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Rapid quantification of uncertainty in permeability and porosity of oil reservoirs for enabling predictive simulation

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  • Ginting, V.
  • Pereira, F.
  • Rahunanthan, A.

Abstract

One of the most difficult tasks in subsurface flow simulations is the reliable characterization of properties of the subsurface. A typical situation employs dynamic data integration such as sparse (in space and time) measurements to be matched with simulated responses associated with a set of permeability and porosity fields. Among the challenges found in practice are proper mathematical modeling of the flow, persisting heterogeneity in the porosity and permeability, and the uncertainties inherent in them. In this paper we propose a Bayesian framework Monte Carlo Markov Chain (MCMC) simulation to sample a set of characteristics of the subsurface from the posterior distribution that are conditioned to the production data. This process requires obtaining the simulated responses over many realizations. In reality, this can be a prohibitively expensive endeavor with possibly many proposals rejection, and thus wasting the computational resources. To alleviate it, we employ a two-stage MCMC that includes a screening step of a proposal whose simulated response is obtained via an inexpensive coarse-scale model. A set of numerical examples using a two-phase flow problem in an oil reservoir as a benchmark application is given to illustrate the procedure and its use in predictive simulation.

Suggested Citation

  • Ginting, V. & Pereira, F. & Rahunanthan, A., 2014. "Rapid quantification of uncertainty in permeability and porosity of oil reservoirs for enabling predictive simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 99(C), pages 139-152.
    • Handle: RePEc:eee:matcom:v:99:y:2014:i:c:p:139-152
    DOI: 10.1016/j.matcom.2013.04.015
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    References listed on IDEAS

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    1. Pereira, F. & Rahunanthan, A., 2011. "A semi-discrete central scheme for the approximation of two-phase flows in three space dimensions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(10), pages 2296-2306.
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    Cited by:

    1. Hashan, Mahamudul & Jahan, Labiba Nusrat & Tareq-Uz-Zaman, & Imtiaz, Syed & Hossain, M. Enamul, 2020. "Modelling of fluid flow through porous media using memory approach: A review," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 643-673.
    2. Ginting, V. & Pereira, F. & Rahunanthan, A., 2015. "Multi-physics Markov chain Monte Carlo methods for subsurface flows," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 118(C), pages 224-238.
    3. Al-Mamun, A. & Barber, J. & Ginting, V. & Pereira, F. & Rahunanthan, A., 2020. "Contaminant transport forecasting in the subsurface using a Bayesian framework," Applied Mathematics and Computation, Elsevier, vol. 387(C).

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