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Determining rock resistivity for saturation estimation in reservoirs is challenging due to the complex nature of pores in the rock. This paper aims to establish a computational relationship between formation factors ( F ) and permeability ( K ) by combining theoretical and experimental data. Firstly, the relationship between the permeability of the curved capillary model and formation factors, as well as the relationship between the permeability of the complex curved capillary model and formation factors, are deduced. Theoretical analysis proved that the formation factors( F ) have a power relationship with permeability( K ) and porosity ( φ ), and confirms the existence of additional resistivity ( R x ). To validate the the theoretical study, we conducted model analysis using open experimental data from thirty-five sandstone cores with different porosity and permeability from the tight gas sandstone in the Western U.S. Basins, which measured resistivity data in saline at 20ppm, 40ppm, and 80ppm, respectively. We confirmed the existences of additional resistivity ( R x ) by fitting the relationship between the rock resistivity of saturated formation water ( R o ) and the formation water resistivity ( R w ). We then fitted the formation resistivity change factor ( F d ) with permeability ( K ), the formation resistivity change factor ( F d ) with porosity ( φ ), the additional resistivity ( R x ) with permeability ( K ), and the additional resistivity ( R x ) with porosity ( φ ). Both changeable formation resistivity change factor ( F d ) and additional resistivity ( R x ) showed a strong linear relationship with permeability ( K ) in logarithmic coordinates. We also verified the existence of a suitable equation using available experimental data by changing formation parameters and permeability. The study shows that the fitting equations may be utilized to determine changeable formation resistivity change factor ( F d ), additional resistivity ( R x ), and the rock resistivity of saturated formation water ( R o ) with varying permeability. The predicted rock resistivity of saturated formation water ( R o ) strongly correlates with the one measured in the laboratory, providing better precision for future reservoir evaluation in saturation estimations.

The characteristics of multiphase flow in porous media are of great significance to various applications, such as reservoir evaluation and engineering geology. The analogy between fluid flow and electric flow provides a new idea for studying multiphase flow properties from geophysical resistivity data. However, a theoretical relationship between relative permeability and resistivity index, which is the key to the successful joint interpretation of multiphase flow and rock electric characteristics in porous media, is poorly understood. Based on fractal theory, a relative permeability-resistivity index model is developed to accurately describe the link between the rock electric and multiphase flow characteristics. The relative permeability is found not only to be related to fluid saturation and resistivity index, but also to be affected by structural parameters, such as the tortuosity fractal dimension, pore fractal dimension, water-phase fractal dimension, and tortuosity ratio. The proposed model reveals the significant effect of structural parameters on the resistivity index and relative permeability, on the other hand, the study provides an effective method to calculate the relative permeability from the resistivity data. By applying the relative permeability-resistivity index model to real cases, it shows that the predicted relative permeability results calculated by our model are in good agreement with experimental data.

Nuclear magnetic resonance (NMR) log is a powerful tool to obtain porosity and oil saturation in reservoir evaluation. NMR echo inversion, however, may give poor information in the two parameters if the ratio of signal-to-noise is not so good. Combining NMR log and some conventional logs, such as GR log, sonic log, and density log, a novel inversion algorithm is developed in this research. First, normalize the logging response, then, insert both the logging response equations and the definition equations of volume model into the NMR echo equations. By conducting the data inversion for both NMR echo and conventional logging data, the porosity and oil saturation can be calculated. The condition number of the inversion matrix is decreased, so, the inversion parameters own better stability and the random weak noise is stifled. Furthermore, the T2 spectral distribution derived from the new inversion seems to be sensitive to the small pores in tight reservoir. Due to the weak noise removal and sensitiveness of small pore, the novel inversion may be utilized in reservoir evaluation in shale oil and gas, such as the identification of “sweet spot”.

Successful evaluation of reservoir resources in gas hydrate-bearing sediments depends on the accurate estimation of reservoir parameters, such as hydrate saturation, porosity, and clay content. Elastic and electrical measurements are affected by several rock and fluid properties and their joint interpretation can provide complementary information and improve the accuracy of reservoir characterization results. In this work, we propose a new rock physics inversion workflow based on 3D rock physics template of elastic and electrical attributes for the direct estimation of reservoir parameters. We first conduct a quantitative analysis of the available well log data and core data to understand the morphology of gas hydrate within the marine sediment, and choose the appropriate elastic rock physics model. Then, we construct the 3D rock physics template by discretizing the 3D space of reservoir parameters and implementing the suitable elastic and electrical models to calculate the Poisson's ratio, P-wave impedance and electrical resistivity for each combination of values of rock and fluid properties. Finally, we superimpose the measurements on the templates and use a grid searching method to find the nearest gridded node to the data point and minimize the objective function of the mismatch between data and model predictions. To investigate the feasibility of our proposed inversion scheme, we test a rock physics model based on effective medium theory and a modified Archie's equation, and invert for reservoir parameters of gas hydrate-bearing sediments at well 1250F and 1247B, in Hydrate Ridge. The good match between inversion results and core data suggests that the proposed inversion scheme is applicable to real data and allows combining elastic and electrical data for reservoir parameter estimation of gas hydrate-bearing sediments.

The conductive paths formed by fractures and cave in complex reservoirs differ from those formed by pores and throats in clastic rocks. In this paper, a new formation model based on fractured and caved reservoirs is established, and the electrical characteristics of rocks are analyzed with different pore structures using resistance law to understand their effects on rock resistivity. The ratio of fracture width to cave radius (C e value) and fracture dip are employed to depict pore structure in this model. Our research shows that the electrical characteristics of rocks in fractured and caved reservoirs are strongly affected by pore structure and porous fluid distribution. Although the rock electrical properties associated with simple pore structure agree well with Archie formulae, the relationships between F and or between I and S w , in more complicated pore structures, are nonlinear in double logarithmic coordinates. The parameters in Archie formulae are not constant and they depend on porosity and fluid saturation. Our calculations suggest that the inclined fracture may lead to resistivity anisotropy in the formation. The bigger dip the inclining fracture has, the more anisotropy the formation resistivity has. All of these studies own practical sense for the evaluation of oil saturation using resistivity logging data.

The conventional GR (gamma ray) index model is widely used to calculate shale volume in a drilling hole. It is just based on the raw downhole GR log. However, it is found that formation porosity and density have effect on the measurement of GR log. This effect is not obvious in compacted formations, but is nonnegligible in soft formations. In this work, a new model based on the concept of matrix GR which is immune to the effect of porosity and density is proposed. We apply the new model and GR index model to two distinct wells, one is ODP Site 1173, representing soft formations, and another is a hydrocarbon exploratory borehole, representing compacted formations. The results of the new model are in better consistent with shale volumes from X-ray diffraction analysis in Site 1173 and well-log inversion in the exploratory hole. At last, we give an explanation to a long-term problem in GR index model that GR index is generally larger than the actual shale volume.

Nuclear magnetic resonance (NMR) T 2 distributions can be employed to understand the geometry of pores, but they are not sensitive enough to determine pore connectivity. In this paper, the pore space in reservoirs is regarded as a series of different sizes of the combination of spherical pores and cylinder pores based on the pore network model and Sphere–Cylinder model. In terms of the optimized T 2 inversion method, T 2 spectral distribution is decomposed into two groups, sphere pore distribution and cylinder pore distribution. It is assumed that cylinder pore controls the connectivity and permeability of the reservoir and the sphere pore is the main place of fluid storage. The more cylinder pores that exist, the better the connectivity and permeability are. The data of eight core plugs are analyzed using this method, and the results are in accordance with those of core analysis, which proves the practicability of our research and provides a basis for the direct evaluation of reservoir pore structure using NMR T 2 distribution.

Many cases have indicated that the conductivity and permeability of porous media may decrease to zero at a nonzero percolation porosity instead of zero porosity. However, there is still a lack of a theoretical basis for the percolation mechanisms of the conductivity and permeability. In this paper, the analytical percolation expressions of both conductivity and permeability are derived based on fractal theory by introducing the critical porosity. The percolation models of the conductivity and permeability were found to be closely related to the critical porosity and microstructural parameters. The simulation results demonstrated that the existence of the critical could lead to the non-Archie phenomenon. Meanwhile, the increasing critical porosity could significantly decrease the permeability and the conductivity at low porosity. Besides, the complex microstructure could result in more stagnant pores and a higher critical porosity. This study proves the importance of the critical porosity in accurately evaluating the conductivity and permeability, and reveals the percolation mechanisms of the conductivity and permeability in complex reservoirs. By comparing the predicted conductivity and permeability with the available experimental data, the validity of the proposed percolation models is verified.