Fast 1D Inversion of Logging-While-Drilling Resistivity Measurements for Improved Estimation of Formation Resistivity in High-Angle and Horizontal Wells

We have developed an efficient inversion method to estimate layer-by-layer electric resistivity from loggingwhile-drilling electromagnetic induction measurements. The method assumes a 1D model based on planarly layered transversely isotropic formations with known bed boundaries, penetrated by arbitrary well trajectories. Forward simulations are based on a 1D reduced model in which borehole and mandrel effects are assumed to be negligible. The stopping criteria, regularization term, regularization parameter, the Jacobian matrix, and inversion variables are automatically estimated by the inversion algorithm, thereby minimizing the required user interaction and expertise. Numerical inversion results of challenging synthetic and field data confirmed the high stability and superior approximation properties of the developed inversion algorithm. We evaluated results indicating that triaxial induction measurements provide significantly more stable inversion results than conventional coaxial measurements, especially in the presence of anisotropic formations.RISE Horizon 2020 European Project GEAGAM (644602) MTM2013-40824-P SEV-2013-0323 CYTED 2011 project 712RT0449 BERC 2014-201

Sensitivity Analysis for the Appraisal of Hydrofractures in Horizontal Wells with Borehole Resistivity Measurements

This paper numerically evaluates the possibility of using borehole electromagnetic (EM) measurements to diagnose and quantify hydraulic fractures that have been arti ficially generated in a horizontal well. Hydrofractures are modeled as thin disks perpendicular to the well and filled with either sand-based or electrically-conductive proppant. The study focuses on the e ect of both thickness and length (radius) of hydrofractures to assess their eff ects on speci fic con figurations of borehole resistivity instruments. Numerical results indicate that several measurements (e.g. those obtained with low- and high-frequency solenoids) could be used to asses the thickness of a fracture. However, only low-frequency measurements performed with electrodes and large-spacing between transmitter and receivers (18 m) exhibit the necessary sensitivity to reliably and accurately estimate the length of long hydrofractures (up to 150 m) in open-hole wells. In the case of steel-cased wells, the casing acts as a long electrode, whereby conventional low-frequency short-spaced, through-casing measurements are suitable for the accurate diagnosis of long hydrofractures (up to 150 m in length).MTM2010-16511 P711RT027

Physics-guided deep-learning inversion method for the interpretation of noisy logging-while-drilling resistivity measurements

Deep learning (DL) inversion is a promising method for real-Time interpretation of logging-while-drilling (LWD) resistivity measurements for well-navigation applications. In this context, measurement noise may significantly affect inversion results. Existing publications examining the effects of measurement noise on DL inversion results are scarce. We develop a method to generate training data sets and construct DL architectures that enhance the robustness of DL inversion methods in the presence of noisy LWD resistivity measurements. We use two synthetic resistivity models to test the three approaches that explicitly consider the presence of noise: (1) adding noise to the measurements in the training set, (2) augmenting the training set by replicating it and adding varying noise realizations and (3) adding a noise layer in the DL architecture. Numerical results confirm that each of the three approaches enhances the noise-robustness of the trained DL inversion modules, yielding better inversion results-in both the predicted earth model and measurements-compared to the basic DL inversion and also to traditional gradient-based inversion results. A combination of the second and third approaches delivers the best results

FAST AND AUTOMATIC INVERSION OF LWD RESISTIVITY MEASUREMENTS FOR PETROPHYSICAL INTERPRETATION

This paper describes an extension of a recently developed fast inversion method (Pardo and Torres-VerdÍn (2015)) for estimating a layer-by-layer electric resistivity distribution from logging-whiledrilling (LWD) electromagnetic induction measurements. The well trajectory is arbitrary and the developed method is suitable for any commercial logging device with known antennae configurations, including tri-axial instruments. There are two key novel contributions in this work: First, the three-dimensional (3D) transversely isotropic (TI) formation is now approximated by a sequence of various "stitched" one-dimensional (1D) sections rather than by a single 1D reduced model. This provides added flexibility in order to approximate complex 3D formations. Second, we introduce the concept of "negative apparent resistivities" in the inversion method. By using the values of attenuation and phase differences that correspond to a "negative" resistivity in a homogeneous formation, the amount of data lost when converting magnetic fields into apparent resistivities is minimized, thus leading to a more robust inversion method that also convergences faster. The developed inversion method can be used to interpret LWD resistivity measurements and to adjust the well trajectory in real (logging) time. Numerical inversion results of challenging synthetic and actual field measurements confirm the high stability and superior approximation properties of the developed inversion algorithm. Because of the efficiency, flexibility, and stability of the inversion algorithm, formation-evaluation specialists can readily employ it for routine petrophysical interpretation and appraisal of complex LWD and wireline resistivity measurements acquired under general geometrical and geological constraints.BERC 2014-2017 SEV-2013-0323 GEAGAM (644602) MTM2013-40824-

Error Control and Loss Functions for the Deep Learning Inversion of Borehole Resistivity Measurements

Deep learning (DL) is a numerical method that approximates functions. Recently, its use has become attractive for the simulation and inversion of multiple problems in computational mechanics, including the inversion of borehole logging measurements for oil and gas applications. In this context, DL methods exhibit two key attractive features: a) once trained, they enable to solve an inverse problem in a fraction of a second, which is convenient for borehole geosteering operations as well as in other real-time inversion applications. b) DL methods exhibit a superior capability for approximating highly-complex functions across different areas of knowledge. Nevertheless, as it occurs with most numerical methods, DL also relies on expert design decisions that are problem specific to achieve reliable and robust results. Herein, we investigate two key aspects of deep neural networks (DNNs) when applied to the inversion of borehole resistivity measurements: error control and adequate selection of the loss function. As we illustrate via theoretical considerations and extensive numerical experiments, these interrelated aspects are critical to recover accurate inversion results

1.5D BASED INVERSION OF LOGGING-WHILE-DRILLING RESISTIVITY MEASUREMENTS IN 3D FORMATIONS

This manuscript describes an extension of a computer method developed for the fast inversion of logging-while-drilling (LWD) resistivity measurements Pardo and Torres-Verdín (2015); Bakr et al. (2016). The method enables to simultaneously invert measurements recorded at different wells using possibly different commercial LWD co-axial and tri-axial logging instruments. The original three-dimensional (3D) transversely isotropic (TI) reservoir is approximated by a sequence of several "stitched" one-dimensional (1D) TI sections. Then, multiple 1.5D semi-analytical solutions are employed for simulation and inversion. The key novel contribution presented here is the ability to invert also for bed boundary locations in addition to the previously available inversion of horizontal and vertical resistivity values. Numerical experiments performed over numerous synthetic examples show that in most of the considered realistic 3D synthetic formations, the inversion method enables to properly recover the formation model composed of resistivity values and bed boundary locations from measurements acquired at multiple wells. Thus, it provides a useful method to properly interpret LWD resistivity measurements, especially in the presence of abnormal readings such as horns, which are prone to misinterpretation. We are currently working on the extension of this method to the case of deep and extra-deep azimuthal resistivity measurements.Marie Sklodowska-Curie grant agreement No 644602 MTM2013-40824-P MTM2016-76329-R SEV-2013-0323 BERC 2014-201

Inversion-based interpretation of 3D borehole directional resistivity measurements acquired in high-angle and horizontal wells

We developed an efficient parallel 3D inversion method to estimate electrical resistivity from deep directional borehole electromagnetic (EM) induction measurements. The method places no restrictions on the symmetry of the assumed subsurface model and spatial distribution of electrical conductivity, and supports arbitrary well trajectories. Parallel direct solvers are employed for fast forward modeling of triaxial induction problems with multiple transmitter-receiver positions. Optimal transmitter-receiver configurations for several induction frequencies are determined for different application conditions. Numerical inversion results of challenging synthetic data confirm the feasibility of full 3D inversionbased interpretations, thus opening the possibility of integrating directional induction measurements with seismic amplitude data for improved petrophysical and fluid interpretations