Interpretation of borehole measurements acquired in high-angle (HA) and horizontal (HZ) wells is challenging due to the significant influence of well trajectory and bed geometrical effects. Experience shows that accurate integrated interpretation of well logs acquired in HA/HZ wells requires explicit consideration of 3D measurement physics. The most reliable alternative for interpretation of well logs in HA/HZ wells is with inversion techniques that correct measurements for shoulder-bed, undulating well trajectory, and bed geometrical effects while taking advantage of high data resolution. We discovered an efficient layer-based inversion workflow for combined, quantitative petrophysical and compositional interpretation of logging-while-drilling sector-based nuclear (density, neutron porosity, photoelectric factor, gamma ray) and array propagation resistivity measurements acquired in HA/HZ wells. A challenging synthetic benchmark example confirmed improved formation evaluation with the layer-based inversion workflow across hydrocarbon-bearing zones in HA/HZ wells, where estimated hydrocarbon pore volume and porosity increased by 10% and 15%, respectively, with respect to conventional interpretation methods. Furthermore, application of the inversion-based method to a field example of HZ well across calcite-cemented siltstone layers confirmed its advantage over conventional interpretation techniques.
Calculation of mineral and fluid volumetric concentrations from well logs is one of the most important outcomes of formation evaluation. Conventional estimation methods assume linear or quasi-linear relationships between volumetric concentrations of solid/fluid constituents and well logs. Experience shows, however, that the relationship between neutron porosity logs and mineral concentrations is generally nonlinear. More importantly, linear estimation methods do not explicitly account for shoulder-bed and/or invasion effects on well logs, nor do they account for differences in the volume of investigation of the measurements involved in the estimation. The latter deficiencies of linear estimation methods can cause appreciable errors in the calculation of porosity and hydrocarbon pore volume. We investigated three nonlinear inversion methods for assessment of volumetric concentrations of mineral and fluid constituents of rocks from multiple well logs. All three of these methods accounted for the general nonlinear relationship between well logs, mineral concentrations, and fluid saturations. The first method accounted for the combined effects of invasion and shoulder beds on well logs. The second method also accounted for shoulder-bed effects but was intended for cases where mudfiltrate invasion is negligible or radially deep. Finally, the third method was designed specifically for analysis of thick beds where mud-filtrate invasion is either negligible or radially deep. Numerical synthetic examples of application indicated that nonlinear inversion of multiple well logs is a reliable method to quantify complex mineral and fluid compositions in the presence of thin beds and invasion. Comparison of results against those obtained with conventional multimineral estimation methods confirmed the advantage of nonlinear inversion of multiple well logs in quantifying thinly bedded invaded formations with variable and complex lithology, such as those often encountered in carbonate formations.
The dual-burst thermal-neutron-decay-time (TDT™) tool brings two enhancements to pulsed-neutron capture logging. The first is a realistic physical model of pulsed neutron decay curves that accounts explicitly for the effects of neutron diffusion and decay in both the wellbore and the formation. The second is the dual-burst system itself, which permits excellent statistical precision with minimal dead-time losses. This paper discusses the physics of the model, operation of the tool, important mathematical considerations for optimum use of the tool, and a demonstration of the tool performance in a laboratory simulation of a log-inject-log (LIL) operation.
Sigma measurements are useful in formation evaluation because they can be used to calculate water saturation independently of resistivity. One of the most advantageous features of the logging-while-drilling (LWD) Sigma tool under study is the use of three detectors to measure time decays from which three Sigmas are calculated: one near thermal-neutron detector, one short-spaced gamma-ray detector, and one long-spaced gamma-ray detector. Each detector has a different volume of investigation. Analogous to array resistivity logs, the multidetector Sigma logs, also called multi-depth of investigation Sigma logs, can indicate the presence of invasion and can be used to estimate true formation Sigma. However, the efficacy of the multidetector Sigma interpretation is conditioned by a high-Sigma contrast between invasion and virgin zones. We used a nonlinear gradient-based fast inversion method that uses the measured three-detector time decays and a reference value for invasion-zone Sigma to estimate the radial length of invasion and virgin formation Sigma. Synthetic logs are generated with realistic noise for numerous realizations that are then used to study the stability of the inversion routine and the estimation of error bars. We used a confidence index derived from the multiple-realization study to define the conditions under which the multiple time-decay problem is not stable. The reliability of the Sigma inversion method was verified in a set of test-pit measurements, two synthetic examples, and a field case. Synthetic results indicate that the inversion of multidetector time decays enables the correction of LWD Sigma measurements for invasion effects and improves the calculation of water saturation whenever there is contrast between invasion- and virgin-zone Sigma of more than 5 capture units. Field example results suggest that the inversion can accurately reproduce three-detector time decays honoring invasion effects evidenced in neutron-density logs while managing the presence of noise.
The quantitative integration of nuclear measurements into the in situ petrophysical and geophysical evaluation of rock formations has been elusive because of the lack of efficient algorithms to simulate them. We discovered a new method for rapid numerical simulation of borehole neutron measurements using Monte Carlo (MC)-derived spatial flux sensitivity functions (FSFs) and diffusion flux-difference (DFD) approximations. The method calculates spatial sensitivity flux perturbations using fluxdifference approximations of one-group neutron diffusion models. By invoking appropriate boundary conditions, the one-group, time-independent neutron diffusion solution is implemented for nonmultiplying systems in 2D and 3D cylindrical coordinates. The solution is differentiated with respect to the neutron cross section to obtain an expression for flux-difference due to cross-section perturbations. Constant transport-correction coefficients for cross-section parameters are calculated with a flux-fitting method to account for deviations of borehole neutron measurements from the physics of diffusion. Thereafter, spatial FSF responses are rapidly and accurately calculated using a first-order Rytov DFD approximation. Estimated flux-differences are next used to calculate lumped higher order perturbation terms. The DFD technique is tested and benchmarked against MC calculations in the presence of standoff, invasion, and well deviation for wireline and logging-whiledrilling tools. Benchmark examples and application in highly deviated wells indicate that neutron porosity logs can be accurately and efficiently simulated with the new DFD method, even in complex geometrical and physical conditions, with errors lower than 1.2 porosity units.
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