Relative permeability is a dimensionless term that has importance when two or more fluids move through the pore spacesfor example, oil and water. Specific or absolute permeability is the permeability of a porous medium to one fluid at 100% saturation. Effective permeability is the permeability to a given phase when more than one phase saturates the porous medium. The effective permeability, then, is a function of saturation. Relative permeability to a given phase is defined as the ratio of effective permeability to the absolute or, in some cases, a base permeability. Relative permeability, then, is also a function of saturation.
In data that were generated prior to 1973, the specific permeability to air was often used as the base permeability. Since that time, the common base has been the hydrocarbon permeability in the presence of irreducible water. For an oil-water reservoir, this would mean the base permeability would be effective permeability to oil at irreducible water. For a gas reservoir, the base permeability would be that to gas in the presence of irreducible water. Figure 1 (Gas-water relative permeability curves) illustrates gas-water relative permeability data when water displaces gas.
Imbibition versus Drainage
The terms imbibition and drainage are also employed when discussing relative permeability tests. Their meanings imply what is happening in the pore space to the wetting phase as relative permeability tests are measured. If the wetting phase is decreasing, that phase is draining and the curve is called a drainage curve. If the wetting phase is increasing or being imbibed during the test, the curve is referred to as an imbibition curve ( Figure 1 ).
For a water-wet reservoir, the drainage curves apply during the time that water is draining from the reservoir and hydrocarbons are accumulating. Once the reservoir rock or laboratory sample has attained an equilibrium water-saturation value and the water is subsequently increased by natural water influx or the introduction of coring or test fluids, the imbibition curves apply. (In oil-wet rock, a reduction in the oil phase by water flooding would be referred to as a drainage curve.) These data are required in many reservoir engineering calculations, and the laboratory tests that develop them should follow the same saturation history as that in the reservoir.
Laboratory Methods for Measuring Relative Permeability
Two major laboratory methods have evolved to measure relative permeability. These are referred to as the steady-state and nonsteady-state techniques.
STEADY STATE: The steady-state test, the older of the two methods, is made at low flow rates, and the test apparatus contains upstream and downstream mixer heads to remove capillary end effects. Most research groups prefer data obtained from this test. Two fluids are injected simultaneously into a core sample and the water saturation is increased slowly. This simulates the slow increase in water saturation that would occur in the formation between the injection and producing wells. Saturation increase is monitored by measuring the gain in weight occurring in the sample or by X-ray technique.
NONSTEADY STATE: The nonsteady-state technique uses a viscous oil and is normally made at a higher flow rate than that present in the reservoir. It is this higher rate that sometimes yields pessimistic estimates of recovery from rocks of intermediate wettability. Heaviside and Black (1983) have analyzed the two techniques and presented recommendations on the most appropriate way to measure water-oil relative permeability depending upon the wetting characteristics of the rock.
The natural preference of a porous medium, which causes one fluid to adhere to its surfaces rather than another, is referred to as wettability. A water-wet porous medium causes water to adhere to its surfaces. The wettability of a rock has a dramatic influence on relative permeability curves. It is therefore necessary that the core samples tested in the laboratory reflect the actual formation wettability, and that initial water saturation in the test sample be of the same magnitude and have the same spatial location as it has in the reservoir. This need has led to the recovery of "native state" cores. These are cores taken with crude oil or with other oil-base fluids that do not alter the wettability or water saturation present in the recovered core.
Figure 2 (Effects of wettability on water-oil relative permeability: imbibition data for Torpedo sandstone) illustrates the effects of core wettability on water-oil relative permeability measurements (Owens and Archer 1971). These data indicate that as the rock becomes more oil-wet, the relative permeability to oil decreases and the relative permeability to water increases at any given saturation. This results in unfavorable recovery efficiency. It also indicates that the residual oil saturation in intermediate to oil-wet rocks is a function of the volume of water that flows through the core sample, and that the relative permeability to water existing at floodout will be much higher for the oil-wet formation. An interesting observation is that the reduction of capillary retentive forces in the oil-wet rock allows a lower residual oil saturation to be achieved in the oil-wet rock if economics would support continued water injection.
Wettability may be estimated from shapes of relative permeability curves; however, it should be remembered that a similar shift in the relative permeability curves can also be caused by changes in other rock properties. This was documented by Morgan and Gordon (1970).