Application of hybrid uncertainty-clustering approach in pre-processing well-logs

2017 
In the subsurface geology, characterization of geological beds by well-logs is an uncertain task. The thesis mainly concerns studying vertical resolution of well-logs (question 1). In the second stage, fuzzy arithmetic is applied to experimental petrophysical relations to project the uncertainty range of the inputs to the outputs, here irreducible water saturation and permeability (question 2). Regarding the first question, the logging mechanism is modelled by fuzzy membership functions. Vertical resolution of membership function (VRmf) is larger than spacing and sampling rate. Due to volumetric mechanism of logging, volumetric Nyquist frequency is proposed. Developing a geometric simulator for generating synthetic-logs of a single thin-bed enabled us analysing sensitivity of the well-logs to the presence of a thin-bed. Regression-based relations between ideal-logs (simulator inputs) and synthetic-logs (simulator outputs) are used as deconvolution relations for removing shoulder-bed effect of thin-beds from GR, RHOB and NPHI well-logs. NPHI deconvolution relation is applied to a real case where the core porosity of a thin-bed is 8.4%. The NPHI well-log is 3.8%, and the deconvolved NPHI is 11.7%. Since it is not reasonable that the core porosity (effective porosity) be higher than the NPHI (total porosity), the deconvolved NPHI is more accurate than the NPHI well-log. It reveals that the shoulder-bed effect is reduced in this case. The thickness of the same thin-bed was also estimated to be 13±7.5 cm, which is compatible with the thickness of the thin-bed in the core box (<25 cm). Usually, in situ thickness is less than the thickness of the core boxes, since at the earth surface, there is no overburden pressure, also the cores are weathered. Dempster-Shafer Theory (DST) was used to create well-log uncertainty range. While the VRmf of the well-logs is more than 60 cm, the VRmf of the belief and plausibility functions (boundaries of the uncertainty range) would be about 15 cm. So, the VRmf is improved, while the certainty of the well-log value is lost. In comparison with geometric method, DST-based algorithm resulted in a smaller uncertainty range of GR, RHOB and NPHI logs by 100%, 71% and 66%, respectively. In the next step, cluster analysis is applied to NPHI, RHOB and DT for the purpose of providing cluster-based uncertainty range. Then, NPHI is calibrated by core porosity value in each cluster, showing low √MSE compared to the five conventional porosity estimation models (at least 33% of improvement in √MSE). Then, fuzzy arithmetic is applied to calculate fuzzy numbers of irreducible water saturation and permeability. Fuzzy number of irreducible water saturation provides better (less overestimation) results than the crisp estimation. It is found that when the cluster interval of porosity is not compatible with the core porosity, the permeability fuzzy numbers are not valid, e.g. in well#4. Finally, in the possibilistic approach (the fuzzy theory), by calibrating α-cut, the right uncertainty interval could be achieved, concerning the scale of the study.
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