We propose a discrete-time formulation for optimization of scheduling in crude-oil refineries considering both the logistics details practiced in industry and the process feed diet and quality calculations. The quantity-logic-quality phenomena (QLQP) involving a non-convex mixed-integer nonlinear (MINLP) problem is decomposed considering first the logistics model containing quantity and logic variables and constraints in a mixed-integer linear (MILP) formulation and, secondly, the quality problem with quantity and quality variables and constraints in a nonlinear programming (NLP) model by fixing the logic results from the logistics problem. Then, stream yields of crude distillation units (CDU), for the feed tank composition found in the quality calculation, are updated iteratively in the following logistics problem until their convergence is achieved. Both local and global MILP results of the logistics model are solved in the NLP programs of the quality and an ad-hoc criteria selects to continue those among a score of the MILP+NLP pairs of solutions. A pre-scheduling reduction to cluster similar quality crude-oils decreases the discrete search space in the possible superstructure of the industrial-sized example that demonstrates our tailor-made decomposition scheme of around 3% gap between the MILP and NLP solutions.

1. Brenno C. Menezes
PostDoc Research Scholar
Carnegie Mellon University
Pittsburgh, PA, US
Jeffrey D. Kelly
CTO and Co-Founder
IndustrIALgorithms
Toronto, ON, Canada
Complex Crude-oil Refinery Scheduling Optimization
EWO Meeting, CMU, Pittsburgh, Mar 15th, 2017.
Ignacio E. Grossmann
R. R. Dean Professor of Chemical Engineering
Carnegie Mellon University
Pittsburgh, PA, US
Faramroze Engineer
Senior Consultant
SK-Innovation
Seoul, South Korea
1st: Feedstock storage Assignment (FSA): MILP
2nd: Crude Blend Scheduling Optimization (CBSO): MILP+NLP
1
Remark: Continuous-time model cannot be
easily implemented by plant operators
Objective: Explore discrete-time model to the limit
- 2h-step for 14 days (168 periods) - 1 CDU
- 2h-step for 7 days (84 periods) - 5 CDUs
- 1h-step for 5 days (120 periods) - 5 CDUs + 2 RFCCs
Motivation 1: Replace Full Space MINLP by MILP + NLP decompositions for large problems
Motivation 2: Partition of crude scheduling in crude assignment and crude blend scheduling

2. Crude
Transferring
Refinery Units Fuel
Deliveries
Fuel
Blending
Crude
Dieting
Crude
Receiving
Hydrocarbon Flow
FCC
DHT
NHT
KHT
REF
DC
B
L
E
N
SRFCC
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-Oils to Fuels
Crude-Oil Scheduling Problem
Receiving or
Storage Tanks
Transferring or
Feedstock Tanks
VDU
1996: Lee, Pinto, Grossmann and Park (MILP), discrete-time
2004: Randy, Karimi and Srinivasan (MILP), continuous-time
2009: Mouret, Grossmann and Pestiaux: MILP+NLP continuous-time
2014: Castro and Grossmann: MINLP ; MILP+NLP, continuous-time
2015: Cerda, Pautasso and Cafaro: MILP+NLP, continuous-time
(336h: 14 days; binary ≈ 4,000; continuous ≈ 6,000; constraints ≈ 100K; CPU(s) ≈ 500)
2
2016 Goal: solve the SK Ulsan refinery scheduling for a week
(38 crude, 2 pipelines, 23 storage tanks, 11 feed tanks, 5 CDUs)
EWO Meeting, Mar 15th, 2017.
MINLP -> MILP + NLP
MINLP Relax y [0,1]
as (0,1) in NLP
Current Benchmark
DICOPT (5,000 binary variables)

3. Crude
Transferring
Refinery Units Fuel
Deliveries
Fuel
Blending
Crude
Dieting
Crude
Receiving
Hydrocarbon Flow
FCC
DHT
NHT
KHT
REF
DC
B
L
E
N
SRFCC
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-Oils to Fuels
Crude-Oil Blend Scheduling Problem
Receiving or
Storage Tanks
Transferring or
Feedstock Tanks
FSA
VDU
(MILP+NLP)
PDH Decomposition (logistics + quality problems)
Includes logistics details
1996: Lee, Pinto, Grossmann and Park (MILP), discrete-time
2004: Randy, Karimi and Srinivasan (MILP), continuous-time
2009: Mouret, Grossmann and Pestiaux: MILP+NLP continuous-time
2014: Castro and Grossmann: MINLP ; MILP+NLP, continuous-time
2015: Cerda, Pautasso and Cafaro: MILP+NLP, continuous-time
(336h: 14 days; binary ≈ 4,000; continuous ≈ 6,000; constraints ≈ 100K; CPU(s) ≈ 500)
3
(MILP)
2016 Goal: solve the SK Ulsan refinery scheduling for a week
(38 crude, 2 pipelines, 23 storage tanks, 11 feed tanks, 5 CDUs)
Minimize the Quality Variation Feedstocks -> Storage Tanks
Reduces optimization search space for further scheduling
2nd Crude Blend Scheduling
Optimization (CSBO)
Yields
Rates (crude diet, fuel recipes, conversion)
(Menezes, Kelly & Grossmann, 2015)
1. JD Kelly, BC Menezes, IE Grossmann, F Engineer, 2017, FOCAPO.
2. JD Kelly, BC Menezes, F Engineer, IE Grossmann, 2017, FOCAPO.
MINLP -> MILP + NLP
1st Feedstock Storage
Assignment (FSA)
FSA
CBSO
EWO Meeting, Mar 15th, 2017.

4. SK Refinery Example
4
The logistics problem (MILP):
33,937 continuous + 29,490 binary variables
8,612 equality and 72,368 inequality constraints
Non-Zeros: 531,204; Degrees-of-freedom: 63,427
CPU(s): 215 seconds (3.58 min) in 8 threads CPLEX 12.6.
The quality problem (NLP):
143,316 continuous variables
88,539 equality and 516 inequality constraint
Non-Zeros: 138,812; Degrees-of-freedom: 54,788
CPU(s): 539 seconds (8.98 min) in the IMPL’ SLP
engine linked to CPLEX 12.6.
MILP-NLP gap : 12% to 10% with two PDH iteration.
Units: 5 CDUs in 9 modes of operation + 4 Blenders
Tanks: 35 among storage and feed tanks.
7 days: 168-hours discretized into 2-hour time-period durations (84 time-periods).
IMPL (Industrial Modeling and Programming Language) using Intel Core i7 machine at 2.7 Hz with 16GB of RAM
EWO Meeting, Mar 15th, 2017.

5. Full Problem in Julia: FSA + Root + CBSO with Factors
5
LogisticsQuality
Yields (for CDU)
Setups
Quality
Yields
Logistics Quality
Setups
Qualogistics
Quality Sub-Solver
Logistics Sub-Solver
“Score”
yjit: Current assignments
1st: Feed tanks to CDU;
2nd: Storage to Feed tanks;
3rd: Feedstock Storage Assignment
xm: CDU Throughputs
(varying for the remaining amount in the feed tanks and
with performance term to smooth throughput)
Multi-period NLP for near past,
current and near future assignments
EWO Meeting, Mar 15th, 2017.
Factors
Factors (for Storage to Feed tanks)
FSA root
CBSO

6. 6
Heavy Fuel Oil (HFO) Blending: HFO_LP x HFO_NLP
NLP Heavy Fuel Oil Blending Flowsheet in UOPSS LP Heavy Fuel Oil Blending Flowsheet in UOPSS
𝑣𝑗,𝑝,𝑡 ෍
𝑗′
𝑥𝑗′,𝑖,𝑡 = ෍
𝑗′
𝑣𝑗′,𝑝,𝑡 𝑥𝑗′,𝑖,𝑡 ∀ 𝑗, 𝑝, 𝑡
𝑣𝑗′,𝑝,𝑡 (volume based properties)
෍
𝑗′
ҧ𝑓𝑗′,𝑝,𝑡 𝑥𝑗′,𝑖,𝑡 = ҧ𝑓𝑗,𝑝=𝑠𝑝𝑒𝑐,𝑡 𝑥𝑗,𝑖,𝑡 + 𝑥𝑗 𝑆𝑇,𝑖,𝑡 ∀(𝑗, 𝑗𝑆𝑇), 𝑝, 𝑡
ҧ𝑓𝑗′,𝑝,𝑡 (factor)
ҧ𝑓𝑗,𝑝=𝑠𝑝𝑒𝑐,𝑡
𝑣𝑗,𝑝,𝑡
𝑤𝑗,𝑝,𝑡𝑗′
𝑗
𝑖
EWO Meeting, Mar 15th, 2017.
𝑥𝑗′,𝑖,𝑡
(flow)

7. 7
Blend Scheduling: MILP-NLP GAP reduction with Factors
7 Days:
MILP: 226.5 (3)
NLP: 173.6 20.15%
15 Days:
MILP: 456.6 (4)
NLP: 432.3 5.3%
15 Days:
MILP: 439.1 (1)
NLP: 437.5 0.3%
7 Days:
MILP: 216.3 (1)
NLP: 215.5 0.3%
with Factors
Min blend in-let as 10%
without Factors

8. 8
Blend Scheduling: MILP-NLP GAP reduction with Factors
7 Days:
MILP: 226.5 (3)
NLP: 173.6 20.15%
15 Days:
MILP: 456.6 (4)
NLP: 432.3 5.3%
15 Days:
MILP: 439.1 (1)
NLP: 437.5 0.3%
7 Days:
MILP: 216.3 (1)
NLP: 215.5 0.3%
with Factors
Min blend in-let as 10%
without Factors

9. 9
7 Days:
MILP: 245.0 (3)
NLP: infeas
15 Days:
MILP: 528.5 (19)
NLP: infeas
15 Days:
MILP: 475.5 (14)
NLP: 464.5 2.3%
7 Days:
MILP: 220.3 (3)
NLP: 218.7 0.7%
Min blend in-let as yields=0%
Blend Scheduling: avoid infeasible NLP with Factors
with Factorswithout Factors

10. 10
7 Days:
MILP: 245.0 (3)
NLP: infeas
15 Days:
MILP: 528.5 (19)
NLP: infeas
15 Days:
MILP: 475.5 (14)
NLP: 464.5 2.3%
7 Days:
MILP: 220.3 (3)
NLP: 218.7 0.7%
Min blend in-let as yields=0%
Blend Scheduling: avoid infeasible NLP with Factors
with Factorswithout Factors

11. Reproduce an Industrial-Sized Problem using Factors
11
The logistics problem (MILP):
45,753 continuous + 28,543 binary variables
8,612 equality and 72,368 inequality constraints
Non-Zeros: 628,795; Degrees-of-freedom: 63,427
CPU(s): 170 seconds (2.83 min) in 8 threads CPLEX 12.6.
The quality problem (NLP):
121,394 continuous variables
99,099 equality and 516 inequality constraint
Non-Zeros: 125,462; Degrees-of-freedom: 22,295
CPU(s): 933 seconds (15.55 min) in the IMPL’ SLP
engine linked to CPLEX 12.6.
MILP-NLP gap : 0.01%.
Units: 5 CDUs without modes + 4 Blenders + VDU + 2 RHDS + 2 RFCC
Tanks: 20 storage and 10 feed; 2 intermediate for each unit
5 days: 120-hours discretized into 1-hour time-period duration
IMPL (Industrial Modeling and Programming Language) using Intel Core i7 machine at 2.7 Hz with 16GB of RAM
EWO Meeting, Mar 15th, 2017.

12. Conclusion
12
Novelty:
• Segregates crude management in storage assignment1 and crude blend
scheduling.2
• Phenomenological decomposition in logistics (MILP) and quality (NLP)
problems applied in a scheduling problem.
Impact for industrial applications:
• UOPSS modeling, pre-solving, and parallel processing, reverse polish
notation, complex number for derivatives, among others, solved for the 1st
time a highly complex refinery scheduling. (MILP 50K binary variables and
NLP 120K continuous with 60% NLP)
1. JD Kelly, BC Menezes, IE Grossmann, F Engineer, 2017, FOCAPO.
2. JD Kelly, BC Menezes, F Engineer, IE Grossmann, 2017, FOCAPO.
EWO Meeting, Mar 15th, 2017.

13. Crude Blend Scheduling (MILP+NLP)
Scheduling
Structure
Time
Supply
Chain
Refinery
Process
Unit
second hour day month year
RTOControl
on-line off-line
week
space
Measured updates/feedback:
a) Fill-Draw delays in Storage Tanks
b) Data Rec in feed tank real composition and properties
Integration in space
(measured or on-line)
Re-Scheduling
On-line Scheduling
Real-time Scheduling
Data-Analysis with Feedback
Data-Analytics + Decision-Making:
a) Distillation Blending and Cutpoint Opt. (ASTM D86 => TBP + flows)
b) Data-Driven RTO (LP to relate the majors pairs of
Depend./Independ. Variables): SSD, SSDR, SSGE, SSGO
• Wide Scheduling: from unloading of crude-oils to delivery of fuels
• Synchronization, Real-time Scheduling with parameter feedback.Next
Steps
13

14. Thank You
14
Q?&A!
www.industrialapplications.club
www.induapps.club
brenno@induapps.club