TITLE:
Homotopy Analysis Solution to Radial Diffusivity Equation of Slightly Compressible Fluid
AUTHORS:
Olugbenga Adebanjo Falode, Victor Sunday Chukwunagolu
KEYWORDS:
Homotopy Analysis Method, Boltzmann Transformation, Exact Solution, Diffusivity Equation
JOURNAL NAME:
Applied Mathematics,
Vol.7 No.9,
May
31,
2016
ABSTRACT: The salient significance of the solution of
radial diffusivity equation to well testing analysis done in oil and gas
industry cannot be over-emphasized. Varieties of solutions have been proposed
to the radial diffusivity equation, of which the Van Everdingen-Hurst constant
terminal rate solution is the most widely accepted and the others are
approximate solution having their respective limitations. The main objective of
this project, being its first application to oil and gas industry, is to use a
new mathematical technique, the homotopy analysis method (HAM) to solve the
radial diffusivity equation for slightly compressible fluid. In Using HAM, the
Boltzmann transformation method was used to transform the radial PDE to ODE,
then a homotopy series was then constructed for the new equation with the
linear boundary condition from the original radial diffusivity equation of
slightly compressible fluid and the final equation then solved using
computation software Maple. The result gotten reveals that the homotopy
analysis method gives good results compared to the Van Everdingen and Hurst
Solution (Exact solution) and thus proves to be very effective, simple, and
accurate when compared to other form of solutions. Hence from the results
gotten, Homotopy Analysis Method can therefore be applied in solving other
non-linear equations in the petroleum engineering field since it is simple and
accurate.