A straight-line plot of p/z vs. Gp (Cumulative Gas Production) is widely used to estimate the Original Gas in Place. It is known as the p/z plot technique. The linearity of that plot has been historically known to be a unique feature of a volumetric (closed) reservoir. In this paper, we show that a uniqueness problem may exist when using the p/z plot. In other words, if the reservoir is in contact with an aquifer, a straight-line may exist on that plot causing a major overestimation of Original Gas in Place. This uniqueness problem is proved to be due solely to the unsteady-state nature of aquifers
A simulation study was performed to determine the conditions for such a misleading straight line. Several examples demonstrate that it is possible to construct a synthetic data set for a water-drive gas reservoir such that a misleading straight-line plot is obtained. This misleading straight-line is shown to be due to certain rate schedules. The conventional material balance equation is coupled with an aquifer mathematical model to obtain this schedule. In this paper, an actual field case is presented as an example of this possible overestimation of Original Gas in Place due to a misleading linear p/z plot.
The material balance equation is an expression of the law of the conservation of mass, which is commonly used in reservoir engineering. For reservoirs with no water influx and no water encroachment and if we neglect formation and water compressibility's, it will have the following form Equation (1) (Available in full paper)
Which can be written also as Equation (2) (Available in full paper)
If we include all the forces that we previously neglected, then we will have the following equation Equation (3) (Available in full paper)
Which can be written also as Equation (4) (Available in full paper)
If we neglect the influence of the formation and water compressibility then Ramagost factor RM will be equal to 1, and therefore equation (4) will be reduced to become as Follows Equation (5) (Available in full paper)
We can re-write equation (2) to be simplified in the following form Follows Equation (6) (Available in full paper)
where the constant, Follows Equation (7) (Available in full paper)
Now, equation 6 is of interest to us because it states that, there is a linear relationship between p/z and the cumulative volume of produced gas Gp as shown by the solid line in Fig. 1. If the trend of this straight -line is extrapolated to p/z = 0, then we can obtain an estimate of the Original Gas in Place, G, since when p/z = 0 Equation (Available in full paper)
It is important at this point to repeat the statement by Chierici1 concerning equation 2 where he says: " The linear relationship is a necessary but not a sufficient condition for the reservoir to be of the closed type".
