FACTORS AFFECTING ABSOLUTE PERMEABILITY







1 (4.54)

where

k_gas is the measured gas permeability

k_liquid is the equivalent liquid permeability or the Klinkenberg-corrected liquid permeability

m is the slope of the straight-line fit

P_mean=(P₁+P₂) /2=mean pressure

It should be noted that in Equation 4.54, the slope of the straight-line fit is a con-stant or a specific value valid for a given gas in a given porous medium; that is, the straight-line fit cannot be generalized. However, the straight-line fit can be used for determining the equivalent liquid permeability when gas permeabilities are mea-sured at other pressure conditions.

4.9 FACTORS AFFECTING ABSOLUTE PERMEABILITY

A number of factors affect the absolute permeability of a reservoir rock. The discus-sion of these factors clearly categorizes and subsequently reviews each factor which can be grouped as rock-related factors, fluid phase-related factors, thermodynamic factors, and mechanical factors:

• Rock-related factors are basic characteristics, structure, or indigenous prop-erties of reservoir rocks, such as grain size and shape and clay cementing.

These can in fact also be termed natural factors.

• The type of fluid medium (i.e., gas/brine/water) used for permeability mea-surement as well as the physical and chemical characteristics of these fluids are also major factors that affect the absolute permeability. These factors can be characterized as artificial or laboratory factors that may temporar-ily affect permeability.

• The thermodynamic factors affecting absolute permeability basically con-sist of temperature effects, and as seen later, based on some literature data, these fall under the category of fluid–rock interaction-induced laboratory artifacts that affect permeability.

• The mechanical factors are related to the effect of mechanical stresses or confining pressures on absolute permeability and also fall under the cat-egory of laboratory artifacts.

4.9.1 ROCK-RELATEDFACTORS

Before discussing the effect of rock-related factors on absolute permeability, revert to Figure 2.1 to consider horizontal and vertical permeabilities. As seen in this figure,

59 Absolute Permeability

core plug samples are normally drilled from the whole core in the horizontal direc-tion, also parallel to the bedding planes. Therefore, permeability measured on such plug samples is called horizontal permeability or k_h. If plugs are drilled along the long axis of the whole core, these samples are perpendicular to the bedding planes and hence yield what is called vertical permeability or k_v.

Horizontal permeability is significant from a conventional well (vertical) pro-duction point of view because fluids flow parallel to the bedding planes in a hori-zontal direction toward the well bore, creating a natural pressure drop as fluids are produced. Vertical permeability is important when dealing with horizontal wells because fluids flow perpendicular to the bedding planes, or in series, toward the well bore, creating a natural pressure drop as reservoir fluids are produced.

Horizontal and vertical permeabilities are greatly impacted by the grain size and shape. In order to understand the effect of grain shape on horizontal permeability, a hypothetical porous medium that consists of uniformly arranged, identically shaped large grains, as shown in Figure 4.11, is considered. This figure clearly shows that k_h≈ kv; that is, if the rock is primarily composed of large and uniformly rounded grains, its permeability is of the same order in both directions because flow paths are somewhat similar. However, if the grains in Figure 4.11 are now altered to uniformly arranged flat grains, as shown in Figure 4.12, then obviously the horizontal permea-bility is greater than the vertical permeapermea-bility because the former is characterized by a relatively unrestricted flow path, whereas relatively restricted or tortuous path char-acterizes the latter. Most reservoir rocks generally have much lower permeabilities in the vertical direction compared to the horizontal permeabilities because grains are small and irregularly shaped. Additionally, reality is much different compared to the hypothetical cases shown in Figures 4.11 and 4.12; most reservoir rocks will be

Flow signifying k_h

Flow signifying k_v

FIGURE 4.11 Schematic representation of a hypothetical porous medium consisting of uniformly arranged, identically shaped large grains (k_h≈ kv).

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composed of a wide variety of grain sizes and shapes, which is described by grain sorting. Poorly sorted (large variation in grain sizes and shapes) reservoir rocks result in lower porosities as well as lower permeabilities because smaller grains will tend to “fill up” or occupy the void spaces between larger grains, thereby degrading the rock quality. However, well-sorted reservoir rocks will generally result in larger void spaces in between, thereby increasing the porosity as well as permeability.

Clay cementing affects both the reservoir rock porosity and permeability because clay cementing basically coats or increases the grain size. This increase in the grain size obviously reduces the pore space and also alters the flow paths by constriction.

4.9.2 FLUID PHASE-RELATEDFACTORS

These are factors that consist of the physical or chemical characteristics of the fluid that affect the absolute permeability. One such factor already addressed is related to the use of gases in permeability measurement—the Klinkenberg effect. Other fluid-related factors are connected with the use of brine and degassed crude oil for permeability measurement.

Although water is generally considered as nonreactive in an ordinary sense, it can have significant impact on permeability, especially for those reservoir rocks that contain clays that swell after coming in contact with water. Clay swelling of course depends on the type of clay minerals present in the reservoir rock. The ion exchange between water and clay minerals is principally responsible for clay swell-ing and enlargement. It is well known that kaolinite and illite are nonswellswell-ing clays;

montmorillonite is a common swelling clay, according to Zhou et al.⁷ Permeability reduces as a result of clay swelling. This particular reduction in the absolute per-meability is also sometimes termed formation damage. Although it is not really a mechanical damage, it is rather a pore network alteration. Although reactive liquids such as brine swell a clay and alter the internal geometry of the porous medium, they do not vitiate Darcy’s law but basically create a new porous medium with perme-ability characterized by the new internal geometry.

Another scenario of permeability reduction is related to mixing incompatible waters in pore spaces of a reservoir rock. For example, incompatibility of forma-tion waters and waters of different salinities, such as seawater, may result in salt precipitation as solubility limits of some of the salt components are exceeded

Flow signifying k_h

Flow signifying k_v

FIGURE 4.12 Schematic representation of a hypothetical porous medium consisting of uni-formly arranged, identically shaped, large, flat grains (k_h > k_v).

61 Absolute Permeability

when certain pressures and temperatures are reached. If salt deposition takes place in the pore spaces, it may again alter the internal geometry of the porous medium, usually resulting in a reduction in permeability. This type of permeabil-ity reduction is also termed formation damage, in the usual petroleum engineer-ing terminology.

This formation damage is greatly significant when water injection (e.g., sea-water) is considered as a potential enhanced oil recovery method. Review of exist-ing literature on formation damage indicates a value of k_final/k_initial (k_seawater/k_brine) as 0.1 in Wojtanowicz et al.⁸ 0.001 in Sarkar and Sharma,⁹ and as low as in the range of 0.01–4.0 × 10⁻⁰⁵ in Gruesbeck and Collins.¹⁰ In the core flooding experiments performed in Bertero et al.¹¹ on three different sandstone cores with porosities in the range of 12.6%–15.0% and air permeabilities in the range of 4–262 mD, permeability reduced by 50% when the scale precipitation volume was more than 1% of the pore volume.

Care should be taken when using degassed crude oil to ensure that core flooding tests for permeability measurement are carried out at high temperatures (preferably reservoir temperatures) because paraffin (wax) deposition may also take place in the pore spaces if a very waxy crude oil is used as a fluid medium at room temperatures.

However, if wax deposition does take place in the pore spaces, this might alter the internal geometry of the pore network temporarily because the deposited wax can always be removed by using high temperatures.

4.9.3 THERMODYNAMICFACTORS

This review of the effect of thermodynamic factors on absolute permeability is restricted to a discussion on literature data based on the investigation of temperature effects on absolute permeability. Although, in an ordinary sense, if the same liquid is used in the experiments but at varying temperatures, ideally temperature should not have any effect on the absolute permeability because varying temperature only affects liquid viscosity (increase in viscosity when temperature decreases and vice versa), which in turn affects the differential pressure. Note the ratio of ΔP/μ is always nearly constant (see Equation 4.7). However, some researchers^12,13 have indicated that the absolute permeability to water for confined sandstones is strongly temperature dependent.

Grunberg and Nissan¹² reported that core temperatures varied from 6°C to 30°C, in which case absolute permeability decreased by a ratio of 0.8 mD/°C. Aruna¹³ reported a reduction in absolute permeability of up to 60% over a temperature range of 21.1°C–149°C. However, it should be noted that the absolute permeability of sand-stones to other fluid mediums (nitrogen, mineral oil, octanol) was reported to have almost no effect of temperature.¹³ Aruna¹³ concluded that water–silica interactions were responsible for the major effects observed with water.

4.9.4 MECHANICALFACTORS

Mechanical factors effecting absolute permeability include the magnitude of over-burden or confining pressure used when flow experiments are carried out. Generally,

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absolute permeability is inversely proportional to overburden pressure because core samples are compacted due to overburden and fluid flow through such samples is rather squeezed, resulting in a reduction in absolute permeability.

One of the most notable outcomes in this area was first reported by Fatt and Davis¹⁴ in 1952, which presented their results on sandstone samples from various formations in North America. Their results indicated a reduction in absolute perme-ability by as much as 60% for some formation samples, when comparing the values between 0 and 15,000 psi confining pressure, expressed as k_{15,000 psi}/k_{0 psi} = 0.4.

In addition to the work of Fatt and Davis,¹⁴ a number of other researchers have shown similar results reviewed in the work of Aruna.¹³ Most of the results indicate that generally speaking, the higher the permeability, the higher the per-centage of reduction. This is also clearly evident from results reported by Putra et al.¹⁵ and Dandekar.⁴ Putra et al. presented absolute permeability measurements for a fractured as well as unfractured Berea sandstone; Dandekar’s⁴ results are on absolute permeability of two North Sea chalk (carbonate) samples at over-burden pressures of 500, 1000, and 1500 psi. These results are shown in Figure 4.13, which indicates a marginal reduction in the absolute permeability when overburden pressure is increased from 500 to 1500 psi for both the unfractured Berea sandstone and the two chalk samples. However, a substantial reduction in the absolute permeability is evident from the results for the fractured Berea sandstone. Most routine and special core analysis tests are usually carried out by applying the representative overburden or confining pressure that is determined from the sample depth and reservoir pressures.

0

250 450 650 850 1050 1250 1450 1650

Overburden pressure, psi

Permeability of North Sea chalk, mD Unfractured Berea

Fractured Berea North Sea chalk 1 North Sea chalk 2

FIGURE 4.13 Effect of overburden pressure on absolute permeability. (Berea sandstone data are from Putra, E. et al., Saudi Aramco J. Technol., 57, 2003; North Sea chalk data are from Dandekar, A.Y., Unpublished data, 1999.)

63 Absolute Permeability