Geological model calibration based on gradual deformation and connectivity function

The connectivity is an important feature of the reservoir geological heterogeneity that effects fluid flow responses. In geostatistical modeling, random realizations are generated to describe reservoir heterogeneities. But these realizations do not necessarily honor connectivity data. Especially in multiple-point geostatistical modeling, ensuring the connectivity data of these realizations consistent with the training image is a challenge. The connectivity data of the training image is an important factor in assessing the quality of simulation results in modeling a fluvial hydrocarbon reservoir with meandering channels. The calibration of geological/geostatistical model realizations by measured data is generally performed through history matching, which is an inversion process. This method requires a parameterization of the geostatistical model to allow the updating of an initial model realization. The gradual deformation method has been used to parameterize geostatistical realizations. This method uses a perturbation mechanism to smoothly modify model realizations generated by sequential (not necessarily Gaussian) simulations while preserving its spatial variability. In this paper, a workflow is presented to calibrate the model realizations to the connectivity data. This workflow ensures that the connectivity of model realizations generated by SNESIM is consistent with the training image, and it is applicable to both multiple-point and two-point geostatistical modeling methods based on sequential simulation. This workflow incorporates the computation of the model connectivity function and its calibration to connectivity data using the gradual deformation method. This involves defining and minimizing an objective function, which quantifies the mismatch between the model connectivity function and the connectivity data. In the case study, multiple initial realizations are utilized to construct a final realization of the reservoir model that honors the connectivity data.