Siroos Azizmohammadi

Is the permeability of naturally fractured rocks scale dependent

The equivalent permeability, keq of stratified fractured porous rocks and its anisotropy is important for hydrocarbon reservoir engineering, groundwater hydrology, and subsurface contaminant transport. However, it is difficult to constrain this tensor property as it is strongly influenced by infrequent large fractures. Boreholes miss them and their directional sampling bias affects the collected geostatistical data. Samples taken at any scale smaller than that of interest truncate distributions and this bias leads to an incorrect characterization and property upscaling. To better understand this sampling problem, we have investigated a collection of outcrop-data based Discrete Fracture and Matrix (DFM) models with mechanically constrained fracture aperture distributions, trying to establish a useful Representative Elementary Volume (REV). Finite-element analysis and flow-based upscaling have been used to determine keq eigenvalues and anisotropy. While our results indicate a convergence towards a scale-invariant keq REV with increasing sample size, keq magnitude can have multi-modal distributions. REV size relates to the length of dilated fracture segments as opposed to overall fracture length. Tensor orientation and degree of anisotropy also converge with sample size. However, the REV for keq anisotropy is larger than that for keq magnitude. Across scales, tensor orientation varies spatially, reflecting inhomogeneity of the fracture patterns. Inhomogeneity is particularly pronounced where the ambient stress selectively activates late- as opposed to early (through-going) fractures. While we cannot detect any increase of keq with sample size as postulated in some earlier studies, our results highlight a strong keq anisotropy that influences scale dependence.

Tensorial Fracture-Matrix Ensemble Relative Permeabilities in Naturally Fractured Reservoirs: Evidence from Discrete Fracture and Matrix Simulations

The prediction of water breakthrough and oil recovery for naturally fractured reservoirs (NFRs) cannot be performed accurately without dynamic upscaled relative permeability functions. Relative permeability is commonly assumed to be a scalar quantity, although a justification for NFRs has yet to be presented. In this study, we show how accurate this assumption is for fracture-matrix ensemble relative permeabilities determined by numeric simulations of unsteady-state core flooding. Numerical determination of relative permeability requires a realistic flow model, a spatially adaptive simulation approach and a sophisticated analysis procedure. To fulfil these requirements, we apply discrete fracture and matrix modelling to well characterised hm-km outcrop analogues. These are parametrized with aperture, permeability, and capillary pressure data. Fracture attributes are allowed to vary from segment to segment, trying to emulate in situ conditions. The finite-element-centered-finite-volume method is used to simulate two-phase flow in the fractured rock, considering different wettability conditions. Our results indicate that the ensemble relative permeability of 2D digital NFR outcrop analog models is a tensor property. The tensors are not necessarily symmetric, and their eigenvalues are not always equal to the diagonal terms. Also, the off-diagonal terms can determine the type, i.e., counter vs co-current imbibition, and the direction of imbibition.