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# Estimating permeability considering mineralogy

Several models have been devised to accommodate the influence of mineralogical textures on permeability (*k*). The first two described below are based on the Kozeny-Carman equation; the third uses a network topology that is independent.

## Use of mineral components

Herron^{[1]} uses Kozeny-Carman's equation where surface area is defined as the ratio of pore surface area to grain volume as a starting point for a model using mineralogical abundances in place of specific surface area. He obtains

where *M*_{i} is the weight fraction of each mineral component in the solid rock and *B*_{i} is a constant for each mineral, so that quartz produces high *k* and clay minerals produce low *k*. Mineral abundances are obtained by performing an element-to-mineral transform on data from a logging tool that measures chemical elemental concentrations by means of neutron-induced gamma ray spectroscopy. The coefficient *A*_{f} is a textural maturity indicator; it can be used to reflect the amount of feldspar alteration to clay minerals. Nelson^{[2]} gives further details on the model.

## Grain-size sorting

Panda and Lake^{[3]} extended the Kozeny-Carman expression to include the effect of grain-size sorting. They assume a sandpack of spherical grains having a log-normal distribution of grain diameters *d*, characterized by:

- Mean diameter
- Standard deviation
- Skewness

Their expression is based on **Eq. 1**, substituting Σ_{g}=6/*D* and incorporating an additional term including standard deviation and skewness. With the additional term accounting for sorting, their extended model agrees well with Beard and Weyl’s data for sandpacks but overpredicts k in consolidated sandstones. To make the model applicable to consolidated sandstones, three types of cement filling the pore space were considered^{[4]}:

- Pore-bridging
- Pore-lining
- Pore-filling cement

Their resulting equation for k includes the sum of surface areas contributed by each of the cement geometries and a tortuosity factor that is a function of cement type, as well as statistical terms describing the log-normal distribution of grain diameters *d*.

## Simulation of quartz system

Bryant *et al.*^{[5]} and Cade *et al.*^{[6]} performed numerical modeling on a pack of (initially) equally sized spheres in a geometry based on a laboratory random pack. Permeability is computed directly by considering flow across the faces of individual linked tetrahedra; thus, the method is independent of the Kozeny-Carman equation. Their method simulates a quartz system in which all surfaces participate in compaction and cementation processes, causing *k* and *Φ* to decrease along a characteristic curve in log(*k*)-*Φ* space. At some point in this process, clay minerals are introduced in grain-rimming or pore-filling geometries, and k decreases more sharply with a continuing decrease in *Φ*. The resulting computed curve in log(*k*)-*Φ* space tracks the effects of progressive diagenesis of a single pack as burial progresses.

## References

- ↑ Herron, M.M. 1987. Estimating the Intrinsic Permeability of Clastic Sediments From Geochemical Data. Presented at the SPWLA 28th Annual Logging Symposium, 1987. SPWLA-1987-HH.
- ↑ Nelson, P. 1994. Permeability-porosity relationships in sedimentary rocks. The Log Analyst 35 (3): 38–62.
- ↑ Panda, M.N. and Lake, L.W. 1994. Estimation of Single-Phase Permeability From parameters of Particle-Size Distribution. American Association of Petroleum Geologists Bull. 78 (7): 1028-1039.
- ↑ Panda, M.N. and Lake, L.W. 1995. A Physical Model of Cementation and Its Effects on Single-Phase Permeablity. American Association of Petroleum Geologists Bull. 79 (3): 431-443.
- ↑ Bryant, S., Cade, C., and Mellor, D. 1993. Permeability Prediction From Geologic Models. American Association of Petroleum Geologists Bull. 77 (8): 1338-1350.
- ↑ Cade, C.A., Evans, I.J., and Bryant, S.L. 1994. Analysis of Permeability Controls: A New Approach. Clay Minerals 29 (4): 491-501. http://dx.doi.org/10.1180/claymin.1194.029.4.08

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