Analytical solution for Non-Darcian effect on transient confined-unconfined flow in a confined aquifer

This paper presents a new analytical solution to investigate the mechanism of transient confinedunconfined flow in a confined aquifer induced by pumping with a large rate during mine drainage.The study focuses on understanding the impact of non-Darcian effect on flow towards a fully penetrated pumping well.The nonlinear relationship between specific discharge and the hydraulic gradient is described using Izbash's equation.A novel approximate method is developed to linearize the mathematical model,and the solution is derived using the Boltzmann transform.The proposed solution is validated by comparing it with previous works.The findings indicate that increased non-Darcian index,quasi-hydraulic conductivity,and specific storage have negatively affect the development of the unconfined region and aquifer drawdown,as greater turbulence flow accelerates recharge to the pumping well.Drawdown is found to be sensitive to the non-Darcian index,quasi-hydraulic conductivity,while it is unaffected by specific yield and specific storage.The conclusions provide valuable insights for mine drainage and the application of geological and hydrological conditions.

Homotopy Analysis Solution to Radial Diffusivity Equation of Slightly Compressible Fluid

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.