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Permeability estimation in tight gas reservoirs
In addition to knowing the values of in-situ stress, it is also extremely important to know the values of formation permeability in every rock layer. The values of permeability control everything from gas flow rate to fracture fluid leakoff. It is impossible to optimize the location of the perforations, the length of the hydraulic fracture, the conductivity of the hydraulic fracture, and the well spacing, if one does not know the values of formation permeability in every rock layer. In addition, one must know the formation permeability to forecast gas reserves and to analyze post-fracture pressure buildup tests. To determine the values of formation permeability, one can use data from logs, cores, production tests, and prefracture pressure buildup tests or injection falloff tests.
Contents
Log-derived permeability
The most data that are available vs. depth comes from openhole logs. If the logs are analyzed correctly, it is often possible to generate estimates of formation permeability vs. depth using the logging data. However, to ensure the values are representative of the permeability of the particular formation, the correlations used must be calibrated with:
- Core data
- Production data
- Pressure transient data
The following equations have been used in the industry over the years to correlate logs with permeability.^{[1]}^{[2]}^{[3]}^{[4]}^{[5]}^{[6]}
Kozeny (1927) and Carman (1938):
Berg (1970):
Timur (1968):
Coates (1974):
Coates (1981):
To use these equations, the values of porosity, water saturation, and irreducible water saturation are obtained from logging data. The various authors suggested ways of determining the values of:
- Surface area
- Grain diameter
- Relative permeability
The equations of Timur and Coates are the most widely used correlations.
In 1993, a paper^{[7]} was published that presented another method for correlating formation permeability with log data, as shown in Eq. 6.
where
e^{1} | = | 5.87–6.89, |
e^{2} | = | 0.2–0.3, |
e^{3} | = | 1.18–2.54, |
e^{4} | = | 1.08–1.65, |
and | ||
U | = | correlation factor. |
Using this equation to correlate log and core data from SFE No. 3,^{[8]} Eq. 7 was derived. The correlation is presented in Fig. 1.
Notice that, once the correlation is developed, only log data from the GR, dual induction, and porosity logs are used to estimate permeability.
In summary, obtaining permeability from logging data is very useful because it provides the engineer with estimates of permeability vs. depth. However, to be accurate, the engineer must correlate the logging data with permeabilities measured from core or computed from production or pressure buildup data.
Production data analyses
Usually, production data are available for technical calculations. Production data can be measured from a well after it is perforated and before it is fracture treated. Also, production data could be available from other nearby wells producing from similar intervals. Using a computer model based on Darcy’s law, one can estimate values of formation permeability. The model can be a simple single-layer, single-phase, single-well analytical model,^{[9]} or it can be a complicated, multiwell, multilayered, multiphase finite difference model. For a typical tight gas reservoir, the simple analytical model is usually adequate.
Fetkovich^{[10]} published type curves that are commonly used to analyze production data, as illustrated in Fig. 2. One can either manually analyze production data using the type curves or one can use an analytical model. Fig. 3 illustrates how one set of production data were analyzed to determine estimates of formation permeability, skin factor, and drainage area using an analytical model. Several papers have been written to better explain how to analyze production data using models.^{[11]}^{[12]}^{[13]}
In tight gas reservoirs, especially when analyzing prefracture production data, it is often difficult to flow the well to produce at rates high enough to measure. In addition, because the well has to be fracture treated to be economic, prefracture flow tests are often not even run. If they are run, the flow period is very short. As such, the main goal is to measure flow rates and pressures and to analyze those data to determine an estimate of formation permeability and, perhaps, the skin factor. Seldom do we have enough data to estimate the drainage area, as shown in Fig. 3.
Pressure buildup testing
Perhaps the most accurate method to determine the value of formation permeability is to run a prefracture pressure buildup (PBU) test. The literature is voluminous^{[11]}^{[12]}^{[13]} on pressure transient testing. That material is not repeated here. Instead, this page discusses several issues concerning PBU testing that are important when testing low permeability gas reservoirs.
A PBU test works well when the formation is well connected to the wellbore, the flow rate is large enough for accurate measurement, and there are no liquid loading effects in the wellbore. The well must be produced long enough so that the radius of investigation of the test is meaningful. Eq. 8 is used to estimate the radius of investigation of any transient in the reservoir for radial flow.
Thus, to determine the length of the production test to sample a reasonable portion of the reservoir, followed by the PBU test, one can select a desired radius and then determine the duration of the test using the "best guess" for the value of permeability. Obviously, the permeability is unknown prior to running the test. Table 1 illustrates typical test times required based on the desired radius and the best guess at formation permeability.
As seen in Table 1, substantial flow times, followed by equal PBU times, are required to sample a large portion of the reservoir in low permeability gas reservoirs. In most cases, the engineer trying to analyze the reservoir would like the production and PBU test to be run as long as possible. On the other hand, because the well is more than likely producing at uneconomic flow rates, and a fracture treatment is required to improve productivity, the operations personnel want to minimize the duration of these tests to minimize costs and get the well producing to sales as soon as possible.
In addition to running the test long enough, the PBU tests in tight gas reservoirs should be analyzed using modern concepts such as^{[14]}:
- Pseudopressure
- Pseudotime
- Effective pseudotime
- Producing pseudotime
- Adjusted pressure
- Adjusted time
Using these concepts helps increase accuracy when large pressure drawdowns exist in the reservoir and changing wellbore storage constants complicate the analyses of the PBU data.
One point testing
In many cases, there are no long-term production data, and operational or cost-related problems prevent one from running a long-term PBU to quantify the formation permeability. However, it is very important to get a rough estimate of formation permeability prior to designing the fracture treatment. Sometimes, the well can be perforated and produced for several hours or days prior to designing and pumping the fracture treatment. If the production and flowing data are accurately measured, the one point method can be used to estimate the value of formation permeability.^{[15]}
In this method, the semisteady-state gas-flow equation and the radius of investigation equation are solved simultaneously for both permeability and radius of investigation. The semisteady-state gas-flow equation is
where
and
Four steps are used to solve Eqs. 9 through 11.
- Assume a value of s and D on the basis of the well completion history, then compute a value for s′ with the measured flow rate.
- Estimate a value for the permeability. An assumption of 1 md for a tight gas reservoir is usually a reasonable guess.
- Using the values of s′ and k, solve Eq. 10 for r_{d}.
- The value of r_{d} can be used in Eq. 9 to compute a new estimate of permeability.
One can iterate until the value of r_{d} and k converge. A weakness in this method is that one has to estimate the value of skin factor; therefore, the procedure should be repeated by assuming different values of skin, s. One can generate a range of permeabilities for a range of assumed values of skin factor.
Nomenclature
A | = | surface area |
c | = | compressibility, 1/psi |
D | = | diameter (for grain size) or constant for computing s′ |
h | = | net pay, ft |
I | = | index |
k | = | permeability, md |
q | = | flow rate, Mcf/D |
r | = | radius, ft |
R | = | resistivity, ohm-m |
s | = | skin |
s′ | = | effective skin factor |
t | = | time, hours or days |
T | = | temperature, °F |
U | = | correlation factor |
φ | = | porosity, fraction |
μ | = | gas viscosity, cp |
ψ | = | pseudopressure |
Subscripts
d | = | drainage |
e | = | at the extremity of the reservoir |
g | = | grain or gas (for flow rate) |
i | = | investigation (for radius) |
ild | = | induction log deep |
rh | = | relative to hydrocarbon flow |
sfl | = | spherically focused log |
t | = | true (for conductivity); total (for compressibility) |
w | = | wellbore (for radius); water (for saturation) |
wf | = | well flowing; free water (for conductivity) |
wir | = | irreducible water |
Superscripts
e | = | exponent |
References
- ↑ Yao, C.Y. and Holditch, S.A. 1996. Reservoir Permeability Estimation From Time-lapse Log Data. SPE Form Eval 11 (1): 69–74. SPE-25513-PA. http://dx.doi.org/10.2118/25513-PA.
- ↑ Berg, R.R. 1970. Method for Determining Permeability from Reservoir Rock Properties. Trans., GCAGS 20: 303.
- ↑ Timur, A. 1968. An Investigation of Permeability, Porosity, and Residual Water Saturation Relationships. The Log Analyst (July/August): 8.
- ↑ Coates, G.R. and Dumanoir, J.L. 1974. A New Approach to Improved Log-Derived Permeability. The Log Analyst (January/February): 17.
- ↑ Schlumberger Log Interpretation Principles/Application, 10. 1989. Houston, Texas: Schlumberger Educational Services.
- ↑ Ahmed, U., Crary, S.F., and Coates, G.R. 1991. Permeability Estimation: The Various Sources and Their Interrelationships. J Pet Technol 43 (5): 578-587. SPE-19604-PA. http://dx.doi.org/10.2118/19604-PA.
- ↑ Yao, C.Y. and Holditch, S.A. 1993. Estimating Permeability Profiles Using Core and Log Data. Presented at the SPE Eastern Regional Meeting, Pittsburgh, Pennsylvania, 2-4 November 1993. SPE-26921-MS. http://dx.doi.org/10.2118/26921-MS.
- ↑ Staged Field Experiment No. 3: Application of Advanced Technologies in Tight Gas Sandstones—Travis Peak and Cotton Valley Formations, Waskom Field, Harrison County, Texas. Gas Research Inst. Report, GRI-91/0048, CER Corp. and S.A. Holditch & Assocs. Inc., February.
- ↑ Holditch, S.A., Gatens III, J.M., McVay, D.A. et al. 1984. An Automated Method of Matching Production Performance Using Dimensionless Solutions. Presented at the SPE Unconventional Gas Recovery Symposium, Pittsburgh, Pennsylvania, 13-15 May 1984. SPE-12846-MS. http://dx.doi.org/10.2118/12846-MS.
- ↑ Fetkovich, M.J. 1980. Decline Curve Analysis Using Type Curves. J Pet Technol 32 (6): 1065–1077. SPE 4629-PA. http://dx.doi.org/10.2118/4629-PA.
- ↑ ^{11.0} ^{11.1} Watson, T.A., Lane, S.H., and III, M.J.G. 1990. History Matching With Cumulative Production Data. J Pet Technol 42 (1): 96-100. SPE-17063-PA. http://dx.doi.org/10.2118/17063-PA.
- ↑ ^{12.0} ^{12.1} Fetkovich, M.D., Guerrero, E.T., Fetkovich, M.J. et al. 1986. Oil and Gas Relative Permeabilities Determined From Rate-Time Performance Data. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, 5-8 October 1986. SPE-15431-MS. http://dx.doi.org/10.2118/15431-MS.
- ↑ ^{13.0} ^{13.1} Ansah, J., Knowles, R.S., and Blasingame, T.A. 2000. A Semi-Analytic (p/z) Rate-Time Relation for the Analysis and Prediction of Gas Well Performance. SPE Res Eval & Eng 3 (6): 525–533. SPE-66280-PA. http://dx.doi.org/10.2118/66280-PA.
- ↑ Gidley, J.L. et al. 1989. Recent Advances in Hydraulic Fracturing, 12, 39-56. Richardson, Texas: Monograph Series, SPE.
- ↑ Lee, W.J., Kuo, T.B., Holditch, S.A. et al. 1984. Estimating Formation Permeability From Single-Point Flow Data. Presented at the SPE Unconventional Gas Recovery Symposium, Pittsburgh, Pennsylvania, 13-15 May 1984. SPE-12847-MS. http://dx.doi.org/10.2118/12847-MS.
Noteworthy papers in OnePetro
Jahabani, A. and Aguilera, R. 2009. Well Testing of Tight Gas Reservoirs. Journal of Canadian Petroleum Technology 48 (10): 64-70. SPE-130066-PA. http://dx.doi.org/10.2118/130066-PA.
External links
Use this section to provide links to relevant material on websites other than PetroWiki and OnePetro
See also
Tight gas drilling and completion
Log analyses in tight gas reservoirs
Core analyses in tight gas reservoirs
Reserves estimation in tight gas reservoirs
Statistical data correlations in tight gas reservoirs