Impact of Sediment Layer on Longitudinal Dispersion in Sewer Systems

Experiments focused on pollution transport and dispersion phenomena in conditions of low flow (low water depth and velocities) in sewers with bed sediment and deposits are presented. Such conditions occur very often in sewer pipes during dry weather flows. Experiments were performed in laboratory conditions. To simulate real hydraulic conditions in sewer pipes, sand of fraction 0.6–1.2 mm was placed on the bottom of the pipe. In total, we performed 23 experiments with 4 different thicknesses of sand sediment layers. The first scenario is without sediment, the second is with sediment filling 3.4% of the pipe diameter (sediment layer thickness = 8.5 mm), the third scenario represents sediment filling 10% of the pipe diameter (sediment layer thickness = 25 mm) and sediment fills 14% of the pipe diameter (sediment layer thickness = 35 mm) in the last scenario. For each thickness of the sediment layer, a set of tracer experiments with different flow rates was performed. The discharge ranges were from (0.14–2.5)·10−3 m3·s−1, corresponding to the range of Reynolds number 500–18,000. Results show that in the hydraulic conditions of a circular sewer pipe with the occurrence of sediment and deposits, the value of the longitudinal dispersion coefficient Dx decreases almost linearly with decrease of the flow rate (also with Reynolds number) to a certain limit (inflexion point), which is individual for each particular sediment thickness. Below this limit the value of the dispersion coefficient starts to rise again, together with increasing asymmetricity of the concentration distribution in time, caused by transient (dead) storage zones.

Uncertainty Quantification of Granular Computing-neural Network Model for Prediction of Pollutant Longitudinal Dispersion Coefficient in Aquatic Streams

Discharge of pollution loads into natural water systems remains a global challenge that threatens water/food supply as well as endangers ecosystem services. Natural rehabilitation of the polluted streams is mainly influenced by the rate of longitudinal dispersion (Dx), a key parameter with large temporal and spatial fluctuates that characterizes pollution transport. The large uncertainty in estimation of Dx in streams limits evaluation of water quality in natural streams and design of water quality enhancement strategies. This study develops a sophisticated model coupled with granular computing and neural network models (GrC-ANN) to provide robust prediction of Dx and its uncertainty for different flow-geometric conditions with high spatiotemporal variability. Uncertainty analysis of Dx GrC-ANN model was based on the alteration of training data fed to tune the model. Modified bootstrap method was employed to generate different training patterns through resampling from a 503 global database of tracer experiments in streams. Comparison between the Dx values estimated by GrC-ANN to those determined from tracer measurements show the appropriateness and robustness of the proposed method in determining the rate of longitudinal dispersion. GrC-ANN model with the narrowest bandwidth of estimated uncertainty (bandwidth-factor =0.56) that brackets the most percentage of true Dx data (i.e., 100%) is the best model to compute Dx in streams. Given considerable inherent uncertainty reported in other Dx models, the Dx GrC-ANN model is suggested as a proper tool for further studies of pollutant mixing in turbulent flow systems such as streams.

Effect of cadmium sorption by river sediments on longitudinal dispersion

This paper concerns the cadmium sorptive effects by river bed sediments on longitudinal dispersion coefficient in an open-channel flow via experimental and numerical study. For this purpose, a circular flume was used with mean diameter of 1.6 m and a width of 0.2 m. The adsorbing bed was considered as a thin layer of the sediment particles with mean diameter of 0.53 mm and three sediment concentrations of 3, 12, and 20 gr/lit. To determine the sorption parameters of the sediments, some experiments were conducted with three cadmium concentrations of 150, 460, and 770 ppb. Then, the dispersion experiments were carried out with and without the bed sediments with the same cadmium concentration as the sorption experiments. A numerical model was then developed to solve the advection-dispersion equation with considering the sorption term by river bed sediments. The longitudinal dispersion coefficients were estimated by comparing the experimental and numerical breakthrough curves. The results showed that, with increasing the sediment concentrations, the sediment sorption rate increased and the longitudinal dispersion coefficient decreased by about 38, 36 and 33 percent, respectively, for cadmium concentrations of 150, 460 and 770 ppb. In addition, by increasing the cadmium concentrations, the changes in the longitudinal dispersion coefficient are decreased. Furthermore, a relationship was developed using non-dimensional longitudinal dispersion as a function of the new parameter of sorption ratio. From a practical point of view, the results of this study demonstrated that, at the presence of riverbed sediment, the cadmium is longitudinally dispersed with more delay in comparison with no sediment at the river bed.

Fate of turbid glacial inflows in a hydroelectric reservoir

Turbidity from glacial meltwater limits light penetration with potential ecological consequences. Using profiles of temperature, conductivity, and turbidity, we examine the physical processes driving changes in the epilimnetic turbidity of Carpenter Reservoir, a long and narrow, glacier-fed reservoir in southwest British Columbia, Canada. Following the onset of permanent summer stratification, the relatively dense inflows plunged into the hypolimnion, and despite the high glacial load entering the reservoir, the epilimnion cleared due to particle settling. Using a one-dimensional (longitudinal) diffusion equation for a decaying substance to describe the variation in epilimnetic turbidity, we obtain two nondimensional parameters: the epilimnetic inflow parameter, $$\mathcal {I}$$ I , a measure of the turbidity flux into the epilimnion; and the dispersion parameter, $${\mathcal {D}}$$ D , a measure of longitudinal dispersion. In the case of Carpenter Reservoir: $$\mathcal {I}\ll 1$$ I ≪ 1 , indicating that turbidity declines over the summer; and $${\mathcal {D}}\ll 1$$ D ≪ 1 , indicating a strong gradient in turbidity along the epilimnion. Using our theoretical formulation of epilimnetic turbidity variations in conjunction with monthly field surveys, we compute the particle settling velocity ($${\sim}{0.25}\,{\hbox {m}\,\hbox {d}^{-1}}$$ ∼ 0.25 m d - 1 ), the longitudinal dispersion coefficient (50–70 $${\hbox {m}^{2}\,\hbox {s}^{-1}}$$ m 2 s - 1 ), and the flux of turbid water into the epilimnion ($${\sim }1{\%}$$ ∼ 1 % of the total inflow). Our approach is applicable to other reservoirs and can be used to investigate changes in turbidity in response to changes in $$\mathcal {I}$$ I and $${\mathcal {D}}$$ D .

Experimental and numerical study of bed roughness effect on longitudinal dispersion

The effects of bed roughness on the longitudinal dispersion coefficient (DL) were experimentally and numerically investigated in the present study. The tracer experiments were first carried out in a circular flume with a diameter of 1.6 m over both smooth and rough beds (coarse sand) with four sizes (ks = d65) of 1.04, 2.09, 3.01, and 4.24 mm. In addition, the one-dimensional advection-dispersion equation was numerically solved. The longitudinal dispersion coefficient was calculated by comparing the numerical and experimental breakthrough curves. The results showed that by increasing the bed roughness height (from zero to 4.24 mm), the longitudinal dispersion coefficient increased by 34%. In addition, the longitudinal dispersivity (λ = DL/V) increased with increasing relative roughness (ks/h), so that the range of longitudinal dispersivities in smooth bed experiments were 0.037–0.049 m and for rough bed (ks = 4.24 mm) were 0.07–0.084 m. In other words, with increasing the bed roughness height from zero (smooth bed) to 4.24 mm, the longitudinal dispersivities increased from 0.037 to 0.077 m, indicating an increase of about 108%. Furthermore, a relationship was developed using non-dimensional longitudinal dispersion (DL/(Vh)) as a function of relative roughness (ks/h). It can be concluded that taking into consideration bed roughness as the driving force of shear dispersion would improve predictive equations of the longitudinal dispersion in the rivers. Since the bottom of all natural rivers has roughness elements with different sizes, the results of this study will definitely be useful in estimating the longitudinal dispersion coefficient in natural rivers and quantifying the effect of roughness in the longitudinal dispersion coefficient equations.

Evaluating longitudinal dispersion of scalars in rural channels of agro-urban environments

In agro-urban environments, the water resource conveyed by rural channels is susceptible to a gradual impoverishment due to the continuous combined sewer overflow release, constituting a pending and urgent issue for water management companies and the entire community. Reliable one-dimensional longitudinal dispersion coefficients D are required to model and study the hydrodynamics and water quality patterns at the scale of rural channel networks. Empirical formulas are usually adopted to estimate D but the accuracy in the prediction could be questionable. In order to identify which are the most suitable formulas to determine D in rural channels, field tracer measurements were carried out in three rural channels with typical geometry and configuration. The obtained D values were then compared with the most commonly used predicting formulas that the literature provides. The accuracy of the predictors was further checked by simulating different flow rates inside the tested channels by using a one-dimensional hydraulic model. Starting from the obtained results, indications and guidelines to choose the most suitable formulas to predict D in rural channels were provided. These indications should be followed when developing realistic quality models in the agro-urban environments, especially in those cases where direct measurements of the longitudinal dispersion coefficient D are not available.