Characteristics of Nuclear LWD Density Measurements in Elliptical Boreholes - A Modeling Study
Authors: Badruzzaman A. , Nguyen P.T. 
Published: December 2007

Abstract
The effect of tool rotation on the density porosity predicted in elliptical boreholes by a nuclear logging-while-drilling density (LWD) measurement is studied using Monte Carlo modeling techniques. Laboratory calibration of such borehole conditions would be difficult. The response of a dual-detector device is calculated by rotating the sonde in the elliptical hole and associated porosity corrections are computed by two averaging procedures, one over the entire borehole and the other over the quadrant of closest contact. An equivalent circular borehole procedure to represent the rotation in elliptical holes is then postulated and successfully tested in the Monte Carlo model to eliminate the large number of CPU-intensive direct Monte Carlo simulations that were found necessary in the elliptical well bore configuration.

Introduction
Nuclear logging-while-drilling (LWD) measurements offer the promise to measure formation porosity and density in logging conditions where wireline measurements will be difficult to perform. These include,poor hole conditions such as that due to utilization of water-based mud,highly deviated or horizontal wells, and"designer" wells where drilling is targeting specific zones of interest.
In many of these cases LWD may be the only feasible logging measurement. Consequently, the question arises as to whether these measurements can be viewed as "wireline replacement."
Early nuclear LWD measurements often did not yield accurate porosity predictions in the field. On closer examination several fundamental differences between LWD and wireline sources were recognized. These include variable rate-of-penetration (ROP), rotating or sliding modes of tool motion, dynamic standoff, much lower acquisition speed, weaker nuclear sources, etc. In fact the nuclear design features of some early nuclear LWD tools were modified versions of corresponding wireline tools.
Recently, hardware, processing and mudcake response characterization advances have been made to improve the performance of nuclear LWD measurements. Hardware advances include improved source retention, inclusion of ultrasonic calipers to measure standoff, a magnetometer to identify the low side in a deviated well. etc. Processing improvements have also been made, for example, the use of quadrant data to achieve a greater information content, utilization of the bottom quadrant data, a spectrum-based algorithm, a rapid sampling technique, and a weighting technique to emphasize small-standoff data. Also, the Monte Carlo modeling technique was used to gain an insight into the response characteristics of a neutron sonde in a horizontal well where the tool rotates at the bottom of the hole with no standoff while the standard calibration is performed in a circular borehole with the built-in standoff due to the presence of the stabilizer.
With dynamic borehole complexities, such as the variable tool standoff as the tool rotates in the hole, it would be difficult to perform laboratory calibration to adequately reflect realistic field conditions. One such situation would be the occurrence of elliptical boreholes. In a recent paper, it was pointed out that even with a three-transducer ultrasonic caliper present, a considerable difference remains between the measured borehole diameter and the effective borehole diameter.
In the present work we examine, via Monte Carlo modeling, the response of an LWD density tool as it rotates in an elliptical borehole. In a standard calibration condition for an LWD density sonde one has a circular borehole with almost no standoff. In an elliptical borehole a dynamic and asymmetric standoff arises as the tool rotates in the borehole. Possible variations in the ellipticity adds to the complexity.
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