Differentiating Formation Compressibility and Water-Influx Effects in Overpressured Gas Reservoirs
- S.W. Poston (Texas A&M U.) | H.Y. Chen (Texas A&M U.) | M.J. Akhtar (Texas A&M U.)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Engineering
- Publication Date
- August 1994
- Document Type
- Journal Paper
- 183 - 187
- 1994. Society of Petroleum Engineers
- 4.6 Natural Gas, 5.4.2 Gas Injection Methods, 5.3.4 Integration of geomechanics in models, 5.1 Reservoir Characterisation, 5.5 Reservoir Simulation, 5.2 Reservoir Fluid Dynamics
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The material-balance equation for overpressured gas reservoirs was rearranged so that the outcome variables are original gas in place (OGIP), formation compressibility, and water-influx values. A set of typical curves is presented to allow comparison of field cases and theoretical situations.
Harville and Hawkins1 and Hammerlindl2 attributed the concave downward shape of the p/z vs. Gp curve exhibited in overpressured gas reservoirs to pore collapse and formation compaction. Hammerlindl calculated PV changes to show that system compressibility changed from 28×10-6 psi-1 at initial conditions to 6×10-6 psi-1 at final conditions. Duggan3 attributed the curvature of the p/z vs. Gp curve to invasion of water from adjacent shale intervals. Reservoir pore collapse was assumed to be negligible. The water-influx concept was supported by the fact that several wells watered out. Wallace4 and Bass5 concluded that water influx was an important drive mechanism in overpressured gas reservoirs. Our experience has indicated that water influx into overpressured gas reservoirs is a fairly common occurrence.
Numerous authors6-11 have presented studies of overpressured gas reservoirs that are based on a particular model. Effects of pressure- and time-dependent formation compressibility, shale or aquifer water influx, or solution gas in the water are usually included, with varying degrees of emphasis and simplifying assumptions. However, a straightforward method to evaluate performance from overpressured gas reservoirs has never been presented. We present a rearranged form of the material-balance equation that provides such a method.
Roach12 arranged the material-balance equation that includes the effect of formation compressibility for an overpressured gas reservoir in a new form. Refs. 13 and 14 showed the utility of this method to predict future performance. Field case history studies illustrated the usefulness of this plotting technique when studying partial-waterdrive gas reservoirs. In this paper, we show how this technique may be used not only to estimate OGIP, effective compressibility, and water-influx values but also to interpret how each of these variables affects the reservoir performance history.
Components of the Material-Balance Equation
The general material-balance equation, including the effects of interstitial water, formation compressibility, water influx, and OGIP may be expressed as
where the energy terms for net water influx, Wen, and effective compressibility, ce, have been included.
Equations 2 and 3
The effective compressibility expression may be rearranged to calculate formation compressibility:
The plotting terms resulting when the equation of a straight line is applied to Eq. 1 are
for the y-axis variable,
for the x-axis variable,
for the y intercept, and
for the slope of the line.
The terms included in the x and y plotting variables of the solution plot are either pressure, cumulative gas production, or the gas deviation factor values. The unknown values (namely, OGIP, formation compressibility, and net water influx) are determined from the results of the fit of the data to a straight line. This derivation selects the outcome variables for the unknown reservoir character values, while the input variables are easily determined from field and fluid property records. Theoretically, the OGIP term may be evaluated without considering the effects of formation compressibility and water influx on performance history.
Solution Plot General Shape
Fig. 1 is an example of a solution plot for a typical pressure-depleting, overpressured gas reservoir. The line is curved at early time, then becomes straight and trends diagonally upward at later times. The derivation indicated the y intercept value of the straight-line extrapolation must be negative. Any positive intercept is theoretically incorrect. The dashed line in Fig. 1 intersects the y axis at zero and represents a critical slope line. Any intersection value above this line is incorrect. The later straight-line portion of the curve has been observed in all case histories studied.
The interpreted slope and intercept values from the straight line are used to determine the outcome variables for the particular case study. Reservoir simulation studies have shown that the straight line indicates steady- or pseudo-steady-state depletion conditions, while the curved line represents unsteady-state or transient conditions.
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