Generalized analytical solution for gravity drainage phenomena in finite matrix block with arbitrary time dependent inlet boundary condition and variable matrix block size

2018 ◽  
Vol 167 ◽  
pp. 227-240 ◽  
Author(s):  
Mahdi Abbasi ◽  
Peyman Rostami ◽  
Mostafa Keshavarz Moraveji ◽  
Mohammad Sharifi
Keyword(s):  
Boundary Condition ◽  
Analytical Solution ◽  
Block Size ◽  
Time Dependent ◽  
Gravity Drainage ◽  
Arbitrary Time ◽  
Finite Matrix ◽  
Matrix Block ◽  
Inlet Boundary Condition

scholarly journals Generalized analytical solution for advection-dispersion equation in finite spatial domain with arbitrary time-dependent inlet boundary condition

2011 ◽  
Vol 8 (2) ◽  
pp. 4099-4120
Author(s):  
J.-S. Chen ◽  
C.-W. Liu
Keyword(s):  
Boundary Condition ◽  
Analytical Solution ◽  
Concentration Field ◽  
Generalized Solution ◽  
Spatial Domain ◽  
Time Dependent ◽  
Hydrodynamic Dispersion ◽  
Arbitrary Time ◽  
Special Cases ◽  
Inlet Boundary Condition

Abstract. This study presents a generalized analytical solution for one-dimensional solute transport in finite spatial domain subject to arbitrary time-dependent inlet boundary condition. The governing equation includes terms accounting for advection, hydrodynamic dispersion, linear equilibrium sorption and first order decay processes. The generalized analytical solution is derived by using the Laplace transform with respect to time and the generalized integral transform technique with respect to the spatial coordinate. Several special cases are presented and compared to illustrate the robustness of the derived generalized analytical solution. Result shows an excellent agreement. The analytical solutions of the special cases derived in this study have practical applications. Moreover, the derived generalized solution which consists an integral representation is evaluated by the numerical integration to extend its usage. The developed generalized solution offers a convenient tool for further development of analytical solution of specified time-dependent inlet boundary conditions or numerical evaluation of the concentration field for arbitrary time-dependent inlet boundary problem.

scholarly journals Generalized analytical solution for advection-dispersion equation in finite spatial domain with arbitrary time-dependent inlet boundary condition

2011 ◽  
Vol 15 (8) ◽  
pp. 2471-2479 ◽  
Author(s):  
J.-S. Chen ◽  
C.-W. Liu
Keyword(s):  
Boundary Condition ◽  
Analytical Solution ◽  
Numerical Solutions ◽  
Generalized Solution ◽  
Spatial Domain ◽  
Time Dependent ◽  
Hydrodynamic Dispersion ◽  
Arbitrary Time ◽  
Special Cases ◽  
Inlet Boundary Condition

Abstract. This study presents a generalized analytical solution for one-dimensional solute transport in finite spatial domain subject to arbitrary time-dependent inlet boundary condition. The governing equation includes terms accounting for advection, hydrodynamic dispersion, linear equilibrium sorption, and first order decay processes. The generalized analytical solution is derived by using the Laplace transform with respect to time and the generalized integral transform technique with respect to the spatial coordinate. Some special cases are presented and compared to illustrate the robustness of the derived generalized analytical solution. Result shows an excellent agreement between the analytical and numerical solutions. The analytical solutions of the special cases derived in this study have practical applications. Moreover, the derived generalized solution which consists an integral representation is evaluated by the numerical integration to extend its usage. The developed generalized solution offers a convenient tool for further development of analytical solution of specified time-dependent inlet boundary conditions or numerical evaluation of the concentration field for arbitrary time-dependent inlet boundary problem.

Boundary Conditions and Initial Value Lines for Unsteady Homentropic Flow Calculations

1970 ◽  
Vol 21 (2) ◽  
pp. 145-162 ◽  
Author(s):  
W. A. Woods ◽  
H. Daneshyar
Keyword(s):  
Boundary Condition ◽  
Analytical Solution ◽  
Boundary Conditions ◽  
Good Accuracy ◽  
Numerical Calculations ◽  
Time Dependent ◽  
Straight Pipe ◽  
Initial Value ◽  
Use Of Time ◽  
The Difference

SummaryA detailed discussion on the difference between an initial value line and a line characterised by a boundary condition has been presented. Two types of boundaries are described and illustrated. To examine each boundary, several different calculations have been performed for a straight pipe. The results of the numerical calculations are compared with an analytical solution. It is shown that known pressure and velocity at the pipe ends give the most accurate results. Comparisons are also made between several practical types of calculations which give similar findings. The use of time-dependent boundaries can lead to errors as large as 40 per cent in derived results. It is shown that good accuracy can be restored by converting the boundaries into initial value lines. It is concluded that in general no more than one time-dependent boundary should be used in any calculation. Finally it is demonstrated that errors are not revealed by means of pressure diagrams alone.

scholarly journals Analytical Solution of Heat Conduction for Hollow Cylinders with Time-Dependent Boundary Condition and Time-Dependent Heat Transfer Coefficient

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Te-Wen Tu ◽  
Sen-Yung Lee
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Transfer Coefficient ◽  
Analytical Solution ◽  
Transfer Coefficient ◽  
Time Dependent ◽  
Physical Parameters ◽  
Expansion Theorem ◽  
Present Solution ◽  
Hollow Cylinders

An analytical solution for the heat transfer in hollow cylinders with time-dependent boundary condition and time-dependent heat transfer coefficient at different surfaces is developed for the first time. The methodology is an extension of the shifting function method. By dividing the Biot function into a constant plus a function and introducing two specially chosen shifting functions, the system is transformed into a partial differential equation with homogenous boundary conditions only. The transformed system is thus solved by series expansion theorem. Limiting cases of the solution are studied and numerical results are compared with those in the literature. The convergence rate of the present solution is fast and the analytical solution is simple and accurate. Also, the influence of physical parameters on the temperature distribution of a hollow cylinder along the radial direction is investigated.

An analytical solution of a two-dimensional temperature field in a hollow cylinder under a time periodic boundary condition using Fourier series

2009 ◽  
Vol 223 (8) ◽  
pp. 1889-1901 ◽  
Author(s):  
G Atefi ◽  
M A Abdous ◽  
A Ganjehkaviri ◽  
N Moalemi
Keyword(s):  
Boundary Condition ◽  
Temperature Field ◽  
Fourier Series ◽  
Temperature Distribution ◽  
Analytical Solution ◽  
Hollow Cylinder ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Separation Of Variables ◽  
Two Dimensional

The objective of this article is to derive an analytical solution for a two-dimensional temperature field in a hollow cylinder, which is subjected to a periodic boundary condition at the outer surface, while the inner surface is insulated. The material is assumed to be homogeneous and isotropic with time-independent thermal properties. Because of the time-dependent term in the boundary condition, Duhamel's theorem is used to solve the problem for a periodic boundary condition. The periodic boundary condition is decomposed using the Fourier series. This condition is simulated with harmonic oscillation; however, there are some differences with the real situation. To solve this problem, first of all the boundary condition is assumed to be steady. By applying the method of separation of variables, the temperature distribution in a hollow cylinder can be obtained. Then, the boundary condition is assumed to be transient. In both these cases, the solutions are separately calculated. By using Duhamel's theorem, the temperature distribution field in a hollow cylinder is obtained. The final result is plotted with respect to the Biot and Fourier numbers. There is good agreement between the results of the proposed method and those reported by others for this geometry under a simple harmonic boundary condition.

Sign in / Sign up

Export Citation Format

Share Document