Mathematical modelling and simulation of pollution transport in Lake Victoria.

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University of Dar es Salaam
This dissertation aims at using mathematical modelling and simulation to study the spread of pollutants in lake Victoria at the Mwanza South part, Mkuyuni area. Considering the meteorological conditions of lake Victoria, the flow of water is largely influenced by wind. So we considered the modelling of pollutant spread by advective and diffusive processes, and we formulated our Initial Boundary Value Problem (IBVP) under this argument. The advective component is modelled based on the model developed by Gunay and Al Rabeh (1991) which was used to study transport processes in the Safaniya Sea, and the diffusive component is modelled using the random walk concept. The displacement of pollutant is the result of superposition of advective and diffusive displacements. These are substituted in the approximated analytical solution of the IBVP to obtain the concentration of pollutant at that particular location. The IBVP also is solved numerically. We employed the Alternating Direction implicit (ADI) method using the Douglas Scheme, where the discretization is taken as D x = D y = 25m, u = v =4.5m/min and time t = 30 minute. Sample data were collected at Mkuyuni area and processed at the Mwanza Regional Water Laboratory where measurements of the Total Suspended Solids(TSS) and Turbidity were made. Due to time constraint measurements of other parameters such as Biological Oxygen Demands{BODs), Chemical Oxygen Demands (CODs) and heavy metals were not done. Comparison of results from the analytical model, the numerical model and the collected data was made. We observed that the average relative errors of the analytical and numerical models over the collected data are 6.068% and 13.93 % respectively. Simulation of the models show that the maximum average of pollutant concentration is found near the shore and reaches the value of 8.9mg/litre for TSS. As one goes further away from the shore the pollutant concentration decreases. For instance at a distance of 1200metres from the shore the concentration is 0.001mg/litre. For many parts there is a very good agreement between the simulated results and data collected from Mkuyuni area. As such we consider the model to be reliable and reasonably accurate for prediction of pollutant spread in most parts of the lake near Mkuyuni area. There is a discrepancy along the VFH shore to the Saanane Islands. This is mainly attributed to the overlap of boundaries thus a modification in the boundary conditions is required. However this is beyond the scope of this study. The Tanzania Bureau of Standard {TBS) has put no limit on effluent standards , it only requires that suspended solids (TSS) should not cause formation of sludge or scum in the receiving waters. The amount of suspended solids of 0.0089g/litre is small and is not expected to form a scum in the lake. Predictions based on these models show that under the existing conditions by the year 2015 the concentration will be 8.3g/litre which is sufficient to cause a scum. Turbidity were found to range from 0.0218g/litre to 0.0169g/litre around the shore. The TBS stipulates that the range limit should not exceed 0.1g/1. Although the range limit is not reached but if the state of pollution inflow is allowed to continue as it is now, the model predicts that at t=10 years from now (i . e . year 2 0 0 6) , the amount will be 4.7g/litre thus the range will be exceeded. We have observed also that after ten years to come most of the pollutants in the lake will have exceeded the TBS level thus BODs will be 7.8g/litre, CODs will be 31.2g/litre and TSS will be 4.9g/litre. With such kind of concentration of BODs, CODs and TSS Mkuyuni area will be dead by the year 2021. Lake Erie, one of the five great lakes in U.S.A died (it had no living organisms) due to excessive pollution but when measures were taken, pollution level was reduced considerably, and the lake life restored.
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Computer simulation, Lake Victoria, Mkuyuni, Mwanza
Masenya, P. K. M. (1996). Mathematical modelling and simulation of pollution transport in Lake Victoria. Master dissertation, University of Dar es Salaam. Available at (