Cellular Vortex Element Modeling of Incompressible Fluid Flow in Confined Subsurface Porous Media

In this paper, numerical models for single phase flow in 1D and 2D using the conservation of mass principles, Darcy’s flow equation, equation of state, continuity equation and the STB/CFB (stock tank barrel/cubic feet barrel) balance were developed and combined. The main advantage of cellular vortex method modelling is that, depending on the analyst's concerns, each cell within the domain can be examined separately or collectively. Additionally, each cell's solution is a result of the erratic behaviour of its nearby cells, with the cells closest to the yield cell having the greatest influence. In other words, the farther a cell is from the yielding cell, the less influence yield and aquifer rate have on that specific cell. General vortex element method is a langragian technique for obtaining solution to engineering problems either in fluids or solids analysis and so does the cellular vortex method. The models were then recast into pressure vorticity equations using convectional algorithms. Formulating transport equations that resemble the typical vorticity transport equation required the use of derived equations. For 365 days, the daily instantaneous aquifer pressure drawdowns and pressure heads were examined using developed numerical models. The developed equations were subsequently solved using cellular vortex element technique. The developed computer program was used to investigate confined aquifer of dimensions with single vertex image. For the aquifer rate of , , the respective average head drawdowns and heads were, and , , respectively. Cellular vortex technique with relative little mathematics has been established to have recorded successes in numerical modeling of fluid flow in aquifer simulation. The axes used to formulate the models were considered to be rectilinear which of course is not in the actual sense. It is therefore also recommended that, the assumptions be relaxed to capture a little more of reality.