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270                                       Intelligent Digital Oil and Gas Fields


          ICD is equalized along the horizontal section, which results in an excellent
          oil-sweep efficacy from the oil-water contact (OWC) to the wellbore.

          7.6.5 Modeling AICDs for Oil Wells

          As mentioned in Section 7.2.2, AICD is the newest family of ICDs that
          are self-regulating fluidic diodes capable of restricting the flow of fluids
          based mainly on differential densities and viscosities. Contrasting with
          an ICD, which generates high-flow restriction for heavy oil, the AICD
          can sometimes be more feasible in restricting water and gas than a tradi-
          tional ICD, which is attributed mainly to the differential density. One of
          the main benefits of AICDs is that it can generate spontaneous changes in
          fluid flow restriction without control lines, moving parts, or download
          mechanical or electrical devices for well intervention and moving
          choke size.
             In some laboratory experiments with single-phase flow (oil or water),
          Least et al. (2012, 2013) showed for the first time the performance of AICDs
          using oil fluids from 3 to 200 cPs. They found that the pressure drop across
          an AICD valve could be governed by the ratio of fluid density and viscosity
          compared with calibrated density and viscosity of the fluid tested at the lab.
          To model the subcritical pressure drop across an AICD, the following
          equations can be used:

                                         ρ 2      μ    β
                           P out  P in ¼ X    mix     std   q α        (7.6)
                                          ρ std  μ mix
                     ρ mix  ¼ water:vol ρ + oil:vol ρ + gas:vol ρ g    (7.7)
                                                   o
                                       w
          where
          P out is the flowing BHP at the outlet in psi,
          P in is the flowing BHP at the inlet of the valve in psi,
                                         3
          q is the total flow rate of fluids in ft /s,
          ρ mix is the fluid density of the mixture phases at pressure and temperature in
                3
          lbm/ft ,
          ρ std is the fluid density measured at laboratory condition used for calibration
                          3
          proposes in lbm/ft ,
          ρ o , ρ w , ρ g is the oil, water, and gas densities at pressure and temperature in
                3
          lbm/ft ,
          μ mix is the mixture fluid viscosity calculated at the average of (P out   P in )in
          cP, μ std is the fluid viscosity measured at laboratory condition used for
          calibration proposes in cP,
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