Computational Geosciences

, Volume 20, Issue 5, pp 1061–1073 | Cite as

Determination of lower and upper bounds of predicted production from history-matched models

  • G. M. van Essen
  • S. Kahrobaei
  • H. van Oeveren
  • P. M. J. Van den Hof
  • J. D. Jansen
Open Access
Original Paper


We present a method to determine lower and upper bounds to the predicted production or any other economic objective from history-matched reservoir models. The method consists of two steps: 1) performing a traditional computer-assisted history match of a reservoir model with the objective to minimize the mismatch between predicted and observed production data through adjusting the grid block permeability values of the model. 2) performing two optimization exercises to minimize and maximize an economic objective over the remaining field life, for a fixed production strategy, by manipulating the same grid block permeabilities, however without significantly changing the mismatch obtained under step 1. This is accomplished through a hierarchical optimization procedure that limits the solution space of a secondary optimization problem to the (approximate) null space of the primary optimization problem. We applied this procedure to two different reservoir models. We performed a history match based on synthetic data, starting from a uniform prior and using a gradient-based minimization procedure. After history matching, minimization and maximization of the net present value (NPV), using a fixed control strategy, were executed as secondary optimization problems by changing the model parameters while staying close to the null space of the primary optimization problem. In other words, we optimized the secondary objective functions, while requiring that optimality of the primary objective (a good history match) was preserved. This method therefore provides a way to quantify the economic consequences of the well-known problem that history matching is a strongly ill-posed problem. We also investigated how this method can be used as a means to assess the cost-effectiveness of acquiring different data types to reduce the uncertainty in the expected NPV.


Computer-assisted history matching Uncertainty Hierarchical optimization Multi-objective optimization 


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© The Author(s) 2016

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • G. M. van Essen
    • 2
  • S. Kahrobaei
    • 1
  • H. van Oeveren
    • 1
  • P. M. J. Van den Hof
    • 3
  • J. D. Jansen
    • 1
  1. 1.Delft University of TechnologyDelftThe Netherlands
  2. 2.Shell Global Solutions International B.V.RijswijkThe Netherlands
  3. 3.Eindhoven University of TechnologyEindhovenThe Netherlands

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