Fast and accurate parameter estimation by means of a semi-implicit extended Kalman filter

An assessment of the time-integration scheme impact on results of data assimilation based on the extended Kalman filter approach is performed. The use of the implicit Euler scheme, which is unconditionally stable for the whole range of time steps both for the model and covariance update, results in a less accurate estimation of permeability distribution, which can be overcome using a parameter estimator based on the explicit Euler scheme. However, the latter strongly limits the maximum time step, which can be used, and leads to inappropriate simulation time. The alternative can be found using a semi-implicit estimator, where a model is updated using the implicit Euler scheme, whereas the propagation of the error covariance matrix in time is based on the explicit time integration scheme. This hybrid approach combines the accuracy of the conventional Kalman filtering with the robustness of the implicit forward modelling. The proposed algorithm is successfully applied for the solution of the one-dimensional problem of permeability estimation in a porous medium for a single phase oil flow.