Simultaneous BOP Selection and Controller Design for the FCC Process
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1 Smultaneous BOP Selecton and Controller Desgn for the FCC Process Benjamn Omell & Donald J. Chmelewsk Department of Chemcal & Bologcal Engneerng
2 Outlne Motvatng Example Introducton to BOP Selecton and Controller Desgn FCC Case Study FCC Process Descrpton and Model Fxed Controller Approach to BOP Selecton (Loeblen & Perkns,1999) Varable Controller Approach (Proft Control)
3 Motvatng Example (Non-sothermal Reactor) F C A, T F V V r A dca F( CAn CA) VrA dt dt F( Tn T ) ( VH / C dt k( T) C A p ) r A Possble Controller: F K c ( T T ( sp) ) F ( sp)
4 Motvatng Example (Lmted Operatng Regon) Process Lmtatons: T( t) T F( t) F (max) (max) - Catalyst protecton or onset of sde reactons - Pump lmt or lmt on downstream unt
5 Motvatng Example (Lmted Operatng Regon) Process Lmtatons: T( t) T F( t) F (max) (max) - Catalyst protecton or onset of sde reactons - Pump lmt or lmt on downstream unt Increase F Increased producton rate
6 Motvatng Example (Performance n Tme Seres) T (sp) T(t) F(t) tme F (sp) tme
7 T(t) Motvatng Example (Performance n Phase Plane) * F(t)
8 T(t) Motvatng Example (Ellptcal Operatng Regon) * F(t)
9 T(t) Motvatng Example (Ellptcal Operatng Regon) * F(t)
10 Motvatng Example (Lmted Operatng Regon) Controller: F K c ( T T ( sp) ) F ( sp) Steady-State Relaton: F ( sp ) f ( T ( sp), w)
11 T(t) Motvatng Example (Ellptcal Operatng Regon) * F(t)
12 T(t) Motvatng Example (Steady-State Operatng Lne) * Increase flow ncrease producton F(t)
13 T(t) Motvatng Example (Steady-State Operatng Lne) * Increase flow ncrease producton F(t)
14 T(t) Motvatng Example (Steady-State Operatng Lne) * Increase flow ncrease producton F(t)
15 T(t) Motvatng Example (Steady-State Operatng Lne) * F(t)
16 Motvatng Example (Performance n Tme Seres) T(t) T (max) T (sp) F K c ( T T ( sp) ) F ( sp) F (sp) F(t) tme F (max) tme
17 Outlne Motvatng Example Introducton to BOP Selecton and Controller Desgn FCC Case Study FCC Process Descrpton and Model Fxed Controller Approach to BOP Selecton (Loeblen & Perkns,1999) Varable Controller Approach (Proft Control)
18 Concept of Back-Off Pont Selecton CV' s Constrant Polytope Backed-off Operatng Ponts Expected Dynamc Operatng Regons Optmal Steady-State Operatng Pont MV' s
19 Economc Based Controller Flexblty analyss Analyss and Desgn Nshda et al. (1974), Grossmann & Sargent (1978), Pstkopoulos & Grossmann (1988), Ahmed & Sahnds (1998) BOP selecton: Steady-state dsturbances Narraway et al., 1991; Narraway & Perkns, 1993, 1994; Loeblen & Perkns, 1996, 1998 Chance constraned optmzaton Charnes & Cooper (1959), Mller & Wagner (1965), Uryasev (2000), Cooper et al. (2002), Henron & Römsch (2004) BOP selecton: Stochastc dsturbances Loeblen & Perkns (1999), van Hessem et al. (2001), Muske, (2003), Peng et al., (2005), Zhao, Huang et al. (2009)
20 Fxed Controller BOP Selecton Loeblen and Perkns (1999): x * EDOR * * u OSSOP Controller s fxed EDORs have fxed szes and shapes
21 Varable Controller BOP Selecton x EDOR Varable Controller * OSSOP * * u EDORs have varable szes and shapes
22 Outlne Motvatng Example Introducton to BOP Selecton and Controller Desgn FCC Case Study FCC Process Descrpton and Model Fxed Controller Approach to BOP Selecton (Loeblen & Perkns,1999) Varable Controller Approach (Proft Control)
23 FCC process Important process n ol refnng Breaks large chan hydrocarbons nto smaller chan hydrocarbons Important to overall proft of refnery
24 Regenerator and Separator (dynamc): W st dc st dt = F cat C sc C st W st c pc dt st dt = F cat c pc T ro T st W dc rgc dt W a do d dt = F ar M ar Wc pc dt reg dt dy f dz = K 1y f COR φt c, y f z = 0 = 1 dy g dz = K 2y 2 f K 3 y g COR φt c, y g z = 0 = 0 dθ dz = = F cat C st C rgc R cb O n O d σ R cb 1 + σ M c = F cat c pc T st + F ar C par T ar F cat c pc + F ar C par T reg ΔH CO + σ 1 + σ ΔH CO 2 R cb M c T cy = T reg + 5,555O d Rser (pseudo steady state): H f F feed T r F cat c cp + F feed c pfl + λf feed c pc Model (Hovd and Skogestad, 1993) dy f dz θ z = T z T r T r, θ z = 0 = 0, T ro = T z = 1
25 Regenerator and Separator (dynamc): W st dc st dt = F cat C sc C st W st c pc dt st dt = F cat c pc T ro T st W dc rgc dt W a do d dt = F ar M ar Wc pc dt reg dt dy f dz = K 1y f COR φt c, y f z = 0 = 1 dy g dz = K 2y 2 f K 3 y g COR φt c, y g z = 0 = 0 dθ dz = = F cat C st C rgc R cb O n O d σ R cb 1 + σ M c = F cat c pc T st + F ar C par T ar F cat c pc + F ar C par T reg ΔH CO + σ 1 + σ ΔH CO 2 R cb M c T cy = T reg + 5,555O d Rser (pseudo steady state): H f F feed T r F cat c cp + F feed c pfl + λf feed c pc Model (Hovd and Skogestad, 1993) dy f dz θ z = T z T r T r, θ z = 0 = 0, T ro = T z = 1
26 Regenerator and Separator (dynamc): W st dc st dt = F cat C sc C st W st c pc dt st dt = F cat c pc T ro T st W dc rgc dt W a do d dt = F ar M ar Wc pc dt reg dt dy f dz = K 1y f COR φt c, y f z = 0 = 1 dy g dz = K 2y 2 f K 3 y g COR φt c, y g z = 0 = 0 dθ dz = = F cat C st C rgc R cb O n O d σ R cb 1 + σ M c = F cat c pc T st + F ar C par T ar F cat c pc + F ar C par T reg ΔH CO + σ 1 + σ ΔH CO 2 R cb M c T cy = T reg + 5,555O d Rser (pseudo steady state): H f F feed T r F cat c cp + F feed c pfl + λf feed c pc Model (Hovd and Skogestad, 1993) dy f dz θ z = T z T r T r, θ z = 0 = 0, T ro = T z = 1
27 Regenerator and Separator (dynamc): W st dc st dt = F cat C sc C st W st c pc dt st dt = F cat c pc T ro T st W dc rgc dt W a do d dt = F ar M ar Wc pc dt reg dt = F cat C st C rgc R cb O n O d σ R cb 1 + σ M c = F cat c pc T st + F ar C par T ar F cat c pc + F ar C par T reg ΔH CO + σ 1 + σ ΔH CO 2 R cb M c T cy = T reg + 5,555O d Rser (pseudo steady state): dy f dz = K 1y f COR φt c, y f z = 0 = 1 dy g dz = K 2y 2 f K 3 y g COR φt c, y g z = 0 = 0 dθ dz = H f F feed T r F cat c cp + F feed c pfl + λf feed c pc Model (Hovd and Skogestad, 1993) dy f dz θ z = T z T r T r, θ z = 0 = 0, T ro = T z = 1
28 Regenerator and Separator (dynamc): W st dc st dt = F cat C sc C st W st c pc dt st dt = F cat c pc T ro T st W dc rgc dt W a do d dt = F ar M ar Wc pc dt reg dt = F cat C st C rgc R cb O n O d σ R cb 1 + σ M c = F cat c pc T st + F ar C par T ar F cat c pc + F ar C par T reg ΔH CO + σ 1 + σ ΔH CO 2 R cb M c T cy = T reg + 5,555O d Rser (pseudo steady state): dy f dz = K 1y f COR φt c, y f z = 0 = 1 dy g dz = K 2y 2 f K 3 y g COR φt c, y g z = 0 = 0 dθ dz = H f F feed T r F cat c cp + F feed c pfl + λf feed c pc Model (Hovd and Skogestad, 1993) dy f dz θ z = T z T r T r, θ z = 0 = 0, T ro = T z = 1
29 Regenerator and Separator (dynamc): W st dc st dt = F cat C sc C st W st c pc dt st dt = F cat c pc T ro T st W dc rgc dt W a do d dt = F ar M ar Wc pc dt reg dt dy f dz = K 1y f COR φt c, y f z = 0 = 1 dy g dz = K 2y 2 f K 3 y g COR φt c, y g z = 0 = 0 dθ dz = = F cat C st C rgc R cb O n O d σ R cb 1 + σ M c = F cat c pc T st + F ar C par T ar F cat c pc + F ar C par T reg ΔH CO + σ 1 + σ ΔH CO 2 R cb M c T cy = T reg + 5,555O d Rser (pseudo steady state): H f F feed T r F cat c cp + F feed c pfl + λf feed c pc Model (Hovd and Skogestad, 1993) dy f dz θ z = T z T r T r, θ z = 0 = 0, T ro = T z = 1
30 Constrants Temperature Constrants metallurgcal lmts T st 1000 K T reg 1000 K T cy 1000 K Process Constrants 100 kg/s F cat 400 kg/s 0 F ar 60 kg/s
31 Optmal S.S. Operatng Pont (OSSOP) Proft functon Φ = P gs F gs + P gl F gl + P ugo F ugo P uog F Feed The OSSOP falls on the temperature constrant Typcal for the most operatng steady state pont to be on a system constrant OSSOP T reg = 1000 K T cy = 1000 K F cat = 320 kg/s F ar = 28 kg/s
32 Optmal S.S. Operatng Pont (OSSOP) Proft functon Φ = P gs F gs + P gl F gl + P ugo F ugo P uog F Feed The OSSOP falls on the temperature constrant Typcal for the most operatng steady state pont to be on a system constrant OSSOP T reg = 1000 K T cy = 1000 K F cat = 320 kg/s F ar = 28 kg/s
33 Optmal S.S. Operatng Pont (OSSOP) Proft functon Φ = P gs F gs + P gl F gl + P ugo F ugo P uog F Feed The OSSOP falls on the temperature constrant Typcal for the most operatng steady state pont to be on a system constrant OSSOP T reg = 1000 K T cy = 1000 K Hgher Temperature F cat = 320 kg/s F ar = 28 kg/s
34 Optmal S.S. Operatng Pont (OSSOP) Proft functon Φ = P gs F gs + P gl F gl + P ugo F ugo P uog F Feed The OSSOP falls on the temperature constrant Typcal for the most operatng steady state pont to be on a system constrant Converson ncreases OSSOP T reg = 1000 K T cy = 1000 K F cat = 320 kg/s F ar = 28 kg/s Hgher Temperature
35 Non-Lnear Model Steady-State Prospectve p m FCC q s s f ( s, m, p) q h( s, m, p) s C T O T C st st d reg rgc F m F cat ar s q m T cy p Tfeed
36 Devaton Varables * *
37 Devaton Varables * Steady-State Perspectve ossop s ' s s ossop m' m m ossop q ' q q BOP BOP BOP *
38 Devaton Varables * Steady-State Perspectve ossop s ' s s ossop m' m m ossop q ' q q BOP BOP BOP * Controller Perspectve x ' x x u ' u u z ' z z
39 Lnear State Dscrete-tme Model Controller Prospectve w k z k u k FCC x k x k 1 Ax k Bu k Gw k z D x D u D d k x k u k w k
40 Outlne Motvatng Example Introducton to BOP Selecton and Controller Desgn FCC Case Study FCC Process Descrpton and Model Fxed Controller Approach to BOP Selecton (Loeblen & Perkns,1999) Varable Controller Approach (Proft Control)
41 Fxed Controller BOP Selecton Loeblen and Perkns (1999): x * EDOR * * u OSSOP Controller s fxed EDORs have fxed szes and shapes
42 Fxed Controller BOP Selecton (Loeblen & Perkns, 1999) General Method Select tunng parameters for BOP selecton Calculate Covarance Perform lnear optmzaton for back-off operaton pont selecton
43 LQR Controller T zkzk z D x k x k D u u k k0
44 LQR Controller T zkzk z D x k x k D u u k k 0 T T T T z z x Qx u R u 2x Mu k k k k k u k k k D D Q D D R D D M L T T T x x u u x u LQR( Q, R, M, A, B)
45 Covarance Analyss Assume controller L s gven and calculate x : u Lx x Lyapunov equaton (FSI case) T x 1 n z z z ( A BL) ( A BL) T G G T ) D x x w T z ( Dx Du L) x( Dx Du L Dw th 0 0 column w T w
46 EDOR Characterzaton max z 2 x 2 mn z 1 x 1
47 Gan Calculated I L x x... nz x x x
48 BOP Optmzaton Problem mn g q ' s.t. s ' As ' Bm ' q ', ', ' s m q q D x D u z q q x mn max ' ( x ' u ') ' q ' q ' x q ' q ' 1/2 max 1/2 mn
49 BOP Optmzaton Problem mn g q ' s.t. s ' As ' Bm' q ', ', ' s m q q D q D q q q q x mn max ' ( x ' u ') ' q ' q ' x q ' q ' 1/2 max 1/2 mn
50 T cy (K) F cat (kg/s) T reg (K) Fxed Controller EDORs O d x F ar (kg/s) C st T (K) st C rgc x 10-3
51 Outlne Motvatng Example Introducton to BOP Selecton and Controller Desgn FCC Case Study FCC Process Descrpton and Model Fxed Controller Approach to BOP Selecton (Loeblen & Perkns,1999) Varable Controller Approach (Proft Control)
52 BOP Optmzaton Problem s', m', q' x, XY,, mn g q ' s.t. s ' As ' Bm' q q D s D m q q q x mn max ' ( x ' u ') ' ( q ' q ' ) x ( q ' q ' ) 1/2 max 1/2 mn
53 BOP Optmzaton Problem s', m', q' x, XY,, mn g q ' s.t. s ' As ' Bm' q q D s D m q q q x mn max ' ( x ' u ') ' ( q ' q ' ) x ( q ' q ' ) 1/2 max 1/2 mn
54 BOP Optmzaton Problem s', m', q' x, XY,, T x 1 z z mn g q ' s.t. s ' As ' Bm' q q D s D m q q q x mn max ' ( x ' u ') ' ( q ' q ' ) x ( q ' q ' ) 1/2 max 1/2 mn T ( A BL) ( A BL) xˆ A C ( C C ) C A xˆ T T 1 T e e v e ( D D L) ( D D L) T D D T D D T z x u xˆ x u x e x w w w n
55 BOP Optmzaton Problem s', m', q' x, XY,, T x 1 z z mn g q ' s.t. s ' As ' Bm' q q D s D m q q q x mn max ' ( x ' u ') ' ( q ' q ' ) x ( q ' q ' ) 1/2 max 1/2 mn T ( A BL) ( A BL) xˆ A C ( C C ) C A xˆ T T 1 T e e v e ( D D L) ( D D L) T D D T D D T z x u xˆ x u x e x w w w n
56 BOP Optmzaton Problem s', m', q' x, XY,, mn g q ' s.t. s ' As ' Bm' q q D s D m q q q x mn max ' ( x ' u ') ' ( q ' q ' ) x ( q ' q ' ) 1/2 max 1/2 mn X A C C C C A AX BY ( AX BY ) X T T x DxeDx ( ) Dx X DuY 0 T T ( Dx X DuY ) X T T 1 T e ( e v) e ( ) T 0
57 BOP Optmzaton Problem s', m', q' x, XY,, mn g q ' s.t. s ' As ' Bm' q q D s D m q q q x mn max ' ( x ' u ') ' ( q ' q ' ) x ( q ' q ' ) 1/2 max 1/2 mn X A C C C C A AX BY ( AX BY ) X T T x DxeDx ( ) Dx X DuY 0 T T ( Dx X DuY ) X T T 1 T e ( e v) e ( ) T 0
58 Reverse-Convex Constrants 1 x x 1 Global soluton obtaned usng branch and bound scheme x ( q' q' ) 1/2 mn ( ' ' ) 1/2 max 1 (z ss, +d mn, 1 ) 2 1 x (z ss, +d max, ) 2 1 q 1q z ss, q' 1 Feasble Regon
59 T cy (K) F cat (kg/s) T reg (K) Controller Optmzaton O d x F ar (kg/s) C st T (K) st C rgc x 10-3
60 T cy (K) T reg (K) Controller Optmzaton O d F cat (kg/s) x F (kg/s) ar C st T (K) st C rgc x 10-3
61 FCC Proft Gross Proft ($/day) BOP loss of proft ($/day) OSSOP $36,905 - Fxed Control $35,768 - $1,137
62 FCC Proft Gross Proft ($/day) BOP loss of proft ($/day) OSSOP $36,905 - Fxed Control $35,768 - $1,137 Proft Control $36,160 - $745
63 Conclusons FCC Case Study Proft loss reduced by 35% Overall proft mproved by 1%
64 Conclusons FCC Case Study Proft loss reduced by 35% Overall proft mproved by 1% Attrbutes of Proft Control Relatonshp between control system performance and plant proft quantfed. Enables proft guded control system desgn Globally optmal search algorthm scheme
65 Acknowledgements s Department of Chemcal and Bologcal Engneerng Armour College of Engneerng and the IIT Graduate College Graduate Students Mke Walker Deepak Sharma Prevous Students Ju-Kun Peng Amt M. Manthanwar
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