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Optimisation of an existing water injection network in an oilfield for multi-period development

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Abstract

Water injection demand for oilfields varies greatly in different development periods. The topology and size of the water injection pipeline network should match the changing demand. Long-term benefits should be considered to avoid the frequent expansion of the network. This paper considers the water demand in multiple periods and develops an MINLP model to optimise the layout and size of the water injection pipeline network for existing pipeline networks. The model aims to minimise construction cost and operating cost. Both pipeline transport and truck transport are considered with pressure constraints, pipeline pressure drop constraints, flow constraints, and supply–demand balance constraints. A piecewise linearisation method is proposed to avoid nonlinear terms in pressure drop and cost constraints. A case from an oilfield in Northwest China is taken as an example to verify the model. The water injection planning of an existing water pipeline network in the future three periods is determined. The results show that 14.6% of the total cost can be saved in the final phase compared to the first phase, which mainly benefited from the reduction of truck transported water volume.

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Data availability

Some or all data, models, or codes that support the research of this study are available from the corresponding author upon reasonable request.

Abbreviations

I :

Set of CPFs, denoted by index i

J :

Set of WISs, denoted by index j

K :

Set of wells, denoted by index k

R :

Set of transport modes, denoted by index r

T :

Set of water injection phase, denoted by index t

L :

Set of expansion level of pipelines and trucks, denoted by index l

A :

Set of water flowrate interval, denoted by index a

\(C_{r}^{{^{EL} }}\) :

Unit transportation cost of transportation mode \(r\) (¥/kW·h and ¥/(km·m3))

\(C_{r,l}^{EU}\) :

Cost when transportation mode \(r\) is expanded to scale \(l\) (¥)

\(L_{i,j}^{CD} ,L_{i,k}^{CW} ,L_{j,j^{\prime}}^{DD} ,L_{j,k}^{DW}\) :

Length of a pipeline (km)

\(Q_{a}^{A}\) :

An average flowrate of flowrate interval \(a\) (m3/s)

\(M\) :

A relatively large number

\(S_{i,t}\) :

A flowrate of water purified by CPF \(i\) in period \(t\) (m3/d)

\(D_{k,t}\) :

Demand at well k in period \(t\) (m3/d)

\(A_{i,j,r}^{CDO} ,A_{i,k,r}^{CWO} ,A_{j,j^{\prime},r}^{DDO} ,A_{j,k,r}^{DWO}\) :

Original transportation capacity of transportation mode \(r\) (m3/d)

\(A_{r,l}^{T}\) :

Transportation capacity of transportation mode \(r\) scale \(l\) (m3/d)

\(\varepsilon_{a}\) :

Coefficients of the Hazen–Williams formula when the flowrate belongs to the flowrate interval \(a\)

\({Dd}_{i,j}\), \({Dd}_{j,{j}^{^{\prime}}}\), \({Dd}_{j,k}\),\({Dd}_{i,k}\) :

Diameter of the pipeline, m

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

A minimum flowrate of flowrate interval \(a\) (m3/s)

\(Q_{a}^{\max }\) :

A maximum flowrate of flowrate interval \(a\) (m3/s)

\(P_{k}^{\min }\) :

A minimum pressure of well \(k\) (MPa)

\(P_{k}^{\max }\) :

Maximum pressure of well \(k\) (MPa)

\(p^{LP}\) :

Maximum pressure of low-pressure pipeline (MPa)

\(p^{HP}\) :

Maximum pressure of high-pressure pipeline (MPa)

\(C_{i,j}^{CD} ,C_{i,k}^{CW} ,C_{j,j}^{DD} ,C_{j,k}^{DW}\) :

The total cost of the pipeline (¥)

\(P_{i,t}^{C1}\) :

The output pressure of low-pressure pumps at CPF \(i\) in period \(t\) (MPa)

\(P_{i,t}^{C2}\) :

The output pressure of high-pressure pumps at CPF \(i\) in period \(t\) (MPa)

\(P_{j,t}^{D1}\) :

Input pressure of WIS \(j\) in period \(t\) (MPa)

\(P_{j,t}^{D2}\) :

The output pressure of low-pressure pumps at WIS \(j\) in period \(t\) (MPa)

\(P_{j,t}^{D3}\) :

The output pressure of high-pressure pumps at WIS \(j\) in period \(t\) (MPa)

\(p_{{_{k} }}^{W}\) :

Input pressure of well \(j\) in period \(t\) (MPa)

\(P_{i,j,t,a}^{CA1}\) :

\(P_{i,k,t,a}^{CA2}\)\(P_{j,j^{\prime},t,a}^{DA1}\)\(P_{j,k,t,a}^{DA2}\)Auxiliary variables

\(Q_{i,j,r,t}^{CD} ,Q_{i,k,r,t}^{CW} ,Q_{j,j^{\prime},r,t}^{DD} ,Q_{j,k,r,t}^{DW}\) :

A flowrate of transportation mode \(r\) in period \(t\) (m3/d)

\(y_{i,j,r,t,l}^{CD} ,y_{i,k,r,t,l}^{CW} ,y_{j,j^{\prime},r,t,l}^{DD} ,y_{j,k,r,t,l}^{DW}\) :

Binary variables. If the pipeline of transportation mode \(r\) scale \(l\) is required to be constructed in the period \(t\), \(y = 1\); otherwise, \(y = 0\)

\(B_{i,j,t,a}^{CD} ,B_{i,k,t,a}^{CW} ,B_{j,j^{\prime},t,a}^{DD} ,B_{j,k,t,a}^{DW}\) :

Binary variable. If the flowrate of the pipeline belongs to the flowrate interval \(a\) in the period \(t\), \(B = 1\); otherwise \(B{ = }0\)

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Acknowledgements

This work was supported by “Pioneer” and “Leading Goose” R&D Program of Zhejiang (2023C04048), Science Foundation of Zhejiang Ocean University (11025092122), Scientific Research Fund of Zhejiang Provincial Education Department (Y202250605), and the EU project “Sustainable Process Integration Laboratory – SPIL”, project No. C.Z.02.1.01/0.0/0.0/15_003/0000456 funded by EU “CZ Operational Programme Research, Development and Education”, Priority 1: Strengthening capacity for quality research.

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Authors and Affiliations

  1. State Key Laboratory for Performance and Structure Safety of Petroleum Tubular Goods and Equipment Materials, CNPC Tubular Goods Research Institute, Xi’an, 710077, People’s Republic of China

    Shuyi Xie

  2. Sinopec Gas Company North China Natural Gas Sales Center, TEDA Modern Service District, Tianjin, People’s Republic of China

    Huixia Feng

  3. Shaanxi Key Laboratory of Lacustrine Shale Gas Accumulation and Exploitation, Research Institute of Shaanxi Yanchang Petroleum (Group) Co., Ltd., Xi’an, 710075, People’s Republic of China

    Zimeng Huang

  4. Sustainable Process Integration Laboratory – SPIL, NETME Centre, Faculty of Mechanical Engineering, Brno University of Technology – VUT Brno, Technická 2896/2, 616 69, Brno, Czech Republic

    Jiří Jaromír Klemeš & Petar Sabev Varbanov

  5. National Engineering Laboratory for Pipeline Safety/MOE Key Laboratory of Petroleum Engineering/Beijing Key Laboratory of Urban Oil and Gas Distribution Technology, China University of Petroleum-Beijing, Fuxue Road No. 18, Changping District, Beijing, 102249, People’s Republic of China

    Jianqin Zheng

  6. Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Ul. Ivana Lučića 5, 10000, Zagreb, Croatia

    Hrvoje Mikulčić

  7. National & Local Joint Engineering Research Center of Harbor Oil & Gas Storage and Transportation Technology/Zhejiang Key Laboratory of Petrochemical Environmental Pollution Control, Zhejiang Ocean University, No.1, Haida South Road, Zhoushan, 316022, People’s Republic of China

    Bohong Wang

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  1. Shuyi Xie
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Xie, S., Feng, H., Huang, Z. et al. Optimisation of an existing water injection network in an oilfield for multi-period development. Optim Eng 25, 199–228 (2024). https://doi.org/10.1007/s11081-023-09804-0

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