On Modeling the Tactical Planning of Oil Pipeline Networks
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1 On Modeling the Tactical Planning of Oil Pipeline Networks Daniel Felix Ferber PETROBRAS ICAPS
2 Introduction The supply chain at Petrobras: Pipeline Networks Oil refined commodities Multi-commodity Multi-period
3 3 Motivation 7km of pipelines!
4 4 Motivation Our main goal: Assure minimal inventory levels at consumer facilities. Decisions: Amount Timeframe Path Flow rate The pipeline network plan: A description of flow among s. Ignores operational details: not yet a schedule.
5 5 Motivation Current solution: Classic network flow model. Solution requires many fixes : Inventory on pipelines, average flow capacity, etc. Not a realistic flow description!
6 6 Motivation Some desired aspects: Inventory of pipelines (in-transit inventory) Transit time Flow capacity Flow reversal Incorporate scheduling aspects into the plan!
7 7 Motivation A linear programming approach: Well-known and proven solution Challenge: NO integer variables! Fast execution Large topologies Suited for tactical planning.
8 8 The Pipeline Operation Pipeline network: a graph of arcs and s (production facility) (delivery location) ' arc (pipeline) transhipment (harbor) ' (production & delivery) Graph G(N, A) N: set of s A: set of arcs
9 9 The Pipeline Operation Flow constraints: enummeration of paths (production facility) (delivery location) ' arc (pipeline) transhipment (harbor) (production & delivery) Graph G(N, A) N: set of s A: set of arcs P: set of paths
10 The Pipeline Operation Layers of commodities : (production facility) (delivery location) ' arc (pipeline) transhipment (harbor) (production & delivery) Graph G(N, A) N: set of s A: set of arcs P: set of paths C: set of commodities
11 The Pipeline Operation In-transit inventory on pipelines In-transit Inventory: diesel gasoline apes (always completely filled!) ar ot Push & Delivery: r push deliver Flow Reversal: deliver push
12 Problem Formulation Node: inbound and outbound paths n N, c C,t T Parameters: γ nc (t ) γ nc Node inventory P nct D nct γ' nc t l α p pct P nct D nct γ nc t γ' nc t Production Demand Decision variables: Node inventory γ nc t
13 3 Problem Formulation Paths: sequence of among facilities and terminals p P, c C,t T, j { l p } Inventory at t Inventory at t l α p pct Decision variables: l p =3 j β pc Parameters: in-transit inventory j α pc t j α pc t α pc t in-transit inventory withdrawal transshipment receipt
14 4 Problem Formulation The arc inventory relaxation : p P, c C,t T, j { l p } l α p pct l p =3 l α p pct l p =3
15 5 Problem Formulation The arc inventory relaxation revealed: p P, c C,t T, j { l p } j j j,(v) j,(vii) j,(iii ) j,(ii ) j + j First deliver current inventory. Only then transport the entering commodity. Keep part of the entering commodity as next inventory.
16 6 Problem Formulation The arc inventory relaxation revealed: p P, c C,t T, j { l p } j j j,(v) j,(vii) j,(iii ) j,(ii ) j + j
17 7 Problem Formulation The arc flow relaxation : a A,t T l α p pct = = = l p =3 Each Arc Total inbound amount = Total outbound amount
18 8 Problem Formulation The arc flow relaxation in action! a A,t T l α p pct T T T T T T l p =3 Each Arc End Total time fits into the time slot j α T pct t
19 9 Example Arc & Inventory Relaxation Model: Classic Network Flow Model: Refinery A Dist. Center B Refinery A Dist. Center B 9. H 9. L 5.L arc ab.h: path ab 5. H 5. L 9. H 9. L 5.L arc ab 5. H 5. L Refinery A Dist. Center B Refinery A Dist. Center B 9. H 4. L arc ab 7. H.L: path ab.h 83% utilization 3.H 8. L 9. H 4. L arc ab 7% utilization 7. H L 5.L
20 Experiments Typical instance: 75 classes of commodities, 5 s, 45 arcs months planning horizon Time Slices Variables Constraints Execution Time, 5, min 8 3,, min
21 Conclusion Network Flow Linear Programming: In-transit inventory Transit time Arc flow capacity Benefits: More accurate flow and utilization rates Closer approximation to reality. Arc flow reversal Challenge achieved: No integer variables for a better pipeline network model!
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