Global Optimization for Scheduling Refinery Crude Oil Operations

Transcription

1 Global Opimizaion for Scheduling Refinery Crude Oil Operaions Ramkumar Karuppiah 1, Kevin C. Furman 2 and Ignacio E. Grossmann 1 (1) Deparmen of Chemical Engineering Carnegie Mellon Universiy (2) Corporae Sraegic Research Exxonmobil Research and Engineering Enerprise-wide Opimizaion Projec

2 Moivaion Scheduling and Planning of crude oil is key problem in perochemical refineries Large cos savings can be realized wih an opimum schedule for he movemen of crude oil Vessels Sorage Tanks Charging Tanks Crude-Disillaion Uni How o coordinae discharge of vessels wih loading o sorage? How o synchronize charging anks wih crude-oil disillaion? Economic refinery operaion 2

3 Crude Supply Sreams Problem Saemen Sorage Tanks Charging Tanks Crude Disillaion Unis Given: (a) Maximum and minimum invenory levels for a ank (b) Iniial oal and componen invenories in a ank (c) Upper and lower bounds on he fracion of key componens in he crude inside a ank (d) Times of arrival of crude oil in he supply sreams (e) Amoun of crude arriving in he supply sreams (f) Fracions of various componens in he supply sreams (g) Bounds on he flowraes of he sreams in he nework (h) Time horizon for scheduling Deermine: (i) Invenory levels in he anks a various poins of ime (ii) Flow volumes from one uni o anoher in a cerain ime inerval (iii) Sar and end imes of he flows in he nework Objecive: Minimize Cos 3

4 Previous Work Lee, H.; Pino, J. M.; Grossmann, I. E.; Park, S. (1996). Mixed Ineger Linear Programming Model for Refinery Shor-Term Scheduling of Crude Oil Unloading wih Invenory Managemen. I&EC Res.,, 35, Jia,, Z.; Ieraperiou,, M. G. (2003). Refinery Shor-Term Scheduling Using Coninuous Time Formulaion: Crude Oil Operaions. I&EC Res.,, 42, Furman,, K. C.; Jia,, Z.; Ieraperiou,, M. G. (2005). A Robus Even-Based Coninuous Time Formulaion for Tank Transfer Scheduling. Work in Progress. 4

5 Scheduling Model Coninuous ime formulaion by Furman e al. (2006) Based on ime evens where inpus and oupus for a uni can ake place in he same ime even Assumpion: No simulaneous inpu and oupu for a ank s Transfers from one ank o anoher are denoed by sreams Formulaion reduces number of binary variables required in he scheduling model Opimizaion model Minimize cos objecive s.. Tank consrains Disillaion uni (CDU) consrains Supply sream consrains Variable bounds (P) Binary Variables Variables in he model o I b, j I b, o V s, j V s, 1 T s, 2 T s, w s, Toal invenory in ank b a end of ime even Invenory of componen j in ank b a end of ime even Toal flow in sream s in ime even Flow of componen j in sream s in ime even Sar ime of flow in sream s in ime even End ime of flow in sream s in ime even Exisence of flow in sream s in ime even 5

6 Time represenaion - Insead of using global imes, evens are used - Insead of iming of individual operaions, iming of ransfers is used Tank A Even Even +1 Tank B 1 T ab, 2 T ab, 1 2 T ab, + 1 T ab, + 1 6

7 Model Consrains Tank consrains Crude inflow Crude Tank Crude ouflow Toal Invenory balances Individual componen balances Non-linear equaions conaining Bilineariies Duraion consrains To bound he flow of a sream ino/from a ank in a paricular ime even Simple sequencing consrains Bounds on componen fracions inside a ank 7

8 Model Consrains (Cond( ) Coninuous operaion consrain Disillaion uni consrains Allocaion consrains A mos one CDU can be charged by a charging ank a a ime A mos one charging ank can charge a CDU a any poin of ime Crude-mix demand consrains Feed Producs.. Crude supply sream consrains Overall mass balances Componen mass balances Sar and end iming consrains 8

9 Non-convex MINLP Objecive funcion: Minimize a cos objecive similar o he one by Jia and Ieraperiou (2003) min oal cos = waiing cos for supply sreams + unloading cos of supply sreams + invenory cos for each ank over scheduling horizon + seup cos for charging CDUs wih differen charging anks Scheduling problem modeled as a Mixed Ineger Nonlinear Program (MINLP) Discree variables used o deermine which flows should exis and when Model is non-linear and non-convex Overall model (P) Non-convex MINLP Convex relaxaion of (P) (obained by linearizing non-linear equaions in Tank consrains and inroducing McCormick esimaors (1976) for bilinear erms) (R) MILP 9

10 Global Opimizaion of MINLP Large-scale non-convex MINLPs such as (P) are very difficul o solve Commercial global opimizaion solvers fail o converge o soluion in racable compuaional imes Special Ouer-Approximaion algorihm proposed o solve problem o global opimaliy NLP fixed 0-1 Upper Bound Maser MILP Lower Bound Guaraneed o converge o global opimum given cerain olerance beween lower and upper bounds Upper Bound : Feasible soluion of (P) Lower Bound : Obained by solving a MILP relaxaion (R) of he non-convex MINLP model wih Lagrangean Decomposiion based cus added o i 10

11 Spaial Decomposiion of he Nework Crude Supply Sreams Sorage Tanks D1 Charging Tanks Crude Disillaion Unis a b c D2 Nework is spli ino wo decoupled sub-srucures D1 and D2 Physically inerpreed as cuing some pipelines (Here a, b and c) Se of spli sreams denoed by p {a, b, c } 11

12 Decomposiion of he model Creae wo copies of he variables peraining o he spli sreams and ge wo ses of duplicae variables :,1,1,1 2,1 { V V, T, T, w } o j 1 1 p,, p, p, p, p, The equaions involving he spli sreams are re-wrien in erms of he newly creaed variables These duplicae variables are relaed by equaliy consrains which are added o (R) o ge model (RP): o,1 o,2 Vp, Vp, = 0 p, and,2,2,2 2,2 { V V, T, T, w } o j 1 2 p,, p, p, p, p, o j 1 2 {, V, T, T w } V p, p, p, p,, p, j,1 j,2 V p, V p, = 0 j, p, 1,1 1,2,, T p T p = 0 p, 2,1 2,2,, T p T p = 0 p, Non-anicipaiviy consrains 1 2,, w p w p = 0 p, Non-anicipaiviy consrains in (RP) are muliplied by Lagrange mulipliers and ransferred o objecive funcion o bring model o a decomposable form which is decomposed ino sub-models (LD1) and (LD2) 12

13 Decomposed Sub-models Sub-problem involves duplicae variables o,1 j,1 1,1 2,1 1 { V V, T, T w } p,, p, p, p,, p, min z 1 s.. = waiing cos for supply sreams + unloading cos of supply sreams + invenory cos for anks in D1 over scheduling horizon + seup coss for charging CDUs in D1 wih differen charging anks + Vo o,1 V j,1 T1 1,1 T2 2,1 λp V p, + λ j, p, V p, + λ p, Tp, + λ p, Tp, + p w, λ p, j p p p p Tank consrains Disillaion uni consrains Supply sream consrains Variable bounds w 1 p, (LD1) Opimize o ge soluion * z 1 Sub-problem involves duplicae variables o,2 j,2 1,2 2,2 2 { V V, T, T w } p,, p, p, p,, p, min z 2 s.. = invenory cos for anks in D2 over scheduling horizon + seup coss for charging CDUs in D2 wih differen charging anks + p Vo o,2 j λp, V p, λ j, p, V p, λ T λ T λ, w j p Tank consrains Disillaion uni consrains Variable bounds V,2 p T1 1,2 p, p, p T2 2,2 p, p, p w p (LD2) 2 p, Opimize o ge soluion * z 2 13

14 Cu Generaion * * Using soluions and we develop he following cus : z 1 z 2 * z 1 waiing cos for supply sreams + unloading cos of supply sreams + invenory cos for anks in D1 over scheduling horizon + seup coss for charging CDUs in D1 wih differen charging anks + Vo o V j T1 1 T 2 2 λp p, + λ j, p, Vp, + λp, Tp, + λp, Tp, + p w, V λp, wp, j p p p p Lagrange Mulipliers * z 2 invenory cos for anks in D2 over scheduling horizon + seup coss for charging CDUs in D2 wih differen charging anks + p λ Vo o V j T1 1 T 2 2 w p, λ j p p p p V p, λ j, p, Vp, λp, Tp, λp, Tp, p, wp, Add above cus o (R) o ge (R ) which is solved o obain a valid lower bound on global opimum of (P) Remark: Updae Lagrange mulipliers and generae more cus o add o (R) 14

15 Advanages of Cu Generaion Lower bound obained is a leas as srong as one from convenional Lagrangean decomposiion or LP relaxaion of (R) Alernaive decomposiion schemes can be used o generae more cus o add o relaxaion (R) Crude Supply Sreams Sorage Tanks Charging Tanks D4 Crude Disillaion Unis D3 15

16 Proposed Algorihm Varian of Ouer-Approximaion ( Duran and Grossmann, 1986) Preprocessing Bound Conracion opional Solve Lower Bounding Problem Includes cuing plane generaion Add Ineger Cus Solve Upper Bounding Problem No UB LB <= olerance? Yes STOP Soluion = UB 16

17 Illusraive Example 3 Supply sreams 6 Sorage Tanks 4 Charging Tanks 3 Disillaion unis Scheduling Horizon Number of supply sreams Arrival Time Incoming Volume of crude 15 hours 3 Fracion of key componen IN IN IN Number of Charging Tanks Tank1 Tank2 Tank3 Tank4 Capaciy Iniial Invenory 5 3 Iniial Fracion of key componen (min max) ( ) ( ) ( ) ( ) Number of Sorage Tanks Capaciy Iniial Invenory 6 Iniial fracion of key componen (min max) Number of CDUs : 3 Waiing cos for supply sreams (Csea): 5 Unloading cos for supply sreams (Cunload): 7 Tank invenory coss (Cinv(b)): sorage anks 0.05 charging anks 0.06 Changeover cos for charged oil swich (Cse): Tank1 Tank2 Tank ( ) 0.03 ( ) 0.05 ( ) Demand of mixed oils by CDUs : oil mix 1 60 oil mix 2 60 oil mix 3 60 oil mix 4 60 Tank ( ) Tank ( ) Tank ( ) Bounds on flowraes in he sreams: Lower Bound : 1, Upper Bound : 40 17

18 Gan char of opimal schedule Opimal Crude Flow Schedule Crude vessel o sorage anks ST6 ST5 ST4 Sar ime of crude unloading 60 IN3 ST3 60 IN2 ST2 IN IN1 ST ime (hrs) --> Crude ransfers beween sorage and charging anks 10 CT4 ST6 20 ST5 CT3 ST4 CT2 ST3 CT1 5 ST2 50 ST ime (hrs) --> 18

19 Opimal Crude Flow Schedule Gan char of opimal schedule Charging schedule for disillaion unis CDU1 being Charged CDU2 being Charged CDU3 being Charged DU3 CT4 CT3 CT4 DU2 CT3 CT2 DU1 CT2 60 CT ime (hrs) --> 19

20 Compuaional Resuls 3 Supply sreams 3 Sorage anks 3 Charging anks 2 Disillaion unis 3 Supply sreams 3 Sorage anks 3 Charging anks 2 Disillaion unis 3 Supply sreams 6 Sorage anks 4 Charging anks 3 Disillaion unis Example Number of Binary Variables Original MINLP model (P) Number of Coninuous Variables Number of Consrains Solvers : MILP CPLEX 9.0, NLP BARON (Sahinidis, 1996) Example Lower bound [obained by solving relaxaion (RP) ] (z RP ) Upper bound [on solving (P-NLP) using BARON ] (z P-NLP ) Relaxaion gap (%) Toal ime aken for one ieraion of algorihm* (CPUsecs) Local opimum (using DICOPT) Example Soluion (z R ) Solving MILP model (R) LP relaxaion a roo node No. of nodes Time aken o solve (R)* (CPUsecs) Soluion (z RP ) Solving MILP model (RP) (including proposed cus) LP relaxaion a roo node No. of nodes Time aken o solve (RP)* (CPUsecs) BARON could no guaranee global opimaliy in more han 10 hours* 20 * Penium IV, 2.8 GHz, 512 MB RAM

21 Summary New coninuous ime formulaion used o represen he scheduling of crude oil a he fron-end of a refinery Scheduling model is a non-convex MINLP Special Ouer-Approximaion algorihm proposed o solve problem o global opimaliy Main idea : Generaion of cuing planes for speeding up soluion of MILP relaxaion 21