Estimating Oil Reservoir Permeability and Porosity from Two Interacting Wells

Authors

  • S. Sutawanir Statistics Research Division Institut Teknologi Bandung
  • Agus Yodi Gunawan Industrial Financial Research Division, Institut Teknologi Bandung
  • Nina Fitriyati Mathematics Department, UIN Syarif Hidayatullah
  • Iskandar Fahmi Oil & Gas Drilling, Production & Management Research Division, Institut Teknologi Bandung
  • Anggita Septiani Undergraduate student of Mathematics Study Program, Institut Teknologi Bandung
  • Rini Marwati Universitas Pendidikan Indonesia

DOI:

https://doi.org/10.5614/j.math.fund.sci.2013.45.2.4

Keywords:

ensemble Kalman filter, flow model, interacting well, sequential estimation, Laplace transform.

Abstract

The Ensemble Kalman Filter (EnKF) can be used as a method to estimate reservoir parameters, such as permeability and porosity. These parameters play an important role in characterizing reservoir performance. The EnKF is a sequential estimation method that uses the parameters at t – 1 (called prior) to estimate the parameters at t adjusted by observations at t (called posterior). In this paper, the EnKF was used to estimate the reservoir parameters for the case of a linear flow of two interacting production-injection oil wells. The Laplace transform was used to obtain an analytical solution of the diffusivity equation. A state space representation was generated using the analytical solution. A simulation study showed that the proposed method can be used successfully to estimate the reservoir parameters using well-pressure observations.

References

Lorentzen, R.J., Naevdal, G., Valles, B., Berg, A.M. & Grimstad, A., Analysis of the Ensemble Kalman Filter for Estimation of Permeability and Porosity in Reservoir Models, SPE96375 Annual Technical Conference, Texas, 9-12 Oct. 2005, 2005 (Technical Conference).

Yu, Y., A Research on the Optimization of Reservoir Model, Delft University of Technology, the Netherlands, 2011.

Mantilla, C.A., Srinivasan, S. & Nguyen, Q.P., Updating Geologic Models Using Ensemble Kalman Filter for Water Coning Control, Engineering, 3, pp. 538-548, 2011.

Gu, Y. & Oliver, D.S., The Ensemble Kalman Filter for Continuous Updating of Reservoir Simulation Models, Journal of Energy Resources Technology, 126, pp. 79-87, 2006.

Carslaw, H.S., Conduction of Heat in Solids, Oxford University, p. 309, 1959.

Wikle, C.K. & Berliner, L.M., A Bayesian Tutorial for Data Assimilation, Physica D, doi:10.10/6/j.physd.2006.09.017, 2006.

Tan, M., Mathematical Properties of Ensemble Kalman Filter, University of Southern California, 2011.

Li, J. & Xiu, D., On Numerical Properties of the Ensemble Kalman Filter for Data Assimilation, Comput. Methods Appl. Mech. Engrg., 197, pp. 3574-3583, 2008.

Downloads

Published

2013-07-01

Issue

Section

Articles