scholarly journals Numerical investigation of a coupled moving boundary model of radial flow in low-permeable stress-sensitive reservoir with threshold pressure gradient

2016 ◽  
Vol 25 (2) ◽  
pp. 024701 ◽  
Author(s):  
Wen-Chao Liu ◽  
Yue-Wu Liu ◽  
Cong-Cong Niu ◽  
Guo-Feng Han ◽  
Yi-Zhao Wan
Keyword(s):  
Pressure Gradient ◽  
Numerical Investigation ◽  
Moving Boundary ◽  
Radial Flow ◽  
Threshold Pressure ◽  
Threshold Pressure Gradient ◽  
Boundary Model

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.

The Moving Boundary Movement of Vertical Fractured Well in Tight Oil Reservoir

2013 ◽  
Vol 868 ◽  
pp. 633-637
Author(s):  
Li Feng Liu ◽  
Xin Wang
Keyword(s):  
Pressure Gradient ◽  
Flow Model ◽  
Moving Boundary ◽  
Flow Characteristics ◽  
Seepage Flow ◽  
Threshold Pressure ◽  
Threshold Pressure Gradient ◽  
Tight Reservoir ◽  
Tight Reservoirs ◽  
Fractured Well

Because of the obvious non-Darcy characteristic of fluid flowing in tight reservoirs, there is a virtual moving boundary at the flow edge, and these percolation models of fractured wells with Darcy formula are no longer applicable. Based on the threshold pressure gradient effect, the unsteady seepage flow model of vertical fractured well was established in the drain area by means of Source and Green's Functions. With the flow characteristics at the boundary of tight reservoir, the motion equation of axes of moving boundary was obtained. By Example analysis, its proved that the moving boundary is approximate circular in the far-field, and it will move slower with the increase of the threshold pressure gradient.

scholarly journals Numerical Solution of a Moving Boundary Problem of One-Dimensional Flow in Semi-Infinite Long Porous Media with Threshold Pressure Gradient

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Jun Yao ◽  
Wenchao Liu ◽  
Zhangxin Chen
Keyword(s):  
Porous Media ◽  
Partial Differential Equations ◽  
Pressure Gradient ◽  
Numerical Solution ◽  
Boundary Problem ◽  
Moving Boundary ◽  
Moving Boundary Problem ◽  
Threshold Pressure ◽  
Threshold Pressure Gradient ◽  
One Dimensional

A numerical method is presented for the solution of a moving boundary problem of one-dimensional flow in semi-infinite long porous media with threshold pressure gradient (TPG) for the case of a constant flow rate at the inner boundary. In order to overcome the difficulty in the space discretization of the transient flow region with a moving boundary in the process of numerical solution, the system of partial differential equations for the moving boundary problem is first transformed equivalently into a closed system of partial differential equations with fixed boundary conditions by a spatial coordinate transformation method. Then a stable, fully implicit finite difference method is adopted to obtain its numerical solution. Finally, numerical results of transient distance of the moving boundary, transient production pressure of wellbore, and formation pressure distribution are compared graphically with those from a published exact analytical solution under different values of dimensionless TPG as calculated from actual experimental data. Comparison analysis shows that numerical solutions are in good agreement with the exact analytical solutions, and there is a big difference of model solutions between Darcy's flow and the fluid flow in porous media with TPG, especially for the case of a large dimensionless TPG.

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