## Abstract

Evaluation of exact analytical solution for flow to a well, under the assumptions made

in its development commonly requires large amounts of computation time and can

produce inaccurate results for selected combinations of parameters. Large computation

times occur because the solution involves the infinite series. Each term of the series

requires evaluation of exponentials and Bessel functions, and the series itself is

sometimes slowly convergent. Inaccuracies can result from lack of computer precision

or from the use of improper methods of numerical computation. This paper presents a

computationally efficient and an accurate new methodology in differential quadrature

analysis of diffusivity equation to overcome these difficulties. The methodology would

overcome the difficulties in boundary conditions implementations of second order

partial differential equations encountered in such problems. The weighting coefficients

employed are not exclusive, and any accurate and efficient method such as the

generalized differential quadrature method may be used to produce the method’s

weighting coefficients. By solving finite and infinite boundary condition in diffusivity

equation and by comparing the results with those of existing solutions and/or those of

other methodologies, accuracy, convergences, reduction of computation time, and

efficiency of the methodology are asserted.

in its development commonly requires large amounts of computation time and can

produce inaccurate results for selected combinations of parameters. Large computation

times occur because the solution involves the infinite series. Each term of the series

requires evaluation of exponentials and Bessel functions, and the series itself is

sometimes slowly convergent. Inaccuracies can result from lack of computer precision

or from the use of improper methods of numerical computation. This paper presents a

computationally efficient and an accurate new methodology in differential quadrature

analysis of diffusivity equation to overcome these difficulties. The methodology would

overcome the difficulties in boundary conditions implementations of second order

partial differential equations encountered in such problems. The weighting coefficients

employed are not exclusive, and any accurate and efficient method such as the

generalized differential quadrature method may be used to produce the method’s

weighting coefficients. By solving finite and infinite boundary condition in diffusivity

equation and by comparing the results with those of existing solutions and/or those of

other methodologies, accuracy, convergences, reduction of computation time, and

efficiency of the methodology are asserted.

Original language | English |
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Pages (from-to) | 233-246 |

Number of pages | 14 |

Journal | Romanian Journal of Physics |

Volume | 59.2014 |

Issue number | 3-4 |

Publication status | Published - 2014 |

## Keywords

- Differential quadrature
- Diffusivity equation
- Finite-radial reservoir
- Infinite-radial reservoir
- Pseudo-steady state
- Unsteady-state