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{{publication
| image = exploring-for-oil-and-gas-traps.png
| width = 120px
| series = Treatise in Petroleum Geology
| title = Exploring for Oil and Gas Traps
| part = Predicting the occurrence of oil and gas traps
| chapter = Predicting reservoir system quality and performance
| frompg = 9-1
| topg = 9-156
| author = Dan J. Hartmann, Edward A. Beaumont
| link = http://archives.datapages.com/data/specpubs/beaumont/ch09/ch09.htm
| pdf =
| store = http://store.aapg.org/detail.aspx?id=545
| isbn = 0-89181-602-X
}}
==Methods==
Analyzing air [[permeability]] (K<sub>a</sub> and [[porosity]] (Φ) data separately to characterize rock quality can be deceiving. Analyzing K<sub>a</sub> and Φ data using the K<sub>a</sub>/Φ ratio or the r<sub>35</sub> method<ref name=ch09r46>Pittman, E., D., 1992, Relationship of porosity to permeability to various parameters derived from mercury injection–[[capillary pressure]] curves for sandstone: AAPG Bulletin, vol. 76, no. 2, p. 191–198.</ref> is much more effective for determining quality. The K<sub>a</sub>/Φ ratio or the r<sub>35</sub> method yields information about the fluid flow and storage quality of a rock.
==Which is better rock?==
Using K<sub>a</sub> and Φ data separately to characterize reservoir rock quality is misleading. Consider the rocks shown in the SEM microphotographs in the figure below. Flow unit 1 is a mesoporous, sucrosic dolomite. Its average Φ is 30% and average K<sub>a</sub> is 10 md. Flow unit 2 is a macroporous, oolitic limestone. Its average Φ is 10% and average K<sub>a</sub> is 10 md.
Initially, we might think that flow unit 1 is higher quality because it has three times more porosity and the same permeability as flow unit 2. However, in terms of fluid flow efficiency and storage, as shown by the K<sub>a</sub>/Φ ratio or r<sub>35</sub>, flow unit 2 is actually the better rock.
In a reservoir section, increasing Φ and constant K<sub>a</sub> indicate pores are becoming more numerous and smaller and pore surface area is increasing. Immobile water saturation for a reservoir (S<sub>w</sub>) becomes greater as more surface is available to the wetting fluid. Higher immobile S<sub>w</sub> decreases the available pore storage space for hydrocarbons. Also, as the pore size decreases, so does the pore throat size. Flow unit 2 above is the better reservoir rock because it has larger pore throats and lower immobile S<sub>w</sub>. K<sub>a</sub>/Φ ratio or r<sub>35</sub> accounts for the interrelationship of K<sub>a</sub> and Φ, making them effective methods for comparing rock quality.
==What is the k<sub>a</sub>/Φ ratio?==
K<sub>a</sub> and Φ are standard components of many reservoir engineering wellbore flow performance equations. The K<sub>a</sub>/Φ ratio reflects rock quality in terms of flow efficiency of a reservoir sample. When clastics and carbonates are deposited, they have a close correlation of particle size to the K<sub>a</sub>/Φ ratio. Mean pore throat radius increases as grain or crystal size increases, but modification to grain shape and size tends to “smear” the distribution.
In the example on the preceding page, flow unit 1 has a K<sub>a</sub>/Φ value of 33 and flow unit 2 has a K<sub>a</sub>/Φ value of 100. Even though Φ is greater and K<sub>a</sub> is the same for flow unit 1, the lower K<sub>a</sub>/Φ value indicates its quality is lower than flow unit 2.
==K<sub>a</sub>/Φ plot==
On the plot below, the contours represent a constant K<sub>a</sub>/Φ ratio and divide the plot into areas of similar pore types. Data points that plot along a constant ratio have similar flow quality across a large range of porosity and/or permeability. The clusters of points on the plot below represent hypothetical K<sub>a</sub>/Φ values for flow units 1 and 2 presented in Figure 9-16. The position of the clusters relative to the K<sub>a</sub>/Φ contours indicates flow unit 2 has higher quality in terms of K<sub>a</sub>/Φ ratio than flow unit 1.
[[file:predicting-reservoir-system-quality-and-performance_fig9-16.png|thumb|{{figure number|9-16}}See text for explanation.]]
[[file:predicting-reservoir-system-quality-and-performance_fig9-17.png|thumb|{{figure number|9-17}}See text for explanation.]]
==What is r<sub>35</sub>?==
H.D. Winland of Amoco used mercury injection-capillary pressure curves to develop an empirical relationship among Φ, K<sub>a</sub>, and pore throat radius (r). He tested 312 different water-wet samples. The data set included 82 samples (56 sandstone and 26 carbonate) with low permeability corrected for gas slippage and 240 other uncorrected samples. Winland found that the effective pore system that dominates flow through a rock corresponds to a mercury saturation of 35%. That pore system has pore throat radii (called port size, or r<sub>35</sub>) equal to or smaller than the pore throats entered when a rock is saturated 35% with a nonwetting phase. After 35% of the pore system fills with a non-wetting phase fluid, the remaining pore system does not contribute to flow. Instead, it contributes to storage.
Pittman<ref name=ch09r46 />) speculates, “Perhaps Winland found the best correlation to be r<sub>35</sub> because that is where the average modal pore aperture occurs and where the pore network is developed to the point of serving as an effective pore system that dominates flow.” The capillary pressure curve and pore throat size histogram below illustrate Pittman's point.
[[file:predicting-reservoir-system-quality-and-performance_fig9-18.png|thumb|{{figure number|9-18}}Modified from .<ref name=ch09r15>Doveton, J., H., 1995, Wireline Petrofacies Analysis: Notes from short course presented in Calgary, Alberta, April 24–28, 176 p.</ref>]]
==The winland r<sub>35</sub> equation==
Winland<ref name=ch09r70>Winland, H., D., 1972, Oil accumulation in response to pore size changes, Weyburn field, Saskatchewan: Amoco Production Company Report F72-G-25, 20 p. (unpublished).</ref><ref name=ch09r71>Winland, H., D., 1976, Evaluation of gas slippage and pore aperture size in carbonate and sandstone reservoirs: Amoco Production Company Report F76-G-5, 25 p. (unpublished).</ref> developed the following equation to calculate r<sub>35</sub> for samples with intergranular or intercrystalline porosity:
:<math>\log \mbox{r}_{35} = 0.732 + 0.588 \log \mbox{K}_{\rm a} - 0.864 \log \Phi</math>
where:
* K<sub>a</sub> = air permeability, md
* Φ = porosity, % (not decimals)
Solving for r:
:<math>\mbox{r}_{35} = 10^{0.732 + 0.588\log {\rm K}_{\rm a} - 0.864 \log \Phi}</math>
==Characterizing rock quality with r<sub>35</sub>==
Rock quality is easily characterized using r<sub>35</sub>. Consider the clusters of points representing flow units 1 and 2 (Figure 9-16) on the K<sub>a</sub>/Φ plot below. The diagonal curved lines represent equal r<sub>35</sub> values. Points plotting along the same lines represent rocks with similar r<sub>35</sub> values and have similar quality. By interpolation, r<sub>35</sub> for flow unit 1 is approximately 1.1μ, and r<sub>35</sub> for flow unit 2 is approximately 3μ. The r<sub>35</sub> in flow unit 2 is almost three times as large as flow unit 1. Therefore, flow unit 2 has better flow quality.
==Advantages of r<sub>35</sub> over k<sub>a</sub>/Φ ratio==
Using r<sub>35</sub> instead of the K<sub>a</sub>/Φ ratio for characterizing rock quality of water-wet rocks has advantages:
* r<sub>35</sub> is an understandable number; K<sub>a</sub>/Φ ratio is a dimensionless number
* r<sub>35</sub> can be determined from capillary pressure analysis and related to K<sub>a</sub>/Φ values
* If two variables are known (K<sub>a</sub>, Φ, or r<sub>35</sub>), then the other variable can be calculated using Winland's equation or estimated from a K<sub>a</sub>/Φ plot with r<sub>35</sub> contours
==Example capillary pressure curves==
Hypothetical capillary pressure curves can be drawn by using r<sub>35</sub> as a point on the curve. The capillary pressure curves below are hypothetical curves for the example presented in Figure 9-19. The curves demonstrate that entry pressures for flow unit 2 are less than those for flow unit 1; therefore, fluid flow in flow unit 2 is more efficient. In the figure below, it takes [[length::28 ft]] of oil column for oil to enter 35% of pore space of flow unit 2 and [[length::70 ft]] to enter 35% of pore space of flow unit 1.
[[file:predicting-reservoir-system-quality-and-performance_fig9-19.png|thumb|{{figure number|9-19}}See text for explanation.]]
[[file:predicting-reservoir-system-quality-and-performance_fig9-20.png|thumb|{{figure number|9-20}}See text for explanation.]]
===Example relative permeability curves===
Below are hypothetical drainage relative permeability curves to represent flow units 1 and 2.
[[file:predicting-reservoir-system-quality-and-performance_fig9-21.png|thumb|{{figure number|9-21}}See text for explanation.]]
==See also==
* [[Pore–fluid interaction]]
* [[Hydrocarbon expulsion, migration, and accumulation]]
* [[Pc curves and saturation profiles]]
* [[Converting Pc curves to buoyancy, height, and pore throat radius]]
* [[What is permeability?]]
* [[Relative permeability and pore type]]
==References==
{{reflist}}
==External links==
{{search}}
* [http://archives.datapages.com/data/specpubs/beaumont/ch09/ch09.htm Original content in Datapages]
* [http://store.aapg.org/detail.aspx?id=545 Find the book in the AAPG Store]
[[Category:Predicting the occurrence of oil and gas traps]]
[[Category:Predicting reservoir system quality and performance]]
| image = exploring-for-oil-and-gas-traps.png
| width = 120px
| series = Treatise in Petroleum Geology
| title = Exploring for Oil and Gas Traps
| part = Predicting the occurrence of oil and gas traps
| chapter = Predicting reservoir system quality and performance
| frompg = 9-1
| topg = 9-156
| author = Dan J. Hartmann, Edward A. Beaumont
| link = http://archives.datapages.com/data/specpubs/beaumont/ch09/ch09.htm
| pdf =
| store = http://store.aapg.org/detail.aspx?id=545
| isbn = 0-89181-602-X
}}
==Methods==
Analyzing air [[permeability]] (K<sub>a</sub> and [[porosity]] (Φ) data separately to characterize rock quality can be deceiving. Analyzing K<sub>a</sub> and Φ data using the K<sub>a</sub>/Φ ratio or the r<sub>35</sub> method<ref name=ch09r46>Pittman, E., D., 1992, Relationship of porosity to permeability to various parameters derived from mercury injection–[[capillary pressure]] curves for sandstone: AAPG Bulletin, vol. 76, no. 2, p. 191–198.</ref> is much more effective for determining quality. The K<sub>a</sub>/Φ ratio or the r<sub>35</sub> method yields information about the fluid flow and storage quality of a rock.
==Which is better rock?==
Using K<sub>a</sub> and Φ data separately to characterize reservoir rock quality is misleading. Consider the rocks shown in the SEM microphotographs in the figure below. Flow unit 1 is a mesoporous, sucrosic dolomite. Its average Φ is 30% and average K<sub>a</sub> is 10 md. Flow unit 2 is a macroporous, oolitic limestone. Its average Φ is 10% and average K<sub>a</sub> is 10 md.
Initially, we might think that flow unit 1 is higher quality because it has three times more porosity and the same permeability as flow unit 2. However, in terms of fluid flow efficiency and storage, as shown by the K<sub>a</sub>/Φ ratio or r<sub>35</sub>, flow unit 2 is actually the better rock.
In a reservoir section, increasing Φ and constant K<sub>a</sub> indicate pores are becoming more numerous and smaller and pore surface area is increasing. Immobile water saturation for a reservoir (S<sub>w</sub>) becomes greater as more surface is available to the wetting fluid. Higher immobile S<sub>w</sub> decreases the available pore storage space for hydrocarbons. Also, as the pore size decreases, so does the pore throat size. Flow unit 2 above is the better reservoir rock because it has larger pore throats and lower immobile S<sub>w</sub>. K<sub>a</sub>/Φ ratio or r<sub>35</sub> accounts for the interrelationship of K<sub>a</sub> and Φ, making them effective methods for comparing rock quality.
==What is the k<sub>a</sub>/Φ ratio?==
K<sub>a</sub> and Φ are standard components of many reservoir engineering wellbore flow performance equations. The K<sub>a</sub>/Φ ratio reflects rock quality in terms of flow efficiency of a reservoir sample. When clastics and carbonates are deposited, they have a close correlation of particle size to the K<sub>a</sub>/Φ ratio. Mean pore throat radius increases as grain or crystal size increases, but modification to grain shape and size tends to “smear” the distribution.
In the example on the preceding page, flow unit 1 has a K<sub>a</sub>/Φ value of 33 and flow unit 2 has a K<sub>a</sub>/Φ value of 100. Even though Φ is greater and K<sub>a</sub> is the same for flow unit 1, the lower K<sub>a</sub>/Φ value indicates its quality is lower than flow unit 2.
==K<sub>a</sub>/Φ plot==
On the plot below, the contours represent a constant K<sub>a</sub>/Φ ratio and divide the plot into areas of similar pore types. Data points that plot along a constant ratio have similar flow quality across a large range of porosity and/or permeability. The clusters of points on the plot below represent hypothetical K<sub>a</sub>/Φ values for flow units 1 and 2 presented in Figure 9-16. The position of the clusters relative to the K<sub>a</sub>/Φ contours indicates flow unit 2 has higher quality in terms of K<sub>a</sub>/Φ ratio than flow unit 1.
[[file:predicting-reservoir-system-quality-and-performance_fig9-16.png|thumb|{{figure number|9-16}}See text for explanation.]]
[[file:predicting-reservoir-system-quality-and-performance_fig9-17.png|thumb|{{figure number|9-17}}See text for explanation.]]
==What is r<sub>35</sub>?==
H.D. Winland of Amoco used mercury injection-capillary pressure curves to develop an empirical relationship among Φ, K<sub>a</sub>, and pore throat radius (r). He tested 312 different water-wet samples. The data set included 82 samples (56 sandstone and 26 carbonate) with low permeability corrected for gas slippage and 240 other uncorrected samples. Winland found that the effective pore system that dominates flow through a rock corresponds to a mercury saturation of 35%. That pore system has pore throat radii (called port size, or r<sub>35</sub>) equal to or smaller than the pore throats entered when a rock is saturated 35% with a nonwetting phase. After 35% of the pore system fills with a non-wetting phase fluid, the remaining pore system does not contribute to flow. Instead, it contributes to storage.
Pittman<ref name=ch09r46 />) speculates, “Perhaps Winland found the best correlation to be r<sub>35</sub> because that is where the average modal pore aperture occurs and where the pore network is developed to the point of serving as an effective pore system that dominates flow.” The capillary pressure curve and pore throat size histogram below illustrate Pittman's point.
[[file:predicting-reservoir-system-quality-and-performance_fig9-18.png|thumb|{{figure number|9-18}}Modified from .<ref name=ch09r15>Doveton, J., H., 1995, Wireline Petrofacies Analysis: Notes from short course presented in Calgary, Alberta, April 24–28, 176 p.</ref>]]
==The winland r<sub>35</sub> equation==
Winland<ref name=ch09r70>Winland, H., D., 1972, Oil accumulation in response to pore size changes, Weyburn field, Saskatchewan: Amoco Production Company Report F72-G-25, 20 p. (unpublished).</ref><ref name=ch09r71>Winland, H., D., 1976, Evaluation of gas slippage and pore aperture size in carbonate and sandstone reservoirs: Amoco Production Company Report F76-G-5, 25 p. (unpublished).</ref> developed the following equation to calculate r<sub>35</sub> for samples with intergranular or intercrystalline porosity:
:<math>\log \mbox{r}_{35} = 0.732 + 0.588 \log \mbox{K}_{\rm a} - 0.864 \log \Phi</math>
where:
* K<sub>a</sub> = air permeability, md
* Φ = porosity, % (not decimals)
Solving for r:
:<math>\mbox{r}_{35} = 10^{0.732 + 0.588\log {\rm K}_{\rm a} - 0.864 \log \Phi}</math>
==Characterizing rock quality with r<sub>35</sub>==
Rock quality is easily characterized using r<sub>35</sub>. Consider the clusters of points representing flow units 1 and 2 (Figure 9-16) on the K<sub>a</sub>/Φ plot below. The diagonal curved lines represent equal r<sub>35</sub> values. Points plotting along the same lines represent rocks with similar r<sub>35</sub> values and have similar quality. By interpolation, r<sub>35</sub> for flow unit 1 is approximately 1.1μ, and r<sub>35</sub> for flow unit 2 is approximately 3μ. The r<sub>35</sub> in flow unit 2 is almost three times as large as flow unit 1. Therefore, flow unit 2 has better flow quality.
==Advantages of r<sub>35</sub> over k<sub>a</sub>/Φ ratio==
Using r<sub>35</sub> instead of the K<sub>a</sub>/Φ ratio for characterizing rock quality of water-wet rocks has advantages:
* r<sub>35</sub> is an understandable number; K<sub>a</sub>/Φ ratio is a dimensionless number
* r<sub>35</sub> can be determined from capillary pressure analysis and related to K<sub>a</sub>/Φ values
* If two variables are known (K<sub>a</sub>, Φ, or r<sub>35</sub>), then the other variable can be calculated using Winland's equation or estimated from a K<sub>a</sub>/Φ plot with r<sub>35</sub> contours
==Example capillary pressure curves==
Hypothetical capillary pressure curves can be drawn by using r<sub>35</sub> as a point on the curve. The capillary pressure curves below are hypothetical curves for the example presented in Figure 9-19. The curves demonstrate that entry pressures for flow unit 2 are less than those for flow unit 1; therefore, fluid flow in flow unit 2 is more efficient. In the figure below, it takes [[length::28 ft]] of oil column for oil to enter 35% of pore space of flow unit 2 and [[length::70 ft]] to enter 35% of pore space of flow unit 1.
[[file:predicting-reservoir-system-quality-and-performance_fig9-19.png|thumb|{{figure number|9-19}}See text for explanation.]]
[[file:predicting-reservoir-system-quality-and-performance_fig9-20.png|thumb|{{figure number|9-20}}See text for explanation.]]
===Example relative permeability curves===
Below are hypothetical drainage relative permeability curves to represent flow units 1 and 2.
[[file:predicting-reservoir-system-quality-and-performance_fig9-21.png|thumb|{{figure number|9-21}}See text for explanation.]]
==See also==
* [[Pore–fluid interaction]]
* [[Hydrocarbon expulsion, migration, and accumulation]]
* [[Pc curves and saturation profiles]]
* [[Converting Pc curves to buoyancy, height, and pore throat radius]]
* [[What is permeability?]]
* [[Relative permeability and pore type]]
==References==
{{reflist}}
==External links==
{{search}}
* [http://archives.datapages.com/data/specpubs/beaumont/ch09/ch09.htm Original content in Datapages]
* [http://store.aapg.org/detail.aspx?id=545 Find the book in the AAPG Store]
[[Category:Predicting the occurrence of oil and gas traps]]
[[Category:Predicting reservoir system quality and performance]]