THE SCALING OF SURFACE-TO-POREVOLUME RATIO ESTIMATES AND ITS USE IN PREDICTING NMR LOG DERIVED PERMEABILITIES IN CLASTIC ROCKS. MODEL DRIVEN FIELD APPLICATIONS FROM THE LUBLIN BASIN, POLAND

摘要

The permeability of clastic materials is controlled by the solid -void distribution function (SVDF). Different studies show that it may suffice to relate permeability to functions of lower order moments of the SVDF, namely porosity, tortuosity, and specific inner surface area. Direct as well as indirect lab methods for measuring surface areas are based on physical processes operating on characteristic length scales. Therefore recipes for matching them on the hydraulic permeability scale, equivalent to the Kozeny-Carman hydraulic capillary radius, are needed. This paper shows the strong correlation between surface area estimates derived from nitrogen gas adsorption (BET), mercury intrusion capillary pressure (MICP), and transverse nuclear magnetic resonance measurements (TNMR) on vintage core plugs of Permian and Carboniferous age from the Lublin Basin, Poland. The physical significance of these correlations is facilitated by comparing results to a fractal void-solid interface model, the Pape pigeon hole model. The pigeon hole model leads to matched scale expressions for the hydraulic permeability, namely the Paris equation for BET, and a variant of the Kozeny-Carman equation for MICP measurements. Using the Lublin Basin dataset, we show the validity of the Paris permeability equation, demonstrate the scale equivalence of MICP and TNMR inner surface estimates, and derive the Kozeny-Carman equation for TNMR data. This latter expression forms the basis for further permeability predictions from TNMR logging tools. For field applications the TNMR permeability estimator is compared with logging expressions derived by Sen and Timur-Coates. Simple multiplier rules are found to match their estimators for clean sands, and a calibrated TNMR log permeability may be arrived at. Finally, two field examples are presented to assess the limits of validity of the approach adopted in this paper and to underline the need for conditional core sampling as suggested by Worthington. We present a case of heuristic equivalence of properly calibrated TNMR permeability log readings with values derived from log data inversion based on Herron’s k-lambda method over uncored well sections. In a counter-example the illitisation of pore throats is not captured by the TNMR log as confirmed by comparing with wireline pretest data, sonic derived mobilities, and subsequent sidewall core analyses.