Reply to ‘Comment on “The analysis of horizontal well pressure behavior in fractured low permeability reservoirs with consideration of the threshold pressure gradient”’

2014 ◽  
Vol 11 (3) ◽  
pp. 038002
Author(s):  
Yu-Long Zhao
Keyword(s):  
Pressure Gradient ◽  
Horizontal Well ◽  
Low Permeability ◽  
Threshold Pressure ◽  
Threshold Pressure Gradient ◽  
Pressure Behavior ◽  
Low Permeability Reservoirs

Threshold Pressure Gradient in Ultra-low Permeability Reservoirs

2008 ◽  
Vol 26 (9) ◽  
pp. 1024-1035 ◽  
Author(s):  
F. Hao ◽  
L. S. Cheng ◽  
O. Hassan ◽  
J. Hou ◽  
C. Z. Liu ◽  
...  
Keyword(s):  
Pressure Gradient ◽  
Low Permeability ◽  
Threshold Pressure ◽  
Threshold Pressure Gradient ◽  
Low Permeability Reservoirs

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

2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
Erhui Luo ◽  
Xiaodong Wang ◽  
Yongle Hu ◽  
Jianjun Wang ◽  
Li Liu
Keyword(s):  
Mathematical Model ◽  
Pressure Gradient ◽  
Transient Response ◽  
Moving Boundary ◽  
Low Permeability ◽  
Threshold Pressure ◽  
Threshold Pressure Gradient ◽  
Pressure Transient ◽  
Multiple Porosity ◽  
Low Permeability Reservoirs

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.

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