Abstract This paper introduces an analytical approach for the performance of the fractured reservoir considering the impact of the matrix block size, shape, and distribution. The objective is better understanding the roles of the variable interporosity flow systems, fracture flowing systems, and reservoir matrix heterogeneity in the responses of the wellbore pressure drop, flow rate, cumulative production, and productivity index. This understanding could help to eliminate the uncertainties and increase the accuracy in characterizing the conventional and unconventional reservoirs where very complex structures of a significant disorder in the matrix block size, shape and distribution could be existed in the porous media. The study uses the well documented multilinear flow model to describe the pressure distribution in the naturally fractured reservoirs depleted by multiple hydraulic fractures considering different matrix block sizes, shapes, and distributions. The analytical models of the flow rate, cumulative production, and the productivity index are also developed in this study from the multilinear flow model. The reservoirs of interest are assumed to have stimulated porous media extending between hydraulic fracture and unstimulated volume extending beyond the fracture tips toward the reservoir boundary. The unstimulated reservoir volume is assumed consisting of uniformly distributed single matrix block size and shape because there is no impact for the hydraulic fracturing process. While the stimulated reservoir volume is considered consisting of a variable matrix block size, shape, and distribution because of the impact of hydraulic fracture propagation. The petrophysical properties of the two porous media, as well as the storativity and interporosity flow coefficient, are assumed functions of the matrix characteristics in the two volumes. The matrix block dimensions (radius or length) are correlated exponentially with the distance from the hydraulic fracture face toward the no-flow boundary between these fractures. Three fracture-matrix fluid flux functions are developed for the reservoirs where the matrix blocks could have a spherical, slab, and cylindrical configuration. The study has reached several conclusions. A positive impact on the reservoir performance is seen when the matrix block size becomes small or when the small size matrix blocks control the distribution of the blocks in the porous media. Reservoir performance is enhanced also when there are several matrix block sizes compared to a single size or very few sizes. It is observed that the reservoirs with spherical blocks may give better performance than the reservoir with slab or cylindrical matrix blocks. In terms of matrix block size and distribution, heterogeneous reservoirs may have a higher productivity index than homogenous reservoirs. The variable matrix block size and distribution in the stimulated reservoir volume is more beneficial than the unstimulated volume. The novel point presented in this paper is developing several analytical models for the wellbore pressure drop, flow rate, cumulative production, and productivity index of hydraulically fractured reservoirs with a consideration given to the matrix block size, shape, and distribution.

中文翻译：

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考虑自然和诱导矩阵块大小、形状和分布的复杂结构裂缝性油藏的性能

摘要 本文介绍了一种考虑基质块大小、形状和分布影响的压裂油藏性能分析方法。目的是更好地理解可变孔隙度流动系统、裂缝流动系统和储层基质非均质性在井筒压降、流速、累积产量和产能指数响应中的作用。这种理解有助于消除不确定性并提高表征常规和非常规储层的准确性，其中多孔介质中可能存在基质块大小、形状和分布显着无序的非常复杂的结构。该研究使用记录良好的多线性流动模型来描述被多个水力压裂耗尽的天然裂缝油藏中的压力分布，考虑到不同的基质块尺寸、形状和分布。在这项研究中，流量、累积产量和生产力指数的分析模型也是从多线性流动模型中发展起来的。假定感兴趣的储层具有在水力压裂和延伸超出裂缝尖端朝向储层边界的未增产体积之间延伸的受激多孔介质。由于对水力压裂过程没有影响，因此假设未增产的储层体积由均匀分布的单个矩阵块大小和形状组成。由于水力压裂扩展的影响，增产储层体积被认为由可变的基质块大小、形状和分布组成。两种多孔介质的岩石物理特性以及储量和孔隙度流动系数被假定为两个体积中基质特征的函数。基质块尺寸（半径或长度）与从水力裂缝面到这些裂缝之间的无流动边界的距离呈指数相关。为储层开发了三种裂缝-基质流体通量函数，其中基质块可以具有球形、板状和圆柱形配置。研究得出了几个结论。当基质块尺寸变小时或当小尺寸基质块控制块在多孔介质中的分布时，可以看到对储层性能的积极影响。与单个大小或非常少的大小相比，当存在多个矩阵块大小时，水库性能也会得到增强。据观察，具有球形块体的储层可能比具有板条或圆柱形基质块体的储层具有更好的性能。在基质块体大小和分布方面，非均质储层可能比均质储层具有更高的产能指数。受刺激储层体积中的可变矩阵块尺寸和分布比未受刺激体积更有利。本文提出的新观点是开发几种井筒压降、流速、