6.8 Finite Reservoir Behavior

Equation 2 66 may represent flow from a finite reservoir, in the absence of skin and turbulent effects. Equation 2 66 may be written in terms of pseudopressure with substitutions for dimensionless quantities, and including an apparent skin factor s ?, as

Superposition of a buildup on the drawdown then gives

For ?t ? t _P;

Equation 6 4, for ?t ? t _P, then simplifies as

A plot of ?( p _ws) versus ( t _P + ? t) ?/ t gives, initially, a straight line of slope m. Extrapolation of the line to an infinite shut-in time ?t, or , does not result in a value for ?( p _i); the extrapolated value is called ? and can be used to obtain p _R, as described later. Figure 6 14 illustrates a typical buildup plot for a finite reservoir. Note that t _P is a pseudoproduction time in hours and is calculated by

where G _p = cumulative production since well completion, mmscfd, q _sc = constant rate in mmscfd just before shut-in, and t _DA is a dimensionless time given by

Figure 6 14: Buildup semilog plot finite reservoir.

If real gas potential ?( p) is replaced by bottom-hole pressure squared, p ², Eq. 6 14 becomes

Equation 6 4 becomes

Equation 6 16 becomes

A plot of versus gives a straight line of...