A Mathematical Model for River Flow Assimilation: A Case Study of Pasikhan River, Iran

The self-purification capacity of rivers is a function of time, space, nature, intensity of the pollution load and the condition of the river bed. Evaluating a river self-purification rate requires determination of the dissolved oxygen levels. The level of pollution and oxygen shortages at critical points along the river should be investigated. In the other words, the estimation of river contaminants is based on the selfpurification capacity. The Streeter-Phelps method is a well-known approach for evaluating the level of dissolved oxygen in a river and it can be restricted to ignore advection and dispersion terms. It is possibleto model the self-purification process knowing the aquatic parameters and pollutants. In this paper, the basic Streeter-Phelps equation has been analytically solved. Advection and dispersion terms have been included in the equation to increase the accuracy of the predictions. The new equation was then modeled using FTCS, Upstream, Lax & Wendroff, and QUICKEST numerical methods. A 2 km section of the Pasikhan River was chosen for field testing and the required water samples were taken and lab tested forDO, BOD5, NO3 and PO4. The analytical and numerical results for predicting dissolved oxygen were compared with the field data. The results showed that all numerical predictions were in good agreement with the measured data, but the Upstream method showed the best results. Furthermore, the results indicated that the numerical methods performed better than the Streeter-Phelps base model. This may have been caused by the addition of the advection and dispersion terms to the Streeter-Phelps base model.