Capillary Pressure PDF

Capillary Pressure 9.1 Capillary Pressure 9.1.1 Interfacial Tension The interfacial tension between two fluids (say fluids 1 and 2), σ12, is the force per unit length required to create new surface and is usually expressed in units of dynes/cm. Interfacial tension is a measure...

Capillary Pressure 9.1 Capillary Pressure 9.1.1 Interfacial Tension The interfacial tension between two fluids (say fluids 1 and 2), σ12, is the force per unit length required to create new surface and is usually expressed in units of dynes/cm. Interfacial tension is a measure of specific surface energy. 9.1.2 Adhesion Tension When two immiscible fluids are brought into contact with a solid surface, the equilibrium configuration is shown schematically in Figure 7.1 Since the interfacial tensions are forces per unit length, the force balance may be written as, σso = σsw + σwo cos θ where θ is called the contact angle, or, 1 Figure 9-1: Wettability for an oil-water-rock system 2 The adhesion tension is defined as, AT = σso − σsw and the contact angle may be written as, 9.1.3 Wettability and Contact Angle The ratio of the areas of the solid wetted by water and oil depend on the value of the contact angle, θ, which depends on the adhesion tension. The smaller the contact angle, the greater the area wetted by the water. The wetting preference of the solid, referred to as the wettability of the solid, is therefore related to the value of the contact angle. 3 9.1.4 Influence of Chemical Properties of Solid and Fluids Since interfacial tensions arise from molecular interactions at the solid-fluid and fluid-fluid interfaces, the chemical properties of the solid surface (mineralogy) and the fluids (oil and water) will influence the value of the contact angle and therefore wettability. 9.1.5 Capillary Pressure Consider the case of a vertical capillary tube placed in a large beaker containing water as shown in Figure 9-2. The glass is preferentially water-wet and the adhesion tension is positive causing the layer to be drawn up in the tube to a height, h, above the free water level in the beaker. If the air pressure at the free water level (h = 0) in the beaker is pa, the water pressure in the capillary at the free water level is also pa - pressures in a static system vary only with depth. The pressure on the water side of the interface in the capillary at h = h, is pw = pa − ρwgh where ρw is the density of water and g is the gravitational constant. 4 The pressure on the air side of the interface in the capillary at h = h, is pg = pa − ρggh where ρg is the density of air. The pressure difference across the interface is pg − pw = (ρw − ρg)gh Since ρg