Estimation of Single-Phase Permeability from Parameters of Particle-Size Distribution

The single-phase permeability of a permeable medium is determined by both the bulk physical properties of the interconnected pore system (e.g., porosity and tortuosity) and the statistics of its particle-size distribution (psd). An expression of the relation between permeability and pore-level properties is the Carman-Kozeny (CK) equation. This equation has historically been used to explain the fundamental causes of permeability because it provides a link between media attributes and flow resistance. Because the CK equation has not been applied to media consisting of mixed particle sizes, we modify the CK equation to express the single-phase permeability of unconsolidated media in terms of both the psd statistics and the bulk physical properties. We find that we can relate permeability to the parameters of a psd for unconsolidated media. This relationship matches published data. It generally fails for permeabilities less than 1 µm2 (~1 darcy), probably because not all of the pore space is supporting flow in this region. With the model partially verified by experimental data, we use it to investigate the nature of permeability-porosity relationships and of the origin of variability in permeability. The latter capability will explain many of the permeability differences observed in outcrop studies.

[1]  H. Brinkman,et al.  On the permeability of media consisting of closely packed porous particles , 1949 .

[2]  J. W. Amyx,et al.  Petroleum reservoir engineering , 1960 .

[3]  Larry W. Lake,et al.  A review of heterogeneity measures used in reservoir characterization , 1989 .

[4]  Chi Tien,et al.  A new model for granular porous media: Part I. Model formulation , 1973 .

[5]  J. Bear.  Dynamics of Fluids in Porous Media , 1975 .

[6]  L. Lake,et al.  Enhanced Oil Recovery , 2017 .

[7]  S. Bryant,et al.  Permeability Prediction from Geologic Models , 1993 .

[8]  Arthur W. Rose,et al.  Porous media: Fluid transport and pore structure (2nd Ed.) , 1993 .

[9]  W. C. Krumbein,et al.  Application of logarithmic moments to size-frequency distributions of sediments , 1936 .

[10]  Donald L. Katz,et al.  Flow of Gases through Consolidated Porous Media , 1953 .

[11]  B. Zinszner,et al.  Hydraulic and acoustic properties as a function of porosity in Fontainebleau Sandstone , 1985 .

[12]  P. K. Weyl,et al.  Influence of Texture on Porosity and Permeability of Unconsolidated Sand , 1973 .

[13]  W. C. Krumbein,et al.  Permeability as a Function of the Size Parameters of Unconsolidated Sand , 1943 .

[14]  G. A. Muccini,et al.  Characteristics of porous beds and structures , 1956 .

[15]  L. Lake,et al.  Effects of stratigraphic heterogeneity on permeability in eolian sandstone sequence, Page Sandstone, northern Arizona , 1989 .

[16]  Adrian E. Scheidegger,et al.  The physics of flow through porous media , 1957 .

[17]  J. Doob.  Stochastic processes , 1953 .

[18]  P. Carman,et al.  Flow of gases through porous media , 1956 .