Rock type influence on permeability

Permeability values of rocks range over many factors of 10; therefore, permeability is plotted on a logarithmic scale. Values commonly encountered in petroleum reservoirs range from a fraction of a millidarcy to several darcies. This page discusses factors affecting permeability associated with different rock types.

Variability with rock type

The log₁₀(k)-Φ plot of Fig.1 shows four data sets from sands and sandstones, illustrating the reduction in permeability and porosity that occurs as pore dimensions are reduced with compaction and alteration of minerals (diagenesis). In these examples:

• k of newly deposited beach sands exceeds 30 darcies
• k of partially consolidated sandstones ranges from 300 to 2,000 md
• k of consolidated sandstones ranges from 0.01 to 100 md
• k of tight gas sandstones is <0.01 md

Porosity is reduced from a maximum of 52% in newly deposited sandstones to as low as 1% in consolidated sandstones. In this page, some of the causes of variability in log₁₀(k)-Φ space are examined.

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  Fig. 1 – Permeability/porosity plot showing newly deposited beach sands and three sample suites from wells in oil and gas fields. Permeability scale ranges from 1,000 darcies to 0.1 μd.

The permeability and porosity of a rock are the result of both depositional and diagenetic factors (Fig. 2) that combine to produce a unique set of pore space geometries as the rock is formed. Consequently, the heavy line in Fig. 2 represents only one of many possible evolutionary paths in log(k)-Φ space. First, consider the depositional factors. Better sorting increases both k and Φ. Gravel and coarse grain size produce anomalously high k even though decreasing Φ. Very fine grains of silt and detrital clay produce low permeability at high porosity. High quartz content can produce efficient systems having good permeability even at low porosity, whereas sandstones with feldspar or lithic grains may develop significant noneffective porosity content. Diagenetic effects, starting with compaction and followed by cementation and alteration of depositional minerals to clays, tend to decrease log(k) proportionately as Φ is decreased. Several examples are presented to illustrate these controls.

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  Fig. 2 – Sketch of the impact of primary depositional features (such as quartz content and sorting, in italics) and diagenetic processes (such as compaction and cementation) on permeability/porosity trends in sandstones.

In newly deposited sands and poorly consolidated sandstones, grain size correlates well with pore size and hence is a primary control on permeability. Grain size ranges for sandstones are defined by factors of two (Fig. 3). For example, a sand with grain diameters between 250 and 500 μm is classed as a medium-grained sand. The sedimentological phi scale provides a convenient label to the size classes, and D=2^-phi is the grain diameter in mm (for example, 2^-3=0.125 mm=125 μm). Also shown in Fig. 3 are size ranges for various types of carbonates. Note that grain diameters can be as large as 2,000 μm in very coarse-grained sands and as small as 1 μm in chalks.

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  Fig. 3 – Grain size categories in sandstone, limestone, and dolostone. Sedimentological scale (phi scale) is logarithmic in powers of two. Grain diameter (d) (crystal size in case of dolostones) is given in micrometers. Limestone and dolostone classes are from Lucia; chalk data are from Mortensen et al. See discussion above for explanation of vertical bars showing grain and pore throat sizes in a consolidated sandstone.

Unconsolidated sandpacks

One laboratory study deserves examination because it illustrates the relationships among grain size, sorting, k, and Φ. Using sand from two Texas rivers, Beard and Weyl sieved 48 sand samples into 8 size classes and 6 sorting classes. Each data point shown in Fig. 4 represents the permeability and porosity of a sample with a unique grain size and sorting. Median grain size ranges from 0.840 mm for the coarse sample to 0.074 mm for the very fine sample. The authors present photomicrographs of thin-section comparators for each of the 48 samples to document the wide range of size and sorting represented by the sample suite. The maximum permeability value for a well-compacted, unconsolidated sandpack is about 500 darcies. Porosity ranges from 23.4% to 43.5%. Note:

• There is a general increase in permeability as grain size increases from very fine to coarse
• Both porosity and permeability increase as sorting progresses from very poor to well sorted

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  Fig. 4 – Permeability/porosity data from unconsolidated artificial sandpacks by Beard and Weyl. Symbols linked with solid lines denote size ranges; dotted lines distinguish sorting classes.

Consider the extremely well-sorted samples represented by the open-circle data points along the right-hand edge of Fig. 4. For these extremely well-sorted samples, porosity is independent of grain size, as it should be for a packing of uniform spheres. However, for those samples that are not well sorted, an increase in coarse grain content results in somewhat decreased Φ even as k increases. This pattern is preserved in some consolidated samples. The extremely well-sorted samples of Fig. 4 also show that log(k) increases in equal increments as grain size increases. The samples were sized so that the mean grain diameter of each adjacent size interval increases by the square root of 2. Permeability increases by a factor of 2 for each increment of grain size. Thus, Beard and Weyl’s data show that permeability is proportional to the square of grain size. Because theoretical models show that flow is proportional to the square of the radius of a pore opening, it can be said that Beard and Weyl’s data demonstrate that pore size is proportional to grain size in sandpacks.

Clays and shales

The permeability of shales and mudstones determines the effectiveness of seals for many hydrocarbon reservoirs, but measurements are few. Neuzil compiled data sets from 12 laboratory studies and 7 field studies that provided ranges of permeability and porosity data in:

• Bottom muds
• Clay
• Unconsolidated sediment
• Glacial till
• Clayey siltstone and sandstone
• Claystone
• Mudstone
• Argillite

Permeability is as high as 1 md in unconsolidated sediment with 70% porosity and as low as 0.01 nanodarcy (nd) in argillite with 5% porosity. With few exceptions, permeability ranges over 3 factors of 10 at a given porosity and decreases progressively as porosity decreases. For example, at a porosity of 20%, permeability ranges from 0.1 μd to 0.1 nd, a range well below the lower limit of k plotted in Fig. 1. Although it was expected that permeability would be scale dependent in clays and shales (regional permeability would be greater than laboratory sample permeability because of fractures), it was found that permeability ranges from the field studies are roughly the same as the laboratory studies, thereby indicating a lack of scale dependence.

Sandstones

Thomson describes continental sandstones from the Lower Cretaceous Hosston formation in Mississippi (Fig. 5) : "Secondary quartz cement and compaction through pressure solution of grains are the principal causes of porosity reduction. The early introduction of large amounts of dolomite has inhibited compaction of framework grains. Kaolinite ranges from 5% to 15% of total rock volume. All samples contain a little illite. The permeability/porosity plots indicate a progressive and uniform loss of permeability as porosity is reduced, suggesting that the sandstones underwent a simple diagenetic history, uncomplicated by such late processes as leaching, development of authigenic clay minerals, and so forth." Thomson also suggests that the introduction of hydrocarbons caused a cessation in diagenesis in the lower part of the reservoir. The effect of grain size remains apparent in the data of Fig. 5, although diagenetic effects have blurred the separations seen in Fig. 4, so some of the medium-grained samples have k as low as in the very fine-grained samples.

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  Fig. 5 – Permeability/porosity data from the Lower Cretaceous Hosston Sandstone from Thomson.

Permeability in Oligocene-Miocene sandstones ranges from <1.0 to >1,000 md (Fig. 6) . Bloch reports that the sandstones were deposited in a variety of environments and that lithology ranges from lithic arkoses to feldspathic litharenites, meaning that 25% or more of the primary grain composition is either lithic fragments or feldspar grains. Up to 30% of porosity is secondary porosity, formed by dissolution of potassium feldspar. Because permeability is >1 darcy at porosity values <20%, the secondary porosity is probably well connected and contributing to flow. Although the samples with coarsest grain sizes tend to have the highest permeability values, the symbols depicting different grain sizes are intermixed, another indication that secondary porosity is contributing to flow.

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  Fig. 6 – Permeability/porosity data from Oligocene and Miocene sandstones from Bloch.

Bos describes results from an exploration well that encountered:

1. Clean sandstone
2. Sandstone with pores filled with kaolinite
3. Laminated sandstone, part clean and part filled with kaolinite (indicated as "laminated" in Fig. 7)
4. Shale

Scanning electron microscope photographs document the extent to which kaolinite fills the pores, thereby reducing k as shown in Fig. 7. Here again we see a linear relationship between log(k) and Φ, with pore-infilling clays reducing both k and Φ in a fairly systematic fashion.

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  Fig. 7 – Permeability/porosity data from a Lower Cretaceous sandstone from the North Sea from Bos.

Wilson contends that many clay coatings, particularly on eolian sandstones, formed on the framework grains before deposition. Their presence actually preserves porosity because quartz overgrowths cannot readily form. According to Wilson, many of the largest petroleum reservoirs (North Sea, North Slope of Alaska) have retained good porosity because of detrital clay coatings. Samples in which kaolinite and illite occur as clay coatings fall within the boundaries of the three upper fields in Fig. 8. However, fibrous illite can form within the pore space in the Rotliegend sandstones (lower two fields in Fig. 8), reducing the permeability one to two orders of magnitude compared with rocks in which clay occurs as grain coatings. Under the scanning electron microscope, the appearance of numerous fine strands of illite within pores makes it obvious why permeability is so impaired. Special core preparation techniques are required to preserve clay textures so that laboratory measurements reflect the in-situ permeability values.

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  Fig. 8 – Permeability/porosity data fields from wells penetrating the Permian (Rotliegend) sandstones of the southern North Sea, measured at ambient conditions, from Wilson.

Carbonates

Samples from an oil-productive dolomite facies in the Williston basin of North Dakota were characterized in terms of the size of dolomite grains. Originally deposited as a carbonate mud, after burial this facies was altered to a sucrosic dolomite or calcareous dolomite with good intercrystalline porosity. At any given porosity, samples with the larger dolomite crystal sizes have the highest permeability (Fig. 9). At a given crystal size, an important control on porosity is the amount of calcite, which is believed to be recrystallized lime mud. Vuggy porosity is 5% or less. Different productive zones in the same field may have different dolomite textures, suggesting that original sediment texture and chemistry were the main factors determining the distribution of crystal sizes.

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  Fig. 9 – Permeability/porosity data from a sucrosic dolomite in the Williston basin of North Dakota, from Petty.

In the North Sea, oil is produced from Cretaceous and Tertiary chalks, even though permeability is <10 md (Fig. 10) . From measurements of specific surface area, the equivalent grain diameter is computed to range from 1.0 to 2.7 μm. As indicated in Fig. 10, the separation between the two chalks is attributed to specific surface area, which is higher in the lower-permeability Danian samples than in the Maastrichtian samples. The addition of pore space produces modest gains in permeability (low slopes for the two data sets in Fig. 10), from which one can infer that a significant fraction of the pore space is poorly connected or of very small size. Mortensen et al. conclude that the intrafossil porosity behaves the same, in terms of flow, as interparticle porosity.

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  Fig.10 – Permeability/porosity data from two chalk reservoirs of Cretaceous (Maastrichtian) and Paleocene (Danian) age, from Mortensen et al.

Lucia found a size effect in limestones and dolostones, as evidenced by dolostone data shown in Fig. 11. To obtain petrophysically viable groupings, Lucia grouped all dolomitized grainstones with mud-dominated samples having large dolomite crystals and grouped dolomitized packstones with mud-dominated samples having medium-sized dolomite crystals (key in Fig. 11). He suggests that the plot can be used to estimate permeability of a nonvuggy carbonate rock if the porosity and particle size are known. He points out that the effect of vugs is to increase porosity but not alter permeability much. In Fig. 11 we can see the quasilinear log(k)-Φ relationship and the decline in slope (and k ) with decreasing grain size. It appears that the fundamental controls observed in the sandstones are also present in these selected carbonates, if care is exercised in categorizing the carbonates in terms of grain or crystal size.

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  Fig. 11 – Permeability/porosity data and classifications for selected nonvuggy dolostones from Lucia.

Empirical trends

Figs. 5 through 11 exhibit a linear or piecewise-linear relationship between log(k) and Φ as determined in many consolidated sandstones and in carbonates if care is taken to isolate rock types. Such linear trends are often seen in samples from an individual rock unit or formation. These trends have the general form of

....................(1)

Eq. 1 is strictly an empirical relationship between log(k) and Φ. It is useful when data from an area of interest are available because log(k) can be predicted simply from Φ. However it masks the dependence of log(k) on pore throat size and thereby obscures the physics of flow in porous media, as is shown in Single phase permeability models based on grain size.

Nomenclature

k	=	permeability
Φ	=	porosity

Noteworthy papers in OnePetro

Use this section to list papers in OnePetro that a reader who wants to learn more should definitely read

External links

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See also

Single phase permeability

Rock types

Permeability determination

Porosity determination

Lithology and rock type determination

PEH:Single-Phase_Permeability