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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
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Motivation – Applications
Food Industry Biotechnological Industry
Chemical Industry Pharmaceutical IndustryMartin Jelemensky (FCFT, STU) Optimal Control of Membrane Processes August 24, 2016 2 / 31
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Motivation
product + impurities
¤£$⇒
separation
product
Operation goals:
Cost function: minimization of production costsState constraints: satisfaction of production quality (product purity)
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Motivation – Membrane Fouling
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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.
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Presentation Outline
1 Membrane Process
2 Membrane Fouling
3 Optimal Operation
4 Fouling Estimation
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Presentation Outline
1 Membrane Process
2 Membrane Fouling
3 Optimal Operation
4 Fouling Estimation
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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)
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Process Control
u(t)
product (c1)
impurity (c2)
q(t, c1, c2)
control variable: α(t) =u(t)
q(t, c1, c2)∈ [0,∞)
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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
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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
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Process Control
u(t)
product (c1)
impurity (c2)
q(t, c1, c2)
constant-volume diafiltration: α(t) = 1 ⇒ u(t) = q(t, c1, c2)
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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
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Presentation Outline
1 Membrane Process
2 Membrane Fouling
3 Optimal Operation
4 Fouling Estimation
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Membrane Fouling
CAUSE : deposit of the solutes in/on the membrane pores
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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.
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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)
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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)
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Presentation Outline
1 Membrane Process
2 Membrane Fouling
3 Optimal Operation
4 Fouling Estimation
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Optimization Objectives
Minimum Time Minimum Diluant Multi Objective
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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.
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Optimization Objectives
Minimum Time Minimum Diluant Multi Objective
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.
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Optimization Objectives
Minimum Time Minimum Diluant Multi Objective
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.
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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
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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,
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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
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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
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Presentation Outline
1 Membrane Process
2 Membrane Fouling
3 Optimal Operation
4 Fouling Estimation
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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.
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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
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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
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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
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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.
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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.
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Publications
Martin Jelemensky (FCFT, STU) Optimal Control of Membrane Processes August 24, 2016 31 / 31
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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.
Martin Jelemensky (FCFT, STU) Optimal Control of Membrane Processes August 24, 2016 31 / 31
![Page 37: Dissertation Thesis Presentation - uiam.skjelemensky/Material/diss_press.pdfDissertation Thesis Presentation Ing. Martin Jelemensk´y Supervisor: prof. Ing. Miroslav Fikar, DrSc. Faculty](https://reader033.vdocuments.net/reader033/viewer/2022043012/5fa97401e2aedf6b8f40047c/html5/thumbnails/37.jpg)
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.
Martin Jelemensky (FCFT, STU) Optimal Control of Membrane Processes August 24, 2016 31 / 31