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Semianalytical solutions for release of fluids from rock matrix blocks with different shapes, sizes, and depletion regimes

机译：从形状，大小和消耗方式不同的岩石基质块中释放流体的半解析解决方案

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摘要

Dual-porosity (DP) models have been extensively used to simulate the flow of fluids (water or gas) in aggregate soils and fractured porous media. The fluid exchange between the rock matrix blocks and the fracture network is very important in DP models. In this study, we present semianalytical solutions for release of a single-phase liquid or gas from cylindrical and spherical matrix blocks with various block size distributions and different pressure depletion regimes in the fracture. The nonlinear pressure diffusivity equations for flow of gas and air are solved analytically using an approximate integral method. It is shown that this solution can be simplified to model flow of slightly compressible fluids like water in DP media. The effect of variable block size distribution on the release rate for different block geometries is studied. Practically it is not feasible to model a large-scale fractured reservoir based on a fine grid approach due to the requirement of large computational time. The presented semianalytical model can be incorporated into numerical models for accurate modeling of the amount of transferred fluid between matrix and fractures using a DP approach. It is shown that the results calculated by the developed model match well with those from fine grid numerical simulations. Furthermore, the developed model can recover the available solutions in the literature for slightly compressible fluids such as water or oil. It can be used to calculate two- or three-dimensional flows in matrix blocks bounded by two or three sets of fractures, respectively.
机译：双孔隙度（DP）模型已被广泛用于模拟聚集土壤和压裂多孔介质中流体（水或气体）的流动。在DP模型中，岩石基质块与裂缝网络之间的流体交换非常重要。在这项研究中，我们提供了从圆柱形和球形基质块中释放出单相液体或气体的半解析解，这些圆柱形和球形基质块在裂缝中具有各种块尺寸分布和不同的压力消耗方式。使用近似积分法解析求解气体和空气流动的非线性压力扩散系数方程。结果表明，该解决方案可以简化为模拟可压缩流体（如水）在DP介质中的流动。研究了可变块尺寸分布对不同块几何形状的释放速率的影响。实际上，由于需要大量的计算时间，因此基于精细网格方法对大型裂缝储层进行建模是不可行的。所提出的半分析模型可以并入数值模型中，以便使用DP方法对基质和裂缝之间的流体转移量进行精确建模。结果表明，所开发模型的计算结果与精细网格数值模拟的结果吻合良好。此外，所开发的模型可以回收文献中针对水或油等可压缩流体的可用解决方案。它可用于计算分别由两组或三组裂缝界定的矩阵块中的二维或三维流动。

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  • 来源
    《Water resources research》 |2013年第4期|2174-2196|共23页
  • 作者

    Ehsan Ranjbar; Hassan Hassanzadeh; Zhangxin Chen;

  • 作者单位

    Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, Calgary, Alberta, Canada;

    Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, 2500 University Drive NW, Calgary, AB T2N 1N4, Canada;

    Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, Calgary, Alberta, Canada;

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