Pollutant Transport In Rivers Research Articles

Parameter optimization algorithms of difference calculation schemes for improving the solution accuracy of diffusion equations describing the pollutants transport in rivers

The problems related to practical realization (as a computer program) of difference schemes of the solution of diffusion equations that describe pollutants transport in the river water are considered in this paper. In particular, the problems of optimum choosing of the algorithm parameters on which depend the accuracy, the time and the possibility of practical realization of the equation solution are considered. The demand to reduce as much as possible the time and the errors of calculations, and also the simplicity of the functions of certain classes used in mathematical models and their maximum accordance to real physical conditions are considered as criteria of optimality.

Modeling and simulation of pollutants transport in rivers

This paper is devoted to mathematical modeling and computer simulation of diffusion and transport of chemicals in rivers. We present one-, two-, and three-dimensional models in terms of time-dependent convection–diffusion–reaction differential equations, further we give the finite difference approximation and appropriate numerical algorithms for these models, and finally we discuss briefly the computer implementation of this methodology in a user friendly software package. To verify the model and the computer code we have used it to study the diffusion and transport of chemicals, in this case NO3 and PO4, in two rivers in Western Georgia flowing into the Black Sea. Namely, we considered the river Khobistskali subject to pollution sources Ochkhomuri and Chanistskali river Choga polluted with NO3. In order to evaluate the quality, the accuracy, and the performance of the methods and the developed software we have applied one-, two- and three-dimensional models to the same case, for which we had data from measurements. By analyzing the difference between the measured and the simulated values of controlled chemicals in the rivers, we have estimated the effect of agricultural activities along the banks of the river (in the interval between two sections) on the pollution degree of the Khobistskali river. In this sense, the example is schematic, since the number, the arrangement, and the capacities of pollution sources of Khobistskali only partially correspond to the real situation. Though, the geometry of the rivers, the arrangement of the control sections, and the concentrations of polluting substances in the rivers matches well the real data.

Methods for predicting dispersion coefficients in rivers

The majority of approaches for predicting pollutant transport in rivers rely on being able to estimate dispersion coefficients. This paper describes four methods for doing this and argues that in most cases practising engineers would rely on one of numerous predictive equations that have been proposed over the past 30 years or so. The paper reviews these equations and discusses some recent improvements to the theoretical representation of pertinent transport processes that implies that the latest predictors should be more reliable than older ones. Use of seven predictors for a simple test case shows considerable scatter in predictive values, indicating that predicting dispersion coefficients remains a difficult task. Interestingly, theoretically based predictors seem to give reasonably consistent, but possibly low, values while predictors that are heavily reliant on regression to observed values seem to overpredict. The paper will be of interest to practising engineers who use computer models to predict the fate of pollutants that are discharged to river systems.

Methods for predicting dispersion coefficients in rivers

The majority of approaches for predicting pollutant transport in rivers rely on being able to estimate dispersion coefficients. This paper describes four methods for doing this and argues that in most cases practising engineers would rely on one of numerous predictive equations that have been proposed over the past 30 years or so. The paper reviews these equations and discusses some recent improvements to the theoretical representation of pertinent transport processes that implies that the latest predictors should be more reliable than older ones. Use of seven predictors for a simple test case shows considerable scatter in predictive values, indicating that predicting dispersion coefficients remains a difficult task. Interestingly, theoretically based predictors seem to give reasonably consistent, but possibly low, values while predictors that are heavily reliant on regression to observed values seem to overpredict. The paper will be of interest to practising engineers who use computer models to predict the fate of pollutants that are discharged to river systems.

Modified box schemes for pollutant transport in rivers with dead zones

AbstractSeveral difference schemes approximating a mathematical model of river pollution are investigated and their truncation error, stability and monotonicity conditions are shown. Based on numerical experiments, the classical six‐point schemes and some new modified box schemes are compared. The latter proved to be not only faster but also more accurate for practically used step lengths.

Linked Sediment/Contaminant Transport Model for Rivers with Application to the Buffalo River, New York

The Buffalo River and its sediments have been polluted by past industrial and municipal discharges and waste disposal. The river contains deposits of moderately to highly contaminated bed sediments. A one-dimensional mathematical model (DIFHEC) for sediment associated pollutant transport in rivers has been developed. The model combines the U.S. Army Corps of Engineers sediment transport model HEC-6—in a version that has been enhanced earlier by including the fine sediment fractions (CERHEC-6, Raggio et al. 1988)—with a contaminant transport formulation that includes advection, dispersion, ad/desorption processes, and contributions due to erosion and deposition. Relying on some available field data, DIFHEC was employed to simulate the sediment associated transport of the heavy metal zinc in the Buffalo River for a maximum river flow sequence out of a 25 year time series. The modeling results show that for these extreme peak flow events the amount of pollutants transported through the river mouth and into Lake Erie is substantial. Furthermore, maximum concentrations occur during the low flow phase following the peak flow.

Unsteady Transport of Pollutants in Rivers Due to Pulse Disposal

Mixing of pollutants in rivers is accomplished by the process of mechanical dispersion. Physically, dispersion may be considered as a hydraulic mixing process, by which the waste concentrations are attenuated while the waste pollutants are being transported downstream. Turbulent diffusion and velocity gradients are the two main mechanisms in dispersion. An exact analytical solution is developed for the two-dimensional unsteady convective-dispersion equation. The solution describes the concentration distribution for a conservative pollutant or substance injected as a pulse (not continuous) into a river by a diffuser pipe installed normal to the direction of the river bank. The river has a constant mean velocity and a relatively large discharge in comparison to the pollution discharge. The solution is developed using Laplace and Finite Fourier Transforms. The distribution of the transporting concentration of the pollutant in the river due to such disposal is developed in terms of error functions, exponential, and trigonometric series. Variations in the location of the diffuser pipe in the river are examined. The concentration distribution is determined across and along the river as a function of time. The effects of variations in river velocity, lateral and longitudinal dispersion coefficients on the mixing patterns are presented. The solution presents variations in concentration distribution in the river with time during and after the pulsing injection period of the pollutant. Sensitivity analysis is carried out to determine significant variations in the solution due to changes in various parameters.

Dispersion Tensor in Rotating Flows

Many environmental flow problems involve mixing and transport of substances in a non-uniform rotating ambient. Dispersion should be treated as a second order tensor in such flows since the principal directon of motion changes continuously. Secondary flows in open channels have been investigated and modeled by various researchers. These flows have been shown to influence the transport of pollutants in rivers and streams. In some studies, dispersion has been represented by a tensor. In practice, simplifying assumptions are made to make the tensor symmetric and, consequently, the mixing coefficient scalar. The general equation governing transport of mass with dispersion treated as a second-order tensor in Cartesian coordinates is considered here. Components of the dispersion tensor are given in terms of dispersion along and snormal to the flow, scaled by the local velocity vector. Simulation results are given for mass transport in two-dimensional rotating flows. The role of cross-variant components of the dispersiosn tensor in the transport process is also examined