Similar Constructive Method of Solution for the Model of Nonlinear Spherical Seepage in Composite Reservoir

2014 ◽  
Vol 700 ◽  
pp. 597-601
Author(s):  
Feng Jiu Zhang ◽  
Xu Xia Xiao ◽  
Shun Chu Li ◽  
Dong Dong Gui ◽  
Qiang Wang
Keyword(s):  
Flow Model ◽  
Boundary Value ◽  
Outer Boundary ◽  
Seepage Flow ◽  
Analytic Solutions ◽  
Flow Equation ◽  
Constructive Method ◽  
Gradient Term ◽  
Transform Method ◽  
Method Of Solution

The nonlinear spherical seepage flow model has been established for the composite reservoir model. The nonlinear spherical seepage flow model considers the well produce at a constant rate, and the quadratic gradient term under three outer boundary conditions (closed, constant pressure and infinite). Firstly, through variable substitutions, the seepage flow equation is linearized; then the model is transformed into the boundary value problem of an ordinary differential equation by employing the Laplace transform method. It has been confirmed that the Laplace space analytic solutions of such boundary value problems has a formula under different external boundaries, using the Similar Constructive Method(it is a simple and effective new idea for solving this class seepage flow model, complicated calculus calculation is avoided). The prospect of this new method is promising for understanding and studying the inherent laws of fluids flow.

A New Method and Applications of the Boundary Value Problem of Differential Equation

2014 ◽  
Vol 937 ◽  
pp. 695-699
Author(s):  
Hong E Li ◽  
Xiao Xu Dong ◽  
Shun Chu Li ◽  
Dong Dong Gui ◽  
Cong Yin Fan
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Kernel Function ◽  
Boundary Value ◽  
Outer Boundary ◽  
Seepage Flow ◽  
Petroleum Engineering ◽  
Constructive Method ◽  
Linear Homogeneous Differential Equation ◽  
The Mathematical Model

The similar structure of solution for the boundary value problem of second order linear homogeneous differential equation has been studied. Based on the analysis of the relationship between similar structure of solution, its kernel function, the equation and boundary conditions, similar constructive method (shortened as SCM) of solution is obtained. According to the SCM, the similar structure of solution and its kernel function are constructed for the mathematical model of homogeneous reservoir which considers the influence of bottom-hole storage and skin effect under the infinite outer boundary condition. The SCM is a new and innovative way to solve boundary value problem of differential equation and seepage flow theory, which is especially used in Petroleum Engineering.

scholarly journals Similar Construction Method of Solution for Solving the Mathematical Model of Fractal Reservoir with Spherical Flow

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Cui-Cui Sheng ◽  
Jin-Zhou Zhao ◽  
Yong-Ming Li ◽  
Shun-Chu Li ◽  
Hu Jia
Keyword(s):  
Boundary Conditions ◽  
Boundary Value ◽  
Outer Boundary ◽  
Petroleum Engineering ◽  
Constructive Method ◽  
Porous Media Model ◽  
Method Of Solution ◽  
Complex Boundary ◽  
Linear Differential ◽  
Set Up

On the basis of similar structure of solution for a second-order linear differential equation's boundary value problem, and our analysis of the relationship between this similar structure and its kernel function, the differential equation, and the boundary conditions, we propose a new simple solution—similar constructive method of solution (SCMS)—and sum up its detailed steps. We set up a porous media model under three kinds of outer boundary conditions (infinite, constant pressure, and closed), in which the influences of fractal dimension, spherical flow, skin effect, and storage are taken into consideration. And then we use SCMS to solve it. The SCMS is a straightforward method for differential equation's boundary value problems with complex boundary conditions, especially for solving the reservoir models in petroleum engineering.

Similar Constructing Method for Solving the Model of the Plane Radial Flow of Dual Permeability Reservoir

2013 ◽  
Vol 419 ◽  
pp. 43-50 ◽  
Author(s):  
Cong Yin Fan ◽  
Shun Chu Li ◽  
Dong Dong Gui ◽  
Ming Hu ◽  
Hui Chun Li
Keyword(s):  
Boundary Value Problem ◽  
Radial Flow ◽  
Boundary Value ◽  
Outer Boundary ◽  
Structural Formula ◽  
Constructive Method ◽  
Well Bore ◽  
Bottom Hole ◽  
Constant Rate ◽  
Seepage Model

A seepage model of producing at a constant rate, based on the three outer boundary (infinite, closed, constant value) conditions and regardless of the well-bore storage and skin effects, is established for the problem of the plane radial flow of dual permeability reservoirs. Firstly, we get dimensionless model by introducing the dimensionless variables. Second, we obtain a boundary value problem of ordinary differential equation in the Laplace space by using the Laplace transformation. Finally, we prove that the solution to the boundary value problem has similar structural formula. Therefore a new method for solving such seepage model is obtainedSimilar Constructive Method (shortened as SCM). And then, according to the modified numerical inversion formula of Stehfest, we draw the curves of bottom-hole under the three kinds of outer boundary conditions by using MATLAB.

Similar Constructive Method of Solution for the Nonlinear Percolation Model in Composite Reservoir

2014 ◽  
Vol 670-671 ◽  
pp. 678-682
Author(s):  
Feng Jiu Zhang ◽  
Xi Tao Bao ◽  
Shun Chu Li ◽  
Dong Dong Gui ◽  
Xiao Xu Dong
Keyword(s):  
Constant Pressure ◽  
Outer Boundary ◽  
Percolation Model ◽  
Constructive Method ◽  
Well Test ◽  
Analysis Software ◽  
Well Test Analysis ◽  
Test Analysis ◽  
Method Of Solution ◽  
Quadratic Gradient

This paper presents a percolation model for the composite reservoir, in which quadratic-gradient effect, well-bore storage, effective radius and three types of outer boundary conditions: constant pressure boundary, closed boundary and infinity boundary are considered. With Laplace transformation, the percolation model was linearized by the substitution of variables and obtained a boundary value problem of the composite modified zero-order Bessel equation. Using the Similar Constructive Method this method, we can gain the distributions of dimensionless reservoir pressure for the composite reservoirs in Laplace space. The similar structures of the solutions are convenient for analyzing the influence of reservoir parameters on pressure and providing significant convenience to the programming of well-test analysis software.

scholarly journals Study on Flow Model and Flow Equation of Shale Gas Based on Micro Flow Mechanism

2021 ◽  
Author(s):  
Huaxun Liu ◽  
Chunyan Jiao ◽  
Shusheng Gao ◽  
Liyou Ye ◽  
Weiguo An
Keyword(s):  
Flow Rate ◽  
Shale Gas ◽  
Gas Flow ◽  
Flow Model ◽  
Seepage Flow ◽  
Flow Equation ◽  
Gas Flow Rate ◽  
Diffusion Flow ◽  
Coupled Flow ◽  
And Diffusion

Abstract Shale flow has microscale effects, and the flow is more complex. In this paper, the flow model and flow equation which can be used in the analysis of shale gas flow is established,which is based on the single nanotube model and combined with pore throat test results of the shale core by high-pressure mercury injection, and calculated the contributions of seepage, diffusion, transition flow and free molecular flow to shale gas flow. The contributions of seepage and diffusion were over 95%, and seepage and diffusion were the main flow patterns. Then, a coupled flow model and the coupled flow equation of shale gas with seepage and diffusion were established, which proposed a calculation method of shale permeability and diffusion by relationship between flow pressure and shale gas flow rate, and finally shale gas flow experiments were carried out and analyzed. The results show that the shale gas flow model and the flow equation established in this paper can describe shale gas flow very well. The shale gas flow rate is composed of seepage flow rate and diffusion flow rate, and the seepage flow rate is proportional to the pseudo pressure difference and is proportional to the pressure square difference at low pressure. The diffusion flow rate is proportional to the difference in shale gas density and is proportional to the pressure difference at low pressure. With shale gas reservoir pressure drops, the proportion of diffusion flow increases. The research results enrich the understanding of shale gas flow; they also have certain reference significance to the development of shale gas reservoirs.

scholarly journals A Study on Solving the Seepage Flow Model of Three-Area Composite Reservoir

2014 ◽  
Vol 670-671 ◽  
pp. 599-603 ◽  
Author(s):  
Xiao Xu Dong ◽  
Shun Chu Li ◽  
Dong Dong Gui ◽  
Feng Jiu Zhang
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Flow Model ◽  
Constant Pressure ◽  
Outer Boundary ◽  
Seepage Flow ◽  
Well Bore ◽  
Analysis Software

This paper studies the seepage flow mathematical model of three-area composite reservoir under three kinds of outer boundary conditions (infinite boundary, constant pressure boundary and closed boundary), in which influences of well-bore storage and skin factor are not taken into consideration. On the basic of theory of similar structure of solution of boundary value problem of differential equation, this paper obtain the solution of the seepage flow model of three-area composite reservoir. The study is not only conducive to further analyze the inherent law of the solution and solve corresponding application problems, but also easy to compile corresponding analysis software.

Similar Constructive Method for Solving the Nonlinear Spherical Percolation Model in Dual-Porosity Media

2013 ◽  
Vol 631-632 ◽  
pp. 265-271 ◽  
Author(s):  
Xi Tao Bao ◽  
Shun Chu Li ◽  
Dong Dong Gui
Keyword(s):  
Outer Boundary ◽  
Percolation Model ◽  
Dual Porosity ◽  
Constructive Method ◽  
Gradient Term ◽  
Well Test ◽  
Structure Of Solutions ◽  
Well Test Analysis ◽  
Gas Field ◽  
Field Development

This paper presents a spherical percolation model for dual-porosity media reservoir, where the quadratic-gradient term, wellbore storage and three types of outer boundary conditions: constant pressure boundary, closed boundary and infinity boundary were considered. Then a new method: Similar Constructive Method was put forward for solving this type of percolation model. And solutions of the dimensionless reservoir pressure and the dimensionless bottomhole pressure in Laplace space were obtained. It was proved that these solutions had a similar structure. The Similar Constructive Method is an elementary and algebraic method, simple and practical. And the similar structure of solutions can simplify the well test analysis software programming and analyze the reservoir parameter’s affection on pressure conveniently. The present research has a great academic significance and application value in oil-gas field development.

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