Borehole Resistivity Simulations of Oil-Water Transition Zones with a 1.5D Numerical Solver

When simulating borehole resistivity measurements in a reservoir, it is common to consider an oilwater contact (OWC) planar interface. However, this consideration can lead to an unrealistic model since in the presence of capillary actions, the mix of two immiscible fluids (oil and water) often appears as an oil-water transition (OWT) zone. These transition zones may be signi cant in the vertical direction (20 meters or above), and in context of geosteering, an e cient method to simulate the OWT zone can maximize the production of an oil reservoir. Herein, we propose an e cient one and a half dimensional (1.5D) numerical solver to accurately simulate the OWT zone in an oil reservoir. Using this method, we can easily consider arbitrary resistivity distributions in the vertical direction, as it occurs in an OWT zone. Numerical results on synthetic examples demonstrate signi cant di erences between the results recorded by a geosteering device when considering a realistic OWT zone vs an OWC sharp interface

A Deep Neural Network as Surrogate Model for Forward Simulation of Borehole Resistivity Measurements

Inverse problems appear in multiple industrial applications. Solving such inverse problems require the repeated solution of the forward problem. This is the most time-consuming stage when employing inversion techniques, and it constitutes a severe limitation when the inversion needs to be performed in real-time. In here, we focus on the real-time inversion of resistivity measurements for geosteering. We investigate the use of a deep neural network (DNN) to approximate the forward function arising from Maxwell's equations, which govern the electromagnetic wave propagation through a media. By doing so, the evaluation of the forward problems is performed offline, allowing for the online real-time evaluation (inversion) of the DNN

Adjoint-based formulation for computing derivatives with respect to bed boundary positions in resistivity geophysics

In inverse geophysical resistivity problems, it is common to optimize for specific resistivity values and bed boundary positions, as needed, for example, in geosteering applications. When using gradient-based inversion methods such as Gauss-Newton, we need to estimate the derivatives of the recorded measurements with respect to the inversion parameters. In this article, we describe an adjoint-based formulation for computing the derivatives of the electromagnetic fields withrespect to the bed boundary positions. The key idea to obtain this adjoint-based formulation is to separate the tangential and normal components of the field, and treat them differently. We then apply this method to a 1.5D borehole resistivity problem. We illustrate its accuracy and some of its convergence properties via numerical experimentation by comparing the results obtained with our proposed adjoint-based method vs. both the analytical results when available and a finite differences approximation of the derivative

Neural network architecture optimization using automated machine learning for borehole resistivity measurements

Deep neural networks (DNNs) offer a real-time solution for the inversion of borehole resistivity measurements to approximate forward and inverse operators. Using extremely large DNNs to approximate the operators is possible, but it demands considerable training time. Moreover, evaluating the network after training also requires a significant amount of memory and processing power. In addition, we may overfit the model. In this work, we propose a scoring function that accounts for the accuracy and size of the DNNs compared to a reference DNNs that provides good approximations for the operators. Using this scoring function, we use DNN architecture search algorithms to obtain a quasi-optimal DNN smaller than the reference network; hence, it requires less computational effort during training and evaluation. The quasi-optimal DNN delivers comparable accuracy to the original large DNN.PDC2021-121093-I00 IA4TES RYC2021-032853-

Bayesian optimization of the PC algorithm for learning Gaussian Bayesian networks

The PC algorithm is a popular method for learning the structure of Gaussian Bayesian networks. It carries out statistical tests to determine absent edges in the network. It is hence governed by two parameters: (i) The type of test, and (ii) its significance level. These parameters are usually set to values recommended by an expert. Nevertheless, such an approach can suffer from human bias, leading to suboptimal reconstruction results. In this paper we consider a more principled approach for choosing these parameters in an automatic way. For this we optimize a reconstruction score evaluated on a set of different Gaussian Bayesian networks. This objective is expensive to evaluate and lacks a closed-form expression, which means that Bayesian optimization (BO) is a natural choice. BO methods use a model to guide the search and are hence able to exploit smoothness properties of the objective surface. We show that the parameters found by a BO method outperform those found by a random search strategy and the expert recommendation. Importantly, we have found that an often overlooked statistical test provides the best over-all reconstruction results

Modeling extra-deep electromagnetic logs using a deep neural network

Modern geosteering is heavily dependent on real-time interpretation of deep electromagnetic (EM) measurements. We have developed a methodology to construct a deep neural network (DNN) model trained to reproduce a full set of extra-deep EM logs consisting of 22 measurements per logging position. The model is trained in a 1D layered environment consisting of up to seven layers with different resistivity values. A commercial simulator provided by a tool vendor is used to generate a training data set. The data set size is limited because the simulator provided by the vendor is optimized for sequential execution. Therefore, we design a training data set that embraces the geologic rules and geosteering specifics supported by the forward model. We use this data set to produce an EM simulator based on a DNN without access to the proprietary information about the EM tool configuration or the original simulator source code. Despite using a relatively small training set size, the resulting DNN forward model is quite accurate for the considered examples: a multilayer synthetic case and a section of a published historical operation from the Goliat field. The observed average evaluation time of 0.15 ms per logging position makes it also suitable for future use as part of evaluation-hungry statistical and/or Monte Carlo inversion algorithms within geosteering workflows.POCTEFA 2014-2020 PIXIL (EFA362/19) MTM2016-76329-

Asymptomatic bacteriuria and pyuria in patients with chronic renal failure undergoing hemodialysis at dialysis centers in Kermanshah, Iran

Pyuria is the presence of increased numbers of polymorphonuclear leukocytes in the urine and is evidence of an inflammatory response in the Urinary Tract Infection (UTI). The aim of this study is determination asymptomatic bacteriuria and pyuria in patients undergoing hemodialysis with chronic renal failure. Out of 103 patients with renal failure undergoing hemodialysis who were able to produce urine with clean catch way, we received urine sample. All samples were examined by the Microbiologist in Central Laboratory of Kermanshah, Iran. The mean age for the patients at diagnosis was 42.4 years (range, 20-67 years). Sixty-four patients (62.5) were male and thirty-nine (37.5) were female. Results have been showed 39 cases were aged between 44-49 years and the highest number cases were middle-aged. Out of 31 patients with leukocytosis, 14 patients had age between 44-49 years and majority of them were male. Pyuria(>10 WBC/HPF or 10 WBC/HPF) developed colony count more than 105 colony-forming units per milliliter that indicating positive culture. Microorganisms didn�t grow in patients (10/19) with pyuria (10 WBC/HPF is a good marker for significant bacteriuria in these patients. © 2015 Academic Journals Inc

A numerical 1.5D method for the rapid simulation of geophysical resistivity measurements

In some geological formations, borehole resistivity measurements can be simulated using a sequence of 1D models. By considering a 1D layered media, we can reduce the dimensionality of the problem from 3D to 1.5D via a Hankel transform. The resulting formulation is often solved via a semi-analytic method, mainly due to its high performance. However, semi-analytic methods have important limitations such as, for example, their inability to model piecewise linear variations on the resistivity. Herein, we develop a multi-scale finite element method (FEM) to solve the secondary field formulation. This numerical scheme overcomes the limitations of semi-analytic methods while still delivering high performance. We illustrate the performance of the method with numerical synthetic examples based on two symmetric logging-while-drilling (LWD) induction devices operating at 2 MHz and 500 KHz, respectively

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