Uncertainty Analysis in Upscaling Well Log data By Markov Chain Monte Carlo Method



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More difficulties are now expected in exploring economically valuable reservoirs because most reservoirs have been already developed since beginning seismic exploration of the subsurface. In order to efficiently analyze heterogeneous fine-scale properties in subsurface layers, one ongoing challenge is accurately upscaling fine-scale (high frequency) logging measurements to coarse-scale data, such as surface seismic images. In addition, numerically efficient modeling cannot use models defined on the scale of log data. At this point, we need an upscaling method replaces the small scale data with simple large scale models. However, numerous unavoidable uncertainties still exist in the upscaling process, and these problems have been an important emphasis in geophysics for years. Regarding upscaling problems, there are predictable or unpredictable uncertainties in upscaling processes; such as, an averaging method, an upscaling algorithm, analysis of results, and so forth. To minimize the uncertainties, a Bayesian framework could be a useful tool for providing the posterior information to give a better estimate for a chosen model with a conditional probability. In addition, the likelihood of a Bayesian framework plays an important role in quantifying misfits between the measured data and the calculated parameters. Therefore, Bayesian methodology can provide a good solution for quantification of uncertainties in upscaling. When analyzing many uncertainties in porosities, wave velocities, densities, and thicknesses of rocks through upscaling well log data, the Markov Chain Monte Carlo (MCMC) method is a potentially beneficial tool that uses randomly generated parameters with a Bayesian framework producing the posterior information. In addition, the method provides reliable model parameters to estimate economic values of hydrocarbon reservoirs, even though log data include numerous unknown factors due to geological heterogeneity. In this thesis, fine layered well log data from the North Sea were selected with a depth range of 1600m to 1740m for upscaling using an MCMC implementation. The results allow us to automatically identify important depths where interfaces should be located, along with quantitative estimates of uncertainty in data. Specifically, interfaces in the example are required near depths of 1,650m, 1,695m, 1,710m, and 1,725m. Therefore, the number and location of blocked layers can be effectively quantified in spite of uncertainties in upscaling log data.