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An MILP-based formulation for minimizing pumping energy costs of oil pipelines: beneficial to both the environment and pipeline companies

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Abstract

Optimal scheduling of pumps operation in fluid distribution networks (e.g., oil or water) is an important optimization problem. This is due to the fact that the dollar cost and also global carbon footprints of such a major transportation are in mega scales. For example, one of our industrial partners, a Canadian oil pipeline operator, spent more than $18.11 million dollars in 2008 for pumping costs. According to our calculations, this would lead to up to 182,460 tons of CO2 emissions annually. Therefore, even slight improvements in operation of a pipeline system can lead to considerable savings in costs and also reducing carbon footprints emitted to the environment (by introducing air pollutions needed to generate those huge amounts of electricity). In this paper, a methodology for determining optimal pump operation schedule for a fluid distribution pipeline system with multi-tariff electricity supply is presented. The optimization problem at hand is a complex task as it includes the extended period hydraulic model represented by algebraic equations as well as mixed-integer decision variables. Obtaining a strictly optimal solution involves excessive computational effort; however, a near optimal solution can be found at significantly reduced effort using heuristic simplifications. The problem is efficiently formulated in this paper based on Mixed-Integer Linear Programming. The proposed model is evaluated on a typical oil pipeline network. The numerical results indicate the effectiveness and computationally efficient performance of the proposed formulation.

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Abbreviations

\(\eta_{j}^{*}\) :

Maximum efficiency of pump j

\(\eta_{j}^{t}\) :

Efficiency of the pump j at time t

\(\mathit{BP}_{j}^{t}\) :

Binary variable that indicates the status of the pump on segment j at time t

CL j :

The constant term of the Darcy-Weisbach equation for segment j

Con i :

Contracted volume of fluid that should be transported in the time frame to the delivery point located on node i

\(\mathit{Cost}_{j}^{t}\) :

Operation cost associated with pump j at time t

DT j :

Minimum down time of the pump j

\(\mathit{FRate}_{j}^{t}\) :

First electricity rate for pump j at time t

\(H_{i}^{t}\) :

Average pressure head associated with node i at time t

\(H_{i}^{\min}\) :

Minimum acceptable head of node i

\(H_{i}^{\mathrm{Max}}\) :

Maximum acceptable head of node i

\(\mathit{HP}_{j}^{t}\) :

Power charged by second rate for pump j at time t

Incidence i,j :

The (i,j) entry of the network incidence matrix

\(\mathit{Lim}_{j}^{t}\) :

Power limit that the rate of electricity is changed for pump j at time t

\(\mathit{LP}_{j}^{t}\) :

Power charged by the first rate for pump j at time t

Op t :

Binary variable which is equal to zero in case the system is shut down at time t and one otherwise

\(P_{j}^{t}\) :

Power consumed by pump j at time t

\(P_{j}^{\mathrm{Max}}\) :

The power that pump j consumes to add the maximum possible head to a fluid with maximum flow rate

\(\mathit{PH}_{j}^{t}\) :

Head added to the network by pump j at time t

\(\mathit{PL}_{j}^{t}\) :

Pressure loss of segment j at time t

\(Q_{j}^{t}\) :

Average flow rate associated with pipeline segment j at time t

\(Q_{j}^{*}\) :

The flow rate associated with the maximum efficiency of pump j

\(\tilde{Q}_{j}\) :

The flow rate associated with zero efficiency point for pump j

\(Q_{j}^{\mathrm{Max}}\) :

Maximum acceptable flow rate of segment j

\(Q_{j}^{\min}\) :

Minimum acceptable flow rate of segment j

\(\mathit{QSink}_{i}^{t}\) :

Discharge flow rate from node i at time t

\(\mathit{QSource}_{i}^{t}\) :

Flow rate of fluid incoming to node i at time t

\(S_{j}^{t}\) :

Ratio of the speed of the pump on segment j at time t to its nominal speed

SH i :

Static head associated with node i

\(\mathit{SRate}_{j}^{t}\) :

Second electricity rate for pump j at time t

UT j :

Minimum up time of the pump j

IU j :

The time pump unit j has to be On at the beginning of the period

ID j :

The time pump unit j has to be Off at the beginning of the period

\(V_{j}^{t}\) :

Valve pressure drop of segment j at time t

G j :

The slope of the head loss versus flow rate linearized equation for segment j

HL j :

The Y-intercept of head loss versus flow rate linearized equation for segment j

A j :

The slope of the pump head versus speed linearized equation for pump j

B j :

The Y-intercept of the pump head versus speed linearized equation for pump j

CS i :

Constant coefficient in head versus discharging flow rate equation for node i

C i :

The slope of the pump head versus discharging flow rate linearized equation for node i

D i :

The Y-intercept of the pump head versus discharging flow rate linearized equation for node i

E j :

The slope of the pump power versus speed linearized equation for pump j

F j :

The Y-intercept of the pump power versus speed linearized equation for pump j

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  1. Software Quality Engineering Research Group, Department of Electrical and Computer Engineering, Schulich School of Engineering, University of Calgary, Calgary, Alberta, Canada

    Ehsan Abbasi & Vahid Garousi

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  1. Ehsan Abbasi
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  2. Vahid Garousi
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Abbasi, E., Garousi, V. An MILP-based formulation for minimizing pumping energy costs of oil pipelines: beneficial to both the environment and pipeline companies. Energy Syst 1, 393–416 (2010). https://doi.org/10.1007/s12667-010-0016-3

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