Modeling of unsteady flow in karst reservoirs using a modified Brinkman's equation

The Brinkman's equation simplifies the numerical modelling of karst reservoirs by allowing the use of a single transport equation to model the flow of fluids in both the free flow and porous regions, in effect reducing the error arising from improper modelling of the interface between the two regions. However, most of the equations available to model flow within karst reservoirs deal with steady flow conditions. This approach however may not be accurate in reservoirs where unsteady conditions exist. We considered the effects of unsteady flow conditions in karst reservoirs by adding an unsteady flow term to the Brinkman's equation. We solved the coupled conservation-transport equations that models unsteady fluid transport in karst reservoirs and then studied the effects of unsteady flow conditions on tracer transport in two different sample reservoirs. The solution method adopted is sequential and involves solving the unsteady Brinkman's model first, followed by advection-diffusion-adsorption equation using the cell-centred finite volume approach. The same problems were also solved using a steady flow Brinkman's model, and the results obtained were compared. were compared. The results show that, inside the caves, the unsteady Brinkman's model yielded lower tracer concentrations at early times when compared to the steady flow model.