In our previous discussion, we assumed that properties, such as, viscosity and density (for use in the Reynolds Number calculation in Equation 6.04) or the density (for use in the Darcy-Weisbach Equation itself in Equation 6.12) were constant over the entire length of the pipe/tubing. As fluids flow up the vertical section of tubing, the pressure drop may cause changes in these properties for slightly compressible fluids. In addition, the upward flow of fluids in the vertical section of tubing is a non-isothermal process, and this may also cause changes in these properties as fluids flow upward. As already mentioned, in the extreme case, fluids may drop below the bubble-point pressure, resulting in multi-phase flow through multiple flow regimes (see Table 6.01). For these cases, Segmented Wells can be used.
Segmented wells are wells where the entire well length is partitioned into multiple, smaller well segments. The pressure drop along one segment is calculated using the local pressure and temperature conditions (assuming an appropriate heat transfer model is available). Once the calculations are performed for one segment of tubing, the Terminal Pressure (pressure at the outlet end of the tubing section - in Figure 6.04) is used as the starting pressure (or inlet pressure, ) for the next segment of the well.
In addition to fluid property changes during flow, there may be design reasons for using segmented wells. For example, the deviated and horizontal wells shown in Figure 6.02 will require the use of segmented wells: at least one segment for the non-vertical section of the tubing and at least one segment for the vertical section of the tubing. In addition, there may be reasons for designing a Tapered Tubing String (a tubing string with different inner diameter tubing sizes along different lengths of the well). These wells are designed to keep a desired flow velocity at different depths in the well.
The use of segmented wells for modeling well production is the most common method of modeling actual wells. Well modeling is a common activity for Production Engineers.