Integration Of Ann Based Proxy Model

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Integration of ANN based Proxy model in EnKF Framework After development of an accurate proxy model based on ANN, the next task is to combine it with existing EnKF framework for assisted history matching. Permeability realizations are represented in terms of eigenvalues and corresponding eigen functions along with random variables using KL expansion as described in section 2.2. Once the eigenvalues and their corresponding eigen functions are determined after truncating terms in KL expansion, a realization can be generated with a certain number of values ξ_i from the standard Gaussian distribution N(0,1) using Eqn. (13). Each vector of random variable represents a permeability realization. These random variable vectors are used as input parameters for development of the proxy models. General workflow for development of the proxy models has been shown in Fig.4. A detailed explanation for proxy model generation will be provided in further section using a real field case study of SAGD reservoir. The proxy models are then used in forecast step of EnKF. EnKF workflow starts from construction of a state vector shown in Eqn. (2). In KL-ANN-EnKF approach, state vector consists of random variables as model parameters representing the permeability field along with production parameters. In forecast step, reservoir simulator is replaced by the proposed ANN proxy model and production parameters are estimated considering random variables as input parameters. Output spread is

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