Formulated Mathematical Model for Delayed Particle Flow in Cascaded Subsurface Water Reservoirs with Validation on River Flow

Migration of pollutant particles into subsurface water reservoirs through point sources is largely involved mixing processes within the system flow. Possible potential pollution to these include municipal wastes, septic loads, landfills, uncontrolled hazardous and sewage storage tanks. The significantly alter their predictive rate flow in reservoirs, therefore time inherent need be accounted for. In this study, mainly rivers streams contaminated (CWPS) was studied a conceptual perspective problem objective formulate discrete delay mathematical model which describes dynamics reservoir that involve single species contaminants such as nitrates, phosphorous, detergents injecting from source. concentration x t pollutants expressed function inflow outflow rates using principle for conservation mass. major assumption made modeling problems tanks instantaneous. Practical realities dictate cannot occur instantaneously throughout tank. So accommodate realities, study refined systems ordinary differential equations (ODEs) generated principles cascading tanks, delayed (DDEs) so leaving at id="M2"> would equal average some earlier instant, id="M3"> − τ id="M4"> > 0 . formulated can used describe simulated on River Nyakomisaro Kisii County, Kenya. Physical kinematic parameters river (cross-sectional lengths, depths, velocities) three sectional were measured obtained parameter values then evaluate coefficients equation. DDEs simulation solved numerically MATLAB dde23 software. From graphical views id="M5"> versus id="M6"> , it established developed cover longer series solutions (characteristic curves) than corresponding ODEs same indicating necessary particle underestimated if are Also, indicated similar tendencies (characteristics) with elapse even though initial id="M7"> different every potentially recognized considered each reservoir. Hence, id="M8"> will imply more vice versa. By introducing delays due constituent quality models make use advection-diffusion equation Qual2kw, findings help better understanding contaminant’s accumulation levels transport resource. These assist, example, water-quality protection agencies Environmental Protection Agency (EPA), World Health Organization (WHO), National Management Authority (NEMA) generate efficient effective remedial strategies control or mitigate risks arising pollution.