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A Study of the Determination of Dimensionless Number and its Influence on the Performance of a Combination Wastewater Reactor
Available online at www.sciencedirect.com
Procedia Environmental Sciences 18 (2013) 579 – 584
2013 International Symposium on Environmental Science and Technology (2013 ISEST)
A study of the determination of dimensionless number and its influence on the performance of a combination wastewater reactor Shiqiang Ding, Lei Liu, Jirun Xu* College of Environmental and Chemical Engineering, Dalian University, Dalian 116622, China
Abstract Dimensionless Peclet number is applied to describe the flow behavior in a specially designed wastewater reactor with compound flow pattern of plug-flow, baffled-flow and mixed-flow. A set of Peclet numbers is obtained for different fluid conditions by measuring the residence time distribution of a tracer in the reactor. Some experiments were made to examine the quantitative influence of on the removal efficiency of COD, NH4+-N and TP, and the results shown that there is an optimum number representing a certain flow pattern at which best removal rates of COD, NH4+-N and TP are obtained. © 2013 The The Authors. Authors. Published Publishedby byElsevier ElsevierB.V. B.V. © 2013 Institute of Technology. Selection and/or peer-review under responsibility of Beijing Selection and peer-review under responsibility of Beijing Institute of Technology. Keywords: compound flow reactor; determination of number;removal rates vs Pe number
1. Introduction It is obvious that the sewage treatment has to be influenced by the flow pattern in the reactor where the sewage processed. In theory, the flow patterns in wastewater reactors can be divided into plug-flow, completely mixed-flow and the combination-flow of both plug and mixed. Usually the dimensionless Peclet number, noted as Pe is used to quantitatively describe the ratio of plug-flow to mixed-flow in an actual reactor with compound-flow pattern [1]. The Pe is defined as uL (1) Pe Ex with
u the characteristic velocity, L the characteristic length and Ex the characteristic diffusion
* Corresponding author. E-mail address: [email protected].
1878-0296 © 2013 The Authors. Published by Elsevier B.V.
Selection and peer-review under responsibility of Beijing Institute of Technology. doi:10.1016/j.proenv.2013.04.078
580
Shiqiang Ding et al. / Procedia Environmental Sciences 18 (2013) 579 – 584
coefficient in the direction of fluid movement. When Pe tends to infinity, there’s no mixing and the flow pattern is ideal plug-flow, when Pe tends to 0, the flow pattern is completely mixed-flow [2, 3]. Apparently, the limit state of Pe tends to infinity or Pe tends to 0 is not of great value in the practical application. Murphy et al[4] found the system can be considered to be completely mixed when Pe 0.5 ; Khudenko et al [5] proposed that the system can be regarded as completely-mixed flow when Ex ! 0.5 4 , and considered to be an ideal plug-flow when Ex 0.05 0.2 . Lee [6], Tang et al [7] studied the concentration distribution of activated sludge system in a reactor with Pe varying from 0.1 to 50, the results indicated that the concentration gradient of activated sludge in the reactor is enlarged with the increase of Pe along the flow direction, while Pe 1 the concentration is little changed. This means that the pollutant removal in a reactor is positively affected by the flow pattern. In this paper, a reactor with a compound flow pattern of plug-flow, baffled-flow and completely mixedflow is designed and the Pe number is determined experimentally as well as the influence of Pe number on the pollutant removal examined. 2. The reactor with compound flow pattern As shown in Fig. 1, the specially-designed reactor used in the experimental research was composed of 6 units with same dimension. The units are separated with movable plates or settled plates. The movable plates can move up or down to control the intensity of baffle-flow. The flow pattern in the reactor is a combination of plug-flow, baffle-flow and mixed-flow.
1 regulating tank; 2 pump; 3 rotometer; 4 movable baffle plate; 5 settled plate;6 anaerobic reaction cell˗7 anoxic reaction cell; 8 aerobic reaction cell; 9 secondary sedimentation tank;10 drained water; 11 recycled sludge; 12 drained sludge Fig. 1.Schematic diagram of the reactor.
Sewage used in the experiment was artificially prepared and its chemical composition is listed in Table 1. The pollutant removal efficiency is determined by measuring MLSSˈSV30ˈCODˈTPˈTN NH4+N ˈ NO3--N in the original and drained sewage respectively, with all the measuring methods corresponding to the National Standards. The sludge is taken from A/O process of a sewage treatment plant, with sludge concentration of 7418mg / L, poor settling characteristics, SV 30 greater than 85%. Table 1. Sewage chemical composition. Species
Content (mg/L)
NaAc
500
(NH4)2SO4
150
KH2PO4
50
CaCl2·H2O
40
MgSO4·7H2O
30
EDTA
20
581
Shiqiang Ding et al. / Procedia Environmental Sciences 18 (2013) 579 – 584
3. Determination of Pe number 3.1. Theoretical basis The dimensionless Pe number is determined by tracer method. After the fluid flow state is stable in the
c 0 is added continuously at the feed end, meanwhile the tracer concentration c t in the drain that is a function of time t is measured, then the a tracer residence time reactor, a tracer with concentration
distribution obtained and the Pe number determined. Defining the tracer mean residence time as tm L / u and the dimensionless time as T dimensionless residence time distribution function can be derived as follows [1]: §1 1 T ·º c t 1 ª ¸» F T Pe «1 erf ¨¨ 2 ¬« c0 T ¸¹¼» ©2 where erf
is the error function, defined as
2
erf y
S
t / tm , the tracer
(2)
2
s ³0 e ds . y
From Eq.2 the dimensionless residence time distribution density function is got:
dF T dT
ª 1 T 2 º exp « » «¬ 4T / Pe »¼ 4 ST 3 / Pe 2 As well as the residence time distribution variance V T derived: E T
1
(3)
uL 2 · § ¨1 e E ¸ 2 2§¨ 1 ·¸ 1 e Pe (4) ¸ Pe ¨ Pe ¹ © ¹ © Eq.3 and Eq.4 show that, if the tracer residence time distribution is measured, then the distribution 2 variance V T calculated and Pe number or diffusion coefficient Ex obtained. In actual work, the continuous function formulated as Eq.3 is processed by discrete method. According to the definition, the density function of residence time distribution of the tracer in the reactor c t , then the discrete form of E t is written as: is E t f ³0 c t dt
VT 2
§E · §E · 2¨ x ¸ 2¨ x ¸ © uL ¹ © uL ¹
2
x
E t
ci t c ¦ i t 'ti
(5)
The average residence time is calculated from:
¦ ti ci t 'ti ¦ ti ci t (6) ¦ ci t ¦ ci t 'ti where ci t is the tracer concentration in the i -the drain sample, 'ti is the sampling time interval, and ti the i -the sampling time. tm
The variance of the residence time distribution density function is defined as V t written as summation form:
³0 t tm E t dt , f ³0 E t dt f
2
2
582
Shiqiang Ding et al. / Procedia Environmental Sciences 18 (2013) 579 – 584
Vt2
while
the
variance
of
¦ ti E t 't i 2 tm ¦ E t 'ti
the
¦ ti E t 2 tm ¦ E t
2
dimensionless
2
residence
time
(7) distribution
function
E T
is
V T 2 = ³0f T 1 E T dT 2
From which substituting T with t / tm following equation can be derived: VT 2
Vt2 tm
(8)
2
According to Eqs.5-8 the distribution variance V T can be calculated step by step from the experimental results, then the Pe number determined by Eq.4. 2
3.2. Measurement results of Pe A KMnO4 solution with concentration of 0.1 g / L is used as tracer, the concentration of tracer in the drain water is measured by using of a visible light spectrophotometer. Influent flow rate in the test were 15, 30, 45, 60 L / h respectively, and different influent flow rate represents different HRT, so at the sampling time for different influent flow rate should be different from each other. Specific sampling time is listed in table 2. Table 2. Sampling time and frequency for different flow rate. Influent flow rate(L/h)
Time interval(min)
Frequency
15 30 45 60
30 20 15 10
12 13 10 10
To save space, here only are given in Table 3 the measurement results when inlet flow rate is 15 L / h . Table 3. Measured tracer concentration. Number of times
min
Concentration (g/L)
1
0
0
2
15
0
3
30
0.027
4
45
0.042
5
60
0.058
6
75
0.062
7
90
0.085
8
105
0.091
9
120
0.089
10
135
0.092
583
Shiqiang Ding et al. / Procedia Environmental Sciences 18 (2013) 579 – 584
According to Eqs.5 to 8, the mean residence time, distribution variance for actual time and 2 2 dimensionless time are calculated in steps as tm =93.7minˈ V t =2581.2min2 ˈ V T =0.294 from the experiment results. The direct calculation of Pe number is more or less difficult from Eq.4, but it can be obtained by trial and error method. It can be seen that in Eq.4, the larger the value of Pe , the smaller the value of V T 2 . Optionally an initial value of Pe is selected and substituted into the right side of Eq.4 to calculate a value of V T 2 , if the value of V T 2 obtained is greater than 0.294 a larger Pe is selected otherwise a smaller Pe selected until the calculated result is 0.294 approximately. In the present embodiment, the trial and error method gives Pe = 5.6. 4. The effect of Pe number
WHVWQXPEHU
SHFOHWQXPEHU
UHPRYDORI&2'˄˅
The effect of Pe number on the removal of CODǃNH4+-N and TP are illustrated Fig. 2ˈFig. 3 and Fig. 4 respectively.
UHPRYDOUDWHRI&2' SHFOHWQXPEHU
Fig. 2. COD removal rate vs. Pe .
WHVWQXPEHU UHPRYDOUDWHRI1+1 SHFOHWQXPEHU
Fig. 3. NH4+-N removal rate vs. Pe .
SHFOHWQXPEHU
UHPRYDOUDWHRI1+1
Shiqiang Ding et al. / Procedia Environmental Sciences 18 (2013) 579 – 584
UHPRYDOUDWHRI73˄˅
SHFOHWQXPEHU
584
WHVWQXPEHU
UHPRYDOUDWHRI73 SHFOHWQXPEHU
Fig. 4. TP removal rate vs. Pe .
5. Conclusion The flow pattern in the sewage reactor has an important impact on the treatment results. It can be seen that dimensionless Pe number plays a useful part in the demonstration of the relative portion of plug-flow and mixed-flow in actual reactor. In the study mentioned above, there are three factors that determine Pe number, including the influent flow-rate, the mixing speed and the gaps between movable plate and reactor bottom. These factors are representing plug-flow, baffled-flow and mixed-flow respectively. In the specially designed reactor, the best removal efficiency of COD, NH4+-N and TP of analog sewage are obtained when Pe is 1.38. In a word, there is an optimum range of Pe number where better pollutant removal can be expected.
References [1] Zhu Bingchen. Chemical reaction engineering. (in Chinese) 4rd ed. Beijing: Chemical Industry Press; 2007. [2] Zhangzi Jie. Activated sludge biological kinetics.(in Chinese) 1rd ed. Beijing: China Environmental Science Press; 1985. [3] GuoM X, Sun P D, Wang R Y, et al. Biological-Hydraulic-Temperature coupled model (FCASM3-Hydro-Temp) for activated sludge system Part 3:Hydraulic and temperature effects. (in Chinese with English abstract) J Acta Scientiae Circumstantiae 2008; 28 (12): 2449 – 2455. [4]Murphy K L, Timpany P L.Design and analysis of mixing for anaeration tank J San Eng ASCE. 1967; 93(5):1-15. [5]Khudenko B M, Shpirt E. Hydrodynamic parameters of diffused air systems. J Wat Res˗1986; 20(7):905-915 [6] Lee T, Newell R B, Wang F Y.Dynamic modeling and simulation of activated sludge process using orthogonal collocation roach J Wat Res. 1999; 32(1):73ü86. [7]Tang Ke. et al. Impact of Peclet number on heat transfer of oscillatory flow in circular channel. J CRYOGENICS.2011; 3:1-5.
Procedia Environmental Sciences 18 (2013) 579 – 584
2013 International Symposium on Environmental Science and Technology (2013 ISEST)
A study of the determination of dimensionless number and its influence on the performance of a combination wastewater reactor Shiqiang Ding, Lei Liu, Jirun Xu* College of Environmental and Chemical Engineering, Dalian University, Dalian 116622, China
Abstract Dimensionless Peclet number is applied to describe the flow behavior in a specially designed wastewater reactor with compound flow pattern of plug-flow, baffled-flow and mixed-flow. A set of Peclet numbers is obtained for different fluid conditions by measuring the residence time distribution of a tracer in the reactor. Some experiments were made to examine the quantitative influence of on the removal efficiency of COD, NH4+-N and TP, and the results shown that there is an optimum number representing a certain flow pattern at which best removal rates of COD, NH4+-N and TP are obtained. © 2013 The The Authors. Authors. Published Publishedby byElsevier ElsevierB.V. B.V. © 2013 Institute of Technology. Selection and/or peer-review under responsibility of Beijing Selection and peer-review under responsibility of Beijing Institute of Technology. Keywords: compound flow reactor; determination of number;removal rates vs Pe number
1. Introduction It is obvious that the sewage treatment has to be influenced by the flow pattern in the reactor where the sewage processed. In theory, the flow patterns in wastewater reactors can be divided into plug-flow, completely mixed-flow and the combination-flow of both plug and mixed. Usually the dimensionless Peclet number, noted as Pe is used to quantitatively describe the ratio of plug-flow to mixed-flow in an actual reactor with compound-flow pattern [1]. The Pe is defined as uL (1) Pe Ex with
u the characteristic velocity, L the characteristic length and Ex the characteristic diffusion
* Corresponding author. E-mail address: [email protected].
1878-0296 © 2013 The Authors. Published by Elsevier B.V.
Selection and peer-review under responsibility of Beijing Institute of Technology. doi:10.1016/j.proenv.2013.04.078
580
Shiqiang Ding et al. / Procedia Environmental Sciences 18 (2013) 579 – 584
coefficient in the direction of fluid movement. When Pe tends to infinity, there’s no mixing and the flow pattern is ideal plug-flow, when Pe tends to 0, the flow pattern is completely mixed-flow [2, 3]. Apparently, the limit state of Pe tends to infinity or Pe tends to 0 is not of great value in the practical application. Murphy et al[4] found the system can be considered to be completely mixed when Pe 0.5 ; Khudenko et al [5] proposed that the system can be regarded as completely-mixed flow when Ex ! 0.5 4 , and considered to be an ideal plug-flow when Ex 0.05 0.2 . Lee [6], Tang et al [7] studied the concentration distribution of activated sludge system in a reactor with Pe varying from 0.1 to 50, the results indicated that the concentration gradient of activated sludge in the reactor is enlarged with the increase of Pe along the flow direction, while Pe 1 the concentration is little changed. This means that the pollutant removal in a reactor is positively affected by the flow pattern. In this paper, a reactor with a compound flow pattern of plug-flow, baffled-flow and completely mixedflow is designed and the Pe number is determined experimentally as well as the influence of Pe number on the pollutant removal examined. 2. The reactor with compound flow pattern As shown in Fig. 1, the specially-designed reactor used in the experimental research was composed of 6 units with same dimension. The units are separated with movable plates or settled plates. The movable plates can move up or down to control the intensity of baffle-flow. The flow pattern in the reactor is a combination of plug-flow, baffle-flow and mixed-flow.
1 regulating tank; 2 pump; 3 rotometer; 4 movable baffle plate; 5 settled plate;6 anaerobic reaction cell˗7 anoxic reaction cell; 8 aerobic reaction cell; 9 secondary sedimentation tank;10 drained water; 11 recycled sludge; 12 drained sludge Fig. 1.Schematic diagram of the reactor.
Sewage used in the experiment was artificially prepared and its chemical composition is listed in Table 1. The pollutant removal efficiency is determined by measuring MLSSˈSV30ˈCODˈTPˈTN NH4+N ˈ NO3--N in the original and drained sewage respectively, with all the measuring methods corresponding to the National Standards. The sludge is taken from A/O process of a sewage treatment plant, with sludge concentration of 7418mg / L, poor settling characteristics, SV 30 greater than 85%. Table 1. Sewage chemical composition. Species
Content (mg/L)
NaAc
500
(NH4)2SO4
150
KH2PO4
50
CaCl2·H2O
40
MgSO4·7H2O
30
EDTA
20
581
Shiqiang Ding et al. / Procedia Environmental Sciences 18 (2013) 579 – 584
3. Determination of Pe number 3.1. Theoretical basis The dimensionless Pe number is determined by tracer method. After the fluid flow state is stable in the
c 0 is added continuously at the feed end, meanwhile the tracer concentration c t in the drain that is a function of time t is measured, then the a tracer residence time reactor, a tracer with concentration
distribution obtained and the Pe number determined. Defining the tracer mean residence time as tm L / u and the dimensionless time as T dimensionless residence time distribution function can be derived as follows [1]: §1 1 T ·º c t 1 ª ¸» F T Pe «1 erf ¨¨ 2 ¬« c0 T ¸¹¼» ©2 where erf
is the error function, defined as
2
erf y
S
t / tm , the tracer
(2)
2
s ³0 e ds . y
From Eq.2 the dimensionless residence time distribution density function is got:
dF T dT
ª 1 T 2 º exp « » «¬ 4T / Pe »¼ 4 ST 3 / Pe 2 As well as the residence time distribution variance V T derived: E T
1
(3)
uL 2 · § ¨1 e E ¸ 2 2§¨ 1 ·¸ 1 e Pe (4) ¸ Pe ¨ Pe ¹ © ¹ © Eq.3 and Eq.4 show that, if the tracer residence time distribution is measured, then the distribution 2 variance V T calculated and Pe number or diffusion coefficient Ex obtained. In actual work, the continuous function formulated as Eq.3 is processed by discrete method. According to the definition, the density function of residence time distribution of the tracer in the reactor c t , then the discrete form of E t is written as: is E t f ³0 c t dt
VT 2
§E · §E · 2¨ x ¸ 2¨ x ¸ © uL ¹ © uL ¹
2
x
E t
ci t c ¦ i t 'ti
(5)
The average residence time is calculated from:
¦ ti ci t 'ti ¦ ti ci t (6) ¦ ci t ¦ ci t 'ti where ci t is the tracer concentration in the i -the drain sample, 'ti is the sampling time interval, and ti the i -the sampling time. tm
The variance of the residence time distribution density function is defined as V t written as summation form:
³0 t tm E t dt , f ³0 E t dt f
2
2
582
Shiqiang Ding et al. / Procedia Environmental Sciences 18 (2013) 579 – 584
Vt2
while
the
variance
of
¦ ti E t 't i 2 tm ¦ E t 'ti
the
¦ ti E t 2 tm ¦ E t
2
dimensionless
2
residence
time
(7) distribution
function
E T
is
V T 2 = ³0f T 1 E T dT 2
From which substituting T with t / tm following equation can be derived: VT 2
Vt2 tm
(8)
2
According to Eqs.5-8 the distribution variance V T can be calculated step by step from the experimental results, then the Pe number determined by Eq.4. 2
3.2. Measurement results of Pe A KMnO4 solution with concentration of 0.1 g / L is used as tracer, the concentration of tracer in the drain water is measured by using of a visible light spectrophotometer. Influent flow rate in the test were 15, 30, 45, 60 L / h respectively, and different influent flow rate represents different HRT, so at the sampling time for different influent flow rate should be different from each other. Specific sampling time is listed in table 2. Table 2. Sampling time and frequency for different flow rate. Influent flow rate(L/h)
Time interval(min)
Frequency
15 30 45 60
30 20 15 10
12 13 10 10
To save space, here only are given in Table 3 the measurement results when inlet flow rate is 15 L / h . Table 3. Measured tracer concentration. Number of times
min
Concentration (g/L)
1
0
0
2
15
0
3
30
0.027
4
45
0.042
5
60
0.058
6
75
0.062
7
90
0.085
8
105
0.091
9
120
0.089
10
135
0.092
583
Shiqiang Ding et al. / Procedia Environmental Sciences 18 (2013) 579 – 584
According to Eqs.5 to 8, the mean residence time, distribution variance for actual time and 2 2 dimensionless time are calculated in steps as tm =93.7minˈ V t =2581.2min2 ˈ V T =0.294 from the experiment results. The direct calculation of Pe number is more or less difficult from Eq.4, but it can be obtained by trial and error method. It can be seen that in Eq.4, the larger the value of Pe , the smaller the value of V T 2 . Optionally an initial value of Pe is selected and substituted into the right side of Eq.4 to calculate a value of V T 2 , if the value of V T 2 obtained is greater than 0.294 a larger Pe is selected otherwise a smaller Pe selected until the calculated result is 0.294 approximately. In the present embodiment, the trial and error method gives Pe = 5.6. 4. The effect of Pe number
WHVWQXPEHU
SHFOHWQXPEHU
UHPRYDORI&2'˄˅
The effect of Pe number on the removal of CODǃNH4+-N and TP are illustrated Fig. 2ˈFig. 3 and Fig. 4 respectively.
UHPRYDOUDWHRI&2' SHFOHWQXPEHU
Fig. 2. COD removal rate vs. Pe .
WHVWQXPEHU UHPRYDOUDWHRI1+1 SHFOHWQXPEHU
Fig. 3. NH4+-N removal rate vs. Pe .
SHFOHWQXPEHU
UHPRYDOUDWHRI1+1
Shiqiang Ding et al. / Procedia Environmental Sciences 18 (2013) 579 – 584
UHPRYDOUDWHRI73˄˅
SHFOHWQXPEHU
584
WHVWQXPEHU
UHPRYDOUDWHRI73 SHFOHWQXPEHU
Fig. 4. TP removal rate vs. Pe .
5. Conclusion The flow pattern in the sewage reactor has an important impact on the treatment results. It can be seen that dimensionless Pe number plays a useful part in the demonstration of the relative portion of plug-flow and mixed-flow in actual reactor. In the study mentioned above, there are three factors that determine Pe number, including the influent flow-rate, the mixing speed and the gaps between movable plate and reactor bottom. These factors are representing plug-flow, baffled-flow and mixed-flow respectively. In the specially designed reactor, the best removal efficiency of COD, NH4+-N and TP of analog sewage are obtained when Pe is 1.38. In a word, there is an optimum range of Pe number where better pollutant removal can be expected.
References [1] Zhu Bingchen. Chemical reaction engineering. (in Chinese) 4rd ed. Beijing: Chemical Industry Press; 2007. [2] Zhangzi Jie. Activated sludge biological kinetics.(in Chinese) 1rd ed. Beijing: China Environmental Science Press; 1985. [3] GuoM X, Sun P D, Wang R Y, et al. Biological-Hydraulic-Temperature coupled model (FCASM3-Hydro-Temp) for activated sludge system Part 3:Hydraulic and temperature effects. (in Chinese with English abstract) J Acta Scientiae Circumstantiae 2008; 28 (12): 2449 – 2455. [4]Murphy K L, Timpany P L.Design and analysis of mixing for anaeration tank J San Eng ASCE. 1967; 93(5):1-15. [5]Khudenko B M, Shpirt E. Hydrodynamic parameters of diffused air systems. J Wat Res˗1986; 20(7):905-915 [6] Lee T, Newell R B, Wang F Y.Dynamic modeling and simulation of activated sludge process using orthogonal collocation roach J Wat Res. 1999; 32(1):73ü86. [7]Tang Ke. et al. Impact of Peclet number on heat transfer of oscillatory flow in circular channel. J CRYOGENICS.2011; 3:1-5.