Page 70 - Standard Handbook Petroleum Natural Gas Engineering VOLUME2

58 Reservoir Engineering

estimation of water saturation. In low-porosity formations, such as the Cotton
Valley sandstone, the saturation was found to vary greatly from the value of 2
[87]. If n is always assumed to be 2, Dorfman contends that many hydrocarbon
zones will be overlooked and many water-producing zones could be tested. As
related by Hilchie [88], most of the values for the saturation exponent have been
obtained at atmospheric conditions and there is the need to obtain laboratory
measurements under simulated reservoir pressure and temperature. At atmos-
pheric pressure, the percentage of smaller pores is larger than at reservoir
pressure [64], which results in the wrong saturation exponent and a higher value
of water saturation [88].
Surface and lnterfaclal Tensions

The term interface indicates a boundary or dividing line between two
immiscible phases. Types of interfaces include: liquid-gas, liquid-liquid, liquid-
solid, solid-gas, and solid-solid. For fluids, molecular interactions at the interface
result in a measurable tension which, if constant, is equal to the surface free
energy required to form a unit area of interface. For the case of a liquid which
is in contact with air or the vapor of that liquid, the force per unit length
required to create a unit surface area is usually referred to as the surface tension.
Interfacial tension is used to describe this quantity for two liquids or for a liquid
and a solid. Interfacial tension between two immiscible liquids is normally less
than the surface tension of the liquid with the higher tension, and often is
intermediate between the individual surface tensions of the two liquids of
interest. Common units of surface or interfacial tension are dynes per centimeter
(or the identical ergs/cm*) with metric units in the equivalent milli-Newton per
meter (mN/m).
The surface tension of pure water ranges from 72.5 dynes/cm at 70°F to
60.1 dynes/cm at 200°F in an almost linear fashion with a gradient of
0.095 dynes/cm/"F [25]. Salts in oilfield brines tend to increase surface tension,
but surface active agents that may dissolve into the water from the oil can lower
surface tension. At standard conditions, surface tensions of brines range from
59 to 76 dynes/cm [25]. As shown in Figure 5-39, dissolved natural gas reduces
surface tension of water as a function of saturation pressure [89].
At a given temperature, surface tension of hydrocarbons in equilibrium with
the atmosphere or their own vapor increases with increasing molecular weight
(Figure 5-40) [go]. For a given hydrocarbon, surface tension decreases with
increasing temperature. At 70°F, surface tensions of crude oils often range from
24 to 38 dyne/cm [25].
The presence of dissolved gases greatly reduces surface tension of crude oil
as shown in Figure 5-41 [91]. Dissolved natural gas reduces surface tension of
crude oil more than previously noted for water, but the amount and nature of
gas determines the magnitude of the reduction. The direct effect of a tem-
perature increase on reduction of surface tension more than counterbalances
the decreased gas solubility at elevated temperatures. Thus, surface tension at
reservoir temperature and pressure may be lower than indicated by figure 541 [25].
Under reservoir conditions, the interfacial interaction between gas and oil
involves the surface tension of the oil in equilibrium with the gas. Similarly,
the interaction between oil and water determines the interfacial tension between
the crude and brine. Listed in Table 5-14 are the surface and interfacial tensions
for fluids from several Texas fields [92].
The effect of temperature on interfacial tensions for some oil-water systems
is shown in Figure 5-42 [92]; the reduction in interfacial tension with increasing