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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.
In this paper, we develop a rigorous 2D inverse algorithm that reconstruct transversely isotropic resistivity structure using multicomponent induction logging data. We first study how 2D anisotropy affects multicomponent induction logging measurements. Based upon these studies, we design a objective function that includes invasion zone length and resistivity, and horizontal and vertical formation resistivity. To reduce trade-off and nonuniqueness of the inversion, we predetermine bed boundaries from petrophysical and wireline measurements and keep these bed boundaries fixed during the inversion. We correct the initial model based upon the data misfit. The model is accepted when the misfit drops to the desired level. We test our algorithm on both synthetic and field data sets.
Abstract The determination of residual and movable hydrocarbons in oil and gas reservoirs requires that the formation resistivities are accurately estimated. For this purpose the log analyst can use several resistivity measurements with different measuring principles providing varying vertical and radial resolutions. Integrating these measurements into a uniform algorithm that solves for the formation resistivities can improve the interpretation. Conventional interpretation methods of electromagnetic measurements use approximate and independent techniques for laterolog and induction logging measurements. These techniques do not necessarily provide the same results for the parameter estimates. Using a joint inversion algorithm that simultaneously solves for all measurements provides an earth model consistent with all measurements. In addition, the ability to resolve is enhanced due to the fact that galvanic and induction tools have different response characteristics in conductive or resistive formations. The laterolog is more sensitive to resistive formations; whereas, the induction tool is more sensitive to conductive formations. The combination of both measurements in a joint inversion process, therefore, increases the overall resolution. The inversion technique not only provides the formation parameter results, but gives the log analyst useful statistical information that can be used as quality control. In contrast with the standard interpretations, which are normally based on a 1-D interpretation, the 2-D inversion can simultaneously solve for a resistivity distribution in the radial and vertical directions. When the resistivity contrast is high, the shoulder bed effects can be very strong. This can be the case if a reservoir is delineated by conductive shales. The different vertical resolutions between deep induction and focussed log measurements appear as an offset between the two curves which could be interpreted as invasion. The 2-D inversion is able to distinguish between shoulder bed and invasion effects and provides more reliable results than a standard 1-D interpretation. Shoulder bed effects may result in underestimating the amount of oil in place if the reservoir is embedded in a conductive formation. The problem of delineating the reservoir and determining the vertical boundaries of the reservoir (and subsequently its thickness, which can be used together with the resistivity to estimate the total amount of hydrocarbon) can be solved using a 2-D inversion. This work demonstrates how the borehole, invasion and shoulder bed effects influence the data and subsequently the results of a standard interpretation. This is shown using synthetic and real field data. Introduction The estimation of accurate formation resistivities requires not only accurate measurements, but also an interpretation process to derive the true formation resistivities from apparent resistivity values. P. 577
In the last decade, since its introduction, the successful use of deep directional electromagnetic measurements for well placement has been based on the application of a real-time automatic multilayer inversion. The basic assumption behind the inversion-based interpretation is that a 1D layered medium can be used to fit the data locally. However, the technology is increasingly used to place the wells in more complex scenarios, where that assumption does not hold. Faulted formations are a common type of scenario encountered in most horizontal drilling projects, whether the wells are geosteered or not. Since a fault is generally seen as a discontinuity in a layered formation, it does not fit the 1D assumption and cannot be accurately imaged with a 1D inversion. When long-spacing deep reading tools are used, the presence of faults badly distorts the 1D inversion results within several tens of feet around the fault event.
This paper proposes a semi-automatic imaging workflow for faulted scenarios based on a series of inversions and processing steps taking advantage of the available directional measurement sensitivities to extract specific features such as the formation layering, resistivities, the remote boundaries, and the position and dip of the crossed fault plane itself. No user inputs are required at the start: the model complexity is increased from 1D to 2D as the workflow progresses, addressing challenges in integration of data of different scales. The inversions provide quality control to ensure that the intermediate results are geologically likely.
The workflow was tested on a large number of synthetic cases at different scales and of increasing complexities to ensure stability. Field data examples include single and multiple fault interpretation where deep measurements were used to evaluate change in formation dip due to drag near the fault. Model consistency, positive match, and good reconstruction of directional data are all indicators of interpretation quality, and that the resulting fault model constitutes an adequate representation of the reservoir geometry at hand. This proves that more information can be obtained from deep directional electromagnetic datasets when specific workflows are designed from knowledge of the measurement physics to address specific complex scenarios with non-1D layered geometries.