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A Multi-objective Optimization Method for Simulating the Operation of Natural Gas Transport System

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Abstract

The optimization of gas pipeline networks plays a pivotal role in ensuring the efficient and economically viable transportation of natural gas. In this research, we have developed a comprehensive mathematical model capable of analyzing diverse network configurations, encompassing both linear and branched topologies. Our scientific investigation aims to explore the optimization potential of gas pipeline networks, employing a sophisticated and systematic approach to enhance network design and operation. The overarching objective is to achieve maximum efficiency and reliability in gas delivery to customers. The optimization process focuses on minimizing power requirements, maximizing gas flow rate, minimizing the fuel consumption, and maximizing line pack to ensure the optimal utilization of the pipeline infrastructure. To accomplish these objectives, our study employs advanced mathematical models that accurately depict network behavior, cutting-edge simulation tools to explore various operational scenarios, and state-of-the-art optimization algorithms to identify the most favorable network configuration and operating conditions. To facilitate this optimization process, we have incorporated the VIekriterijumsko KOmpromisno Rangiranje (VIKOR) method, a potent multi-criteria decision-making technique. Through the application of this approach to two case studies, we have demonstrated its effectiveness in identifying optimal network configurations. Furthermore, we have conducted an analysis to determine the total cost and fuel consumption associated with different network configurations, offering valuable insights for decision-making purposes. The results of our study underscore the superiority of our approach in identifying more economical networks compared to existing methods. By embracing the proposed approach, gas transportation networks can be optimized to achieve superior cost-efficiency and reduced fuel consumption.

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Abbreviations

MMscf:

Million standard cubic feet per day

MCDM:

Multi-criteria decision making

AHP:

Analytic hierarchy process

TOPSIS:

Technique for order preference by similarity to ideal solution

GRA:

Grey relational analysis

IPI:

Iran–Pakistan–India

TAPI:

Turkmenistan–Afghanistan–Pakistan–India

CPM:

Critical path method

GA:

Genetic algorithm

MINLP:

Mixed integer nonlinear programming

NGPS:

Natural gas pipeline networks

PSO:

Particle swarm optimization

DIMENS:

Decoupled implicit method for efficient network simulation

BNs:

Bayesian networks

MINLP:

Mixed integer nonlinear programming

\({\text{LHV}}\) :

Is the lower heating value of gas mixture in kJ/kg

\({{\text{LHV}}}_{i}\) :

The mass low heating value of molecules composing the gas in kJ/kg

Q :

Is volumetric flow rate in MMscf

P b :

Is base pressure in psia

T b :

Is base temperature in °R

P 1 :

Is upstream pressure in psia

P 2 :

Is downstream pressure in psia

T f :

Is gas flowing temperature in °R

G :

Is gas gravity, dimensionless

\({\rho }_{{\text{g}}}\) :

Is gas density in lb/\({{\text{ft}}}^{3}\)

\({\rho }_{{\text{air}}}\) :

Is air density in lb/\({{\text{ft}}}^{3}\)

Z :

Is gas compressibility factor

D :

Is pipe inside diameter in inch

L e :

Is equivalent length in mile

\({p}_{{\text{d}}}\) :

Is discharge pressure of compressor

\({p}_{{\text{S}}}\) :

Is suction pressure of compressor

\({C}_{{\text{pi}}}\) :

Is heat capacity flow rate of the streams gas component i

\({T}_{{\text{SC}}}\) :

Is the suction temperature of compressor

\({P}_{{\text{SC}}}\) :

Is the suction pressure of compressor

\(\dot{m}\) :

Is gas flow rate in lb/s

\({{\text{M}}.{\text{wt}}}_{ ({\text{avg}}.)}\) :

Is average molecular weight of gas

\({\mathrm{mole \%}}_{ (i)}\) :

Is the mole percent of each component in gas

\({M}_{i}\) :

Is the molecular weight of gas component i

\({T}_{{\text{PC}}}\) :

Is the pseudo critical temperature °R

\({y}_{i}\) :

Is the mole fraction of percent of gas component i, dimensionless.

\({P}_{{\text{PC}}}\) :

Is the pseudo critical pressure psi

P avg . :

Is average pressure in psi

T :

Is gas temperature in K

T c :

Is the critical temperature in k

P c :

Is the critical pressure in psi

K :

Is specific heat ratio (Cp/Cv) assume it to be 1.26

T 1 :

Is suction temperature in °R

W :

Is rate of power in hp

P :

Station horsepower

\({\dot{m}}_{{\text{f}}}\) :

Is the mass flow rate of consumed gas as fuel for the compressor in lb/s

\({m}_{{\text{c}}}\) :

Is the gas flow throughput in the compressor

\({\eta}_{{\text{m}}}\) :

Is the mechanical efficiency of compressor it is ranging between 0.8–0.9 (taking = 0.9)

\({\eta}_{i}\) :

Is the isentropic efficiency of compressor

\({\eta}_{{\text{d}}}\) :

Is the driver efficiency of compressor its value up to 0.5 for centrifugal compressor (taking = 0.35)

\(\varepsilon \) :

Roughness height of pipeline surface

\(f\) :

The friction factor

b:

Base

f:

Flowing

g:

Gas

e:

Equivalent

d:

Discharge

s:

Suction

i :

Component i

SC:

Suction of compressor

PC:

Pseudo critical

avg:

Average

c:

Critical

f:

Fuel

m:

Mechanical

i:

Isentropic

d:

Driver

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Acknowledgements

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors

Author information

Authors and Affiliations

  1. Chemical and Petroleum Refining Engineering Department, Faculty of Petroleum and Mining Engineering, Suez University, Suez, 41522, Egypt

    Nourhan E. Mohammad, Y. R. Yassmen & S. Aly

  2. Chemical Engineering Department, Higher Institute of Engineering, Shorouk Academy, Shorouk City, Cairo, 11837, Egypt

    Mostafa. H. Hussein

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  1. Nourhan E. Mohammad
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  2. Y. R. Yassmen
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  3. S. Aly
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Contributions

Conceptualization, SA, MH; methodology, MH, SA; investigation, NE, YY; resources, YY, NE, MH; writing—original draft preparation, NE; writing—review and editing, MH; supervision, SA, MH; all authors have read and agreed to the published version of the manuscript.

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Correspondence to Mostafa. H. Hussein.

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Appendix A

Appendix A

Gas Density

The density and pressure of a gas as shown in the following equation form are associated by entering the compression coefficient, Z in the paradigm.

$$ \rho = \frac{{{\text{PM}}}}{{{\text{ZRT}}}}, $$
(29)

where, R is universal gas constant, M: is the gas average molecular weight and relies on its composition. Gas molecular weight is estimated by means of easy blending rule stated in the succeeding equation form in which Yi and Mi are the mole fractions and molecular weights of sorts, respectively:

$$ M = \sum M_{i} Y_{i} . $$
(30)

Compressibility Factor

The compression coefficient compressibility factor, Z, is utilized to change the perfect gas equation to consideration for the real gas demeanor. Conventionally, the compression coefficient is estimated by means of an equation of status:

$$ Z = 1 + \left( {0.257 - 0.533\frac{{T_{{\text{C}}} }}{T}} \right)\frac{{P_{{{\text{avg}}}} }}{{P_{{\text{C}}} }}. $$
(31)

The Average Pseudo-critical Properties of the Gas Mixture

The pseudo-critical temperature (Tc) and pseudo-critical pressure (Pc) of natural gas can be approximated using appropriate blending rules based on the critical properties of individual gas components:

$$ T_{{\text{C}}} = \sum T_{{{\text{C}}i}} Y_{i} , $$
(32)
$$ P_{{\text{C}}} = \sum P_{{{\text{C}}i}} Y_{i} . $$
(33)

Average Pressure

The average pressure of gas can be calculated from the below formula by [35]:

$$ P_{{{\text{avg}}}} = \frac{2}{3}\left( {P_{1} + P_{2} - \frac{{P_{1} *P_{2} }}{{P_{1} + P_{2} }}} \right). $$
(34)

Specific Gravity

The specific gravity of a fluid is calculated by dividing the density of the fluid by the density of a reference fluid, such as water or air, at a standard temperature:

$$ S_{{\text{g}}} = { }\frac{{\text{density of gas}}}{{\text{density of air}}} = { }\frac{{M_{{{\text{gas}}}} }}{{M_{{{\text{air}}}} }}. $$
(35)

Average Molecular Weight of Gas Mixture

The gas molecular weight is estimated through blending rule as:

$$ {\text{M}}.{\text{wt}}_{{\left( {{\text{avg}}.} \right)}} = \sum M_{i} Y_{i} . $$
(36)

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Mohammad, N.E., Yassmen, Y.R., Aly, S. et al. A Multi-objective Optimization Method for Simulating the Operation of Natural Gas Transport System. Korean J. Chem. Eng. (2024). https://doi.org/10.1007/s11814-024-00136-y

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