The conventional rock physics models used for interpretation of resistivity measurements (e.g., Archie's model) need to be calibrated using core measurements. This becomes challenging when core measurements are not available or significant vertical variation in rock types and pore structure is commonplace. Conventional models also assume homogeneous pore structure and uni-modal pore-size distribution. To overcome these challenges, we introduce a new workflow for water/hydrocarbon saturation assessment, in which model parameters are geometry related and can be estimated from analysis of the pore structure. Such workflow enables reliable interpretation of resistivity measurements in the presence of complex multi-modal pore structure. Furthermore, we investigate the consistency of the estimated model parameters (i.e., electrical constriction factor and tortuosity) in the pore-scale domain through the same rock types, for the purpose of developing a workflow for field applications. We first obtain high-resolution pore-scale computerized tomography (CT) images from rock samples in the same rock type and quantify pore-network characteristics (e.g., constriction factor, pore- and throat-size distributions) of the samples at different water saturation levels. Image analysis is used to obtain geometrical constriction factor. We obtain electrical resistivity of the samples through numerically solving Maxwell's equations, which is used as an input in the introduced model.

We successfully applied the introduced method to pore-scale images from three carbonate formations. We verified the consistency of the obtained parameters in the pore-scale domain by applying the method in other rock samples of the same rock type. Results demonstrated consistency in estimated electrical constriction factors and tortuosity values in each rock type. We observed variation of model parameters in different rock types. The introduced method successfully captured the variation of the pore structure within the formation and honored the geometrical heterogeneity of the complex carbonate rocks. Finally, we used the new workflow and Archie's model to estimate water saturation. The new workflow enhanced water saturation estimates by 30% compared to Archie's model with default parameters (i.e., a = 1 and m = n = 2).

The outcomes of this paper can potentially minimize core-based calibration efforts for well-log-based water saturation assessment in rocks with complex pore structures such as carbonates. The introduced rock physics model captures the complexity of pore-network geometry and rock fabric and converged toward a more mechanistic model where most parameters have physical and geometrical meaning. The results are promising for enhanced assessment of water saturation in carbonate formations with minimal calibration efforts.

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