5.10 Multi-phase, Multi-Rate Buildup Analysis

The basic equations used for multi-phase pressure buildup analysis are quite similar to those used for single phase. The basic equation is

where the flow rates q1 through q _n are re-expressed in total fluids q _t (stb) as

Eq. 5-88 is that of a straight line of the form Y = b + mX where Y = p _ws where

Figure 5-24 shows a hypothetical flow history of a well. Upon shut-in, a plot of the bottom-hole shut-in pressure versus the dimensionless summation Cartesian (Eq. 5-88) assumes a characteristic shape given in Figure 5-25. After the wellbore effects have dissipated, the straight-line relationship holds and the observed slope can be translated into values of total mobility:

Figure 5-24: Flow history of an oil well

Figure 5-25: Typical pressure buildup

The gas and oil formation volume factors are pressure-dependent. It is recommended that as a first approximation they may be selected at the highest observed pressure. Later, for subsequent runs if desired they may be selected at average pressures given below:

To calculate the skin factor and its associated pressure drop, the following equations are used:

The factor, F, in Eq. 5-92 corrects for short flow times. In most other cases, F will equal or approach to 1.

In Eq. 5-92, the total compressibility, c _t, is

For multiphase flow, below the saturation or bubble point pressure:

The gas compressibility may be estimated from correlation charts such as those...