# Shuffled Complex Evolution-Based Performance Enhancement and Analysis of Cascade Liquefaction Process for Large-Scale LNG Production

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## Abstract

**:**

^{®}v10 and then coupled with the SCE approach, which is coded in MATLAB

^{®}2019a. The refrigerant composition and operating pressures for each cycle of the MFC process were optimized considering the approach temperature inside the LNG heat exchanger as a constraint. The resulting optimal MFC process saved 19.76% overall compression power and reduced the exergy destruction up to 28.76%. The thermodynamic efficiency (figure of merit) of the SCE-optimized process was 25% higher than that of the published base case. Furthermore, the optimization results also imply that there is a trade-off between the thermodynamic performance improvement and the computational cost (no. of iterations). In conclusion, SCE exhibited potential to improve the performance of highly nonlinear and complex processes such as LNG processes.

## 1. Introduction

^{®}v10 is used. Hysys-simulated MFC process is linked with MATLAB

^{®}2019a to establish optimization environment. The performance enhancement is analyzed in terms of composite curves, exergy destruction and figure of merit.

## 2. Methodology: Shuffled Complex Evolution Approach

_{i}(energy consumption in our case) is computed at each x sample in the absence of prior distribution and by using uniform sampling distribution.

_{1}represents a sample with minimum energy consumption in the MFC process.

^{1}to A

^{p}such that each complex contains m samples, as shown in Equation (1). Here complex or community or population is a subset of array D that contains S feasible samples of decision variables of MFC process and their corresponding energy consumption. It means, in the MFC case, all samples of decision variables in array D are divided into p complexes in such a way that each complex will have few samples of decision variables.

- (i)
- B and L are sorted such that q points are arranged in ascending order with respect to their respective function values and centroid g is thereafter computed using the expression given in Equation (2):$$g=[1/(q-1)]{\displaystyle \sum _{j=1}^{q-1}{\mu}_{j}\text{}}$$
- (ii)
- The New point $r=2g-{\mu}_{q}$ is computed in the so-called reflection step.
- (iii)
- A mutation is performed in this step such that if r lies within Ω, energy consumption by the MFC process is computed and Step (iv) is performed; else, the smallest hypercube $H\subset {\mathbb{R}}^{n}$ containing ${A}^{k}$ is calculated and f
_{z}is computed by randomly generating a point z within H. Finally, we set $r=z$ and ${f}_{r}={f}_{z}$. - (iv)
- A contraction process is performed in this step such that if ${f}_{r}<{f}_{q}$, ${\mu}_{q}$ is replaced by r and Step ($vi$) is performed; else $c=(g+{\mu}_{q})/2$ is computed followed by f
_{c}. - (v)
- If ${f}_{c}<{f}_{q}$, ${\mu}_{q}$ is replaced by c and Step ($vi$) is performed; else, f
_{z}is computed by randomly generating a point Z within H. Finally, ${\mu}_{q}$ is replaced by z. - (vi)
- Step ($i$) through ($vi$) are repeated α times, where α is a user-defined parameter that has a value of ≥1.0.

^{k}using the original positions in L. A

^{k}is subsequently sorted in order of the increasing energy consumption value.

## 3. Process Simulation and Description

^{®}V10. The fundamental assumptions considered while simulating the process are as follows:

- (i)
- Peng–Robinson with EOS enthalpy/entropy calculation option was selected for thermodynamic properties calculations.
- (ii)
- The adiabatic efficiency for each compressor was fixed at 80%.
- (iii)
- The minimum temperature approach and pressure drop in LNG exchangers was kept constant at 3 °C and 1 bar, respectively.
- (iv)
- Interstage cooling medium was water, and the water-cooler outlet temperature was 40 °C.
- (v)
- The pressure drop of the water coolers was 0.30 bar.
- (vi)
- Furthermore, it was also assumed that the NG feed composition and conditions remain constant.

## 4. Simulation–Optimization Environment

## 5. Results and Discussion

#### 5.1. Pre-Cooling Cycle Composite Curves

#### 5.2. Liquefaction Cycle Composite Curves

#### 5.3. Sub-Cooling Cycle Composite Curves

## 6. Thermodynamic Performance: Exergy Analysis and Figure of Merit

_{i}to the actual required work W

_{r}for liquefaction, which can be described by Equation (3):

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

$f$ | Objective function |

Ex_{in} | Exergy in |

Ex_{out} | Exergy out |

NG | Natural gas |

T | Temperature (°C) |

P | Pressure (bar) |

MR | Mixed refrigerant |

MFC_SCE-X | SCE-optimized MFC process corresponding to X iterations |

Subscripts | |

SCE | Shuffled complex evolution |

CCE | Competitive complex evolution |

I | i^{th} compressor |

−ve | Negative |

+ve | Positive |

Abbreviations | |

N_{2} | Nitrogen |

C_{1} | Methane |

C_{2} | Ethane |

C_{3} | Propane |

nC_{4} | n-butane |

M | Mass flow rate (kg/h) |

TCF | Trillion cubic feet |

MFC | Mixed fluid cascade |

LNG | Liquefied natural gas |

TDCC | Temperature difference composite curves |

THCC | Temperature-heat flow composite curves |

DMR | Dual mixed refrigerant |

JTV | Joule–Thomson valve |

C_{3}MR | Propane precooled mixed refrigerant |

W_{i} | i^{th} compressor work |

DMR | Dual mixed refrigerant |

X_{i} | Key design variables |

SMR | Single mixed refrigerant |

kW | Kilowatt |

MITA | Minimum internal temperature approach |

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**Figure 4.**TDCC and THCC of (

**a**) and (

**b**) the base case, (

**c**) and (

**d**) SCE-optimized process corresponding to 300 iterations and (

**e**) and (

**f**) SCE-optimized process corresponding to 700 iterations, for the pre-cooling heat exchanger of MFC–LNG process.

**Figure 5.**Temperature difference composite curves (TDCC) and temperature–heat flow composite curves (THCC) of (

**a**) and (

**b**) the base case, (

**c**) and (

**d**) SCE optimized process corresponding to 300 iterations and (

**e**) and (

**f**) SCE-optimized process corresponding to 700 iterations, for the liquefaction heat exchanger of MFC–LNG process.

**Figure 6.**TDCC and THCC of (

**a**) and (

**b**) the base case, (

**c**) and (

**d**) SCE-optimized process corresponding to 300 iterations and (

**e**) and (

**f**) SCE-optimized process corresponding to 700 iterations, for the sub-cooling heat exchanger of MFC–LNG process.

Property | Value |
---|---|

T (°C) | 32 |

P (bar) | 50 |

$\dot{\mathrm{n}}$ (kmol/hr) | 1.0 (17.82 kg/h) |

Composition (mol·%) | |

C_{1} | 91.35 |

C_{2} | 5.36 |

C_{3} | 2.14 |

i-C_{4} | 0.46 |

n-C_{4} | 0.47 |

i-C_{5} | 0.01 |

n-C_{5} | 0.01 |

N_{2} | 0.20 |

Objective Function: | |||

Specific energy consumption (kWh/kg-NG) | $Minimize\text{}f(X)=Min.\left(\frac{{\displaystyle {\sum}_{i=0}^{n}{W}_{i}}}{{m}_{NG}}\right)$ | ||

Constraint: | |||

Minimum internal approach temperature (°C) | $\begin{array}{cccc}\Delta {T}_{\mathrm{min}1}\left(X\right)\ge 3;& \Delta {T}_{\mathrm{min}2}\left(X\right)\ge 3;& \Delta {T}_{\mathrm{min}3}\left(X\right)\ge 3,& \end{array}$ where, ${X}_{lb}<X<{X}_{ub}$, and X is a vector of the design variables | ||

Decision Variables | Units | Lower Limit | Upper Limit |

Precooling cycle | |||

Evaporation pressure (stream 100-3) | bar | 2 | 8 |

Condensation pressure (stream 100-8) | bar | 10 | 25 |

Ethane flow rate, ${m}_{C2}$ | kg/h | 6.8 | 24.8 |

Propane flow rate, ${m}_{C3}$ | kg/h | 9.5 | 28.0 |

n-butane flow rate, ${m}_{nC4}$ | kg/h | 12.0 | 55.0 |

Liquefaction cycle | |||

Evaporation pressure (stream 101-4) | bar | 2 | 8 |

Condensation pressure (stream 101-9) | bar | 10 | 35 |

Methane flow rate, ${m}_{C1}$ | kg/h | 2.2 | 7.5 |

Ethane flow rate, ${m}_{C2}$ | kg/h | 10.0 | 35.0 |

Propane flow rate, ${m}_{C3}$ | kg/h | 5.5 | 22.0 |

Sub-cooling cycle | |||

Evaporation pressure (stream 102-5) | bar | 2 | 8 |

Condensation pressure (stream 102-1) | bar | 35 | 60 |

Methane flow rate, ${m}_{C1}$ | kg/h | 1.623 | 5.5 |

Ethane flow rate, ${m}_{C2}$ | kg/h | 1.771 | 7.5 |

Nitrogen flow rate, ${m}_{N2}$ | kg/h | 0.85 | 3.5 |

Decision Variables | Units | Base Case | SCE-Optimized Process | |
---|---|---|---|---|

No. of Iterations | ||||

300 | 700 | |||

Precooling cycle | ||||

Evaporation pressure (stream 100-3) | bar | 3.50 | 4.19 | 3.80 |

Condensation pressure (stream 100-8) | bar | 25.00 | 21.09 | 19.10 |

Pressure ratio | 7.14 | 5.03 | 5.03 | |

Ethane flow rate, ${m}_{C2}$ | kg/h | 15.00 | 16.69 | 12.51 |

Propane flow rate, ${m}_{C3}$ | kg/h | 12.36 | 16.05 | 14.23 |

n-butane flow rate, ${m}_{nc4}$ | kg/h | 42.00 | 36.75 | 32.89 |

Precooling MR flow rate | kg/h | 69.36 | 69.49 | 59.63 |

Liquefaction cycle | ||||

Evaporation pressure (stream 101-4) | bar | 1.42 | 5.17 | 2.49 |

Condensation pressure (stream 101-9) | bar | 32.00 | 31.58 | 27.51 |

Pressure ratio | 22.54 | 6.11 | 11.05 | |

Methane flow rate, ${m}_{C1}$ | kg/h | 1.750 | 9.99 | 3.02 |

Ethane flow rate, ${m}_{C2}$ | kg/h | 23.90 | 22.40 | 22.87 |

Propane flow rate, ${m}_{C3}$ | kg/h | 6.49 | 12.14 | 9.29 |

Liquefaction MR flow rate | kg/h | 32.14 | 44.53 | 35.18 |

Subcooling cycle | ||||

Evaporation pressure (stream 102-5) | bar | 2.00 | 3.58 | 2.02 |

Condensation pressure (stream 102-9) | bar | 58.00 | 50.50 | 49.90 |

Pressure ratio | 29.00 | 14.11 | 24.70 | |

Methane flow rate, ${m}_{C1}$ | kg/h | 4.57 | 5.56 | 4.48 |

Ethane flow rate, ${m}_{C2}$ | kg/h | 2.42 | 2.56 | 2.66 |

Nitrogen flow rate, ${m}_{N2}$ | kg/h | 0.75 | 1.39 | 0.50 |

Subcooling MR flow rate | kg/h | 7.74 | 9.51 | 7.64 |

MITA(X)_{LNG-100} | °C | 5.2 | 3.0 | 3.0 |

MITA(X)_{LNG-101} | °C | 4.9 | 3.0 | 3.0 |

MITA(X)_{LNG-102} | °C | 4.2 | 3.0 | 3.0 |

LNG liquid fraction | 0.95 | 0.95 | 0.95 | |

Total compression power | kW | 5.953 | 5.057 | 4.773 |

Specific compression power | kWh/kg | 0.334 | 0.284 | 0.268 |

Relative energy saving | % | 14.97 | 19.76 | |

Elapsed time | Sec | 17,840 | 49,190 |

Streams | Base Case | MFC_300 | MFC_700 | |||
---|---|---|---|---|---|---|

T (°C) | P (bar) | T (°C) | P (bar) | T (°C) | P (bar) | |

100−01 | 40 | 24.4 | 40 | 20.49 | 40 | 18.5 |

100−02 | −25 | 23.4 | −25 | 19.49 | −25 | 17.5 |

100−03 | −30.22 | 3.5 | −28 | 4.193 | −28 | 3.802 |

100−04 | 14.13 | 3.4 | 16.66 | 4.093 | 36.22 | 3.702 |

100−05 | 14.13 | 3.4 | 16.66 | 4.093 | 36.22 | 3.702 |

100−06 | 14.13 | 3.4 | 16.66 | 4.093 | 36.22 | 3.702 |

100−07 | 15.7 | 25 | 17.94 | 21.09 | 37.52 | 19.1 |

100−08 | 105.9 | 25 | 93.16 | 21.09 | 110 | 19.1 |

100−09 | 40 | 24.7 | 40 | 20.79 | 40 | 18.8 |

100−10 | 38.3 | 24.7 | 40.52 | 20.79 | 40 | 18.8 |

100−11 | 40 | 24.4 | 40 | 20.49 | 40 | 18.5 |

101−01 | 40 | 31.7 | 40 | 31.28 | 35.98 | 27.21 |

101−02 | −25 | 30.7 | −25 | 30.28 | −25 | 26.21 |

101−03 | −100 | 29.7 | −100 | 29.28 | −100 | 25.21 |

101−04 | −107 | 1.42 | −112.9 | 5.167 | −107.1 | 2.492 |

101−05 | −48.26 | 1.32 | −28.02 | 5.067 | −53.7 | 2.392 |

101−06 | −48.45 | 1.22 | −28.16 | 4.967 | −54.56 | 2.292 |

101−07 | −48.45 | 1.22 | −28.16 | 4.967 | −54.56 | 2.292 |

101−08 | −46.47 | 32 | −26.15 | 31.58 | −52.88 | 27.51 |

101−09 | 138.8 | 32 | 88.83 | 31.58 | 87.32 | 27.51 |

101−10 | 40 | 31.7 | 40 | 31.28 | 40 | 27.21 |

101−11 | 40 | 31.7 | 40 | 31.28 | 35.98 | 27.21 |

102−01 | 40 | 57.7 | 12.48 | 50.2 | 34.12 | 49.6 |

102−02 | −25 | 56.7 | −25 | 49.2 | −25 | 48.6 |

102−03 | −100 | 55.7 | −100 | 48.2 | −100 | 47.6 |

102−04 | −155 | 54.7 | −155 | 47.2 | −155 | 46.6 |

101−05 | −160.2 | 2 | −158 | 3.58 | −158 | 2.016 |

102−06 | −104.3 | 1.9 | −103 | 3.48 | −103.5 | 1.916 |

102−07 | −104.3 | 1.9 | −103 | 3.48 | −103.5 | 1.916 |

102−08 | −104.3 | 1.9 | −103 | 3.48 | −103.5 | 1.916 |

102−09 | 137.9 | 58 | 86.43 | 50.5 | 123.2 | 49.9 |

102−10 | −101.5 | 58 | −100.2 | 50.5 | −100.7 | 49.9 |

102−11 | 40 | 57.7 | 40 | 50.2 | 40 | 49.6 |

102−12 | 40 | 57.7 | 12.48 | 50.2 | 34.12 | 49.6 |

NG FEED | 32 | 50 | 32 | 50 | 32 | 50 |

NG−01 | −25 | 49 | −25 | 49 | −25 | 49 |

NG−02 | −100 | 48 | −100 | 48 | −100 | 48 |

NG−03 | −148.8 | 47 | −148.8 | 47 | −148.8 | 47 |

NG−04 | −158.5 | 1.209 | −158.5 | 1.209 | −158.5 | 1.209 |

**Table 5.**Expressions for exergy destruction calculations in different equipment associated with the MFC–LNG processes [21].

Equipment | Exergy Destruction (kW) |
---|---|

Compressor | $E{x}_{dest}=\left(\dot{\mathrm{m}}\right)\left(E{x}_{in}-E{x}_{out}\right)-\dot{\mathrm{W}}$ |

Pump | $E{x}_{dest}=\left(\dot{\mathrm{m}}\right)\left(E{x}_{in}-E{x}_{out}\right)-\dot{\mathrm{W}}$ |

Interstage coolers | $E{x}_{dest}=\left(\dot{\mathrm{m}}\right)\left(E{x}_{in}-E{x}_{out}\right)$ |

Phase separator | $E{x}_{dest}=\left(\dot{\mathrm{m}}\right)E{x}_{in}-\left(\dot{\mathrm{m}}\right)E{x}_{Liq}-\left(\dot{\mathrm{m}}\right)E{x}_{Vap}$ |

JT valve | $E{x}_{dest}=\left(\dot{\mathrm{m}}\right)\left(E{x}_{in}-E{x}_{out}\right)$ |

LNG heat exchanger | $E{x}_{dest}={\displaystyle \sum}\left(\dot{\mathrm{m}}\right)E{x}_{in}-{\displaystyle \sum}\left(\dot{\mathrm{m}}\right)E{x}_{out}$ |

Equipment | Exergy Destruction (kW) | Exergy Destruction (kW) | Exergy Destruction (%) | Exergy Destruction (kW) | Exergy Destruction (%) |
---|---|---|---|---|---|

Base Case | SC_300 | SC_700 | |||

Compressors | |||||

K−100 | 0.3511 | 0.3193 | −9.05 | 0.2920 | −16.84 |

K−101 | 0.4165 | 0.3927 | −5.71 | 0.3488 | −16.24 |

K−102 | 0.1454 | 0.1355 | −6.81 | 0.1364 | −6.19 |

Net exergy destruction | 0.9130 | 0.8475 | −7.17 | 0.7772 | −14.87 |

Pumps | |||||

P−100 | 0.0025 | 0.0010 | − | 0.0000 | − |

P−101 | 0.0000 | 0.0000 | − | 0.0004 | − |

P−102 | 0.0000 | 0.0017 | − | 0.0003 | − |

Net exergy destruction | 0.0025 | 0.0027 | −99.99 | 0.0007 | −100 |

Cryogenic LNG exchangers | |||||

LNG−100 | 0.4356 | 0.2620 | −39.87 | 0.2075 | −52.37 |

LNG−101 | 0.6502 | 0.4378 | −32.68 | 0.3531 | 163.4 |

LNG−102 | 0.2214 | 0.1905 | −13.97 | 0.1850 | −16.43 |

Net exergy destruction | 1.3073 | 0.8902 | −31.9 | 0.7456 | 61.03 |

Air Coolers | |||||

E−100 | 1.0094 | 0.8109 | −19.66 | 0.8792 | −12.9 |

E−102 | 0.3620 | 0.1683 | −53.52 | 0.1221 | −66.27 |

E−103 | 0.0893 | 0.0300 | −66.4 | 0.0667 | −25.26 |

Net exergy destruction | 1.4607 | 1.0092 | −30.91 | 1.0680 | −26.88 |

Phase Separators | |||||

V−100 | 0.0000 | 0.0310 | − | 0.0048 | − |

V−101 | 0.0557 | 0.0212 | −61.88 | 0.0388 | −30.3 |

V−102 | 0.0269 | 0.0150 | −44.38 | 0.0000 | −100 |

Net exergy destruction | 0.0826 | 0.0672 | −18.6 | 0.0436 | −47.18 |

Joule-Thomson (Flash) Valves | |||||

JTV−100 | 0.0805 | 0.0605 | −24.8 | 0.0463 | −42.48 |

JTV−101 | 0.0925 | 0.1404 | 51.73 | 0.0825 | −10.8 |

JTV−102 | 0.0594 | 0.0559 | −5.93 | 0.0466 | −21.57 |

JTV−111 | 0.1319 | 0.1319 | 0 | 0.1319 | 0 |

Net exergy destruction | 0.3644 | 0.3887 | 6.69 | 0.3074 | −15.64 |

Overall process exergy destruction | 4.1304 | 3.2055 | −22.39 | 2.9425 | −28.76 |

MFC Process | Actual Work kW | Thermodynamic Efficiency (%) | Relative Improvement in Thermodynamic Efficiency (%) |
---|---|---|---|

Base case | 5.953 | 32.8 | – |

MFC_SCE-300 | 5.057 | 38.7 | 18.0 |

MFC_SCE-700 | 4.773 | 41.0 | 25.0 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Majeed, K.; Qyyum, M.A.; Nawaz, A.; Ahmad, A.; Naqvi, M.; He, T.; Lee, M.
Shuffled Complex Evolution-Based Performance Enhancement and Analysis of Cascade Liquefaction Process for Large-Scale LNG Production. *Energies* **2020**, *13*, 2511.
https://doi.org/10.3390/en13102511

**AMA Style**

Majeed K, Qyyum MA, Nawaz A, Ahmad A, Naqvi M, He T, Lee M.
Shuffled Complex Evolution-Based Performance Enhancement and Analysis of Cascade Liquefaction Process for Large-Scale LNG Production. *Energies*. 2020; 13(10):2511.
https://doi.org/10.3390/en13102511

**Chicago/Turabian Style**

Majeed, Khaliq, Muhammad Abdul Qyyum, Alam Nawaz, Ashfaq Ahmad, Muhammad Naqvi, Tianbiao He, and Moonyong Lee.
2020. "Shuffled Complex Evolution-Based Performance Enhancement and Analysis of Cascade Liquefaction Process for Large-Scale LNG Production" *Energies* 13, no. 10: 2511.
https://doi.org/10.3390/en13102511