Ensemble-Based Relative Permeability Estimation Using B-Spline Model |
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Authors: | Heng Li Shengnan Chen Daoyong Yang Paitoon Tontiwachwuthikul |
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Institution: | (1) Alberta Energy and Utilities Board, 4999-98th Avenue, Edmonton, AB, Canada, T6B 2X3;(2) Hycal Energy Laboratories Ltd, 1338 A-36th Avenue NE, Calgary, AB, Canada, T2E 6T6 |
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Abstract: | A novel technique has been developed to implicitly estimate relative permeability by history matching the production data
with the ensemble Kalman filter (EnKF) method. Water and oil relative permeability curves were approximated using the B-spline
model, which has been modified to better represent the relative permeability curves. Compared to the existing implicit approaches,
the newly developed technique did not require the use of the gradient of the objectives function and thus, was easy to implement.
The newly developed technique has been validated by accurately evaluating relative permeability in a two-dimension synthetic
heterogeneous reservoir. The case study showed that the estimated relative permeability was improved gradually as observation
data were assimilated and that a good estimation of relative permeability curves can be effectively obtained. In this study,
three estimation scenarios assimilating various types of observation data were examined and compared. It was also found that
the oil relative permeability was sensitive to the oil production rate (OPR) data, as OPR was directly affected by oil relative
permeability. On the other hand, water relative permeability was more sensitive to the bottomhole pressure data of the producers.
Additionally, the production data, obtained prior to water breakthrough, contributed more to the estimation of the two-phase
relative permeability curves. |
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