Integration Of Proxy Model With Enkf Algorithms For Time Efficient Assisted History Matching

2098 WordsNov 1, 20169 Pages
Methodology This section contains the mathematical background and stepwise procedure for EnKF algorithm, KL expansion and ANN based proxy model. Integration of proxy model with EnKF algorithms for time efficient assisted history matching is also explained in this section. Ensemble Kalman Filter Algorithm EnKF is a Monte Carlo data assimilation method, which has gained popularity over recent years for assisted history matching due to its ability to include available observations sequentially in time. Aanonsen et al. (2009) reviewed the application of EnKF in reservoir engineering for estimation of reservoir parameters. EnKF procedure utilizes an ensemble of model states (e.g. realizations of reservoir properties such as porosity and permeability) to estimate the covariance matrices used in model updating process. Initial ensemble is generated based on the prior knowledge of the reservoir derived from various sources as well logs, core and seismic analysis. In general, simulation techniques such as Sequential Gaussian Simulation (SGS) and Sequential Indicator Simulation (SIS) are used to generate multiple realizations. These realizations are consistent with the initial state of the reservoir. In the next step, all the reservoir models in ensemble are forwarded typically using the numerical reservoir simulation. Mean and covariance of predicted model states is calculated and used in turn to calculate Kalman gain. Next, in the update (or analysis) step, each geological
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