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Special Topics & Reviews in Porous Media: An International Journal

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ISSN Печать: 2151-4798

ISSN Онлайн: 2151-562X

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PRESSURE BEHAVIOR OF VERTICAL WELLS IN LOW-PERMEABILITY RESERVOIRS WITH THRESHOLD PRESSURE GRADIENT

Том 2, Выпуск 3, 2011, pp. 157-169
DOI: 10.1615/SpecialTopicsRevPorousMedia.v2.i3.10
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Краткое описание

The threshold pressure gradient, which is associated with non-Darcy flow in low permeability reservoirs, is defined as the level of pressure gradient that must be attained to enable the fluid to overcome the viscous forces and start to flow. If the pressure gradient is small, then the flow velocity increases slowly and obeys a nonlinear relationship, but when the pressure gradient starts to exceed the threshold pressure gradient, it increases quickly and starts to obey the linear relationship. With low velocity and non-Darcy flow, the fluid flow boundary is controlled by the threshold pressure gradient and can extend outward continuously, while the fluid beyond this boundary cannot flow. This paper presents analytical solutions to the pressure transient equations of vertical wells in isotropic low-permeability reservoirs with threshold pressure gradient. These solutions are obtained by using Green’s functions method with numerical approximations. A method to determine the location of the moving boundary front is also presented. It is concluded that, at any time, smaller threshold pressure gradient results in smaller resistance to flow; thus, a single-well control radius is larger and the moving boundary front is moving farther away from the wellbore. Furthermore, a greater threshold pressure gradient results in more resistance to flow, meaning a much stronger driving force is required to reach the same flow rate. Unlike the material balance equation, we conclude that both pressure transient radius and pressure drop at the wellbore are approximately linear functions of the cubic root of producing time and not the square root of producing time. Its proposed equations find that the moving boundary front is sensitive to the value of the threshold pressure gradients. Furthermore, at any given value of threshold pressure gradient, we calculate lower bottom-hole pressure than those calculated by the material balance equations. Finally, the solution procedure we propose is a fast tool to evaluate well performance in low permeability reservoirs.

ЦИТИРОВАНО В
  1. Zhao Yu-Long, Zhang Lie-Hui, Wu Feng, Zhang Bo-Ning, Liu Qi-Guo, Analysis of horizontal well pressure behaviour in fractured low permeability reservoirs with consideration of the threshold pressure gradient, Journal of Geophysics and Engineering, 10, 3, 2013. Crossref

  2. Zhao Yu-Long, Zhang Lie-Hui, He Zhi-Xiong, Zhang Bo-Ning, Productivity for Horizontal Wells in Low-Permeability Reservoir with Oil/Water Two-Phase Flow, Mathematical Problems in Engineering, 2014, 2014. Crossref

  3. Lu Jing, Comment on ‘Analysis of horizontal well pressure behaviour in fractured low permeability reservoirs with consideration of the threshold pressure gradient’, Journal of Geophysics and Engineering, 11, 3, 2014. Crossref

  4. Wang Xiao-dong, Zhu Guang-ya, Wang Lei, Exact analytical solutions for moving boundary problems of one-dimensional flow in semi-infinite porous media with consideration of threshold pressure gradient, Journal of Hydrodynamics, 27, 4, 2015. Crossref

  5. Liu Wenchao, Yao Jun, Numerical Investigations of the Effect of Nonlinear Quadratic Pressure Gradient Term on a Moving Boundary Problem of Radial Flow in Low-Permeable Reservoirs with Threshold Pressure Gradient, Mathematical Problems in Engineering, 2015, 2015. Crossref

  6. Liu Wenchao, Yao Jun, Chen Zhangxin, Zhu Weiyao, An exact analytical solution of moving boundary problem of radial fluid flow in an infinite low-permeability reservoir with threshold pressure gradient, Journal of Petroleum Science and Engineering, 175, 2019. Crossref

  7. Zeng Jie, Wang Xiangzeng, Guo Jianchun, Zeng Fanhua, Zhang Qiushi, Composite linear flow model for multi-fractured horizontal wells in tight sand reservoirs with the threshold pressure gradient, Journal of Petroleum Science and Engineering, 165, 2018. Crossref

  8. Luo Erhui, Wang Xiaodong, Hu Yongle, Wang Jianjun, Liu Li, Analytical Solutions for Non-Darcy Transient Flow with the Threshold Pressure Gradient in Multiple-Porosity Media, Mathematical Problems in Engineering, 2019, 2019. Crossref

  9. Liu Wenchao, Zhang Qitao, Zhu Weiyao, Numerical simulation of multi-stage fractured horizontal well in low-permeable oil reservoir with threshold pressure gradient with moving boundary, Journal of Petroleum Science and Engineering, 178, 2019. Crossref

  10. Liu Wenchao, Analytical study on a moving boundary problem of semispherical centripetal seepage flow of Bingham fluid with threshold pressure gradient, International Journal of Non-Linear Mechanics, 113, 2019. Crossref

  11. Liu Wenchao, Exact analytical solutions of non-Darcy seepage flow problems of one-dimensional Bingham fluid flow in finite long porous media with threshold pressure gradient, Journal of Petroleum Science and Engineering, 184, 2020. Crossref

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