Application of an efficient materials perturbation technique to Monte Carlo photon transport calculations in borehole logging

This paper describes a simple, accurate and efficient technique for the calculation of materials perturbation effects in Monte Carlo photon transport calculations. It is particularly suited to the application for which it was developed, namely the modelling of a dual detector density tool as used in borehole logging. However, the method would be appropriate to any photon transport calculation in the energy range 0.1 to 2 MeV, in which the predominant processes are Compton scattering and photoelectric absorption. The method enables a single set of particle histories to provide results for an array of configurations in which material densities or compositions vary. It can calculate the effects of small perturbations very accurately, but is by no means restricted to such cases. For the borehole logging application described here the method has been found to be efficient for a moderate range of variation in the bulk density (of the order of ±30% from a reference value) or even larger changes to a limited portion of the system (e.g. a low density mudcake of the order of a few tens of mm in thickness). The effective speed enhancement over an equivalent set of individual calculations is in the region of an order of magnitude or more. Examples of calculations on a dual detector density tool are given. It is demonstrated that the method predicts, to a high degree of accuracy, the variation of detector count rates with formation density, and that good results are also obtained for the effects of mudcake layers. An interesting feature of the results is that relative count rates (the ratios of count rates obtained with different configuration) can usually be determined more accurately than the absolute values of the count rates.