Analysis of flocculation in a jet clarifier. Part 2 - Analysis of aggregate size distribution versus Camp number

Highlights

• Floc size distributions in the flocculation zone are almost insensitive to the jet flow rate.

• The number of flocs in the recirculation loop is 10 times larger than in injection.

• Efficiency of the jet clarifier is related to the almost constant value of Gt.

Abstract

Among the various existing technologies for water treatment, the jet clarifier is considered as an effective and compact system as it couples flocculation and clarification in a single unit. In this work, a quasi-two-dimensional apparatus was designed to visualise the interaction between floc size distribution and hydrodynamics in the flocculation zone of a jet clarifier. Measurements of the number of flocs and their size distributions are performed by means of shadowgraphy method and image analysis. Thanks to a coupling between population size distributions and results on local hydrodynamics, the evolution of the number of aggregates along the jet is directly correlated to the recirculation loop present in the flocculation zone. The relative independence of the floc size distributions on the flow rate is discussed in light of the Camp number Gt which remains constant for different flow rates investigated and can thus explain the efficiency of the jet clarifier in terms of flocculation.

Introduction

Conventional water treatment technologies, consisting in coagulation, flocculation, sedimentation, and/or filtration, have widely been used to eliminate suspended particles and colloids that cause turbidity. To speed up the removal of suspended solids, raw water must first be coagulated and flocculated to create large aggregates that can easily settle. To that end, addiction of a chemical such as either aluminum sulfate or ferric chloride under rapid mixing results in the destabilization of the negatively charged suspended particles that are thereafter brought together by the action of slow mixing, a process commonly known as flocculation. The theory of agglomeration was firstly developed by Smoluchowski at the beginning of the 20th century (Smoluchowski, 1917). The fundamentals of his theory are presented and discussed in more recents papers such as those of Elimelech et al. (1995); Thomas et al. (1999) or Gregory (2013). Smoluchowski (1917) considered collisions of spherical particles in uniform and laminar shear flow assuming that the velocity gradients (G) induced by the shear generate relative motion between particles and thus the possibility to collide and aggregate. With his model, the number of collisions $J_{ij}$ between particles i and j of diameters d_i and d_j can be quite simply expressed as stated in Eq. 1.

$$J_{ij}=\frac{G}{6}{n}_i{n}_j{\left(d_i{+d}_j\right)}^3$$

where n_i and n_j are the particle number concentrations. Smoluchowski (1917) thus defined the orthokinetic collision rate coefficient k_ij as Eq. 2.

$$k_{ij}=\frac{G}{6}{\left(d_i{+d}_j\right)}^3$$

This expression is one of basic elements to discuss the agglomeration kinetics, through the Population Balance Equation of Eq. 3.

$$\frac{d{n}_k}{dt}=\frac{1}{2}\sum _{\begin{array}{c}i+j\to k\\ i=1\end{array}}^{i=k-1}{k}_{i,j}{n}_i{n}_j-n_k\sum _{k=1}^{\text{∞}}{k}_{ij}{n}_i$$

The terms on the right hand side of Eq. 3 deal respectively with the birth and the death of aggregates of size k. The first term represents the rate of of formation of flocs of size k from the agglomeration of any pair of flocs such that i + j → k. The second term is the rate at which a aggregate of size k collides with any other aggregate.

Given a certain number of assumptions (Gregory, 2013), it is possible to express from Eq. 3 the rate of change of total particle concentration $n_T$ under the following form:

$$\frac{d{n}_T}{dt}=-\frac{4G\varphi n_T}{\pi }$$

where $\varphi$ corresponds to the total volume of particles.

$$\varphi =\frac{\pi d^3{n}_T}{6}$$

As $\varphi$ can be seen as constant during an aggregation process then Eq. 4 becomes a first-order rate expression and can be integrated into Eq. 6:

$$\frac{n_T}{n_0}=exp\left(-\frac{4\varphi Gt}{\pi }\right)orGt=\frac{\text{l}\text{n}\left(\frac{n_T}{n_0}\right)}{\frac{4}{\pi }\varphi }$$

This simplified model is recalled here to illustrate some important features of flocculation and shows that the extent of flocculation depends on the non-dimensional term Gt. The total number of collisions occurring in the suspension, is thus related to Gt, known as the Camp Number which is a performance indicator and a basic design criteria. For typical water treatment, the recommended values of the Camp Number range between 1⋅10⁴ and 2⋅10⁵ (Camp, 1955). Hence, specification of the Camp number and either the spatially averaged velocity gradient (G) or residence time (t) suffices to determine the total tankage and mixing power required (Chen and Liew, 2002). Indeed, the global velocity gradient (G) is defined as:

$$\text{G =}\sqrt{\frac{\text{P}}{\text{μV}}}$$

where P power supplied or dissipated in the tank, V the volume of the tank and μ the dynamic viscosity of the fluid. P is connected to the viscous dissipation rate of the total kinetic energy ε as:

$$\text{ε =}\frac{\text{P}}{\rho \text{V}}$$

Where $\rho$ is the density of the fluid. Thus, the global velocity gradient G can be directly connected to ε

$$\text{G =}\sqrt{\frac{\epsilon }{\nu }}$$

Where $\nu$ is the kinematic viscosity of the fluid. The average velocity gradient G employed in the flocculation tanks studied by the early study of Camp ranged from 20 to 75 s⁻¹, and the hydraulic retention times (t) from 10 to 100 min (Camp, 1955). Nowadays, flocculators are commonly designed to have Gt values in the range of 10⁴ to 2.10⁵, G values may range from 7 to 100 s⁻¹ and residence times are typically in the range 20−45 min (Chen and Liew (2002); Gregory (2013)). For any water, there is an optimum combination of G and t.

Among the various existing technologies for water treatment, the jet clarifier is considered as an effective and compact system as it couples flocculation and clarification in a single unit (Degremont (2007); Pani and Patil (2007); Romphophak et al. (2016); Watanabe (2017)). Jet flocculators represent an interesting alternative to conventional impeller mixing as they do not involve any mechanical component (Patwardhan and Gaikwad, 2003) and also because their maintenance cost is reduced. The flocculation is generally realized in a mixing zone and the clarification/sedimentation is held through flow in buffered zones (Romphophak et al. (2016)). In hydraulic jet flocculators, the incoming jet induces a top to bottom circulation that results in an efficient mixing (Kumar et al. (2009); Jayanti (2001)).

Many articles are devoted to the mixing induced by jets in which parameters such as tank geometry (height, diameter, form), nozzle diameter, jet configuration (side entry jets, vertical jets, inclined jets…), jet velocity or outflow position have extensively been studied. Among these studies, the reviews of Patwardhan and Gaikwad (2003) and Randive et al. (2018) focused mainly on the mixing time correlation and the works of Grenville and Tilton (1996, 2011) presented simple models that correlates blend time data from jet mixing vessels for tall tanks. In 2006, Wasewar (2006) proposed a critical analysis of the available literature and drawn general conclusions about the design of jet mixed tanks. Based on experimental results on flocculation, Kumar et al. (2009) suggested that the incoming jet induces a top to bottom circulation resulting in efficient mixing. More recently Romphophak et al. (Submitted to Chemical Engineering Research and Design) experimentally studied the hydrodynamics of quasi-two-dimensional jet clarifier using Particle Image Velocimetry (PIV). Their results revealed that the flocculation zone exhibits a large circulation loop whose flow rate is at least 10 times greater than the inlet jet flow rate resulting thus in a very efficient mixing. Based on a specific PIV data processing, they estimated the local shear rate and then its space-averaged value showing that the Camp Number (Gt) is almost constant in the flocculation zone whatever the inlet flow rate.

On a flocculation point of view, numerous studies have proven a direct connection between floc size and hydrodynamics. Investigators such as Thomas (1964); Parker et al. (1972); François (1987) or Ducoste et al. (1997; Ducoste and Clark, 1998) shown that the steady-state maximum floc size is related to the average intensity of the turbulent fluid motion, especially ε or G under the following equation:

$$d_{max}\propto \frac{C}{{\epsilon }^n}\text{o}\text{r}\propto G^{-\gamma }$$

Where C is linked to the strength of the floc and n or γ are coefficients depending on flocculation conditions and hydrodynamics. Those pioneer works were then continued by coupling experimental analyses of floc size distribution and hydrodynamics, namely by PIV. Comparing the flocculation efficiency in a 70 L mixing tank with two different impellers (Rushton turbine and Lightnin A310), Bouyer et al. (2004) showed that G is not sufficient to characterize floc size distribution and that the floc size depends on the history of mixing. Then, Coufort et al. (2005) found that, in a jar and in a Taylor Couette reactor, the most probable floc size depends on the mode of the distribution of ε and that for similar hydrodynamic conditions, flocs formed from elementary particles are larger than flocs formed from aggregates resulting from break-up stages. In their papers of 2014 and 2017, Vlieghe et al. (2014; 2017) performed flocculation of bentonite in a turbulent Taylor–Couette reactor under various shear rates and monitored morphological characteristics of individual flocs. They showed that although size and shape are obviously correlated, their dependency to hydrodynamics is not the same. These four previous studies agreed on the fact that the floc size was close to the Kolmogorov microscale (η) and that the size distribution was calibrated by the turbulence. Based on numerical simulations (CFD) and experimental results, He et al. (2018a; and 2018b) focused on the effect of mixing generated in baffled and unbaffled square stirred tanks with different liquid heights on the floc growth. They provide useful insights into the design and operation of stirrer tanks flocculators and suggest an optimal combination between circulation time (t_c), impeller speed (N_d) and height of the baffle to achieve a maximal floc growth rate and turbidity removal.

To our present knowledge, the literature about the floc size, either in terms of average size or size distribution, is rather scarce in the case of jet flocculators. The main available data are generally presented in terms of turbidity removal and their conclusions do not converge on all points. Romphophak et al. (2016) studied the effect of flow rate used on the jet clarifier to reduce the turbid synthetic water: it was concluded that efficiency of about 80% can be achieved at the flow rates of 40–70 L/h (values of Gt). Kumar et al. (2009) showed that, for square and circular flocculators (37,000 < Gt < 60,000), the turbidity removal was maximum when the nozzle was located 50% of the height of the tank and that when the detention time increases the residual turbidity sharply falls. In the case of higher Camp numbers (90,000 < Gt < 216,000), Randive et al. (2020) showed that tank geometry is crucial in determining the effective turbidity removal rate and circular basins should be privileged. They also found that (1) in circular tank, turbidity removal was in the range of 80%–90% whatever the nozzle diameter; (2) increasing the retention time definitely promotes maximum turbidity removal and (3) whatever the tank geometry, jets positioned at bottom of the flocculation chamber provide better turbidity removal. In their study, citing the work of List and Imberger (1973), Sobrino et al. (1996) mentioned that when the expanding jet collides the wall, the flocs are entrained in the bottom part of the chamber resulting in the formation of a recirculation loop leading to an increase of the concentration of flocs promoting thus their collisions. Sobrino et al. (1996) also mentioned that the effluent residual turbidity was essentially independent of the flow rate and associated this result to a nearly constant value of Gt without being able to prove it.

The overall goal of this work is to better understand the relationship between the aggregate size distribution and the hydrodynamics in the flocculation zone of the jet clarifier. To that end, flocculation experiments were carried out in a quasi-two-dimensional jet clarifier whose local and global hydrodynamics have prior been studied in terms of local and global velocity gradients (Romphophak et al. (Submitted to Chemical Engineering Research and Design)).