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.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-3035 |
| Date | 15 May 2009 |
| Creators | Ma, Xianlin |
| Contributors | Datta-Gupta, Akhil, Efendiev, Yalchin |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation, text |
| Format | electronic, application/pdf, born digital |
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