Identification of channel geometry, facies boundaries, and characterization of channel petrophysical properties are critical for performance predictions of channelized reservoirs. Level set methods have shown great promise to effectively parameterize facies boundaries and allow for changing channel geometry and connectivity during history matching. An outstanding challenge is efficient updating of channel geometry as well as channel petrophysics during history matching. Also, seismic data can provide important information and needs to be used as constraints.
In this paper, a novel two-step history matching workflow is proposed where the channel geometry is modeled using level sets and the internal heterogeneity within the channel facies is modeled using parameterization with linear basis functions, specifically the Grid Connectivity Transform (GCT) basis. Facies boundaries are first represented by the level set function where seismic information is incorporated and the boundaries are gradually moved by solving the level set equation under the seismic constraints. For history matching, Markov Chain Monte Carlo (MCMC) method is employed to minimize production data misfit by adjusting channel geometry and channel petrophysics.
The proposed approach is applied to both 2D and 3D examples. First, we examine the effectiveness of the level set approach by comparison with other approaches for channelized reservoirs, such as Discrete Cosine Transform and Discrete Wavelet Transform. The level set approach is shown to outperform other methods significantly in terms of reproducing channel geometry. Second, we show that the use of seismic constraints helps preserve the structure of facies distributions and geologic realism during history matching. Finally, calibrated facies models are further updated by adjusting the internal channel permeability distributions to fine-tune the history matching. The permeability changes are carried out by perturbing the coefficients of the GCT bases. High and low permeability regions are clearly depicted within the channels and production data misfit is significantly reduced during this second stage. We demonstrate the power and utility of the approach using both 2D and 3D applications.
Previous approaches focused on conditioning channelized models to well data but seismic constraints in level set were not considered. The successful integration of seismic constraints can help not only improve channelized reservoir history matching performance significantly, but also extend applicability of the level set method from simple channelized models to more complicated ones. Also, the GCT approach, for the first time, is shown to capture internal heterogeneity of the channel architecture.