Kim, Jong Uk (2009-08). Production Data Integration into High Resolution Geologic Models with Trajectory-based Methods and A Dual Scale Approach. Doctoral Dissertation.
Thesis
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.
