Optimal Control of Membrane Processes in the Presence of Fouling. Dissertation Thesis Presentation. Ing. Martin Jelemenský
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1 Optimal Control of Membrane Processes in the Presence of Fouling Dissertation Thesis Presentation Ing. Martin Jelemenský Supervisor: prof. Ing. Miroslav Fikar, DrSc. Faculty of Chemical and Food Technology Slovak University of Technology in Bratislava August 24, 2016 I AM Martin Jelemenský (FCFT, STU) Optimal Control of Membrane Processes August 24, / 31
2 Motivation Applications Food Industry Biotechnological Industry Chemical Industry Pharmaceutical Industry Martin Jelemenský (FCFT, STU) Optimal Control of Membrane Processes August 24, / 31
3 Motivation $ separation product + impurities product Operation goals: Cost function: minimization of production costs State constraints: satisfaction of production quality (product purity) Martin Jelemenský (FCFT, STU) Optimal Control of Membrane Processes August 24, / 31
4 Motivation Membrane Fouling Martin Jelemenský (FCFT, STU) Optimal Control of Membrane Processes August 24, / 31
5 Goals of Thesis Study of optimal operation of membrane processes in the presence of membrane fouling. Characterization of fully analytical optimal operation in the presence of membrane fouling. Implementation and verification of the proposed optimal operation in case studies and comparison of the results with traditional control approaches. Martin Jelemenský (FCFT, STU) Optimal Control of Membrane Processes August 24, / 31
6 Presentation Outline 1 Membrane Process 2 Membrane Fouling 3 Optimal Operation 4 Fouling Estimation Martin Jelemenský (FCFT, STU) Optimal Control of Membrane Processes August 24, / 31
7 Presentation Outline 1 Membrane Process 2 Membrane Fouling 3 Optimal Operation 4 Fouling Estimation Martin Jelemenský (FCFT, STU) Optimal Control of Membrane Processes August 24, / 31
8 Process Description u(t) product (c 1) impurity (c 2) q(t,c 1,c 2) permeability of membrane rejection coefficient (R) : absolutely impermeable for product (R 1 = 1) perfectly permeable to impurities (R 2 = 0) Martin Jelemenský (FCFT, STU) Optimal Control of Membrane Processes August 24, / 31
9 Process Control u(t) product (c 1) impurity (c 2) q(t,c 1,c 2) control variable: α(t) = u(t) q(t,c 1,c 2 ) [0, ) Martin Jelemenský (FCFT, STU) Optimal Control of Membrane Processes August 24, / 31
10 Process Control u(t) product (c 1) impurity (c 2) q(t,c 1,c 2) concentration mode: α(t) = 0 u(t) = 0 and q(t,c 1,c 2 ) > 0 Martin Jelemenský (FCFT, STU) Optimal Control of Membrane Processes August 24, / 31
11 Process Control u(t) product (c 1) impurity (c 2) q(t,c 1,c 2) pure dilution mode: α(t) = u(t) > 0 and q(t,c 1,c 2 ) = 0 Martin Jelemenský (FCFT, STU) Optimal Control of Membrane Processes August 24, / 31
12 Process Control u(t) product (c 1) impurity (c 2) q(t,c 1,c 2) constant-volume diafiltration: α(t) = 1 u(t) = q(t,c 1,c 2 ) Martin Jelemenský (FCFT, STU) Optimal Control of Membrane Processes August 24, / 31
13 Traditional Control Approach TD - traditional diafiltration α(t) {0,1} 1 c 2,0 c 0 α = 0 α(t) impurity α = 1 0 c 2,f c f time c 1,0 c product 1,f Martin Jelemenský (FCFT, STU) Optimal Control of Membrane Processes August 24, / 31
14 Presentation Outline 1 Membrane Process 2 Membrane Fouling 3 Optimal Operation 4 Fouling Estimation Martin Jelemenský (FCFT, STU) Optimal Control of Membrane Processes August 24, / 31
15 Membrane Fouling CAUSE : deposit of the solutes in/on the membrane pores Martin Jelemenský (FCFT, STU) Optimal Control of Membrane Processes August 24, / 31
16 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, Martin Jelemenský (FCFT, STU) Optimal Control of Membrane Processes August 24, / 31
17 Membrane Fouling Feed Retentate Permeate flow Permeate q(t) = AJ Membrane fouling approaches 1) Membrane area fouling 2) Permeate flux fouling q(t) = A(t)J q(t) = AJ(t) Martin Jelemenský (FCFT, STU) Optimal Control of Membrane Processes August 24, / 31
18 Membrane Fouling Feed Retentate Permeate flow Fouling model n = [0, 2) Permeate q(t,c 1,c 2,K,n) = AJ(t,c 1,c 2,K,n) ) J(t,c 1,c 2,K,n) = J 0 (1+K(2 n)(aj 1 0) 2 n t n 2 n = 2 J(t,c 1,c 2,K) = J 0e Kt aaaaaaaaaaaaaaaaaaaassa Flux of unfouled membrane J 0 (c 1,c 2 ) Martin Jelemenský (FCFT, STU) Optimal Control of Membrane Processes August 24, / 31
19 Presentation Outline 1 Membrane Process 2 Membrane Fouling 3 Optimal Operation 4 Fouling Estimation Martin Jelemenský (FCFT, STU) Optimal Control of Membrane Processes August 24, / 31
20 Optimization Objectives Minimum Time Minimum Diluant Multi Objective Martin Jelemenský (FCFT, STU) Optimal Control of Membrane Processes August 24, / 31
21 Optimization Objectives Minimum Time Minimum Diluant Multi Objective M. Jelemenský, 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 , Martin Jelemenský (FCFT, STU) Optimal Control of Membrane Processes August 24, / 31
22 Optimization Objectives Minimum Time Minimum Diluant Multi Objective M. Jelemenský, 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, Štrbské Pleso, Slovakia, pp , Martin Jelemenský (FCFT, STU) Optimal Control of Membrane Processes August 24, / 31
23 Optimization Objectives Minimum Time Minimum Diluant Multi Objective M. Jelemenský, 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 , Martin Jelemenský (FCFT, STU) Optimal Control of Membrane Processes August 24, / 31
24 Optimization Problem min α(t) tf 0 1dt s.t. ċ 1 = c1 2 AJ(t,c 1,c 2,K,n) (1 α) c 1,0 V 0 AJ(t,c 1,c 2,K,n) ċ 2 = c 1 c 2 α c 1,0 V 0 c i (t 0 ) = c i,0 i = 1,2 c i (t f ) = c i,f i = 1,2 α [0, ) Solution : 1) Numerical: various methods of dynamic optimization (CVP, OC) 2) Analytical: Pontryagin s minimum principle Martin Jelemenský (FCFT, STU) Optimal Control of Membrane Processes August 24, / 31
25 Analytical Solution of Optimal Operation 0 α = α(t,c 1,c 2,K,n) Traditional control modes concentration mode α = 0 pure dilution mode c 2 α = S(t,c 1,c 2,K,n) = 0 Advanced control mode singular surface S = S(t,c 1,c 2,K,n) singular control c 1 α = α(t,c 1,c 2,K,n) M. Jelemenský, A. Sharma, R. Paulen, and M. Fikar : Time-optimal control of diafiltration processes in the presence of membrane fouling. Computers & Chemical Engineering, vol. 91, pp , Martin Jelemenský (FCFT, STU) Optimal Control of Membrane Processes August 24, / 31
26 Case Study Separation goal separation product + impurities product Permeate flux model J 0 (c 1 ) = kln ( clim c 1 ) Fouling intermediate fouling model (n = 1) 1 J(t,c 1 ) = 1 J 0 (c 1 ) +K it Martin Jelemenský (FCFT, STU) Optimal Control of Membrane Processes August 24, / 31
27 Results 6 1 impurities [g/dl] C-CVD Ki = 0 Ki = 0.01 Ki = 0.03 α C-CVD Ki = 0 Ki = 0.01 Ki = product [g/dl] time [h] K i [h 1 ] [%] Martin Jelemenský (FCFT, STU) Optimal Control of Membrane Processes August 24, / 31
28 Presentation Outline 1 Membrane Process 2 Membrane Fouling 3 Optimal Operation 4 Fouling Estimation Martin Jelemenský (FCFT, STU) Optimal Control of Membrane Processes August 24, / 31
29 Estimation of Fouling Parameters complete fouling intermediate fouling internal fouling cake fouling M. Jelemenský, M. Klaučo, 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 , Martin Jelemenský (FCFT, STU) Optimal Control of Membrane Processes August 24, / 31
30 Case Study Separation goal c 1,0 = 10mol/m 3 c 2,0 = 100mol/m 3 c 1,f = 100mol/m 3 c 2,f = 1mol/m 3 Model of permeate flux J 0 (c 1 ) = k ln c lim c 1 k,c lim = known On-line estimation of fouling parameters (K, n) J(t,c 1,K,n) = J 0 ( 1+K(2 n)(aj0 ) 2 n t ) 1 n 2 Measured outputs y = ( c 1, c 2, J, dj ) T dt Martin Jelemenský (FCFT, STU) Optimal Control of Membrane Processes August 24, / 31
31 Results Fouling Parameters Estimation K estimated (n = 0) estimated (n = 1) estimated (n = 1.5) true value n estimated (n = 0) estimated (n = 1) estimated (n = 1.5) true value time[h] time[h] Martin Jelemenský (FCFT, STU) Optimal Control of Membrane Processes August 24, / 31
32 Results Internal Fouling Model (n = 1.5) c2[mol/m 3 ] α ideal case estimated case initial case ideal case estimated case initial case c 1[mol/m 3 ] time[h] case t f [h] ideal estimated initial Martin Jelemenský (FCFT, STU) Optimal Control of Membrane Processes August 24, / 31
33 Conclusions Optimal control theory was proposed for analysis of time-optimal control of membrane processes in the presence of fouling. Derivation of fully analytical optimal operation in the presence of membrane fouling. Significant savings compared to traditional operation even at lower fouling. On-line estimation of unknown fouling parameters using Extended Kalman filter. Satisfactory convergence of estimated fouling parameters with minor differences between ideal and estimated state and control trajectories. Martin Jelemenský (FCFT, STU) Optimal Control of Membrane Processes August 24, / 31
34 Publications Journals R. Paulen M. Jelemenský M. Fikar Z. Kovacs : Optimal balancing of temporal and buffer costs for ultrafiltration/diafiltration processes under limiting flux conditions. Journal of Membrane Science, vol. 444, pp , R. Paulen M. Jelemenský Z. Kovacs M. Fikar : Economically optimal batch diafiltration via analytical multi-objective optimal control. Journal of Process Control, vol. 28, pp , M. Jelemenský R. Paulen M. Fikar Z. Kovacs : Time-Optimal Operation of Multi-Component Batch Diafiltration. Computers & Chemical Engineering, vol. 83, pp , M. Jelemenský A. Sharma R. Paulen M. Fikar : Time-optimal control of diafiltration processes in the presence of membrane fouling. Computers & Chemical Engineering, vol. 91, pp , Martin Jelemenský (FCFT, STU) Optimal Control of Membrane Processes August 24, / 31
35 Publications Martin Jelemenský (FCFT, STU) Optimal Control of Membrane Processes August 24, / 31
36 Publications Journals R. Paulen M. Jelemenský M. Fikar Z. Kovacs : Optimal balancing of temporal and buffer costs for ultrafiltration/diafiltration processes under limiting flux conditions. Journal of Membrane Science, vol. 444, pp , R. Paulen M. Jelemenský Z. Kovacs M. Fikar : Economically optimal batch diafiltration via analytical multi-objective optimal control. Journal of Process Control, vol. 28, pp , M. Jelemenský R. Paulen M. Fikar Z. Kovacs : Time-Optimal Operation of Multi-Component Batch Diafiltration. Computers & Chemical Engineering, vol. 83, pp , M. Jelemenský A. Sharma R. Paulen M. Fikar : Time-optimal control of diafiltration processes in the presence of membrane fouling. Computers & Chemical Engineering, vol. 91, pp , Martin Jelemenský (FCFT, STU) Optimal Control of Membrane Processes August 24, / 31
37 Publications Conferences M. Jelemenský, 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 , M. Jelemenský, A. Sharma, R. Paulen, M. Fikar: Multi-Objective Optimization of Batch Dialfiltration Processes in the Presence of Membrane Fouling. Editor(s): M. Fikar and M. Kvasnica, InProceedings of the 20th International Conference on Process Control, Slovak Chemical Library, Štrbské Pleso, Slovakia, pp.84 89, M. Jelemenský, A. Sharma, R. Paulen, M. Fikar : Time-optimal Operation of 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 , M. Jelemenský, M. Klaučo, 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 , Martin Jelemenský (FCFT, STU) Optimal Control of Membrane Processes August 24, / 31
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