Flow in fractured porous media is crucial for production of oil/gas reservoirs and exploitation of geothermal energy. Flow behaviors in such media are mainly dictated by the distribution of fractures. Measuring and inferring the distribution of fractures is subject to large uncertainty, which, in turn, leads to great uncertainty in the prediction of flow behaviors. Inverse modeling with dynamic data may assist to constrain fracture distributions, thus reducing the uncertainty of flow prediction. However, inverse modeling for flow in fractured reservoirs is challenging, owing to the discrete and non‐Gaussian distribution of fractures, as well as strong nonlinearity in the relationship between flow responses and model parameters. In this work, building upon a series of recent advances, an inverse modeling approach is proposed to efficiently update the flow model to match the dynamic data while retaining geological realism in the distribution of fractures. In the approach, the Hough‐transform method is employed to parameterize non‐Gaussian fracture fields with continuous parameter fields, thus rendering desirable properties required by many inverse modeling methods. In addition, a recently developed forward simulation method, the embedded discrete fracture method (EDFM), is utilized to model the fractures. The EDFM maintains computational efficiency while preserving the ability to capture the geometrical details of fractures because the matrix is discretized as structured grid, while the fractures being handled as planes are inserted into the matrix grids. The combination of Hough representation of fractures with the EDFM makes it possible to tune the fractures (through updating their existence, location, orientation, length, and other properties) without requiring either unstructured grids or regridding during updating. Such a treatment is amenable to numerous inverse modeling approaches, such as the iterative inverse modeling method employed in this study, which is capable of dealing with strongly nonlinear problems. A series of numerical case studies with increasing complexity are set up to examine the performance of the proposed approach.

Summary Naturally or hydraulically fractured reservoirs usually contain fractures at various scales. Among these fractures, large-scale fractures might strongly affect fluid flow, making them essential for production behavior. Areas with densely populated small-scale fractures might also affect the flow capacity of the region and contribute to production. However, because of limited information, locating each small-scale fracture individually is impossible. The coexistence of different fracture scales also constitutes a great challenge for history matching. In this work, an integrated approach is proposed to inverse model multiscale fractures hierarchically using dynamic production data. In the proposed method, a hybrid of an embedded discrete fracture model (EDFM) and a dual-porosity/dual-permeability (DPDP) model is devised to parameterize multiscale fractures. The large-scale fractures are explicitly modeled by EDFM with Hough-transform-based parameterization to maintain their geometrical details. For the area with densely populated small-scale fractures, a truncated Gaussian field is applied to capture its spatial distribution, and then the DPDP model is used to model this fracture area. After the parameterization, an iterative history-matching method is used to inversely model the flow in a fractured reservoir. Several synthetic cases, including one case with single-scale fractures and three cases with multiscale fractures, are designed to test the performance of the proposed approach.