SIMULATION OF SOLUTE TRANSPORT IN UNSTEADY STREAMFLOWS

Abstract

The subject of pollutant mixing and its transport in streams has been at the forefront of research for the determination of pollutant concentration along the river course and for regulating disposal of pollutants in rivers. While abundant literature is available for solute transport modelling under steady flow conditions, only a few researchers have studied the problem of solute transport in rivers under unsteady streamflow conditions. Majority of the studies available in literature employ complex numerical algorithms for solution of the governing equations of flow and solute transport phenomena, which require river cross-section details at close spatial intervals, in addition to flow and solute concentration measurements at those locations. The existing models do not allow the integration of flow. and solute transport model parameters and simultaneous flow and solute routing. Further, existing transient storage models for simulating solute transport in the presence of transient storage zones along river reach require complex numerical solution algorithms. The present study attempts to overcome the above limitations in modelling the longitudinal dispersion of solutes under unsteady flow conditions using the following approach: 1. Simplification of the Advection-Dispersion (AD) equation for solute transport modelling and coupling it with a flow routing model based on the Approximate Convection- Diffusion (ACD) equation for simultaneous routing of flow and solute. 2. Simplification of the governing equations of the Transient Storage (TS) model for solute transport modelling along the river reach and coupling it with the flow routing model based on the ACD equation. Important assumptions used in the development of this approach, are: i) the flow in small reach length Ax is steady and uniform over a routing time interval At, but varies from one time interval to the next interval, and ii) the concentration varies linearly within a small reach length Ax. ii Similarity between the simplified form of the (AD) equation governing the solute transport, and the Approximate Convection-Diffusion (ACD) equation (Perumal and Ranga Raju, 1999) governing the flow transport is established. The similarity of the simplified forms of the flow transport and solute transport equations has enabled the development of the AD-VPM model for studying solute transport in rivers under steady flow conditions. The appropriateness of the AD-VPM model is first tested under steady flow conditions by reproducing the analytical solution of the AD equation for a given uniform pulse input and for different combinations of flow velocity (U) and dispersion coefficient (DL). It is found from the analysis of a number of numerical experiments that analytical solution of the AD model is closely reproduced by the proposed AD-VPM model as indicated by the Nash-Sutcliffe criterion, it 99% , when DL,5_ 415.64 U1•71 defining the applicability domain of the AD-VPM model. The proposed AD-VPM model has also been verified under steady flow conditions using i) two laboratory test data, and ii) three field experiments data, (the Colorado River, the Rhine river, and the Missouri river). The dispersion coefficient, which is a parameter in the AD-VPM model is estimated using the relationship suggested by MCQuivey-and Keefer (1974) because of its simplicity and accuracy. Satisfactory reproduction of the C-t curves demonstrates the suitability of the AD-VPM model for its application under steady flow conditions, within its applicability domain. The acceptable performance of the AD-VPM model for steady flow conditions, has enabled to extend it for studying solute transport under unsteady flow conditions. This is achieved by integrating the parameters of the AD-VPM model with the parameters of the VPM flow routing model for simultaneous routing of the solute under unsteady flow conditions. Numerical experiments on two hypothetical channels having a width of 50m and 100m, characterised by different Manning's roughness coefficient and bed slope values, demonstrate the ability of the AD-VPM model for solute transport by reproducing the results obtained from the numerical solution of the coupled Saint-Venant equations for flow routing and the AD equations (SVE-AD iii for an uniform pulse input, and ii) using two field experiments data ( Mimram river and Uvas Creek). Since the form of the ATS model is same as that of the AD model, the applicability criterion of the ATS-VPM model under steady flow conditions is considered as the same as that obtained for the AD-VPM model with U replaced by the solute transport velocity (Us) and DL replaced by the ATS dispersion coefficient (Dun). The ATS-VPM model has been extended to study solute transport in rivers under unsteady flow conditions, following the same approach as adopted in the case of AD-VPM model. Numerical experiments on three hypothetical channels of different characteristics demonstrate the adequacy of the ATS-VPM model, by satisfactorily simulating the C-t curves as obtained by the numerical algorithm solutions of the Saint-Venant's Equations and the TS equations (SVE-TS model). The ATS-VPM model has also been verified for its applicability using the field experiments data of Huey creek recorded under unsteady flow conditions (Runkel et al., 1998). Based on the study it is concluded that the proposed AD-VPM and ATS-VPM models simulate the solute transport in rivers and streams under steady as well as unsteady flow conditions satisfactorily within their applicability