scale-up and Safety Analysis

20 40 60 80 100 120 0

200

400

600

800

1000

1200

Temperature, C

Heat

Flo

w/V

olu

me,

watt

s/lit

er

Heat Generation :

qgen/Vrctr= A* e{-Ea/RT} f(CA,CB)

Heat Removal :

qcool/Vrctr= (UA/Vrctr){Trctr-Tjacket}

Increasing UA/Vrctr

& Lowering Tjacket


ppt00 5


Traditional Heat Flow Calorimetry Using The Mettler RC1

Reactor temp., (Tr) is controlled by adjustment of jacket temp. (Tj)

Jacket flow is sufficiently high that Tj is virtually constant, ±0.1OC

QFLOW = U A ( Tr - Tj )

Calibration U A = QCALdt

(Tr - Tj)dt

Temperature

Controller

QCAL QFLOW

Tr Tj


ppt00 6


Profiles for a Simple Batch Co-Polymerization

0 50 100 150 200 250

-10

-5

0

5

10

0

20

40

60

80

100

120

140

Time, minutes

Tr-

Tj,

oC

Tr,

oC


ppt00 7


Reaction Exotherm Profile for a Polymerization Process

0 50 100 150 200 250 300 -60

-40

-20

0

20

40

0

20

40

60

80

100

120

140

Time, minutes

Heat

Pro

du

cti

on

, w

att

s

Tr,

oC


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Heat Transfer Characterization

ppt00 9


Heat Transfer in CSTR’s Can be Correlated According to Empirical and Fundamental Models

Nu

Pr

Re

hTk

Cpk

ND

2

Nu Pr Rewall

C 1 3 2 3

014/ /

.

1 1 1U U h *


ppt00 10


Heat transfer characteristics of RC1 MP10 is similar to large scale reactors

0 1 2 3 4 5 6 -1

0

1

2

3

Log (Re) L

og

[N

u/(

Pr0

.33)]

Slope = 0.69

0.14

wall

32

31

RePrCNu

fluid

Number NusseltNu

Number ReynoldsRe

Number PrandtlPr

fluid

DiameterTankfluid

fluid

fluid

fluid

fluidfluid

k

Th

μ

NDρ

k

Cp

2


ppt00 11



Heat Transfer Characterized By a Single Correlation Equation for a Stirred Tank Reactor

14.0

3/2

*111

wall

rctroN

NZVCUU

31

22

rctr

rctrrctrrctr gCpk

Material Heat Transfer Parameter

3/1

3

24

TgND o

Reactor Geometric Parameter

ppt00 12



Wilson Plot Reveals Heat Transfer Resistances

3.0

2.5

2.0

1.5

1.0

0.5

0.0 0 1 2 3 4 5 6 7 8

(No/N) 2/3

1/U

Resistance of

Reactor Fluid

Resistance of Reactor

Wall and Jacket Fluid

Intercept = 1/U*

Slope = 1/(C V Z)

ppt00 13



Wilson Plot For Glycerol Reveals Impact of Temp. on Heat Transfer Coefficient

3.0

2.5

2.0

1.5

1.0

0.5

0.0 0 1 2 3 4 5 6 7 8

25oC

40oC

55oC

U* = 120 W/(m2 K)

1.5 liter Lab Reactor

K)W/(mU 2

100

32

100

rpmN

ppt00 14



Material Heat Transfer Parameter for Various Fluids at 30oC

Water 27,100

Toluene 7,710

Sulfuric Acid 8,820

Isopropanol 5,960

Glycerol 1,690

Polymers 100 to ~10,000 cp 5,000 to ~500

Material V, W/(m2 K)

ppt00 15


Deviations From Wilson Plot Indicate Mixing Problems

1/U

1/U*

(N/No)-2/3

Decreasing N(rpm) • High Wall Viscosity

• Poor mixing

• Pseudoplastic Fluid

Stagnant

Zone

Mixed

Zone


ppt00 16



Heat transfer with anchor impeller at 100 rpm with glycerol in MP10 lab reactor (1.5 liter, heat load = 25 kW/m3)

V hr U

TroC

cp

W/(m2 K) r

mm

TjoC

TrwoC

cp

w)0.14

25 940 1400 115 58.1 2.4 14 19 1600 0.93

40 274 2100 169 68.4 1.6 31 36 380 0.96

55 89 3000 276 83.7 0.9 48 53 100 0.98

U* = 120 W/(m2 K) Measured values

ppt00 17



Comparisons of VisiMix predictions and Experiments for Heat Transfer with Anchor Impeller at 100 rpm with Glycerol in the Mettler Toledo RC1 MP10 glass lab reactor

Inlet

Jacket

Temp. oC

Reactor

Temp. oC

Reactor

fluid

, cP

Re Overall Heat

transfer coeff. U

W/(m2 K)

Heat

removal

rate, W

Experiment 14 25 940 13

58.1 25.0

VisiMix 59.5 27.0


68.4 25.0

VisiMix 70.5 26.2


83.7 25.0

VisiMix 80.0 23.2

ppt00 18


Review article for coils in Agitated Vessels


ppt00 19


Tranter Prime Surface Heat Exchangers can serve as both baffles and heat exchangers

Plate coils are fabricated by

embossing channels on

opposing plates and

welding plates together.

Uniform temperature

distribution.


Photos from Tranter Inc. product brochure www.tranter.com

http://www.tranter.com/

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Reaction Rate Analysis: Hydrogenation

ppt00 21



Examples from a Hydrogenation/Oxidation process development laboratory

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Process Rates for Reductive Alkylation Help Identify Interaction of Feed Rate and Mixing

R-NH2 + 2 H2C=O + 2 H2 R-N(CH3)2 + 2 H2O + Q heat

1 1 2 2 3 3

.35

.30

.25

.20

.15

.10

.05

.00

800

600

400

200

0

0 2 4 6 8 10 12

Time, hrs.

No

rma

lize

d

Ra

tes

, 1

/hr

RP

M

Formaldehyde Hydrogen

Heat


ppt00 23



No baffle Baffle

ppt00 24



RC1 MP10 hydrogen mass transfer correlation in MeOH and IPOH

Isopropanol/H2

V*kLa = 0.2009*N - 98.949

R2 = 0.9667

Methanol/H2

V*kLa = 0.3077*N- 130.11

R2 = 0.9325

0

50

100

150

200

250

300

350

400

450

500 700 900 1100 1300 1500 1700 1900

rpm

Vliq

uid(c

m3)*

kLa

(s-1

)

ppt00 25


Lets take a look at developing a semi-batch process chemistry for Nitrobenzene hydrogenation to Aniline : The Engineer’s View!

NO2 + 3H2 NH2 + 2H2O

Hreaction = -537 kJ / mole


ppt00 26


Semi-batch operation can be used to simulate features of continuous operation under specific conditions

= Qin Cin - Rate VR dN dt

dN dt

= Qin Cin - Qout Cout- Rate VR

at high conversion

Continuous

Semi-batch

with small volume changes

dN dt

= Qin Cin - Rate V(t)


ppt00 27


Feed rate affects reaction rate during multi-ramp feed experiments. Lessons: 1) Calorimetry is a convenient method for measuring the overall reaction rates, 2) Programing feeds allow rapid kinetic characterization.

0 20 40 60 80 100 120 140

320

240

160

80

0

Time, minutes

Rea

cti

on

Rate

, w

att

s

Theoretical Feed Controlled Rate (~Infinitely Fast Reaction) =

Q = Feed rate x DHreaction

Reaction Rate


ppt00 28


Recall that the reduction of nitrobenzene can take two paths! Maybe changing conditions change between the paths.

NO2 NO H2

NOH H

H2 NH2

H2

Nitrobenzene Nitrosobenzene Phenylhydroxylamine Aniline

Phenylhydrazine Aniline

N + N

O -

H2

N N

H2

N H

N H

H2 2 NH2

Azoxybenzene

Azobenzene


ppt00 29


Nitrobenzene

When the feed rate was too fast for conditions (catalyst type, catalyst amount, pressure) nitrobenzene and intermediates accumulated to “poison” catalyst. Lesson: Engineers really do need Chemists!

0 20 40 60 80 100 120 140

Rea

cti

on

Rate

, w

att

s

Wt%

In

term

ed

iate

s

240

200

160

120

80

40

0

Time, minutes

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0

Azoxy-

benzene

Azobenzene


ppt00 30


Pressure increases the maximum rate which can be achieved. Identical programed multi-ramp feed experiments used to characterize process capability. Lesson: Use programed recipes to test conditions, catalysts, raw material quality.

0 40 80 120 160 200

200

160

120

80

40

0

Time, minutes

Rea

cti

on

Ra

te,

wa

tts

Ma

ss o

f F

eed

Ad

ded

, g

ram

s

Total Reactor Pressure

11 barg

8 barg

Feed Addition 50% Aniline/ 50% Nitrobenzene

200

160

120

80

40

0


ppt00 31



Programmed “ Disturbance ” Patterns Can Be Used to Screen Catalyst Performance

200

0 2 4 6 8 10

Reaction Time, hrs

Reacti

on

Exo

therm

, W

att

s

Three Increasing Feed Ramps; Repeated

150

100

50

0

1a 2a 3a 1b 2b 3b

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ppt00 33


Biazzi Impeller and mixing system


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Reaction Rate Analysis : Soybean oil hydrogenation

ppt00 35



Mass transfer tells us how fast we absorb H2

H2 (gas) H2 (liquid)

Rate of Absorption = kLa (sec-1) { [H2]sat.- [H2]bulk }

“Rate”

Constant

Increases with Agitation

Intensity and H2 Flow

Driving

Force

Increases with Pressure

and Usually Increases with

Temperature

ppt00 36



Hydrogenation of Soybean Oil

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

O H H H H H H H H H H H H H H

C C C C C C C C C C C C C C C C C C C H

O H H H H H H H H H H H H H H H H H H

C R’

H

H C O

H C O

H C O

H

GLYCEROL GLYCEROL

FATTY ACID FATTY ACID C R’

O

Approximately 50% of double bonds are

Polyunsaturates

ppt00 37


Olefin Hydrogenation Reactions

H2 +

Catalyst

+ ~23 kcal/mole H2

R' R R' R

cis

H2 +

R R'

Catalyst

+ ~23 kcal/mole H2

R R'

trans

H2

Catalyst R R'

trans

R' R

cis


ppt00 38


Process Conditions Impact Soybean Oil Hydrogenation Rates: Calsicat E-479D

Reaction Time, minutes

0

50

100

150

200

250

0 30 60 90 120 150 180 210 240

Rate

, w

att

s/k

g

30 psig, 180oC, kla=0.013 /sec





ppt00 39


0

50

100

150

200

250

% Conversion

Rate

, w

att

s/k

g

Polyunsaturate Monosaturate

100 80 60 40 20 0

30 psig, 180 C, kla=0.013/sec

30 psig, 180 C, kla=0.2/sec

45 psig, 180 C, kla=0.013/sec

30 psig, 200 C, kla=0.013/sec

Various Process Conditions Reveal a Consistent Transition @ ~50% Conversion


ppt00 40


Catalysts can be Screened for Selectivity and Activity

0

50

100

150

200

250

% Conversion

Rate

, w

att

s/k

g

Selective Catalyst

w/ High Activity

Non Selective

Catalyst

100 80 60 40 20 0


ppt00 41


Key Spectral Features of Soybean Oil

3011 cm-1

cis-isomer Virgin Oil

1749 cm-1

ester

50% Hydrogenated

965 cm-1

trans-isomer

100% Hydrogenated

3000 2500 2000 1500 1000

Wavenumber, cm-1


ppt00 42


FTIR Profiles Track trans - Formation

Wavenumber cm-1

1050 1000 950 850 800 750 700 900

200

150

100

50

0 Time,

min. 0.30

0.35

0.40

0.45

Ab

so

rban

ce


ppt00 43


FTIR Profiles Track cis- Disappearance

Wavenumber cm-1

3100 3050 2950 2900 2850 2800 3000

Time,

min. 0.30

0.50

0.90

0.70

Ab

so

rban

ce

200

150

100

50

0


ppt00 44


cis -trans -isomer Fraction during Soybean Oil Hydrogenation : Calsicat E-428D

% Conversion

Fra

cti

on

0.0

0.2

0.4

0.6

0.8

1.0

30 psig, 180oC

kla = 0.013 sec-1 (1000 rpm)

cis-isomer trans-isomer

100 80 60 40 20 0


ppt00 45


trans- Formation for Selective Calsicat E-428D is Not Sensitive to Process Variables

0

20

40

60

80

% Conversion

% T

ran

s i

n U

nre

acte

d

Do

ub

le B

on

ds

30 psig, 180 C, kla=0.013 /sec

30 psig, 180 C, kla=0.2 /sec

45 psig, 180 C, kla=0.013 /sec

30 psig, 200 C, kla=0.013 /sec

7 psig, 160 C to 215 C, Breen [1]

60 40 20 0


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Reaction Rate Analysis : Propoxylation of an aromatic amine

ppt00 47


MDA Propylene Oxide Reactions to Mono-, Di-, Tri- and Quad- Substituted Products

N H 2

N H 2

O 1.

N H 2

N H O H

198.27 58.08 256.35 A

PO M

1

N H 2

N H O H

O

N H O H

N H

O H 314.43 D12

2 M

N H O H

N H

O H

O

N H O H

N O H

C H 2

O H

4.

372.51

D12 T

4


ppt00 48


Symmetry and Similarity Suggest Kinetic Models with 2 Independent Rate Constants

Rate 1 = k1 CA CPO

Rate 2 = k2 CM CPO

Rate 3 = k3 CM CPO

Rate 4 = k4 CD12 CPO

Rate 5 = k5 CD11 CPO

Rate 6 = k6 CT CPO

k2 = k1/2

k4 = 2 k3

k5 = k1/2

k6 = k3

k1 = A1 exp{-E1/RT}

k3 = A3 exp{-E3/RT} © R.M.Machado, 2015

ppt00 49


Typical Rate Profile at 85oC

0

10

20

30

40

50

60

70

80

0 2 4 6 8 10

Time, hr

Reac

tio

n R

ate

, w

att

s

0

1

2

3

4

5

PO

Ad

ded

, g

mo

les

Propylene Oxide

Reaction Rate


ppt00 50



Comparison of Actual and Simulated Rate Profiles

0 1 2 3 4 5 6 7 8 9 10

Time, hrs

Reacti

on

Rate

, Q

r, w

att

s

85oC

100oC Lines = Simulation

Points = Data

70oC

ppt00 51



Final Rate Parameters Show Primary Amines ~10 x’s Faster than Secondary Amines

k1 = k1(To)exp{E1/RTo(1-To /T)}

k3 = k3(To)exp{E3/RTo(1-To /T)}

k1 = 6.29 x10-6 m3/(mol s) exp{48.2 kJ/mol /RTo(1-To /T)}

k3 = 6.45 x10-7 m3/(mol s) exp{48.5 kJ/mol /RTo(1-To /T)}

To = 85oC

ppt00 52


Comparison of Predicted and Observed Component Mass at all Temperatures

0.00

0.10

0.20

0.30

0.40

0.00 0.10 0.20 0.30 0.40

Component mass (observed), kg

Co

mp

on

en

t m

as

s

(pre

dic

ted

), k

g

Mono Di

Tri Quad

Parity


ppt00 53



Impact of PO Stoichiometry on Selectivity at 85oC

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Moles Propylene Oxide/Mole MDA

Mo

le F

rac

tio

n A

min

e G

rou

ps

Primary Tertiary

Secondary

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Reaction Rate Analysis: Oxidation of an alcohol

ppt00 55



Discrimination of Kinetic Models

Composition analysis alone is an incomplete method of

determining accurate kinetic models

Analysis of continuous rate measurement in

combination with composition is the best way to

discriminate various kinetic models

ppt00 56



Model Discrimination: CA0=100 gmole/m3, CB0=80 gmole/m3

A+B C

0

20

40

60

80

100

120

0 20 40 60

Time, minutes

Co

nce

ntr

ati

on

of

A,

gm

ole

/m 3

0.0

0.4

0.8

1.2

1.6

2.0

Reac

tio

n R

ate

, g

mo

le/(

m 3

min

)

0-order

1st-order

2nd-order

0-order

1st-order

2nd-order

Lines = Rate

Points = Concentration

ppt00 57



Case History: Alcohol Oxidation with Heterogeneous Catalysis

OH

R+ O2 + M

+OH

-

R

CO-M

+

O

+ 2 H2O

OH

R + M+OH

-

R

CO-M

+

O

+ 2 H2

Cat.

Original research determined that this reaction was 1st

order in the alcohol. The batch kinetics data was

based exclusively on composition samples,

approximately 10 samples per experiment. Oxygen

pressure was held constant.

ppt00 58



Batch Alcohol Oxidation to Carboxylate Salt

0

50

100

150

200

250

0 50 100 150 200

Time, minutes

Rate

, w

att

s

0

1

2

3

4

5

Pre

ssu

re,

barg

Rate

Pressure

OH

R+ O2 + M

+OH

-

R

CO-M

+

O

+ 2 H2O

ppt00 59



Typical Reaction Characterization of Alcohol Oxidation with a Slurry Catalyst indicates more complex Kinetics

Substrate Concentration (based on thermal conversion)

Rate

, m

ole

/[se

c m

3]

Pre

ssu

re,

barg

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0% 10% 20% 30% 40% 50% 0

1

2

3

4

5

6

Rate

Pressure

1st order region

Ost order region

ppt00 60



Typical Heterogeneous Kinetics: Oxidation of Substrate S

catalyst Weight%% where,

O & S inorder -1st ,%

0@

O inorder -1st S, inorder -Zero ,%

@

Transfer, Masshigh With

1

%

2.,1

2

.,1

.,

1

2

2

22

2

wt

CCwtkRate

C

K

CwtkRate

C

CC

CK

CCwtkRate

satOS

S

satO

S

satOO

S

OS Simple model

explains results!

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Thermal Safety Analysis: Propoxylation of an aliphatic amine

ppt00 62



Illustration Problem: Propylene Oxide Addition to an Amine; A(amine) + B(propylene oxide) C

Homogeneous Liquid Phase

The amine is in large excess over propylene oxide

– Reaction is 1st-order in propylene oxide

Reactor volume can be assumed constant

Propylene oxide is added at a constant rate over time,

tadd

OR1 NH2 + R1 N

HOH

ppt00 63



Heat Evolution is a Function of Reactor Temperature and Feed Rate, 60oC

0 200 400 600 800 0

5

10

15

20

Time, minutes

Heat

Evo

luti

on

, w

att

s

50

150

200

100

Mass o

f P

O, g

ram

s

PO + Amine Alcohol

ppt00 64



Accumulated propylene oxide can be considered “Stored Energy” during semi-batch addition

time, minutes 0 200 400 600 800

0.0

0.5

1.0

1.5

2.0

2.5

no

rmali

zed

reac

tio

n

rate

(W)/

tota

l h

ea

t (J

),

(s-1

) x

1000/6

0

Stored reaction

energy @ end

of PO addition

Time

Tem

p.

This is what could happen

if we loose cooling at the

end of the addition! End of addition

ppt00 65



Increasing addition time reduces maximum exotherm and stored reaction energy

0 200 400 600 800 0

2

4

6

8

10

time, minutes

120 min. addition time

for propylene oxide

480 min. addition time

for propylene oxide

no

rmali

zed

reacti

on

rate

(W)/

tota

l h

eat

(J),

(s-1

) x

100

0/6

0

ppt00 66



Increasing reactor temperature reduces stored reaction energy

0 200 400 600 800 0.0

0.5

1.0

1.5

2.0

2.5

time, minutes

60oC

75oC

105oC

no

rmali

zed

reacti

on

rate

(W)/

tota

l h

eat

(J),

(s-1

) x 1

000/6

0

ppt00 67



MTSR After Cooling Loss Just at the Point of Complete Propylene Oxide Addition (120 minutes)

Limiting

Temp. 110oC

37oC

80oC

Reactor Temp.,oC, During Addition of PO

0 50 100 150 75 25 125 0

50

100

150

25

75

125

Fin

al R

eacto

r Tem

p.,

oC

Net Adiabatic DT = 100oC

ppt00 68



MTSR After Cooling Loss Just at the Point of Complete Propylene Oxide Addition

120 min.

Reactor Temp.,oC, During Addition of PO

0 50 100 150 75 25 125 0

50

100

150

25

75

125

Fin

al R

ea

cto

r Te

mp

.,oC

30 min.

480 min.

Addition Rate

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General Conclusions

ppt00 70


Reaction Calorimetry

Realtime rate feedback allows investigators to

interact and optimize processes online

Addition Strategy and Feed Rates are key process

design variables

Thermal Reaction Profiles generated to

– compare process strategies

– screen raw materials with programmed “Disturbance” patterns; temperature, feed rate, pressure. agitation

– “process thermal spectra”

Heat transfer characterization of difficult materials

and intermediates © R.M.Machado, 2015

ppt00 71


Reaction Calorimetry

Characterizes Kinetics, Mass Transfer, Heat

Transfer, Thermodynamics, Physical Property

Changes

Thermal Data Allows Efficient Development of

– Optimized processes

– Scaleable process

– Safe processes


ppt00 72


Online FTIR

Monitors Selectivity in Complex Reaction Sequences

ConcIRT Provides Rapid Analysis without Standards


ppt00 73



Semibatch Processes at High Temperature Can be Advantageous

Lower reaction mass viscosity

– Improved mixing

– Improved heat transfer

Higher heat removal driving force, Tr-Tj

Increased kinetic reaction rates

– Shorter batch times

Improved reagent and product solubility

Reduced risk of reagent accumulation

– Lower stored exotherm energy

ppt00 74



Semibatch Processes at High Temperature may also create unwanted results

Increase rate of by-product formation

– Lower selectivity due to by-product formation

– Color problems

Increase pressure from increased solvent vapor

pressure

Longer cool down time

ppt00 75


Reinaldo “Ray” Machado

phone: (484) 553-3612

E-mail: [email protected]

Website: www.rm2tech.com

Ray is the instructor of short course

“Fundamentals of Scale-up”, which may be offered at your site.

Reinaldo (Ray) Machado is the developer and instructor of a popular industrial short course, “Fundamentals of

Scale-up” which he teaches part time. Proceeds from the course supports EWB, Engineers Without Borders.

Ray is also currently employed by Air Products and Chemicals, Inc. in Allentown, PA where he serves as a

senior process engineer supporting both the Electronics and Performance Materials Divisions. He also serves

as a senior consultant specializing in gas/liquid reaction engineering and electrochemical engineering and

provides global support for hydrogenation and oxidation applications for both internal and external customers.

Ray has broad technical experience in applied reactor engineering, scale-up of chemical reaction processes,

mass transfer, heat transfer, applied reaction calorimetry, hydrogenation, electrochemical engineering,

sulfonation, amination, propoxylation, polymerization, and plastics recycling.

Ray received a Ph.D. in chemical engineering with a concentration in chemistry from the University of

Wisconsin, Madison, and a B.A. in chemistry and mathematics from Frostburg State University. He has served

as a part-time instructor of a short course, “Scale-Up Considerations in Chemical Processes,” at Lehigh

University and currently teaches industrial courses on the fundamentals of scale-up. He holds 17 patents, has

collaborated on 17 publications, and is a member of the American Institute of Chemical Engineers and the

American Chemical Society. © R.M.Machado, 2015

mailto:[email protected]

http://www.rm2tech.com/

ppt00 76


(c) Reinaldo Machado; rm2technologies LLC 2011

Titration by Reinaldo Machado

Into the acid brew, fall bitter drops of base.

Whirling pink ribbons, consumed without a trace.

Each fresh drop gives life, to stronger crimson swirls. A spinning fatal dance, in twisting eddy whirls.

A hesitant drop descends, into the vortex roll. A fiery flash of red transforms the mixture whole. © 2011 Reinaldo Machado

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