Identifiability of Location and Magnitude of Flow Barriers in Slightly Compressible Flow
- Siavash Kahrobaei (Delft University of Technology) | M. Mansoori Habibabadi (Delft University of Technology; Sharif University of Technology) | Gerard J. P. Joosten (Shell Global Solutions International) | Paul M. J. Van den Hof (Eindhoven University of Technology) | Jan-Dirk Jansen (Delft University of Technology)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- June 2016
- Document Type
- Journal Paper
- 899 - 908
- 2016.Society of Petroleum Engineers
- history matching, flow barrier, model maturation, identifiability, transfer function
- 4 in the last 30 days
- 149 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 10.00|
|SPE Non-Member Price:||USD 30.00|
Classic identifiability analysis of flow barriers in incompressible single-phase flow reveals that it is not possible to identify the location and permeability of low-permeability barriers from production data (wellbore pressures and rates), and that only averaged reservoir properties in between wells can be identified. We extend the classic analysis by including compressibility effects. We use two approaches: a twin experiment with synthetic production data for use with a time-domain parameter-estimation technique, and a transfer-function formalism in the form of bilaterally coupled four-ports allowing for an analysis in the frequency domain. We investigate the identifiability, from noisy production data, of the location and the magnitude of a low-permeability barrier to slightly compressible flow in a 1D configuration. We use an unregularized adjoint-based optimization scheme for the numerical time-domain estimation, by use of various levels of sensor noise, and confirm the results by use of the semianalytical transfer-function approach. Both the numerical and semianalytical results show that it is possible to identify the location and the magnitude of the permeability in the barrier from noise-free data. By introducing increasingly higher noise levels, the identifiability gradually deteriorates, but the location of the barrier remains identifiable for much-higher noise levels than the permeability. The shape of the objective-function surface, in normalized variables, indeed indicates a much-higher sensitivity of the well data to the location of the barrier than to its magnitude. These theoretical results appear to support the empirical finding that unregularized gradient-based history matching in large reservoir models, which is well-known to be a severely ill-posed problem, occasionally leads to useful results in the form of model-parameter updates with unrealistic magnitudes but indicating the correct location of model deficiencies.
|File Size||698 KB||Number of Pages||10|
Ahn, S. and Horne, R. N. 2010. Estimating Permeability Distributions From Pressure Pulse Testing. Presented at the SPE Annual Technical Conference and Exhibition, Florence, Italy, 19–22 September. SPE-134391-PA. http://dx.doi.org/10.2118/134391-MS.
Blom, R. S. and Van den Hof, P. M. 2010. Multivariable Frequency Domain Identification Using IV-based Linear Regression. Proc., 2010 49th IEEE Conference on Decision and Control, Atlanta, Georgia, 15–17 December, 1148–1153. http://dx.doi.org/10.1109/CDC.2010.5717297.
Carslaw, H. S. and Jaeger, J. C. 1959. Conduction of Heat in Solids, second edition. Oxford, UK: Oxford University Press.
Dogru, A. H., Dixon, T. N., and Edgar, T. F. 1977. Confidence Limits on the Parameters and Predictions of Slightly Compressible, Single-Phase Reservoirs. SPE J. 17 (1) 42–56. SPE-4983-PA. http://dx.doi.org/10.2118/4983-PA.
Feitosa, G. S., Chu, L., Thompson, L. G. et al. 1994: Determination of Permeability Distribution From Well-Test Pressure Data. J Pet Technol 46 (7): 607–615. SPE-26047-PA. http://dx.doi.org/10.2118/26047-PA.
Gao, G. and Reynolds, A. C. 2006. An Improved Implementation of the LBFGS Algorithm for Automatic History Matching. SPE J. 11 (1): 5–17. SPE-90058-PA. http://dx.doi.org/10.2118/90058-PA.
Glover, K. and Willems, J. C. 1974. Parametrizations of Linear Dynamical Systems: Canonical Forms and Identifiability. IEEE Trans. Automat. Contr. 19 (6): 640–646. http://dx.doi.org/10.1109/tac.1974.1100711.
Grader, A. S. and Horne, R. N. 1988. Interference Testing: Detecting a Circular Impermeable or Compressible Subregion. SPE Form Eval 3 (2): 420–428. SPE-15585-PA. http://dx.doi.org/10.2118/15585-PA.
Hollaender, F., Hammond, P. S., and Gringarten, A. C. 2002: Harmonic Testing for Continuous Well and Reservoir Monitoring. Presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 29 September–2 October. SPE-77692-PA. http://dx.doi.org/10.2118/77692-MS.
Joosten, G. J. P., Altintas, A., and Sousa, P. D. 2011. Practical and Operational Use of Assisted History Matching and Model-Based Optimisation in the Salym Field. Presented at the SPE Annual Technical Conference and Exhibition, Denver, 30 October–2 November. SPE-146697-MS. http://dx.doi.org/10.2118/146697-MS.
Kahrobaei, S., Mansoori, M., Joosten, G. J. P. et al. 2014. Hidden Information in Ill-posed Inverse Problems. Oral presentation given at ECMOR XIV – 14th European Conference on the Mathematics of Oil Recovery, Catania, Italy, 8–11 September. http://dx.doi.org/10.3997/2214-4609.20141825.
Kraaijevanger, J. F. B. M., Egberts, P. J. P., Valstar, J. R. et al. 2007. Optimal Waterflood Design Using the Adjoint Method. Presented at the SPE Reservoir Simulation Symposium, Houston, 26–28 February. SPE-105764-MS. http://dx.doi.org/10.2118/105764-MS.
Levitan, M. M. and Crawford, G. E. 2002. General Heterogeneous Radial and Linear Models for Well-Test Analysis. SPE J. 7 (2) 131–138. SPE-78598-PA. http://dx.doi.org/10.2118/78598-PA.
Oliver, D. 1996. Multiple Realizations of the Permeability Field From Well Test Data. SPE J. 1 (2): 145–154. SPE-27970-PA. http://dx.doi.org/10.2118/27970-PA.
Oliver, D. S., Reynolds, A. C., and Liu, N. 2008. Inverse Theory for Petroleum Reservoir Characterization and History Matching. Cambridge, UK: Cambridge University Press.
Shah, P. C., Gavalas, G. R., and Seinfeld, J. H. 1978. Error Analysis in History Matching: The Optimum Level of Parameterization. SPE J. 18 (3): 219–228. SPE-6508-PA. http://dx.doi.org/10.2118/6508-PA.
Stallman, R. 1952. Nonequilibrium Type Curves Modified for Two-Well Systems. US Department of the Interior.
Van den Hof, P. M., Van Doren, J. F., and Douma, S. G. 2009. Identification of Parameters in Large Scale Physical Model Structures, for the Purpose of Model-Based Operations. In Model-Based Control – Bridging Rigorous Theory and Advanced Control, ed. P. M. J. Van den Hof, C. Scherer, and P. S. C. Heuberger, 125–143. New York City: Springer.
Van Doren, J. F. M. 2010. Model Structure Analysis for Model-Based Operation of Petroleum Reservoirs. PhD dissertation, Delft University of Technology, Delft, the Netherlands.
Van Doren, J. F. M., Van den Hof, P. M. J., Jansen, J. D. et al. 2008. Determining Identifiable Parameterizations for Large-Scale Physical Models in Reservoir Engineering. Proc., 17th International Federation for Automatic Control World Congress, Seoul, South Korea, 6–11 July, 11421–11426.
Watson, A. T., Gavalas, G. R., and Seinfeld, J. H. 1984. Identifiability of Estimates of Two-Phase Reservoir Properties in History Matching. SPE J. 24 (6): 697–706. SPE-12579-PA. http://dx.doi.org/10.2118/12579-PA.
Yaxley, L. M. 1987. Effect of a Partially Communicating Fault on Transient Pressure Behavior. SPE Form Eval 2 (4): 590–598. SPE-14311-PA. http://dx.doi.org/10.2118/14311-PA.
Zandvliet, M. J., Van Doren, J. F. M., Bosgra, O. H. et al. 2008. Controllability, Observability and Identifiability in Single-Phase Porous Media Flow. Computat. Geosci. 12 (4): 605–622. http://dx.doi.org/10.1007/s10596-008-9100-3.