An Integrated Approach to the Biological Reactor–Sedimentation Tank System

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Article An Integrated Approach to the Biological Reactor–Sedimentation Tank System

Serena Conserva 1, Fabio Tatti 1, Vincenzo Torretta 2 , Navarro Ferronato 2,* and Paolo Viotti 1

1 Department of Civil, Building and Environmental Engineering (DICEA), Sapienza University of Rome, Via Eudossiana 18, 00184 Rome, Italy; [email protected] (S.C.); [email protected] (F.T.); [email protected] (P.V.) 2 Department of Theoretical and Applied Sciences (DISTA), University of Insubria, Varese, Via G.B. Vico 46, 21100 Varese, Italy; [email protected] * Correspondence: [email protected]

Received: 20 April 2019; Accepted: 9 May 2019; Published: 14 May 2019

Abstract: Secondary clarifiers are demanded to separate solids created in activated sludge biological processes to achieve both a clarified effluent and to manage the biological processes itself. Indeed, the biological process may influence the sludge characteristics, and conversely, the settling efficiency of the sedimentation basin plays an important role on the biological process in the activated sludge system. The proposed model represents a tool for better addressing the design and management of activated sludge system in wastewater treatment plants. The aim is to develop a numerical model which takes into account both the conditions in the biological reactor and the sludge characteristics coupled to the hydrodynamic behavior of a clarifier tank. The obtained results show that the different conditions in the reactor exert a great influence on the sedimentation efficiency.

Keywords: activate sludge; numerical model; secondary clariﬁer; treatment eﬃciency

1. Introduction Sedimentation basins are used in wastewater treatment plants to separate suspended solids from water. Secondary clarifiers are used to remove settleable solids created in biological processes such as the activate sludge process being an active part of the process itself. Settling basins are mainly designed using simple rules based on detention time, overflow rate, and solid loadings, which ensure that flow velocities in the basins are sufficiently low to allow solid particles to settle and to be removed, and yet sufficiently high so that the basin volumes are not excessively large. Compliance with the effluent requirements depends greatly on the efficiency of the secondary clarifiers. The tank performance is strongly influenced by hydrodynamic processes together with physical effects, such as density-driven flow, gravity sedimentation, flocculation, and thickening. Development and application of numerical models to calculate the velocity pattern in sedimentation tanks assumes a remarkable importance because it is proven that the actual characteristics of flow differ strongly from the supposed uniform distribution, and they have a relevant influence on the settling efficiency. Since the 1970s, simulations of the flow field in rectangular sedimentation tanks have been carried out [1–6]. Research activities have been focused on the behavior of sedimentation and flotation of activated sludge in turbulent flows, mainly with numerical models able to simulate detailed geometries and boundary conditions, on the structure of inlet and removal process. The numerical models relative to sedimentation tanks operating in conditions of uniform density can be distinguished mainly for the adopted model of turbulence; for the choice of the boundary conditions; for the discretization method;

Resources 2019, 8, 94; doi:10.3390/resources8020094 www.mdpi.com/journal/resources Resources 2019, 8, 94 2 of 19 and for the procedure used in the numerical resolution. The precursor in flow fields modeling in primary sedimentation tanks was the author of [2]. In his work, the turbulent viscosity was calculated on the base of the Prandtl’s theory on the mixing length. In 1981, the author of [7] proposed a model for primary sedimentation distinguishing the velocity field from the concentration one and introduced the hypothesis that the two fields can be solved separately (not coupling hypothesis). They adopted a finite elements technique to determine the flow and calculated the eddy diffusivity coefficient (υt) through the turbulent kinetic energy “k” and its viscous dissipation “ε” (k-ε model proposed by [8]). The k-ε model is the most used turbulent model due to its robustness and reasonable accuracy for the prediction of turbulent flow in secondary sedimentation tanks [9–17]. In 1983, the authors of [18] developed a numerical model for rectangular sedimentation tanks, determining the velocity field and the suspended solids distribution. The authors used the hypothesis that the flow is a bi-phase turbulent flow. In primary sedimentation basins, where the inlet concentration is low, the simulation of liquid phase can be considered separately from the solid one, assuming that the particle presence does not influence the mechanisms of fluid flow, with the exception of turbulent mixing. Although the flow is generally three-dimensional, the bi-dimensional representation in the forecast of the velocity distribution was thought adapted, also for the computational difficulty of the 3D representation. Several authors considered models in which the influence of densiometric forces of mass on the hydrodynamic field is neglected and the equations of the motion are solved independently from the transport one [5,9,19–21]. A mathematical model to predict, by direct computation, the behavior of the bottom current and surface return flow and simultaneously determine their distributional effects on the sedimentation process was proposed by [22]. Many studies were carried out to investigate the role of the reaction baffle position on the performance of the sedimentation unit [13,23–26]. In particular, the author of [23] proposed a numerical model for estimating the velocity field and suspended solids distribution in a secondary circular clarifier with density differences. The model predicted an important phenomenon known as the density waterfall that occurs for large radius baffles. A comparison of the solid’s concentration distribution for a tank with a small skirt radius shows that this one reduces the density waterfall effect and significantly improves the clarifier performances. Other authors assumed that particles settle as in a monodisperse suspension, with a velocity dependent on the concentration even in zones where the sludge is diluted [23,27–29], simulated a tertiary sedimentation tank with a relatively low inlet concentration by considering several classes of particles, each characterized by a constant settling velocity. Although their transport model simulates the effects of densiometric forces on the flow field, the discrete settling model cannot account for hindered settling conditions of highly concentrated suspensions. Despite such numerous numerical studies, few papers considered the interaction between the biological reactor and the sedimentation units. This work presents a model which takes into account the complete system. The proposed model can then be easily used as a tool for the design and management of activated sludge systems in wastewater treatment plants. The velocity field and the suspended solid concentration in the vertical plan of symmetry of the circular secondary sedimentation basins are solved by means of the differential equations describing the turbulent flow and the suspended solids transport in cylindrical coordinates. Modification of solid concentration values at the inlet of the sedimentation tank are considered by means of a mass balance model on both the substrate and biomass in the oxidation tank [30]. The numerical study is supported by measuring the sludge characteristics and the velocity field in a real circular sedimentation tank at an existing wastewater treatment plant in Rome. Attention has been given to the system resulting from the combination of the aerated reactor and the secondary clarifier to determine the influence of any variation in the biological sludge characteristics on the removal efficiency of the sedimentation unit by taking into account the actual velocity field established in the clarifier. Therefore, the numerical model calculates and modifies the flow field and the concentration Resources 2019, 8, x FOR PEER REVIEW 3 of 20 Resources 2019, 8, 94 3 of 19 characteristics (i.e., varying the settling velocity or the boundary conditions) and the processes that take place inside of the activated sludge reactor. In this way, it is possible to consider the reactor– distribution in the sedimentation tank according to the sludge settling characteristics (i.e., varying the clarifier like an integrated system in which the operating efficiencies of the two units are mutually settling velocity or the boundary conditions) and the processes that take place inside of the activated influenced and can also be used to define the best management actions. The efficiency of an activated sludge reactor. In this way, it is possible to consider the reactor–clarifier like an integrated system in sludge reactor depends on several aspects which have to be taken into account during the which the operating efficiencies of the two units are mutually influenced and can also be used to define management phases to optimize the treatment results. the best management actions. The efficiency of an activated sludge reactor depends on several aspects which2. The have“Biological to be taken Reactor–Clarifier” into account during System the as management a Whole phases to optimize the treatment results. 2. TheIn “Biologicala biological Reactor–Clarifier”wastewater treatment System system, as a effic Wholeient performance of the secondary clarifier is essential because the system depends on the concentration of activated sludge available in the In a biological wastewater treatment system, efficient performance of the secondary clarifier biological reactor. The purpose of the activated sludge recycled from the clarifier is then fundamental, is essential because the system depends on the concentration of activated sludge available in the as known, to maintain enough concentration of sludge in the reactor for reaching the required degree biological reactor. The purpose of the activated sludge recycled from the clarifier is then fundamental, of treatment in an engineering valid time. Therefore, sludge recycled from the final clarifier to the as known, to maintain enough concentration of sludge in the reactor for reaching the required degree inlet of the aeration tank is the essential feature of the process. of treatment in an engineering valid time. Therefore, sludge recycled from the final clarifier to the inlet The performance of sedimentation units is strongly affected by several factors, such as the inlet of the aeration tank is the essential feature of the process. concentration (X), the settling characteristics of the sludge, and last, but not least, the hydrodynamic The performance of sedimentation units is strongly affected by several factors, such as the inlet field, which in turn depends on the sludge extraction, the geometrical characteristics of the basin, and concentration (X), the settling characteristics of the sludge, and last, but not least, the hydrodynamic the inflow. The scheme adopted in the model is reported in Figure 1. field, which in turn depends on the sludge extraction, the geometrical characteristics of the basin, and the inflow. The scheme adopted in the model is reported in Figure1.

Figure 1. Schematic of complete–mix reactor with cellular recycle and wasting from the recycle line.

AFigure mass 1. balance Schematic is used of complete–mix to evaluate bothreactor the with biomass cellular growth recycle and and the wasting other managementfrom the recycle parameters. line.

ARate mass of accumulationbalance is used toRate evaluate of ﬂow both of theRate biomass of ﬂow growth of and Netthe growthother management of parameters.of microorganism microorganism microorganism out microorganism = + Rate ofwithin accumulation the system Rateinto of flow the systemof − Rateof the of system flow of within Net the growth system of of microorganismboundary = microorganismboundary - microorganismboundary out +boundary microorganism withinMass the balancesystem for the microorganisms: into the system of the system within the system boundary boundary boundary boundary dX Mass balance for the microorganisms:V = QX [( Q Q )Xe+Q X ]+r0gV. (1) dt 0 − − w w R dX V =QX -Q-Q X +Q X +rʹ V. (1) Mass balance for the substrate:dt 0 w e w R g Mass balance for the substrate:dS V = QS0 [(Q Qw)S + QwS]+rSuV, (2) dtdS − − V =QS0-Q-Q S+Q S+rSuV, (2) ’ dt w w in which r g is the net growth of cells, S the substrate concentration, S0 the substrate concentration in ’ ininlet which wastewater, r g is the Vnet the growth volume of ofcells, the S biological the substrate reactor, concentration, and rSu the substrateS0 the substrate utilization concentration rate. in inlet wastewater, V the volume of the biological reactor, and rSu the substrate utilization rate.

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The following input data are required:

Geometrical characteristics of the basins (biological reactor and clariﬁer); •

Hydraulic loads: Inlet wastewater flowrate (Q), recirculated sludge flowrate (QR), and waste sludge flowrate (Qw);

Organic loads: Inlet chemical oxygen demand (COD) and biomass concentration in reactor. • The model allows simulating two different conditions: Standard condition: The effective operating condition of the plant. It is possible to simulate the process efficiency (COD removal in the biological reactor, total suspend solids (TSS) concentration in the effluent from the clarifier) and the biomass concentration in the aerated reactor when hydraulic and organic loads are known. Critical condition: The model allows to evaluate the optimal values of QR and Qw to obtain a preset effluent substrate concentration. This option is useful when important variations of hydraulic and/or organic loads are expected to occur. In Figure2, a simplified scheme of the proposed model is shown. It is important to remark that it is possible:

To modify the settling characteristics of the sludge by varying the coefficients in the settling • velocity equation; To set input parameters (fitting of Q and Q ) depending on the value of sludge concentration • R W extracted from the clarified bottom (XR). Resources 2019, 8, x FOR PEER REVIEW 5 of 20

Figure 2. Flowchart of numerical model. The presented model allows, therefore, evaluating the operating conditions in the biological The presented model allows, therefore, evaluating the operating conditions in the biological reactor (the actual concentration of the biomass X and the waste amount) starting from deﬁned reactor (the actual concentration of the biomass X and the waste amount) starting from defined conditions in the sedimentation tank (XR, QR). On the other hand, such conditions are dependent on the biomass concentration X at different times and on the waste sludge flowrate Qw. In this way, the biological reactor and the clarifier are mutually affected and behave like a single unit. The velocity field and the sludge concentration distribution are simulated by means of the numerical integration of the Navier–Stokes equations in an axial symmetrical form. The sludge concentration distribution is solved by means of the mass balance equation to take into account the real phenomena of turbulence, transport, and diffusion. The model allows calculating: • The velocity field in the sedimentation tank; • The distribution of suspended solids (SS) concentration in the sedimentation tank; • The SS concentration trend at the bottom of the clarifier; • The SS concentration trend in the outlet section; • The SS concentration trend in the biological reactor.

3. Simulation of Sedimentation Process In the present study, the phenomena linked to thermal and concentration gradients were neglected and a not coupled procedure to reduce computational burden was adopted. In fact, the attention was principally focused on the management aspect (biological reactor–sedimentation tank system). Several hypotheses are generally encountered in the literature [31] to allow for an easier numerical solution. One consists of the so called “rigid lid” approximation [10,23,24,28], which can be used thanks to the low values of the velocity.

3.1. Governing Equations

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conditions in the sedimentation tank (XR,QR). On the other hand, such conditions are dependent on the biomass concentration X at different times and on the waste sludge flowrate Qw. In this way, the biological reactor and the clarifier are mutually affected and behave like a single unit. The velocity field and the sludge concentration distribution are simulated by means of the numerical integration of the Navier–Stokes equations in an axial symmetrical form. The sludge concentration distribution is solved by means of the mass balance equation to take into account the real phenomena of turbulence, transport, and diffusion. The model allows calculating:

The velocity ﬁeld in the sedimentation tank; • The distribution of suspended solids (SS) concentration in the sedimentation tank; • The SS concentration trend at the bottom of the clariﬁer; • The SS concentration trend in the outlet section; • The SS concentration trend in the biological reactor. • 3. Simulation of Sedimentation Process In the present study, the phenomena linked to thermal and concentration gradients were neglected and a not coupled procedure to reduce computational burden was adopted. In fact, the attention was principally focused on the management aspect (biological reactor–sedimentation tank system). Several hypotheses are generally encountered in the literature [31] to allow for an easier numerical solution. One consists of the so called “rigid lid” approximation [10,23,24,28], which can be used thanks to the low values of the velocity.

3.1. Governing Equations The equations describing axisymmetric, two-dimensional, unsteady, turbulent flow for cylindrical coordinates in a circular settling clarifier are: The r-momentum equation: ! !! ∂u ∂u ∂u 1 ∂p 1 ∂ ∂u 1 ∂ ∂u +u +v = + rυt + rυt , (3) ∂t ∂r ∂y −ρ ∂r r ∂r ∂r r ∂y ∂y the y-momentum equation: ! !! ∂v ∂v ∂v 1 ∂p 1 ∂ ∂v 1 ∂ ∂v +u +v = + rυt + rυt , (4) ∂t ∂r ∂y −ρ ∂y r ∂r ∂r r ∂y ∂y and the continuity equation: ∂ru ∂rv + = 0. (5) ∂r ∂y Symbols u and v represent mean velocity components in the r- and y-direction, respectively, p is the pressure, ρ the fluid density, and υt the eddy viscosity (which is considered constant and uniform inside the computational domain). For a two-dimensional, unsteady flow, the convection–diffusion equation can be written as follows:

! 2 ! ∂C ∂(uC) ∂((v vs)C) 1 ∂ ∂C ∂ C + + − = rDr +Dy , (6) ∂t ∂r ∂y r ∂r ∂r ∂y2 where C is the suspended solids concentration, vs is the settling velocity of suspended solids, Dr and Dy are the turbulent diﬀusion in the r-direction and y-direction, respectively. By using the Reynolds Resources 2019, 8, x FOR PEER REVIEW 6 of 20

The equations describing axisymmetric, two-dimensional, unsteady, turbulent flow for cylindrical coordinates in a circular settling clarifier are: The r-momentum equation:

∂u ∂u ∂u 1 ∂p 1 ∂ ∂u 1 ∂ ∂u +u +v =- + rυ + rυ , (3) ∂t ∂r ∂y  ∂r r ∂r t ∂r r ∂y t ∂y

the y-momentum equation:

∂v ∂v ∂v 1 ∂p 1 ∂ ∂v 1 ∂ ∂v +u +v =- + rυ + rυ , (4) ∂t ∂r ∂y  ∂y r ∂r t ∂r r ∂y t ∂y

and the continuity equation: ∂ru ∂rv + =0. (5) ∂r ∂y Symbols u and v represent mean velocity components in the r- and y-direction, respectively, p is the pressure, ρ the fluid density, and υt the eddy viscosity (which is considered constant and uniform inside the computational domain). For a two-dimensional, unsteady flow, the convection–diffusion equation can be written as follows:

∂C ∂uC ∂v-v C 1 ∂ ∂C ∂2C + + s = rD +D , (6) ∂t ∂r ∂y r ∂r r ∂r y ∂y2 where C is the suspended solids concentration, v is the settling velocity of suspended solids, Dr and Resources 2019 8 Dy are the turbulent, , 94 diffusion in the r-direction and y-direction, respectively. By using the Reynolds6 of 19 analogy between mass transport and momentum transport, the dispersion coefficient is related to υt by:analogy between mass transport and momentum transport, the dispersion coeﬃcient is related to

υt by: υ υ = υt t = υtt DDr r= ; ;DDy y= , ,(7) (7) σσsrsr σsysy σ σ inin which which σsrsr andand σsysy areare the the Schmidt Schmidt numbers numbers (assumed (assumed equal equal 1.0) 1.0) [28]. [28].

3.2.3.2. Computational Computational Domain Domain TheThe examined examined secondary secondary clarifier clarifier is is composed composed of of a a circular circular basin, basin, with with a a central central feeding feeding system, system, havinghaving a a total total diameter diameter of of 52 52 m. m. The The tank tank is is equipped equipped with with a a baffle baffle located located in in proximity proximity of of the the inlet inlet section.section. The The effluent effluent outlet outlet is is realized realized throug throughh two two weirs, weirs, one one intermediate intermediate and one peripheral. TheThe detailed detailed characteristics characteristics of of th thee basin basin are are shown shown in Figure 33..

Figure 3. Vertical section of the circular clarifier. Figure 3. Vertical section of the circular clarifier. After setting the system geometry within the integration domain, a square mesh grid was overlapped to it. The mesh dimensions are ∆r = ∆y = 0.2 m. A dimensionless calculation domain was then obtained by dividing all the considered spatial variables by a reference length l0 = 4m corresponding to the water head in the basin. Similarly, all other relevant variables (i.e., the coefficient of eddy viscosity υt and the velocities of the fluid (u,v) also referred to l0, the inlet water velocity u0, or T0 = l0/u0 so as to obtain unit-less values.

3.3. Boundary Conditions Solution of the partial equation set governing the phenomenon is only possible if a consistent series of boundary conditions are specified. Inlet section. The profile is assigned starting from the fluid velocity at the inlet of the sedimentation basin. The assumed hypothesis is that such velocity has only the horizontal component uinlet. The examined clarifier is in fact fed from the center with a capacity of approximately 1500 m3/h. The recirculate flowrate has to be added to this value. The profile of the suspended solids concentration is based on the relation: ! ∂C ∂C (vC)m = (vC)v + Dr +Dy . (8) ∂r ∂y v

In this way,it is possible to transform a flow which is mainly convective into a convective–dispersive flow with energy losses and strong dispersion effects. The inlet boundary condition for the concentration value is the Dirichlet condition. The assigned values are the fed substrate concentration and the reactor value of biomass concentration. Free-surface boundary. The rigid lid approximation was used. The vertical component of velocity is then considered null. Resources 2019, 8, 94 7 of 19

As for the upper boundary condition, a null mass ﬂux through the free surface of the water was imposed. This condition is mathematically represented as:

C(m, i) = 0. (9)

Verticalwalls. The model allows opened or closed contours. In the latter case, the adopted conditions are of impenetrability and “slip condition” for the flow and no mass flux for the solid’s concentration. Bottom of basin. It has been possible to define a series of boundary conditions able to ensure both fluid and solid mass conservation in the transport equation using considerations derived from mono-dimensional case studies. A single sedimentation column experiment allows fitting the correct boundary conditions. In the mono-dimensional case (vertical direction) the equation takes the form:

∂C ∂C ∂2C +(v v ) = Dy . (10) ∂t − s ∂y ∂y2

It is possible to neglect diffusion phenomena since no real hydrodynamic field is present; Resources 2019, 8, x FOR PEER REVIEW 8 of 20 the transport equation then becomes: ∂C ∂C t+1 Δt t = vs t ,t (11) C = ∂t -∂y +C . (13) mm-1 Δy mm-2 mm-1 mm-1 introducing the flow φ = vsC: A sludge flowrate is extracted from the bottom∂C ∂ofφ the sedimentation tank to be recirculated or = . (12) wasted. It is assumed, therefore, that the extracted∂t flow∂y is: t In this way the concentration variationt witht time is assumed to be dependent only on the(14) flow mm-1=veCmm-1, differences along the vertical. WhereSuch ve is abased model on was theapplied extracted to flowrate a sedimentation (QR + QW column) and on test the performed geometrical on characteristics a real sludge, andof the the settler.results in terms of comparison between the position in time of the experimental interface height and the simulated one are shown in Figure4.

Figure 4. Interface height vs. time: Comparison between experimental data and model simulations. Figure 4. Interface height vs. time: Comparison between experimental data and model simulations. The concentration at the bottom (in the node mm-1) is given by the relation: Outlet boundary. ∆t It is considered as a weir witht+ 1a hydraulic= φ tload equalφt to the+ verticalt mesh dimension ∆y. Cmm 1 mm 2 mm 1 Cmm 1. (13) − ∆y − − − − 3.4. Solution Procedure In the present work, it was chosen to solve the equations governing the physical phenomenon in terms of primitive variables (u, v, p). Integration of the system of differential equations was realized through a semi-implicit finite differences algorithm (A.D.I. method).

4. Model results

4.1. Comparison of Predicted and Experimental Velocities The vectoral field of velocities in the basin (Figure 5) was calculated assuming that the speed of the water through the weirs is oriented only in the r direction.

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A sludge ﬂowrate is extracted from the bottom of the sedimentation tank to be recirculated or wasted. It is assumed, therefore, that the extracted ﬂow is:

φt t t mm 1= veCmm 1, (14) − − where ve is based on the extracted ﬂowrate (QR + QW) and on the geometrical characteristics of the settler. Outlet boundary. It is considered as a weir with a hydraulic load equal to the vertical mesh dimension ∆y.

3.4. Solution Procedure In the present work, it was chosen to solve the equations governing the physical phenomenon in terms of primitive variables (u, v, p). Integration of the system of differential equations was realized through a semi-implicit finite differences algorithm (A.D.I. method).

4. Model Results

4.1. Comparison of Predicted and Experimental Velocities

ResourcesThe 2019 vectoral, 8, x FOR ﬁeld PEER of REVIEW velocities in the basin (Figure5) was calculated assuming that the speed9 of 20 of the water through the weirs is oriented only in the r direction.

Figure 5. Velocity field: Comparison between experimental data and model simulations. Figure 5. Velocity field: Comparison between experimental data and model simulations. Several studies aimed at measuring the hydrodynamic field in sedimentation basins have shown thatSeveral velocities studies values aimed are between at measuring some the millimeters hydrodynamic and some field centimeters in sedimentation per second basins [32 have,33]. shown In this thatstudy, velocities such measures values are were between carried some out with millimeters an Argonaut and some ADV centimet (Dopplerers 3D per velocimeter) second [32,33]. sensor In in this the study,circular such secondary measures sedimentation were carried tank out atwith the an wastewaters Argonaut ADV treatment (Doppler plant 3D of Romavelocimeter) Ostia (Italy). sensor in the circularThe position secondary of sedimentation the measurement tank pointsat the wa wasstewaters obviously treatment decided plant based of Roma on theOstia numerical (Italy). discretizationThe position adopted, of the checking measurement at every points time wa thats theobviously main characteristics decided based (inlet, on the Qw ,QnumericalR) could discretizationbe considered adopted, rather constant; checking this at every allowed time reaching that the a main time-averaged characteristics flow field,(inlet, which Qw, Q wasR) could used be to consideredcalibrate the rather numerical constant; model. this allowed reaching a time-averaged flow field, which was used to calibrateA representative the numerical test model. case is shown in Figure6, where measurements and numerical simulations of theA representative horizontal velocity test case profiles is shown are compared. in Figure The6, where agreement measurements between and experiments numerical and simulations numerical ofmodel the horizontal is quite good, velocity although profiles the are values compared. calculated The agreement by the model between in the experiments central zone and of the numerical basin are modelquite higheris quite thangood, those although observed the va atlues the calculated field. This by might the model be due in to the the central presence zone of of settled the basin sludge, are quitewhich higher can modify than those the actual observed section. at the field. This might be due to the presence of settled sludge, which can modify the actual section. 4.2. Settling Velocity of Suspended Solids 4.2. SettlingThe settling Velocity of of discrete, Suspended non-flocculating Solids particles can be analyzed by means of the classic Stokes’ sedimentationThe settling law. of discrete, Particles non-flocculating in a relatively diluted particles solution can be analyzed will not act by asmeans discrete of the particles classic Stokes’ but will sedimentationrather coalesce law. during Particles sedimentation. in a relatively As flocculation diluted solution occurs, will the not mass act of as particles discrete increases,particles but and will they rather coalesce during sedimentation. As flocculation occurs, the mass of particles increases, and they settle faster. As the ambient sediment concentration increases, the interparticle spacing is reduced, so the chance of particle collisions increases. This means that the settling velocity of the suspension will decrease when the concentration increases.

Figure 6. Profile of horizontal velocity: Comparison between experimental measures and numerical simulation.

A reasonable description of the complete settling process should be a settling rate that initially increases to a maximum, then decreases with increasing of concentration.

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Figure 5. Velocity field: Comparison between experimental data and model simulations.

Several studies aimed at measuring the hydrodynamic field in sedimentation basins have shown that velocities values are between some millimeters and some centimeters per second [32,33]. In this study, such measures were carried out with an Argonaut ADV (Doppler 3D velocimeter) sensor in the circular secondary sedimentation tank at the wastewaters treatment plant of Roma Ostia (Italy). The position of the measurement points was obviously decided based on the numerical discretization adopted, checking at every time that the main characteristics (inlet, Qw, QR) could be considered rather constant; this allowed reaching a time-averaged flow field, which was used to calibrate the numerical model. A representative test case is shown in Figure 6, where measurements and numerical simulations of the horizontal velocity profiles are compared. The agreement between experiments and numerical model is quite good, although the values calculated by the model in the central zone of the basin are quite higher than those observed at the field. This might be due to the presence of settled sludge, which can modify the actual section.

4.2. Settling Velocity of Suspended Solids The settling of discrete, non-flocculating particles can be analyzed by means of the classic Stokes’ Resourcessedimentation2019, 8, 94 law. Particles in a relatively diluted solution will not act as discrete particles but9 ofwill 19 rather coalesce during sedimentation. As flocculation occurs, the mass of particles increases, and they settle faster. As the ambient sediment concentration increases, the interparticle spacing is reduced, so settlethe chance faster. of As particle the ambient collisions sediment increases. concentration This means increases, that the settling the interparticle velocity of spacingthe suspension is reduced, will sodecrease the chance when of the particle concentration collisions increases. increases. This means that the settling velocity of the suspension will decrease when the concentration increases.

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A large number of empirical formulas were proposed to describe the relationship between solids concentration and solids settling velocity; such relations generally assume the form of an exponential curve which fits particularly well the second part of the curve: -kC vs=v0e , (15) Figure 6. Profile of horizontal velocity: Comparison between experimental measures and WhereFigure v0 is 6.the Profile Stokes of velocityhorizontal and velocity: k is an Comparison empirical coefficient.between experimental measures and numerical numerical simulation. Asimulation. series of batch-settling tests were conducted, and the results (summarized in Figure 7) show that the exponential formula can be successfully fitted to experimental data obtained at A reasonable description of the complete settling process should be a settling rate that initially concentrationsA reasonable higher description than 2000 of mg/l. the complete settling process should be a settling rate that initially increases to a maximum, then decreases with increasing of concentration. increasesThe presented to a maximum, numerical then decreasesmodel enables with increasingto vary the of settling concentration. characteristics of the sludge and, A large number of empirical formulas were proposed to describe the relationship between solids therefore, the constants present in the relation used to describe the velocity. In such way, it is possible concentration and solids settling velocity; such relations generally assume the form of an exponential to estimate the effects of the sludge characteristics on the concentration field in the clarifier. curve which fits particularly well the second part of the curve: The calculation procedure is allowed to start with an empty (from solids) tank; sludge is entirely recirculated in the oxidation tank until a prefixed valuekC of X is reached. vs= v0e− , (15) The mean residence time inside the basin is approximately 4 hours; therefore, the adopted wheresimulation v0 is thetime Stokes is about velocity 5 hours. and kIt iswas an empiricalin fact observed coefficient. that the variation of the concentration’s distributionA series does of batch-settling not turn out to tests be meaningful were conducted, when andcarrying the results out extended (summarized simulations in Figure (because7) show the thatsteady the state exponential conditions formula are reached). can be successfully fitted to experimental data obtained at concentrations higher than 2000 mg/l.

Figure 7. Experimental data of settling velocity.

The presented numericalFigure model 7. Experimental enables to vary data theof settling settling velocity. characteristics of the sludge and, therefore, the constants present in the relation used to describe the velocity. In such way, it is possible In the present work, two simulations were carried out by varying the sedimentation velocity of to estimate the effects of the sludge characteristics on the concentration field in the clarifier. solid particles:

-3 -0.0005×C case (a) vs = 3 × 10 × e (m/s) to simulate good settling characteristics of the sludge (experimental data 2007); -4 -0.0007×C case (b) vs = 6 × 10 × e (m/s) to simulate worse settling characteristics of the sludge (experimental data 2005).

In Figure 8a,b, the concentration distribution fields of suspended solid calculated with the above values for the settling velocity are reported. Both simulations were carried out in the same conditions of sludge extraction from the bottom (recirculation ratio b = 1) and with equal coefficients of diffusivity (Δr = Δy = 0.001). The basin fills up when the settling characteristics of the sludge get worse. The iso-concentration curves raise from the bottom and approach the outlet section.

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The calculation procedure is allowed to start with an empty (from solids) tank; sludge is entirely recirculated in the oxidation tank until a preﬁxed value of X is reached. The mean residence time inside the basin is approximately 4 h; therefore, the adopted simulation time is about 5 h. It was in fact observed that the variation of the concentration’s distribution does not turn out to be meaningful when carrying out extended simulations (because the steady state conditions are reached). In the present work, two simulations were carried out by varying the sedimentation velocity of solid particles:

3 0.0005 C case (a) vs= 3 10− e (m/s) to simulate good settling characteristics of the sludge × × − × (experimental data 2007); 4 0.0007 C case (b) vs= 6 10− e (m/s) to simulate worse settling characteristics of the sludge × × − × (experimental data 2005).

In Figure8a,b, the concentration distribution fields of suspended solid calculated with the above values for the settling velocity are reported. Both simulations were carried out in the same conditions of sludge extraction from the bottom (recirculation ratio b = 1) and with equal coefficients of diffusivity (∆r = ∆y = 0.001). The basin fills up when the settling characteristics of the sludge get worse.Resources The2019, iso-concentration 8, x FOR PEER REVIEW curves raise from the bottom and approach the outlet section. 11 of 20

-3 -0.0005×C (a) vs = 3 × 10 × e (m/s)

-4 -0.0007×C (b) vs = 6 × 10 × e (m/s)

FigureFigure 8.8. Iso-concentration lines.

Noticeably, aa non-negligiblenon-negligible increaseincrease inin thethe concentrationconcentration valuesvalues atat thethe outletoutlet nodesnodes is observed (Figure(Figure9 a,b),9a,b), until until a steadya steady state state condition condition is reached is reached after after approximately approximately 2 h of 2 simulation. hours of simulation. In particular, In theparticular, diﬀerence the of difference one order of of one magnitude order of inmagnitude the sedimentation in the sedimentation velocity v0 determines velocity v0 twicedetermines a change twice in thea change values in of the concentration values of concentration in the outlet in nodes. the outlet nodes.

-3 -0.0005×C (a) vs = 3 × 10 × e (m/s)

Resources 2019, 8, x FOR PEER REVIEW 11 of 20

-3 -0.0005×C (a) vs = 3 × 10 × e (m/s)

-4 -0.0007×C (b) vs = 6 × 10 × e (m/s)

Figure 8. Iso-concentration lines.

Noticeably, a non-negligible increase in the concentration values at the outlet nodes is observed (Figure 9a,b), until a steady state condition is reached after approximately 2 hours of simulation. In Resources 2019, 8, 94 11 of 19 particular, the difference of one order of magnitude in the sedimentation velocity v0 determines twice a change in the values of concentration in the outlet nodes.

Resources 2019, 8, x FOR PEER REVIEW 12 of 20 -3 -0.0005×C (a) vs = 3 × 10 × e (m/s)

-4 -0.0007×C (b) vs = 6 × 10 × e (m/s)

FigureFigure 9.9.Concentration Concentration trendtrend atat thethe outletoutlet nodes.nodes.

AA balancebalance betweenbetween thethe massmass presentpresent inin thethe basinbasin afterafter 44 hourshours ofof simulationsimulation andand thethe oneone ofof thethe basinbasin inletsinlets waswas providedprovided to to verifyverify thethe reliabilityreliability of of thethe obtainedobtained results.results. ResultsResults shownshown inin TableTable1 1are are basedbased onon thethe concentrationsconcentrations reported reported in in Table Table2 .2.

TableTable 1. 1.Mass Mass balancebalance inin thethe sedimentation sedimentation tank. tank.

3-3 4 -4 v0 = 3 10 − m/s v0=6 10 − m/s v0 = 3×× 10 m/s v0×= 6 × 10 m/s Mass (kg)(kg) MassMass (kg) (kg) inlet 36,000 36,000 inlet 36,000 36,000 inside tank 22,694 33,427 insideoutlet tank 0.066222,694 39.97 33,427 extract 16,104.49 2711.26 outletTOTAL 0.0662 38798 36178 39.97 extract 16,104.49 2711.26 TOTAL 38798 36178

ResourcesResources 20192019, ,88, ,x 94 FOR PEER REVIEW 1312 of of 20 19

Table 2. Calculated suspended solids (SS) concentration in the clarifier. Table 2. Calculated suspended solids (SS) concentration in the clariﬁer. -3 -0.0005×C -4 -0.0007×C vs = 3 × 10 × e (m/s) vs = 6 × 10 × e (m/s) 3 0.0005 C 4 0.0007 C vs=3 10− (e− × ) (m/s) vs=6 10− (e− × ) (m/s) Concentration× × (mg/l) ×Concentration× (mg/l) Concentration (mg/l) Concentration (mg/l) inside tank 2922.26 4304.39 inside tank 2922.26 4304.39 bottombottom 7097.58 7097.58 74,089.05 74,089.05 surface 23.51 1103.43 surface 23.51 1103.43

TheThe model model allows allows for for any any variation variation of of Q QRR andand Q QWW toto be be considered considered depending depending on on the the sludge sludge concentrationconcentration (X) (X) in in the the biological biological reactor. reactor. According According to the to variation the variation of such of suchflowrates, flowrates, the flow the field flow andfield the and distribution the distribution of suspended of suspended solids solids concentr concentrationation are arecalculated calculated with with respect respect to tothe the new new conditionsconditions of of inlet, inlet, outlet, outlet, and and extraction. extraction.

4.3.4.3. Biological Biological Reactor–Clarifier Reactor–Clarifier System System InIn a a first first stage, stage, a a series series of of numerical numerical simulation simulation were were carried carried out out for for a a deep deep evaluation evaluation of of model model sensitivitysensitivity to to the the operative operative parameters andand forfor definingdefining the the most most significative significative period period to to be be adopted adopted for forthe the experimental experimental data data collection. collection. FigureFigure 10a,b 10a,b shows shows the the biomass biomass growth growth inside inside th thee reactor reactor until until a a prefixed prefixed value value is is obtained obtained (X(Xexpectedexpected = 3000= 3000 mg/l) mg /andl) and the the related related concentration concentration at at the the sedimentation sedimentation tank tank bottom bottom (X (XRR) )starting starting fromfrom an an empty empty tank tank condition condition (X (XRR == 0)0) when when aa sludge sludge with with good good sedimentation sedimentation characteristics characteristics is is considered.considered. The The removal removal of of the the exceeding exceeding biomass biomass starts when the Xexpectedexpected isis reached reached in in the the biological biological reactor.reactor. From From Figure Figure 10b, 10b, it it is is possible possible to to observe observe the the discontinuity discontinuity point point which which marks marks the the instant instant whenwhen sludge sludge extraction extraction begins. begins.

(a) (b)

FigureFigure 10. 10. MixedMixed liquor liquor suspended suspended solids solids (MLSS) (MLSS) concentration concentration trend trend in in the the biological biological reactor reactor (a (a) )and and sludgesludge concentration concentration trend trend in in the the recirculate recirculate flowrate ﬂowrate ( (bb).).

FollowingFollowing this, this, a a series series of tests werewere conductedconducted toto simulate simulate the the e ffeffectsects of of a stronga strong variation variation on on the theinlet inlet COD COD concentration, concentration, which which makes makes it necessary it necessary to operate to operate an intervention an intervention on the sludge on the extraction sludge extractionflow or on flow the recycleor on the flowrate. recycle The flowrate. model The should model allow should modifying allow themodifying values of the the values management of the managementparameters (sludge parameters extraction (sludge and extraction/or recycle and/or of sludge) recycle to reach of sludge) correct operatingto reach correct conditions operating within conditionsthe shortest within feasible the time. shortest feasible time. TheThe used used initial initial conditions conditions are: are: • No solids in the clarifier; No solids in the clarifier; •• Initial COD concentration in the reactor equal to 50 mg/l; • Initial COD concentration in the reactor equal to 50 mg/l; • Initial mixed liquor volatile suspended solids (MLVSS) concentration in the reactor equal to 2890 Initial mixed liquor volatile suspended solids (MLVSS) concentration in the reactor equal to • mg/l; Figure2890 mg 11a,b/l; shows the biomass concentration in the reactor vs. time for two different operative conditions.

Resources 2019, 8, 94 13 of 19

Resources 2019, 8, x FOR PEER REVIEW 14 of 20 Figure 11a,b shows the biomass concentration in the reactor vs. time for two diﬀerent Resources 2019, 8, x FOR PEER REVIEW 14 of 20 operative conditions.

(a) (b)

Figure 11. Mixed liquor(a) suspended solids (MLSS) concentration trend in the (biologicalb) reactor (a) and sludge concentration trend in the recirculate flowrate (b). FigureFigure 11. 11. MixedMixed liquor liquor suspended suspended solids solids (MLSS) (MLSS) concentration concentration trend trend in in the the biological biological reactor reactor (a (a) )and and sludgeBysludge observing concentration concentration the profiles, trend trend in in theit the is recirculate recirculatepossible flowrateto flowrate analyze ( (bb). ).the reliance of the biomass growth linked to the kinetic parameter in the reactor but also to the recycling concentration [34]. Such a low value of By observing the profiles, it is possible to analyze the reliance of the biomass growth linked to the XR canBy bringobserving a strong the dilutionprofiles, effectit is possible in the biomass to analyze concentration the reliance in of the the biological biomass reactor,growth especiallylinked to theifkinetic this kinetic lasts parameter parameter for a long in the timein reactorthe (i.e., reactor butthe time alsobut alsotowhich the to recycling this eneeded recycling concentration to define concentration the [ 34interventions).]. Such[34]. aSuch low a value low ofvalue XR canof XbringR canFigure abring strong 12a,ba strong dilution shows dilution e fftheect COD ineffect the vs. in biomass thetime biomass in concentration the reactor concentration and in thethe in biologicalsludge the biological extraction reactor, reactor, especiallyflowrate, especially which if this ifchangeslasts this forlasts adepending longfor a timelong on (i.e.,time the the (i.e., inlet time the organic whichtime which load is needed and, is needed consequently, to define to define the interventions). the the biomass interventions). growth. FigureSludgeFigure 12a,b 12extractiona,b shows shows rate the the adjustmentCOD COD vs. vs. time time represents in in the the reactor reactoran operative and and the the intervention sludge sludge extraction extraction frequently flowrate, flowrate, used which whichin the changestreatmentchanges depending depending plant management; on on the the inlet inlet it organic organicis necessary load load and,when and, consequently, consequently, high variation the the in biomass biomassthe organic growth. load occurs. Sludge extraction rate adjustment represents an operative intervention frequently used in the treatment plant management; it is necessary when high variation in the organic load occurs.

(a) (b)

FigureFigure 12. 12. WasteWaste sludge sludge(a) flowrate ﬂowrate ( a)) and and substrate concentration tren trendd in the(b ) biological reactor (b).

TheSludgeFigure calibration 12. extraction Waste sludgeand rate validation flowrate adjustment ( aof) andthe represents substratemodel was concentration an based operative on trenthree interventiond in different the biological frequently phases: reactor The used ( bfirst). in two the weretreatment devoted plant to management; the evaluation it isof necessary the characteristic when high parameters variation in(calibration the organic phase), load occurs. the last one to validateTheThe calibrationthe calibration numerical and and validationmodel. validation The of of calibrationthe the model model wasof was the based based flow on on field three three parameter different different phases: phases:was pointed The The first first on two twothe wereturbulentwere devoted devoted diffusion to to the the coefficient evaluation evaluation (regar of of the theding characteristic characteristic the velocity parameters parametersfield, the flow (calibration (calibration at the outlet phase), phase), could the the guarantee, last last one one to in to validatethisvalidate phase, the the numericalnumerical calibration model. model. results), The The calibrationand calibration velocities of the measuredof flowthe flow field on parameterfieldthe real parameter sedimentation was pointed was pointed ontank the were turbulent on used. the turbulentTodiff allowusion diffusion coefor ffidirectcient coefficient (regardingcomparison (regar the with velocityding model the field, velocity results, the flowfield,field at themeasures the flow outlet at were the could outlet taken guarantee, could instantaneously guarantee, in this phase, inat thisdefinedthe phase, calibration sampling the calibration results), locations. and results), velocities For the and transport measured velocities model, on measured the the real sedimentation sedimentationon the real sedimentation characteristics tank were used. tank of Towere the allow sludge used. for Toweredirect allow derived comparison for direct from with comparisonthe modelcolumn results, tests,with andmodel field for measures results, the diffusion werefield takenmeasures coefficients, instantaneously were very taken low atinstantaneously values defined (due sampling to theat definedsmalllocations. turbulent sampling For the effects locations. transport present For model, in the the thetransport tank) sedimentation were model, cons idered.the characteristics sedimentation In the end, of the characteristicsa comparison sludge were with of derived the real sludge data, from werederivedthe column derived from tests, fromfurther and the direct for column the measures di fftests,usion and on coe theforfficients, sedithe mentationdi veryffusion low coefficients, tank, values was (due used very to thefor low smallthe values validation turbulent (due phase.to eff theects smallpresent Threeturbulent in theexperimental tank) effects were present campaigns considered. in the tank)were In the carriedwere end, cons out. a comparisonidered. Analysis In the of with theend, realchemical a comparison data, values derived with and from realof furtherflow data, at derivedthedirect inlet, measures from recycling further on flow, the direct sedimentation and measures sludge extraction on tank, the wassedi flowmentation used were for themeasured tank, validation was at used the phase. samplingfor the validation points shown phase. in FigureThree 1. experimental campaigns were carried out. Analysis of the chemical values and of flow at the inlet,P1 = recycling inlet section flow, and sludge extraction flow were measured at the sampling points shown in FigureP2 1. = biological reactor P1 = inlet section P2 = biological reactor

Resources 2019, 8, 94 14 of 19

Three experimental campaigns were carried out. Analysis of the chemical values and of flow at the inlet, recycling flow, and sludge extraction flow were measured at the sampling points shown in Figure1. ResourcesP1 2019= inlet, 8, x sectionFOR PEER REVIEW 15 of 20 P2 = biological reactor P3 = recycle from clarifier P3 = recycle from clarifier P4 = outlet section P4 = outlet section A numerical simulation was carried out for each campaign, and the results are shown in the A numerical simulation was carried out for each campaign, and the results are shown in the following paragraphs. following paragraphs. Campaign 1. The first campaign was aimed at defining the kinetic constants for the organic Campaign 1. The first campaign was aimed at defining the kinetic constants for the organic substance removal. substance removal. COD at the inlet and at the outlet, TSS in the oxidation tank, in the recycle flow, and at the outlet COD at the inlet and at the outlet, TSS in the oxidation tank, in the recycle flow, and at the outlet were measured and a volatile suspended solids (VSS)/TSS rate equal to 0.75 was calculated. were measured and a volatile suspended solids (VSS)/TSS rate equal to 0.75 was calculated. In Table 3, the hydraulic loads measured at the plant and used in the simulation are shown. The In Table3, the hydraulic loads measured at the plant and used in the simulation are shown. input value of COD is the average of the measured values. The input value of COD is the average of the measured values. The obtained data were used as input parameters to the numerical model and for the calibration phase. The following values Tablewere 3.assignedExperimental to the values kinetic of constants: hydraulic loads. • Y =0.45 mgVSS/mgCOD; − • Kd = 0.08 d 1; Unit Campaign 1 Campaign 2 Campaign 3 • ks = 80 mgCOD/l;Q m3/h 2631 2662 2956 − 3 • K = 2.0 d 1; QR m /h 3178 3180 2692 3 The assigned valuesQw mwere/d evaluated 1680 by means of 1680several runs until 1680 a minimum value of the θ quadratic mean errorh could hbe reached. 3.20 3.82 3.39 b 1.21 1.19 from 1.20 to 0.9

Table 3. Experimental values of hydraulic loads. The obtained data were used as input parameters to the numerical model and for the calibration phase. The followingUnit values Campaign were assigned 1 to the kinetic Campaign constants: 2 Campaign 3 Q m3/h 2631 2662 2956 Y = 0.45 mgVSS/mgCOD; • KQR= 0.08 dm13/h; 3178 3180 2692 • d − 3 kQs =w 80 mgCODm /d /l; 1680 1680 1680 • 1 Kθh= 2.0 d− ; h 3.20 3.82 3.39 • Theb assigned values were 1.21evaluated by means of 1.19 several runs until from a minimum 1.20 to 0.9 value of the quadratic mean error could be reached. In thethe followingfollowing graphs, graphs, the the comparison comparison between between experimental experimental data data and and calculated calculated values values of COD of COD(Figure (Figure 13a) and 13a) TSS and (Figure TSS (Figure13b,c) concentration 13b,c) concentratio in the din ﬀinerent the sectionsdifferent of sections the system of the is reported. system is reported.

(a) (b)

Figure 13. Cont.

Resources 2019, 8, 94 15 of 19 Resources 2019, 8, x FOR PEER REVIEW 16 of 20 Resources 2019, 8, x FOR PEER REVIEW 16 of 20

(c) (d) (c) (d) FigureFigure 13. 13. CampaignCampaign 1: 1: Chemical Chemical oxygen oxygen demand demand (COD) (COD) concentration concentration (a (a) )and and total total suspend suspend solids solids Figure 13. Campaign 1: Chemical oxygen demand (COD) concentration (a) and total suspend solids (TSS)(TSS) concentration concentration in in biological biological reactor reactor ( (bb),), in in recycling recycling flowrate ﬂowrate ( (cc),), and and in in the the effluent eﬄuent ( d).). (TSS) concentration in biological reactor (b), in recycling flowrate (c), and in the effluent (d).

CampaignCampaign 2. 2. TheThe values values of of the the kinetic kinetic parameters parameters obtain obtaineded in in the the first ﬁrst campaign campaign were were then then also also Campaign 2. The values of the kinetic parameters obtained in the first campaign were then also usedused in in this this second second test. test. In In the the following following graphs, graphs, the the numerical numerical simulation simulation results results vs. vs. the the experimental experimental used in this second test. In the following graphs, the numerical simulation results vs. the experimental valuesvalues for for COD COD (Figure (Figure 14a)14a) and and TSS TSS (Figure (Figure 14b–d)14b–d) are are shown. shown. values for COD (Figure 14a) and TSS (Figure 14b–d) are shown.

(a) (b) (a) (b)

(c) (d) (c) (d) Figure 14. Campaign 2: COD concentration (a) and TSS concentration in biological reactor (b), in FigureFigure 14. CampaignCampaign 2: 2: COD COD concentration concentration (a (a) )and and TSS TSS concentration concentration in in biological biological reactor reactor ( (bb),), in in recycling flowrate (c), and in the effluent (d). recyclingrecycling flowrate flowrate ( (cc),), and and in in the the effluent effluent ( d). Campaign 3. In this case, a reduction of the recycle flowrate value (b = 1.2 until 0.9, Table 3) was CampaignCampaign 3. 3. InIn this this case, case, a a reduction reduction of of the the recycle recycle flowrate flowrate value value (b (b == 1.21.2 until until 0.9, 0.9, Table Table 33)) waswas imposed to the plant management. As shown from the analysis of the reported profiles (Figure 15a imposedimposed to the plantplant management.management. AsAs shown shown from from the the analysis analysis of of the the reported reported profiles profiles (Figure (Figure 15a–d), 15a and Figure 15b–d), the numerical model forecasts a reduction of the TSS concentration in the reactor and Figure 15b–d), the numerical model forecasts a reduction of the TSS concentration in the reactor and, consequently, an increase of the COD concentration at the outlet. The comparison between the and, consequently, an increase of the COD concentration at the outlet. The comparison between the

Resources 2019, 8, x FOR PEER REVIEW 17 of 20 experimental values (sampling obtained on the day after) shows the same trend predicted by the numerical model. The compared error analysis for the three considered cases, shown in Table 4, indicates that simulated values fit experimental ones well, except for the case of COD, where the model provides overestimated values, particularly in the second and third campaigns.

Table 4. Quadratic mean error.

Campaign 1 Campaign 2 Campaign 3 COD in P4 6.42 % 19.80% 32.76% Resources 2019, 8, 94 16 of 19 TSS in P2 6.06 % 2.51% 2.60% the numericalTSS in P3 model forecasts a reduction4.81 % of the TSS concentration 8.93% in the reactor 3.18% and, consequently, an increaseTSS in ofP4 the COD concentration9.17 at % the outlet. The comparison 3.50% between the 21.97% experimental values (sampling obtained on the day after) shows the same trend predicted by the numerical model.

(a) (b)

FigureFigure 15. 15. CampaignCampaign 3: 3: COD COD concentration concentration (a (a) )and and TSS TSS concentration concentration in in biological biological reactor reactor ( (bb),), in in recyclingrecycling flowrate ﬂowrate ( (cc),), and and in in the the effluent eﬄuent ( d)).)).

5. ConclusionsThe compared error analysis for the three considered cases, shown in Table4, indicates that simulated values ﬁt experimental ones well, except for the case of COD, where the model provides overestimatedThe paper values,is not intended particularly to inintroduce the second new and concepts third campaigns. about wastewater treatment but rather aimed at overcoming the classical methods used to design and manage wastewater treatment plants, with respect to the activated sludgeTable system. 4. Quadratic Once the mean geometrical error. characteristics of the biological reactor and of the clarifier have been fixed, monitoring inlet COD concentrations is enough to control eventual problems which can occurCampaign in the case 1 of sudden Campaign variations 2 of the Campaign organic 3 or hydraulic loads. COD in P4 6.42% 19.80% 32.76% TSS in P2 6.06% 2.51% 2.60% TSS in P3 4.81% 8.93% 3.18% TSS in P4 9.17% 3.50% 21.97%

5. Conclusions The paper is not intended to introduce new concepts about wastewater treatment but rather aimed at overcoming the classical methods used to design and manage wastewater treatment plants, with respect to the activated sludge system. Once the geometrical characteristics of the biological reactor and of the clarifier have been fixed, monitoring inlet COD concentrations is enough to control Resources 2019, 8, 94 17 of 19 eventual problems which can occur in the case of sudden variations of the organic or hydraulic loads. By measuring the sludge main characteristics, the best sludge extraction or the best recycle flow may be evaluated, allowing for significant energy saving, especially for big plants. Management strategies suitable to face any variation in the inlet or in the sludge settling characteristics can be defined in a short time by selecting the most effective intervention based on the results provided by the proposed numerical model. The calibration and validation phases have shown the validity of this approach, which considers the reactor–clarifier system as a whole. The response time of the numerical model was confirmed by the analysis carried out on a real plant, and the eventual correction to be operated in to reach the standard efficiency values for the plant could be evaluated in a few hours without attempting to correct the trend based solely on empirical experience.

Author Contributions: Conceptualization, F.T. and S.C.; methodology, P.V., F.T., and S.C.; software, F.T. and S.C.; validation, P.V., V.T., F.T., and S.C.; formal analysis, F.T.; investigation, S.C.; resources, P.V.; data curation, S.C.; writing—original draft preparation, S.C.; writing—review and editing, S.C. and N.F.; visualization, S.C.; supervision, V.T. and P.V.; project administration, P.V. Funding: This research received no external funding. Conﬂicts of Interest: The authors declare no conﬂict of interest.

Nomenclature b = QR/Q Recirculation ratio [-] 3 C Concentration [M L− ] · 3 COD Chemical oxygen demand [M L− ] · 2 1 Dr Coefficient of diffusivity (r direction) [L T− ] 2· 1 Dy Coefficient of diffusivity (y direction) [L T ] · − e Nepero number [-] k Empirical coefficient [-] l0 Water head in the basin [L] 3 MLVSS Mixed liquor volatile suspended solids [M L− ] 3 · MLSS Mixed liquor suspended solids [M L− ] 2 1 · p Pressure [M T− L− ] · 3· 1 Q Inlet flowrate [L T− ] · 3 1 Qe=Q-Qw Outlet flowrate (from biological reactor) [L T− ] 3 1 · QR Return sludge flowrate [L T− ] 3 · 1 Qw Waste sludge flowrate [L T ] · − r Horizontal coordinate [L] 1 r’g Net growth of cells [T− ] 1 rsu Substrate utilization rate [T− ] S Substrate concentration [M L 3] · − S Substrate concentration in inlet wastewater [M L 3] 0 · − SS Suspended solids [M L 3] · − TSS Total suspend solids [M L 3] · − T0=l0/u0 Time interval [T] 1 u Mean velocity component (r direction) [L T− ] 1 · u0 Water inlet velocity [L T− ] · 1 v Mean velocity component (y direction) [L T− ] 1 · ve Sludge extraction velocity [L T− ] 1 · v0 Stokes velocity [L T− ] · 1 vs Settling velocity [L T ] · − V Aeration tank volume [L3] y Vertical coordinate [L] 3 X Concentration of suspended solids in the aeration tank [M L− ] 3 · Xe Concentration of suspended solids in the effluent [M L ] · − Resources 2019, 8, 94 18 of 19

X Inlet concentration of suspended solids [M L 3] 0 · − X Return sludge concentration [M L 3] R · − ∆r, ∆y Mesh dimensions [L] 1 2 φ=vC Flow (y direction) [M T− L− ] · · 2 1 υt Eddy viscosity coeﬃcient [L T ] · − ρ Fluid density [M L 3] · − σsr Schmidt numbers (r direction) [-] σsy Schmidt numbers (y direction) [-]

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