Page 473 - Standard Handbook Petroleum Natural Gas Engineering VOLUME2

Flow of Fluids 429

1. pressure gradient due to elevation
ysine = (2)

d
2. pressure gradient due to acceleration

3. pressure gradient due to viscous forces (friction)

2 =(g)=, +(g)= +(g) (6-64)

f

The acceleration element is the smallest one and sometimes is neglected.
The total pressure at the bottom of the tubing is a function of flowrate and
constituting three pressure elements:

1. wellhead pressure-back pressure exerted at the surface from choke and
wellhead assembly
2. hydrostatic pressure-due to gravity and the elevation change between well-
head and the intake to the tubing
3. friction losses, which include irreversible pressure losses due to viscous drag
and slippage
Figure 6-37 illustrates this situation for each single-phase and two-phase flow.
Possible pressure losses in a complete system are shown in Figure 6-35. For a
given f lowrate, wellhead pressure and tubing size there is a particular pressure
distribution along the tubing. The pressure-depth profile is called a pressure
traverse and is shown in Figure 6-38. Gas liberation, gas expansion and oil
shrinkage along the production tubing can be treated as a series of successive
incremental states where saturated oil and gas coexist in equilibrium (flash
process). This model is shown in Figure 6-39. At (a) the single-phase oil enters
the wellbore; (b) marks the first evolution of gas, at the mixture’s bubble point;
and both (c) and (d) show the traverse into the two-phase region. Note that the
gas and oil P-T diagrams describing equilibrium phases at points (c) and (d)
are not the same. This means that the composition of equilibrium gas and oil
phases changes continuously in the two-phase region. As the two-phase region
is entered and gas is liberated, oil and gas phases change in volume and
composition, but they are always in a saturated state, the gas at its dew point
and the oil at its bubble point. In Figure 640 the separation process is shown
in forms of the resulting gas and oil.
Engineering analysis of two-phase fluid flaw in pipes has focused primarily on
the problem of predictive pressure drop, or pressure gradient from Equation 6-64.