RAPID SIMULATION OF BOREHOLE NUCLEAR MEASUREMENTS WITH APPROXIMATE SPATIAL FLUX-SCATTERING FUNCTIONS

摘要

The Monte Carlo method has been the foremost numerical technique used to simulate borehole nuclear measurements. This is due to its detailed geometrical capabilities, high numerical accuracy, and ability to incorporate specific tool configurations and complex spatial distributions of material properties. Although recent advances in computer technology have considerably reduced the computer time required by Monte Carlo simulations of borehole nuclear measurements, the efficiency of the method is still not sufficient for either inversion techniques or joint interpretation with other borehole measurements. We develop and benchmark fast approximate numerical procedures to simulate neutron and density porosity logs making use of Monte Carlo-derived spatial fluxscattering functions (FSFs) for specific nuclear tool configurations. To this end, we describe the flux at detectors due to particles emitted by the radioactive source with the integral representation of Boltzmann’s transport equation. Subsequently, we use the Monte Carlo Code MCNP to calculate the associated Green’s function and the background particle flux included in the integral form of the transport equation. The solution of the integral equation is approximated with a Born series expansion that includes various orders of interaction between material properties and sources in the calculation of particle flux.Simulations performed with the new approximations entail percent errors of less than 10% with respect to Monte Carlo-simulated nuclear logs. Moreover, for the case of density FSFs we observed a maximum shift in the radially-integrated radial length of investigation (radial J-functions) of 0.3 inches due to variations of formation density. For the case of neutron FSFs the maximum change in the radial length of investigation due to variations of modified migration length was approximately equal to 2 inches. The approximations introduced in this paper enable the simulation of borehole nuclear measurements in seconds of CPU time compared to several days of CPU time with MCNP.