An Efficient Well Test Forward Model Based on the Fast Marching Method - Application to Geomodel Sorting

Abstract

Constructing realistic 3D geo-models that honour well test data is today a challenge because of the highly non linear nature of the underlying inversion problem and the complexity of geo-modelling and flow simulation tools. Flow simulation is commonly performed using finite difference based software in order to compute the propagation of a pressure front. In the case of a well test, a good approximation can be obtained by solving the Eikonal equation with the fast marching algorithm (Xie et al., 2012). This results in computing the diffusive time of flight at every location of the geomodel according to a 3D defined speed property, which is a function of the permeability. The diffusive time of flight is directly related to the pressure front propagation by a function involving the flow regime which occurs at every time of the propagation. In its initial expression, the fast marching algorithm is designed for Cartesian grids and isotropic speed fields, limiting its applicability to simplistic reservoir models. We propose a new formulation of the Fast Marching algorithm, based on the work published by Jbabdi et al. (2008). It allows solving the Eikonal equation in corner point grids that represent structurally and stratigraphically complex reservoirs where the permeability field is anisotropic and not aligned on the grid. Fast marching based well test forward model requires being able to evaluate the flow regime at every time of the pressure front propagation. In order to speed up the forward model, the flow regimes are frequently approximated. This induces time distortion in the simulated well test which may lead to misevaluate the quality of a geomodel with regard to the monitored well test. We propose an objective function, based on the dynamic time warping algorithm, which computes distance between monitored and simulated well test by removing time distortion effect. The proposed methodologies are applied, in a first basic application, to rank geo-models according to a monitored well test. We demonstrate that the results are comparable with ranks obtained using a finite difference based flow simulator. This represents an important step toward automation of well test match in geo-modelling tools. Jbabdi, S., Bellec, P., Toro, R., Daunizeau, J., Pelegrini-Issac, M., Benali, H., 2008. Accurate anisotropic fast marching for diffusion-based geodesic tractography. Journal of Biomedical Imaging 2008, 2. Xie, J., Gupta, N., King, M., Datta-Gupta, A., 2012. Depth of investigation and depletion behavior in unconventional reservoirs using fast marching methods, SPE Europec/EAGE Annual Conference.