Optimization and Engineering

, Volume 20, Issue 4, pp 1227–1248 | Cite as

Multiperiod optimization model for oilfield production planning: bicriterion optimization and two-stage stochastic programming model

  • Utsav Awasthi
  • Remy Marmier
  • Ignacio E. GrossmannEmail author
Research Article


In this work, we present different tools of mathematical modeling that can be used in oil and gas industry to help improve the decision-making for field development, production optimization and planning. Firstly, we formulate models to compare simultaneous multiperiod optimization and sequential single period optimization for the maximization of net present value and the maximization of total oil production over long term time horizons. This study helps to identify the importance of multiperiod optimization in oil and gas production planning. Further, we formulate a bicriterion optimization model to determine the ideal compromise solution between maximization of the two objective functions, the net present value (NPV) and the total oil production. To account for the importance of hedging against uncertainty in the oil production, we formulate a two-stage stochastic programming model to compute an improved expected value of NPV and total oil production for uncertainties in oil prices and productivity indices.


Bicriterion optimization Mixed-integer Nonlinear programming Multiperiod optimization Nonlinear programming Oilfield production planning Stochastic programming 

List of symbols



Linear cost for first stage decisions


discount factor for NPV at time t


Cost of gas compression at time t


Maximum amount of oil that can be produced from a well


Productivity index of well w


Gas price at time t


Oil price at time t


Number of scenarios


Maximum amount of liquid that can be separated in the separator


Time horizon


Cost of water treatment at time t



Scenarios {1…., S}


Time {1, 2…, TH}


Wells {well 1, well 2, …}


g(x, ys)

Stochastic model constraints


Gas oil ratio of a well w at time t, which is a function (fGOR) of cumulative oil produced


Pressure of well w at time t, which is a function (fPR)of cumulative oil produced


Water cut of well w at time t, which is a function (fWCT) of cumulative oil produced

\( \psi_{s} \left( {x,y_{s} } \right) \)

Second stage problem



Total cost associated with gas compression and water treatment at time t


Total revenue generated from oil and gas production at time t


Net present value


Liquid produced from well w at time t


Cumulative oil produced form well w at time t


Oil produced from well w at time t


Gas produced from well w at time t


Total liquid produced at time t


Total gas produced at time t


Total oil produced at time t


Total water produced at time t


First stage decision variables


Second stage decision variables


Total oil production



The authors acknowledge financial support from Total and from the Center of Advanced Process Decision-Making at Carnegie Mellon.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Utsav Awasthi
    • 1
  • Remy Marmier
    • 2
  • Ignacio E. Grossmann
    • 1
    Email author
  1. 1.Department of Chemical EngineeringCarnegie Mellon UniversityPittsburghUSA
  2. 2.TOTAL SA – CSTJFPauFrance

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