Modeling Reservoir Temperature Transients and Reservoir-Parameter Estimation Constrained to the Model
- Obinna O. Duru (Stanford University) | Roland N. Horne (Stanford University)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- December 2010
- Document Type
- Journal Paper
- 873 - 883
- 2010. Society of Petroleum Engineers
- 5.6.11 Reservoir monitoring with permanent sensors
- permanent downhole gauges
- 6 in the last 30 days
- 1,007 since 2007
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Permanent downhole gauges (PDGs) provide a continuous source of downhole pressure, temperature, and sometimes flow-rate data. Until recently, the measured temperature data have been largely ignored, although a close observation of the temperature measurements reveals a response to changes in flow rate and pressure. This suggests that the temperature measurements may be a useful source of reservoir information.
In this study, reservoir temperature-transient models were developed for single- and multiphase-fluid flows, as functions of formation parameters, fluid properties, and changes in flow rate and pressure. The pressure fields in oil- and gas-bearing formations are usually transient, and this gives rise to pressure/temperature effects appearing as temperature change. The magnitudes of these effects depend on the properties of the formation, flow geometry, time, and other factors and result in a reservoir temperature distribution that is changing in both space and time. In this study, these thermometric effects were modeled as convective, conductive, and transient phenomena with consideration for time and space dependencies. This mechanistic model included the Joule-Thomson effects resulting from fluid compressibility and viscous dissipation in the reservoir during fluid flow.
Because of the nature of the models, the semianalytical solution technique known as operator splitting was used to solve them, and the solutions were compared to synthetic and real temperature data. In addition, by matching the models to different temperature-transient histories obtained from PDGs, reservoir parameters such as average porosity, near-well permeabilities, saturation, and some thermal properties of the fluid and formation could be estimated. A key target of this work was to show that temperature measurements, often ignored, can be used to estimate reservoir parameters, as a complement to other more-conventional techniques.
|File Size||3 MB||Number of Pages||11|
Bear, J. 1972. Dynamics of Fluids in Porous Media. Oxford, UK:Environmental Science Series, Elsevier.
Bejan, A. 2004. Convection Heat Transfer, third edition. Hoboken, NewJersey, USA: John Wiley & Sons.
Bravo, H.R. and Jiang, F. 2001. Using groundwater temperaturedata to constrain parameter estimation in a groundwater flow model of a wetlandsystem. Water Resour. Res. 38 (8): 1153-1166.doi:10.1029/2000WR000172.
Breiman, L. and Friedman, J.H. 1985. Estimating Optimal Transformations forMultiple Regression and Correlation. J. of American StatisticalAssociation 80 (391): 580-598. doi:10.2307/2288473.
Dawkrajai, P., Analis, A.R., Yoshioka, K., Zhu, D., Hill, A.D., and Lake,L.W. 2004. A Comprehensive Statistically-Based Method to Interpret Real-TimeFlowing Well Measurements. US DOE Office of Fossil Energy Project IDDE-FC26-03NT15402, CPGE, University of Texas at Austin, Austin, Texas, USA.
Filippov, A.I. and Devyatkin, E.M. 2001. Barothermal Effect in aGas-Bearing Stratum. High Temperature 39 (2): 255-263.doi:10.1023/A:1017526900775.
Holden, H., Larlsen, K.H., and Lie, K.-A. 2000. Operator splitting methods fordegenerate convection-diffusion equations, II: Numerical examples with emphasison reservoir simulation and sedimentation. Computational Geosciences 4 (4): 287-323. doi:10.1023/A:1011582819188.
Horne, R.N. and Shinohara, K. 1979. Wellbore Heat Loss in Production andInjection Wells. J Pet Technol 31 (1): 116-118.SPE-7153-PA. doi: 10.2118/7153-PA.
Izgec, B., Kabir, C.S., Zhu, D., and Hasan, A.R. 2007. Transient Fluid and Heat FlowModeling in Coupled Wellbore/Reservoir Systems. SPE Res Eval &Eng 10 (3): 294-301. SPE-102070-PA. doi:10.2118/102070-PA.
Kacur, J. and Frolkovic, P. 2002. Semi-analytical solutions for contaminanttransport with nonlinear sorption in 1D. Technical report SFB 359, Contract No.02 E 9148 2, University of Heidelberg, Heidelberg, Germany (30 September2002).
Khan, L.A. and Liu, P.L.-F. 1995. An operator splittingalgorithm for coupled one-dimensional advection-diffusion-reactionequations. Computer Methods in Applied Mechanics and Engineering 127 (1-4): 181-201. doi:10.1016/0045-7825(95)00839-5.
Masters, J.I. 1955. SomeApplications in Physics of the P Function. J. of Chemical Physics 23 (10): 1865-1874. doi:10.1063/1.1740595.
Maubeuge, F., Arquis, E., and Bertrand, O. 1994. MOTHER: A Model for InterpretingThermometrics. Paper SPE 28588 presented at the SPE Annual TechnicalConference and Exhibition, New Orleans, 25-28 September. doi:10.2118/28588-MS.
Nield, D.A. and Bejan, A. 1998. Convection in Porous Media, secondedition. New York City: Springer-Verlag.
Özisik, M.N. 1993. Heat Conduction, second edition. New York City:John Wiley & Sons.
Ramazanov, A.Sh. and Nagimov, V.M. 2007. Analytical model for thecalculation of temperature distribution in the oil reservoir during unsteadyfluid inflow. Oil and Gas Business 1/2007 (17.05.07):532.546-3:536.42.
Ramazanov, A.Sh. and Parshin, A.V. 2006. Temperature distribution in oil andwater saturated reservoir with account of oil degassing. Oil and GasBusiness 1/2006 (10.04.06): 532.546-3:536.42.
Ramey, H.J. Jr. 1962. WellboreHeat Transmission. J Pet Technol 14 (4): 427-435;Trans., AIME, 225. SPE-96-PA. doi: 10.2118/96-PA.
Rath, V., Wolf, A., and Bücker, M. 2006. Three-dimensional joint Bayesianinversion of hydrothermal data using automatic differentiation. Presented atthe Workshop on Geothermal Reservoir Engineering, Stanford, California, USA, 30January-1 February.
Remešiková, M. 2004. Solution ofconvection-diffusion problems with nonequilibrium adsorption. J. ofComputational and Applied Mathematics 169 (1): 101-116.doi:10.1016/j.cam.2003.11.005.
Sagar, R.K., Doty, D.R., and Schmidt, Z. 1991. Predicting Temperature Profiles in aFlowing Well. SPE Prod Eng 6 (6): 441-448.SPE-19702-PA. doi: 10.2118/19702-PA.
Sharafutdinov, R.F. 2001. Multi-Front Phase TransitionsDuring Nonisothermal Filtration of Live Paraffin-Base Crude. Journal ofApplied Mechanics and Technical Physics 42 (2): 284-289.doi:10.1023/A:1018832120659.
Shiu, K.C. and Beggs, H.D. 1980. Predicting Temperatures in FlowingOil Wells. J. Energy Resour. Technol. 102 (1): 2-11.doi:10.1115/1.3227845.
Valiullin, R.A., Sharafutdinov, R.F., and Ramazanov, A.Sh. 2004. A researchinto thermal fields in fluid-saturated porous media. Powder Technology -Lausanne 148 (1): 72-77.
Valocchi, A.J. and Malmstead, M. 1992. Accuracy of operator splitting foradvection-dispersion-reaction problems. Water Resour. Res. 28 (5): 1471-1476. doi:10.1029/92WR00423.
Woodbury, A.D. and Smith, L. 1988. Simultaneous inversion ofhydrogeologic and thermal data: 2. Incorporation of thermal data. WaterResour. Res. 24 (8): 356-372. doi:10.1029/WR024i003p00356.
Yoshioka, K. 2007. Detection of Water or Gas Entry into Horizontal Wells byUsing Permanent Downhole Monitoring Systems. PhD dissertation, Texas A&MUniversity, College Station, Texas, USA.