Optimal design of an oil pipeline with a large-slope section

ABSTRACT

One of the important issues in the operation of a long-distance oil pipeline in a large-slope area is pressure control, especially for the section after the turning point. In this study, a method to optimally design an oil pipeline with a large-slope section is proposed. The method is based on a stochastic mixed-integer linear programming model with minimal total cost as the objective function to determine the size of the pipeline, the location, the operational plan of pump stations and the location of pressure reduction stations. Hydraulic calculations and different types of oil product are considered. The uncertainty in flow rates of the pipeline is studied by the proposed stochastic programming approach. This method is applied to a real case of designing an oil product pipeline in a large-slope area.

KEYWORDS:

• Oil pipeline
• large slope
• design
• pressure control
• mixed-integer linear programming

Acknowledgement

The authors are grateful to all study participants.

Disclosure statement

No potential conflict of interest was reported by the authors.

Nomenclature

Indices and sets

${\text{N}}_{\mathrm{E}}$	=	End node of the pipeline
${\text{N}}_{\mathrm{P}}$	=	Set of nodes which connect pipeline arcs afterwards
${\text{N}}_{\mathrm{R}}$	=	Set of nodes which connect pressure reduction station, pump station and fictitious station arcs afterwards
${\text{N}}_{\mathrm{A}}$	=	Set of all the nodes, ${\text{N}}_{\mathrm{E}},{\text{N}}_{\mathrm{P}},{\text{N}}_{\mathrm{R}}\in {\text{N}}_{\mathrm{A}}$
${\text{L}}_{\mathrm{P}}$	=	Set of pipeline arcs
${\text{L}}_{\mathrm{R}}$	=	Set of pressure reduction station, pump station and fictitious station arcs
${\text{L}}_{\mathrm{H}}$	=	Set of station arcs adjacent to the turning point and end point of the large-slope section
${\text{L}}_{\mathrm{C}}$	=	Set of station arcs before the turning point of the large-slope section
${\text{L}}_{\mathrm{E}}$	=	Set of station arcs after the turning point of the large-slope section
${\text{L}}_{\mathrm{A}}$	=	Set of all the arcs, ${\text{L}}_{\mathrm{P}},{\text{L}}_{\mathrm{R}},{\text{L}}_{\mathrm{H}},{\text{L}}_{\mathrm{C}},{\text{L}}_{\mathrm{E}}\in {\text{L}}_{\mathrm{A}}$
A	=	Set of flow rates, denoted by index a
O	=	Set of oil types, denoted by index o
G	=	Set of pipeline sizes, denoted by index g
Y	=	Set of pump operational plans, denoted by index y

Parameters

P	=	Design pressure of the pipeline (MPa)
S	=	Yield stress of the pipeline (MPa)
E	=	Weld joint factor
F	=	Design factor based on nominal wall thickness
t	=	Wall thickness of the pipeline (mm)
D	=	Outer diameter of the pipeline (mm)
m	=	A parameter related to the flow state
$p_s$	=	Pressure of the starting point of the pipeline (MPa)
$p_{\mathrm{z}}$	=	Pressure of the end point of the pipeline (MPa)
$\epsilon$	=	Factor of the pressure–flow equation
Q	=	Flow rate of the pipeline (m3/h)
$\nu$	=	Kinematic viscosity of the fluid (Pa·s)
d	=	Inner diameter of the pipeline (mm)
L	=	Length of the pipeline (km)
$\rho$	=	Density of the fluid (kg/m3)
$g_a$	=	Gravitational acceleration (m/s2)
$\mathrm{\Delta }h$	=	Maximum allowable elevation difference (m)
${\phi }_j$	=	Distance of pipeline arc j (km)
$\eta$	=	Depreciation rate
$C_{\mathrm{UP}g}$	=	Construction cost of pipeline sized g per unit length (yuan)
$C_{\mathrm{UD}}$	=	Construction cost of pressure reduction station (yuan)
$C_{\mathrm{UZ}}$	=	Construction cost of pump station (yuan)
$C_{\mathrm{UO}y}$	=	Operational cost of pump station under y pump operational plan (yuan)
$S_{\mathrm{A}}$	=	Number of flow rate types
$S_{\mathrm{O}}$	=	Number of oil product types
$C_{\mathrm{D}g,o}$	=	Flow coefficient of pipeline sized g and transport type o oil product in the mass balance equations
$Q_{\mathrm{A}a}$	=	Flow rate a to the power of 1.877, (m3/h)1.877
M	=	A sufficiently large number
${\alpha }_y$	=	Constant term of the pump characteristic equation under y pump operational plan
${\beta }_y$	=	Linear term of the pump characteristic equation under y pump operational plan
$p_{\mathrm{S}}$	=	Known pressure of the basic node (MPa)
$B_{\mathrm{KC}i}$	=	0–1 parameter, equal to 1 if node i is a basic node at which pressure is determined, and equal to 0 otherwise
$z_i$	=	Elevation of node i (MPa)
W	=	Design factor of the pipeline
$P_{\mathrm{G}g,o}$	=	Design pressure for pipeline sized g for transporting type o oil product (MPa)
$P_{\mathrm{D}min}$	=	Minimal pressure of the pipeline (MPa)
$P_{\mathrm{E}max}$	=	Maximum pressure of the end node of the pipeline (MPa)

Decision variables

${T_{\mathrm{P}}}_{j,g}$	=	0–1 variable, equal to 1 if a pipeline sized g is built in arc j, and equal to 0 otherwise
${T_{\mathrm{D}}}_j$	=	0–1 variable, equal to 1 if a pressure reduction station is built in arc j, and equal to 0 otherwise
$T_{\mathrm{Z}j,y,a,o}$	=	0–1 variable, equal to 1 if a pump station is built under y pump operational plan for transporting type o oil product at flow rate a in arc j, and equal to 0 otherwise
$p_{i,a,o}$	=	Pressure of node i for transporting type o oil product at flow rate a (MPa)
$C_{\mathrm{F}j,a,o}$	=	Pressure drop of the pressure reduction station (MPa)
$T_{\mathrm{G}j}$	=	0–1 variable, equal to 1 if there is a fictitious station in arc j, and equal to 0 otherwise
$B_{i,i^{\mathrm{\prime }}}$	=	0–1 variable, equal to 1 if the elevation difference of two pressure reduction stations i and i’ is less than the maximum allowable elevation difference, and equal to 0 otherwise

ORCID

Bohong Wang http://orcid.org/0000-0003-1206-475X

Additional information

Funding

This work was part of the Program of ‘Study on Optimization and Supply-Side Reliability of Oil Product Supply Chain Logistics System’ funded under the National Natural Science Foundation of China [grant number 51874325].