In-silico simulation of porous media: Conception and development of a greedy algorithm

Cubic porous networks consisting of several millions of voids of different sizes are efficiently simulated through a greedy algorithm. The porous network is built on the basis of the Dual Site-Bond Model in which a cavity (site) is always larger than any of its delimiting throats (bonds). When the initial configuration of the cubic network is established by means of a random (Monte Carlo) seeding on a lattice of sites and bonds, the proper allocation of more pore elements becomes troublesome and time-consuming, and there even exists the chance of not achieving a valid pore network. The complexity of this pioneering Monte Carlo algorithm, in the best case, increases according to the third power of the number of pore elements and, in the worst case is asymptotic to infinity. Here, we have succeeded in the development of an smart non-mistake initial seeding situation of sites and bonds that behaves in the way of a greedy algorithm. An initial ordering of sites according to their sizes allows a proper assemblage of these hollows throughout the cubic lattice. From this configuration, the pore network evolves toward the most probable one by a series of legitimate random swappings between sites and bonds. The complexity of the greedy algorithm remained proportional to the cubic power of the total number of sites. In general the execution time of the greedy algorithm results to be faster than that employed with the previous Monte Carlo algorithm.

Topological representation of a 100×100×100100×100×100 cubic pore network constructed by the NoMISS Greedy algorithm. Small sites are colored in light gray, medium size sites in gray and large sites in black.Figure optionsDownload as PowerPoint slideResearch Highlights
► The Dual Site-Bond Model (DSBM) is used to represent in a simple way a porous network.
► A Monte-Carlo algorithm is presented to rapidly generate consistent cubic pore networks, which connect sites (cavities) via bonds (pore throats), drawn from respective size distributions and including a desired spatial correlation between the different pore elements.
► The method is very efficient by properly organizing the growth of the network in a systematic manner using appropriate lists and pointers, excluding impossible configurations a priori.
► The description of the greedy algorithm is methodical and detailed, with examples to demonstrate its efficiency with respect to prior algorithms.
► For the validation of this new NoMISS algorithm a critical analysis provides valid pore networks with a very satisfactory agreement with the theoretical expectations of the DSBM.
► The temporal complexity of the new algorithm can be readily analyzed and, in the worst case, when there exists a high overlap between the site and bond-size distributions, the complexity of the NoMISS algorithm becomes N×N×NN×N×N where N = is the number of pore elements at edge of the cubic lattice.
► Besides, in the new NoMISS approach, the spatial complexity remains as N×N×NN×N×N regardless of the overlap between size distributions.
► The performance in terms of execution times shows a drastic diminution, sometimes of several orders of magnitude, when employing the new NoMISS algorithm if compared to old approaches.