Pore Space Microstructure Evolution of Regular Sphere Packings Undergoing Compaction and Cementation

We examine the pore space structure evolution of ordered uniform sphere packs: simple cubic (SC), body centered cubic (BCC), and face centered cubic (FCC), undergoing simple diagenetic processes that reduce their pore spaces. Focus is on the occurrence of pore space microstructure changes or transitions, which are followed through their characteristic or critical pore lengths (lc). For almost all the cubic packings undergoing either compaction or cementation there are no singularities in lc. This is a consequence of having a single pore shape controlling flow at all stages of the process. However, this is not so for the BCC packing under cementation, for which lc is non-monotonic exhibiting a kink at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\phi \approx 0.1452}$$\end{document} , the porosity at which the pore shape controlling flow switches to a different form and position. These results for uniform compaction/cementation complement our previous works on pore networks under random shrinkage. Kinks in lc as porosity decreases signal pore space microstructure transitions that anticipate sudden changes in the permeability–porosity relation as porosity decreases. The consequences are great; clearly lc is not a constant unless the diagenetic process is mild. A lc function of compaction/cementation advancement should be used above a transition and a different lc function below. For the sphere packs here, once the diagenetic process has reduced the pore space substantially, a lc function of compaction/cementation advancement is mandatory if we are to capture all significant flow features.