Capillary Number Dependent Hysteretic Model Sample Clauses

Capillary Number Dependent Hysteretic Model or An important new extension of these models is the inclusion of their dependence on interfacial tension via the trapping number. The capillary number traditionally used by both the groundwater and oil reservoir literatures has been generalized by Xxx [1995] and is now called the trapping number. We assume that 1) the capillary pressure parameters n and m are independent of trapping number and 2) the residual oil saturation (Smax ) and residual water (or microemulsion) saturation (Swr) are functions of trapping number. We compute the residual water and residual oil saturations as a function of trapping number as follows: ⎛ Slow − Shigh ⎞ Sℓr = min⎜ Sℓ , Shigh + ℓr ℓr ⎟ where ℓ = w (or microemulsion), oil (3.12) ⎝ ℓr where the Shigh and Slow are the phase ℓ residual saturations at high and low trapping numbers, Tℓ is the ℓr ℓr adjustable parameter. This correlation was derived based on the experimental data for n-decane (Xxxxxxx, 1990) and have recently been successfully applied to residual PCE as a function of trapping number measured by Xxxxxxx et al. [1996]. The trapping number NTℓ is computed as NTℓ = (3.13) − k ⋅ ∇Φ → → ℓ ' − k ⋅ g ( ρ → [ → ℓ' − ρ )∇h ℓ ] σ ℓℓ' where h is the vertical depth (positive downward), ρℓ and ρℓ' are the displaced and displacing fluid densities, and the gradient of the flow potential is given by ∇Φℓ' = ∇Pℓ' − g ρℓ' ∇h . or