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==Capillary pressure concepts==

==Capillary pressure concepts==

[[File:charles-l-vavra-john-g-kaldi-robert-m-sneider_capillary-pressure_1.png|thumb|{{figure_number|1}}Effects of interaction of adhesive and cohesive forces on [[wettability]]. (a) If adhesive forces are greater than the cohesive forces, the fluid spreads out on the surface and is termed '''''wetting. '''''(b) If cohesive forces exceed adhesive forces, the liquid beads up and is termed nonwetting. The measure of relative [[wettability]] is the contact angle (θ), which is measured through the denser phase.]]

[[File:charles-l-vavra-john-g-kaldi-robert-m-sneider_capillary-pressure_1.jpg|thumb|{{figure_number|1}}Effects of interaction of adhesive and cohesive forces on [[wettability]]. (a) If adhesive forces are greater than the cohesive forces, the fluid spreads out on the surface and is termed '''''wetting. '''''(b) If cohesive forces exceed adhesive forces, the liquid beads up and is termed nonwetting. The measure of relative [[wettability]] is the contact angle (θ), which is measured through the denser phase.]]

Capillary pressure results from interactions of forces acting within and between fluids and their bounding solids. These include both ''cohesive'' forces (surface and interfacial tension) and ''adhesive'' (liquid-solid) forces. When adhesive forces are greater than cohesive forces, the liquid is said to be ''wetting'' (Figure 1a). When cohesive forces exceed adhesive forces, the liquid is ''nonwetting'' (Figure 1b). The relative [[wettability]] of the fluids is described by the ''contact angle'' (θ), which is the angle between the solid and the fluid-fluid interface as measured through the denser fluid (Figure 1). (For information on the measurement of [[wettability]], see the chapter on [[Wettability]]in Part 5.)

Capillary pressure results from interactions of forces acting within and between fluids and their bounding solids. These include both ''cohesive'' forces (surface and interfacial tension) and ''adhesive'' (liquid-solid) forces. When adhesive forces are greater than cohesive forces, the liquid is said to be ''wetting'' (Figure 1a). When cohesive forces exceed adhesive forces, the liquid is ''nonwetting'' (Figure 1b). The relative [[wettability]] of the fluids is described by the ''contact angle'' (θ), which is the angle between the solid and the fluid-fluid interface as measured through the denser fluid (Figure 1). (For information on the measurement of [[wettability]], see the chapter on [[Wettability]]in Part 5.)

[[File:charles-l-vavra-john-g-kaldi-robert-m-sneider_capillary-pressure_2.png|thumb|{{figure_number|2}}The wetting phase rises above the original or free surface in the capillary tube experiment until adhesive and gravitational forces balance. Capillary pressure (P_c) is the difference in pressure measured across the interface in the capillary (''P''_c = ''P''_nw - ''P''_w). This pressure results from the contrast in pressure gradients caused by the different densities of the nonwetting (''ρ''_nw) and wetting (''ρ''_w) phases (right).]]

[[File:charles-l-vavra-john-g-kaldi-robert-m-sneider_capillary-pressure_2.jpg|thumb|{{figure_number|2}}The wetting phase rises above the original or free surface in the capillary tube experiment until adhesive and gravitational forces balance. Capillary pressure (P_c) is the difference in pressure measured across the interface in the capillary (''P''_c = ''P''_nw - ''P''_w). This pressure results from the contrast in pressure gradients caused by the different densities of the nonwetting (''ρ''_nw) and wetting (''ρ''_w) phases (right).]]

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''_c) 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''_c) 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:

The pressure at which mercury first enters the sample (after the mercury has filled any surface irregularities on the sample) is termed the ''displacement pressure'' (''P''_d). The percentage of pore volume saturated by mercury at the maximum pressure is the ''maximum saturation'' (''S''_max). The unsaturated pore volume at that pressure is the ''minimum unsaturated pore volume'' (''u''_min) (Figure 3). This is sometimes incorrectly referred to as irreducible saturation. This term is inappropriate for the air-mercury system because saturation depends on applied pressure and on the duration of the experiment (Wardlaw and Taylor, 1976)<ref name=Wardlaw_etal_1976 />.

The pressure at which mercury first enters the sample (after the mercury has filled any surface irregularities on the sample) is termed the ''displacement pressure'' (''P''_d). The percentage of pore volume saturated by mercury at the maximum pressure is the ''maximum saturation'' (''S''_max). The unsaturated pore volume at that pressure is the ''minimum unsaturated pore volume'' (''u''_min) (Figure 3). This is sometimes incorrectly referred to as irreducible saturation. This term is inappropriate for the air-mercury system because saturation depends on applied pressure and on the duration of the experiment (Wardlaw and Taylor, 1976)<ref name=Wardlaw_etal_1976 />.

[[File:charles-l-vavra-john-g-kaldi-robert-m-sneider_capillary-pressure_3.png|thumb|{{figure_number|3}}Mercury injection capillary pressure curve terminology.]]

[[File:charles-l-vavra-john-g-kaldi-robert-m-sneider_capillary-pressure_3.jpg|thumb|{{figure_number|3}}Mercury injection capillary pressure curve terminology.]]

After the maximum pressure is reached, the pressure is reduced in steps and air (the wetting phase) is allowed to imbibe into the sample. The amount of mercury expelled from the sample at each pressure is expressed as a percentage of total pore volume or bulk volume. Again, pressure is plotted against mercury saturation in the withdrawal curve (Figure 3). The volume of pore space still saturated with mercury after pressure is reduced to the minimum is called ''the residual mercury saturation'' (S_R).

After the maximum pressure is reached, the pressure is reduced in steps and air (the wetting phase) is allowed to imbibe into the sample. The amount of mercury expelled from the sample at each pressure is expressed as a percentage of total pore volume or bulk volume. Again, pressure is plotted against mercury saturation in the withdrawal curve (Figure 3). The volume of pore space still saturated with mercury after pressure is reduced to the minimum is called ''the residual mercury saturation'' (S_R).

* ''P''_c = capillary pressure in dynes/cm² (1 psi = 69035 dynes/cm²)

* ''P''_c = capillary pressure in dynes/cm² (1 psi = 69035 dynes/cm²)

[[File:charles-l-vavra-john-g-kaldi-robert-m-sneider_capillary-pressure_4.png|thumb|{{figure_number|4}}Idealized mercury injection capillary pressure curve shapes. Note that all of the curves have identical displacement pressures and minimum unsaturated pore volumes, but that the saturation profiles would differ dramatically due to differences in pore throat size distributions.]]

[[File:charles-l-vavra-john-g-kaldi-robert-m-sneider_capillary-pressure_4.jpg|thumb|{{figure_number|4}}Idealized mercury injection capillary pressure curve shapes. Note that all of the curves have identical displacement pressures and minimum unsaturated pore volumes, but that the saturation profiles would differ dramatically due to differences in pore throat size distributions.]]

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&deg; (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&deg; (unsorted).

It should be noted that although these more specialized procedures are quite informative, especially for approximating hydrocarbon recovery efficiencies, they are also relatively labor intensive and expensive when compared to routine mercury injection tests.

It should be noted that although these more specialized procedures are quite informative, especially for approximating hydrocarbon recovery efficiencies, they are also relatively labor intensive and expensive when compared to routine mercury injection tests.

[[File:charles-l-vavra-john-g-kaldi-robert-m-sneider_capillary-pressure_5.png|thumb|{{figure_number|5}}Effect of capillary pressure (left) on water saturation (right). At any given height above the free water level, water saturations vary widely among rock types (A-E) due to diffferences in capillarity. For example, at 50 ft above free water level, water saturations vary from 18% (rock type A) to 95% (rock type E). A well drilled into an interbedded sequence of these rock types would show multiple oil-water contacts and a highly irregular vertical saturation profile. Note also the wide transition zone in rock type B caused by poor sorting of the pore throats.]]  

[[File:charles-l-vavra-john-g-kaldi-robert-m-sneider_capillary-pressure_5.jpg|thumb|{{figure_number|5}}Effect of capillary pressure (left) on water saturation (right). At any given height above the free water level, water saturations vary widely among rock types (A-E) due to diffferences in capillarity. For example, at 50 ft above free water level, water saturations vary from 18% (rock type A) to 95% (rock type E). A well drilled into an interbedded sequence of these rock types would show multiple oil-water contacts and a highly irregular vertical saturation profile. Note also the wide transition zone in rock type B caused by poor sorting of the pore throats.]]  

==See also==

==See also==