Kang, Suk Sang 1975- (2012-12). Model Calibration, Drainage Volume Calculation and Optimization in Heterogeneous Fractured Reservoirs. Doctoral Dissertation.
We propose a rigorous approach for well drainage volume calculations in gas reservoirs based on the flux field derived from dual porosity finite-difference simulation and demonstrate its application to optimize well placement. Our approach relies on a high frequency asymptotic solution of the diffusivity equation and emulates the propagation of a 'pressure front' in the reservoir along gas streamlines. The proposed approach is a generalization of the radius of drainage concept in well test analysis (Lee 1982), which allows us not only to compute rigorously the well drainage volumes as a function of time but also to examine the potential impact of infill wells on the drainage volumes of existing producers. Using these results, we present a systematic approach to optimize well placement to maximize the Estimated Ultimate Recovery.
A history matching algorithm is proposed that sequentially calibrates reservoir parameters from the global-to-local scale considering parameter uncertainty and the resolution of the data. Parameter updates are constrained to the prior geologic heterogeneity and performed parsimoniously to the smallest spatial scales at which they can be resolved by the available data. In the first step of the workflow, Genetic Algorithm is used to assess the uncertainty in global parameters that influence field-scale flow behavior, specifically reservoir energy. To identify the reservoir volume over which each regional multiplier is applied, we have developed a novel approach to heterogeneity segmentation from spectral clustering theory. The proposed clustering can capture main feature of prior model by using second eigenvector of graph affinity matrix.
In the second stage of the workflow, we parameterize the high-resolution heterogeneity in the spectral domain using the Grid Connectivity based Transform to severely compress the dimension of the calibration parameter set. The GCT implicitly imposes geological continuity and promotes minimal changes to each prior model in the ensemble during the calibration process. The field scale utility of the workflow is then demonstrated with the calibration of a model characterizing a structurally complex and highly fractured reservoir.