Is mixing to blame for process scale-up failure?

Revision 1

Jocelyn Doucet, P.Eng., Ph. D. CEO Pyrowave

Adjunct Pr. Dept. Chem Engineering, Polytechnique

© Jocelyn Doucet, 2016

Blue box

The problem Scaling up processes is difficult

There are three main elements involved in process developments

Thermodynamics

Kinetics

Transfers Heat

Mass

Momentum

Thermodynamics

Kinetics

Transfers Heat

Mass

Momentum

Pressure, Temperature,

Concentrations

Velocities, characteristic

dimensions

Lab scale Full scale

Pressure, Temperature,

Concentrations

Blue box

Interphase reaction Our views is that transport phenomena is intimately linked to mixing

Lab scale

𝑣

𝑘𝐿𝑎(𝐶∗𝐵 − 𝐶𝐵)

𝑟𝐴 = 𝑘 𝑇 𝐶𝐴𝐶𝐵

𝐶𝐴 𝑡 , 𝐶𝐵 𝑡 𝐴 + 𝐵 → 𝐶

𝑑

𝑑𝑡𝐶𝐴 𝑡 = −𝑘 𝑇 𝐶𝐴𝐶𝐼

𝑑

𝑑𝑡𝐶𝐼 𝑡 = 𝑘𝐿𝑎 𝐶

∗ − 𝐶𝐼 − 𝑘 𝑇 𝐶𝐴𝐶𝐼

Remarks

𝛻𝑣 ↓, 𝐷 ↑, 𝑎/𝑉 ↓

𝑣 ↓, 𝑘𝐿 ↓

Mass transfer is a 𝒇(𝒗)

𝐷

Full scale

𝒗’

𝒌′𝑳𝒂′(𝐶∗𝐵 − 𝐶𝐵)

𝑟𝐴 = 𝑘 𝑇 𝐶𝐴𝐶𝐵

𝐶𝐴 𝑡 , 𝐶𝐵 𝑡 𝐴 + 𝐵 → 𝐶

𝑫′

Blue box

Solid-solid heat transfer Mixing is also playing a key role in heat transfer

𝜌𝑖𝐶𝑝,𝑖𝑇𝑖 𝑇𝑤

𝜌𝑖𝐶𝑝,𝑖𝑑

𝑑𝑡𝑇𝑖 = 𝛻 ∙ −𝑘𝛻𝑇

𝑣

𝜌𝑖𝐶𝑝,𝑖𝑇𝑖

Blue box

Solid-solid heat transfer Mixing is also playing a key role in heat transfer

𝑇𝑤

𝜌𝑖𝐶𝑝,𝑖𝑑

𝑑𝑡𝑇𝑖 = 𝛻 ∙ −𝑘𝛻𝑇

• Residence time at

wall is critical

• Probability of hitting

the wall is 𝑓(𝑣 )

Heat transfer is 𝒇(𝒗)

𝑣

Blue box

Scale-up Why are we so far from the real solution when scaling up processes?

Two observations I made 1) We are approaching transfer problems as mixing problems too quickly.

• It limits the possibilities for alternate solutions beyond mixing theory

2) We are spending too much time and $ on models/CFD and not doing the

right experimental work. • Industrials want an operating point, not a theory.

• All models work just fine for a very small onset of cases, but are totally off with

realistic systems.

Blue box

How do we do scale-up normally? Maintaining flow regime by scaling up mixing operations

Calculation of

𝒗, 𝑵𝒑 , 𝑲𝑻, etc

Identify hydrodynamic

parameters

Extrapolation

to large scale

Large unit

Lab scale

technology

Selection of the mixing device

Parameters

Selection of mixing

device and power to

keep mixing similar

Application to new large scale conditions

Process problems

Blue box

How do we approach this? Maintaining flow regime by scaling up mixing operations

Identify hydrodynamic

parameters

Extrapolation

to large scale

Large unit

Lab scale

technology

Characterization of the mixing device

Parameters

Selection of mixing

device and power to

keep mixing similar

Application to new large scale conditions

Optimization of

mixing device

Process problems

Calculation of

𝒗, 𝑵𝒑 , 𝑲𝑻, etc

Blue box

Taking a step back Is it really a mixing problem more so than a problem about transfers?

Transfers Heat

Mass

Momentum

Mixing

Hydrodynamics

Global transfert

coefficients

P/V

𝑁𝑄

𝐾𝑇

Fields Tools

𝛻𝑣 (Shear rates)

𝑣 ∙ 𝑑𝑆 (RTD)

𝑝 , 𝑣

Estimation of

Estimation of

Blue box

Example I Classical tire pyrolysis has a big heat transfer problem

Blue box

Example of heat transfer Classical tire pyrolysis has a big heat transfer problem

Insulating layer

Tires RTD at surface → 0

Heat transfer with tires → 0

In the mixing framework: segregation must be prevented

Blue box

Taking a step back Is it really a mixing problem more so than a problem about transfers?

Transfers Heat

Mass

Momentum

Mixing

Hydrodynamics

How can we heat otherwise than using

the wall?

How can we minimize segregation?

Fields Tools

Can we add baffles?

Can we rotate faster/slower?

Particle size?

Blue box

Example of heat transfer Microwave tire pyrolysis is insensitive to fouling

Insulating layer

Tires RTD at surface → 0

Heat transfer with tires: unchanged

The problem is now to contain microwaves safely in the reactor: that we know how to do!

Blue box

How do we approach this? Maintaining flow regime by scaling up mixing operations

Identify hydrodynamic

parameters

Extrapolation

to large scale

Large unit

Lab scale

technology

Characterization of the mixing device

Parameters

Selection of mixing

device and power to

keep mixing similar

Application to new large scale conditions

Optimization of

mixing device

Process problems

Calculation of

𝒗, 𝑵𝒑 , 𝑲𝑻, etc

Blue box

How did we approach this? Revisiting the technology to maintain proper heating rates

Extrapolation

to large scale

Large unit

Characterization of the

heating device

Parameters

Selection of large scale

MW reactor to keep heating

rate similar

Application to new

large scale conditions

Change to

microwave

heating

Process problems

Identify hydrodynamics

Lab scale

MW reactor

Calculation of

Heating rates, etc

Blue box

Example II Aerobic fermentation of yeasts in CSTR

Air

Agitator/sparger

Air

Blue box

Example III Agitator has two functions

Air

Air

Fluid circulation (momentum transfer)

Air dispersion (mass transfer)

Air

Work

P

Blue box

How do we approach this? Increasing oxygen transfer by scaling up mixing operations

Identify hydrodynamic

parameters

Extrapolation

to large scale

Large unit

Lab scale

technology

Characterization of the mixing device

Parameters

Selection of mixing

device and power to

keep mixing similar

Application to new large scale conditions

Optimization of

sparger to increase

𝑘𝐿𝑎

Process problems

Calculation of

𝒗, 𝑵𝒑 , 𝑲𝑻, etc

Blue box

Taking a step back Is it really a mixing problem more so than a problem about transfers?

Transfers Heat

Mass

Momentum

Mixing

Hydrodynamics

How can we transfer more oxygen in

the broth?

What agitator and conditions will

increase 𝑘𝐿𝑎?

Fields Tools

Can we increase P/V ratio?

Can we increase shear to reduce

bubble size (agitator design, number

etc)?

Blue box

Aerobic fermentation Oxygen limiting process – how to increase oxygen transfer

Air

Air

Work

P

We need more oxygen

a) Agitator design (𝑘𝐿𝑎)

a) Reduce bubble size

b) Increase shear rate

b) Increase the gradient (no mixer

involved)

𝑞 = 𝑘𝐿𝑎(𝐶∗𝐵 − 𝐶𝐵)

Blue box

Aerobic fermentation Playing with the equilibrium to speed-up transfer

𝑃 (𝑎𝑡𝑚) 1

7 𝑑𝑥𝑂2𝑑𝑡

= 𝑘𝐿𝑎(𝟕 − 𝑥)

𝑃 (𝑎𝑡𝑚) 1 2

7

14

𝑑𝑥𝑂2𝑑𝑡

= 𝑘𝐿𝑎(𝟏𝟒 − 𝑥)

𝑥𝑂2

𝑚𝑔/𝐿

𝑥𝑂2

𝑚𝑔/𝐿

Blue box

Increasing mass transfer Increase pressure to reach atmospheric condition equilibrium faster

0

2

4

6

8

10

12

14

16

0 1 2 3 4

𝑷 = 𝟏 𝒃𝒂𝒓

𝑷 = 𝟐 𝒃𝒂𝒓𝒔

0.6 t/𝑘𝐿𝑎

𝑥𝑂2

𝑚𝑔/𝐿

Blue box

Increasing mass transfer Reduce bubble size by using porous media to increase 𝑘𝐿𝑎

Blue box

Aerobic fermentation Recirculating on high pressure offside sparger

Air

Air P

Compressed

air 2 bars

Porous

diffuser

Air saturation

at 2 bars

More oxygen

in the broth

150% increase in

production rate

Blue box

Few observations Scaling up is challenging when hydrodynamics is involved

• Maintaining similar hydrodynamic conditions is often impossible • Velocity field

• Pressure field

• Power to volume

• Hydrodynamics is responsible for scale-up problems because it

impacts local transfers • The solution is not always mixing!

• The solution can lie in a different approach.

• Must ensure that the problem is really a problem of mixing and not a problem of

transfer.

Blue box

Second observation We are spending too much time and $ on models/CFD and not doing the right experimental work

• We need an operating point, not a theory!

• CFD and computer simulations provide solution to the Navier-Stokes equation

and solves for P and 𝒗 fields.

• Problem when using CFD for scale-up in real conditions

• They require numerous constitutive equations that increase with increasing

number of phases

• Turbulence is still an issue

• Resolution is cut off to cut computational time

• Complex boundary conditions create poor numerical conditioning

• At the end of this, CFD does not give mixing and transfer values, it gives 𝒗 and P

fields.

CAD

simulations

Blue box

How we do computer design now? Using CFD models to reproduce lab data and give scale-up guidance

Lab work

Iteration on parameters

to fit experiments

Generate

large scale

mesh

Optimum

parameters

Results

(mixing time

etc)

Iteration on geometries

and components

Optimum

config

Commercial

design

Extrapolation zone

3D printing

the geometry

Blue box

How can we use computer now? How can we do the right experiment to get a working point?

Large scale

geometry

Results

(mixing time

etc)

Iteration on geometries

and components until satisfactory

Optimum

config

Commercial

design

Large scale

exp

Non-intrusive

methods Materials range

Wide size range

Tracer

Detector

Amplifier/

Discriminator

High speed

counter

(x,y,z)

Position

reconstruction

(f -1)

Doucet, J., Bertrand, F., Chaouki, J., Powder

Technology 181, 195-204 (2008).

Non-intrusive techniques Time series analysis is well established for extracting mixing information on flows

Velocity field

Rushton Turbine

0 0.5 10

0.2

0.4

0.6

0.8

1

r/R

z/H

−1 −0.5 00

0.2

0.4

0.6

0.8

1

r/R

z/H

RPT CFD

30

Flat surface for CFD simulations Use of zero-thickness baffles

Velocity fields can be recovered Time series analysis is well established for extracting mixing information on flows

Blue box

Do we really need 𝒗 ? Most of our work needs transfer rates and RTDs , i.e. the integrated form

0 0.5 10

0.2

0.4

0.6

0.8

1

r/R

z/H

−1 −0.5 00

0.2

0.4

0.6

0.8

1

r/R

z/H

Typically we start with

the velocity field

Then …

We integrate the trajectories of a set Ω of

particles flowing on the field to calculate

• Lyapunov exponents

• Diffusion coefficients

• Residence time distribution

• Some sort of « Mixing efficiency »

−0.1 0 0.10

0.1

0.2

r (m)

Z (

m)

𝒗Ω

𝑑𝑡

Blue box

Working with 𝒙 𝒕 1) Using time series analysis for extraction of dynamic properties

Flow dimensions

Lyapunov exponents

Entropies

Particle tracer time-series

Lypanunov exponent: sensitivity to initial

conditions Doucet et al. Granular Matter, 10 (2008), 133-138

Blue box

Measuring mixing with 𝒙 𝒕 2) Using time series analysis for evaluation of mixing rate

Normalized position of a cluster of particles from time series

Doucet et al. CheRD, 86 (2008), 1313-1321

Calculate correlation

between 𝑥 𝑡 and 𝑥 (𝑡0) for each particles

𝐶𝑖𝑗 = 𝜌 X𝑖𝑡,X𝑗

0

M = CC𝑇

• First eigenvalue of M is

related to mixing rate

• First eigenvector of M is

the direction of minimum

mixing

At 𝑡0, correlation is 1, system is NOT mixed

At 𝑡 → ∞, correlation tends to limit value,

• system is mixed (=0)

• or not (≠0)

Blue box

What if we have 𝒙 𝒕 instead 3) We can extract mapping functions like Markov chains

𝑡𝑛 𝑡𝑛+1

P 𝑋𝑛 𝑋𝑛+1 = P𝑋𝑛

Blue box

What if we have 𝒙 𝒕 instead We can extract mapping functions like Markov chains

𝑡𝑛 𝑡𝑛+1

P 𝑋𝑛 𝑋𝑛+1 = P𝑋𝑛

Blue box

What if we have 𝒙 𝒕 instead We can extract mapping functions like Markov chains

𝑡𝑛 𝑡𝑛+1

P 𝑋𝑛 𝑋𝑛+1 = P𝑋𝑛

Blue box

Mixing with mapping functions Extracting dynamical information from stochastic models

Levin et al. Markov Chains and Mixing Times

a) Invariant state – Steady state

b) Kolmogorov Entropy

c) Mixing time – convergence rate

of the chain

Limit distribution (eigen problem)

Mixing time

Entropies

XP = 𝜆X

X𝑘 − 𝝅 ≤ 𝐶 𝜆∗𝑘

𝛑P = 𝛑

𝜏(𝜀) ≥ln(2𝜀)

ln 𝜆∗

Blue box

Examples Application to a rotating drum

Doucet et al. Computers and Chem. Eng., 32 (2008), 1334-1341

CFD Mapping

Mixing

dynamics

Invariant distribution

Blue box

Examples Application to a rotating drum

Doucet et al. Computers and Chem. Eng., 32 (2008), 1334-1341

CFD Mapping

Mixing

dynamics

a) Invariant state – Steady state

b) Kolmogorov Entropy

c) Mixing time – convergence rate

of the chain

Eigenvalue spectrum

𝜏 1/𝑒 ≥ln 2𝜀

ln 𝜆∗=

ln2𝑒

ln 0.9962= 81

Blue box

The 3D printing Example of solid-solid mixing in plastic degradation

1. Several iterations of the

drum were made.

2. The segregation

patterns were observed

rapidly

3. Baffle orientations was

changed

4. The RTDs were

determined

5. After validated at small

scale, a larger prototype

was built

Blue box

The pilot prototyping Example of solid-solid mixing in plastic degradation

Catalyst attrition

Dynamic angle of repose

Catalyst/fines segregation

Blue box

Conclusions Scaling up processes is difficult because transfers are not kept similar

1. Mixing is often guilty because it is used to promote transfers.

a) If transfers are affected, take a step back

b) Consider the transfer problem and consider it at the transfer level

c) See if an alternate technology can solve the transfer problem

2. CFD is limitative in predicting the mixing performance at different scale

because of the constitutive equations limitations

a) Keep in mind we need a working point, not a theory.

b) CAD can be used to build various 3D printed geometries and test real fluid in

similar flow conditions before building a pilot unit

c) Modern non-intrusive techniques can be used to measure mixing in a

Lagrangian way and more rapidly than converging a simulation

d) Time-series analysis and a variety of stochastic techniques can be used to

analyse the performance without the velocity field.

Is mixing to blame for process scale-up failure?

Revision 1

Jocelyn Doucet, P.Eng., Ph. D. CEO Pyrowave

Adjunct Pr. Dept. Chem Engineering, Polytechnique

© Jocelyn Doucet, 2016