Optimal Operation of IntegratedChemical ProcessesWith Application to Ammonia Synthesis

Julian Straus

2

Presentation Outline

1. Introduction– Ammonia Process (Chapter 2)

– Optimal Operation (Chapter 3)

2. Optimal Operation for Subprocesses– Economic Nonlinear Model Predictive Control (Chapter 5)

– Self-optimizing Control with Extremum-Seeking Control (Chapter 6+7)

– Feedback Real-time Optimization (Chapter 8)

3. Optimal Operation through Introduction of Surrogate Models– Main Procedure (Chapter 10)

– Variable Reduction using PLS Regression (Chapter 11+12)

– Application of Self-optimizing Variables (Chapter 13)

– Sampling for Surrogate Model Generation (Chapter 14)

4. Conclusion

Julian Straus | Optimal Operation of Integrated Chemical Processes – With Application to the Ammonia Synthesis

17.August2018

3

Presentation Outline

1. Introduction– Ammonia Process (Chapter 2)

– Optimal Operation (Chapter 3)

2. Optimal Operation for Subprocesses– Economic Nonlinear Model Predictive Control (Chapter 5)

– Self-optimizing Control with Extremum-Seeking Control (Chapter 6+7)

– Feedback Real-time Optimization (Chapter 8)

3. Optimal Operation through Introduction of Surrogate Models– Main Procedure (Chapter 10)

– Variable Reduction using PLS Regression (Chapter 11+12)

– Application of Self-optimizing Variables (Chapter 13)

– Sampling for Surrogate Model Generation (Chapter 14)

4. Conclusion

Julian Straus | Optimal Operation of Integrated Chemical Processes – With Application to the Ammonia Synthesis

17.August2018

4

Ammonia Process

• Haber Bosch process: Fixation of atmospheric nitrogen

• Developed in 1910s

• Strong competition and high energy demand Integration of the process Difficult optimization of the process

• Split into 2 sections1. Synthesis gas production

2. Ammonia synthesis

Julian Straus | Optimal Operation of Integrated Chemical Processes – With Application to the Ammonia Synthesis

1. I

ntro

du

ctio

n

2 2 33H N 2NH

17.August2018

Chapter 2

5

Optimal Operation

• Aim: minimizing production cost through process control

• Control structure frequently hierarchical

• Optimal operation results in an optimization problem

Julian Straus | Optimal Operation of Integrated Chemical Processes – With Application to the Ammonia Synthesis

1. I

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Scheduling(weeks)

Site-wide optimization(day)

Local optimization(hour)

Supervisory control(minutes)

Regulatory control(seconds)

0( ), ( )min ( ), ( ), ( )( )

. .

dynJ t t t dt

ts

x ux d u

0

( ), ( ), ( ) , [0, )

( ), ( ), ( ) , [0, )

(0)

x f x d u

0 h x d u

x x

t t t t

t t t t

17.August2018

Chapter 3

S. Skogestad, Plantwide control: the search for the self-optimizing control structure, J. Proc Control. 10 (2000) 487-506

6

Optimal Operation

• Implementation of optimal operation

Julian Straus | Optimal Operation of Integrated Chemical Processes – With Application to the Ammonia Synthesis

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y

u

Optimizer

Process

Objective

d

Open-loop

yu

Optimizingcontroller

Process

Objective

d

Closed-loopwithout control layer

Closed-loopwith control layer

yu

cs

Controller

Optimizer

Process

Objective

H

˗+

d

( )c H ym

17.August2018

S. Skogestad, Plantwide control: the search for the self-optimizing control structure, J. Proc Control. 10 (2000) 487-506

7

Optimal Operation- Integrated Processes

• Optimizer for dynamic or steady-state optimization problem required

Model of the process

• Problems of integrated process:– Nested Recycle Loops

– Convergence of the Flowsheet

– Simulation noise

• Two different approaches1. Optimal operation of subprocesses

2. Simplified model for optimization of the overall process

Julian Straus | Optimal Operation of Integrated Chemical Processes – With Application to the Ammonia Synthesis

1. I

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ctio

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17.August2018

8

Presentation Outline

1. Introduction– Ammonia Process (Chapter 2)

– Optimal Operation (Chapter 3)

2. Optimal Operation for Subprocesses– Economic Nonlinear Model Predictive Control (Chapter 5)

– Self-optimizing Control with Extremum-Seeking Control (Chapter 6+7)

– Feedback Real-time Optimization (Chapter 8)

3. Optimal Operation through Introduction of Surrogate Models– Main Procedure (Chapter 10)

– Variable Reduction using PLS Regression (Chapter 11+12)

– Application of Self-optimizing Variables (Chapter 13)

– Sampling for Surrogate Model Generation (Chapter 14)

4. Conclusion

Julian Straus | Optimal Operation of Integrated Chemical Processes – With Application to the Ammonia Synthesis

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• Three bed ammonia reactor

• Three manipulated variables u

• Heat integration for reduced cost through reactor outlet heat exchanger

• Cost function: rate of extent of reaction x

• Exhibits limit cycle and reactor extinction

Julian Straus | Optimal Operation of Integrated Chemical Processes – With Application to the Ammonia Synthesis

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Sub

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es2

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Case Study – Ammonia Reactor

x 3 3Inlet NH Outlet NH, ,Inlet 3in [kg NH /s]m w w

Bed 1

Bed 2

Bed 3

Inlet

Outlet

u1

u2

u3

17.August2018

J. Morud, S. Skogestad, Analysis of Instability in an Industrial Ammonia Reactor, AIChE J. 44 (1998) 888-895

Chapter 4

10

• Solves dynamic optimization problem for a time horizon

• Implements first calculated input of the trajectory

• Problems:– Required time for solving the optimization problem

– Feasibility of the solution to the optimization problem and stability

Julian Straus | Optimal Operation of Integrated Chemical Processes – With Application to the Ammonia Synthesis

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Economic Nonlinear Model Predictive Control

0( ), ( )min ( ), ( ), ( )

. .

( )max

dy

t

nJ t t t dt

s t

x ux d u

0

]( ), ( ), ( ) , [0,

( ), ( ), ( ) , [0,

(0)

]

max

max

t t t t t

t t t t t

x f x d u

0 h x d u

x x

maxt

yu

Optimizingcontroller

Process

Objective

d

Closed-loopwithout control layer

17.August2018

Chapter 5

11

• Constant setpoint policy

Selection of controlled variables

• Based on steady-state optimization consideringthe disturbances and local linearization

• What happens if remaining plant is neglectedwhen calculating H?

Julian Straus | Optimal Operation of Integrated Chemical Processes – With Application to the Ammonia Synthesis

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Self-optimizing Control (SOC)

c Hy

d0 yd0

uController Local plant

y

c

-cs

H

Remaining plant

dGlobal

plant

Closed-loopwith control layer

yu

cs

Controller

Optimizer

Process

Objective

H

˗+

d

( )c H ym

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Chapter 6

12

Requires adjustment of setpoint to controllers

Julian Straus | Optimal Operation of Integrated Chemical Processes – With Application to the Ammonia Synthesis

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Self-optimizing Control (SOC)Lo

ss [%

]Lo

ss [%

]

Loss

[%]

Loss

[%]

Original Setpoint Adjusted Setpoint17.

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13

• Extremum-seeking control as optimizing layer for setpoint adjustment

• Self-optimizing control for fast close-to-optimal disturbance rejection

Julian Straus | Optimal Operation of Integrated Chemical Processes – With Application to the Ammonia Synthesis

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Self-optimizing Control (SOC) + Extremum-seeking Control (ESC)

Extremum-seeking

controller

y

u

Processd

Setpointcontrol

H

J(y)

u cs

cm

dither

Ju

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Chapter 7

14 Julian Straus | Optimal Operation of Integrated Chemical Processes – With Application to the Ammonia Synthesis

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Self-optimizing Control (SOC) + Extremum-seeking Control (ESC)

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• ESC rather slow

• E-NMPC complicated through online optimization

• Translation of optimization problem into afeedback problem:

Julian Straus | Optimal Operation of Integrated Chemical Processes – With Application to the Ammonia Synthesis

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Sub

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Feedback Real-time Optimization

yu

Optimizingcontroller

Process

Objective

d

Closed-loopwithout control layer

y

uProcess

d

Contoller(PI)

,s uJ 0

ymeas

ny1ˆ uJ CA B D

, ,

, ,

.

y

f x d u

y h x d

x

u

Linearizemodel from

u to J

Gradientestimation

ˆˆ,x d

A B

C D

17.August2018

Chapter 8

16 Julian Straus | Optimal Operation of Integrated Chemical Processes – With Application to the Ammonia Synthesis

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Feedback Real-time OptimizationFlowrate Disturbance

(measured)Activity disturbance

(estimated)17.

August2018

17

Presentation Outline

1. Introduction– Ammonia Process (Chapter 2)

– Optimal Operation (Chapter 3)

2. Optimal Operation for Subprocesses– Economic Nonlinear Model Predictive Control (Chapter 5)

– Self-optimizing Control with Extremum-Seeking Control (Chapter 6+7)

– Feedback Real-time Optimization (Chapter 8)

3. Optimal Operation through Introduction of Surrogate Models– Main Procedure (Chapter 10)

– Variable Reduction using PLS Regression (Chapter 11+12)

– Application of Self-optimizing Variables (Chapter 13)

– Sampling for Surrogate Model Generation (Chapter 14)

4. Conclusion

Julian Straus | Optimal Operation of Integrated Chemical Processes – With Application to the Ammonia Synthesis

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• Detailed models often computational expensive to solve

• Introduction of surrogate models reduces computation load

• Surrogate model:Simple input (u)-output (ysurr) representation ( ) of a detailed model

• Input: Connection and decision variables

• Output: Connection and economic variables

Julian Straus | Optimal Operation of Integrated Chemical Processes – With Application to the Ammonia Synthesis

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Surrogate Model

'( )surry g u

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u Detailedmodel

ysurr

19

Original (steady-state) optimization problem:

1. Split original model g into n submodels gi

2. Calculate surrogate models gi,k’ for submodels gi

3. Combine surrogate models in big model through connection constraints

4. Optimize new problem

Julian Straus | Optimal Operation of Integrated Chemical Processes – With Application to the Ammonia Synthesis

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Main Procedure

,min , ,

.

(

.

)

s

J

tx u

x d u

, ,

, ,

0 g x d u

0 h x d u

,min , ,

.

(

.

)x u

x u d

s

J

t

, , ,

, ,

' , ,

,

1

, 1

1

, ,

i k i k i k i i

i k i k

i i i i

i n k i

i n k i

i n

0 y g d z u

0 z y

0 h x d u

17.August2018

Chapter 10

, ,i k i k0 z y

20 Julian Straus | Optimal Operation of Integrated Chemical Processes – With Application to the Ammonia Synthesis

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Main Procedure- Ammonia Synthesis

u2 d2

Reaction

z1,2 y1,2

u1 d1

SynGasMakeUp

Feed

d3u3

SeparationRefrigeration

y3,1

z3,1

y2,3 z2,3

NH3

17.August2018

1,2 1,20 z y

3,1 3,10 z y

2,3 2,30 z y

P-243

21

• Connection variables can result in high number of independent variables nu

• Sampling and surrogate model fitting computation expensive with high nu

• Reduction necessary:1. Introduction of linear mass balances

Julian Straus | Optimal Operation of Integrated Chemical Processes – With Application to the Ammonia Synthesis

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Variable Reduction using PLSR

yl

y

ynlSurrogateDefinition

u

LinearBalances

yaux

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Chapter 11

22

• Connection variables can result in high number of independent variables nu

• Sampling and surrogate model fitting computation expensive with high nu

• Reduction necessary:1. Introduction of linear mass balances

2. Reduction of nu through PLSR:

Julian Straus | Optimal Operation of Integrated Chemical Processes – With Application to the Ammonia Synthesis

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Variable Reduction using PLSR

u’DimensionReduction

yl

y

ynlSurrogateDefinition

u

LinearBalances

yaux

Tu W u

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Chapter 11

23

• Connection variables can result in high number of independent variables nu

• Sampling and surrogate model fitting computation expensive with high nu

• Reduction necessary:1. Introduction of linear mass balances

2. Reduction of nu through PLSR:

3. Fitting of surrogate model using new latent and dependent variables

Julian Straus | Optimal Operation of Integrated Chemical Processes – With Application to the Ammonia Synthesis

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Variable Reduction using PLSR

' uun n

u’DimensionReduction

yl

y

ynlSurrogateDefinition

u

LinearBalances

yaux

nlsurr

aux

yy

y

Tu W u

17.August2018

nl

ly

y

y

Chapter 11

24

• Reaction section, ammonia synthesis loop– 7 feed variables

– 3 manipulated variables

– 3 dependent variables

• Surrogate model structure

Julian Straus | Optimal Operation of Integrated Chemical Processes – With Application to the Ammonia Synthesis

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Variable Reduction using PLSR

nS2

nS1

THEx

2 2 3 4, , , Ar,

T

H N NH CH ,z in in in in iin n nip T n n n n n

T1 2S S HExMV n n T

Tsurrout outp Ty

1 1

2 2

, ,

T

3 3

1,2,3 (1)

( ) (2)

( ) (3)

(5)

( ) (4)

x

x

u

u

u W u

u

out

out

i out i in i

k k

n n

k

p g

T g

g

17.August2018

25 Julian Straus | Optimal Operation of Integrated Chemical Processes – With Application to the Ammonia Synthesis

Op

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Variable Reduction using PLSR- Outlet Pressure

1 2 3 4 5 6 7 8 9

max 𝜀[%]

0.00

0.25

0.20

0.15

0.10

0.05

0.30

3.5

0 %

0.7

3 %

0.4

6 %

Number of latent variables nu‘

0.000

0.025

0.020

0.015

0.010

0.005

0.030

1 2 3 4 5 6 7 8 9

𝜀[%]

Number of latent variables nu‘0.

856

%0.

191

%0.

056

%

17.August2018

26 Julian Straus | Optimal Operation of Integrated Chemical Processes – With Application to the Ammonia Synthesis

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Variable Reduction using PLSR- Extent of Reaction

1 2 3 4 5 6 7 8 9

max 𝜀[%]

Number of latent variables nu‘

3.5

4.0

0.0

2.5

2.0

1.5

1.0

0.5

3.0

14.3

%6.

5 %

4.3

%

1 2 3 4 5 6 7 8 9

𝜀[%]

Number of latent variables nu‘

0.0

0.5

0.4

0.3

0.2

0.1

0.6

0.7

0.8

3.5

7 %

1.1

8 %

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• Idea: Simplify response surface through change of independent variables (sample interesting regions)

• Initial independent variables:– Feed

– Manipulated variables

• Initial dependent variables– Output

• Change of variables from u to c via self-optimizingcontrol principles, i.e. add equality constraints:

Julian Straus | Optimal Operation of Integrated Chemical Processes – With Application to the Ammonia Synthesis

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Application of Self-optimizing Variables

Bed 1

Bed 2

Bed 3

Inlet

Outlet

u1

u2

u3

3 2 2

T

NH , H /N ,in in in in inm p T w R z

T1 2 3u u u u

surr

outTy

SOCg c Hy 0

17.August2018

Chapter 13

28

• Aim: Maximize rate of extentof reaction

• Local SOC variables per bed

Julian Straus | Optimal Operation of Integrated Chemical Processes – With Application to the Ammonia Synthesis

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Application of Self-optimizing Variables

Bed 1

T10

out

Bed 2Bed 3

T20T30 w30

u3

in

u2 u1

Tin,1Tin,2Tin,3

17.August2018

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• Aim: Maximize rate of extentof reaction

• Local SOC variables per bed

• 4 different SOC variablecombination tested

– Inlet temperatures

Julian Straus | Optimal Operation of Integrated Chemical Processes – With Application to the Ammonia Synthesis

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Application of Self-optimizing Variables

Bed 1

T10

out

Bed 2Bed 3

T20T30 w30

u3

in

u2 u1

Tin,1Tin,2Tin,3

17.August2018

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• Aim: Maximize rate of extentof reaction

• Local SOC variables per bed

• 4 different SOC variablecombination tested

– Inlet temperatures

– Inlet and outlet temperatures

Julian Straus | Optimal Operation of Integrated Chemical Processes – With Application to the Ammonia Synthesis

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Application of Self-optimizing Variables

Bed 1

T10

out

Bed 2Bed 3

T20T30 w30

u3

in

u2 u1

Tin,1Tin,2Tin,3

17.August2018

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• Aim: Maximize rate of extentof reaction

• Local SOC variables per bed

• 4 different SOC variablecombination tested

– Inlet temperatures

– Inlet and outlet temperatures

– 1 optimal temperature per bed

– 2 optimal temperatures per bed

• Error with respect to true optimum

Julian Straus | Optimal Operation of Integrated Chemical Processes – With Application to the Ammonia Synthesis

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Application of Self-optimizing Variables

Bed 1

T10

out

Bed 2Bed 3

T20T30 w30

u3

in

u2 u1

Tin,1Tin,2Tin,3

17.August2018

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Extent of reaction

Julian Straus | Optimal Operation of Integrated Chemical Processes – With Application to the Ammonia Synthesis

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Application of Self-optimizing Variables

4.3

5 %

0.7

4 %

In In-Out Opt 1 Opt 20.0

0.5

0.4

0.3

0.2

0.1

0.6

max 𝜖[%]

0.00

0.10

0.08

0.06

0.04

0.02

0.12

𝜖[%]

17.August2018

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• Limit cycle behavior and reactor extinction close to optimal point

• Complicates normal sampling

Julian Straus | Optimal Operation of Integrated Chemical Processes – With Application to the Ammonia Synthesis

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Application of Self-optimizing Variables

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• Sampling crucial for:– Performance of surrogate model

– Computational expense

• Common sampling approaches– Predefined

– Adaptive

• Aim: Sampling without– Surrogate model fitting

– Over-sampling

Julian Straus | Optimal Operation of Integrated Chemical Processes – With Application to the Ammonia Synthesis

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Sampling for Surrogate Model Generation

Development of a sampling methodbased on partial least square regression

17.August2018

Chapter 14

35 Julian Straus | Optimal Operation of Integrated Chemical Processes – With Application to the Ammonia Synthesis

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• Weights Wk change with growing sampling space ( )

• Convergence of the significant weights

3

Sampling for Surrogate Model Generation

17.August2018 T u W u

36

• Convergence corresponds to flattening in error improvement:Reaction section ( sampled points)

Julian Straus | Optimal Operation of Integrated Chemical Processes – With Application to the Ammonia Synthesis

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Sampling for Surrogate Model Generation

10-2 10-1 100

10-2

10-1

100

10-2 10-1 100100

101

102

103n

p= 100

np

= 200

np

= 500n

p= 1000

np

= 100

np

= 200

np

= 500n

p= 1000

2000pn

17.August2018

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Presentation Outline

1. Introduction– Ammonia Process (Chapter 2)

– Optimal Operation (Chapter 3)

2. Optimal Operation for Subprocesses– Economic Nonlinear Model Predictive Control (Chapter 5)

– Self-optimizing Control with Extremum-Seeking Control (Chapter 6+7)

– Feedback Real-time Optimization (Chapter 8)

3. Optimal Operation through Introduction of Surrogate Models– Main Procedure (Chapter 10)

– Variable Reduction using PLS Regression (Chapter 11+12)

– Application of Self-optimizing Variables (Chapter 13)

– Sampling for Surrogate Model Generation (Chapter 14)

4. Conclusion

Julian Straus | Optimal Operation of Integrated Chemical Processes – With Application to the Ammonia Synthesis

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Conclusion

• Optimal operation methods– Self-optimizing control in recycle systems

– Combination of self-optimizing control and extremum-seeking control for removal of steady-state loss

– Feedback real-time optimization for fast disturbance rejection

• Optimization of integrated process– Method for surrogate model-based optimization

– Independent variable reduction through PLS regression

– Simplification of response surface through self-optimizing variables

– Termination criteria for sampling without the need of surrogate model fitting

Julian Straus | Optimal Operation of Integrated Chemical Processes – With Application to the Ammonia Synthesis

4. C

oncl

usi

on

17.August2018

Thank you for attending my defense