Statistical Correlation and Modelling of Carbonate Heterogeneity
Price, David P
In many carbonate reservoirs, much of the porosity is in the form of micropores (with diameter 1-10 microns). This porosity lies far below the resolution of any conventional wireline logging tools and can only be observed through the analysis of extracted core. To investigate the spatial distribution of the microporosity over a large range of length scales requires accurate depth matching of extracted core to wireline data. With such a correlation up- and down-scaling relationships can be developed between porosity relationships observed at different length scales. The scaling relationships can then be used to infer the distribution of microporosity in regions of the borehole without extracted core. This thesis presents a new, general method for the accurate correlation of extracted core to wireline logs using their statistical properties. The method was developed using an X-ray computed tomography (CT) scan of a section of extracted carbonate core and well log data from the so-called Fullbore MicroImager (FMI) resistivity tool. Using geological marker features the extracted core was constrained to correspond to a 2ft (609mm) section of FMI data. Using a combination of statistics (mean, variance and the range from variograms of porosity), combined in a likelihood function, the correlation was reduced to an uncertainty of 0.72" (18.29mm). When applied to a second section of core, the technique reduced the uncertainty from 2ft (609mm) down to 0.3ft (91mm). With accurate correlation between core and wireline logs, the scaling relationships required to transfer porosity information between scales could be investigated. Using variogram scaling relationships, developed for the mining industry, variograms from the CT scan were up-scaled and compared with those calculated from associated FMI data. To simulate core samples in regions of the borehole without extracted core, two statistical simulation techniques were developed. The techniques both capture twopoint spatial statistics from binarised, horizontal slices of FMI data. These statistics iv are combined to obtain multi-point statistics, using either neighbourhood averaging or least squares estimation weighted by variance. The multi-point statistics were then used to simulate 2-D slices of 'virtual' core. Comparisons between the two techniques, using a variety of features, revealed that the neighbourhood averaging produced the most reliable results. This thesis thus enables, for the first time, core-to-log depth matching to the resolution of the logging tools employed. Spatial statistics extracted from the core and up-scaled can then be compared with similar statistics from the precisely-located log data sampling the volume of rock around the borehole wall. Finally simulations of 'virtual' core can be created using the statistical properties of the logs in regions where no core is available.