Ensemble-based Seismic History Matching with Distance Parameterization for Complex Grids

Recently, a distance parameterization of flood fronts derived from seismic anomalies was proposed as a solution in combination with the ensemble Kalman filter (EnKF), which is known as an efficient method for conditioning of multiple reservoir models to observed data. Even though the distance parameterization in terms of front positions is efficient and effective in reducing both nonlinearity and the effective number of seismic data, which improves the performance of the EnKF, the method adopted for distance computation therein is only applicable for reservoir models with regular Cartesian grids because large errors will be introduced otherwise. In this paper, we improve the applicability of the distance parameterization in terms of front positions by extending the fast marching method for solution of the Eikonal equation to complex simulation grids. This is realized by taking advantage of a diagonal stencil in the fast-marching implementation which allows more accurate calculations of distances between observed and simulated fronts, and by an isoparametric mapping which provides a transformation from the Cartesian to curvilinear coordinates. The improvements of the proposed methods are demonstrated through a number of numerical experiments on corner-point grid including a 3D synthetic case of Norne full-field model.