On the basis of a well-based model (Model I) developed in a previous work (Liu and Valkó in SPE J 2019. https://doi.org/10.2118/197049-PA ), in which a fractional production decline model is developed based on anomalous diffusion to structurally account for the heterogeneity related to the complex fracture network, we incorporate two more components, i.e., the tempered anomalous diffusion and a source term, in the present work to develop a generalized model, namely Model II. Because of the two new components, Model II is capable of physically considering both the scale lower bound of heterogeneity and the influx from the matrix into the conductive fracture system. It consequently enables the new model to describe the complete sequence of regimes for the production of the slightly compressible single-phase fluid from the fractured unconventional reservoirs. Then, in the case studies, the synthetic data used in the previous work are better fitted to the new type curves in all observed periods, which demonstrates the advantage of Model II over Model I regarding the late-time flow regimes. In addition, the good fit of other sets of synthetic data to the Model II type curves exhibits the claimed capabilities of the new model and indicates the production of this type could be well characterized by seven parameters, i.e., $$\alpha$$ α , $$c$$ c , $${\lambda }_{\mathrm{D}}$$ λ D , $$\omega$$ ω , $$\sigma$$ σ , $$\tau$$ τ , and $$\mathrm{EUR}$$ EUR . Finally, the characteristics of Model II are further investigated by analyzing the effects of several parameters on the production performance, based on which some insights about the practice of developing unconventional reservoirs using massive hydraulic fracturing are provided.

中文翻译：

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一种用于说明压裂非常规油藏生产体制完整序列的部分递减模型

基于先前工作（Liu and Valkó in SPE J 2019. https://doi.org/10.2118/197049-PA）开发的基于井的模型（模型 I），其中部分产量递减模型是基于异常扩散开发以在结构上解释与复杂裂缝网络相关的非均质性，我们在目前的工作中加入了另外两个组件，即缓和异常扩散和源项，以开发一个广义模型，即模型 II。由于这两个新组件，模型 II 能够在物理上考虑非均质性的尺度下限和从基质流入导电裂缝系统。因此，它使新模型能够描述从裂缝性非常规储层生产微可压缩单相流体的完整制度序列。然后，在案例研究中，以前工作中使用的合成数据在所有观察到的时期都更好地拟合了新型曲线，这证明了模型 II 在后期流态方面优于模型 I。此外，其他合成数据集与模型 II 类型曲线的良好拟合展示了新模型声称的能力，并表明这种类型的生产可以用七个参数很好地表征，即 $$\alpha$$ α , $$c$$ c , $${\lambda }_{\mathrm{D}}$$ λ D , $$\omega$$ ω , $$\sigma$$ σ , $$\tau$$ τ , 和 $$\mathrm{EUR}$$ EUR 。最后，