Analytical rate transient analysis (RTA) techniques are widely adopted for analyzing production data obtained from hydraulically fractured horizontal wells in tight or shale reservoirs. However, for a detailed characterization of the uncertain distributions of those complex heterogeneous and multi-scale fractures, numerical simulation and assisted history-matching approaches are often preferred. Generally, RTA results can be used to constrain the initial distributions of fracture properties (e.g., transmissivity, aperture, or intensity). A set of initial models are then perturbed during the assisted history-matching step. Unfortunately, the final updated models may deviate substantially from the initial RTA estimates; moreover, specific information regarding the flow regimes is not incorporated directly into the history-matching step. In this paper, a new assisted history-matching workflow is presented, where RTA results are used to constrain not only the initial DFN models, the interpreted flow regimes are also used to formulate a localization scheme for more efficient updating of the pertinent DFN model parameters. The outcome is an ensemble of DFN realizations that are calibrated to both geologic and dynamic production data.
First, RTA interpretations and other pertinent geological data are used to infer the prior probability distributions of the unknown fracture parameters, from which an ensemble of initial DFN models is sampled. Next, the DFN models are subjected to numerical multiphase flow simulation; the predicted production profiles are compared with the actual historical production data. Finally, the fracture parameters are adjusted following an indicator-based probability perturbation method, which is capable of minimizing the objective function and reducing the uncertainties in the unknown fracture parameters simultaneously. A key feature is that the flow regimes identified from RTA are used to formulate a localization strategy, where individual segments of the production data is used to tune only a specified subset of the unknown model parameters. The adoption of localization strategies in other settings has been demonstrated to improve the convergence behavior of such ill-posed inverse problems.
In a case study, the method is applied to characterize the probability distributions of four parameters in a multifractured shale gas well: primary fracture transmissivity, aperture of the secondary fracture, transmissivity of the secondary induced fracture and global fracture intensity. Results of the sensitivity analysis reveal that the production performance is most sensitive to these particular parameters. Their probability distributions are updated following the proposed approach to match the production history. Multiple realizations of the DFN model are sampled.
A probabilistic approach facilitates the representation of uncertainties in fracture parameters via multiple equally-probable DFN models and their corresponding upscaled flow-simulation models. A more comprehensive and robust approach is presented for integrating specific RTA interpretations and estimations into various steps of the history-matching process.