Scheduling of Crude Oil Movements at Refinery Front-end

Transcription

1 Scheduling of Crude Oil Movemens a Refinery Fron-end Ramkumar Karuppiah and Ignacio Grossmann Carnegie Mellon Universiy ExxonMobil Case Sudy: Dr. Kevin Furman Enerprise-wide Opimizaion Projec March 15,

2 Moivaion - Scheduling and Planning of flow 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 Charging Crude-Disillaion Uni How o coordinae discharge of vessels wih loading o sorage? How o synchronize charging anks wih crude-oil disillaion? 2

3 Crude Disillaion Uni 3

4 Problem Saemen Crude oil supply sreams 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) Toal and componen invenory levels in he anks a various poins of ime (ii) Volumes of oal and componen flows from one uni o anoher in a cerain ime inerval (iii) Sar and end imes of he flows in each sream of he sysem. Objecive: Minimize Cos MILP Model: Lee, Pino, Grossmann, Park (1996) 4

5 Assumpions MINLP Model 1. Perfec mixing akes place in each ank. 2. Negligible change in specific graviies on mixing. 3. Discree flows of volumes ino and from a ank. 4. Simulaneous inpus ino and oupus from a ank are no allowed. 5. Each disillaion uni can be charged by a mos one charging ank a a poin of ime. 6. Each charging ank can charge a mos one disillaion uni a a poin of ime. 7. All he disillaion unis have o be operaed coninuously hroughou he enire ime horizon. 5

6 Scheduling Model Coninuous ime formulaion by Furman e al. (2006) Sae Task Nework Represenaion Based on ime evens where inpus and oupus o an uni can ake place in he same ime even No simulaneous inpu ino and from a ank Formulaion reduces number of binary variables required in he scheduling model Opimizaion model : min cos objecive (P) s.. Tank consrains Disillaion uni consrains Supply sream consrains Variable bounds 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 Binary variable peraining o exisence of flow in sream s in ime even 6

7 Consrains in Model Tank consrains Overall mass balance Individual componen balance Non-linear equaions conaining Bilineariies Logic consrains o Relaed o he exisence of a flow ino or from a ank in a ime even Duraion consrains o To bound he flow of a sream ino/from a ank in a paricular ime even Simple sequencing consrains Invenory bounds Bounds on componen fracions inside a ank Inpu and oupu resrains over whole horizon 7

8 Consrains in Model (Cond ) Disillaion uni consrains Coninuous ime operaion consrain Allocaion consrains o Only one CDU can be charged by a charging ank in a ime even o Only one charging ank can charge a CDU in a ime even Crude-mix demand consrains 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 + changeover cos for charging CDUs wih differen charging anks Overall model (P) Non-convex MINLP Convex relaxaion of (P) (obained by linearizing non-linear equaions in Tank consrains and inroducing McCormick convex envelopes (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 Global opimizaion solvers fail o converge o soluion in racable compuaional imes (e.g. BARON) 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 wihin olerance of lower and upper bounds Upper Bound : Feasible soluion of (P) obained by fixing he binary variables o he values obained from he soluion of he relaxaion and solving he resuling NLP Lower Bound : Obained by solving a convex relaxaion (R) of he non-convex MINLP model wih Lagrangean Decomposiion based cus added o i 10

11 Upper Bound Local soluion of NLP- non-rigorous Lower bound on Global Opimum Convex relaxaion (R) is a large MILP and is also difficul o solve Generae cus o add o relaxaion o srenghen i and reduce soluion imes Karuppiah and Grossmann (2006) Cu generaion performed by a spaial decomposiion of he nework srucure 11

12 Spaial Decomposiion of he nework Crude oil arrivals Sorage Tanks Charging Tanks Crude Disillaion Unis D1 b a D2 Nework is spli ino wo decoupled sub-srucures D1 and D2 Physically inerpreed as cuing some pipelines (Here a and b ) Se of spli sreams denoed by p {a, b } 12

13 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 in model (R) 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, p, and,2,2,2 2,2 { V V, T, T, w } o j 1 2 p,, p, p, p, p, {, V, T, T w } o j 1 2 V p, p, p, p,, p, j,1,2 j V p, = V p, j, p, 1,1 1,2,, Tp = Tp p, 2,1 2,2,, Tp = Tp p, Non-anicipaiviy consrains 1 2,, wp = wp 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) 13

14 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 + changeover cos 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) Globally 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 = invenory cos for anks in D2 over scheduling horizon + changeover cos for charging CDUs in D2 wih differen charging anks + p Vo o,2 p p λ, V, λ,, V, λ T λ T λ, w j p V j p j,2 p p T1 1,2 p, p, p T2 2,2 p, p, p w p 2 p, Globally opimize o ge soluion s.. Tank consrains Disillaion uni consrains Variable bounds (LD2) * z 2 14

15 Cu Generaion * Using soluions and z we develop he following cus : * z 1 2 * z 1 waiing cos for supply sreams + unloading cos of supply sreams + invenory cos for anks in D1 over scheduling horizon + changeover cos 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 + changeover cos for charging CDUs in D2 wih differen charging anks + p λ Vo o V j T1 1 T 2 2 w p, p j p p p p p p λp j p p p p V, λ,, V, λ, T, λ, T,, w, p 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) 15

16 Advanages of Cu Generaion Lower bound obained is sronger (or as srong) han one from convenional Lagrangean decomposiion or LP relaxaion of (R) Alernaive decomposiion schemes can be used o generae more cus o ighen relaxaion (R) c D2 d D1 16

17 Proposed Algorihm Ouer-Approximaion based algorihm: Sep1: Preprocessing Bounds on he variables in he model are deermined by physical inspecion of he nework srucure and using he numerical daa given Sep2: Lower Bound Generaion Generae a valid lower bound on he soluion by solving (R ) Sep3: Upper bound Fix ineger variables in (P) o he values obained from soluion of (R ) and solve resuling non-convex NLP denoed by (P-NLP) Sep4: Ineger Cu Making use of he ineger soluion of (R ), add an ineger cu o model (R ) o preclude he curren combinaion of ineger variables from re-appearing in fuure ieraions Sep5: Convergence Ierae beween solving models (R ) and (P-NLP) ill he lower bound exceeds he upper bound or he relaxaion gap beween he lower and upper bounds is less han a specified olerance 17

18 Illusraive Example 3 Supply sreams 6 Sorage Tanks 4 Charging Tanks 3 Disillaion unis Scheduling Horizon Number of Inpu sources IN1 IN2 IN3 Arrival Time Number of Sorage Tanks Tank1 Capaciy Incoming Volume of crude Iniial Invenor y hours 3 Fracion of key componen Iniial fracion of key componen (min max) ( ) Number of Charging Tanks Tank1 Tank2 Tank3 Tank4 Capaciy Iniial Invenory 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): 30 3 Tank2 Tank3 Tank4 Tank ( ) 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 ( ) Bounds on flowraes in he sreams: Lower Bound 1.5, Upper Bound 70 18

19 Opimal Crude Flow Schedule Gan char of opimal schedule Invenory Profiles for Sorage Tanks Sorage ank 2 (ST2) Sorage Tank 3 (ST3) Sorage Tank 4 (ST4) 60 Invenory --> ime (# unis) --> Invenory Profiles for Charging Tanks Charging ank 1 (CT1) Charging Tank 2 (CT2) Charging Tank 3 (CT3) Charging Tank 4 (CT4) Invenory --> ime (# unis) --> 19

20 Opimal Crude Flow Schedule Gan char of opimal schedule Charging schedule of Disillaion unis CDU1 being charged CDU2 being charged CDU3 being charged DU3 CT CT3 CT4 DU2 30 CT3 CT DU CT2 60 CT ime (# unis) --> 20

21 Preliminary Compuaional Resuls MINLP 57 binary variables, 439 coninuous variables and 1564 consrains Sub-opimal soluions obained (using GAMS/ DICOPT) : 447 or 463 vs (global) Proposed Algorihm : Solvers Used : MILP CPLEX 9.0, NLP CONOPT3 Cu generaion ime* = s Lower bound : On solving (R) (wihou cus) On solving (R ) (wih proposed cus) Upper bound : Toal ime* aken o solve problem = s Soluion Time* (sec) Lower and Upper bounds converge wihin 1 % olerance a 1 s ieraion of algorihm BARON (Sahinidis, 1996) could no find global soluion in more han 10 hours* * Penium IV, 2.8 GHz, 512 MB RAM 21

22 Fuure work 1. Consider addiion of RLT consrains o srenghen maser problem 2. Consider global soluion of NLP subproblems 3. Increase model accuracy 4. Exend ime horizon 5. Inegraion wih downsream refinery 22