The Fayetteville Shale is composed dominantly of clay, carbonate, and siliciclastic minerals. A variety of facies have been described by other workers and in this study, defined by mineral content, biota, fabric, and texture. Because the Fayetteville Shale is one of the top shale-gas producing plays in the U.S., an inquiry into key drivers of good-quality production is worthwhile. In particular, a hypothesis that intervals of high clay content should be avoided as production targets is investigated in this study. A high level of separation between wire-line log neutron porosity (NPHI) and density porosity (DPHI) in the Fayetteville Shale is observed in contrast to the wire-line log responses from the Barnett and Haynesville Shales. Clay minerals have a significant effect on NPHI, which in turn affects separation between NPHI and DPHI (PHISEP). X-Ray Diffraction (XRD) clay data was available for three wells, and efforts to correlate XRD results to PHISEP led to establishing NPHI as a reasonable proxy for clay. Using NPHI as a proxy it was possible to pick clay-rich intervals, map them across the study area, and to determine net clay in the Fayetteville Shale. Maps of net clay-rich intervals were compared to a map of production, but revealed no obvious correlation. Stratigraphic cross-sections showing the clay-rich intervals revealed a clay-poor interval in the upper part of the lower Fayetteville. This interval is the primary target for horizontal well completion. It is bounded above and below by more clay-rich intervals. Establishing the clay-rich intervals via porosity log separation (PHISEP) is one tool to help determine possible stratigraphic zones of gas production and can lead to a better understanding of intervals in which to expect production. / text

My dissertation is based on a unified self-consistent scaling framework which is consistent with key behavior exhibited by many spatially/temporally varying earth, environmental and other variables. This behavior includes tendency of increments to have symmetric, non-Gaussian frequency distributions characterized by heavy tails that often decay with lag; power-law scaling of sample structure functions (statistical moments of absolute increments) in midranges of lags, with breakdown in power-law scaling at small and/or large lags; linear relationships between log structure functions of successive orders at all lags, also known as extended self-similarity; and nonlinear scaling of structure function power-law exponents with function order. The major question we attempt to answer is: given data measured on a given support scale at various points throughout a 1D/2D/3D sampling domain, which appear to be statistically distributed and to scale in a manner consistent with that scaling framework, what can be said about the spatial statistics and scaling of its extreme values, on arbitrary separation or domain scales? To do so, we limit our investigation in 1D domain for simplicity and generate synthetic signals as samples from 1D sub-Gaussian random fields subordinated to truncated monofractal fractional Brownian motion (tfBm) or truncated fractional Gaussian noise (tfGn). Such sub-Gaussian fields are scale mixtures of stationary Gaussian fields with random variances that we model as being log-normal or Lévy α/2-stable. This novel interpretation of the data allows us to obtain maximum likelihood estimates of all parameters characterizing the underlying truncated sub-Gaussian fields. Based on synthetic data, we find these samples conform to the aforementioned scaling framework and confirm the effectiveness of generation schemes. We numerically investigate the manner in which variables, which scale according to the above scaling framework, behave at the tails of their distributions. Ours is the first study to explore the statistical scaling of extreme values, specifically peaks over thresholds or POTs, associated with such families of sub-Gaussian fields. Before closing this work, we apply and verify our analysis by investigating the scaling of statistics characterizing vertical increments in neutron porosity data, and POTs in absolute increments, from six deep boreholes in three different depositional environments.

Made available in DSpace on 2015-03-03T13:59:42Z (GMT). No. of bitstreams: 1 FranciscoWFA.pdf: 1362232 bytes, checksum: 33548c2a28a5c7d6034cf165f163a691 (MD5) Previous issue date: 2009-05-22 / ?Peng was the first to work with the Technical DFA (Detrended Fluctuation Analysis), a tool capable of detecting auto-long-range correlation in time series with non-stationary. In this study, the technique of DFA is used to obtain the Hurst exponent (H) profile of the electric neutron porosity of the 52 oil wells in Namorado Field, located in the Campos Basin -Brazil. The purpose is to know if the Hurst exponent can be used to characterize spatial distribution of wells. Thus, we verify that the wells that have close values of H are spatially close together. In this work we used the method of hierarchical clustering and non-hierarchical clustering method (the k-mean method). Then compare the two methods to see which of the two provides the best result. From this, was the parameter ? (index neighborhood) which checks whether a data set generated by the k- average method, or at random, so in fact spatial patterns. High values of ? indicate that the data are aggregated, while low values of ? indicate that the data are scattered (no spatial correlation). Using the Monte Carlo method showed that combined data show a random distribution of ? below the empirical value. So the empirical evidence of H obtained from 52 wells are grouped geographically. By passing the data of standard curves with the results obtained by the k-mean, confirming that it is effective to correlate well in spatial distribution / Peng foi o primeiro a trabalhar com a T?cnica DFA (Detrended Fluctuation Analysis), uma ferramenta capaz de detectar auto-correla??o de longo alcance em s?ries temporais com n?o-estacionaridade. Nesse trabalho, a t?cnica de DFA ? utilizada para obter o expoente de Hurst (H) do perfil el?trico de Porosidade Neutr?nica dos 52 po?os petrol?feros Campo de Namorado, situado na Bacia de Campos ? RJ. A finalidade ? saber se o expoente de Hurst pode ou n?o ser usado para se caracterizar uma distribui??o espacial dos po?os. Assim, queremos verificar se os po?os que apresentam valores pr?ximos de H est?o espacialmente pr?ximos entre si. Neste trabalho foi utilizado o m?todo de agrupamento hier?rquico e o m?todo de agrupamento n?o hier?rquico (m?todo do k-m?dia). Em seguida comparamos os dois m?todos para ver qual dos dois fornece o melhor resultado. A partir disso, foi criado o par?metro (?ndice de vizinhan?a) o qual verifica se um conjunto de dados gerados pelo m?todo km?dia, ou de forma aleat?ria, forma de fato padr?es espaciais. Altos valores de indicam que os dados est?o agregados, enquanto que baixos valores de indicam que os dados est?o espalhados (sem correla??o espacial). Com aux?lio do m?todo de Monte Carlo observou-se que dados agrupados aleatoriamente apresentam uma distribui??o de inferior ao valor emp?rico. Portanto os dados emp?ricos de H obtidos dos 52 po?os est?o agrupados espacialmente. Ao cruzar os dados das curvas de n?vel com os resultados obtidos pelo k-m?dia, confirmam que este ? eficaz para correlacionar po?os em distribui??o espacial