Page 88 - Standard Handbook Petroleum Natural Gas Engineering VOLUME2

76 Reservoir Engineering

Thus, the absolute permeability is the permeability measured when the
medium is completely saturated with a single fluid. Effective permeability is the
permeability to a particular fluid when another fluid is also present in
the medium. For example, if both oil and water are flowing, the effective
permeability to oil is k, and that to water is k,. The sum of the effective
permeabilities is always less than the absolute permeability [17]. As noted in
the previous section, permeability is commonly expressed in millidarcies (md).
Relative Permeabilitles

If the effective permeabilities are divided by a base permeability (i.e., the
absolute permeability), the dimensionless ratio is referred to as the relative
permeability, namely k, for gas, k, for oil, and k, for water:
k
kw
k =A* k, = L. k, =- (5-78)
Fg k’ k’ k
where kg, k,, and kw, are the effective permeabilities to gas, oil, and water,
respectively, and k is some base permeability that represents the absolute
permeability. For gas-oil two-phase relative permeabilities, the base permeability
is often the equivalent liquid permeability. For oil-water two-phase relative
permeabilities, three different base permeabilities are often used [ 1331:
1. The permeability to air with only air present.
2. The permeability to water at 100% S1.
3. The permeability to oil at irreducible water saturation.
Wyckoff and Botset [76] are generally credited with preforming the first gas
and liquid relative permeabilities which were conducted in unconsolidated
sandpacks in 1936. In these early experiments, a relationship was observed
between the liquid saturation of a sand and the permeability to a liquid or gas
phase [76,134]. At about the same time, Hassler, Rice, and Leeman [l35]
measured relative air permeabilities in oil-saturated cores. In 1940, relative
permeability measurements were extended to consolidated cores by Botset [ 1361.
Since then, a number of dynamic (fluid displacement or fluid drive) methods
[83,137-1431 and static (or stationary-phase) methods [ 144-1501 have been
proposed to determine relative permeabilities in core samples. In the latter
methods, only the nonwetting phase is allowed to flow by the use of a very low
pressure drop across the core; hence, this method is applicable only to the
relative permeability of the nonwetting phase. The dynamic methods include:
(1) steady-state methods in which fluids are flowed simultaneously through a
core sample at a fixed gas-oil or water-oil ratio until equilibrium pressure
gradients and saturations are achieved, and (2) unsteady-state methods in which
an oil-saturated core is flooded with either gas or water at a fixed pressure drop
or flow rate so that the average fluid saturation changes result in a saturation
gradient. The most popular steady-state procedure is the Penn State method [83],
but the most common dynamic test is the unsteady-state method because of the
reduced time requirement. The various methods have been evaluated [ 139,1511
and generally provide similar results.
Based on the initial work of Leverett [loo] and Buckley and Leverett [152],
Welge [153] was the first to show how to calculate relative permeability ratios
in the absence of gravity effects. Subsequently, Johnson, Bossler, and Naumann