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Archie Saturation Equation

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Archie’s Saturation Equation

• Objectives– Review Archie’s experiments

• Effects of changing water filled volume• Effects of changing water saturation• Effects of changing water salinity

– Review several ways of using Archie’s equation• To compute formation water saturation• To compute formation water resistivity• To forecast formation resistivity

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FormationWater only

Ohm Meter

φ = 100%Sw = 100%

Cube 1 filled with Formation Water

Rt = Rw

∞ 0

Archie’s Experiment

Voice Over TextThe basis for all initial interpretations of logging data collected via Wireline or LWD is the empirically derived equation known as Archie’s equation. This empirical formula is used to estimate water saturation in a reservoir using formation Resistivity, porosity and formation water Resistivity. To explain the Archie’s equation a cube is used as a model so that the reading is directly calibrated to Resistivity as explained in the previous section. In the first experiment the cube was filled with formation water. The porosity was 100% since there was no rock in the cube. The water saturation was 100% since all the available pore space was filled with formation water. Under such conditions the measured cube Resistivity was the same as formation water Resistivity.

Screen TextArchie’s equation is the basis of all initial interpretations of logging data. This empirical formula is used to estimate SW in a reservoir using Rt, Φ and RW. To explain theArchie’s equation a cube is used as a model so that the reading is directly calibrated to Resistivity, as explained in the previous section. In the first experiment the cube was filled with formation water. The Φ was 100% since there was no rock in the cube. The SW was 100% since all the available pore space was filled with formation water. Under such conditions the measured cube Resistivity (Rt) was the same as RW.

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Ohm Meter

φ = 70%Sw = 100%

Cube 2 filled with Formation Water & Sand

Rt > Rw

Rock Matrix

Formation Water

φ

∞ 0

Archie’s Experiment

Rt ∝ 1/ φ2

with Sw = constant.

Voice Over Text

In the second experiment sand was added to the cube so that the porosity was 70%. The water saturation was still 100% as there were no hydrocarbons in the cube. The measured cube Resistivity was found to be higher than the formation water Resistivity since the conductive water was replaced by non-conductive sand. By varying the porosity it was found that the Resistivity reading varied inversely to the square of the porosity.

Screen Text

In the second experiment sand was added to the cube so that the Φ was 70%. The SWwas still 100% as there were no hydrocarbons in the cube. The measured cube Resistivity (Rt) was found to be higher than RW since the conductive water was replaced by non-conductive rock. By varying the Φ it was found that Rt ∝ 1/ Φ2 with Sw= constant.

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Ohm Meter

φ = 70%Sw = 50%

Cube 3 filled with Formation Water, Sand & Oil

Rt > Rw

Rock Matrix

Formation Waterφ

∞ 0

Hydrocarbon

Sw

Sh

Archie’s Experiment

Rt ∝ 1/ Sw2

with φ = constant.

Voice Over TextIn the third experiment half the water from the previous experiment was replaced with oil. This resulted in an unchanged porosity of 70% and the water saturation of 50% since half the pore space is now occupied by oil. The Resistivity reading was found to be higher than the Rt from the previous experiment since half the conductive water was replaced by non-conductive oil. By varying the amount of water saturation with afixed porosity it was found that the Resistivity reading varied inversely to the square of the water saturation.

Screen TextIn the third experiment half the water from the previous experiment was replaced with oil. This resulted in an unchanged Φ of 70% and the Sw of 50% since half the pore space was now occupied by oil. The measured cube Resistivity (Rt) was found to be higher than the Rt from the previous experiment since half the conductive water was replaced by non-conductive oil. By varying the Sw it was found that Rt ∝ 1/ Sw

2 with Φ= constant.

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Ohm Meter

φ = 70%Sw = 50%Rw reduced

Cube 4 filled with Formation Water, Oil & Sand

Rt reduced

Rock Matrix

Formation Waterφ

∞ 0

Hydrocarbons

Sw

Sh

Salinity increased

Archie’s Experiment

Rt ∝ Rwwith Sw, φ = constant

Voice Over TextIn the fourth experiment the salinity of the formation water was increased by adding some salt to it, resulting in a reduced formation water Resistivity. By varying the salinity and holding the porosity and water saturation constant it was found that the measured cube Resistivity was directly proportional to the formation water Resistivity.

Screen TextIn the fourth experiment the salinity of the formation water was increased by adding some salt to it, resulting in the reduced Rw. By varying the salinity, it was found that Rt∝ Rw with Sw ,Φ = constant.

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Generalized Archie’s Equationa Rw

φm Swn

Rt =

Archie’s Equation

Rw

φ2 Sw2

Rt = 1 Rw

φ RtSw =

Rt ∝ 1/ φ2 with Sw = constant.Rt ∝ 1/ Sw

2 with φ = constant.Rt ∝ Rw with Sw, φ = constant

Archie’s Experiment: Conclussions

Rw =φm Sw

n Rt

a

a Rw

φm Rt

Swn =

Voice Over TextThus the Archie’s equation was developed. Since it was developed in 1942, petrophysicistshave tested this equation by repeating the experiments for almos t every conceivable rock type. While Archie’s equation held true for most non-shaly formation types, their experiments showed that it needed to be updated for variables such as cementation, tortuosity, granular shape and size. Thus the generalized Archie’s equation was proposed for non-shaly formation types, where “A” is the local correction factor to take into account a myriad of variables that can affect a formation at a given location. “M” is the cementation factor which represents how the grains in a formation are held together. It also varies based on local formation characteristics.“N” is the saturation exponent. The values of A, M and N can be found experimentally from log data and core analysis.

Screen TextThus the Archie’s equation was developed. Since it was developed in 1942, petrophysicistshave tested this equation by repeating the experiments for almos t every conceivable rock type. While Archie’s equation held true for most non-shaly formation types, their experiments showed that it needed to be updated for variables such as cementation, tortuosity, granular shape and size. Thus the generalized Archie’s equation was proposed for non-shaly rocks, where :a : is the local correction factor to take into account a myriad of variables that can affect a formation at a given location m : is the cementation factor which represents how the grains in a formation are held together. It also varies based on local formation characteristicsn : is the saturation exponent The values of a, m and n can be found experimentally from log data and core analysis.

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Archie’s Saturation Equation

• Summary– Formation resistivity is affected by changing:

• water volume• water saturation• water salinity

– Archie’s equation can be used to compute:• Forecast formation resistivity, Rt: needs a, m, n, φ, Sw, Rw• Formation water saturation, Sw: needs a, m, n, φ, Rw, Rt• Formation water resistivity, Rw: needs a, m, n, φ, Sw, Rt