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.

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.

A New Method for Solving Boundary Value Problem of Composite Hermit Equations

2013 ◽  
Vol 753-755 ◽  
pp. 2851-2854 ◽  
Author(s):  
Jun Hua Shi ◽  
Shun Chu Li ◽  
Xiao Lin Wang ◽  
Dong Dong Gui
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Practical Method ◽  
Structural Formula ◽  
New Method ◽  
Constructive Method

The paper is devoted to studying the solution for boundary value problem of composite Hermit equations. Based on the obtained solution with similar structural formula, a new method which is called as Similar Constructive Method (shortened as SCM) was put forward for solving this type of boundary value problem. The SCM is a simply and practical method, which provides convenience for solving boundary value problems of composite differential equations.

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.

scholarly journals Hydrodynamic interactions among multiple circular cylinders in an inviscid flow

2012 ◽  
Vol 712 ◽  
pp. 505-530 ◽  
Author(s):  
R. Sun ◽  
C. O. Ng
Keyword(s):  
Boundary Value Problem ◽  
Numerical Solutions ◽  
Boundary Value ◽  
Cyclic Permutation ◽  
Neumann Boundary ◽  
Hydrodynamic Interactions ◽  
Circular Cylinders ◽  
Constructive Method ◽  
Nonlinear Phenomena ◽  
Inviscid Fluid

AbstractHydrodynamic interactions among multiple circular cylinders translating in an otherwise undisturbed inviscid fluid are theoretically investigated. A constructive method for solving a Neumann boundary-value problem in a domain outside $N$ circles (one kind of Hilbert boundary-value problem in the complex plane) is presented in the study to derive the velocity potential of the liquid. The method employs successive offset functions combined with a ‘generalized cyclic permutation’ in turn to satisfy the impenetrable boundary condition on each circle. The complex potential is therefore expressed as $N$ isolated singularities in power series form and used to get instantaneous added masses of $N$ submerged circular cylinders. Then, based on the Hamilton variational principle, a dynamical equation of motion in vector form is derived to predict nonlinear translations of the submerged bodies under fully hydrodynamic interactions. Also, the equivalence of the energy-based Lagrangian framework and a momentum-type one in the two-dimensional body–liquid system is proved. It implies that the pressure integration around a submerged body is holographic, which provides information about velocities and accelerations of all bodies. The numerical solutions indicate some typical dynamical behaviours of more than two circular cylinders which reveal that interesting nonlinear phenomena would appear in such a system with simple physical assumptions.

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.

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.

THE SECOND BOUNDARY VALUE PROBLEM OF RIEMANN'S TYPE FOR BIANALYTICAL FUNCTIONS WITH DISCONTINUOUS COEFFICIENTS

2004 ◽  
Vol 9 (3) ◽  
pp. 193-200
Author(s):  
L B. Bolottn
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Unit Circle ◽  
Boundary Value ◽  
Discontinuous Coefficients ◽  
Constructive Method ◽  
Analytical Functions ◽  
Basic Boundary

The paper is devoted to the investigation of one of the basic boundary value problems of Riemann's type for bianalytical functions with discontinuous coefficients. In the course of work there was made out a constructive method for solution of the problem in a unit circle. There was also found out that the solution of the problem under consideration consists in consequent solutions of two Riemann's boundary value problems for analytical functions in a unit circle. Besides, the example is constructed.

THE FIRST BASIC BOUNDARY VALUE PROBLEM OF RIEMANN'S TYPE FOR BIANALYTICAL FUNCTIONS IN A PLANE WITH SLOTS

2005 ◽  
Vol 9 (2) ◽  
pp. 91-98
Author(s):  
I. B. Bolotin ◽  
K .M. Rasulov
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Constructive Method ◽  
Analytical Functions ◽  
Basic Boundary

The paper is devoted to the investigation of one of the basic boundary value problems of Riemann's type for bianalytical functions. In the course of work there was made out a constructive method for solution of the problem given in a plane with slots. There was also found out that the solution of the problem under consideration consists of consequent solutions of two Riemann's boundary value problems for analytical functions in a plane with slots. Besides, a picture of solvability of the problem is being searched and its Noether is identified. Šiame darbe tyrinejamas uždavinys, kai ieškoma dalimis bianaliziniu funkciju, nykstančiu begalybeje, apribotu greta kontūro trūkio tašku ir šiame kontūre tenkinančiu dvi kraštines salygas. Parodoma, kad sprendžiamas uždavinys suvedamas i sprendima dvieju Rimano uždaviniu analizinems funkcijoms.

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