text: RIC wettability characterization technique is based on a modified form of Washburn's equation (1921). The technique enables relatively quick and accurate measurements of wettability in terms of contact angle while requiring no complex equipment. The method is applicable for any set of reservoir fluids, on any type of reservoir rock and at any heterogeneity level. It characterizes wettability across the board from strongly water to strongly oil wet conditions.
  The step of deriving the modified form of Washburn equation for a rock/liquid/liquid system involves acquiring a Washburn equation for a rock/air/liquid system. The Washburn equation for a rock/air/liquid system is represented by:
  Herein, "t" is the penetration rate of liquid into a porous sample, "μ" is the liquids viscosity,  "ρ" is the liquids density, "γ" is the liquids surface tension, "θ" is the liquids contact angle, "m" is the mass of the liquid that penetrates the porous sample and "C" is the constant of characterization of the porous sample. evaluating a value of "γ" using a young’s equation for a rock surface/water/air system (Figure 2) and a value of "γ" using young’s equation for a liquid/liquid/rock system is represented as:
  "γ" is the surface tension between the oil and water system, "γ" is the surface tension between oil and solid system and "γ" is the surface tension between water and the solid system. Using  Young's equation for a rock surface/ water/air system and substituting in equation (2) to obtain equation 3:
  Rearranging equation (1) to factor out γ obtains equation (4), wherein γ a liquid-vapor surface tension is:
  Realizing that γ (liquid–vapor surface tension) is equivalent to γ (oil–air surface tension), or γ (water–air-surface tension), substituting equation (4) in equation (3) and cancelling out similar terms obtains equation (5):
  Therein, γ is liquid-vapor surface tension, γis oil-air surface tension, γ is water-air surface tension, µ is viscosity of oil and  µ is viscosity of water. cosθ is contact angle between water and oil; representing a relationship between a mass of water imbibed into the core sample and a mass of oil imbibed in the core sample with an equation (6):
  Therein ρ is density of water and V is volume of water imbibed, ρ is density of oil and V is volume of oil imbibed, the amount of water imbibed and amount of oil imbibed under gravity are same; and air behaves as a strong non-wetting phase in both an oil–air–solid and a water–air–solid systems, thereby indicating that both oil and water behave as strong wetting phases, resulting in equal air/oil and air/water capillary forces for the same porous media and for a given pore size distribution. Thus, a mass change of a core sample due to water imbibition is equal to a mass change of a core sample due to oil imbibition, because water or oil penetration of the porous media at any time is a function of a balance between gravity and capillary forces. The mass of water imbibed into a core sample is approximately equal to a mass of oil imbibed in the core sample core samples of a same rock type and dimensions, and for equal capillary forces;
  Cancelling out g in equation(6) gives equation (7):
  which means
  Therein, m is mass of water and m is mass of oil. Factoring out </small> from Eq. 5 to obtain Eq. 9, gives Modified Washburn Equation:
  Therein θ is the contact angle of liquid/liquid/rock system, μ is a viscosity of oil phase, μ is a viscosity of water phase, ρ is density of oil phase in g/cm, ρ is density of water phase in g/cm, m is mass of fluid penetrated into a porous rock, t is time in min, γ_ is the surface tension between an oil and a water in dyne/cm, and ∁ is a characteristic constant of the porous rock.