A Dual-Grid Automatic History-Matching Technique With Applications to 3D Formation Testing in the Presence of Oil-Based Mud-Filtrate Invasion
- Mayank Malik (University of Texas at Austin) | Carlos Torres-Verdin (University of Texas at Austin) | Kamy Sepehrnoori (University of Texas at Austin)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- March 2009
- Document Type
- Journal Paper
- 164 - 181
- 2009. Society of Petroleum Engineers
- 4.1.5 Processing Equipment, 5.5 Reservoir Simulation, 5.2.1 Phase Behavior and PVT Measurements, 5.3.2 Multiphase Flow, 5.5.11 Formation Testing (e.g., Wireline, LWD), 4.1.2 Separation and Treating, 5.2.2 Fluid Modeling, Equations of State, 1.8 Formation Damage, 5.2 Reservoir Fluid Dynamics, 1.11 Drilling Fluids and Materials, 5.5.8 History Matching, 5.6.1 Open hole/cased hole log analysis
- 1 in the last 30 days
- 494 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 12.00|
|SPE Non-Member Price:||USD 35.00|
Probe-type formation testers are often used to estimate permeability and anisotropy from pressure-transient measurements. The interpretation of these measurements is not trivial in the presence of oil-based-mud (OBM) -filtrate invasion because of miscibility with formation oil and gas. Simple analytical expressions of spherical and linear single-phase flow may not give correct estimates of permeability in miscible or partially miscible flow regimes. Because pressure transients are nonlinearly dependent on permeability, repeated 3D numerical simulations become necessary to honor measured pressure transients.
We describe the development and successful implementation of a new inversion method that efficiently estimates permeability and anisotropy with a cascade sequence of least-squares minimizations. Measurements consist of pressure transients acquired at the sandface with a probe-type wireline formation tester (WFT). The new inversion method executes the forward 3D problem only in an outer loop. In the inner loop, we perform fast minimizations with an equivalent 2D cylindrical grid. Transient measurements of pressure at the sandface simulated with the 2D cylindrical grid are correlated to the corresponding measurements simulated with the 3D grid. Once the 2D minimization is completed, we perform a 3D simulation of transient pressure to update the 2D/3D correlation parameter and a new 2D minimization is initialized until convergence is reached. The process repeats itself until the simulated 3D pressure transients reproduce the field measurements within prestipulated error bounds.
We perform tests of the new inversion algorithm on synthetic and field data sets acquired in the presence of OBM-filtrate invasion. Results confirm that our coupled 2D/3D hybrid inversion approach enables significant savings in computer time and provides reliable and accurate estimates of permeability and anisotropy. In most cases, we are able to estimate permeability under 2% error within 20% of the computational time required by 3D minimization. Sensitivity analysis indicates that permeability estimates may be biased by noisy measurements as well as by uncertainty in flow rates, relative permeability, radial extent of invasion, formation damage, and location of bed boundaries.
|File Size||2 MB||Number of Pages||18|
Alpak, F.O., Elshahawi, H., Hashem, M., and Mullins, O.C. 2008. Compositional Modeling ofOil-Based-Mud-Filtrate Cleanup During Wireline Formation Tester Sampling.SPE Res Eval & Eng 11 (2): 219-232. SPE-100393-PA. doi:10.2118/100393-PA.
Angeles, R., Torres-Verdín, C., Lee, H.-J., Alpak, F.O., and Sheng, J. 2007.Estimation of Permeability andPermeability Anisotropy From Straddle-Packer Formation- Tester MeasurementsBased on the Physics of Two-Phase Immiscible Flow and Invasion. SPEJ. 12 (3): 339-354. SPE-95897-PA. doi: 10.2118/95897-PA.
Brooks, R.H. and Corey, A.T. 1964. Hydraulic properties of porous media.Hydrology Paper No. 3, Colorado State University, Fort Collins, Colorado.
Broyden, C.G. 1965. A class ofmethods for solving nonlinear simultaneous equations. Mathematics ofComputation 19 (92): 577-593. doi:10.2307/2003941.
Collins, D.A., Nghiem, L.X., Li, Y.K., and Grabenstetter, J.E. 1992. An Efficient Approach to AdaptiveImplicit Compositional Simulation With an Equation of State. SPE ResEng 7 (2): 259-264. SPE-15133-PA. doi: 10.2118/15133-PA.
Gok, I.M., Onur, M., Hegeman, P.S., and Kuchuk, F.J. 2006. Effect of an Invaded Zone onPressure-Transient Data From Multiprobe and Packer-Probe Wireline FormationTesters. SPE Res Eval & Eng 9 (1): 39-49.SPE-84093-PA. doi: 10.2118/84093-PA.
Habashy, T.M. and Abubakar, A. 2004. A general framework forconstraint minimization for the inversion of electromagnetic measurements.Progress in Electromagnetic Research 46: 265-312.doi:10.2528/PIER03100702.
Levenberg, K. 1944. A method for the solution of certain problems in leastsquares. Quart. Appl. Math. 2: 164-168.
Lohrenz, J., Bray, B.G., and Clark, C.R. 1964. Calculating Viscosities of ReservoirFluids From Their Compositions. J. Pet Tech 16 (10):1171-1176; Trans., AIME, 231. SPE-915-PA. doi:10.2118/915-PA.
Madsen, K., Nielsen, H.B., and Tingleff, O. 2004. Methods for Non-LinearLeast Squares Problems, second edition. Lyngby, Denmark: Informatics andMathematical Modelling, Technical University of Denmark (DTU).
Malik, M., Torres-Verdín, C., and Sepehrnoori, K. 2007. Axially symmetriccompositional simulation of formation tester measurements. J. Pet. Sci.Eng. 59 (3-4): 333-349. doi:10.1016/j.petrol.2007.05.004.
Marquardt, D.W. 1963. Analgorithm for least-squares estimation on nonlinear parameters. SIAM J.Appl. Math. 11 (2): 431-441. doi:10.1137/0111030.
McCalmont, S., Onu, C., Wu, J., Kiome, P., Sheng, J.J., Adegbola, F.,Rajasingham, R., and Lee, J. 2005. Predicting Pump-Out Volume and TimeBased on Sensitivity Analysis for an Efficient Sampling Operation: PrejobModeling Through a Near-Wellbore Simulator. Paper SPE 95885 presented atthe SPE Annual Technical Conference and Exhibition, Dallas, 9-12 October. doi:10.2118/95885-MS.
Peng, D-Y. and Robinson, D.B. 1976. A new two-constant equation ofstate. Ind. Eng. Chem. Fund. 15 (1): 59-64.doi:10.1021/i160057a011.
Torres-Verdín, C., Druskin, V.L., Fang, S., Knizhnerman, L.A., andMalinverno, A. 2000. A dual-gridinversion technique with applications to the interpretation of dc resistivitydata. Geophysics 65 (6): 1733-1745.doi:10.1190/1.1444858.
Wu, J., Torres-Verdín, C., Proett, M.A., Sepehrnoori, K., and Belanger, D.2002. Inversion of Multi-PhasePetrophysical Properties Using Pumpout Sampling Data Acquired With a WirelineFormation Tester. Paper SPE 77345 presented at the SPE Annual TechnicalConference and Exhibition, San Antonio, Texas, USA, 29 September-2 October.doi: 10.2118/77345-MS.
Zeybek, M., Ramakrishnan, T.S., Al-Otaibi, S.S., Salamy, S.P., and Kuchuk,F.J. 2004. EstimatingMultiphase-Flow Properties From Dual-Packer Formation-Tester Interval Tests andOpenhole Array Resistivity Measurements. SPE Res Eval & Eng7 (1): 40-46. SPE-87474-PA. doi: 10.2118/87474-PA.