Brenno C. MenezesPostDoc Research ScholarCarnegie Mellon UniversityPittsburgh, PA, US

Jeffrey D. KellyCTO and Co-FounderIndustrIALgorithmsToronto, ON, Canada

Industrial View of Crude-oil Scheduling Problems

EWO Meeting, CMU, Pittsburgh, Mar 9th, 2016.

Ignacio E. GrossmannR. R. Dean Professor of Chemical EngineeringCarnegie Mellon UniversityPittsburgh, PA, US

Faramroze EngineerSenior Consultant SK-InnovationSeoul, South Korea

1st: Crude to Tank Assignment (CTA) for Improved Scheduling: MILP2nd: Crude Blend Scheduling Optimization (CBSO): MILP+NLP

1

Remark: Continuous-time model cannot be easily implemented by plant operators

Objective: Explore to the limit discrete-time model - 8h-step (shift) for 2-4 weeks (42-84 periods) - 2h-step for 7 days (84 periods)- 1h-step for 4 days (48 periods)

Motivation: Replace Full Space MINLP by MILP + NLP decompositions for large problems

Crude Transferring

Refinery Units Fuel Deliveries

Fuel Blending

Crude Dieting

Crude Receiving

Hydrocarbon Flow

FCC

DHT

NHT

KHT

REF

DC

BLENSRFCC

Fuel gas

LPG

Naphtha

Gasoline

Kerosene

Diesel

Diluent

Fuel oil

Asphalt

Crude-Oil Management Crude-to-Fuel Transformation Blend-Shop

Charging or Feed Tanks

Whole Scheduling: from Crude to Fuels Crude-Oil Scheduling Problem

Receiving or Storage Tanks

Transferring or Feedstock Tanks

CTA CBSO

VDU

(MILP+NLP)

PDH Decomposition (logistics + quality problems) Includes logistics details

1996: Lee, Pinto, Grossmann and Park (MILP), discrete-time2004: Randy, Karimi and Srinivasan (MILP), continuous-time2009: Mouret, Grossmann and Pestiaux: MILP+NLP continuous-time2014: Castro and Grossmann: MINLP ; MILP+NLP, continuous-time2015: Cerda, Pautasso and Cafaro: MILP+NLP, continuous-time(336h: 14 days; binary ≈ 4,000; continuous ≈ 6,000; constraints ≈ 100K; CPU(s) ≈ 500)

2

(MILP)

EWO Meeting, Mar 9th, 2016.

1st Crude to Tank Assignment (CTA)

2016 Goal: solve the SK Ulsan refinery scheduling for a week (38 crude, 2 pipelines, 23 storage tanks, 11 feed tanks, 5 CDUs)

Improve the polyhedral space of optimization for CDU dietReduces optimization search space for further scheduling

2nd Crude Blend Scheduling Optimization (CSBO)

Yields Rates (crude diet, fuel recipes, conversion)

(Menezes, Kelly & Grossmann, 2015)

Charging or Feed Tanks

Clusters

Crude(feedstock)

cr crude (or time)cp yield or propertytk storage tank

yield or property (pr): naphtha-yield (NY)diesel-yield (DY)diesel-sulfur (DS) residue-yield (RY)

1st Crude Tank Assignment (CTA) for Improved Scheduling

Charging Tanks

Tanks(storage)

y = binary variables (setup su)

3

CTA CBSO

EWO Meeting, Mar 9th, 2016.

Min= ∑𝐜𝐜𝐜𝐜∑𝐜𝐜𝐩𝐩∑𝐭𝐭𝐭𝐭𝐱𝐱𝐜𝐜𝐜𝐜,𝐜𝐜𝐩𝐩,𝐭𝐭𝐭𝐭

𝐦𝐦𝐦𝐦𝐱𝐱 𝐩𝐩𝐜𝐜𝐜𝐜𝐜𝐜,𝐜𝐜𝐩𝐩 −𝐦𝐦𝐦𝐦𝐦𝐦 𝐩𝐩𝐜𝐜𝐜𝐜𝐜𝐜,𝐜𝐜𝐩𝐩

Receiving or Storage Tanks

Transferring or Feedstock Tanks

−𝐦𝐦𝐦𝐦𝐱𝐱 𝐩𝐩𝐜𝐜𝐜𝐜𝐜𝐜,𝐜𝐜𝐩𝐩 ≤ 𝐱𝐱𝐜𝐜𝐜𝐜,𝐩𝐩𝐜𝐜,𝐭𝐭𝐭𝐭≤ 𝐦𝐦𝐦𝐦𝐱𝐱 𝐩𝐩𝐜𝐜𝐜𝐜𝐜𝐜,𝐜𝐜𝐩𝐩 ∀ 𝐜𝐜𝐜𝐜, 𝐜𝐜𝐩𝐩, 𝐭𝐭𝐭𝐭

−𝐦𝐦𝐦𝐦𝐱𝐱(𝐩𝐩𝐜𝐜𝐜𝐜𝐜𝐜,𝐜𝐜𝐩𝐩) 𝐲𝐲𝐭𝐭𝐭𝐭(𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐭𝐭𝐜𝐜𝐜𝐜),𝐜𝐜𝐩𝐩 ≤ 𝐱𝐱𝐭𝐭𝐭𝐭(𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐭𝐭𝐜𝐜𝐜𝐜),𝐜𝐜𝐩𝐩≤ 𝟎𝟎 ∀ 𝐜𝐜𝐩𝐩, 𝐭𝐭𝐭𝐭

𝐩𝐩𝐜𝐜𝐜𝐜𝐜𝐜𝐲𝐲𝐜𝐜𝐜𝐜,𝐜𝐜𝐩𝐩 ≤ 𝐱𝐱𝐜𝐜𝐜𝐜,𝐜𝐜𝐩𝐩≤ 𝐩𝐩𝐜𝐜𝐜𝐜𝐜𝐜𝐲𝐲𝐜𝐜𝐜𝐜,𝐜𝐜𝐩𝐩 ∀ 𝐜𝐜𝐜𝐜, 𝐜𝐜𝐩𝐩

𝐱𝐱𝐜𝐜𝐜𝐜,𝐩𝐩𝐜𝐜,𝐭𝐭𝐭𝐭 = 𝐱𝐱𝐜𝐜𝐜𝐜,𝐜𝐜𝐩𝐩𝐲𝐲𝐜𝐜𝐜𝐜,𝐜𝐜𝐩𝐩= −𝐱𝐱𝐭𝐭𝐭𝐭(𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐭𝐭𝐜𝐜𝐜𝐜),𝐜𝐜𝐩𝐩𝐲𝐲𝐭𝐭𝐭𝐭(𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐭𝐭𝐜𝐜𝐜𝐜),𝐜𝐜𝐩𝐩 ∀ 𝐜𝐜𝐜𝐜, 𝐜𝐜𝐩𝐩, 𝐭𝐭𝐭𝐭

x = continuous variables (flow f)

∑𝐭𝐭𝐭𝐭 𝐲𝐲𝐜𝐜𝐜𝐜,𝐜𝐜𝐩𝐩𝐭𝐭𝐭𝐭 =1 ∀ 𝐜𝐜𝐜𝐜, 𝐜𝐜𝐩𝐩

MILP

𝐲𝐲𝐜𝐜𝐜𝐜,𝐜𝐜𝐩𝐩

𝐲𝐲𝐭𝐭𝐭𝐭(𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐭𝐭𝐜𝐜𝐜𝐜),𝐜𝐜𝐩𝐩

“k-means” clustering (KM) and “fuzzy c-means” clustering (FCM) algorithms found in Bezdek et. al. (1984).

perimeter

Arrow

Ports

f and su

f and su

f

- Uses crude assay data- Multi-period NT=NCrude- Neglects logistics details:

initial volume, holdup, ssspipeline flow, etc.

Determines Crude-oil Segregation Rules

𝐱𝐱𝐜𝐜𝐜𝐜,𝐜𝐜𝐩𝐩

𝐱𝐱𝐭𝐭𝐭𝐭(𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐭𝐭𝐜𝐜𝐜𝐜),𝐜𝐜𝐩𝐩

𝐱𝐱𝐜𝐜𝐜𝐜,𝐜𝐜𝐩𝐩,𝐭𝐭𝐭𝐭

Assign crude to only one cluster

Define one crude per time

Solver: CPLEX 12.6 in 8 threads

Cluster 1 Membership (16): 1, 4, 6, 8, 12, 13, 15, 21, 28, 30, 34, 36, 40, 41, 43, 45

Cluster 2 Membership (9): 3, 9, 14, 24, 25, 27, 32, 33, 37

Cluster 3 Membership (18): 2, 5, 10, 11, 16, 17, 18, 19, 20, 22, 26, 29, 31, 35, 38, 39, 42, 44

Cluster 4 Membership (2): 7, 23

Cluster 1 Means: 18.75, 20.84, 0.1594, 8.58

Cluster 2 Means: 32.88, 13.61, 0.0900, 1.53

Cluster 3 Means: 14.08, 17.06, 0.2300, 18.64

Cluster 4 Means: 7.72, 10.31, 1.83, 35.39

NY DY DS RY

4EWO Meeting, Mar 9th, 2016.

Ultra heavy

Light

Heavy

1st Crude Tank Assignment (CTA) for Improved Scheduling

asasasa

2nd Crude Blend Scheduling Optimization (CBSO-QL)

5

MILP(QL) + NLP(QQ)• Key logistics details … (QL)

1st: 9-h fill-draw-delay for storage tanks.2nd: 3-h uptime (run-length) for blend header.

6th: 19-h uptime for tank-to-CDU flows.

3rd: flow-out at-a-time for the blend header.4th: 3-h fill-draw-delay for charge tanks.

5th: 1 or 2 flow-in at-a-time for the CDU.

7th: 0-h downtime (continuous) for the CDU.8th…: Charging tank transitions

Sequence-dependent (Kelly and Zyngier, 2007)

EWO Meeting, Mar 9th, 2016.

CBSOCTA

Mixing-time Uptime-Use Multi-Use Other types Quantity + Logic

CBSOCTA

asasasa

6

MILP(QL) + NLP(QQ)• Key quality details… (QQ)

1st: Feed Tank diet (primary).2nd: 2 or more Feed Tank diet (secondary).3rd: CDU models (modes of operations).

Fractionation Index (Alattas et al., 2012, 2013); Improved Swing-Cut (Menezes et al., 2013), Distillation Blending (Kelly et al., 2014)

2nd Crude Blend Scheduling Optimization (CBSO-QQ)

EWO Meeting, Mar 9th, 2016.

Drawback: ↑ binary variables, Option: NLP models

Yields Rates (crude diet, fuel recipes, conversion)

Quantity + Quality

7

2nd Crude-oil Blend Scheduling Optimization-PDH(Menezes, Kelly & Grossmann, 2015)

EWO Meeting, Mar 9th, 2016.

6,736 continuous variables

6,057 equality and 1,640 inequality (DoF=679)

CPU(s): 4.9s with SLPQPE_CPLEX 12.6

4,881 continuous and 2,998 binary variables

2,323 equality and 11,105 inequality (DoF=5,556)

CPU(s): 210s with CPLEX 12.6 in 8 threads

ZMILP=963 ZNLP=839

CBSO for 14 days with 2h-step= 168 periods

MILP(QL) + NLP(QQ)Yields Rates (crude diet, fuel recipes, conversion)

12.8% MILP-NLP Gap

T=[0,2h] QL QQ T=[2,4h] QL QQS1 12.75 5.00 S1 12.75 5.00S2 77.25 38.87 S2 77.25 5.00S3 5.00 5.80 S3 5.00 10.92S4 5.00 50.32 S4 5.00 79.07

F1 Tank diet (%)

2nd Crude-oil Blend Scheduling Optimization (CBSO-IMF-QL)

8Gantt Chart: Crude blender, CDU and Feed Tanks Holdup.

EWO Meeting, Mar 9th, 2016.

Blender

Feed Tanks

CDU

Time (step 2h)

To tank F1 To tank F2

9Gantt Chart: Feed Tank F1 Holdup and its crude composition.

EWO Meeting, Mar 9th, 2016.

2nd Crude-oil Blend Scheduling Optimization (CBSO-IMF-QQ)

Feed Tank 1

Crude composition (C1-C6)

Time (step 2h)

Conclusion

10EWO Meeting, Mar 9th, 2016.

Novelty:

• Segregates crude management in storage assignment and crude blendscheduling.

• Phenomenological decomposition in logistics (MILP) and quality (NLP)problems applied in a scheduling problem.

• Details all logistics relationships from practiced industrial operations.

11EWO Meeting, Mar 9th, 2016.

ConclusionImpact for industrial applications:

• Quickly reproduced (2weeks) using the structural programming language IMPL

• UOPSS modeling, pre-solving, and parallel processing permitted to solve an 2htime-step discrete-time formulation for a highly complex refinery in Ulsan (38crude, 23 storage tanks, 11 feed tanks, 5 CDUs): for 6-7 days (72-80 time-periods)considering included after the pre-solving

14,753 continuous and 8,481 binary variables;

5,029 equality and 32,852 inequality constraints (DoF=18,205)

CPU: 10.8 min (Cplex 12.6) and 3.6 min (Gurobi 6.5.0) (both in 8 threads)8.4 min (Gurobi 6.5.0) (1 thread)

14,239 continuous and 9,937 binary variables

5,869 equality and 38,517 inequality constraints (DoF=21,307)

CPU: 50.8 min (Cplex 12.6) (in 8 threads)

6 days 7 days

No results (Gurobi 6.5.0)@ 0.0% GAP @ 0.2% GAP

12

13

14

Sets (.usp)

Configuration (.iml)

15

6 days

Included after pre-solving

Statistics (.sdt) Configuration (.iml), cont…..

16

7 days

Included after pre-solvingStatistics (.sdt)Configuration (.iml), cont…..

17

Constraints (.ndt)

Configuration (.iml), cont…..

18

V2r_xmf(m=39,t=1)=20.833 kbbl/2h

CDU1 throughput in mode ‘mod1’

CDU1,mod1 is identified as object 39

Results (.dtv) Configuration (.iml), cont…..

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List of variables List of constraints