New explicit formulations for accurate estimation of aeration- related parameters in steady-state

20 Pages·2017·2.44 MB·English

Global NEST Journal, Vol 19, No X, pp XX-XX
Copyright© 2017 Global NEST
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New explicit formulations for accurate estimation of aeration-
related parameters in steady-state completely mixed activated
sludge process
YETILMEZSOY K.*
Department of Environmental Engineering, Faculty of Civil Engineering, Yildiz Technical University, 34220, Davutpasa, Esenler, Istanbul,
Turkey
Received: 13/06/2015, Accepted: 13/03/2017, Available online: 29/03/2017
*to whom all correspondence should be addressed:
e-mail: [email protected] ; [email protected]
wastewater. The aeration tank, where the biological
Abstract
reactions occur and air (or oxygen) is injected in the mixed
This paper presents new and explicit equations to estimate liquor, constitutes the hearth of this process. Nevertheless,
aeration-related parameters such as standard oxygen aeration is a critical operation and a major energy
requirement, daily energy consumption and total mass consumer in most wastewater treatment plants (Roman
transfer coefficient for the diffused aeration. The proposed and Mureşan, 2014). From the economical point of view,
formulations are derived for the steady-state completely the supply of oxygen accounts for an important part of the
mixed activated sludge process based on the nonlinear running costs of an activated sludge-based wastewater
regression analysis by using the Richardson’s extrapolation treatment process. For conventional wastewater activated
method and the Levenberg–Marquardt algorithm. The sludge plants, aeration systems are usually the single
applicability of the proposed models has been investigated largest consumer of energy at wastewater treatment
for a wide range of thirteen inputs consisting of the installations, typically accounting for 30% (or 45%) to 50%
fundamental biological, hydraulic, and physical design (or 60%) of a treatment facility’s total electrical energy use
variables, and tested against a total of 1500 additional (Bolles, 2006; Casey, 2009). Therefore, an effective control
computational scenarios. All estimations are proven to be and optimization of the air supply may significantly reduce
satisfactory with very high determination coefficients (R2) the operational costs of an activated sludge-based
between 0.961–0.965, 0.967–0.972 and 0.980–0.984, wastewater treatment plant (Makinia and Wells, 1999;
respectively, for the prediction of standard oxygen Fayolle et al., 2007). Aeration control aims not only at
requirement, daily energy consumption and total mass energy savings but will also guarantee that the
transfer coefficient for diffused aeration. The proposed microorganisms are adequately supplied with oxygen at all
models offer sufficiently simple and practical mathematical times (Roman and Mureşan, 2014). In this regard, it is clear
formulations incorporating routinely obtainable that careful attention is essential to the adequate design,
parameters, which are readily available for all activated operation and control of aeration equipment, particularly
sludge-based treatment plants. Besides eliminating the at large wastewater treatment plants.
need for additional time or computational effort typically
Diffused (or fine bubble) air systems are broadly classified
performed in the theoretical procedure, the developed
as coarse or fine bubble systems, depending on the size of
equations have simple coefficients to be easily used for
bubble generated. Fine bubble diffused air systems are
manual calculations with a hand-held calculator. The
probably superior to all other commercially available
statistical results clearly exhibit that the proposed
systems in terms of their energy efficiency in oxygen
equations are accurate enough to be used in estimation of
transfer (Casey, 2009; Fayolle et al., 2007). However, under
the studied aeration parameters based on the practical
activated sludge process conditions, the oxygen transfer
ranges of the corresponding design variables.
efficiency of diffused air systems is influenced by several
Keywords: Completely mixed activated sludge; Energy factors, including geometry of the reactor, temperature,
consumption; Mass transfer coefficient; Nonlinear barometric pressure, and the liquid composition
regression; Oxygen requirement; Statistical analysis (Varolleghem, 1994). Because the characteristics of the
aerobic process are time-varying and site-specific, it is
1. Introduction
necessary to calculate the mass transfer efficiencies under
The activated sludge-based process currently represents field conditions. Therefore, a number of process-related
one of the most widespread and commonly used variables are needed to be taken into account with
technology to remove organic pollutants from the sufficient accuracy for purposes of optimal aeration
2
control, failure diagnosis and process performance in full various mechanistic models have been introduced for the
operation (Varolleghem, 1994). Considering these complex assessment of a number of activated sludge-based
interactions of variables associated with this process, problems such as modeling of activated sludge thickening
various aeration strategies can be implemented by means in secondary clarifiers (Giokas et al., 2002), modeling of the
of computational methods for a realistic evaluation of the steady-state biofilm activated sludge reactor under
aeration system (Makinia and Wells, 1999; Makinia, 2010). substrate limiting conditions (Fouad and Bhargava, 2005a;
Fouad and Bhargava, 2005b), modeling of temperature
The oxygen is transferred to the water by a mass transfer
dynamics for activated sludge systems (Makinia et al.,
coefficient (ka), which describes how fast the oxygen is
L
2005), estimation of completely mixed activated sludge
transferred to be dissolved in water. It has been stated that
reactor volume (Yetilmezsoy, 2010), prediction of the
for a good aeration performance, the rate of dissolved
reduction of biosolids production by ozonation of the
oxygen supplied to the bioreactor should be equal to the
return activated sludge (Isazadeh et al., 2014), and
rate of oxygen consumed by the mixed liquor under any
prediction of the waste sludge volumetric flow rate
given set of circumstances (Roman and Mureşan, 2014). In
(Yetilmezsoy, 2016). Although many other studies
this regard, Painmanakul et al. (2009) have reported that it
(Nuhoglu et al., 2005; Mulas, 2006; Pamukoglu and Kargi,
is frequently necessary to determine this coefficient when
2007; Szilveszter et al., 2010; Bagheri et al., 2015; Liu and
designing and evaluating the performance of the aeration
Wang, 2015) have focused on different modeling
systems. They also emphasized that a better forecast of the
methodologies in the operation of activated sludge-based
ka value would help the optimization of the installations in
L
treatment plants, however, to date, there are no sound
term of both cost and effectiveness. In another study, Al-
papers in literature regarding the development of explicit
Ahmady (2011) conducted a dimensional analysis
mathematical formulations that can be directly used for
procedure to evaluate the factors affecting the oxygen
the prediction of the present aeration-related parameters
mass transfer coefficient (ka). The study concluded that
L
in the steady-state completely mixed activated sludge
increasing airflow rate, diffusers coverage area and
process without writing a set of theoretical statements. To
submergence of diffusers increased the value of ka while
L
the best of the author’s knowledge, this work is the first
increasing Froude number, ratio of the height of water in
study specifically aimed at investigating new and practical
the tank to the length of the tank, and bubbles diameter
expressions for the direct estimation of aeration-related
showed an adverse influence on this coefficient.
parameters as a function of the most common biological,
Concerning to the estimation of the value of mass transfer
hydraulic, and physical design variables used in the design.
coefficient, however, there are almost no papers in the
literature proposing a practical equation that takes into In consideration of the foregoing facts, the overall
account the most common biological, hydraulic, and objectives of this study were: (1) to develop simple and
physical design variables used in the design of activated explicit equations for practising engineers and researchers,
sludge plants. Many of the proposed correlations are highly which makes it possible to accurately estimate aeration-
theoretical, and not always applicable in practice, since the related parameters (standard oxygen requirement, daily
most of parameters used in the mathematical structure of energy consumption, and total mass transfer coefficient for
these models are not readily available or routinely diffused aeration) for the diffused aeration in the steady-
obtainable for all activated sludge-based treatment plants. state completely mixed activated sludge process; (2) to
On the other hand, although some of the previous verify the model predictions by means of various powerful
expressions (Chen et al., 1980; Goto and Andrews, 1985; statistical performance indicators; (3) to assess the
Holmberg, 1986; Reinius and Hultgren, 1988) seem to have predictive capabilities of the developed models by
a simple mathematical structure, however, they neglect comparing the model outputs with the results of a total of
the effect of several process-related variables, and do not 1500 additional and different computational scenarios; and
directly reflect the actual behavior the large-scale aeration (4) to validate the applicability of the proposed equations
units. To overcome the limitations and problems by comparing the consistency of simulation results with the
associated with the existing models, a more practical existing literature data.
approach for the accurate prediction of the value of the
2. Methodology
mass transfer coefficient could be interesting for engineers
and researchers who are concerned with the aeration in 2.1. Representation of input and output variables
activated sludge process.
In the planning stage of modeling and simulation-based
Mathematical modeling and computer simulation of studies, selection of the most appropriate model
biological systems are valuable and powerful tools for components is a crucial factor in order to recognize
describing and evaluating their performance under both possible technical faults and to reduce computation time,
dynamic and steady-state conditions (Yetilmezsoy, 2010; as well as to develop an accurate modeling methodology
Kumar, 2011; Yetilmezsoy, 2012; Yetilmezsoy et al., 2015). for a specific environmental process (Yetilmezsoy et al.,
With the increasing practical experience, continuously 2015; Kanat and Saral, 2009; Yetilmezsoy and Sapci-Zengin,
developed and improved activated sludge-based models 2009). For the present case, the model variables and their
have been utilized to quantify and to evaluate the process respective ranges were chosen in accordance with the
performance (Makinia and Wells, 1999; Makinia, 2010; relevant literature (Yetilmezsoy, 2010; Yetilmezsoy, 2016;
Yetilmezsoy, 2010; Yetilmezsoy, 2016). In recent years,
3
Orhon and Artan, 1994; Muslu, 1996a; Muslu, 1996b; static pressure caused by wastewater depth in the areation
Qasim, 1998; Crites and Tchobanoglous, 1998). basin, measured in head of water (m), and X13 = Ha:
elevation or altitude above sea level (m). These input
For modeling and simulation purposes, thirteen
variables were used for the estimation of three aeration-
fundamental biological, hydraulic, and physical design
related outputs: f = SOR : standard oxygen requirement
variables, which are the most commonly used design 1 d
for the diffused aeration (kg O /h), f = E: daily energy
parameters, were considered as the following inputs: X = 2 2 c
1
consumption (kWh/day), and f = ka : total mass transfer
Q: influent wastewater flow rate (m3/sec), X = θ: mean 3 L d
2 c
coefficient for the diffused aeration (day–1).
cell residence time (days), X = Y: growth yield coefficient
3
(kg MLVSS/kg BOD ), X = S: influent soluble substrate Detailed definitions of the present model components,
5 4 i
concentration (kg BOD /m3), X = X: concentration of the which are among the most widely used and monitored
5 5
cells (volatile suspended solids) in the reactor (kg parameters in activated sludge-based treatment plants,
MLVSS/m3), X = φ = X/X : volatile suspended solids to can be found in several studies (Bolles, 2006; Yetilmezsoy,
6 TSS
total suspended solids ratio (kg MLVSS/kg MLSS), X = S : 2010; Orhon and Artan, 1994; Muslu, 1996a; Muslu, 1996b;
7 e
effluent total substrate concentration (kg BOD /m3), X = Qasim, 1998; Crites and Tchobanoglous, 1998; Eroglu,
5 8
X : effluent total suspended solids concentration (kg 1991; Celenza, 1999; Toprak,, 2000; Shammas et al., 2009;
e
MLSS/m3), X9 = kd: microorganism endogenous decay Loehr, 2012).
coefficient (day–1), X = T : ambient air temperature (°C),
10 a The general schematic of the major parameters used in the
X = T: influent wastewater temperature (°C), X = H:
11 i 12 proposed models is depicted in Figure 1.
+ Ha X1 Ta
X13 X10 INPUT VARIABLES
from primary clarifier X4 X2 X7 X8 to
Q, S i Tc Q + Q r , S e , Xe secondary
clarifier
T
i Aeration X3 X6
Q r , Xr basin X/XTSS
X11 (Return sludge) H - Xh12 Y X X9 Tww
d k
d
Blower X5
Air
hd Diffusers
OUTPUT VARIABLES
Y1 Y2 Y3
SOR E k a
d c L d

Figure 1. General schematic of the major parameters used in the proposed models
2.2. Steady-state procedure for the completely mixed volume used for calculation of mean cell residence time
activated sludge process (θ) accounts volume of the aeration tank only, (3)
c
completely mixed flow regime is maintained in the aeration
In this study, a theoretical procedure (Table 1) was
tank, (4) wastewater was distributed along with return
conducted as the primary step of the nonlinear-based
sludge uniformly from one side of the tank to the other, (5)
computational analysis to produce a sufficient number of
waste stabilization occurs only in the aeration tank, (6) all
data points to be used in modeling and simulation of
reactions take place in the aeration basin so that the
standard oxygen requirement for the diffused aeration
substrate in the aeration basin is of the same concentration
(SOR ), daily energy consumption (E) and mass transfer
d c
as the substrate in the secondary clarifier and in the
coefficient (ka ) for diffused aeration.
L d
effluent, (7) there is no microbial degradation of organic
2.3. Assumptions matter and no biomass growth in the secondary clarifier,
and (8) waste stabilization is carried out by the
In this study, the following assumptions are made to
microorganisms occurs in the aerator unit. The design
describe the specific aspects of the process: (1) the system
parameters and numerical assumptions considered in the
is assumed to run under a steady-state condition for
present computational analysis are summarized in Table 2.
biomass (dX/dt = 0, X = 0) and substrate (dS/dt = 0), (2) the
0
Table 1. Set of steady-state design equations considered in theoretical procedure
Steady-state design equations Equation no
[1] The effluent soluble substrate concentration (C: mg BOD /L) and the substrate utilization efficiency (or biological
5
treatment efficiency: E ) are calculated as follows (Yetilmezsoy, 2010; Yetilmezsoy, 2016; Muslu, 1996a; Muslu,
b
1996b):
CS (X f A) (1a)
e e b
E (%)(S C)/S100 (1b)
b i i
where S is the influent substrate concentration (mg BOD /L), S is the total effluent substrate concentration as the
i 5 e
discharge standard for the receiving water (mg BOD /L), X is the effluent total suspended solids concentration (mg
5 e
MLSS/L), f is the biodegradable fraction of X , A is the ultimate biochemical oxygen demand (BOD ≈ COD) of per kg of
b e u
bacteria cells (or the oxygen requirement for oxidizing per unit of biomass: g O equivalent/g MLVSS), and ψ is the ratio
2
of BOD to ultimate BOD (commonly ψ = BOD /BOD = 0.68 for the substrate decay coefficient of k = 0.1 day–1).
5 u 5 u
[2] The volume of the completely mixed activated sludge reactor (V : m3) is determined by the following steady-state
R
or empirical equations (Yetilmezsoy, 2010; Fouad and Bhargava, 2005a; Fouad and Bhargava, 2005b; Muslu, 1996a;
Muslu, 1996b; Toprak, 2000):
QYS C QS C Y  Q(Y )S C
V  c i  c i   obs c i (2a)
R X1kdc  X 1kdc X
(0.294)(Q)(Y)()0.7(S)1.1
V  c i (2b)
R (X)(k )0.33(C)0.04
d
where Q is the influent wastewater flow rate (m3/day), θ is the mean cell residence time (MCRT) or the sludge age (day)
c
or the solids retention time (SRT), Y is the growth yield coefficient (kg MLVSS/kg BOD ), Y is the observed growth yield
5 obs
coefficient (kg MLVSS/kg BOD ), X is the concentration of the cells (volatile suspended solids) in the reactor (kg
5
MLVSS/m3), k is the coefficient of endogenous respiration (day–1), and others (S and C) are defined in previous equations.
d i
[3] The food to microorganism (F/M: kg BOD /kg MLVSS/day) ratio, the volumetric organic loading (L: kg
5 v
BOD /m3/day), the hydraulic retention time (θ : hour), and the waste (excess) sludge mass flow rate (P: kg
5 h x
MLVSS/day) as a function of S, Q, X, V , θ, k , Y, E , substrate utilization rate (r : kg BOD /m3/day) are obtained from
i R c d b su 5
the following equations (Yetilmezsoy, 2016; Mulas, 2006; Orhon and Artan, 1994; Muslu, 1996a; Muslu, 1996b;
Qasim, 1998; Toprak, 2000; US EPA, 1977):
S  S C
YQ iS C YQS i 
1 YQSi Ck  Si i k  i  Si k YQSiEbk (3a)
c XVR d XVR d XVR d  XVR  d
1 QS  F  F  1  1
c YXVRi Ebkd YMEbkd M c kdYEb (3b)
V QS S XQS  QS  F 
h  QR Lv  VRi hi Lv X VRi XXVRi  XM (3c)
  S C 
P Yr k XV Y i k XV YQS Ck XV (3d)
x su d R   h  d  R i d R
In the computational analysis, the following control ranges were considered for the present activated sludge process
(Yetilmezsoy, 2010; Yetilmezsoy, 2016; Muslu, 1996a; Muslu, 1996b; Qasim, 1998): F/M = 0.2–0.6 kg BOD /kg
5
MLVSS/day, L = 0.8–2.0 kg BOD /m3/day, θ = 5–15 days, θ = 3–5 h, and r = Q/Q from 0.20 (or 0.25) to 0.50 (or 1.0).
v 5 c h r
[4] The wastewater temperature within the aeration basin (T : °C) is calculated by conducting a heat balance around
ww
the reactor, resulting the following equation (Muslu, 1996a; Celenza, 1999; Loehr, 2012; Wang et al., 2009):
(A )(f)(T )(Q)(T) (V /H)(f)(T )(Q)(T)
T  R a i  R a i (4)
ww (A )(f)Q (V /H)(f)Q
R R
where A is the surface area of the aeration basin (m2), f is the proportionality factor (f = 0.5 for Eastern United States
R
and f = 2.5 for Midwestern United States), T is the ambient air temperature (°C), T is the influent wastewater
a i
temperature (°C), H is the average wastewater depth in the areation basin (m), and others (Q and V ) are defined in
R
previous equations.
[5] The air pressure (p ) and the density of air (ρ ) as a function of altitude H (above sea level) are determined by
a a a
using the following equations (Bugbee and Blonquist, 2006):
gM
 LH RL
p p 1 a (5a)
1 0 T0 
5
5.25588
 2.25577 
p2 p01 105 Ha (5b)
   H 5.25328
p3 p0p01144307.a69231  (5c)
1n3 p p ...p p p p
pa  npi  1 2n n  1 32 3 (5d)
i1
(p 103)(M ) (p 103)(M )
a  a RT a  Ra(T LH )a (5e)
0 a
where p , p and p are the air pressure (kPa) at altitude H (m), p is the sea level standard atmospheric pressure (101.325
1 2 3 a 0
kPa), p is the average air pressure (kPa) to be used in calculation of the density of air, L is the temperature lapse rate
a
(0.0065 K/m), T is the sea level standard temperature (288.15 K), g is the earth-surface gravitational acceleration
0
(9.80665 m/s2), M is the molar mass of dry air (0.0289644 kg/mol), R is the ideal (universal) gas constant (8.31447
a
J/mol/K), and ρ is the density of air based on the molar form of the ideal gas law (kg/m3).
a
[6] The effective oxygen percentage as a function of barometric pressure (p : kPa) from sea level to any elevation is
a
determined as follows (Bugbee and Blonquist, 2006):
O2(%)20.95(100/pa)(0.2095)(pap0) (6)
[7] The theoretical oxygen requirement (ThOR: kg O /day) is calculated by knowing influent and effluent BOD of
2
wastewater, and the amount of organisms wasted from the system (Yetilmezsoy, 2010):
Q(S) Q(S S ) XV 
ThOR  (A)(Px) i e (A) cR (7)
[8] The dissolved oxygen saturation concentration (C: mg O /L) at a given temperature (between T = 4°C – 30°C) and
s 2
total dissolved solids (TDS) concentration (mg/L) is obtained by one of the following empirical equations (Eroglu,
1991; ASCE, 1997; von Sperling, 2007; Ma et al., 2013):
468 (0.0036TDS)
Cs (31.6T) (21.2T) (8a)
Cs (4750.00265TDS)/(33.5T) (8b)
C 14.652(4.1022101)(T)(7.9910103)(T2)(7.7774105)(T3) (8c)
s
[9] The comprehensive oxygen solubility correction factor (F ) is calculated from the following equations (Muslu,
a
1996b; Qasim, 1998; von Sperling, 2007):
Fa 1(Ha/9450) (9a)
1(10.33)(p /101.325)H 
Fa 2 a10.33 (1EO2) (9b)
where E is the oxygen transfer efficiency of air diffusers (or mass of O transferred/mass of O supplied, usually E =
O2 2 2 O2
0.06 – 0.12), 10.33 and 101.325 are the water column (m) and kilopascal (kPa) equivalents of the absolute atmospheric
pressure at sea level (1 atm), respectively, and others (p and H) are defined in previous equations.
a
[10] Based on the above definitions, the value of standard oxygen requirement (SOR: kg O /h) is calculated from the
2
following equation (Roman and Mureşan, 2014; Makinia, 2010; Muslu, 1996b; Qasim, 1998; Makinia and Wells, 2000):
1  ThOR 
SOR 24CwwFaCmin/C20(Tww20) (10)
where C is the dissolved O concentration (mg O /L) in wastewater at temperature T , β is the salinity surface tension
ww 2 2 ww
factor (a ratio of O saturation concentration in wastewater to that in clean water) for wastewater (usually β =
2
C /C = 0.70 – 0.98 and typically 0.90 for wastewater), C is the minimum dissolved O concentration
20(wastewater) 20(clean water) min 2
(mg O /L) maintained in the areation basin, C is the dissolved O concentration (mg O /L) at standard 20°C, α is the
2 20 2 2
oxygen transfer correction factor (a ratio of O transfer in wastewater to that in clean water) for diffused aeration
2
(usually α = ka / ka = 0.40 – 0.80), θ is the Arrhenius constant or temperature correction coefficient
L (wastewater) L (clean water)
(usually θ = 1.015 – 1.040 and typically θ = 1.024) for both diffused and mechanical aeration applications, and others
(ThOR and T ) are defined in previous equations.
ww
6
[11] The peak factor (T : h/day) for oxidizing carbonaceous biological matter (or fluctuation factor for BOD
1 5
concentration) is selected depending on the equivalent population (E ), which is computed for a given amount of
p
wastewater (q: L/capita/day) discharged per capita and per day as follows (Toprak, 2000):
T 8 if E 5000
1 p

T 12 if 5000E 20,000
Q  1 p
Ep  q f(T1)TT11157 iiff 12000,0,00000EEp 10300,00,00000 (11)
 1 p
T 21 if E 300,000
 1 p
[12] The total hourly oxygen requirement (R : kg O /h) and the standard oxygen requirement (O: kg O /h) are also
o 2 c 2
determined as complementary alternatives to Eqs. (7) and (10), respectively, from the following equations (Eroglu,
1991; Toprak, 2000):
1  E QS   1 X/
Ro T1(a)10b0103iT2(kre) 103 (VR) (12a)
R  C  D R  C 
Oc oCww 10Cmin DT1w0w oCww 10Cmin(1.0188)(10Tww) (12b)
where T is the peak factor for oxidizing carbonaceous biological matter (or fluctuation factor for BOD concentration:
1 5
hour/day), a is the oxygen requirement for oxidizing carbonaceous biological matter (or oxygen requirement for
removing per unit of BOD : kg O /kg BOD ), T is the time factor for endogenous respiration (24 h/day), k is the
5 2 5 2 re
respiration rate coefficient (kg O /kg MLSS/day), σ is a correction factor for dissolved O saturation concentration, C is
2 2 10
the dissolved O concentration (mg O /L) at 10°C, D ve D are the diffusion coefficients (10-9 m2/s) at 10°C and
2 2 10 Tww
temperature T , respectively, and others (E , Q, S, X, φ, V , C , and C ) are given in previous parts.
ww b i R ww min
[13] Based on the data (Eroglu, 1991) showing the effect of the sludge load (L: kg BOD /kg MLSS/day) on the
s 5
respiration rate coefficient (k : kg O /kg MLSS/day), a third order inverse polynomial empirical function with a very
re 2
high determination coefficient (R2 = 0.9994, minimum residual = –0.00285, maximum residual = 0.00158) was also
derived by the author within the scope of the present study as follows:
QS 0.03705 4.07896103 1.39049104
Ls (X/)(iVR)kre 0.23173 Ls  Ls2  Ls3  (13)
[14] According to Eqs. (10) and (12b), the average standard oxygen requirement for the diffused aeration (SOR : kg
d
O /h), which is used as the first output variable (f ) in the subsequent modeling study, is obtained as follows to take
2 1
into account the effects of different parameters (i.e., F , T , k , etc.):
a 1 re
SORO
SORd  2 c f1(Xi)f1(X1,X2,X3,...,Xn) (14)
[15] Based on the value of standard oxygen requirement obtained from Eq. (14), the theoretical air requirement under
field conditions (ThARfc: m3/h), the theoretical air requirement (ThAR: m3/h), actual air requirement (AAR: m3/h),
and the air flow rate (Q ) in m3/min are computed from the following expressions:
b
SOR ThARfc AAR
ThARfc d ThAR AAR(ThAR)(SF) Q 
()O (%)/100 E a b 60 (15)
a 2 O2
where (SF) is the safety factor for air requirement, and others (SOR , ρ , O (%), and E ) are defined in previous
a d a 2 O2
equations.
[16] The daily energy consumption (E: kWh/day) of the diffused aeration system is computed based on the
c
assumption of adiabatic conditions as follows (Casey, 2009; Muslu, 1996b; Qasim, 1998):
(w)(R)(T )p 0.283  
Ec (Pm)(t) (8.41)(b0)  poiunt 1(SF)b(t) (16a)
Ec ((8Q.b41a)()(Rb))((6T0a s/2m7i3n))hL(Hpa/h1d0)1.1302.533/10.330.2831(SF)b(t) (16b)
where P is the total power requirement (kW) for blowers, t is the effective operating time (i.e., t = 24 h/day if the power
m
is supplied at full power all day), w is the air mass flow rate (kg/s), 8.41 is the constant (kg/kmol), η is the blower
b
efficiency for the diffused aeration system, T is the inlet or ambient air temperature (T =T + 273 [=] K), p is the
0 0 a out
absolute outlet or air supply pressure (atm), p is the absolute inlet or ambient barometric pressure (atm), ∑h is the total
in L
head losses (see Table 1) in air piping system and diffusers (m), h is the distance between the bottom of the areation
d
7
basin and the top of submerged diffusers, (SF) is the safety factor for blower power, and others (Q , ρ , R, T , p , and H)
b b a a a
are explained in previous steps.
[17] According to Eq. (16b), the daily energy consumption (E: kWh/day) of the diffused aeration system, which is
c
considered as the second output variable (f ) in the nonlinear regression analysis, is defined as follows:
2
Ec (Pm)(t)f2(Xi)f2(X1,X2,X3,...,Xn) (17)
[18] Finally, the total mass transfer coefficient for the diffused aeration (ka : day–1) is computed from the following
L d
equation (Henderson, 2002):
()(R )(Hh )(Q )(60 min/h)(24 h/day)
kLad  f air d (Cb)(V ) (18)
20 R
where α is the admixtures correction factor, R is the O flow per volume and immersion depth in clean water at S = 0
f air 2 0
and a specified temperature T = 20°C (g/m3/m), and others (H, h , C , and V ) are expressed in previous equations.
d 20 R
[19] Based on the gas/liquid mass transfer (film or penetration) theory, ka describes the oxygen transfer coefficient
L d
for the diffused aeration, which has the dimension of the inverse of time, a is defined as A /V (where A : total gas
d G L G
surface [=] m2, and V: liquid volume [=] m3) and describes the interfacial area (m2/m3) in diffused aeration, while k
L L
is the liquid film coefficient (m/s) and describes the velocity of the transport (Henkel, 2010).
According to Eq. (19), the total mass transfer coefficient for the diffused aeration (ka : day–1), which is considered as
L d
the third output variable (f ) in the nonlinear regression analysis, is given as follows:
3
kLad f(f,Rair,H,hd,Qb,C20,VR)f3(Xi)f3(X1,X2,X3,...,Xn) (19)
Table 2. Design parameters and assumptions to be used in the computational analysis
Constituents Values used in the computational analysis
Empirical formula of bacteria cells C H NO (MW = 113 g/mol) (Yetilmezsoy,
5 7 2
2010; Comeau, 2008)
Ultimate biochemical oxygen demand (BOD ≈ COD) of per kg of bacteria A = 1.42 g O equivalent/g cell (MLVSS)
u 2
cells (or oxygen requirement for oxidizing per unit of biomass) (Yetilmezsoy, 2010; Martinez et al., 2004)
Biodegradable fraction of X (in terms of effluent total suspended solids f = 65% (Muslu, 1996b; Toprak, 2000)
e b
concentration)
Substrate decay coefficient k = 0.1 day–1 (Yetilmezsoy, 2010)
Ratio of BOD to ultimate BOD (BOD ) ψ = BOD /BOD = 0.68 (Celenza, 1999)
5 u 5 u
Propotionality factor (or overall heat transfer coefficient) f = 0.50 (Muslu, 1996b; Celenza, 1999)
Oxygen transfer efficiency of air diffusers (or mass of O transferred/mass 8% or E = 0.08 (Qasim, 1998)
2 O2
of O supplied) (E = 0.06 – 0.12)
2 O2
Salinity surface tension factor (a ratio of O saturation concentration in β = 0.90 (Roman and Mureşan, 2014; Qasim,
2
wastewater to that in tap water) for wastewater (β = 0.70 – 0.98) 1998; Toprak, 2000)
Minimum dissolved O concentration maintained in the areation basin C = 1.5 mg/L (Bolles, 2006; Toprak, 2000;
2 min
(C = 1.0 or 1.5 – 2.0 mg/L) Ghangrekar and Kharagpur, 2014)
min
Oxygen transfer correction factor (a ratio of O transfer in wastewater to α = 0.75 (Roman and Mureşan, 2014; Qasim,
2
that in tap water) for diffused aeration (α = 0.4 – 0.8) 1998)
Arrhenius constant or temperature correction coefficient (θ = 1.015 – θ = 1.024 (Qasim, 1998; Toprak, 2000)
1.040) for diffused aeration application
Safety factors for air requirement and blower power (SF) = 1.50 (Bolles, 2006; von Sperling,
a
2007) and (SF) = 1.20, respectively.
b
Blower efficiency for diffused aeration systems (η = 0.70 – 0.90) 75% or η = 0.75 (Bolles, 2006)
b b
Amount of wastewater discharged per capita and per day q = 200 L/capita/day
Oxygen requirement for oxidizing carbonaceous biological matter (or a = 0.5 kg O /kg BOD (Eroglu, 1991; Toprak,
2 5
oxygen requirement for removing per unit of BOD ) (a = 0.45 – 0.65 kg 2000)
5
O /kg BOD )
2 5
Respiration rate coefficientused for computation of R . k = 0.010 – 0.20 kg O /kg MLSS/day
o re 2
depending on the L (Eroglu, 1991)
s
Peak factor for oxidizing carbonaceous biological matter (or fluctuation T = 8 – 21 h/day depending on the
1
factor for BOD concentration) (T = 8 – 21 hour/day) equivalent population (Toprak, 2000)
5 1
Time factor for endogenous respiration T = 24 h/day (Toprak, 2000)
2
A correction factor for dissolved O saturation concentration(σ = 0.60 – σ = 0.80 (Eroglu, 1991; Toprak, 2000)
2
0.90 for wasterwater, and σ = 1.0 for pure water)
Oxygen flow per volume and immersion depth in clean water (S = 0, T = R = 16 g/m3/m (Makinia and Wells, 2000)
0 air
20°C)
8
Total head losses in air pipings = 5-25 cm 25 cm (Muslu, 1996b; Qasim, 1998)
Air filter losses for the centrifugal blower = 13-76 mm 50 mm (Muslu, 1996b; Qasim, 1998)
Silencer losses for the centrifugal blower = 13-38 mm 30 mm (Muslu, 1996b; Qasim, 1998)
Check valve and fittings losses = 20-203 mm 200 mm (Muslu, 1996b; Qasim, 1998)
Diffuser losses for fine bubble aeration = 40-50 cm 400 mm (Muslu, 1996b; Qasim, 1998)
Allowance for clogging of diffusers and miscellaneous head losses under 100 cm (Muslu, 1996b; Qasim, 1998)
emergency conditions
Depth of submergence (water depth above the diffusers) (H – h ) = (H – 0.30) m (Muslu, 1996b;
d
Qasim, 1998)
2.4. Computational procedure
In this study, MATLAB® R2009b (V7.9.0.529, The MathWorks, Inc., Natick, MA, US) and DataFit® (V8.1.69, Oakdale
Engineering, PA, US) softwares running on a CPU N280 (Intel® Atom™ Processor 1.66 GHz, 0.99 GB of RAM) PC, were used
for simulation and modeling purposes, respectively. The main structure of the present calculation protocol and the
corresponding computational pathways are depicted in Figure 2.
In the first step of the computational analysis, A MATLAB®-based algorithm (Figure 2) was constructed for the processing
of a series of compulsory design calculations (i.e., several biological conversions, determination of reactor volume,
definition of a heat mass balance around the aeration basin, calculation of air pressure as a function of the elevation factor,
determination of the saturation concentration of the oxygen at operating temperature, determination of oxygen content
and density of air as a function of absolute atmospheric pressure at elevation above sea level, formulation of equivalent
population as a function of peak factor (or fluctuation factor for BOD ), computation of required blower power, etc.) based
5
on the theoretical procedure (see Section 2.2).
In the second step of the computational analysis, a total of 500 different operating scenarios were implemented at random
for simulating a wide range of thirteen inputs consisting of thirteen fundamental biological, hydraulic, and physical
variables (see Section 2.1). Then the simulated data was stored as a [500×16] matrix (for X and Y, i = 1,2,..13 and j = 1,2,3)
i j
in the workspace of MATLAB® software for the further nonlinear regression-based analysis (see Section 2.5). Data statistics
of the simulated operating variables in the present computational analysis are summarized in Table 3.
START
for and length loop
Introduction of model variables Simulation step: X = Xmin + (Xmax- Xmin) * rand (1, n) 1) Effluent soluble substrate concentration Implementation of process control
2) Biological treatment efficiency to describe the new input components
3) Volume of the aeration basin
X1 = Influent wastewater flow rate (m3/sec) 4) Food to microorganism (F/M) ratio
X2 = Mean cell residence time (days) 5) Volumetric organic loading
X3 = Growth yield coefficient (kg MLVSS/kg BOD5) 6) Hydraulic retention time (HRT) Development of process control strategy
X4 = Influent soluble substrate concentration (kg BOD5/m3) 7) Sludge recirculation ratio
X5 = Concentration of the cells (volatile suspended solids) in the reactor (kg MLVSS/m3) 8) Excess sludge mass flow rate
X6 = Volatile suspended solids to total suspended solids ratio (kg MLVSS/kg MLSS) 9) Wastewater temperature within the aeration basin
X7 = Effluent total substrate concentration (kg BOD5/m3) 10) Air pressure and density of air
X8 = Effluent total suspended solids concentration (kg MLSS/m3) 11) Effective oxygen percentage
XXXXX91111 0123= ==== M EAIAinclmvferleouvbroeaiaerntgginote atnw naw aoiiSsrasr mt sttoaeetr elmweetiwtndapua dteidentoreer ag tr thtae eudebnmre ooeWppvu (teoesh°rrC aksdin)seteu pactrha aelecey e( v a°ceCroel )e(amftfiioc)ine nbta (sdina y(m-1)) 11111112345678))))))) TDSTCEShotqliousaetumasdnoiolvgdp rhlaeearveol treelidhuocdn eara otlo nyldx pxo s yooayixgvxpngyeeyudegn gl noear e rxentsneiys oa rqgprnetueeuiqriqnraruaeu tisitrmioireooenemlnum nr becate inotl(nietSntty cOc efoaRnec)tftrfoaicrtiieonnt Dfoer soirbejedc rteivseYtrsiEc ?Stions NO
19) Theoretical air requirement under field conditions
Definition of design factors and assumptions Table 1 20) Total power requirement for blowers 1) Standard oxygen requirement (SOR) = Y1
Stored in the Workspace 2212)) DToatialyl emnaesrsg ytr aconnsfseurm cpoteioffnicient 32)) TDoatialyl menaesrsg ytr acnosnfseurm copetioffnic i=e nYt 2= Y3
Formulation of biological, hydraulic, physical variables Stored in the Workspace
Stored in the Workspace
Data validation SIMULATED DATA Data verification
Existing literature data Statistical analysis Testing set
Stored in the Workspace
END
Figure 2. Flowchart of the computational prediction process in MATLAB® environment
Table 3. Data statistics of the simulated operating variables considered in the present computational analysis (n = 1000 for
each variable)
Component Units Minimum Maximum Average SDa
Input variables (X)
i
X = Q [m3/sec] 0.047 0.579 0.323 0.150
1
X = θ [days] 5.03 14.97 10.27 2.87
2 c
X = Y [kg MLVSS/kg BOD ] 0.401 0.799 0.606 0.115
3 5
X = S [kg BOD /m3] 0.20 0.40 0.30 0.059
4 i 5
X = X [kg MLVSS/m3] 2.0 5.48 3.77 1.05
5
X = φ [kg MLVSS/kg MLSS] 0.600 0.899 0.744 0.091
6
X = S [kg BOD /m3] 0.020 0.045 0.033 0.007
7 e 5
X = X [kg MLSS/m3] 0.005 0.020 0.013 0.004
8 e
X = k [day–1] 0.040 0.075 0.057 0.010
9 d
X = T [°C] –5.0 30.0 12.7 10.6
10 a
9
X = T [°C] 5.0 24.9 15.2 5.8
11 i
X = H [m] 3.0 5.0 3.98 0.59
12
X = H [m] 3 2998 1511.5 857.6
13 a
Output variables (Y)
i
Y = SOR [kg O /h] 60.70 1676.5 608.8 319.7
1 d 2
Y = E [kWh/day] 3441.3 149,630 41,031 25,811
2 c
Y = ka [day–1] 159.73 2324.8 709.79 333.07
3 L d
aStandard deviation
2.5. Nonlinear regression analysis-based modeling 2.6. Verification of simulation results
The simulated data was imported from the MATLAB® Finally, the predictive capabilities of the developed models
workspace used as an open database connectivity data were tested against the results of a total of 1500 additional
source, and then the nonlinear regression analysis was and different computational scenarios. For this purpose,
conducted within the framework of DataFit® software the overall testing set (a total of 24,000 different data
package containing 298 two-dimensional (2D) and 242 points composed of an input matrix of [1500×13] and an
three-dimensional (3D) nonlinear regression models. The output matrix of [1500×3]) was randomly allocated into
nonlinear convergence criteria were selected for the three sub-testing groups (as three [500×16] matrices
following values of the solution preferences: regression including output variables) for each model (i.e., n = 500 for
1
tolerance = 1×10–10, maximum number of iterations = 1000, SOR , n = 500 for E and n = 500 for ka , where n , n , n
d 2 c 3 L d 1 2 3
and diverging nonlinear iteration limit = 10. When are the number of randomly generated testing scenarios)
performing the nonlinear regression, the Richardson’s to evaluate the predictive capability of the proposed
extrapolation method was used to calculate numerical formulations.
derivatives for the solution of the models (see Section 3.1).
2.7. Statistical analysis
The nonlinear regression analysis was conducted based on
the Levenberg–Marquardt method with double precision. In order to describe the overall performance of the
Each independent operating variable (X) was assumed to proposed equations, quantifying the goodness of the
i
be equally important (I = 1.0), and no particular safety estimate should be implemented as a crucial part of the
i
precautions were considered in the construction of the model development (Yetilmezsoy and Abdul-Wahab,
models, as similarly conducted in the previous studies of 2014). For this purpose, various descriptive statistical
the author (Yetilmezsoy, 2010; Yetilmezsoy, 2012; indicators such as coefficient of determination (R2), mean
Yetilmezsoy, 2016; Yetilmezsoy and Sapci-Zengin, 2009; absolute error (MAE), root mean square error (RMSE),
Yetilmezsoy, 2005; Yetilmezsoy, 2006; Yetilmezsoy, 2007; systematic and unsystematic RMSE (RMSES and RMSEU,
Yetilmezsoy and Sakar, 2008; Yetilmezsoy, 2012; respectively), index of agreement (IA), the factor of two
Yetilmezsoy and Abdul-Wahab, 2014). (FA2), fractional variance (FV), proportion of systematic
error (PSE), coefficient of variation (CV) and Durbin–
In the computational analysis, the stepwise selection
Watson statistic (DW) were computed as helpful
procedure (SSP) was performed as the combination of the
mathematical tools and robust statistics to assess the
forward selection and backward elimination procedures for
model’s prediction performance and determine the
variable selection process within the framework of DataFit®
residual error of the estimation.
software. The SSP begins with a forward step (with no
variables in the model). After the forward step, the p values The obtained output data (SORd, Ec, and kLad) were
of the variable coefficients are re-examined and any now statistically evaluated by means of several appropriate
insignificant variables are removed in a backward step. This parametric (unpaired or two-sample and matched-pair t
process continues until no variables are either added or tests) or non-parametric tests (the Mann-Whitney U (or the
removed from the model. The SSP is more generally Wilcoxon rank-sum) test and the Kruskal-Wallis test with
popular than either the forward or backward procedures. the Dwass-Steel-Chritchlow-Fligner method). Prior to
applying parametric tests, the Shapiro-Wilk W and the
As the nonlinear regression models were solved on the
Levene’s tests were consecutively implemented as
DataFit® numeric computing environment, they were
preconditions to ensure that the considered subsets
automatically sorted according to the goodness-of-fit
(theoretically calculated values and predicted values) had a
criteria into a graphical interface. Additionally, regression
normal or non-normal distribution, and variances (or
variables (i.e., β and β , β , β , …, β ), standard error of
0 1 2 3 13
standard deviations) of the paired groups were
the estimate (SEE), coefficient of multiple determination
homogeneous or unequal. When the output values were
(R2), adjusted coefficient of multiple determination (R 2),
a
not normally distributed, non-parametric tests were
number of nonlinear iterations (NNI) were computed to
implemented. Results were assessed with two-tailed p
evaluate the performance of the regression models.
values to reflect the statistical significance between paired
Moreover, t-ratios and the corresponding p-values were
groups (α = 0.05 or 95% confidence). The parametric or
also calculated for the appraisal of the significance of the
non-parametric tests were conducted by using a licensed
regression coefficients. An alpha (α) level of 0.05 (or 95%
statistical software package (StatsDirect, V2.7.2,
confidence) was used to determine the statistical
StatsDirect Ltd., Altrincham, Cheshire, UK).
significance of the model components.
10
Based on the other descriptive statistics (i.e., minimum, 3.1. Proposed formulations and estimation of SOR , E and
d c
lower quartile (Q ), median (Q ), upper quartile (Q ), ka
1 2 3 L d
maximum) of independent samples (theoretical data and
The computational analysis including a total of 8000
testing outputs), box-and-whisker plots were also drawn by
different data points (or 500 random operating scenarios in
writing a solution script in the M-file Editor within the
the form of a [500×16] matrix for X and Y, where i =
framework of MATLAB® software to appraise the statistical i j
1,2,..,13 and j = 1,2,3) was carried out for thirteen input and
results in a pictorial manner. The built-in functions
three output variables. The results of the nonlinear
boxplot([x1,x2],'Param1',val1,
regression analysis give the final form of the proposed
'Param2',val2,...) (Statistics Toolbox) and
models as a new function of the selected biological,
subplot(m,n,p) (MATLAB® Function Reference) were
hydraulic, and physical design variables in Eqs. (20)–(21).
implemented in MATLAB® for creating these types of
These are shown below.
display.
3. Results
f 2.93Q0.024 0.077Y 3.64S 0.0097X 0.281 (20)
1 c i
3.28S 2.58X 0.227k 0.0005T 0.0048T 0.0162H
e e d a i
0.00003H 4.19SOR expf 
a d 1
f 2.92Q0.024 0.101Y 3.72S 0.013X 0.257 (21)
2 c i
3.2S 2.01X 0.403k 0.0036T 0.005T 0.088H
e e d a i
0.00045H 7.23E expf 
a c 2
f 0.177Q0.048 1.88Y 0.063S 0.271X 0.246 (22)
3 c i
0.153S  X 6.42k 0.0001T 0.0038T 0.253H
e e d a i
0.00032H 5.34k a expf 
a L d 3
where Q is the influent wastewater flow rate (m3/sec), Y is ≈ 0.0000). Additionally, the calculated F value (S2/S 2 = F
r e cal-
the growth yield coefficient (kg MLVSS/kg BOD ), S is the = 1189.3725) was found to be greater than the critical (or
5 i 1
influent soluble substrate concentration (kg BOD /m3), θ is tabulated) F value (F ) = F = S2/S 2 = F =
5 c α,df,n−(df+1) 0.05,13,486 r e cr
the mean cell residence time (days), S is the total effluent 1.7403) at the 5% level, indicating that the computed
e
substrate concentration (kg BOD /m3), X is the effluent Fisher’s variance ratio at this level was large enough to
5 e
total suspended solids concentration (kg MLSS/m3), and k justify a very high degree of adequacy of the SOR model.
d d
is the microorganism endogenous decay coefficient (day–1), According to the Fisher’s F-test, the ANOVA indicated that
X is the concentration of the cells in the reactor (kg the proposed E model was also highly significant (F =
c model-2
MLVSS/m3), φ = X/X is the volatile suspended solids to 1765.5427 >> F = 1.7403, Prob(F) ≈ 0.0000).
TSS cr model-2
total suspended solids ratio (kg MLVSS/kg MLSS), T is the Furthermore, the Fisher’s F-test concluded with 95%
a
ambient air temperature (°C), T is the influent wastewater certainty that the proposed ka model explained a
i L d
temperature (°C), H is the elevation or altitude above sea significant amount of the variation in the dependent
a
level (m), and H is the average wastewater depth in the variable (F = 2085.9952 >> F = 1.7403, Prob(F)
model-2 cr model-3
areation basin (m). ≈ 0.0000).
The relationship between the proposed models given in In the literature, it has been reported that the t-ratio
Eqs. (20)–(21), and the steady-state theoretical data is represents the ratio of the estimated parameter effect to
outlined in Figure 3. The determination coefficients (R2 = the estimated parameter standard deviation. Moreover,
0.9704 for SOR , R2 = 0.9795 for E, and R2 = 0.9824 for ka ) the p-value is used as a useful tool to check the significance
d c L d
demonstrated that only 2.95%, 2.05%, and 1.77% of the of each of the coefficients. The variable with the larger t-
total variations were unexplained by the proposed SOR , E, ratio and with the smaller p-value is considered as the more
d c
and ka models respectively. As seen from Figure 3, the significant parameter in the regression model (Yetilmezsoy
L d
predictions of Eqs. (20)–(21) correspond very well with the and Sapci-Zengin, 2009; Yetilmezsoy and Sakar, 2008;
theoretical values, implying that the proposed equations Yetilmezsoy et al., 2009; Yetilmezsoy and Abdul-Wahab,
satisfactorily account for the prediction of the aeration- 2012). It is also noted that values that yield Prob(t) factors
related parameters in a wide range of the studied variables. (or p-values) of greater than 0.9 may be neglected until all
remaining factors are calculated at once (Fingas and
The analysis of variance (ANOVA) showed that the
Fieldhouse, 2009). In other words, the Prob(t) or p-value is
proposed SOR model was highly significant, as was evident
d
the probability that input can be dropped without affecting
from the Fisher’s F-test ((MS) /(MS) = F =
model-1 error-1 model-1
the regression or goodness-of-fit (Yetilmezsoy et al., 2011).
1189.3725) with a very low probability value (Prob(F)
model-1