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Analytical Solutions for Non-Darcy Transient Flow with the Threshold Pressure Gradient in Multiple-Porosity Media

机译：非达西瞬态流量的分析解决方案，多孔隙介质中阈值压力梯度

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摘要

Low-velocity non-Darcy flow can be described by using the threshold pressure gradient (TPG) in low-permeability porous media. The existence of the TPG yields a moving boundary so that fluid starts to flow inside this boundary when the pressure gradient overcomes the viscous forces, and beyond this boundary, there will be no flow. A mathematical model of considering the TPG is developed to describe the flow mechanism in multiple-porosity media. By defining new dimensionless variables, the nonlinear mathematical model can be solved analytically. This new approach has been validated with several approximate formulas and numerical tools. The diffusion of the moving boundary varying with time is analyzed in detail in multiple-porosity media, and then the effect of the moving boundary on pressure transient response is investigated and compared with that of the traditional three boundary types (closed boundary, infinite-pressure boundary, and constant-pressure boundary). Sensitivity analysis is conducted to study the effect of the TPG on pressure and pressure derivative curves and rate decline curves for single-porosity media, dual-porosity media, and triple-porosity media, respectively. The results show that the moving boundary exerts a significant influence on reservoir performance at a relatively early time, unlike the other three boundary types, and only a boundary-dominated effect at the late time. The larger the threshold pressure gradient, the smaller the diffusion distance of the moving boundary and the rate of this well at a given dimensionless time. At the same time, the pressure transient response exhibits a higher upward trend because of a larger TPG. All behavior response might be explained by more pressure drop consumed in low-permeability reservoirs. The finding is helpful to understand the performance of low-permeability multiple-porosity media and guide the reasonable development of low-permeability reservoirs.
机译：可以通过使用低渗透性多孔介质中的阈值压力梯度（TPG）来描述低速非达到流动。 TPG的存在产生了移动边界，使得当压力梯度克服粘性力，并且超出该边界时，流体在该边界内部开始流动，并且不会有流动。考虑TPG的数学模型是开发的，描述了多孔隙介质中的流动机制。通过定义新的无量值变量，可以在分析上解决非线性数学模型。这种新方法已被验证有几种近似公式和数字工具。在多孔隙介质中详细分析移动边界随时间的扩散，然后研究了移动边界对压力瞬态响应的影响，并与传统的三个边界类型（闭合边界，无限压力）进行比较边界，恒压边界）。进行敏感性分析以研究TPG对单孔隙介质，双孔隙率和三孔隙率介质的压力和压力衍生物曲线和速率下降曲线的影响。结果表明，与其他三种边界类型不同，移动边界对储层性能产生重大影响，与其他三种边界类型不同，并且在后期的边界主导效果。阈值压力梯度越大，移动边界的扩散距离越小，并且在给定的无量纲时间内阱的速率越小。同时，由于TPG较大，压力瞬态响应表现出更高的上升趋势。所有行为响应都可以通过低渗透油藏的压力下降来解释。该发现有助于了解低渗透性多孔介质的性能，并指导低渗透油藏的合理发展。

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  • 来源
    《Mathematical Problems in Engineering》 |2019年第19期|2618254.1-2618254.13|共13页
  • 作者

    Luo Erhui; Wang Xiaodong; Hu Yongle; Wang Jianjun; Liu Li;

  • 作者单位

    PetroChina Res Inst Petr Explorat & Dev Beijing 100083 Peoples R China;

    China Univ Geosci Sch Energy Resources Beijing 100083 Peoples R China;

    PetroChina Res Inst Petr Explorat & Dev Beijing 100083 Peoples R China;

    PetroChina Res Inst Petr Explorat & Dev Beijing 100083 Peoples R China;

    PetroChina Res Inst Petr Explorat & Dev Beijing 100083 Peoples R China;

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