Ma, Xianlin (2008-08). History matching and uncertainty quantificiation using sampling method. Doctoral Dissertation. Thesis uri icon

abstract

  • Uncertainty quantification involves sampling the reservoir parameters correctly from a posterior probability function that is conditioned to both static and dynamic data. Rigorous sampling methods like Markov Chain Monte Carlo (MCMC) are known to sample from the distribution but can be computationally prohibitive for high resolution reservoir models. Approximate sampling methods are more efficient but less rigorous for nonlinear inverse problems. There is a need for an efficient and rigorous approach to uncertainty quantification for the nonlinear inverse problems. First, we propose a two-stage MCMC approach using sensitivities for quantifying uncertainty in history matching geological models. In the first stage, we compute the acceptance probability for a proposed change in reservoir parameters based on a linearized approximation to flow simulation in a small neighborhood of the previously computed dynamic data. In the second stage, those proposals that passed a selected criterion of the first stage are assessed by running full flow simulations to assure the rigorousness. Second, we propose a two-stage MCMC approach using response surface models for quantifying uncertainty. The formulation allows us to history match three-phase flow simultaneously. The built response exists independently of expensive flow simulation, and provides efficient samples for the reservoir simulation and MCMC in the second stage. Third, we propose a two-stage MCMC approach using upscaling and non-parametric regressions for quantifying uncertainty. A coarse grid model acts as a surrogate for the fine grid model by flow-based upscaling. The response correction of the coarse-scale model is performed by error modeling via the non-parametric regression to approximate the response of the computationally expensive fine-scale model. Our proposed two-stage sampling approaches are computationally efficient and rigorous with a significantly higher acceptance rate compared to traditional MCMC algorithms. Finally, we developed a coarsening algorithm to determine an optimal reservoir simulation grid by grouping fine scale layers in such a way that the heterogeneity measure of a defined static property is minimized within the layers. The optimal number of layers is then selected based on a statistical analysis. The power and utility of our approaches have been demonstrated using both synthetic and field examples.
  • Uncertainty quantification involves sampling the reservoir parameters correctly from a
    posterior probability function that is conditioned to both static and dynamic data.
    Rigorous sampling methods like Markov Chain Monte Carlo (MCMC) are known to
    sample from the distribution but can be computationally prohibitive for high resolution
    reservoir models. Approximate sampling methods are more efficient but less rigorous for
    nonlinear inverse problems. There is a need for an efficient and rigorous approach to
    uncertainty quantification for the nonlinear inverse problems.
    First, we propose a two-stage MCMC approach using sensitivities for quantifying
    uncertainty in history matching geological models. In the first stage, we compute the
    acceptance probability for a proposed change in reservoir parameters based on a
    linearized approximation to flow simulation in a small neighborhood of the previously
    computed dynamic data. In the second stage, those proposals that passed a selected
    criterion of the first stage are assessed by running full flow simulations to assure the
    rigorousness.
    Second, we propose a two-stage MCMC approach using response surface models for
    quantifying uncertainty. The formulation allows us to history match three-phase flow
    simultaneously. The built response exists independently of expensive flow simulation,
    and provides efficient samples for the reservoir simulation and MCMC in the second
    stage. Third, we propose a two-stage MCMC approach using upscaling and non-parametric
    regressions for quantifying uncertainty. A coarse grid model acts as a surrogate for the
    fine grid model by flow-based upscaling. The response correction of the coarse-scale
    model is performed by error modeling via the non-parametric regression to approximate
    the response of the computationally expensive fine-scale model.
    Our proposed two-stage sampling approaches are computationally efficient and
    rigorous with a significantly higher acceptance rate compared to traditional MCMC
    algorithms.
    Finally, we developed a coarsening algorithm to determine an optimal reservoir
    simulation grid by grouping fine scale layers in such a way that the heterogeneity
    measure of a defined static property is minimized within the layers. The optimal number
    of layers is then selected based on a statistical analysis.
    The power and utility of our approaches have been demonstrated using both
    synthetic and field examples.

publication date

  • August 2008