Date post: | 15-Apr-2017 |
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The logistics problem: ZMILP=695.68,333 continuous + 3,508 binary variables
3,957 equality and 15,810 inequality constraints
Non-Zeros: 59,225 ; Degrees-of-freedom: 7,884
CPU(s): 176.0 seconds / 8 threads in CPLEX 12.6.
The logistics problem: : ZMILP=12830,925 continuous and 29,490 binary variables
6,613 equality and 79,079 inequality constraints
(degrees-of-freedom = 53,802)
CPU: 128.8 seconds using 8 threads in CPLEX 12.6.
Jeffrey D. Kelly,1 Brenno C. Menezes,2 Faramroze Engineer,3 Ignacio E. Grossmann2
Crude-Oil Blend Scheduling Optimization of an
Industrial-Sized Refinery: a Discrete-time Benchmark
Goal: solve a discrete-time formulation for optimization of scheduling in
crude-oil refineries considering both the logistics details practiced in industry
in an MILP problem and the process feed diet and quality calculations in an
NLP model.
Figure 1. Crude-oil refining scheduling: from crude-oils to fuels.
1industri@lgorithms, Toronto, Canada. 2Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, United States. 3SK-Innovation, Seoul, South Korea.
2. BC Menezes, JD Kelly, IE Grossmann, Comput Aided Chem Eng, 37, 2015.
Figure 2. Proposed Reductions and PDH Algorithm
Proposed Algorithm: The quantity-logic-quality phenomena is decomposed
considering first the logistics model (MILP) and, secondly, the quality
problem with in an NLP model by fixing the logic results from the logistics
problem.2
A pre-scheduling reduction to cluster similar quality crude-oils1
decreases the discrete search space in the possible superstructure of
assignments.
SK Example: UOPSS modeling, pre-solving, and parallel processing
solved a discrete-time formulation with 7 days/2h-step (84 periods) for a
highly complex refinery (34 crude, 24 storage tanks, 11 feed tanks, 5
CDUs in 9 modes).
1. JD Kelly, BC Menezes, IE Grossmann, F Engineer, 2017, FOCAPO.
Future Work: the next steps are planned for further development
• Factors in bulk qualities (LP) between Storage and Feed Tanks in the MILP
• Wide-Scheduling: from Crude-Oil Unloading to Delivery of Fuels
• Initialization, Synchronization, Real-time Scheduling with Parameter
Feedback
The quality problem: ZNLP=110102,539 continuous variables
58,019 equality and 768 inequality constraints
(degrees-of-freedom = 44,520)
CPU: 103.3 seconds in the IMPL’ SLP engine
linked to CPLEX 12.6.
Crude blend scheduling (MILP+NLP) (this work)
Clustering1 (MILP)
Figure 4. Crude-Oil Blend Scheduling: illustrative example.
x = continuous variables (flow f)
y = binary variables (setup su)
unit perimeter (sink, source)
tank
in-port (i)
out-port (j)
arrow (mode does not apply)
x = continuous variables (flow f)
(shape+mode)
𝑥𝐿𝑦 ≤ 𝑥 ≤ 𝑥𝑈𝑦 ∀ u, arrow
mixers
splitters
𝑦𝑢 + 𝑦𝑢′ ≥ 2𝑦𝑎𝑟𝑟𝑜𝑤for u->(arrow)->u’ (links)
1
𝑥𝑢𝑈 𝑗 𝑥𝑗𝑖 ≤ 𝑦𝑢 ≤
1
𝑥𝑢𝐿 𝑗 𝑥𝑗𝑖 ∀ (i, u)
1
𝑥𝑢𝑈 𝑖 𝑥𝑗𝑖 ≤ 𝑦𝑢 ≤
1
𝑥𝑢𝐿 𝑖 𝑥𝑗𝑖 ∀ (u, j)
u = unit, perimeter and tank
The quality problem: ZNLP=701.919,400 continuous variables
14,862 equality and 696 inequality constraint
Non-Zeros: 26,430 ; Degrees-of-freedom: 4,538
CPU(s): 16.8 seconds in the IMPL’ SLP engine
linked to CPLEX 12.6.MILP-NLP gap: 0.09% with only one PDH iteration.
MILP-NLP gap: from 5% to 3.5% with two PDH iterations.
Figure 5. Proposed Reductions and PDH Algorithm
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.
Figure 3. PDH search for MILP+NLP optimal solutions
𝑷 𝑴𝒂𝒙 𝒁 =
𝒕
𝒎∈𝑴𝑭𝑼
𝒑𝒓𝒊𝒄𝒆𝒎,𝒕 𝒙𝒎,𝒕 −
𝒎∈𝑴𝑪𝑫𝑼
𝒘𝒆𝒊𝒈𝒉𝒕 𝒙𝒎,𝒕𝑳𝑶𝑫 + 𝒙𝒎,𝒕
𝑼𝑷𝑫
s.t.
𝒙𝒎,𝒕+𝟏 − 𝒙𝒎,𝒕 + 𝒙𝒎,𝒕𝑳𝑶𝑫 − 𝒙𝒎,𝒕
𝑼𝑷𝑫 = 𝟎 ∀𝒎 ∈ 𝑴𝑪𝑫𝑼, 𝒕
Formulation: Structural Programming Language in IMPL using the
UOPSS (unit-operation-port-state superstructure).
The objective maximizes the gross margin from fuels revenues subtracting the
performance of the CDU throughputs, giving by the deviation from the quantity
in the previous time-period against the current time-period, minimizing the 1-
norm or linear deviation of the flow in consecutive time-periods.
Storage tanksFeed tanks
Storage tanks
Feed tanks
CDUs
Crude-Oils
blenders
in Foundations of Computer Aided Process Operations
Jan 9th 2017, Tucson, United States
Conclusion:
• a phenomenological decomposition of logistics (MILP) and quality (NLP)
is applied to solve industrial-sized problems to feasibility with a
demonstration of the theory in practice.
• Computing Skills in IMPL handles huge NLPs: techniques as reverse
polish notation, derivatives using complex numbers, derivatives by groups
with same pattern, SLP linking with MILP solvers, among others.