Comparison of Monte Carlo and discrete ordinates methods in a three-dimensional well-logging problem

In this paper, the authors compare the Monte Carlo and the two discrete ordinates methods (nodal and conventional) in the benchmark well-logging problem. Although the problem is prototypical of well-logging systems, it severely tests the capabilities of transport methods. The Monte Carlo calculations were performed with the Los Alamos code, MCNP. The discrete ordinates calculations were performed using the Schlumberger three-dimensional nodal transport code, LENA3D (Linear Expansion Nodal Anisotropic 3D). The three-dimensional discrete nodal transport method developed and coded in LENA3D appears to be significantly faster than the Monte Carlo method in MCNP for this problem. The linear surface flux nodal method yields the accuracy of a Monte Carlo calculation with more than an order of magnitude less computing time for this problem. The method thus offers the potential for performing large-scale three-dimensional transport calculations to complement Monte Carlo methods in well-logging and other radiation transport problems.