There is growing evidence showing that water injection may induce formation fracturing around injectors in tight reservoirs. Because waterflood-induced fractures (WIFs) are not strengthed by proppants, they close gradually during the field-testing period, which results in "fracture-closure-induced" flow rate, shrinking fracture length (SFL) and decreasing fracture conductivity (DFC). In this paper, we propose a novel semi-analytical model to characterize the BHP behavior of water injectors under the influence of WIF. We consider that pressure losses take place within three sections: reservoir, WIF and wellbore. Flows between reservoir and WIF are linked through a fracture-storage coefficient and fracture-face skin factor, while flows between WIF and wellbore are coupled via wellbore-storage coefficient and choked-fracture skin factor. Finite difference and perturbation theory methods are deployed to include the SFL and DFC effects, respectively. Duhamel principle is invoked to characterize flow rate changes caused by wellbore and fracture storage effects. Results show that bi-storage effects can be identified as two unit slopes in the pressure derivative curve. In the abscense of extra pressure drop between wellbore and WIF, i.e., choked-fracture skin equals to zero, a prolonged storage period with a considerably large storage coefficient can be obtained. In addition, we find that SFL could cause the variable fracture storage effect while DFC may lead to the upward of pressure derivative curve at late times. Finally, the model is successfully applied in the Changqing Oilfield to validate its reliability.

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