Permeability-Porosity Relation and Preferential Flow in Heterogeneous Vuggy Carbonates

The present study investigates fluid flows and permeabilities through vuggy carbonates via a single-phase fluid-flow experiment and a numerical model simulation using X-ray CT. 3D imaging of flow paths in vuggy carbonate samples reveals that fluid flows through vuggy carbonates are generally characterized by the formation of preferential flow paths due to heterogeneous porosity distributions within the rocks. Only a part of pores (typically <50% of the total pore volume) effectively contributes to the flow, while the other pores contain stagnant fluids. Histograms of local porosity for all samples are characterized by lognormal distributions with different geometric mean, m_φ (fraction), and standard deviation, σ_φ, values, depending on the heterogeneities of the rocks. Percentage of the pore volume that effectively contributes to the flow over the total pore volume, V_F, which results from the formation of preferential flow paths, linearly decreases with increasing the geometric standard deviation, i.e. intensity of formation of vug pores or spatial correlation of pores: V_F = -155σ_φ + 255. Global permeabilities of the samples are not related to their He porosities, unlike those of non-vuggy carbonates, because of the fact that a part of pores contributes to the flows. In case of vuggy carbonates, the global permeability, K (m²), is a function of both the geometric mean and standard deviation values, where the larger geometric mean and standard deviation values are, the higher the global permeability is. A new permeability-porosity relation of vuggy carbonates, in addition to the existing class I-III relations of non-vuggy carbonates, namely class IV (four) relation is found to be described as K = 4.573×10^-10 Φ_IV^7.77, where Φ_IV = m_φ × σ_φ² is a modified fractional porosity for vuggy carbonates having Interparticle and Vug (IV) porosities. This equation implies that the global permeability is higher for vuggy carbonates having more spatially correlated (σ_φ) larger pores (m_φ × σ_φ).