|Publisher||Society of Petroleum Engineers||Language||English|
|Content Type||Journal Paper|
|Title||Estimation of Permeability From Well Logs Using Resistivity and Saturation Data|
|Authors||Salih Saner, Mimoun Kissami, Subhi Al Nufaili, The Research Inst., King Fahd U. of Petroleum and Minerals|
|Journal||SPE Formation Evaluation|
|Volume||Volume 12, Number 1||Pages||27-31|
|Copyright||1997. Society of Petroleum Engineers|
An experimental relationship between permeability, water saturation, and rock resistivity has been suggested. This relationship can be used for interpreting anyone of these three parameters when the other two are known. For example, the relationship can be used in interpreting permeability from resistivity logs when water saturation is known. This study is based on electrical measurements of core samples of different permeabilities.
Brine saturation, Sw, and corresponding rock resistivity, R t, were used together to express the permeability of the rock. To eliminate the brine-resistivity effect, the rock resistivity was represented by an apparent formation factor, Fa, which is the ratio of the partially saturated rock resistivity to the brine resistivity, Rw. It was observed that the apparent formation factor vs. water-saturation curves for samples of different permeabilities were arranged similarly to capillary pressure curves, and each permeability is represented by a unique curve. Therefore, permeability was expressed as a function of the apparent formation factor and the brine saturation. When fractional brine saturation is 1.0, permeability becomes a function of formation factor only.
Water saturation and apparent formation factor are the parameters that can be calculated from well logs. When water saturation and apparent formation factor are known, permeability can be estimated from the suggested relationship. Data points from the oil zone, transition zone, or water zone can be used for computations. Permeability determinations are sensitive to the accuracy of water-saturation data near irreducible water saturations, although at high water saturations, accuracy of resistivity measurements becomes more significant for correct permeability results.
Openhole well logs were used to determine the reservoir parameters. Permeability of a rock is a very important parameter, but its estimation from well logs has not yet been well established. Timur,1 Morris and Biggs,2 and Coates and Dumanoir3 developed methods, which use porosity and irreducible water-saturation data, for sandstone reservoirs. None of these methods can be applied to wells drilled in the water zones. In the present study, a permeability estimation method, which can be applied in water, transition, and oil zones, has been introduced. The method is based on the relationship between permeability, rock resistivity, and water saturation of core electrical data of a carbonate reservoir. This procedure also can be applied to sandstone reservoirs.
Correlation between porosity and permeability for a particular rock type is a basic procedure applied in core-data interpretation. However, this correlation may not always be satisfactory because of pore heterogeneity and pore geometry. Rocks with a similar porosity but different permeability are very common in a reservoir. Carbonate rock data especially show scattering and poor correlation on a permeability vs. porosity plot. Thus, use of the relationship between porosity and permeability is not a favorable method for calculating permeability.
In this study, the correlation between the two flow properties, namely, electrical current flow and fluid flow, was investigated. The fluid-flow property is represented by permeability, and the current flow property is represented by conductivity, which is the reciprocal ofresistivity. Both of these properties are functions of porosity and pore interconnections. When the conductivity or resistivity is concerned, porosity and interconnectivity of pores are represented by a factor known as the formation resistivity factor, F, which is defined as the ratio of 100% brine-saturated rock resistivity, Ro, to brine resistivity, Rw, 4 or the ratio of tortuosity, τ, to porosity, φ:
Resistivity of a partially brine-saturated rock, Rt, is a function of F, brine resistivity, R w, water saturation, Sw, and saturation exponent, n.4
Eg. 2 can be rewritten as
Apparent formation factor, F a, expresses the rock resistivity for any brine saturation.5 This parameter is a constant for each brine saturation and does not change when different salinity brines are used. Fa is defined as the ratio of Rt to Rw:
From Eq. 3 and Eq. 4, the following equation can be derived:
Eg. 5 defines a rational relation of the apparent formation factor (Fa =FS−n w) with respect to Sw , for all rocks having the same F value. For rocks with a different F value, another curve will be defined.
Eg. 5 explains formation factor F as a function of apparent formation factor, Fa, water saturation, Sw, and saturation exponent, n. For a given Rw, if water saturation and rock resistivity are known, then F can be calculated. Because F is a function of porosity and tortuosity, permeability, k , should be a function of F. Eventually, if permeability can be represented as a function of F, it also can be represented as a function of Fa and Swn according to Eq. 5, namely:
After establishing the relationship in Eg. 6, the permeability of a rock can be calculated from resistivity and water-saturation data.
The relationship between k and F was not used directly, because F cannot be calculated from resistivity logs in hydrocarbon zones. Estimation of F from porosity (F=1/φ m) is an indirect method and requires the cementation factor, m, value to be known at each data point.
Laboratory Data Used
An electrical properties study was conducted on 75 core plugs from a Saudi Arabian carbonate reservoir. Helium porosity and gas-permeability measurements of core plugs were conducted under 200 psi confining pressure. Porous-plate air/brine desaturation and four-pole resistivity measurement methods were applied under ambient conditions. Resistivity data at various water saturations were used in applications.
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