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We investigate the effects of anisotropy on the finite-size scaling of connectivity and conductivity of continuum percolation in three dimensions. We consider a system of size X×Y×Z in which cubic bodies of size a×b×c are placed randomly. We define two aspect ratios to request anisotropy then we expect that the displacement of average connected fraction P (averaged over the realizations), about the isotropic universal curves will be a function of the two aspect ratios. This is accounted by considering an apparent percolation threshold in each direction which leads to 50% of realizations connecting in that direction. We find the aspect ratios' dependency of the apparent threshold and investigate the finite-size scaling transformations for the mean connected fraction and its associated fluctuations. Moreover, we apply a single phase pressure solver to determine the conductivity of various realizations of the system. Finally we apply the same idea to account for the effect of anisotropy on the conductivity scaling.

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The connectivity of high conductivity pathways in geological formations depend on the spatial distribution of geological heterogeneities that may appear on various length scales. Appropriate modeling of this is crucial within in hydrology and petroleum systems. The approach taken in this study is to use percolation theory to quantify the connectivity, hydraulic conductivity, and breakthrough time behavior between an injector and a producer within such systems. In particular, a three-dimensional overlapping sandbody model is considered which assumes that the geological formation can be split into either conductive flow units (i.e., good sands) or non-conductive units (i.e., poor sands). The results are the master curves for the formation connectivity as well as the hydraulic conductivity and breakthrough time. The percolation approach is then validated against Burgan offshore reservoir dataset which reveal good matches when compared with the results obtained from computationally expensive conventional methods.