Modeling of fluid flow considering radially symmetric reservoirs is common in groundwater science and petroleum engineering. The Hankel transform is suitable for solving boundary value problems, considering this flow geometry. However, there are few applications of this transform for reservoirs with a finite wellbore radius, although there are formulas of the finite Hankel transform for homogeneous boundary conditions. In this work, we refer to them as the Cinelli formulas, which are used to obtain novel solutions for transient fluid flow in bounded naturally fractured reservoirs with time-varying influx at the outer boundary, i.e., a technique to incorporate inhomogeneous boundary conditions based on the Cinelli formulas is developed. An analysis shows that the results of the solutions are highly oscillating and slowly convergent. Nevertheless, we show that this problem is largely overcome when the long-time solution is expressed as a closed relationship. Accordingly, we present the characteristic drawdown pressure curves and its Bourdet derivatives for a double-porosity reservoir with influx recharge. These curves allow us to distinguish between the pressure drops of a single-porosity reservoir with influx recharge from that of a double-porosity closed reservoir, which have been stated in the literature to resemble one another. Similarly, double- and triple-porosity reservoirs are analyzed.

中文翻译：

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带通量补给的天然裂缝性储层流体流动模型的解和类型曲线

考虑径向对称油藏的流体流动模型在地下水科学和石油工程中很常见。考虑到这种流动几何形状，汉克尔变换适合于解决边值问题。但是，尽管对于均匀边界条件有有限的Hankel变换公式，但对于具有有限井眼半径的储层，此变换几乎没有应用。在这项工作中，我们将其称为Cinelli公式，用于获得有界自然裂缝储层中瞬态流体在外边界时随时间变化的瞬态流体流动的新解，即一种基于非均质边界条件的技术。开发了Cinelli公式。分析表明，解决方案的结果高度振荡且收敛缓慢。不过，我们表明，将长期解决方案表示为封闭关系时，可以大大克服此问题。因此，我们给出了具有补给量的双孔隙油藏的特征降压曲线及其Bourdet导数。这些曲线使我们能够区分具有补给量的单孔储层的压降与双孔封闭储层的压降之间的关系，这在文献中已被描述为彼此相似。同样，对双孔和三孔储层进行了分析。这些曲线使我们能够区分具有补给量的单孔隙度油藏的压降与双孔隙度封闭油藏的压降之间的关系，这在文献中已被描述为彼此相似。同样，对双孔和三孔储层进行了分析。这些曲线使我们能够区分具有补给量的单孔隙度油藏的压降与双孔隙度封闭油藏的压降之间的关系，这在文献中已被描述为彼此相似。同样，对双孔和三孔储层进行了分析。