Page 354 - Fundamentals of Reservoir Engineering

REAL GAS FLOW: GAS WELL TESTING 289

8.12 PRESSURE BUILDUP ANALYSIS IN SOLUTION GAS DRIVE RESERVOIRS

The pressure buildup theory described in sec. 7 of the previous chapter was developed
for liquid flow and is therefore only appropriate for pressure surveys in undersaturated
oil reservoirs. For routine pressure surveys conducted throughout the producing
lifetime of the field, it is more likely that the average pressure will be below bubble point
so that there will be two phases, liquid oil and free gas, in the reservoir.
17
To analyse pressure buildup tests under these circumstances, Raghavan has
suggested the use of the integral transformation

p k(S )
′
m(p) = ro o dp (8.62)
p b µ o B o

which again is referred to as a pseudo pressure, only in this case applied to the flow of
oil, as denoted by the subscript "o". The k ro(S o ) is the oil relative permeability, which is
a function of the oil saturation, while the other parameters, µ o and B o are functions of
pressure. This leads to a certain degree of difficulty in determining the relation between
pressure and saturation required to evaluate equ. (8.62). Raghaven has shown that
this relationship can be obtained from the gas-oil ratio equation which expresses the
ratio of the reservoir gas to oil rates at the time of closure of the well, i.e.

(R R )B g (rb / gas) k rg µ o
−
s
B o (rb / oil) = µ g k ro
k rg µ B
or R = R + o o (8.63)
s
µ g k ro B g

In this relationship, R is the fixed value of the producing GOR at the time of closure and
therefore, since k rg and k ro are functions of the oil saturation and B o, B g and R s are
functions of pressure, equ. (8.63) implicitly defines the pressure-saturation relationship.
The steps in evaluating the pseudo pressure integral, equ. (8.62), are then

1) Using the value of R at the time of the survey, determine the relation k rg/k ro as a
function of the pressure, using equ. (8.63).

2) Providing gas-oil relative permeability curves are available (k ro and k rg as
functions of S o, refer sec. 4.8) the relation between k ro and pressure can be
determined.

3) Using the trapezoidal rule, evaluate m(p) as a function of pressure, in the same
′
way as demonstrated in table 8.1.
It should be noted that this m(p) function only reflects conditions near the well at the
′
time of the survey and must be re-calculated for each pressure survey, as R varies.

Using the m(p) pseudo pressure, the constant terminal rate solution of the radial
′
diffusivity equation can be expressed in dimensionless form as