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

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

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

( P_c )_Drainage = ( 2σcosθ_R ) / r

Case 2: Equilibrium

θ_E = equilibrium or static contact angle

P_c = ( 2σcosθ_E ) / r

Case 3: Displacement by imbibition

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

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

( P_c)_Imbibition = ( 2σcosθ_A ) / r

Figure 2-62: Contact Angle Hysteresis during the Displacement

In general it can be stated that:

Therefore at the same saturation:

Figure 2‑63 shows dynamic contact angle behavior

Figure 2-63: Dynamic Contact Angle Behavior

Figure 2-64: Static Values of Advancing and Receding Contact Angles at Rough Surfaces versus Values at Smooth Surfaces (where θ_E refers to smooth surface measurements)