Real-Time Simulation of Deep Azimuthal Resistivity Tool in 2D Fault Model Using Neural Networks

Abstract

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.

Modeling extra-deep electromagnetic logs using a deep neural network

“…For the full range of 901 logging positions along the well, the evaluation takes 0.13 s, that is, 0.15 ms per logging position, which should suffice even for the most demanding RT inversion algorithms. The p erformance results are similar to those reported in Kushnir et al (2018).…”

“…Recently, there have been several noteworthy works aimed at well-log approximation: He and Misra (2019) use a neural network to predict missing dielectric dispersion logs from available logs. Shahriari et al (2020a) and Kushnir et al (2018) use a DNN to approximate the forward problem for a 1D medium. Because the forward problem is continuous and has a unique solution, the approximations deliver acceptable accuracy but have certain limitations.…”

“…The model in Shahriari et al (2020a) is restricted to only three layers. Kushnir et al (2018) approximate a more complex 2D model with a geologic fault but only consider traditional deep azimuth measurements (above 400 kHz) acquired with shorter (up to 1.0 m) spacing instruments.…”

Massive database generation for 2.5D borehole electromagnetic measurements using refined isogeometric analysis

“…DL methods are fast, but require a massive training dataset. To decrease the online computational time during field operations, we often produce such a large dataset a priori (offline) using tens of thousands of simulations of borehole resistivity measurements (see, e.g., Kushnir et al, 2018). To generate the database for DL inversion, we employ simulation methods to solve Maxwell's equations with different conductivity distributions (Earth models).…”

Modeling extra-deep electromagnetic logs using a deep neural network

“…This is in part because the inverse problem may have multiple solutions. [32], [33] use a DNN to approximate the forward problem for a 1D medium. Since the forward problem is continuous and has a unique solution, the approximated forward function delivers an acceptable accuracy.…”