The microscopic displacement efficiency is affected by the following factors: interfacial and surface tension forces, wettability, capillary pressure, and relative permeability.
When a drop of one immiscible fluid is immersed in another fluid and comes to rest on a solid surface, the surface area of the drop will take a minimum value owing to the forces acting at the fluid-fluid and rock-fluid interfaces. The forces per unit length acting at the fluid-fluid and rock-fluid interfaces are referred to as interfacial tensions. The interfacial tension between two fluids represents the amount of work required to create a new unit of surface area at the interface. The interfacial tension can also be thought of as a measure of the immiscibility of two fluids. Typical values of oil-brine interfacial tensions are on the order of 20 dynes/cm to 30 dynes/cm. When certain chemical agents are added to an oil-brine system, it is possible to reduce the interfacial tension by several orders of magnitude.
The tendency for a solid to prefer one fluid over another is called wettability. Wettability is a function of the chemical composition of both the fluids and the rock. Surfaces can be either oil wet or water wet, depending on the chemical composition of the fluids. The degree to which a rock is either oil wet or water wet is strongly affected by the absorption or desorption of constituents in the oil phase. Large, polar compounds in the oil phase can absorb onto the solid surface, leaving an oil film that may alter the wettability of the surface.
The concept of wettability leads to another significant factor in the recovery of oil. This factor is capillary pressure. To illustrate capillary pressure, consider a capillary tube that contains both oil and brine, the oil having a lower density than the brine. The pressure in the oil phase immediately above the oil-brine interface in the capillary tube will be slightly greater than the pressure in the water phase just below the interface. This difference in pressure is called the capillary pressure, Pc, of the system. The greater pressure will always occur in the nonwetting phase. An expression relating the contact angle, θ; the radius, rc, of the capillary in feet; the oil-brine interfacial tension, σwo, in dynes/cm; and the capillary pressure in psi is given by
This equation suggests that the capillary pressure in a porous medium is a function of the chemical composition of the rock and fluids, the pore-size distribution of the sand grains in the rock, and the saturation of the fluids in the pores. Capillary pressures have also been found to be a function of the saturation history, although this dependence is not reflected in Eq. (10.2). For this reason, different values of capillary pressure are obtained during the drainage process (i.e., displacing the wetting phase by the nonwetting phase), then during the imbibitions process (i.e., displacing the nonwetting phase with the wetting phase). This hysteresis phenomenon is exhibited in all rock-fluid systems.
It has been shown that the pressure required to force a nonwetting phase through a small capillary can be very large. For instance, the pressure drop required to force an oil drop through a tapering constriction that has a forward radius of 0.00002 ft, a rearward radius of 0.00005 ft, a contact angle of 0°, and an interfacial tension of 25 dynes/cm is 0.71 psi. If the oil drop were 0.00035-ft long, a pressure gradient of 2029 psi/ft would be required to move the drop through the constriction. Pressure gradients of this magnitude are not realizable in reservoirs. Typical pressure gradients obtained in reservoir systems are of the order of 1 psi/ft to 2 psi/ft.
Another factor affecting the microscopic displacement efficiency is the fact that when two or more fluid phases are present and flowing, the saturation of one phase affects the permeability of the other(s). The next section discusses in detail the important concept of relative permeability.
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