A heuristic formula for turbulence-induced flocculation of cohesive sediment

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Abstract

This paper presents new measurements on the settling velocity of mud flocs in the Lower Sea Scheldt, Belgium, and compares the results with data obtained previously in the Tamar estuary, UK. The data show that the flocs are fairly compact with a fractal dimension of about 2.2, which is indicative for reaction limited aggregation processes, characteristic in dynamic aquatic systems with large tidal flow velocities and high SPM (suspended particulate matter) concentrations. The data also reveal a fairly small dependency of the settling velocity from SPM concentrations, consistently much smaller than earlier data published in literature.

Furthermore, a simple explicit formulation is proposed for the settling velocity of cohesive sediment in estuaries and coastal seas. It is derived from an analytical solution of a Lagrangean flocculation model, which accounts for turbulence-induced aggregation and floc break-up. Also the effects of variations in SPM and of a limited residence time of the flocs in the turbulent water column are included.

The model has been calibrated against data from settling velocity measurements carried out in the Tamar estuary. Values of the measured settling velocity vary between 0.5 and 5 mm s−1 at SPM-values between 0.05 and 8 g l−1. Using the tuned coefficients, the model describes the observations satisfactory, with an overall relative standard deviation of 30%. Also, the well-known and observed increase in settling velocity with turbulent shear stress at low stresses and the opposite trend at high stresses is described properly. Next, the model is applied to the new data obtained in the Lower Sea Scheldt estuary, again comparing favourably with overall relative standard deviations of 30–50%. It appeared that the coefficients of the model can be determined from independent measurements, but two of them have to be determined by trial and error, for which a simple procedure is proposed.

Introduction

The recent increase in world trade in general and in container shipment in particular necessitates an extension of harbour basins and key walls of the Port of Antwerp, Belgium. For this purpose, the Deurganckdok is under construction, a 4500 × 500 m2 basin with open connection to the Lower Sea Scheldt. As this basin is located near the turbidity maximum of the estuary, the authorities need three-dimensional sediment transport models to assess and manage the fine sediment dynamics in the estuary, amongst which assessment of volumes of maintenance dredging, the environmental impact of dumping of dredged material, etc. Therefore, the Flemish government initiated an extensive program of model development and field work, the latter to collect data to determine sediment properties and data to calibrate the models under development. In this paper, we focus on one aspect of the model development and field work, i.e. the behaviour of the settling velocity of the sediment and a formulation describing its variations with shear stress, SPM (suspended particulate matter) concentration and residence time in the water column.

The transport and fate of fine suspended sediment in open, natural water systems, such as rivers, estuaries, coastal areas and oceans is governed to a large extent by the settling velocity of the sediment particles. For non-cohesive sediment, e.g. sand, this settling velocity is a unique function of the particle's diameter, its shape and the water viscosity, and can be determined straightforward with large accuracy. However, for cohesive sediment this is not the case, as the sediment is clustered in porous flocs of varying size and an ever varying composition of clay particles, silt, sometimes fine sand, organic material and a lot of water.

In low-energetic conditions at low SPM concentration, such as met in many rivers, the sediment is flocculated, but floc size and composition are fairly constant, as the flocculation time at these hydro-sedimentological conditions is quite large, e.g. Winterwerp and Van Kesteren (2004) and Winterwerp (2005).

In high-energetic conditions at high SPM concentration, such as met in many estuaries and coastal seas, floc size and composition may change continuously (Krone, 1984). This was depicted by Dyer (1989) in a conceptual diagram suggesting that floc size changes with SPM-values and turbulent shear. At low shear rates, the floc size increases with shear rate, whereas at larger shear rates, the opposite trend is expected. This diagram motivated many researchers to carry out detailed studies on the flocculation behaviour of cohesive sediment, which necessarily has to be carried out in elaborative field studies, because of the large fragility of the flocs. This, in turn, required the development of instruments for in-situ monitoring of the flocs.

One such instrument, INSSEV (IN-Situ SEttling Velocity) was developed by Fennessy et al. (1994), and has been used extensively by Manning, 2001, Manning, 2004a, Manning, 2004b. On the basis of large data sets in macrofloc (D > 160 μm) and microfloc (D < 160 μm) settling velocity, together with the relative floc mass distribution, Manning (2004c) derived empirical relations between the settling velocity of flocs and SPM-values and turbulent shear rate, following Dyer's diagram.

Winterwerp (1998) reasoned that the ascending branch of Dyer's diagram at low shear rates should be attributed to non-equilibrium conditions. In this phase of the flocculation process, the flocculation time is larger than the residence time of the flocs in the turbulent water column, as a result of which equilibrium floc sizes cannot be attained, contrary to the right part of the diagram where the flocculation time is short because of the large shear rates. Winterwerp, 1998, Winterwerp, 2002 developed a three-dimensional flocculation model, which indeed depicts this behaviour. However, using this model is too time-consuming to be used in operational models, and therefore parameterization is necessary to obtain an algebraic formulation that can be applied efficiently in three-dimensional sediment transport models.

In this paper, such a parameterization is proposed, based on the flocculation model by Winterwerp, 1998, Winterwerp, 2002. The underlying derivation is presented in Section 2 of this manuscript. The model is calibrated against an extensive data set from the Tamar estuary and the sensitivity of the model to the physical parameters is discussed. Section 3 describes the field campaign in the Lower Sea Scheldt and the INSSEV instrument to measure settling velocity, and presents the major data on settling velocity and relevant parameters obtained during the survey. In Section 4 the model is applied to the new data from the Lower Sea Scheldt estuary. Section 5 presents a brief discussion on the results of the measurements and the applicability of this new flocculation model. We note that this paper deals with the physical forcing of flocculation. The effects of biology in general, and of secretions by algae and bacteria, such as EPS and TEP are not treated explicitly; for state-of-the-art reviews, the reader is referred to Droppo et al. (2005). However, it has been indicated where and how these effects may be accounted for in the parameters of the flocculation model proposed.

Section snippets

Derivation of the flocculation model

The basis of the flocculation formula proposed in this paper is the three-dimensional flocculation model described in Winterwerp (2002) and its Lagrangean form (Winterwerp, 1998). This model describes flocculation as the result of turbulence-induced aggregation and floc break-up. The latter two processes work continuously, and at equilibrium, they balance. The model has one characteristic floc size, which can be regarded as the median floc size. We apply fractal theory to relate floc size and

Site description

The drainage basin of the Scheldt river covers an area of nearly 22,000 km2 and is situated in the northeast part of France, the west part of Belgium and the southwest part of The Netherlands (Fig. 4). The tide in the estuary is semi-diurnal. The tidal wave penetrates the estuary up to Gentbrugge, 156 km inland from the mouth. The mean tidal range is 3.85 m at the mouth and increases up to 5.24 m at Schelle (91 km from mouth). The average freshwater discharge is about 100 m3 s−1, with extreme values

Application of the flocculation model to Lower Sea Scheldt data

In this section we apply the heuristic flocculation formula and model parameters k2, k3, k4 and D0 from Table 1, as obtained from calibration of the model against data from the Tamar estuary, to the data of the Lower Scheldt estuary. We use the results of Fig. 6, i.e. nf = 2.15 and m = 0.44; the water depth is set at its local value h = 15 m. These parameters are summarized in Table 1 for convenience.

Fig. 8 shows a comparison of the model predictions and the data. Table 3 presents the goodness of fit,

Discussion and conclusions

We have carried out new series measurements of the settling velocity of cohesive sediment flocs in the Lower Sea Scheldt, Belgium, and compared the data with the results of earlier measurements in the Tamar estuary. These rivers are situated in temperate climate zone, and are fairly dynamic in the sense that they are characterized by mesotidal conditions, high flow velocities and high turbidity. This is reflected by fairly dense flocs with large fractal dimensions, of about 2.2, which is

Acknowledgements

We like to thank Ministry of the Flemish Community (Ministerie van de Vlaamse Gemeenschap) for the funding of the project, and their permission to publish the results. Staff from ms Zeeschelde and Gems International are acknowledged for the good collaboration during the field measurements. Finally, Dr. Ken Kingston (University of Plymouth) is acknowledged for his assistance with the initial stages of the model calibration.

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