A quadratic cumulative production model for the material balance of an abnormally pressured gas reservoir

The premise of this research is the concept, development, and application of an approximate relation for the material balance of abnormally-pressured gas reservoirs. The approximation is formulated directly from the rigorous material balance for the case of an abnormally-pressured gas reservoir.

The primary assumption in this derivation is that WGp <1 or Ce(p)(pi-p)<1. Further, we can proceed by assuming that W is either constant or some arbitrary function. If we assume W=constant, then the following form results:

At first glance there may be concern that this approximation is not sufficiently valid for field applications ? however, we have shown this relation to be an extraordinarily accurate approximation of the rigorous material balance.

This result is suited not only for use as a characteristic model, but also for use as a data analysis mechanism (i.e., this result is used to develop a suite of analysis plots, plotting functions, a type curve, etc.).

In this work we provide the following new results:

1. A suite of 6 (six) plotting functions based on the p/z-Gp2 material balance model.
2. A suite of 4 (four) p/z-Gp performance plots which are used to calibrate analysis.
3. A new type curve in terms of a dimensionless pressure function (pD=(pi/zi-p/z)/pi/zi) versus a dimensionless cumulative production function (GpD=Gp/G), where the type curve solution is based on the new p/z-Gp^2 (a quadratic material balance) model.