Formulated Mathematical Model for Delayed Particle Flow in Cascaded Sub-Surface Water Reservoirs with Validation on River Flow

Ombaki Richard; Kerongo Joash; Okwoyo M. James

doi:10.20944/preprints201811.0201.v1

Preprint Article Version 1 This version is not peer-reviewed

Version 1 : Received: 7 November 2018 / Approved: 8 November 2018 / Online: 8 November 2018 (10:24:30 CET)

Pollution of sub-surface water reservoirs mainly rivers and streams through contaminated water point sources (CWPS) was studied. The objective was to formulate a discrete time delay mathematical model which describes the dynamics of reservoir pollution using mixing-problem processes that involve single species contaminants such as nitrates, phosphorous and detergents. The concentration of pollutants was expressed as a function of the inflow and outflow rates using the principle for the conservation of mass. Systems of ODEs generated from principles of mixing problems were refined into a system of DDEs so that the concentration of pollutant leaving the reservoir at time would be determined at some earlier instant, for the delay. The formulated model is a mathematical discrete time delay model which would be used to describe the dynamics of sub-surface water reservoir pollution. The results from the validation of the model were analyzed to determine how time delays in the mixing processes affect the rate of particle movement in water reservoirs.

Particle Flow, Sub-Surface Water, Reservoirs Pollution

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Formulated Mathematical Model for Delayed Particle Flow in Cascaded Sub-Surface Water Reservoirs with Validation on River Flow

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