Local non-vuggy modeling and relations among porosity, permeability and preferential flow for vuggy carbonates

Abstract

It is challenging to predict the permeability of a vuggy carbonate based on a bulk porosity indicator such as the effective porosity obtained by helium porosimetry. The primary reason is that heterogeneity in the local porosity distribution within the rock may cause nonuniform fluid flow or preferential flow due to the large amount of hydraulically ineffective pore spaces. Here we present the results of a new X-ray computed tomography (CT) based numerical fluid-flow analysis for various types of vuggy carbonate samples, together with experimental visualization of the flow paths within some samples. To numerically analyze the preferential flow, the samples are modeled as aggregates of submillimeter-scale non-vuggy carbonates with different porosities for which the widely-used Lucia bulk porosity-permeability relations of non-vuggy carbonate rock are applied (local non-vuggy modeling). The local porosity distribution is estimated using X-ray computed tomography of the samples. The local permeability distribution is then estimated based on the local porosity distribution, and a single-phase Darcy flow simulation is performed. This provides the bulk porosity and permeability and the preferential flow within the samples, which are consistent with experimentally measured values and visualized flow paths. Both lognormal and normal distributions of local porosity are identified. Preferential flow is associated with a lognormal distribution, and the geometric standard deviation is related to the degree of preferential flow. We show that, in the case of a normal local porosity distribution, the bulk permeability can be predicted based on a bulk porosity indicator such as the effective porosity measured using helium porosimetry. Additionally, we show that in the case of a lognormal local porosity distribution, the permeability is a function of the geometric mean and the geometric standard deviation of the distribution. This new method will contribute to better evaluation and modeling of vuggy carbonate reservoirs/aquifers for hydrocarbon production, carbon storage, and water resource conservation.