dissertation thesis presentation - uiam.skjelemensky/material/diss_press.pdfdissertation thesis...

Optimal Control of Membrane Processes inthe Presence of Fouling

Dissertation Thesis Presentation

Ing. Martin Jelemensky

Supervisor: prof. Ing. Miroslav Fikar, DrSc.

Faculty of Chemical and Food TechnologySlovak University of Technology in Bratislava

August 24, 2016

IAM

Martin Jelemensky (FCFT, STU) Optimal Control of Membrane Processes August 24, 2016 1 / 31

Motivation – Applications

Food Industry Biotechnological Industry

Chemical Industry Pharmaceutical IndustryMartin Jelemensky (FCFT, STU) Optimal Control of Membrane Processes August 24, 2016 2 / 31

Motivation

product + impurities

¤£$⇒

separation

product

Operation goals:

Cost function: minimization of production costsState constraints: satisfaction of production quality (product purity)


Motivation – Membrane Fouling


Goals of Thesis

Study of optimal operation of membrane processes in the presence ofmembrane fouling.

Characterization of fully analytical optimal operation in the presence ofmembrane fouling.

Implementation and verification of the proposed optimal operation in casestudies and comparison of the results with traditional control approaches.


Presentation Outline

1 Membrane Process

2 Membrane Fouling

3 Optimal Operation

4 Fouling Estimation



1 Membrane Process

2 Membrane Fouling

3 Optimal Operation



Process Description

u(t)

product (c1)

impurity (c2)

q(t, c1, c2)

permeability of membrane – rejection coefficient (R) :absolutely impermeable for product (R1 = 1)perfectly permeable to impurities (R2 = 0)


Process Control

u(t)

product (c1)

impurity (c2)

q(t, c1, c2)

control variable: α(t) =u(t)

q(t, c1, c2)∈ [0,∞)


Process Control

u(t)

product (c1)

impurity (c2)

q(t, c1, c2)

concentration mode: α(t) = 0 ⇒ u(t) = 0 and q(t, c1, c2) > 0


Process Control

u(t)

product (c1)

impurity (c2)

q(t, c1, c2)

pure dilution mode: α(t) = ∞ ⇒ u(t) > 0 and q(t, c1, c2) = 0


Process Control

u(t)

product (c1)

impurity (c2)

q(t, c1, c2)

constant-volume diafiltration: α(t) = 1 ⇒ u(t) = q(t, c1, c2)


Traditional Control Approach

TD - traditional diafiltrationα(t) ∈ {0, 1}

α(t)

time

0

1

α = 1

α = 0

product

c0

cf

c1,0 c1,f

impurity

c2,0

c2,f



1 Membrane Process

2 Membrane Fouling

3 Optimal Operation



Membrane Fouling

CAUSE : deposit of the solutes in/on the membrane pores


Standard Fouling Models

Complete blocking model (n = 2) Intermediate blocking model (n = 1)

Internal blocking model (n = 1.5) Cake filtration model (n = 0)

J. Hermia, Constant pressure blocking filtration laws-application to power-law non-Newtonian

fluids, Trans. IchemE, vol. 60, no. 183, 1982.


Membrane Fouling

Feed Retentate

Permeate

Permeate flow

q(t) = AJ

Membrane fouling approaches

1) Membrane area foulingq(t) = A(t)J

2) Permeate flux foulingq(t) = AJ(t)


Membrane Fouling

Feed Retentate

Permeate

Permeate flow

q(t, c1, c2,K , n) = AJ(t, c1, c2,K , n)

Fouling modeln = [0, 2)

J(t, c1, c2,K , n) = J0

(

1 + K(2− n)(AJ0)2−n

t)

1

n − 2

n = 2J(t, c1, c2,K) = J0e

−Ktaaaaaaaaaaaaaaaaaaaassa

Flux of unfouled membrane

J0(c1, c2)



1 Membrane Process

2 Membrane Fouling

3 Optimal Operation



Optimization Objectives

Minimum Time Minimum Diluant Multi Objective




M. Jelemensky, R. Paulen, M. Fikar, and Z. Kovacs. Time-optimal Diafiltration in the Presence

of Membrane Fouling. In Preprints of the 19th IFAC World Congress, Cape Town, South Africa,

pp. 4897–4902, 2014.




M. Jelemensky, A. Sharma, R. Paulen, and M. Fikar: Multi-Objective Optimization of Batch

Dialfiltration Processes in the Presence of Membrane Fouling. In Proceedings of the 20th

International Conference on Process Control, Slovak Chemical Library, Strbske Pleso, Slovakia,

pp. 84–89, 2015.




M. Jelemensky, A. Sharma, R. Paulen, and M. Fikar : Time-optimal Operation of Diafiltration

Processes in the Presence of Fouling. In 12th International Symposium on Process Systems

Engineering And 25th European Symposium on Computer Aided Process Engineering, Elsevier

B.V, Copenhagen, Denmark, pp. 1577–1582, 2015.


Optimization Problem

minα(t)

∫ tf

0

1 dt

s.t. c1 = c21AJ(t, c1, c2,K , n)

c1,0V0(1− α)

c2 = −c1c2AJ(t, c1, c2,K , n)

c1,0V0α

ci(t0) = ci ,0 i = 1, 2

ci(tf) = ci ,f i = 1, 2

α ∈ [0,∞)

Solution :

1) Numerical: various methods of dynamic optimization (CVP, OC)2) Analytical: Pontryagin’s minimum principle


Analytical Solution of Optimal Operation

α =

0

α(t, c1, c2,K , n)

∞

c1

c2

S(t, c1, c2,K , n) = 0

Traditional control modes

concentration mode

α = 0

pure dilution mode

α = ∞

Advanced control mode

singular surface

S = S(t, c1, c2,K , n)

singular control

α = α(t, c1, c2,K , n)

M. Jelemensky, A. Sharma, R. Paulen, and M. Fikar : Time-optimal control of diafiltrationprocesses in the presence of membrane fouling. Computers & Chemical Engineering, vol. 91,

pp. 343–351, 2016.Martin Jelemensky (FCFT, STU) Optimal Control of Membrane Processes August 24, 2016 22 / 31

Case Study

Separation goal

product + impurities

⇒separation

product

Permeate flux model

J0(c1) = k ln

(

clim

c1

)

Fouling – intermediate fouling model (n = 1)

1

J(t, c1)=

1

J0(c1)+ Kit


Results

0 5 10 15 20 25 30 35 40 45

0

1

2

3

4

5

6

C-CVDKi = 0Ki = 0.01Ki = 0.03

product [g/dL]

impurities

[g/dL]

0 5 10 15 20 25 ... 80 85

0

0.2

0.4

0.6

0.8

1

C-CVDKi = 0Ki = 0.01Ki = 0.03

α

time [h]

Ki[h−1] ∆[%]

0 120.01 520.03 260



1 Membrane Process

2 Membrane Fouling

3 Optimal Operation



Estimation of Fouling Parameters

complete fouling intermediate fouling

internal fouling cake fouling

M. Jelemensky, M. Klauco, R. Paulen, J. Lauwers, F. Logist, J. Van Impe, M. Fikar :

Time-Optimal Control and Parameter Estimation of Diafiltration Processes in the Presence of

Membrane Fouling. In 11th IFAC Symposium on Dynamics and Control of Process Systems,

including Biosystems, vol. 11, pp.242 – 247, 2016.


Case Study

Separation goal

c1, 0 = 10mol/m3 c2, 0 = 100mol/m3

c1, f = 100mol/m3 c2, f = 1mol/m3

Model of permeate flux

J0(c1) = k lnclim

c1k , clim = known

On-line estimation of fouling parameters (K , n)

J(t, c1,K , n) = J0(

1 + K(2 − n)(AJ0)2−nt

)

1

n − 2

Measured outputs

y =

(

c1, c2, J,dJ

dt

)T


Results – Fouling Parameters Estimation

0 2 4 6 8 10 12

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

estimated (n = 0)estimated (n = 1)estimated (n = 1.5)true value

time [h]

K

0 2 4 6 8 10 12

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

estimated (n = 0)estimated (n = 1)estimated (n = 1.5)true value

time [h]

n


Results – Internal Fouling Model (n = 1.5)

0 50 100 150 200 250

0

20

40

60

80

100

ideal caseestimated caseinitial case

c1 [mol/m3]

c2[m

ol/m

3]

0 5 10 15 20

0

0.2

0.4

0.6

0.8

1

1.2

ideal caseestimated caseinitial case

time [h]

α

case tf [h]

ideal 10.39estimated 10.41initial 15.91


Conclusions

Optimal control theory was proposed for analysis of time-optimal control ofmembrane processes in the presence of fouling.

Derivation of fully analytical optimal operation in the presence of membranefouling.

Significant savings compared to traditional operation even at lower fouling.

On-line estimation of unknown fouling parameters using Extended Kalmanfilter.

Satisfactory convergence of estimated fouling parameters with minordifferences between ideal and estimated state and control trajectories.


Publications – Journals

R. Paulen – M. Jelemensky – M. Fikar – Z. Kovacs : Optimal balancing oftemporal and buffer costs for ultrafiltration/diafiltration processes underlimiting flux conditions. Journal of Membrane Science, vol. 444, pp. 87 – 95,2013.

R. Paulen – M. Jelemensky – Z. Kovacs – M. Fikar :Economically optimal batch diafiltration via analytical multi-objective optimalcontrol. Journal of Process Control, vol. 28, pp. 73 – 82, 2015.

M. Jelemensky – R. Paulen – M. Fikar – Z. Kovacs : Time-OptimalOperation of Multi-Component Batch Diafiltration. Computers & ChemicalEngineering, vol. 83, pp. 131 – 138, 2015.

M. Jelemensky – A. Sharma – R. Paulen – M. Fikar : Time-optimal controlof diafiltration processes in the presence of membrane fouling. Computers &Chemical Engineering, vol. 91, pp. 343 – 351, 2016.


Publications


Publications – Journals

R. Paulen – M. Jelemensky – M. Fikar – Z. Kovacs : Optimal balancing oftemporal and buffer costs for ultrafiltration/diafiltration processes underlimiting flux conditions. Journal of Membrane Science, vol. 444, pp. 87 – 95,2013.

R. Paulen – M. Jelemensky – Z. Kovacs – M. Fikar :Economically optimal batch diafiltration via analytical multi-objective optimalcontrol. Journal of Process Control, vol. 28, pp. 73 – 82, 2015.

M. Jelemensky – R. Paulen – M. Fikar – Z. Kovacs : Time-OptimalOperation of Multi-Component Batch Diafiltration. Computers & ChemicalEngineering, vol. 83, pp. 131 – 138, 2015.

M. Jelemensky – A. Sharma – R. Paulen – M. Fikar : Time-optimal controlof diafiltration processes in the presence of membrane fouling. Computers &Chemical Engineering, vol. 91, pp. 343 – 351, 2016.


Publications – Conferences

M. Jelemensky, R. Paulen, M. Fikar, and Z. Kovacs. Time-optimalDiafiltration in the Presence of Membrane Fouling. In Preprints of the 19th

IFAC World Congress, Cape Town, South Africa, pp. 4897–4902, 2014.M. Jelemensky, A. Sharma, R. Paulen, M. Fikar: Multi-ObjectiveOptimization of Batch Dialfiltration Processes in the Presence of MembraneFouling. Editor(s): M. Fikar and M. Kvasnica, InProceedings of the 20th

International Conference on Process Control, Slovak Chemical Library,Strbske Pleso, Slovakia, pp.84–89, 2015.M. Jelemensky, A. Sharma, R. Paulen, M. Fikar : Time-optimal Operationof Diafiltration Processes in the Presence of Fouling. Editor(s): Krist V.Gernaey and Jakob K. Huusom and Rafiqul Gani, In 12th International

Symposium on Process Systems Engineering And 25th European Symposium

on Computer Aided Process Engineering, Elsevier B.V, Copenhagen,Denmark, pp.15771582, 2015.M. Jelemensky, M. Klauco, R. Paulen, J. Lauwers, F. Logist, J. Van Impe,M. Fikar : Time-Optimal Control and Parameter Estimation of DiafiltrationProcesses in the Presence of Membrane Fouling. In 11th IFAC Symposium on

Dynamics and Control of Process Systems, including Biosystems, vol. 11,pp.242 – 247, 2016.


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