This paper presents the derivation of a general gas material balance that has particular application to high-pressure gas reservoirs, [both normal pressured and overpressured (geopressured)]. Its main application is to calculate original gas in place and assist in calculating remaining recoverable reserves from pressure/production data.
The form of the material-balance equation is (p/z)[1-ce(p)(pi-p)]=(p/Z)i(1-Gp/G), which includes a pressure-dependent cumulative effective compressibility term ce (p)that is defined in terms of the following reservoir parameters: pore compressibility, water compressibility, gas solubility, and total water associated with the gas reservoir volume. "Associated" water includes connate water, water within interbedded shales and nonpay reservoir rock, and any limited aquifer volume, cephysically represents the cumulative change in hydrocarbon pore volume (PV)calculated by compressibility effects and encroaching water.
High pressure gas reservoirs typically have concave downward p/z vs. Gp plots which may result in serious overestimation of original gas in place and remaining recoverable reserves. The proposed form of the gas material balance equation provides a method to linearize the p/z vs. Gp plot, and thereby predict the true original gas in place. A method is suggested to determine initial gas in place by analyzing the behavior of cumulative effective compressibility back calculated from pressure/production data. The ce(p) function determined by this procedure, or estimated from logs and geological maps when sufficient production data is not available, is then used to forecast pressure/cumulative behavior. Two field examples are provided showing the application of the material balance equation to high pressure gas reservoirs.
High pressure gas reservoirs experiencing depletion drive to have downward curving p/z vs. Gp behavior. Incorrect extrapolation of early depletion data may result in serious overestimation of original gas in place and remaining reserves.
Bruns et al.1work in 1965 was a result of a field study conducted a large moderately overpressured gas reservoir in the Texas Gulf Coast area. Investments were made, and never needed, based on linear extrapolation of the early field p/z vs. Gp performance to an apparent original gas in place that was later found to be overstated by about 200 Bscf. Fig. 5 in Ref. 1 (Run 20) shows the concave downward curvature typical for the pressure response of a limited external aquifer system that simulated the reservoir's response.
This type of "limited" aquifer behavior, where pressure in the reservoir and aquifer are virtually equal, led to the derivativation of a general material balance for high pressure gas reservoirs (see Appendix, Ref. 2). The derivation includes pressure-dependent rock and water compressibility(with gas evolving from solution). All water and rock volumes associated with the reservoir and available for expansion, including a limited aquifer volume, were included in a cumulative effective compressibility term ce(p). Rock and water compressibilities were defined to account for cumulative changes in volume to be multiplied by the cumulative pressuare drop (pi-p); instantaneous compressibilities are not used at all. The final form of the material balance is similar to that published by Ramagost and Farshad,3 except that they considered ce, as a constant. The general gas material balance as presented in this paper defines a cumulative effective compressibility ce(p) as a function of pressure.
Harville and Hawkins4 and Hammerlindl5 attribute the concave dowaward shape of p/z vs. Gpcurves obtained in abnormally pressured gas reservoirs entirely to pore collapse and formation compaction. No definition of pore collapse is given in Ref. 4, but a plot of back calculated PV change indicated a system compressibility change from 28´10-6 psi-1 at initial pressure to about 6´10-6 psi-1 at low pressures. This magnitude of PV change implies associated water volume. The decreasing "system"compressibility is expected for an overpressured reservoir with pressure-dependent PV compressibility, and based on results presented in this paper pore collapse is not a necessary condition for such behavior.
The Anderson "L" reservoir performance presented by Duggan6 shows curved p/z vs. Gp field behavior which was primarily attributed to shale water influx with no evidence of reservoir pore compaction. The water influx drive mechanism was supported by the fact that several wells watered out. Wallace7 also concluded that shale water influx is an important drive mechanism in abnormally pressured gas reservoirs. Bass8 discounts shale water influx, and attributes curved p/zvs. Gp behavior to peripheral water influx from a limited aquifer and formation compaction treated with a constant PV compressibility cf. For a limited aquifer, Bass defines a term Fp as the ratio of peripheral water PV to the PV of gas-bearing rock.
Roach9 and Ramagost and Farshad3 both use the term [1-ce(pi-p)] for geopressured and abnormally pressured gas reservoirs. Both authors consider ce a constant and they consider the Anderson "L"example.
Bernard1 does not accept the rock collapse theory as the cause for overpressured p/z vs. Gp behavior, concluding that water influx is the basic drive mechanism. He also uses p/z[1-c(pi-p)] where c is a "catch-all"term for treating the effects of rock and water compressibility, a small steady-state acting aquifer, and steady state shale water influx. He further states that the term c is almost impossible to quantify in terms of reservoir properties.
Begland and Whitehead,11 Prasad and Rogers,12 and Wang and Teasdale13all present studies of overpressured gas reservoirs based on computer models. Refs. 11 and 12 treat cfand cw as functions of pressure, including the effect of solution gas in the water. Extemal water sources are also included in Refs. 12 and 13. The differential forms of the material balance used in these references correctly apply instantaneous compressibility in a history-matching approach to determine initial gas in place. A direct plot of (p/z)[1-ce(pi-p)] vs. Gp was not made because the ce term had not been defined.
Poston and Chen14 analyzed several abnormally pressured gas reservoirs, and recognized that calculated values of ce>30´10-6 psi-1 required to linearize the material-balance plot reflected the influence of water influx.
Bourgoyne15 demonstrates that reasonable values of shale permeability and compressibilities treated as a function of pressure can be used to match abnormal gas reservoir performance behavior. He points out, however, that determining kand cf of the shale necessary for modeling this behavior is practically impossible.
Ambastha16 uses Bourgoyne's general material-balance equation to develop a graphical matching technique based on a constant effective compressibility ce. The example given in that paper shows a lack of uniqueness in determining initial gas in place.