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Abstract Logging-while-drilling (LWD) Resistivity Measurements in high-angle and horizontal wells cannot be used for quantitative calculation directly, since they are easily influenced by borehole/formation geometry, surrounding beds and other factors. Although Least-Squares (LS) inversion method is widely used to reconstruct the actual reserve resistivity, it assumes that the measurement data are corrupted with pure Gaussian noise. This assumption makes it cannot work when the measured data are contaminated by non-Gaussian noise. Furthermore, in highly deviated wells, LWD apparent resistivity measurements always show "horns" near the bed boundaries where the resistivity contrastsare high. These "horns" can also decrease the inversion accuracy. In this paper, we propose a new robust nonlinear inversion algorithm that uses Huber criterion as a solution for handling the measured data mentioned above. Compared with Least-Squares inversion, this method requires one additional parameter, namely, the threshold of Huber criteria, δ. This parameter is very important and must be chosen carefully. By varying δ, Huber inversion method can be divided into two parts. If the absolute error of simulated response (compared to the measured response) is greater than δ, l1 norm inversion is used. Otherwise, l2 norm inversion method is used. This method combines advantages of both l1 and l2 inversion and works best if the resistivity data contains non-Gaussian noises as well as "horns". Meanwhile, during the inversion process, we introduce a new approximate method for computing the Jacobian matrix and desired step, which could improve the calculation results. Besides, since currentmulti-resolution LWD resistivity tools could providemultiple compensated resistivity measurements, a linear optimization combination method of iterative stepsis introduced for multi-resolution resistivity curves. The weights can be adjustedaccording to the LWD resistivity sensitivity for borehole deviation, resistivity contrast at bed boundaries, and the contaminated extent by noise. This optimal procedure could further improve the computation accuracy. A series of numerical simulations for different conditions are analyzed and discussed, the comparison of LS and Huber inversion shows that Huber algorithm is more robust and stable when the measurements contain both data of "horns" and non-Gaussian noise. Therefore, this method is more suitable for routine petrophysical interpretation and quantitative formation evaluation.
Jia, Hengtain (CNPC Drilling Research Institute) | Sheng, Limin (CNPC Drilling Research Institute) | Dou, Xiurong (CNPC Drilling Research Institute) | Deng, Le (CNPC Drilling Research Institute) | Guan, Kang (CNPC Drilling Research Institute) | Fan, Jinhui (CNPC Drilling Research Institute)
Abstract Rock resistivity has a close relationship with lithology, reservoir properties and oil-bearing capacity. Resistivity measurement while drilling (MWD) device is designed to judge Lithology, divide oil/gas/water layer and analyze the oil-bearing capacity, permeability and porosity of reservoir according to measurements of rock resistivity. It is used for real-time evaluation of stratum. The porous stratum is commonly high in resistivity. Low resistivity measured often implies the existence of saturation water. However, the collected information that reflects the resistivity signal contains a lot of noise components. It is difficult to accurately reflect the formation resistivity. The near-bit RMWD device based on wavelet packet noise reduction algorithm can measure the resistivity of stratum at first time because of the method of measurement while drilling. It can also precisely denoise the measured data of lateral resistivity, bit resistivity and azimuthal resistivity by the algorithm of wavelet packet decomposition and the best wavelet tree of reconstruction signal based on information entropy, so as to improve the accuracy and reliability of resistivity measurement.
A reconstruction of subsurface profile is well concentrated in well logging. In this study, an effective reconstruction model is applied on subsurface profile generating. The model is based on the processing where total variation (TV) denoising method introduced by Rudin et al. (1992) is applied on the inversion model. The method has been tested for simulated three-layer underground model in different cases. By using this model, a relatively good reconstruction on noisy subsurface profile is realized. It has a satisfying performance on irregular or missing boundaries which are caused by the real noisy measurement. Finally we discuss a further implementation by this method.
Presentation Date: Wednesday, October 19, 2016
Start Time: 3:35:00 PM
Presentation Type: ORAL