Analysis of fractures using fuzzy logic method

Many of the problems faced in engineering and science can be effectively modeledmathematically. However, in constructing these models many assumptions have to bemade which are often not true in the real world. For some applications, the sets that willhave to be defined are easily identifiable. For other applications, they will have to bedetermined by knowledge acquired from an expert or group of experts. Once the names of fuzzy sets have been established, one must consider their associated membershipfunctions. Development of this idea has led to many successful implementations of fuzzy logic systems, also called Fuzzy Inference Systems (FIS). A Fuzzy Inference System is asystem that uses fuzzy sets to make decisions or draw conclusions.The approach adopted for acquiring the shape of any particular membership functionis often depend on the application. In some applications, membership functions must beselected directly by a `statistical' approach or by an automatic generation of shapes. Thedetermination of membership functions can be categorized as being either manual orautomatic. The manual approaches rely only on the experience of an expert. All of themanual' approaches suffer from the fact that they rely on subjective interpretation ofwords.A new indirect fracture detection technique called Fuzzy Logic Integrated System(FLIS) from well logs is presented in this paper. The FLIS can be widely used for fracturedetection with high precision in comparison with image logs in zones of interest. Thismethod is very suitable for multiple well logs, where changes in the log- shapes areaffected by the fractures. Therefore, the above method should be used correctly. Fuzzymembership of the log data serves also as an indicator for the classification of results andprovides valuable information concerning the reliability of the fracture zones.The procedures of executing the fuzzy logic are as follows: First, based on theRockLog program (Ghassem Alaskari, 2005), the well log data on each zone of interest areanalyzed and plotted in the log format. Second, anisotropic parameters necessary for theevaluation of highly fractured zones from image logs are determined and compared withthe full data set. Third, using FLIS algorithm written for this purpose, fractures can beidentified in each zone of interest. Fourth, the comparison between the results given in thethird step with the core samples at the same intervals (the fracture density and fracture types) in each zone can be identified.The above procedure has been used successfully for determining fractured reservoirzones in the South-Pars field from an open-hole well log data. A comparison betweencore samples and image logs was done for the same intervals detected by this technique.As described earlier, a fuzzy set is fully defined by its membership function. How best todetermine the membership function is the main question that needs to be addressed. The degree of applicability of this technique is checked by image logs and core samples forthe same region, where a full well data was available.