Variation of Permeability with Porosity in Sandstone Diagenesis Interpreted with a Fractal Pore Space Model

Abstract

Permeability is one of the key rock properties for the management of hydrocarbon and geothermal reservoirs as well as for aquifers. The fundamental equation for estimating permeability is the Kozeny-Carman equation. It is based on a capillary bundle model and relates permeability to porosity, tortuosity and an effective hydraulic pore radius which is defined by this equation. Whereas in clean sands the effective pore radius can be replaced by the specific surface or by the grain radius in a simple way, the resulting equations for permeability cannot be applied to consolidated rocks. Based on a fractal model for porous media, equations were therefore developed which adjust the measure of the specific surface and of the grain radius to the resolution length appropriate for the hydraulic process. These equations are calibrated by a large data set for permeability, formation factor, and porosity determined on sedimentary rocks. This fractal model yields tortuosity and effective pore radius as functions of porosity as well as a general permeability-porosity relationship, the coefficients of which are characteristic for different rock types. It can be applied to interpret the diagenetic evolution of the pore space of sedimentary rocks due to mechanical and chemical compaction with respect to porosity and permeability.

Influence of depth, temperature, and structure of a crustal heat source on the geothermal reservoirs of Tuscany: numerical modelling and sensitivity study

“…Laboratory measurements show that the permeability of flysch and sandstones is highly variable and depends on porosity, clay content, micro-fractures, and cementation (observed values range between 10 −12 and 10 −19 m 2 (e.g. Hajto 2015;Pape et al 2000)). The Ligurian units in Tuscany show low permeabilities and are known to act as aquicludes (e.g.…”

A Fractal Permeability Model Coupling Boundary-Layer Effect for Tight Oil Reservoirs

“…Equation (25) shows that the slope of lg K and φ is dependent on tortuosity fractal dimension D T . Therefore, for the porous media with the same D T , the slope of lg K and φ should be same.…”

“…21,22 Fractal theory has been widely used for predicting permeability of porous media. [23][24][25][26][27] Yu and Cheng 24 developed a fractal permeability model for bi-disperse porous media, and fractal dimension and tortuosity fractal dimension were determined with boxing-counting method. Xu and Yu 26 developed the constant for the Kozeny-Carman (KC) equation based on fractal characteristics of porous media and capillary model.…”

Using BIB-SEM Imaging for Permeability Prediction in Heterogeneous Shales

“…By choosing a tortuosity of = 10 a good fit between intrinsic and calculated permeability could be established. Values of around 5 to 10 are commonly used for permeability predictions in very tight rock samples that are strongly lithified and feature very lowporous rock fabrics (e.g., [71,[74][75][76][77]), though one should be careful as different notations of the CTM exist in the literature (regarding versus 2 ). For validating the BIB-SEM based permeabilities, the results are compared to the experimentally derived permeabilities measured on the exact same sample plugs.…”