Inverse problems associated with reservoir characterization are typically underdetermined
and often have difficulties associated with stability and convergence of the
solution. A common approach to address this issue is through the introduction of prior
constraints, regularization or reparameterization to reduce the number of estimated
parameters.
We propose a dual scale approach to production data integration that relies on a
combination of coarse-scale and fine-scale inversions while preserving the essential
features of the geologic model. To begin with, we sequentially coarsen the fine-scale
geological model by grouping layers in such a way that the heterogeneity measure of an
appropriately defined 'static' property is minimized within the layers and maximized
between the layers. Our coarsening algorithm results in a non-uniform coarsening of the
geologic model with minimal loss of heterogeneity and the ?optimal? number of layers is
determined based on a bias-variance trade-off criterion. The coarse-scale model is then
updated using production data via a generalized travel time inversion. The coarse-scale
inversion proceeds much faster compared to a direct fine-scale inversion because of the
significantly reduced parameter space. Furthermore, the iterative minimization is much
more effective because at the larger scales there are fewer local minima and those tend to
be farther apart. At the end of the coarse-scale inversion, a fine-scale inversion may be
carried out, if needed. This constitutes the outer iteration in the overall algorithm. The
fine-scale inversion is carried out only if the data misfit is deemed to be unsatisfactory. We propose a fast and robust approach to calibrating geologic models by
transient pressure data using a trajectory-based approach that based on a high frequency
asymptotic expansion of the diffusivity equation. The trajectory or ray-based methods
are routinely used in seismic tomography. In this work, we investigate seismic rays and
compare them with streamlines. We then examine the applicability of streamline-based
methods for transient pressure data inversion. Specifically, the high frequency
asymptotic approach allows us to analytically compute the sensitivity of the pressure
responses with respect to reservoir properties such as porosity and permeability. It
facilitates a very efficient methodology for the integration of pressure data into geologic
models.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-2009-08-3243 |
| Date | 2009 August 1900 |
| Creators | Kim, Jong Uk |
| Contributors | Datta-Gupta, Akhil |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | thesis, text |
| Format | application/pdf |
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