TY - JOUR

T1 - Analysis of diffusivity equation using differential quadrature method

AU - Razminia, K.

AU - Razminia, A.

AU - Kharrat, R.

AU - Baleanu, D.

PY - 2014

Y1 - 2014

N2 - Evaluation of exact analytical solution for flow to a well, under the assumptions madein its development commonly requires large amounts of computation time and canproduce inaccurate results for selected combinations of parameters. Large computationtimes occur because the solution involves the infinite series. Each term of the seriesrequires evaluation of exponentials and Bessel functions, and the series itself issometimes slowly convergent. Inaccuracies can result from lack of computer precisionor from the use of improper methods of numerical computation. This paper presents acomputationally efficient and an accurate new methodology in differential quadratureanalysis of diffusivity equation to overcome these difficulties. The methodology wouldovercome the difficulties in boundary conditions implementations of second orderpartial differential equations encountered in such problems. The weighting coefficientsemployed are not exclusive, and any accurate and efficient method such as thegeneralized differential quadrature method may be used to produce the method’sweighting coefficients. By solving finite and infinite boundary condition in diffusivityequation and by comparing the results with those of existing solutions and/or those ofother methodologies, accuracy, convergences, reduction of computation time, andefficiency of the methodology are asserted.

AB - Evaluation of exact analytical solution for flow to a well, under the assumptions madein its development commonly requires large amounts of computation time and canproduce inaccurate results for selected combinations of parameters. Large computationtimes occur because the solution involves the infinite series. Each term of the seriesrequires evaluation of exponentials and Bessel functions, and the series itself issometimes slowly convergent. Inaccuracies can result from lack of computer precisionor from the use of improper methods of numerical computation. This paper presents acomputationally efficient and an accurate new methodology in differential quadratureanalysis of diffusivity equation to overcome these difficulties. The methodology wouldovercome the difficulties in boundary conditions implementations of second orderpartial differential equations encountered in such problems. The weighting coefficientsemployed are not exclusive, and any accurate and efficient method such as thegeneralized differential quadrature method may be used to produce the method’sweighting coefficients. By solving finite and infinite boundary condition in diffusivityequation and by comparing the results with those of existing solutions and/or those ofother methodologies, accuracy, convergences, reduction of computation time, andefficiency of the methodology are asserted.

KW - Differential quadrature

KW - Diffusivity equation

KW - Finite-radial reservoir

KW - Infinite-radial reservoir

KW - Pseudo-steady state

KW - Unsteady-state

UR - http://www.scopus.com/inward/record.url?scp=84899156965&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84899156965

VL - 59.2014

SP - 233

EP - 246

JO - Romanian Journal of Physics

JF - Romanian Journal of Physics

SN - 1221-146X

IS - 3-4

ER -