Summary
Successful production in fractured reservoirs is significantly dependent on knowledge of the location, orientation, and conductivity of the fractures. Early water breakthrough can be prevented and sweep efficiency can be improved with the help of comprehensive and accurate information of fracture distributions. However, it is a challenge to estimate fracture distributions by conventional-history-matching methods because of the complexity of such reservoirs. Although there has been great progress in assisted-history-matching techniques during the last 2 decades, estimating fracture distributions in fractured reservoirs is still inefficient because of the strong heterogeneity and spatial discontinuity of model parameters. The performance of assisted-history-matching methods, such as the ensemble Kalman filter, can be significantly degraded by the non-Gaussian distributions of the parameters, such as effective permeability and porosity. On the other hand, although the geometric shapes of fractures may be generated properly at the initial step, they are difficult to preserve after updating, which results in geologically unrealistic fracture-distribution maps. In this study, we develop an assisted-history-matching method for fractured reservoirs with a Hough-transform-based parameterization. The facies maps of fractured reservoirs are parameterized into Hough-function fields in a discrete Hough space, whereas each gridblock in the Hough domain represents a fracture defined by its two Cartesian coordinates: angle θ of its normal and ρ of its algebraic distance from the origin in the flow domain. The length and axial position of the fractures are defined by two additional parameters on the same grid. The Hough-function value of each gridblock in the Hough domain is used as the indicator of the existence of the fracture in the facies map. When this parameterization is implemented in assisted history matching, the parameter fields in the Hough space, instead of the facies maps, are updated conditional on the production history. An inverse transform is performed to generate facies maps for the reservoir simulator. Pointwise prior information, such as known fractures discovered from well-log data, as well as the statistics of fracture orientation, can be honored by the inverse transform throughout the history-matching process. Applications and the effectiveness of this method are demonstrated by 2D synthetic-waterflooding examples. The fracture distributions in reference fields are identified by this method, and updated models are capable of providing improved predictions for prolonged periods of production.
Gaussian Processes Proxy Model with Latent Variable Models and Variogram-Based Sensitivity Analysis for Assisted History Matching