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started wikifying fully
If the end of a narrow capillary tube is placed in a wetting fluid, net adhesive forces draw the fluid into the tube (Figure 2). The wetting phase rises in the capillary above the original interface or ''free surface'' until adhesive and gravitational forces are balanced. Because the wetting and nonwetting fluids have different densities, they also have different pressure gradients (Figure 2). ''Capillary pressure'' (P<sub>c</sub>) is defined as the difference in pressure across the meniscus in the capillary tube. Put another way, capillary pressure is the amount of extra pressure required to force the nonwetting phase to displace the wetting phase in the capillary. Capillary pressure can be calculated as follows:
If the end of a narrow capillary tube is placed in a wetting fluid, net adhesive forces draw the fluid into the tube (Figure 2). The wetting phase rises in the capillary above the original interface or ''free surface'' until adhesive and gravitational forces are balanced. Because the wetting and nonwetting fluids have different densities, they also have different pressure gradients (Figure 2). ''Capillary pressure'' (P<sub>c</sub>) is defined as the difference in pressure across the meniscus in the capillary tube. Put another way, capillary pressure is the amount of extra pressure required to force the nonwetting phase to displace the wetting phase in the capillary. Capillary pressure can be calculated as follows:
:<math>\mathbf{Equation}</math>
:<math>P_\mathrm{c} = (\rho_\mathrm{w} - \rho_\mathrm{nw}) g h</math>, or
:<math>P_\mathrm{c} = \frac{2\sigma\cos\theta}{r_\mathrm{c}}</math>
where
where
* ''ρ''<sub>w</sub> = density of the wetting nonwetting fluid
* ''ρ<sub>w</sub>'' = density of the wetting nonwetting fluid
* ''ρ''<sub>nw</sub> = density of the nonwetting fluid
* ''ρ<sub>nw</sub>'' = density of the nonwetting fluid
* ''g'' = gravitational constant
* ''g'' = gravitational constant
* ''* h'' = height above the free surface
* ''h'' = height above the free surface
* ''σ'' = interfacial tension
* ''σ'' = interfacial tension
* ''θ'' = contact angle between the fluids and the capillary tube
* ''θ'' = contact angle between the fluids and the capillary tube
* ''r<sub>c</sub>'' = radius of the capillary
* ''r''<sub>c</sub> = radius of the capillary
These equations show that capillary pressure increases with greater height above the free surface and with smaller capillary size.
These equations show that capillary pressure increases with greater height above the free surface and with smaller capillary size.
Data from the mercury injection curve can be used to approximate the distribution of pore volume accessible by throats of given effective radii (in cm) using the following equation:
Data from the mercury injection curve can be used to approximate the distribution of pore volume accessible by throats of given effective radii (in cm) using the following equation:
:<math>\mathbf{Equation}</math>
:<math>r\mathrm{c} = \frac{2\sigma\cos\theta}{P_\mathrm{c}}</math>
where
where
* ''σ'' = interfacial tension of the air-mercury system (480 dynes/cm)
* ''σ'' = interfacial tension of the air-mercury system (480 dynes/cm)
* ''θ'' = air/mercury/solid contact angle (140°)
* ''θ'' = air/mercury/solid contact angle (140°)
* ''P<sub>c</sub>'' = capillary pressure in dynes/cm<sup>2</sup> (1 psi = 69035 dynes/cm<sup>2</sup>)
* ''P''<sub>c</sub> = capillary pressure in dynes/cm<sup>2</sup> (1 psi = 69035 dynes/cm<sup>2</sup>)
Note that this equation calculates the radius of a cylindrical capillary tube; however, real pore throats have very complex geometries. Therefore, the calculated values represent the ''effective'' radii of the pore throats, which may not equal their actual dimensions. Samples dominated by throats of similar size (well sorted) have broad, flat plateaus (Figure 4). As sorting becomes poorer, the plateau steepens then disappears and the slope of the curve approaches 45_ (unsorted).
Note that this equation calculates the radius of a cylindrical capillary tube; however, real pore throats have very complex geometries. Therefore, the calculated values represent the ''effective'' radii of the pore throats, which may not equal their actual dimensions. Samples dominated by throats of similar size (well sorted) have broad, flat plateaus (Figure 4). As sorting becomes poorer, the plateau steepens then disappears and the slope of the curve approaches 45° (unsorted).
Data from the mercury withdrawal (air imbibition) curve can provide information regarding the efficiency with which the nonwetting phase can be withdrawn from the pore system. ''Withdrawal efficiency'' (W<sub>E</sub>) is defined as the ratio of the mercury saturation in the sample at minimum pressure after pressure is reduced (S<sub>R</sub>) to the saturation at maximum pressure (S<sub>max</sub>) (Figure 3) (Wardlaw and Taylor, 1976)<ref name=Wardlaw_etal_1976 />. Because few samples reach 100% mercury saturation at routinely available injection pressures, data are normalized by the following equation:
Data from the mercury withdrawal (air imbibition) curve can provide information regarding the efficiency with which the nonwetting phase can be withdrawn from the pore system. ''Withdrawal efficiency'' (''W''<sub>E</sub>) is defined as the ratio of the mercury saturation in the sample at minimum pressure after pressure is reduced (S<sub>R</sub>) to the saturation at maximum pressure (S<sub>max</sub>) (Figure 3) (Wardlaw and Taylor, 1976)<ref name=Wardlaw_etal_1976 />. Because few samples reach 100% mercury saturation at routinely available injection pressures, data are normalized by the following equation:
:<math>\mathbf{Equation}</math>
:<math>W_\mathbf{E} = \frac{S_\mathrm{max} - S\mathrm{R}}{S_\mathrm{max}} \times 100%</math>
Withdrawal efficiency in the air-mercury system is controlled exclusively by pore geometry, which can be interpreted from the capillary pressure curves and by direct observation of the rock or an epoxy resin pore cast. Critical pore geometry factors affecting withdrawal efficiency include effective pore throat heterogeneity; the ratio of pore body to pore throat size (r<sub>b</sub>/r<sub>t</sub>); and the number of throats connecting each pore (coordination number). Table 1 shows the effect of these parameters on withdrawal efficiency.
Withdrawal efficiency in the air-mercury system is controlled exclusively by pore geometry, which can be interpreted from the capillary pressure curves and by direct observation of the rock or an epoxy resin pore cast. Critical pore geometry factors affecting withdrawal efficiency include effective pore throat heterogeneity; the ratio of pore body to pore throat size (r<sub>b</sub>/r<sub>t</sub>); and the number of throats connecting each pore (coordination number). Table 1 shows the effect of these parameters on withdrawal efficiency.
Before mercury injection data can be applied to reservoirs, the data must be converted from the air-mercury system to the brine-hydrocarbon system of the reservoir using the following relationship:
Before mercury injection data can be applied to reservoirs, the data must be converted from the air-mercury system to the brine-hydrocarbon system of the reservoir using the following relationship:
:<math>\mathbf{Equation}</math>
:<math>P_\mathbf{C_{b/hc}} = P_\mathbf{C_{a/m}} \times \frac{\sigma_\mathrm{b/hc}\cos\theta_\mathrm{b/hc}}{\sigma_\mathrm{a/m}\cos\theta_\mathrm{a/m}} </math>
where
where
* ''P''<sub>Cb/hc</sub> = capillary pressure in the brine-hydrocarbon system of the reservoir
* ''P<sub>Cb</sub>hc/'' = capillary pressure in the brine-hydrocarbon system of the reservoir
* ''P''<sub>Ca/m</sub> = capillary pressure in the air-mercury system
* ''P<sub>Ca</sub>m/'' = capillary pressure in the air-mercury system
* ''σ''<sub>b/hc</sub> = interfacial tension of the brine-hydrocarbon system
* ''σ<sub>b</sub>hc/'' = interfacial tension of the brine-hydrocarbon system
* ''σ''<sub>a/m</sub> = interfacial tension of air-mercury system
* ''σ<sub>a</sub>m/'' = interfacial tension of air-mercury system
* ''θ''<sub>b/hc</sub> = contact angle of the brine-hydrocarbon-solid system
* ''θ<sub>b</sub>hc/'' = contact angle of the brine-hydrocarbon-solid system
* ''θ''<sub>a/m</sub> = contact angle of the air-mercury-solid system
* ''θ<sub>a</sub>m/'' = contact angle of the air-mercury-solid system
Ideally, values for brine-hydrocarbon contact angle, surface tension, and fluid densities at reservoir temperature and pressure should be determined in the laboratory using actual reservoir fluids. However, these measurements are difficult and expensive, so approximations such as those given in Tables 2 and 3 are commonly used.
Ideally, values for brine-hydrocarbon contact angle, surface tension, and fluid densities at reservoir temperature and pressure should be determined in the laboratory using actual reservoir fluids. However, these measurements are difficult and expensive, so approximations such as those given in Tables 2 and 3 are commonly used.
Having converted the capillary pressure data to the hydrocarbon-brine system of the reservoir and knowing the hydrocarbon and brine densities from laboratory analysis, we can now calculate the amount of hydrocarbon column required (height above the free water level or level where ''P''<sub>c</sub> = 0) to attain a pressure of interest:
Having converted the capillary pressure data to the hydrocarbon-brine system of the reservoir and knowing the hydrocarbon and brine densities from laboratory analysis, we can now calculate the amount of hydrocarbon column required (height above the free water level or level where ''P''<sub>c</sub> = 0) to attain a pressure of interest:
:<math>\mathbf{Equation}</math>
:<math>h = \frac{P_\mathbf{h}}{0.433(\rho_\mathrm{b} - \rho_\mathrm{hc}}</math>
where
where
* ''h'' = height above the free water level (in ft)
* ''h'' = height above the free water level (in ft)
* ''P<sub>c</sub>'' = hydrocarbon-brine capillary pressure (in psi)
* ''P''<sub>c</sub> = hydrocarbon-brine capillary pressure (in psi)
* ''ρ<sub>b</sub>'' = specific density of brine at ambient conditions (in gm/cm<sup>3</sup>)
* ''ρ''<sub>b</sub> = specific density of brine at ambient conditions (in gm/cm<sup>3</sup>)
* ''ρ<sub>hc</sub>'' = specific density of hydrocarbons at ambient conditions (in gm/cm<sup>3</sup>)
* ''ρ''<sub>hc</sub> = specific density of hydrocarbons at ambient conditions (in gm/cm<sup>3</sup>)
* ''0.433'' = the gradient of pure water at ambient conditions
* 0.433 = the gradient of pure water at ambient conditions
This information can be used to compare expected fluid saturations of different rock types at given levels in the reservoir (Figure 5). (For information on the application of capillary pressure data to evaluating [[fluid contacts]], see the chapter on [[Fluid contacts]] in Part 6.)
This information can be used to compare expected fluid saturations of different rock types at given levels in the reservoir (Figure 5). (For information on the application of capillary pressure data to evaluating [[fluid contacts]], see the chapter on [[Fluid contacts]] in Part 6.)
If the capillary pressure data from the suspected seal are available or can be estimated, the maximum hydrocarbon column each rock type could have before the seal begins leaking can be calculated by the following:
If the capillary pressure data from the suspected seal are available or can be estimated, the maximum hydrocarbon column each rock type could have before the seal begins leaking can be calculated by the following:
:<math>\mathbf{Equation}</math>
:<math>h_\mathrm{max} = \frac{P_\mathbf{dS} - P_\mathrm{dR}}{0.433(\rho_\mathrm{w} - \rho_\mathrm{hc}}</math>
where
where
* ''h<sub>max</sub>'' = height of the hydrocarbon column (in feet)
* ''h<sub>max</sub>'' = height of the hydrocarbon column (in feet)
* ''P<sub>dS</sub>'' = brine-hydrocarbon displacement pressure of the seal (in psi)
* ''P<sub>dS</sub>'' = brine-hydrocarbon displacement pressure of the seal (in psi)