Building materials such as bricks, concrete and sandstone all are porous. These materials may interact with their environment leading to degradation of the structures with time. A specific example is that the constituent ions in the hydrated cement paste matrix may leach out from the concrete and cause the concrete structure to become weak.

The medial axis mathematically preserves the topology of the pore space; it is difficult, however, to identify pores unambiguously. Furthermore, pores normally encompass more than one junction of the medial axis; therefore, various merging algorithms have to be developed to trim the skeleton and fuse the junctions together while avoiding unrealistically high coordination numbers. The choice of threshold value for throat quality can be problematic without being examined by real flow simulations. In conclusion, medial axis algorithms readily capture the interconnectivity of the pore spaces but encounter the problem in identifying pores.

A coarse grained mathematical formula containing the sorption isotherm is used to reflect the effects of sorption on the change of pore sizes. For example, the adsorbate obstruction can be simulated by reducing the throats radii as a function of the concentration of the moving species.

To account for the changes caused by dissolution and precipitation, a mathematical construct should be developed to modify the pore-pore conductivities by relating these changes to changes in pore volumes. It is important to note that while the surface area fractions assigned to different minerals do change, the model does not change the total surface area. Because the reactions are modelled at equilibrium, the reaction rate is independent of surface area. Thus the simulation results are negligibly affected in the situation.

The development of robust methods to engineer biofilms in porous media requires predictive mathematical models capable of determining the evolution of biofilms under different flow conditions.

Due to the complexity of the pore structure and the change of the environmental conditions, a great deal of experimental, theoretical and numerical approaches have been proposed and developed to study transport processes through porous media during the past decades. The measurements are highly sensitive to the material composition, sample preparation, methodology and testing environment. Analytical solutions are typically restricted to problems with assumed homogeneous properties and specific boundary conditions, some of which have limited practical relevance or are complicated to evaluate.

Pore-scale simulations have improved the understanding of large-scale natural processes and informed large-scale geotechnical applications. Their importance comes from the fact that they can produce rather cost-effective and accurate predictions for local transport (diffusion/permeation), and at the same time allow for systematic variations of the system's parameters (pore space geometries, fluid properties, and boundary conditions) to assess their impact, which is much more difficult to achieve than with experiments. With pore-scale models one can make improved assessments of macroscopic transport properties by varying the pore space structure parameters. This offers a way to understand the scale dependence of continuum transport parameters. Such scale dependence cannot be captured by an effective medium Darcy approach. The pore-scale modelling is dominated by particle-based methods. These include the promising lattice Boltzmann method and smoothed particle hydrodynamics.

I hope it is helpful for you.

All the best.

Percolation theory for the beginning, maybe?

Maybe I am not the right person which has the authority to give complete comments on your research. However, I have some experience in Mathematical modeling and numerica parameterizations, in particular in education. In that sense I can make some comments anticipating that the model will be designed numerically in finite difference form. Idea about subject of the project (face this comparison) is fresh and very attractive. However, making this model is a huge challenge due to culture and language. A mathematical modeling research of the pore network was developed here at the University where I am a Visiting Professor. http://repositorio.ufes.br/jspui/handle/10/4013

see

[Society of Petroleum Engineers SPE International Oilfield Nanotechnology Conference and Exhibition - Noordwijk, The Netherlands (2012-06-12)] SPE International Oilfield Nanotechnology Conference and Exhibition - A New Mathematical Model for Colloidal Flow in Rocks: Accounting for Pore Geometry and Network Topology in Bimodal Media

You, Zhenjiang, Bedrikovetsky, Pavel https://booksc.xyz/book/18908594/28f881

Proceedings [EAGE Publications BV ECMOR XVI - 16th European Conference on the Mathematics of Oil Recovery - Barcelona, Spain (2018.09.03-2018.09.06)] ECMOR XVI - 16th European Conference on the Mathematics of Oil Recovery - Adaptive Pore Network Model With Localization Of Time-Step

Regaieg, M., Moncorgé, A.

https://booksc.xyz/book/76108552/edd26a