Sharif Digital Repository

An upscaling method such as renormalization converts a detailed geological model to a coarse one. Although flow equations can be solved faster on a coarse model, its results have more errors. Numerical dispersion, heterogeneity loss, and connectivity misrepresentation are the factors responsible for errors. Connectivity has a great effect on the fluid distribution and leakage pathways in EOR processes or CO2 storage. This paper deals with the description and quantification of connectivity misrepresentation in the upscaling process. For detection of high-flow regions, the flow equations are solved under simplified single-phase conditions. These regions are recognized as the cells whose fluxes... 

In the present paper we investigate the problem of water propagation in 2 dimensional (2D) petroleum reservoir in which each site has the probability p of being occupied. We first analyze this propagation pattern described by Darcy equations by focusing on its geometrical features. We find that the domain-walls of this model at p=pc ≃ 0.59 are Schramm-Loewner evolution (SLE) curves with κ=3.05 ∓ 0.1 consistent with the Ising universality class. We also numerically show that the fractal dimension of these domain-walls at p=pc is Df ≃ 1.38 consistent with SLEκ=3. Along with this analysis, we introduce a self-organized critical (SOC) model in which the water movement is modeled by a chain of...