Scaling and critical behavior of lattice and continuum porous media with different connectivity configurations

Determination of the connectivity and conductivity of porous media is of great importance in evaluation of fluid transport in different systems including petroleum formations, ground water hydrology, and contaminant transport. Among the conventional methods for connectivity forecasting, the percolation approach is an efficient method that can provide an estimate for both connectivity and conductivity of a porous medium as well as their uncertainties. In the classic percolation approach, connectivity is considered between two lines at the opposite sides of a 2-D porous medium (i.e., injectors and producers in the petroleum terminology). While in reality, the connectivity can be between point-shaped locations (e.g., point-to-point connection in a 2-D areal cross sectional map of a 3-D porous medium containing vertical wells). In this study, by implementing an object-based Monte Carlo simulations algorithm, the connectivity and conductivity behavior of a system with the point-shaped connectivity model is compared with that in the conventional line-shaped models. The focus of the research is on the evaluation of scaling and critical percolation properties of both lattice and continuum systems with different connectivity configurations. Having calculated the percolation threshold values as well as universal percolation exponents in both percolation systems, the scaling functions of connectivity and conductivity will be evaluated for both connectivity models. These scaling functions can be used to predict the connectivity and conductivity behavior of a system with any size by simple algebraic calculations. The results show that the point-to-point connection behavior of the site and continuum percolation is similar to each other but is different from that in the conventional line-to-line connectivity model.