In most cases, interpretation of resistivity measurements is performed using 1D multilayered formation models that are used to fit data locally in real-time applications. While drilling high-angle or horizontal wells, more complex scenarios may occur, such as faults, pinch-outs, or unconformities. In these cases, resistivity logging data inversion should be performed using at least a 2D model, which is a more complex computational problem. This paper presents a neural networks approach for solving this problem exemplified by the application of a deep azimuthal resistivity tool for geosteering in the vicinity of a tectonic fault. The tool operational frequencies of 400 kHz and 2 MHz produce eight measurements with a coaxial arrangement of transmitters and receivers, and two azimuthally sensitive measurements with axial transmitters and transverse receivers. This paper considers a 2D model of a tectonic fault composed of three parallel layers on the one side of a displacement plane and the same three layers on the other side dislocated at a certain distance along the displacement plane. The model is described with nine independent parameters. The artificial neural networks (ANNs) were designed and trained to calculate the tool signals based on the model parameters. The training was carried out using a synthetic database of 4·105 elements containing the model parameters and corresponding tool signals. The database was calculated using distributed computations with in-house Pie2D software that used the boundary integral equation technique. To estimate the accuracy of the ANNs designed, the signals calculated with the networks were compared against the exact values obtained with Pie2D for an independent sample of 1.8·104 points. The comparison gave a good match for all 10 measurements, with the relative error comprising less than one standard tool measurement error for most points of the sample. Computation with the ANN required a few microseconds to calculate one signal, while the algorithm based on boundary integral equations required several minutes. The obtained acceleration of ~106 indicates many opportunities for modeling and inversion of logging-while-drilling data.

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Dielectric dispersion measurements are increasingly used by petrophysicists to reduce uncertainty in their hydrocarbon saturation analysis, and subsequent reserves estimation, especially when encountered with challenging environments. Some of these challenges are related to variable or unknown formation water salinity and/or a changing rock texture which is a common attribute of carbonate reservoirs found in the Middle East. A new multi-frequency, multi-spacing dielectric logging service, utilizes a sensor array scheme which provides wave attenuation and phase difference measurements at multiple depths of investigation up to 8 inches inside the formation. The improvement in depth of investigation provides a better measurement of true formation properties, however, also provides a higher likelihood of measuring radial heterogeneity due to spatially variable shallow mud-filtrate invasion. Meaningful petrophysical interpretation requires an accurate electromagnetic (EM) inversion, which accommodates this heterogeneity, while converting raw tool measurements to true formation dielectric properties. Forward modeling solvers are typically beset with a slow processing speed precluding use of complex, albeit representative, formation petrophysical models. An artificial neural network (ANN) has been trained to significantly speed up the forward solver, thus leading to implementation and real-time execution of a complex multi-layer radial inversion algorithm. The paper describes, in detail, the development, training and validation of both the ANN network and the inversion algorithm. The presented algorithm and ANN inversion has shown ability to accurately resolve mud filtrate invasion profile as well as the true formation properties of individual layers. Examples are presented which demonstrate that comprehensive, multi-frequency, multi-array, EM data sets are inverted efficiently for dis-similar dielectric properties of both invaded and non-invaded formation layers around the wellbore. The results are further utilized for accurate hydrocarbon quantification otherwise not achieved by conventional resistivity based saturation techniques. This paper presents the development of a new EM inversion algorithm and an artificial neural network (ANN) trained to significantly speed up the solution of this algorithm. This approach leads to a fast turnaround for an accurate petrophysical analysis, reserves estimate and completion decisions.

The dielectric dispersion of porous media saturated with water and oil is described by the Havriliak–Negami curve in the frequency range 10 kHz – 50 MHz with characteristic values of polarization parameters. Laboratory data show the relationship between porosity and polarization parameters. This relationship allows us to determine porosity of water-and-oil saturated formation under downhole conditions, using borehole dielectric logging methods. In this study, a possibility of using borehole electromagnetic (EM) inductive measurements for determining dispersion of complex dielectric permittivity of the formation, including the invaded zone was investigated. The influence of the inductive measurement error when finding formation porosity when determining polarization parameters of the frequency dependence of complex dielectric permittivity (the Havriliak–Negami spectrum) was studied. For this study, a vertically oriented coil is placed in the well (along the borehole wall), creating a harmonic electromagnetic field. Several receivers that are aligned with the borehole axis measure this harmonic electromagnetic field. By using the magnetic field values on the well axis, we solve the inverse problem of determining complex dielectric permittivity of the formation, taking into account the invaded zone. Dielectric permittivity of the formation is calculated at different frequencies and is then used to restore the frequency dispersion curve, which enables us to find polarization parameters for the Havriliak-Negami polarization curve, taking into account the measurement error. Subsequently, these parameters can be used to find formation porosity. The proposed method of finding porosity uses inductive logging technology and is an alternative to the method based on the mixing formulae.