Computational Experience with Piecewise Linear Relaxations for Petroleum Refinery Planning
Abstract
:1. Introduction
2. Problem Description on Refinery Planning Model
3. Computational Experiments
3.1. Reformulation as Relaxation Models
3.2. Computational Results
4. Concluding Remarks
Supplementary Materials
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Nomenclature
Sets and indices | |
Set of process unit u | |
Set of CDU fraction p | |
Set of gridpoints for segment n | |
Parameters | |
Segment size (i.e., length) | |
M | Big-M parameter |
Gridpoint for segment n | |
qn | Length of segment n |
Continuous variables | |
Load of process unit u | |
Weight transfer ratio of fraction p (for CDU) | |
Deviation of partitioned variables in bilinear term from lower bound | |
Auxiliary variable for relaxation | |
Variable for reformulation to replace bilinear terms | |
Binary variables | |
Disjunction in bm scheme | |
Disjunction in nf5 and nf6t formulations |
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Method | Relation Type | Feature | Application |
---|---|---|---|
Fixed yield | Linear | Simple; amenable to large-scale models (especially LP); can cater for different operating modes | Simulation [18], planning optimization (LP [18], NLP [7,19], MINLP [20]), and scheduling optimization (MILP [8]) |
Swing cut | Linear or nonlinear | More accurate than fixed yield; can represent multiple operating modes [21] | Planning optimization (LP [22], MILP, NLP [16,23,24,25,26,27,28,29], and MINLP [30]) |
Fractionation index | Nonlinear | High accuracy (considers relative volatility and phase equilibrium) | Planning optimization (NLP [21] and MINLP) [31,32] |
Computing platform | GAMS 30.3.0/CPLEX 12; 1.9 GHz (speed, Intel Core i3); 8192 MB (RAM) |
No. of continuous variables | 49 |
No. of nonlinear variables | 42 |
No. of constraints | 61 |
No. of nonconvex terms | 21 (bilinear) |
Bilinear Term | Count |
---|---|
5 | |
4 | |
4 | |
4 | |
4 | |
Total | 21 |
Convergence Indicator for | Convergence Indicator (%) for | |||||||
---|---|---|---|---|---|---|---|---|
bm | nf6t | nf5 | de | bm | nf6t | nf5 | de | |
0.25 | 0.89 | 0.95 | 0.90 | 0.71 | 0.11 | 0.50 | 0.10 | 0.29 |
0.5 | 0.84 | 0.97 | 0.97 | 0.69 | 0.16 | 0.03 | 0.03 | 0.31 |
1 | 0.92 | 0.90 | 0.89 | 0.68 | 0.08 | 0.10 | 0.11 | 0.32 |
1.5 | 0.93 | 0.96 | 0.85 | 0.59 | 0.07 | 0.04 | 0.15 | 0.41 |
2 | 0.97 | 0.77 | 0.92 | 0.56 | 0.03 | 0.23 | 0.08 | 0.44 |
3 | 0.95 | 0.85 | 0.99 | 0.89 | 0.05 | 0.15 | 0.01 | 0.11 |
4 | 0.91 | 0.70 | 0.80 | 0.91 | 0.09 | 0.30 | 0.20 | 0.09 |
Relative Difference (%) | ||||
---|---|---|---|---|
bm | nf6t | nf5 | de | |
0.25 | 0.642 | 0.493 | 0.465 | 0.530 |
0.5 | 0.450 | 0.298 | 0.259 | 0.458 |
1 | 0.320 | 0.255 | 0.251 | 0.472 |
1.5 | 0.290 | 0.405 | 0.295 | 0.395 |
2 | 0.267 | 0.480 | 0.318 | 0.375 |
3 | 0.360 | 0.566 | 0.400 | 0.341 |
4 | 0.490 | 0.652 | 0.455 | 0.250 |
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Rana, Z.A.; Khor, C.S.; Zabiri, H. Computational Experience with Piecewise Linear Relaxations for Petroleum Refinery Planning. Processes 2021, 9, 1624. https://doi.org/10.3390/pr9091624
Rana ZA, Khor CS, Zabiri H. Computational Experience with Piecewise Linear Relaxations for Petroleum Refinery Planning. Processes. 2021; 9(9):1624. https://doi.org/10.3390/pr9091624
Chicago/Turabian StyleRana, Zaid Ashraf, Cheng Seong Khor, and Haslinda Zabiri. 2021. "Computational Experience with Piecewise Linear Relaxations for Petroleum Refinery Planning" Processes 9, no. 9: 1624. https://doi.org/10.3390/pr9091624