Service companies developed forward Nuclear Geophysical Models like SNUPAR and MSTAR to assist in the design of their nuclear logging tools and in the prediction of their response to porous media that contain any minerals and any fluids in any combination.  Given a formation's mineral and fluid content, including chemical formulas, densities, and volume fractions, a forward model can predict logging tool responses to that formation. 

Forward models are also used to help construct Chart Books with departure curves and environmental corrections for unusual mineral and fluid conditions. A big advantage is that these same models can be used to generate the input information called "material specification cards" needed to define a formation to the Monte Carlo program MCNP, thereby maintainling the coherence between the nuclear geophysical models, the charts and environmental corrections they provide, and the more sophistocated MCNP models.

Clearly the most difficult/challenging aspect of these initial efforts was describing the slowing down of fast neutrons and how this process is related to formation porosity.

Earlier forward models assumed that the minerals and fluids of both the pores and the host matrix are homogeneously distributed with infinitesimal sizes in much the same way that oxygen, nitrogen, carbon dioxide, water and other molecules form earth’s atmosphere; also, no laminae were present. These assumptions were used historically for mathematical convenience despite the obvious fact that real earth formations contain minerals and fluids that are inhomogeneously distributed throughout.

After a time, even many experts came to believe that pore size effects on nuclear logging tools were negligible in every case.

To make matters worse, density, neutron, and pulsed neutron logging tools are routinely calibrated in laboratory formations and shop calibrators that are carefully constructed to be homogeneous with no laminae and very small pore sizes, or no pores at all !

Forward models are registered / calibrated with laboratory data and also with Monte Carlo Methods. However, forward models remain the method of choice in vuggy and laminated porous media because the number of formation zones in these cases can present formidable problems for Monte Carlo modelers and laboratory test cell designers whenever pore size, laminae, and fractal dimension
are considered.