  This study presents a new computational approach for simulating the microbial
decomposition of organic matter, from 3D micro-computed tomography (micro-CT)
images of soil. The method employs a valuated graph of connected voxels to
simulate transformation and diffusion processes involved in microbial
decomposition within the complex soil matrix. The resulting model can be
adapted to simulate any diffusion-transformation processes in porous media. We
implemented parallelization strategies and explored different numerical
methods, including implicit, explicit, synchronous, and asynchronous schemes.
To validate our method, we compared simulation outputs with those provided by
LBioS and by Mosaic models. LBioS uses a lattice-Boltzmann method for diffusion
and Mosaic takes benefit of Pore Network Geometrical Modelling (PNGM) by means
of geometrical primitives such as spheres and ellipsoids. This approach
achieved comparable results to traditional LBM-based simulations, but required
only one-fourth of the computing time. Compared to Mosaic simulation, the
proposed method is slower but more accurate and does not require any
calibration. Furthermore, we present a theoretical framework and an application
example to enhance PNGM-based simulations. This is accomplished by
approximating the diffusional conductance coefficients using stochastic
gradient descent and data generated by the current approach.
