Analytical water saturation model using capacitance-resistance simulation: Clean and shaly formations

The strategies of reservoir development plans are constructed based on the economic values of reservoirs original hydrocarbon in place, which is always affected by the uncertainty in estimating water saturation. Maximum precision in water saturation is needed for reserve calculations or for decisions on whether to complete wells drilled in offshore or in unconventional hydrocarbon resources. Therefore, the development of a suitable model based on fundamental physics is sorely needed to cope with the demands of the present and future evaluation of petroleum reserves and also to overcome the shortages of current empirical models. In this study, an analytical model for the estimation of water saturation using traditional resistivity logs has been developed using capacitance-resistance modeling (CRM). This philosophy simulates the physics of saturated rock behavior to electric current by a resistor connected to a capacitor, which gives the overall electric system behavior. This system has a first order differential mathematical law. The advantage of analytical model is that it has no adjustable parameters, such as those exist in Archie's and other shaly empirical or electrochemical models. Moreover, it works in both clean and shaly formations of any kind of shale deposition within the rock matrix, which are usually determined from core analysis and laboratory experiments that consume time and cost. The mathematical derivation allows using the model for any values of porosity, shale volume, shale resistivity and true formation resistivity. Therefore, the model provides very significant outcomes of water saturation compared to Archie's and shaly empirical models. Model's reliability has been verified using laboratory measurements covering very wide range of shale content 0-0.8, shale resistivity 0.1-48 omega m, formation water resistivity 0.02-10 omega m and formation porosity 0.015-0.48.