DEVELOPMENT OF ENSEMBLE KALMAN FILTER (ENKF) FOR SOME RESERVOIR DIFFUSIVITY MODELS

• Main Author: FITRIYATI (NIM: 30109001), NINA
• Format: Dissertations
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/23497
• Institution: Institut Teknologi Bandung

The decline of oil production depends on reservoir characteristics such as permeability and porosity. The Arps model involves the flow rate of oil production, but it <br /> <br /> does not consider these characteristics yet. The relation between the characteristics and the flow rate is described by the diffusivity equation. Since solution of diffusivity <br /> <br /> equation in term of reservoir characteristics is nonlinear, the EnKF state-space is used to estimate the reservoir characteristics. This dissertation presents the development of EnKF for some reservoir diffusivity <br /> <br /> models i.e. line source, cylindrical source, interacting two production wells and interacting two production-injection wells. The diffusivity equation is solved by <br /> <br /> the Laplace transform and its inverse is found analytically or numerically using the Gaver-Stehfest Algorithm. In EnKF, the permeability or porosity estimation <br /> <br /> processes is calculated through the updating processes. The validation of EnKF is analyzed using convergence in probability which is visualized by using the statistical <br /> <br /> quality control methodology where the limit of the chart is calculated based on the Chebyshev inequality. <br /> <br /> The result shows that the EnKF can be used to estimate the reservoir parameters using diffusivity equation. The simulation study shows that the estimate converges to the true value. Application of the EnKF depend on the solution complexity of the diffusivity equation. The proposed method has not yet been applied for a real data due to the difficulties of fitting appropriate diffusivity equation.