Download or read book Application of Fractals to Reservoir Characterization written by Ayşe Dönmez Zeybek and published by . This book was released on 2000 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Reservoir description is an important step to make reliable reservoir performance predctons. In general, reservoir description can be defined as the process of describing various reservoir characteristics (e.g., porosity, permeabiIity, thickness,etc.) that honor all the available data (e.g., geological, geophysical, petrophysical,production data). The appropriate way to reach this goal is to integrate all available data from different sources; geologic knowledge, seismic data, well test pressure data, production history, etc. However, how to efficiently integrate all these data coming from different sources is a challenge to the person or team working inreservoir description area.Although, geostatistical methods (Kriging, cokriging, etc. ) are well-suited tointegrate static (1inear or hard) data coming from geology, logs, seismic and core analysis, they are limited when applied to dynamic data such as well test pressure,tracer test and production data. Because dynamic data are non-linear with respect tomodel parameters, conditioning to dynamic data possesses some difficulties. inrecent years, it has been shown that the inverse problem theory based on Bayesian estimation provides a powerful methodology not only to generate rock property fields conditioned to both static and dynamic data, but also to assess the uncertaintyin performance predictions. To date, standard applications of inverse problem theory given in the literature assume that rock property tields obey multinormal(Gaussian) distribution and are second order stationary. in this work, the main objective is to extend the inverse problem theory to cases where rock property tields( only porosity and permeabiIity tields are considered) come from fractal distributions so that one can be able to generate fractal rock property tields conditioned to both static and well test pressure data.Recent studies have shown that ftactals like fractional Gaussian noise (fGn) and fractional Brownian motion ( fBm) are promising approaches to characterize porosity and/or permeabiIity , in general the hydraulic property variations in the subsurface.in the literature, there exist stochastic interpolation methods that can be used to generate conditional fractal simulations honoring variograms and hard data(measurements of porosity and permeabiIity at wells). However, there exists nostudy in the literature that considers generating fractal flelds conditioned to dynamicdata, in particular to well-test pressure data. Thus, the objective of this work is togenerate fractal (fGn and fBm) porosity and permeability tields conditioned tovariograms, hard data and well-test pressure data by using the inverse problemtheory .The thesis is organized as follows. In Chapter 2, we begin by presenting the theoryof fractal and fractal distributions in detail. Because, in this work, we define rockproperty fields, specifically permeability and porosity , using the fractaldistributions, we note various statistical properties of fGn and ffim distributions.We also provide the methods that can be used to generate unconditional realizationsof isotropic or anisotropic ffim/fGn random functions. In Chapter 3, we review theinverse problem theory based on Bayesian estimation, because in this study, we usethis theory to generate rock property fields (porosity and permeability) conditioned to both well-test pressure, static ( core and well log) and geostatistical data. Becauseour objective in this study is to extend the inverse problem methodology to generateporosity and permeability fields that show fractal (fGn and ffim) behavior, we show how one can extend the commonly used inverse problem methodology based onstationary Gaussian fields to fractal fields. In Chapter 4, we present one, two, andthree dimensional applications of inverse problem theory based on Bayesian estimation (explained in Chapter 3) to generate fGn/fBm porosity and 1n-permeability fields conditioned to well-test pressure, static ( core and well log) and geostatistical data for single phase problems. In Chapter 5, we study transport over fracture network that can be considered as a fractal object. We present fractal pressure transient behavior and analysis of a single or multiple vertical well systems (with wellbore storage and skin effects) producing in fractured reservoirs without matrix participation. Nonlinear regression analysis for pressure data from such systems is presented and discussed for analysis purposes. Also, analysis of aninterference pressure data from Kizildere geothermal field using fractal model is presented.