S.W. Poston, H.Y. Chen, A. Deshpande
Texas A&M University
College Station, Tex.
To determine original gas in place (OGIP), gas operators can reduce testing costs by replacing static pressures with short-term build-up pressures. These cost savings are the result of reduced well downtime and less lost production during testing.
This new, isochronal, transient p/z (pressure divided by gas compressibility factor) method uses transient, or shut-in pressure build-up data measured with respect to shut-in time.
The slope of these isochronal plots is the same as the standard, static pressure (p/z-vs.-G,) plot.
CONCEPT
Besides the transient, or shut-in pressure build-up data, p,s, measured with respect to shut-in time, this method requires initial pressure and cumulative production, GP, measured at the time of shut-in.
The normal p/z-vs.-Gp plot is a straight line for a pressure depleting gas reservoir with low-to-moderate pressure. Reference 1 demonstrates that the transient build-up pressure, pws, divided by the appropriate z-factor term (pws/z) will be less than the static pressure (p/z) plot. That reference theorizes that the isochronal, transient p/z-vs.-Gp plot will have the same slope as a plot using stabilized pressure data.
Fig. 1 illustrates the relationship between the static and the isochronal, transient p/z lines.
EQUATIONS
The Chen-Vu equation, Equation I in the equation box (see also nomenclature box), combines the gas material balance and the transient and pseudosteady-state solutions to the gas flow equation. 2 The equation is for either the constant pressure or constant-rate production cases.
Equation 2 defines the difference between p/z at static and shut-in pressures.
From Equation 2 and an expression for dimension-less time, Equation 1 can be rearranged to obtain Equation 3. Equation 3 implies that the term on the equation's left-hand side, delta (p/z), will be constant if all the parameters on the right-hand side remain constant. Remember, delta (p/z) represents the vertical distance between the transient, pws/Z, and the static pressure p/z plot.
The equation produces a line with a slope obtained from the isochronal, transient pressure data. The line can be shifted upward to the known p/zi and then extended to intersect the GP axis at the OGIP. Therefore, the need for using static pressures in the p/z plot becomes unnecessary.
APPLICATION
The average viscosity-compressibility, mu-cg, [see equation] term is the primary problem with the isochronal, build-up pressure analysis. The term mu-cg changes in almost a linear manner and remains essentially constant at higher pressures. However, the slope of mu-cg varies nonlinearly at low pressures.
An arithmetic average of mu-cg is accurate enough for high to moderate pressures but gives incorrect values at low pressures.
Previous work 3 shows that the average gas viscosity and compressibility must be evaluated over the area of the integral between the static reservoir pressure (p) and the bottom hole shut-in pressure pws.
The term delta (p/z) will not remain the same over time if there is a significant difference between p and pws. The changing mu-cg at large pressure differentials is the main problem with isochronal, transient pressure p/z method.
However, research shows that mu-cg remains largely unchanged when drawdown pressures remain sufficiently high and close to the linear portion of the curve or if the drawdown is not significant. 2
A large number of simulation studies, 3 4 indicate that the static reservoir pressure and the flowing bottom hole pressure do not vary appreciably for reservoirs with a permeability greater than 0.5 md. Therefore, for gas reservoirs of 0.5 md or greater, mu-cg evaluated at the unknown p and at pws may be safely assumed to be the same.
ERROR PLOT
A commercial, radial, single-phase simulator was used to model the behavior of a well located in the center of a gas reservoir. Assumptions included no well bore storage and formation damage.
The study evaluated combinations of permeabilities, thickness, and producing rates that ranged as follows:
- Drainage area = 160 and 640 acres
- Reservoir temperature 220 F.
- Gas gravity = 0.7
- Porosity = 10%
- Permeability = 0.1, 0.5, 1, 1.5, 3, and 5 md
- Sand thickness = 10, 20, and 30 ft
- Producing rates 100, 175, and 250 Mscfd.
A well completed in the simulated reservoir was periodically closed in during each depletion study. Transient build-up and static pressures were calculated and applied to the normal and isochronal (p/z-vs.-Gp) material balance plotting techniques.
After determining the OGIP from the extrapolated static and isochronal methods, an error-vs.-shut-in time curve for various combinations of permeability, thickness, and gas flow rate was calculated.
A series of curves illustrated the effect of shut-in time on the percent error. These curves were coalesced to a single figure by grouping the kh/q terms for each study.
Fig. 2 is the error plot for reservoirs with a permeability of 0.5 md or greater.
The gas flow rate does not affect the error curves significantly at these higher permeabilities because the bottom hole flowing pressure, pwf, is not appreciably different than p.
The pwf value is the outer limit of any pws value. If pwf lies within acceptable limits, then pws must lie within these limits also, because pws must be closer to p.
The error in estimating OGIP is within 15% of all simulated values when the kh/q is more than 0.03 md-ft/Mscfd.
Transient pressures in the p/z-vs.-Gp plot for low kh/q give inaccurate estimates of OGIP for low-permeability reservoirs. This is caused by the large drawdown effect during production.
ERROR PLOT EXAMPLE
As an illustration of the error plot's utility, assume that a well is producing at a rate of 750 Mscfd from a 20-ft thick sand interval. The well drainage area is 160 acres, sand porosity is 15%, and permeability is 3 md.
Conventional calculations indicate that the well must be shut-in for at least 33 days to attain static conditions.
What will be the error in OGIP if an isochronal, transient, p/z plot is used in place of the normal static p/z-vs.-Gp plot? From Fig. 2, the error in OGIP is only 3% for a pressure obtained after a 5-hr shut-in.
The error chart values are not unique because the fluid property changes are not taken into account in the correlation parameter. There will be some variation according to the character of the gas, but for most cases this variation will not be sufficiently large to alter the values in Fig. 2.
FIELD STUDY
For a North Texas well, the isochronal pressure and static pressures were compared in a p/z-vs.-G. plot. The data from five pressure build-up tests, Table 1, were used.
Four of the five tests were taken early in the life of the reservoir. The time to attain static conditions indicates that the build-up pressures had not stabilized in the last four tests, even after 70 hr of shut-in time.
There was little loss in reservoir pressure over the period spanning the first three build-up tests. This circumstance causes a less pleasing spread than one would hope for.
The Mathews-Brons-Hazebroek method was used to calculate the average static reservoir pressure, p.
The well was assumed to be in the center of a 640 acre circular drainage area. This is a close approximation to the geological interpretation.
The change in the skin factor from a positive to a negative value after Apr. 3, 1987, was caused by a hydraulic fracture treatment.
The p/z-vs.-Gp values plotted in Fig. 3 illustrate that the static and isochronal plots are nearly parallel. Note the small difference in the isochronal and static lines.
It is evident that the 30 min isochronal pressure gives an answer as accurate as the static pressure extrapolation. Note that this observation is correct as long as the pressure measurement is beyond the well bore Storage and skin effects.
The static pressure extrapolation to the x axis gives an OGIP of 19.8 bcf. This slope shifted to the p/zi intercept and extrapolated to the x axis essentially gives the same OGIP value.
Fig. 3b accentuates the difference between the isochronal and static pressure lines.
Note that the 15-min line is not parallel. This is probably caused by a pressure drop induced by apparent well bore damage. The skin effect would cause the apparent reservoir permeability to be reduced to less than the k=0.5 lower limit.
The calculated reservoir permeability is approximately 7 md. Recall that the isochronal chart discussed in the previous section is useful for all reservoirs displaying a reservoir permeability greater than 0.5 md. A gas gravity of 0.68 was input into a standard correlation to calculate the z factors.
The error plot (Fig. 2) illustrates why this divergence occurred. From Buildup No. 2, kh/q = 224 md-ft/2.628 MMscfd or 0.085 md-ft/Mscfd. Using 0.085 in Fig. 2, the error plot indicates a 2.5% error for a 1 hr shut-in time. The actual error between the static and 1-hr isochronal extrapolations is 1.8%.
Similarly, a 2.0% error between the static and isochronal values is determined when the shut-in time is increased to 6 hr. The actual error between the static and 1-hr isochronal extrapolations is 1.2%.
ACKNOWLEDGMENT
The authors wish to thank the Gas Research Institute (GRI), Oryx Energy Co., and Kerr McGee Producing Corp. for funding this project.
REFERENCES
- Sullivan, S.A., and Poston, S.W., "Using Short-Term Pressure Build-up Tests for Reserves Estimation in Tight Gas Reservoirs," Paper No. SPE 17707, Gas Technology Symposium, Dallas, 1988.
- Vu, T.D., Poston, S.W., and Chen, H.Y., "Using Short-Term Pressure Build-up Tests to Calculate Gas Reserves," Paper No. SPE 20111, Permian Basin Oil and Gas Recovery Conference, Midland, Tex., 1990.
- Protos, N.E., "Application of the Isochronal, Transient p/z Plotting Method for Determination of Original Gas In Place, to Low Permeability Reservoirs," Master of Science Graduate Thesis, Texas A&M University, August 1991.
- Guerini, A.F., "Criteria to Determine Gas Reserves Using Short Time Build-up Tests," MS Graduate Thesis, Texas A&M University, December 1991.
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