Fundamentals of Fluid Flow in Porous Media


Chapter 2

Multi-phase Saturated Rock Properties:

Capillary Pressure Hysteresis: Contact Angle Hysteresis During Displacement

According to the definition ‘hysteresis’ occurs when a measured variable depends on the direction of change of an independent variable.  According to eq.(2‑78) contact angle hysteresis will cause hysteresis in the capillary pressure. Consider a capillary tube containing two immiscible fluids (Figure 2‑62):

Case 1: Displacement by drainage

θR = receding contact angle (i.e. wetting phase receding)

Occurs when the non-wetting phase displaces the wetting phase by increasing Pnw.

( Pc )Drainage = ( 2σcosθR ) / r

Case 2: Equilibrium

θE = equilibrium or static contact angle

Pc = ( 2σcosθE ) / r

Case 3: Displacement by imbibition

θA = advancing contact angle (i.e. Wetting phase is advancing)

Occurs when the non-wetting phase is displaced by the wetting phase by a decrease Pnw

( Pc)Imbibition = ( 2σcosθA ) / r

Contact Angle Hysteresis During Displacement
Figure 2-62: Contact Angle Hysteresis during the Displacement

In general it can be stated that:
Equation 2-99

Therefore at the same saturation:
Equation 2-100

Figure 2‑63 shows dynamic contact angle behavior

Dynamic Contact Angle Behavior
Figure 2-63: Dynamic Contact Angle Behavior

Static values of advancing and receding contact angles at rough surfaces versus values at smooth surfaces
Figure 2-64: Static Values of Advancing and Receding Contact Angles at Rough Surfaces versus Values at Smooth Surfaces (where θE refers to smooth surface measurements)




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