| Abstract |
An important method for reservoir assesment is to build a numerical reservoir simulation model. Part of a good reservoir management, the simulation model should be able to capture both thermodynamic processes and uncertainty based on geoscience or other studies. Sometimes, the simulation model can not represent the reservoir condition due to errors from data uncertainty, numerical computation or conceptual model itself. This research tried to optimize the reservoir simulation using Kalman filter which has been known as an algorithm to estimate variables by assimilating simulation results and measurement data. A test or synthetic model of steam dominated geothermal system was built as an object of this study to be validated using a known Kalman Filter of Hybrid type (HKF). Its ability to estimate rock permeability using pressure data was being studied by comparing the output, both of the test model and reservoir simulation coupled with HKF. There are 3 (three) performance parameters was being analyzed i.e. effect of number of ensemble, initial guess and range of ensemble initialization. In this study, the HKF algorithm has been successfully implemented in geothermal reservoir simulation. This algorithm is able to eliminate uncertainty either in the data or numerical approach to get rock permeability distribution. From the sensitivity study, using 40, 100 and 200 number of ensembles, it concludes that ensemble number does not significantly affect the HKF performance. Using initial guess with RMSE (Root Mean Square Error) of 124 mD, the HKF resulted 93 mD, 91.77 mD and 91.79 mD in the end of looping for number of ensembles of 40, 100 and 200 ensembles, respectively. There are 2 (two) factors which lead to this result, first that the model is not sensitive with the variation of permeability within propagation process. The second factor is that there was a problem in the software for parallel simulation which disable to write the pressure output for some blocks if the initial condition is specified by saturation and temperature. The initial guess play important role to the accuracy of the algorithm. Changing the initial guess could result RMSE reduction down to 5 mD. The range of ensemble initialization also has significant effect to HKF’s performance. In the first experiment, using a wide value of range of 1 to 400 mD for good permeability layer of the reservoir, it converged only from 124 mD to 92 mD in the end of looping. While in the second experiment, using a narrower range from 150 to 250 mD, it could converge to 16 mD. Furthermore, there is no singularity effect that found using HKF, which strengthen the capability of the algorithm. In order to improve the computation, it is suggested to couple the HKF algorithm with TOUGH2 program by having an interface to bridge simulator and the HKF algorithm. |