Climbing the Effluent Filtration Tree: Modelling, Mechanisms & Applications—A Monograph

Abstract

Particle filtration is a major building block in effluent treatment facilities for water reuse in agriculture, industry, and the community. Yet, its incorporation in modern hybrid treatment systems still lacks basic know-how for process optimization. This paper aims to provide a profound understanding of particle filtration vis-à-vis its various reuse applications. The methodology used follows a road map depicted as a growing tree, representing the author’s research from roots to top: roots—basic modeling, mechanisms; tree trunk—filter design approach for reuse; branches—enhanced particle removal; and tree crown—pretreatment, bioparticle, and nanoparticle removal. Contact deep-bed filtration process optimization, algorithms for economically optimal filter design, tertiary filtration and membrane pretreatment, and related energy issues are being discussed. Some of the conclusions are that pilot plant planning should be primarily derived from particle surface interactions with filter media, based on measurements of mineral particle or bioparticle size, shape, and physicochemical characteristics, and applying attachment-detachment models. Filter design optimization would comprise of selecting efficient water quality processes first, followed by economic optimization for final design parameters. A holistic approach in the design of filtration facilities, standing alone or incorporated in hybrid systems, is also considered.

1. Introduction

The world is facing a growing shortage of water supply due to climate change and population growth, the Middle East is one example, Singapore, California, China, Mexico and some regions in Europe are others [1]. Although there is increasing precipitation in the Northern Hemisphere, there is every probability, particularly in North America and Europe, that meteorological and surface soil moisture droughts will considerably increase in duration and frequency under 1.5–2 °C warming [2]. The Natural water reservoirs cannot support the growing demand in those areas; some of them have suffered from recent droughts and years of groundwater over-pumping. The strategy of thirsty countries focuses today on massive Water Generation through water reuse, seawater/brackish water desalination, and rain harvesting [3,4]. Water conservation, rain enhancement, and stormwater utilization have also been developed. The above trends are expanding the hydrological cycle. Instead of having only natural water resources created by the atmosphere, wastewater and seawater are entering the hydrological cycle as additional water resources.

The expanding reuse of wastewater has been a driver for different countries to amend their water reuse regulations and standards with the main purpose to protect human health and the environment while maximizing reused water applications. In 2010, Israel issued new official effluent reuse standards, covering agricultural unrestricted irrigation and recharge to streams, with stream reclamation in mind. Thinking filtration, TSS monthly average MCL (maximum contaminant level) is 10 mg/L for both uses. The European Commission approved its updated recommended guidelines in 2018, a similar TSS MCL is included. Reference is provided in Section 8 Future Direction below.

Particle filtration is a major building block in effluent treatment facilities for water reuse in agriculture, industry, and the community. Yet, its incorporation in modern hybrid treatment systems still lacks basic know-how for process optimization. To get there, it is important to grasp the role of filtration in the water cycle while zooming in on the process itself. The author’s urge to find better ways to bring clean water to the world brought him to focus on the removal of contaminates in filtering processes, which led to the pioneering investigations of attachment-detachment mechanisms in particle interaction with filter media. Identifying detachment mechanisms and their impact on filtering performance were then formulated into a game-changing model enabling filter design optimization and filtering process development in drinking water purification [5], pre-treatment before membranes, and wastewater tertiary treatment for reuse or safe disposal [6,7].

The evolution of the above-mentioned research in the field of filtration can be visualized as the path from roots (the basics) to fruits (innovative processes) that can better cope with current water scarcity and public health challenges. Also, the tree symbolizes agriculture and green areas which are major consumers of reused wastewater (Figure 1).

Naturally and undoubtedly, wastewater filtration theory is a branch of water filtration theory and is being continuously fed by it.

This paper leads the professional reader through the development of applied research in this area. It is done in a unique, original way, as a monograph describing the Author’s experience from studying basic mechanisms to developing mathematical models and their application to design parameters optimization and innovative solutions. Energy as an operation and optimization membrane filtration factor is also developed, as well as its potential recovery in electroflocculation processes. Each model or process discussed was a novelty at its time. It is believed that such an article, on top of its scientific and engineering value, would be highly educational for the young researcher.

Having said that, this paper aims to provide a profound understanding of particle filtration vis-à-vis its various reuse applications. The methodology used follows a road map depicted as a growing tree, representing the author’s research from roots to top: roots—basic modeling, mechanisms; tree trunk—filter design approach for reuse; branches—enhanced particle removal; and tree crown—pretreatment, bioparticles, and nanoparticles removal. The diversity of the topics and processes in this work has dictated to incorporate their specific material and methods information in their relative section rather than in a conventional “Materials and Methods” section.

2. Mechanisms in Removing Particles from Wastewater Effluents

2.1. Straining

Straining is generally regarded as the basic process of filtration, as its mechanism seems to be quite simple: the flow of particles through porous media, in which the pore size is smaller than the size of the particles in the flow. Even though many researchers have stressed the advantage of granular filtration over straining in filtering colloidal and submicron particles [8,9], the possibility of retaining such particles cannot be excluded in the cake formed by straining. It has been demonstrated that even when the majority of particles in the suspension are smaller within one order of magnitude than the screen pore, screens will become clogged [10]. However, PSD analysis and microscopic examination confirmed the formation of amorphous, compact aggregates in the filtrate, larger than particles in the influent, toward the end of the run (Figure 2).

This means that a detachment phenomenon exists, in which case two things happen: (a) the head-loss development rate across the filter declines and, more importantly, (b) the particle aggregates detached from the cake reach the irrigation system and may accumulate there and clog drippers downstream, as also observed by farmers and irrigation guides in the field [10].

2.2. Deep-Bed Filtration

In deep-bed granular filters, also known as rapid or high rate filters, the suspended particle size is smaller than the filter grain size, their removal occurs inside the porous media and is dominated by physical-chemical mechanisms. Particles in wastewater effluents are mostly colloidal and negatively charged, thus repelling each other and becoming stabilized. Positive ions are attracted to the negatively charged particle, forming what is known as the electrical double-layer model, which is presented and discussed in many papers and textbooks. A common, somewhat qualitative measure of the stabilizing energy is the electrokinetic surface potential, often referred to as ζ (zeta) potential (ZP). Practically and roughly, three “stability zones” represented by ZP may be determined (

Table 1. Colloidal Stability Zones determined by zeta potential measurements.

I	0 to −7 mv	Low potential	Low stability, tendency to coagulate
II	−10 to −15 mv	Medium potential	Medium repulsion, low to medium stability
III	≥|−20| mv	High potential	High repulsion, stable

).

ZP measurements of particles originated in various types of wastewater treatment plants effluents in Israel ranged −10 mV to −18 mV, pointing out that (a) their stability in suspension being in Stability Zone II is quite similar, and (b) they are less stable than various surface water bodies which their ZP value implies Stability Zone III and need more intensive coagulation [11].

The particle removal process mechanism in a granular filter undergoes (a) physical transport of the colloidal particle to the vicinity of the grain surface, where (b) van-der-Waals attraction forces overtake the electrostatic double-layer repulsion—usually minimized by using coagulants—and, after accumulation of internal deposits, (c) particle detachment dominated by hydrodynamic shear forces takes place [12,13]. Macroscopically, the active layer in a deep-bed filter is advancing with time as a clogging front, providing a picture somewhat similar to granular activated carbon adsorption or ion-exchange processes (Figure 3).

A comprehensive understanding of filtration mechanisms is a primary condition for good filter design. It is particularly important in the case of wastewater effluents filtration, where dissolved organic matter (DOM) is present in large concentrations, providing the colloidal particles with a kind of “protective envelope”, thus making attachment harder than in the case of water containing mineral colloids e.g., clays alone. That partly explains why experimental contact-coagulation-filtration with alum brought about early breakthroughs, resulting in shorter filtration runs than expected [14]. An additional reason here could be the voluminous, yet weak and non-uniform morphological nature of the humic-alumno deposits accumulating on the grain surfaces inside the bed which, later in the run, were ripped-off by the increasing shear (detachment) forces. In the following experiments, the addition of flocculant aid such as high molecular weight cationic polyelectrolyte strengthened the internal deposit structure while using a coarser, uniform deep media, ending up with longer filtration runs. The authors emphasize, that “There was an optimum polymer dose range, lower and higher doses than optimum giving shorter filtration runs.” [14]. It is quite typical for polyelectrolytic coagulants that overdosing is relatively rapid on a dose-removal efficiency curve.

Figure 3. Change in head loss and hydraulic gradient (slope tangent) with cationic polyelectrolyte through coarse media. Uniform (UC = 1.17) quartz sand media, av. grain size = 1.38 mm, filtration velocity = 20 m/h, Kaolinite suspension concentration = 20 mg/L, and polymer (Catfloc) dose = 0.05 mg/L Reprinted with permission from [12]. Journal AWWA 1974.

Figure 3. Change in head loss and hydraulic gradient (slope tangent) with cationic polyelectrolyte through coarse media. Uniform (UC = 1.17) quartz sand media, av. grain size = 1.38 mm, filtration velocity = 20 m/h, Kaolinite suspension concentration = 20 mg/L, and polymer (Catfloc) dose = 0.05 mg/L Reprinted with permission from [12]. Journal AWWA 1974.

Particle size distribution (PSD) measurements are a good instrument for the evaluation of effluent filterability. Having that in mind, effluent samples taken from irrigation reservoirs containing oxidation ponds and from an activated sludge plant were filtered through granular beds and filter screens [15]. Three different grain media sizes were tested: 0.7 mm, 0.84 mm, and 1.2 mm. Observing all the results in removal efficiency of particles greater than 10 μm by the granular beds, the minimum was 40% and the maximum was 85%. Such removal range is not rare in filtering wastewater effluents without pre-coagulation where the attachment forces are relatively weak. It could depend on whether a screen filter preceded the granular filter or not and on the effluent type. Yet, examining filter screens’ performance in retaining TSS demonstrated a highly exponential clogging rate with only 1–2% removal efficiency. Also, smaller particles ranging 1–2 μm in size were hardly removed, suggesting that minimum transport theory applies. The major reason for the span in the efficiencies was that, in all cases, particle removal ratio increased as a function of grain size and bed depth, and decreased with filtration velocity increase, affecting the smaller particles more. It was also demonstrated, that PSD was superior to TSS or turbidity as parameters in testing wastewater effluents’ filterability [15].

Figure 4 depicts some of the results described above concerning particle removal efficiency vs. filtration rate. It can be observed, that particles larger than 10 μm are removed with a constant removal efficiency of about 80%, most probably due to some dynamic equilibrium between particles accumulating and detaching on the filter bed surface. Activated sludge effluent filtration showed similar behavior.

PSD experimental results corresponded well to the power-law distribution function for both filters influent and filtrates. Considering the most basic form of the function, the power-law exponent absolute value was larger for the coarse media filtrate than for the finer media (e.g., 2.01 vs. 1.80), pointing to a greater number of particles smaller than 10 μm in the latter. As could be expected, the finer filter media developed a considerably higher head loss rate than the coarser filter media, although some surface removal was observed there. The removal of the larger particles while having a relatively low head loss, can be regarded as an advantage of the coarse filter over the fine filter in retaining a larger volume of suspended solids. This phenomenon can be attributed to several factors: pore geometry, grain surface roughness, diffusion, gravity deposition mechanisms, and interstitial hydraulic gradients.

Another work demonstrated the superiority of contact filtration of effluents to filtration without using coagulants [16]. Effluent TSS, Turbidity, and BOD before filtration ranged during the experiments from 16 to 60 mg/L, 6 to 28 mg/L, and 5 to 23 mg/L (approx.) respectively. The latter did not serve as a filtration parameter. Effluent pH was in the range of 7.3–8.5. The filter bed headloss gradient, representing bed resistance, was measured without coagulant addition for 1.1 mm and 1.5 mm grain size at a 15 m/h filtration rate of 1 cm/cm and 0.65 cm/cm respectively. In the first process, applications of alum or cationic polymer alone or both combined were compared using filtration models. Particle size, particle density, and deposit attachment strength were used as parameters. As expected, secondary effluent filtration without coagulant addition was relatively ineffective. Results show that an effective alum dose for contact filtration ranges between 10–20 mg/L. The 10 mg/L is superior, while the latter creates a bulky deposit. Application of low anionic, high molecular weight polymer in small doses ranging from 0.05 to 0.1 mg/L strengthens the alum-particle bond. The authors [16] further describe their findings by giving wide attention to the strength polymers are contributing to filter deposits vs. relative weakness of alum deposits, the latter is susceptible to hydraulic shear forces exerted in high filtration velocity or increase during the filtration run, when the deposit is accumulating while flowrate is being kept constant. That is because a high molecular weight cationic polymer has a higher attachment strength than that of the alum, possibly due to its hydrogen bonding and bridging effect, resulting in a smaller detachment with increased velocity or increased filtration run length. The pressure gradient increase and the filtration efficiency for wastewater are proportional to the polymer dose in the (1–7 mg/L) range. Compared to high molecular weight polymers, the pressure build-up with medium-molecular weight polyelectrolytes is milder. High cationic, low molecular weight polymers are not effective at doses up to 7 mg/L. The pressure build-up is slow following measured ripening. In high particle loadings, the differences among the various treatments are less pronounced. Given controlling filter performance, the physicochemical treatment seems to be a more influential and more flexible operational parameter than grain size, of which influence seems to be more pronounced at low filtration rates (5–10 m/h).

Conventional tertiary treatment consists of chemical coagulation followed by flocculation, sedimentation, filtration, and disinfection. In the case of in-line, i.e., contact filtration, equipment, and chemical costs are minimized. As a rule of thumb, in the case where influent particle sizes larger than 1 µm dominate the PSD, the application of a suitable cationic polyelectrolyte at a minimum dosage can assist in optimizing the process. At low suspended loadings of solids or in cases where submicron particles dominate, the application of alum in combination with a polyelectrolyte as a flocculant aid can result in effective, low-cost filtration.

2.3. Slow Sand Filtration

Slow sand filtration (SSF), or more general slow granular filtration (SGF), is largely designed for drinking water supply for suspended solids and microorganisms removal, by flow through fine granular media at a velocity of 0.1–0.2 m/h. The difference in water content between surface water and secondary effluents does not allow direct application of the SSF process, which is known for centuries for purifying surface water, to the tertiary treatment of secondary effluent. A long-term study has examined the possibility of slow granular filtration as an advanced treatment of secondary effluents for reuse purposes as well as filter performance under various design regimes [17]. Slow granular filtration runs were performed using four different filter columns for studying various parameters. The total height and diameter of each filter were 2.50 m and 2.00 m respectively and the bed depth was 0.7 m. The influent (secondary effluent) was aerated in the water column above the bed, and the filtration rate was 0.15 m/h. 0.6 mm and 0.25 mm sand, or tuff grains were compared as sole beds or in a dual-filter format.

The major results of those experiments can be summarized as follows: Filtration cycle could last as much as 60 days before surface cleaning; for well-treated activated sludge effluent, COD and BOD were reduced by 50% and 80%, respectively; while trying to better filter performance and reduce upper layer clogging rate by controlling the biological activity in the filter column, neither wetting/drying regime nor upper column darkening was found effective; microspheres sorption was mostly irreversible, a large fraction remained attached to the solid matrices; and, Hamra (red loam) soil retained microspheres to a larger extent than sand did. The addition of 20 cm of tuff (tufa) on top of the sand bed did not improve effluent quality, yet exhibited a big economical advantage by extending the run by 60% as compared with sand only (

Table 2. Comparison of filtration runs for different filter media: filter a—20 cm tuff above 50 cm sand; filter b—sand only. Reprinted with permission from [18]. IWA Publishing 2003.

	Filter A Tuff-Sand	Filter B Sand
Filtration run, days	80	51
Turbidity removal, %	61.6	51
TSS removal, %	40.6	59
COD removal, %	32.4	46
TSSeff (average), mg/L	8	6.3
Turbidityeff (average), NTU	1.1	1.2
Water filtered, m3/m2	91.6	58.2

).

It can be learned from this work, among others, that small communities, where land is commonly abundant, can use secondary effluents treated by SGF directly and effectively as an alternative to SAT (soil-aquifer treatment). As to filter media design, the smaller the grain size (e.g., 0.25 mm) the filtrate quality is better, but the filtration run gets shorter, and vise-versa—the larger the grain size (e.g., 0.6 mm), the filtrate quality is lower, yet the filtration run gets longer. In such a case, extending the filter bed length could improve filtrate quality while keeping the run long. The filtration cycle can also be optimized by introducing a tuff layer on top of the sand media, the longer run created can be attributed to the different morphology and chemical properties of the tuff. Another noticeable outcome of this research is, that the water column above the bed plays an important role in the filtration process by enhancing microbiological activity which controls the TSS and COD concentrations as well as the availability of biodegradable matter to bacteria. Regarding the role of the dissolved oxygen concentration in the water column above and along the bed, it can be a good indicator for the ripening of the biological layer, so-called “Schmutz Decke”, developing on the top part of the filter bed.

3. Pilot Plant Design and Decision-Making Approach

The application of mathematical models simulating the filtration process to filter design depends on pilot work aimed at producing filtration parameters and/or equation constants values. To be successful, pilot work planning, construction, and operation must rely on proficient comprehension of filtration theory and hydraulic constraints, as described in detail by Adin et al. [19]. Of course, materials and monitoring can and should be upgraded according to up-to-date technology, available budget, and local conditions. Generation of filter design parameters comprises two steps: (a) pilot plant study, usually ending with more than one combination of filter media and filter operation variables that could give similar filtration efficiency, meaning several alternatives; and (b) economic comparison of those options, since the real question then is which one is also the most cost-effective.

Bearing that in mind, a model for obtaining the design and operation parameters of granular filters at the lowest cost is proposed. It is composed of two successive stages: process optimization and economic optimization [20]. In the first stage, the filtration system is divided into three subsystems, which are: filter bed, chemical pretreatment, and backwashing. The optimization of each subsystem is carried out while the parameters of the other subsystems remain unchanged. Practically, the filtration rate is often considered to be an independent variable. Parameters of filter media capable of producing the filtrate goal are provided by the process optimization model from data obtained by the pilot plant study.

Adin et al. [19] strongly advise that, to maximize particle retention in the filter, chemical pretreatment is inevitable, must include polyelectrolytes, and should be designed to provide effective particle-coagulant/flocculant-media interactions. The coagulation step has to provide uniform particle-coagulant interactions, which highly depend on the design of the mixing scheme, power dissipation, and duration. It is noted that not all particles found in water will interact with the same polymer under the same water ionic content and pH conditions. Some waters will probably contain colloids of different surface characteristics, whose removal will require separate treatment from that accorded to the bulk of the particles present. As to floc-filter grain interaction, it would appear that floc formation is not very helpful unless it emanates from physical or physicochemical contact with the filter grains. Once an effective pretreatment is reached, the next step of optimum filter configurations development can take place by studying media grain size, depth, and filtration rate relationships. Coarse, deep, single-medium filters simplify filter design and backwash requirements.

The parameters obtained provide the basic data for cost estimates further employed for economical optimization. At this stage, Equation (1) is proposed for the overall annualized capital cost of the filtration plant:

TACC = M₁A^x₁ + M₂(AL)^x₂ + M₃(AV_B)^x₃

(1)

in which the first right term relates the cost of the filter house to the filter area; the second term links media cost to media volume and, the third one links backwashing facility costs to the flow rate of backwash [20]. Values of the M constants and x exponents are determined by regression analysis of cost data given by existing filtration plants. Costs affecting operation and maintenance, i.e., energy, wash water, and wasted chemicals costs, are computed using separate equations.

Granular/sand/deep-bed/dual-media/mixed-media filtration keeps on maintaining its capabilities and economic attractiveness when compared to membrane filtration around the world; the above described paves the way for a variety of innovations, such as flexible filter bed with controlled porosity, fibber filter for pre-treatment, hybrid of electrocoagulation and wetland, and furthermore.

4. Filtration Modeling

4.1. High Rate, Deep-Bed Filtration Modeling

As previously mentioned, observations of different deep-bed filtration operations have brought us to the conclusion, that the breakthrough curves which characterize such accumulative processes can be described and predicted through the utilization of an accumulation-detachment model [13,14]. The basic scheme of its equations is consistent with many natural phenomena of material accumulation, where an accumulation rate equals an accumulation term minus a term that represents the disturbance to this accumulation. The first term is constantly affected by the second (e.g., granular adsorption, ion exchange, and sediment transport in rivers).

Consequently, the filtration process can be described macroscopically by three sets of mathematical expressions, i.e., continuity (mass balance) equation, kinetic equation, and head loss development expression [13]. The continuity equation is given by:

v(∂C/∂x)_t + (∂σ/∂t)_x = 0

(2)

where x and t are bed depth and time, C is the concentration of particulates in the water, v is the approach velocity, and σ is the specific deposit (mass of particulate per volume of media). A kinetic equation to be solved with the above expression is given by:

∂σ/∂t = K_avC(F − σ) − K_dσJ

(3)

K_a is the attachment coefficient and K_d is the detachment coefficient. F is the theoretical filter capacity (mass/volume) and J is the hydraulic gradient. Head loss across the granular media as a function of the specific deposit based on Shekhtman’s expression is:

(J₀/J) = [1 − (σ/ε₀γ)^0.5]³

(4)

J₀ is the initial hydraulic gradient, ε₀ is the clean bed porosity and γ is the solid concentration in the deposit, and is calculated [14] from

γ = F/ε₀

(5)

Furthermore, the density of the deposit ρ_d including water can be expressed as:

ρ_d = 1 + γ(1 − 1/ρ_s)

(6)

where the specific gravity of water is considered 1. ρ_s is the density of the dry matter. Size density and attachment strength of filter deposits produced by the interaction of effluents with alum, alum-polymer aids, and cationic polymers as primary flocculants and the filter media during contact filtration, can be calculated and compared using microscopic, single collector filtration models [16].

4.2. PSD Introduction into the Filtration Model

While dealing with effluent suspensions it seems to be an obvious conclusion that particle size should not be represented in the filtration models by only one representative diameter [21]. Assuming a power-law PSD function, the total number N_t of p particles of sizes i to n entrapped in the bed is expressed by

n            n
Nt = AΣX_p^−a − BΣX_p^−b
p = i        p = i

(7)

where A,a, and B,b are PSD function parameters of the filter influent and the filtrate respectively, and X represents variable particle size. N_t can be substituted, for example, into a mathematical model such as the Kozeny-based one developed by O’Melia & Ali [22], which incorporates “mean” particle diameter. Applying some mathematical manipulations yields the hydraulic gradient

h/L = 36(k/g)(μ/ρ)v(1 − ε)₂ε⁻³(S₁/6)²dc⁻²T²

(8)

where

T = [(1 + δQS₂/N_cd_c²)/(1 + R/N_cd_c³)]²

(9)

n              n
Q = AΣX_p^2−a − BΣX_p^2−b
p = I          p = i

(10)

n              n
R = AΣX_p^3−a − BΣX_p^3−b
p = i          p = i

(11)

h—head loss, L—bed depth, k—Kozeny’s constant, g—gravity constant, μ—water absolute viscosity, ρ—water density, v—filtration rate, ε—bed porosity, S₁, S₂—media grain, and deposit shape factors, respectively [23,24], dc—media grain diameter, δ—a fraction of particles serving as collectors retained by a grain, Nc—number of grains per unit bed volume. Q and R represent differences between the filter influent and the filtrate PSD.

Secondary effluent from a municipal activated sludge plant was filtered at a rate of 8 m/h through three columns containing 0.15 m pretreated, uniform, and cleaned sand media. The sand grains, as previously stated, had geometric mean sizes of 0.767 mm, 0.917 mm, and 1.3 mm. Filter influent and filtrate samples were taken 60 min after the start of each run. A sample of experimental results corresponding to the PSD function in logarithmic form is depicted in Figure 5. Correlation coefficients lie in the 0.96–0.99 range.

For implementation purposes, the PSD for the filter influent and the PSD for the filtrate may be expressed, respectively, as:

Y₁ = AX^−a

(12)

Y_n = BX^−b

(13)

The degree of correlation between the distribution function coefficients of the filter influent (A, a) and those of the filtrate (B, b) was evaluated. The best correlation was found to be linear. The linear correlation between the coefficients A and B may be expressed as follows:

B = mA + n

(14)

and the correlation between a and b as:

b = pa + q

(15)

m, n, p, q, are constants. Consequently, the filtrate PSD may be expressed as:

Y_n = (mA + n) X−(pa+q)

(16)

thus, the filtrate PSD can be predicted by determining the filter influent PSD provided that the filter media parameters are known. Furthermore, Equation (16) can be substituted in Equation (8), allowing the prediction of head loss for a granular filter under specific influent and media conditions.

4.3. Slow Sand Filtration (SSF, SGF) Modeling

Slow sand filtration modeling, unlike rapid filtration, has not been given much attention as far as mathematical modeling is concerned, for secondary wastewater effluent in particular [18].

The continuity equation applies to SSF as well as for in-depth filtration:

v(∂C/∂x)_t + (∂σ/∂t)_x = 0

where x and t are bed depth and time, C is the concentration of particulates in the water, v is the approach velocity, and σ is the specific deposit (mass of particulate per volume of media).

A common, conventional way to express filtration efficiency is by introducing the filter coefficient λ from the Iwasaki-Ives equation [25]:

−(∂C/∂x)_t = λC

(17)

λ is a function of the specific deposit and presents the joint effects of the transport and attachment mechanisms that dominate particle removal.

Retamoza et al. [26] studied iron and manganese removal from groundwater by SSF. They observed that the SSF process resembles rapid filtration to the accumulation patterns within the bed, showing that both biological and inert deposits accumulation were greater in the upper part of the filter bed and decreased with depth. Based on that, the following mathematical model is proposed:

Δσ = v[(C₀ − C_e) Δt]/Δx + vY[(S₀ − S_e) Δt]/Δx = 0

(18)

where,

Ce = C₀ exp(−λx) and S_e = S₀ exp (−Krem x)

(19)

Y is the yield coefficient and Krem is the substrate removal constant. S0 − Se refers to substrate removal.

The SSF earlier described can simulate an integrated system, consisting of 3 layers in series: the overhead water layer, the thin biological “Schmutz Decke” developing at the top part of the filter bed, and the bulk of the porous bed. As such, the granular bed itself can be regarded as two fixed bed reactors operated in series [17], where the upper, dense grain-particle-biomass interacting layer induces exponential head loss development rate as a function of time or water volume passing per surface unit area, as shown in Figure 6. Since the upper layer behaves after a short time like a strainer and practically controls the filter head, Boucher’s law [27] may be adopted for the head loss formulation:

H = H₀e^IV

(20)

hence

H/H₀ = e^Ivt

(21)

where H and H₀ are head loss and initial head loss, V is volume passing through the filter per unit area, v is filtration velocity/rate, t is time passing from the beginning of the run and I is a filtration index, its value may be calculated from experimental data for characterizing and comparing various filtration conditions. Equation (21) may be better used for that purpose since it enables a normalized comparison. The flow regime of SSF is laminar, thus Darcy’s law or Kozeny-Carman equation may apply for calculating H_o and the small contribution of the deeper bed. Equations (20) and (21) can be linearized by using them in logarithmic form. The faster the microbial growth, the faster the clogging rate is, resulting in a steeper head loss curve expressed by greater I.

5. Hybrid Processes for Enhanced Particle Removal and Fouling Prevention

5.1. Membrane Filtration Coupled with Flocculation Pretreatment

To produce disinfected clear water out of wastewater effluents suitable for different kinds of applications, membrane filtration would be adequate. The main limitation is the fouling of the membrane. To reduce fouling, the characteristics of particles approaching the membrane have to be manipulated, so that they would be transported away from its surface by the hydraulic shear force. Appropriate addition of flocculant in a pre-treatment stage would aggregate particles and form large, light yet strong flocs that can be transported by lateral migration and improve flux. That concept was tested by Soffer et al. [28] in treating primary effluent. Ferric chloride was applied as pretreatment then filtration of the flocculated suspension by membranes ranging from UF (50 KDa) to NF took place in various configurations. That resulted in an improvement in the filtration flux. High molecular weight cut-off (MWCO) membranes fouled faster. pH 5.5 (charge neutralization zone) provided better removal and lower fouling intensity than pH 7.8 (sweep coagulation zone) (Figure 7). Ultrafiltration of 4 KDa at acidic pH of 5.5 and 150 mg/L ferric chloride could reduce DOC by 70% and UV-254 nm by 60%. The quality of the filtrate was better than that obtained with nanofiltration at basic pH7.8 with the same flocculant dose and the fouling was lower with a 4 KDa membrane. The fouling mechanism here seems to be internal pore clogging, while cake formation becomes more notable with time. Thus, to produce very clear water for possible reuse in industrial areas, coupling flocculation with a UF membrane might be the best compromise [28]. Such a hybrid flocculation-membrane process would be optimized in two successive steps: (a) obtaining the best flocculation conditions, usually by experimental work aiming at finding the correct dosage-pH-shear gradient G for best suspended solids and organic matter removal, and (b) applying the previous resulting flocculation conditions for optimizing membrane filter performance.

Another issue concerning membrane filtration that operators are looking for is the detection of fouling emerging points as early as possible. Measuring flux decrease is not sensitive enough. It was found that flux reduction was usually accompanied by a positive change in zeta potential and iso-electric point of the membrane. In membrane filtration of iron colloid suspension, an initially large change in zeta potential (without charge reversal) was observed even after relatively small amounts of iron particles were filtered through the membrane [29,30]. A control experiment demonstrated that this should probably be attributed to fouling and not to iron adsorption equilibrium. That leads to the conclusion that change in zeta potential can be used as an indicator for the onset of fouling even for small flux reductions.

Table 3. Comparison of threshold flux (L/m²∙h) with critical flux for iron colloid, at pH 7 and 100 mg/L as ferric chloride hexahydrate. Data from [29].

Stirring Speed (rpm)	Critical Flux	Threshold Flux (Based on Deposit)	Threshold Flux (Based on ZP)
40	40 < Jcr < 60	Jcr < 20	~0
160	60 < Jcr < 120	Jcr < 20	10 < Jcr < 20
400 (both 100 and10 mg/L)	120 < Jcr < 240	Jcr < 20 *	40
640	ND	60 < Jcr < 120	40

ND—not detected. * Jcr~240 L/m²-h for 10 ppm suspension.

demonstrates that UF membrane critical flux after iron suspension filtration can be evaluated more accurately by zeta potential than by pressure drop or change in iron concentration.

5.2. Electrocoagulation/Electroflocculation (EC, CF or ECF)

Electrocoagulation is an environmentally friendly electrochemical process, in which the water or wastewater flows through an electrical field determined by metallic electrodes, e.g., iron or aluminum. The metallic ions are inserted into the water from the anode surface and perform coagulation and flocculation [31,32], the flocs are further removed by sedimentation, flotation, and/or filtration. Oxidation-reduction processes that occur simultaneously may bring about the reduction of organics, heavy metal precipitation, and disinfection. Operation is quite simple—a knob is turned to control current intensity or voltage. Low energy is required which could be obtained from alternative sources. Potential for hydrogen energy recovery also exists there awaiting further development.

ECF- mechanisms and their applications have been thoroughly investigated by Adin and his team over the last 15 years. In summary [33], EC can effectively serve as a pretreatment process and unit operation for fouling mitigation when coupled with MF or UF in the advanced treatment of secondary effluents. Ferrous ions released from an iron electrode seem to be oxidized into ferric which hydrolyzes and flocculates both the humic substances and other particles carried in the effluent suspension. The flocs formed in the process increase the permeability of the cake structure which builds up on the membrane surface, leading to a decrease in external resistance. The effect of EC on internal fouling during membrane filtration of secondary effluents is still a matter of congestion, deserving further investigation.

Coupling nature-based processes, such as constructed wetlands (CW), with a physicochemical treatment process like EC in the treatment of activated sludge effluent, can be highly efficient. While CW removes organic matter and N compounds and provides a transport-attachment trap to turbidity, ECF effectively reduces phosphate in both soluble and particulate forms, something that most CW plants cannot do. Adin emphasizes, that “ECF may lead to energy conservation through hydrogen co-generation, low voltage application, reduced chemical transportation, hybridization with other low energy treatment processes and by membrane fouling reduction”.

A way of demonstrating the advantage of ECF pretreatment to untreated suspensions intended for membrane filtration is by conducting internal and external fouling experiments [34]. A considerable difference was reflected between the two (Figure 8). Filtration of an untreated suspension resulted in severe membrane fouling, which stemmed from the formation of a very thin, dense layer upon the membrane surface, letting only a small number of open pores deliver the flow. With EF pretreatment fouling was substantially smaller, since the solid iron-hydroxide deposits formed a thick, porous layer that protected the pores from clogging and could enable a reasonable flow transport (Figure 8b). The external fouling experiment did not show any significant difference between suspensions that had been ECF treated, and those that had not.

Computing the ratio between filtration energies of untreated and EF-treated suspensions on a similar basis is another way developed for comparing pretreated and untreated membrane filtration concerning fouling occurrence. Several steps were taken in getting there. The filtration curve of the untreated suspension was reconstructed according to fouling parameters found in the experiments using Kuberkar and Davis’s generalized model [34]. A novel computer program was used then to calculate the operating pressure at which an untreated suspension would be subjected to the same filtration time as an EFC-treated suspension. The ratio between filtration energies of untreated and EFC-treated suspensions was calculated using the following equation:

$${\mathrm{E}}_{\mathrm{ratio}}=\frac{{\mathrm{E}}_{\mathrm{without} \mathrm{EF}}}{{\mathrm{E}}_{\mathrm{with} \mathrm{EF}}}=\frac{{\Delta \mathrm{P}}^{*}\mathrm{V}}{{\Delta \mathrm{P}}_0\mathrm{V}}=\frac{{\Delta \mathrm{P}}^{*}}{{\Delta \mathrm{P}}_0}$$

(22)

where ${\mathrm{E}}_{\mathrm{with} \mathrm{EF}}$ and ${\mathrm{E}}_{\mathrm{without} \mathrm{EF}}$ are the filtration energies for EFC-treated and untreated suspensions respectively, at the same filtration times, ∆P₀ is the operational actual filtration operation pressure, and ∆P* is the calculated pressure required for the untreated suspension to have the same filtration time as the treated suspension. The energy ratio (${\mathrm{E}}_{\mathrm{ratio}}$) represents the value by which the experimental filtration energy must be multiplied so that an untreated suspension will be filtered at the same time as a suspension pretreated by EFC. The optimal pretreatment parameters can be determined by using ${\mathrm{E}}_{\mathrm{ratio}}$, e.g., pH level or mixing residence time at the flocculation unit operation (Figure 9).

The basic reactions occurring near the electrodes are expressed by Mollah et al. [35]. Hydrogen co-generation potential can be calculated accordingly [33]. The meaning of those reactions is, that of every +2 electrons one H mole is formed, and that of every Al mole (+3e) − 1.5 H moles are formed. Stoichiometric calculations would show that for each 9 g dissolution of Aluminum 1 g of Hydrogen is formed.

Hydrogen energy potential was estimated for a 100 m³/h ECF reactor serving an enhanced primary sedimentation basin at the activated sludge wastewater treatment plant of Yavne, Israel (Figure 10). 30 mg/L of iron coagulant were dosed continuously by applying iron sacrificial anodes. Hydrogen production is estimated at 3.85 kg/day. The predicted gas volume, considering 25 L/mole was 48,000 L/day. Burning in air, the hydrogen (H₂) reacts with oxygen (O₂) to form water (H₂O) (Equation (23)).

2H₂(g) + 1/2O₂(g) → 2H₂O(g)

(23)

Accordingly, the total energy released in forming H₂O (2 × O-H) would be 2 × 462.8 or 925.6 kJ/mole.

Gas formation does not occur when working in a potential range below the decomposition potential of water (1.6–1.8 V). If, after the coagulation-flocculation phase, gas formation is allowed, the separation process along the gravitational settling will be completed by electrofloatation. The separation of floating particles takes place at a much higher separation rate than that of settling. The process results in more than 90% turbidity and suspended solids removal [36].

Figure 10. Enhanced primary sedimentation by electrocoagulation at the wastewater treatment plant of Yavne, Israel.

Figure 10. Enhanced primary sedimentation by electrocoagulation at the wastewater treatment plant of Yavne, Israel.

5.3. Silver Nanoparticles Application to Biofouling Prevention

One of the widely investigated ways to control biofilm formation in a membrane filtration system for improving its performance is the impregnation of the membrane surface with antimicrobial materials. One disadvantage of such a fixed layer approach is that the antimicrobial effect can be quickly masqued by the cake that is building up on the membrane surface. Dror-Ehre et al. [37,38] have investigated a different idea to overcome such an obstacle, in which silver nanoparticles (Ag-NPs) would be introduced continuously or intermittently into the water stream approaching the membrane surface. Exposure to silver nanoparticles in bench-scale experiments resulted in retardation in the formation of biofilm by model bacteria. It also resulted in a lower flux decline in the UF membrane system thus improving its performance (Figure 11).

6. Discussion

This paper is based on the Author’s own scientific and technological experience. Wastewater effluent filtration science and technology development is depicted as a growing tree, sprouting in the 1970s, when the Author started publishing his first papers on the subject. The scientific roots of water filtration which have had a great impact on effluent filtration are, in fact, much deeper, and may be attributed first to Darcy [39], i.e., Darcy’s Law for flow in porous media and Iwasaki [40], who came up with turbidity filtration kinetics exponential function (Equation (17)), both experimenting with slow sand filters. Effluent filtration scientific work regarding water reclamation and reuse started to pick up in the mid-1920s when overcoming water scarcity and environmental pollution started becoming a necessity.

Water filtration theory has been primarily based on, and widely developed from, Iwasaki-Ives Equation (17) and derivatives [30] with its filtration coefficient λ mentioned earlier. However, filtration models that stem from that theory disregard the fact that detachment forces are also active within the filter bed, becoming more and more influential as the bed becomes clogged and hydraulic shear forces intensify. The latter can bring about an early breakthrough of effluent unless coagulants and flocculants—iron or alum plus polymer—are added at the correct pH. That is also important in preventing internal or external clogging of membranes (Figure 8). In such a case, the flocs formed in the pretreatment step must have a specific gravity close to the water while maintaining a strong structure, so shear forces along the membrane would easily transport them away and would not shear them apart. The same applies to bioflocs aggregated in submerged MBR systems. As presented earlier, zeta potential (ZP) could serve as an alarming indicator of membrane fouling development as well as coagulant type and dosage for certain pH values.

Nanotechnology-based consumer products inevitably enter the aquatic environment, wastewater being their major carrier. An OECD report [41] shows that engineered nanoparticles (NPs) are present in the leachates from landfills and are released to surface water. NPs are viewed as emerging pollutants. They can be toxic and may cause cancer, neurodegenerative diseases, and other types of diseases. The findings suggest, among others, that NP eco-environmental risks demonstrate a strong need to develop effective water treatment processes for their removal. On the other hand, silver nanoparticles (Ag-NPs) could be useful since they are detrimental to bacteria such as those which adhere to membrane surfaces or pipes’ inner surfaces and form biofilms. Several research groups have been investigating membrane surface impregnation with anti-microbial Ag-NPs included, to kill bacteria that are carried onto those surfaces. In that case, particularly for dead-end systems, it could be estimated that, after some time, the membrane surface would be covered by deposits, which would make the NPs ineffective. Rather, the introduction of small concentrations continuously or intermittently into the flow before reaching the membrane, could not only inactivate bacteria adhering to the membrane but inactivate some of it in the approaching stream, as presented earlier. In any case, more research is necessary as to how to prevent different NPs from being used as treatment aids from reaching the environment.

One thing that the young researcher can take from this paper is that particle characteristics and their manipulation is the common denominator of all types of filtration processes. It is also believed that such a time-lined presentation of filtration research by an individual researcher and co-workers could assist young professionals to better understand filtration and improve filtration research, development, and design.

7. Conclusions

While concentrating on effluent filtration, this work integrates a variety of filtration research findings, each one being a novelty at its time, into a unique scientific road map. In-depth learning of filtration scientific and technological development from roots to top, can be a mind opener and provide excellent tools for researchers and practitioners in advancing their work in water filtration in general, and wastewater filtration—where water quality is predominantly more complex—in particular. Particle characteristics are the common denominator of all types of filtration processes. Pilot plant planning would be primarily based upon understanding particle interactions with filter media, and measurements of mineral particles or bioparticle size distribution, shape, and physicochemical characteristics. Attachment-detachment models should be applied in cases where particle detachment is observed, such as in high-rate, deep-bed filters, and strainers where it might negatively affect filter performance and downstream irrigation systems. In membrane filter the pre-generation of large, yet light particles reduce membrane fouling. Such processes to be efficient need colloid stabilization, obtained by coagulation or coagulation-flocculation pretreatment. Coupling electrocoagulation-flocculation with the membrane is highly productive for that purpose, easy to control, and energy efficient. Coagulant addition is, however, unnecessary in slow sand filters treating effluents, where bio-physical reactions on the top of small sand media surface prevail, and particle detachment can hardly occur. The addition of a somewhat coarser media layer on top may result in improved performance. Injecting silver nano-particles into the flow before reaching the membrane could continuously inactivate bacteria in the effluent approaching or settling on the membrane surface or cake. Design optimization for different filters would comprise of two main steps: (a) comparing alternative filtration processes that would produce similar target water quality results, followed by (b) economic optimization for the final selection of the alternative and design parameters.

8. Future Directions

Predictions of population growth, climate change, and availability make wastewater a major present and future water resource, along with seawater, brackish groundwater, and stormwater, thus revolutionizing the natural hydrological water cycle, making it a more holistic and sustainable one. Water quantity would be primarily dominated by water quality and more energy dependent. Wastewater filtration science and technology would play a major role in the holistic water cycle by being integrated into it. As earlier mentioned, regulations and standards relating to wastewater reuse have been issued by many countries, Israel and the EC are among them. Shoushtarian and Negahban-Azar [42] have published an excellent reference for the global situation concern, containing detailed information about the water quality parameters’ MCLs. In the future, more specific standards concerning filtration and the control of emerging bioparticles and nanoparticles would be continuously upgraded, strongly pushed by rapidly advancing scientific knowledge. The holistic approach in the design of filtration facilities, standing alone or incorporated into hybrid systems, would imply more challenges upstream due to water carrying emerging materials and microbial contaminants and, more challenges downstream as well, due to the increasing need for water reuse, potable uses included. Therefore, effluent filtration applied research would have to consider increasing hybridization with complementing pre- and post-processes, such as electrocoagulation and other advanced oxidation processes (AOP). The development of filtering biomaterials has taken some steps forwards during the last decade [43,44,45,46]. Most of the investigations of biomaterials have focused recently on their application as adsorbents of heavy metals and dissolves organics from contaminated drinking water sources, e.g., fruit peals, Graphene, or charcoal, rather than on particle filtration in wastewater effluents treatment. Yet, some of them are going in the effluent filtration direction, e.g., coagulation or membrane. One should consider, though, that large populations in the world lack operation and maintenance capacity nor have financial resources or energy for applying state-of-the-art unit processes like MBR or industrial catalysis. More appropriate filtration technologies would be further developed there, like slow or rapid filters based on local granular media or different local natural materials like different types of woods, coupled with renewable energy sources, such as solar, wind, and water.