Prediction of permeability in dual fracture media by multivariate regression analysis

One of the most important characteristics of naturally fractured rocks for simulating the flow in the hydrocarbon reservoir is permeability. There are two major approaches in modeling fluid flow in fractured rocks: the discrete fracture network (DFN) model which is a special case of DFM models where fractures and matrix of rock mass are treated explicitly. DFN models consider the flow only in fracture pattern and neglect the rock matrix conductivity, and the dual porosity (DP)/dual fracture (DF) model. In the latter method two overlaid media are considered: rock matrix and fractures. In this study the permeability of 2D fractured and permeable rock matrix is calculated using a distinct element method when the rock matrix is modeled by Voronoi tessellations. Totally 860 models of the synthetic fracture networks were generated based on different fracture features with different fracture densities and aperture patterns and different sizes of Voronoi tessellations that exemplify different grain sizes in rock matrix and micro-apertures. According to the literature, this is the first case which such sensitivity analysis about the effect of geometrical parameters of fractures and grain patterns is considered which is the main objective of this research work. The results show a significant difference between calculated permeability of dual fracture models and discrete fracture network (DFN) models. Using all calculated models permeability, a practical equation is proposed that consists of different statistical and fractal characteristics of fracture patterns using multivariate regression analysis (MRA). High correlation coefficient value was emerged between different input parameters. Thus the principal component regression (PCR) was used to eliminate this problem.