A least squares history matching consists of measured data and corresponding values calculated from model using a set of parameters. The model can be a numerical reservoir simulator as well as an analytical model. The ensemble Kalman filter (EnKF) was introduced for strongly nonlinear fluid flow dynamics history matching. It is an iterative estimation using Monte Carlo simulation. The updating scheme uses the traditional Kalman filter (KF) update, where the gain is calculated from the sample covariance. One iteration of the EnKF consists of two steps, a forecast and an updating step. The forecast step is calculated by using the forward function which can be an analytical or numerical solution. In a complex reservoir model, the analytical solution was not available and a numerical approach was designed to solve the model. In the case where analytical solution is available, the numerical solution can be compared. Therefore, to ensure the numerical approach, a comparison of numerical to analytical forward step is needed.

In this study, an analytical solution for radial flow toward a well is compared with a numerical solution. The EnKF iterative estimation is coupled with line source well model and bounded constant rate no flow reservoir model. The parameter used in this study is permeability which is an important parameter related to well productivity. Future reservoir performance can be predicted based on parameters estimation results. Results obtained numerically using Stehfest algorithm to the line source and bounded constant rate no flow models agree closely with the analytical approach in spite of nonlinearities involved.