Delivering A Simple Convincing Saturation Model with Infinite Rock Type Using Iterated Fractal Function System

Abstract

The purpose of this paper is to design a saturation height function which can overcome the measurement insufficiency and can also be applied to the reservoir models where core measurements are not available at all for all kind of siliciclastic reservoirs. This paper adopts a quantitative approach. The data is collected from the integration of core and log data. This approach is based on the assumption that sandstone reservoirs having similar Rock Quality Index (RQI), has similar capillary pressure behavior as regards water saturation. Universal capillary pressure curves were generated from 22 core plugs in Malaysia, using actual core data. Empirical relations between curve fitting parameters and core plug RQI values were developed. The universal capillary pressure curves were then used in other wells to calculate water saturation which has no core data. For those wells, the pseudo RQI values were calculated using the porosity and permeability derived from the log. A water saturation function was derived, as a function of RQI and HAFWL, with these pseudo RQI values and height above the Free Water Level. The results of this study portray that saturation modelled through this saturation height function matched very well with resistivity derived saturation. Water saturation resulting from generalized capillary curves was contrasted in wells without core data to that computed from resistivity logs. These water saturation results were found to be more realistic than those calculated purely from resistivity logs. The results confirmed the assumption that the universal capillary pressure curves can be used without core data to predict water saturation in wells. A well that has intercepted a hydrocarbon accumulation effectively represents a massive core sample of the reservoir. It is now possible to calculate the saturation reliably in any well. RQI is known over the entire hydrocarbon column. At the saturation anywhere in a reservoir can be determined, and the FWL known or estimated with reasonable certainty. It is in principle viable to evaluate Sw directly based on the drainage capillary theory. This study provides an insight into the universal saturation height function as a basic formulation in designing, developing, and appropriate strategies to model water saturation. This study not only helps subsurface study team in modelling water saturation, but it also offers new insights concerning the ability and capability of the strong direct relationship among rock quality index, height above free water level, and water saturation. This study uses an extended concept of Cuddy et al. (1993) to describe how water saturation varies with height above the free water level (FWL). Cuddy proposed the relationship of bulk Volume of Water vs Height above the FWL to derive water saturation. This approach requires conversion from BVW to SW. The proposed function, called K-function does not require the conversion.