Rocks can be classified as "Archie" or "non-Archie" types depending on the relationship between pore geometry, resistivity, and porosity. Carbonate reservoirs have complex pore networks and Archie's law cannot be applied to estimate the water saturation in these types of reservoirs. Several models for complicated porosity systems have been proposed, to determine the water saturation based on the well logs and laboratory experimental data. A mathematical model (such as Archie's equation) which appropriately describes the conduction of a specific rock depends on the conduction mechanism. The conduction mechanism, in turn, is determined by pore geometry as well as nongeometric factors such as wettability and the presence of conductive or surface conductive minerals. In general, the measured (Resistivity Index) RI curves cannot be described by an Archie's law and the measurements at very low saturation are often a key observation to confirm a non-Archie behavior.

A large variety of shapes can be observed. These shapes can be explained qualitatively and quantitatively using two model's dual porosity conductivity model and triple porosity conductivity model (DPC and TPC) in which the different porosity systems are connected either in series or in parallel, or a combination of both. Hence, only two of three adjustable parameters are needed to model the experimental results.

In this work, a triple porosity systems saturation models are presented. This model can be used to determine the water saturation based on combined NMR/log data, NMR measurements are used to obtain the volume fraction of each pore network (Macro, Meso and Micro pores). Moreover, the factors affecting the electrical parameters are thoroughly investigated, such as; cementation factor, lithology constant, and saturation exponents. The relations between these parameters and the petrophysical properties are explained. A sensitivity analysis is performed to show the effect of each parameter on the resistivity index (RI) curves. A simple procedure is proposed to estimate the conductivity ratio between each of the two and three networks based on the lab data, using this approach the ratio of saturation exponents can be determined, which further reduces the number parameters needed to be fitted to one, and consequently improving the model's accuracy. The proposed model for triple porosity systems has been validated by employing published investigational data which had RI versus water saturation curves; the result of this validation produces adequate match between actual data and those predicted using the new model.. The new model for Non-Archie rock has been developed which can help petrophysicist to find the water saturation based on resistivity properties in and triple porosity systems with greater level of certainty.

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