Discrete fracture network (DFN) models can explicitly represent the geometrical properties of each individual fracture (e.g. size, orientation, shape, and aperture) and fracture sets, where these comprising fracture properties are sampled from specific probability distributions. Nevertheless, integrating these DFN models during a production history matching remains difficult. A robust model updating technique, with the capabilities of incorporating the variability in the fracture parameters across hydraulic fracture stages and mitigating the uncertainty inherent in the non-linear relationship between a set of fracture parameters and the corresponding upscaled reservoir model properties, is required. It is important to update pertinent DFN model parameters, such that they are calibrated to both stochastic reservoir models and dynamic production data.
In this study, rate transient analysis (RTA) interpretations are used to infer the prior probability distributions of the unknown varying DFN parameters across each stage of the hydraulic fracture and the intersecting secondary fractures associated with each hydraulic fracture stage; an ensemble of the initial DFN models are sampled. This is followed by numerical multiphase flow simulation of the upscaled model and comparison between the predicted production responses with the actual historical data. An indicator-based probability perturbation method is then used to minimize the objective function and consequently reduce the uncertainties in the unknown fracture parameters. An essential detail is that flow regimes identified through RTA study are used to develop a localization scheme, where multiple flow regimes are inferred from the production data, and different portions of the production data are used to perturb specific model parameters corresponding to that particular flow regimes. The adoption of localization schemes is targeted at improving the convergence behavior of such ill-posed inverse problem. The designed probabilistic framework characterizes the posterior probability distributions of twenty-four DFN parameters of a multi-staged (4 stages) hydraulically-fractured horizontal shale gas well in the Horn River Basin: primary fracture transmissivity (Tpf), secondary fracture aperture (re), secondary fracture transmissivity (Tsf), global fracture intensity of the secondary fracture (Psf32G), secondary fracture length (L) and height (H); The proposed approach does not only sample multiple realizations of the DFN model, it updates (through the adopted history matching workflow) the probability distributions of these impacting DFN parameters. The results reveal the flexibility in obtaining unknown secondary fracture parameters that are not easily inferred by other methods such as cores and microseismic interpretations.
