Estimation and Removal of Tidal Effects From Pressure Data
- Yong Zhao (ConocoPhillips Co) | Albert C. Reynolds (University of Tulsa)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- March 2009
- Document Type
- Journal Paper
- 144 - 152
- 2009. Society of Petroleum Engineers
- 5.6.4 Drillstem/Well Testing, 4.1.5 Processing Equipment, 4.1.2 Separation and Treating, 5.1.2 Faults and Fracture Characterisation
- 1 in the last 30 days
- 603 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 12.00|
|SPE Non-Member Price:||USD 35.00|
We consider field pressure data from two wells, one offshore and one onshore. The onshore well is shut-in and experiences only a very small pressure decline due to interference, whereas in the offshore case, the late time buildup data appear to be severely corrupted by ocean tidal effects. The objectives in both cases are to determine the tidal signal that can be used to estimate formation compressibility and to remove the tidal signal from the measured data.
For the onshore well, we use a Savitzky-Golay (SG) filter to smooth the pressure data. Subtracting the smooth data from the measured signal yields a modified signal that ideally represents the earth tidal signal plus measurement error. As the main harmonic components of the earth tidal signal are known, we perform a least-squares fit of the modified pressure data with a series of sines and cosines that contain only the known frequencies of the earth tide. By subtracting the series obtained by least-squares fitting from the true signal, we remove the effect of the earth tide.
In the offshore case, the time span of data that are severely affected by tidal effects is too short to use the SG filter with confidence. As the reservoir pressure change due to the tides is well approximated by a damped and delayed version of the seafloor response, a least-squares fit of the data with a function that follows the underlying buildup trend plus an attenuated-delayed response of the measured seafloor pressure trace allows one to obtain a good estimate of the attenuation factor and time delay so that the tidal component of the bottomhole pressure change can be determined and removed from the measured pressure.
|File Size||889 KB||Number of Pages||9|
Biot, M.A. 1941. Generaltheory of three-dimensional consolidation. J. Appl. Phys.12 (2): 155-164. doi: 10.1063/1.1712886.
Bredehoeft, J.D. 1967. Response of well-aquifersystem to earth tides. Journal of Geophysical Research72 (12): 3075-3087. doi:10.1029/JZ072i012p03075.
Chang, E. and Firoozabadi, A. 2000. Gravitational Potential Variations ofthe Sun and Moon for Estimation of Reservoir Compressibility. SPE J.5 (4): 456-465. SPE-67952-PA. doi: 10.2118/67952-PA.
Chen, H. and Lee, R. 1995. Coupled Fluid Flow and Geomechanicsin Reservoir Study - I. Theory and Governing Equations. Paper SPE 30752presented at the SPE Annual Technical Conference and Exhibition, Dallas, 22-25October. doi: 10.2118/30752-MS.
Dean, G., Hardy, R., and Eltvik, P. 1994. Monitoring Compaction andCompressibility Changes in Offshore Chalk Reservoir. SPE Form Eval19 (1): 73-76. SPE-23142-PA. doi: 10.2118/23142-PA.
Langaas, K., Nilsen, K.I., and Skjaeveland, S.M. 2006. Tidal Pressure Response andSurveillance of Water Encroachment. SPE J. 24 (10):335-344. SPE-95763-PA. doi: 10.2118/95763-PA.
Levitan, M.M. and Phan, V. 2003. Identification of Tidal Signal inWell Test Pressure Data. Paper SPE 84376 presented at the SPE AnnualTechnical Conference and Exhibition, Denver, 5-8 October. doi:10.2118/84376-MS.
Melchior, P.J. 1978. The Tides of The Planet Earth. Oxford, UK:Pergamon Press.
Nur, A. and Byerlee, J.D. 1971. An exact effective stress law for elasticdeformation of rock with fluids. J. Geophys. Res. 76 (26):6414-6419.
Press, W.H., Flannery, B.P., Teukolsky, S.A., and Vetterling, W.T. 1992.Numerical Recipes in Fortran 77: The Art of Scientific Computing, secondedition. Cambridge, UK: Cambridge University Press.
Rai, H. 2005. Analyzing rate data from permanent downhole gauges. Technicalreport, Stanford University Petroleum Research Institute (SUPRI-D), Stanford,California (June 2005).
Rai, H. and Horne, R.N. 2007. Analyzing Simultaneous Rate andPressure Data From Permanent Downhole Gauge. Paper SPE 110097 presented atthe SPE Annual Technical Conference and Exhibition, Anaheim, California, USA,11-14 November. doi: 10.2118/110097-MS.
Reynolds, A.C., Oliver, D.S., Li, G., Dong, Y., Zhao, Y., Eydinov, D., Gao,G., Chen, S., and Han, M. 2005. Data integration for the generation of highresolution reservoir models. Technical report, Project No. DE-FC26-04NT15517,US DOE/NETL, Washington, DC (2005).
Savitzky, A. and Golay, M.J.E. 1964. Smoothing and differentiation ofdata by simplified least squares procedures. Analytical Chemistry36 (8): 1627-1639. doi:10.1021/ac60214a047.
Schwiderski, E.W. 1980. Ocean tides, part I: Global ocean tidal equations.Marine Geodesy 3: 161-255.
Smit, D. and Sayers, C.M. 2005. Can tidal-driven pressure changes revealreservoir properties for use in 4D monitoring? World Oil226 (3): 37-43.
Takeuchi, H. 1950. On the earth tide of the compressible earth of variabledensity and elasticity. Transactions of the American Geophysical Union31 (5): 651-689.
Van Der Kamp, G. and Gale, J.E. 1983. Theory of earth tide andbarometric effect in porous formations with compressible grains. WaterResources Research 19 (2): 538-544.doi:10.1029/WR019i002p00538.
Xu, S. 1997. FORTRAN Subroutines for Commonly Used Algorithms, secondedition. Beijing: Tsinghua University Press.
Zimmerman, R.W. 1991. Compressibility of Sandstones. Amsterdam:Elsevier.