Wan xing Wan jinbao Zhao jin Tao kun

(The environment science and engineering school of Nanchang University Nanchang ,Jiangxi 330029 email:jbwan@ncu.edu.cn)

Abstract: The studying object of this research aims at mathematical model of membrane bioreactor(MBR)system for municipal wastewater treatment.In this research,an equation to calculate hydraulic retention time (HRT) in the MBR is successfully derived from the theoretical discussion and experiment data analysis,and expressed as （h）.The calculation results are in agreement with the experiment data,which will provide valuable reference for engineering design.

Keywords: membrane bioreactor;mathematical model;hydraulic retention time

1. Introduction

The scientists have done much on the mathematical model and simulation of membrance bioreactor.In the overseas, Davydov.L.S.(1995)^[1] ananlysed the mechanism for microbiological processes,taking place in a dialysis membrane hollow-fiber bioreator,using a two-phase model.Based on these calculations,the efficiency of using such devices with different types of ultrafiltration membranes has been estimated;Pavasant,P(1996)^[2]presented a mathematical model of membrane-attached biofilm(MAB)behavior in a single-tube extractive membrane bioreactor(STEMB).The model is capable of predicting the correct trends in system variables such as biofilm thickness,DCE fiux across the membrane,carbon dioxide evolution,and suspended biomass;Strachan,L.F.(1997)^[3]descrides two simple mathematical models developed to compare extractive membrane bioreactor(EMB)flow configurations and the results of experiments performed to test the models.Trusek Holownia,A.(2001)^[4]presented the mathematical model of membrane two-phase bioreactor,verified with data of enzymatic dipeptide ZalaPheOMe synthesis by the use nezyme-thermolysin,in two-phase ethylacetate-water system.Carvalho,C.M.L(2001)^[5] describe the conversion degree in a membrane bioreactor for the synthesis of short-chain esters as a function of the flow rate.The approach included the analysis of the MBR operation as a CSTR,a PFR,and a series of continuous reactors,the comparative efficiency of these reacor types is discussed,the enzyme distribution was estimated for all the cases.Lee Yonghun(2002)^[6]developed a mathematical model for the submerged membrane bioreactor(SMBR)combining the activated sludge model No.1(ASM1)with a membrane fouling model.Using the model,one can easily predict not only effluent qulity but also membrane fouling behavior during the SMBR process.

In China, although the applications of the computer in the membrane bioreactor field is still in the beginning stage,the scientific researchers have done some job at unit operation and the modeling of the dealing flow, the model solution,verification and expression.He yiliang(2001)^[7]of the ShangHai Jiaotong University developed a mathematical model for the membrane bioreactor with the viewpoint of “double separation”.The first step separate the solid and liquid of the mixation under the pressure,the last step is the separated liquid get to the membrane surface through the sediment stage, the organic molecule and colloid were separated from water;

Ren nanqi(2001)^[8]of the Harbin Institute of Technology described a mathematical model by using the SMBR,point out the way to caculate the model,verified the necessity to optimize the membrane discreteness.

2.Methods

2.1Whole material equation of MBR

In the volume(V)filled with wastewater,(fig2.1)according to conservation of mass,the equation ralationship of the organic can be describe as:

（2.1）

1. air 2.input 3.permeance output 4.output 5.constant flow pump 6.bioreactor 7.membrane discreteness
Figure2.1 SMBR materiel equation sketch map

2.1.1 Reaction kinetics model of the organic degradation

A.W.Lawrence and P.L.McCarty put forward the relationship between the wipe off velocity of the bottom material and the conversation of microbe in the oxidation ponder based on Monod equation:：

（2.4）

In the process of the microbe degrade sediment,the increase velocity of the microbe and the decrease velocity of the sediment has a ratio relation:

（2.5）

bases Michaelis-Menten equation，Y can be expressed as：

（2.6）

take（2.6）into（2.5），simplify as：

（2.7）

This formula is the kinetics relation between the sediment degradation velocity and the surplus concentration.

2.1.2 Membrane fouling kinetics model

Bases on normal Darcy law,the filtration model is :

（2.10）

The formula is the dependance of the organic material accumulation rate, pressure difference and pressure caused by the membrane fouling（ΔP＇）, operational pressure （ΔP ）,viscidity of the liquor（μ） ; membrane‘s resistance（R_m）, 濃差極化邊界阻力（R_b1）、fouling resistance（R_f） concentration of the inflow S_e.

According to formulas（2.9）and（2.14）,the formula of the membrane bioreactor hydraulic retention time can be deduced.

2.1.3 Hydraulic retention time（HRT）formula deduce

In the membrane bioreactor treatment system, hydraulic retention time（HRT）is a very important parameter，Not only relate to the treatment effection of the system,but also decide the size of the volume of the bioreactor directly,even to effect the capital construction investment .So,a reasonable HRT has an important meaning to ensure the output water quality and saving the outlay of the construction

Put the formulaes （2.9）and （2.14）into（2.3），the formula of the HRT is :

2.1.4 Simplify the HRT formula

2.1.5 Confirm the parameters of HRT formula

The formula（2.16） is relatively complexity,，in order to apply，it need to simplify more.For the change of Y_G,μ_m,E have little effect to HRT,Take Y_G,μ_m,E as constant ，the formula can be simplified：

The K,K_s is ready parameter in the formula( 2.17),which are determined mainly by sewage and the type of microbe,To diverse sewage,it can be decided by experiment.According to the study on this research aims at mathematical model of membrane bioreactor(MBR)system for municipal wastewater treatment,the auther adopt a method of request average to dispel the simultaneous equations ,the eventuate is K=0.0114（h^-1）

3.Result and discussion

Choose different HRT in the experiment，T=3h,4h,5h,6h。Mensurate the organic consentration S₀ of the input under different HRT, the organic consentration of the supernatant liquor in the MBR and the output organic consentration S_e，The result show in fig 4.1 and 4.2（_T=4h,6h）.The activate sludge concentration X₀ in the MBR show in tablet 4.3 under different concentration of input and output.　　　　　

tablet 4.1 diminish effction of HRT=6

Time

（d）

input

（L/h）

inptutCOD

（mg/l）

Supernatant liquorCOD

（mg/l）

outputCOD

（mg/l）

Diminish rate（%） Supernatant liquor Film filtration Output 1 4.5 463.8 28.9 7.6 93.7 73.7 98.4 2 4.5 477.8 32.5 8.5 93.2 73.8 98.2 3 4.5 478.4 28.9 10.2 93.9 64.7 97.9 4 4.5 473.1 30.2 9.1 93.6 69.9 98.1 5 4.5 471.8 30.1 9.8 93.6 67.4 97.9 6 4.5 474.3 31.2 9.2 93.4 70.5 98.1 7 4.5 466.8 28.9 7.9 93.8 72.7 98.3 8 4.5 480.3 30.2 8.3 93.7 72.5 98.3 Average 4.5 473.3 30.1 8.8 93.6 70.8 98.2
Tablet 4.2　diminish effection of HRT= 4

Time

（d）

input

（L/h）

imputCOD

（mg/l）

Supernatant liquorCOD

（mg/l）

Output

COD

（mg/l）

Diminish rate（%） Supern-atant liquor

Film filtratio-n Output 1 7.0 289.1 41.8 8.1 85.5 80.6 97.2 2 7.0 240.7 31.3 11.2 87.0 64.2 95.3 3 7.0 283.4 46.1 12.8 83.7 72.2 95.5 4 7.0 243.9 30.1 7.7 87.7 74.4 96.8 5 7.0 262.1 35.4 9.8 86.5 72.3 96.3 6 7.0 260.5 34.2 9.6 86.9 71.9 96.3 7 7.0 265.9 38.3 10.6 85.6 72.3 96.0 8 7.0 268.7 41.3 10.0 84.6 75.8 96.3

Average 7.0 264.3 37.3 10.0 86.0 73.2 96.2

It is obvious that,with the HRT added from 3h to 6h,the COD diminish ration of the supernatant liquor increase from 85.4% to 93.6%,which show that along with the extend of the HRT, the contamination in the water increase the contact time wih the microbe,the oxidate decompose ratio by microbe was enchanced,so the diminish ratio of COD was enchanced as well as.Yet with HRT prolong, the treatment ability will fall on the same time, consider the elements of the output water and the treatment ability generally,determine the HRT be 4h in this experiment.

　Tab.4.3　 X₀ of differ input and output’contamination concentration* S₀Average（mg/l） 473.3 334.6 264.3 454.2 S_eAverage（mg/l） 8.8 8.4 10.0 17.9 X₀（mg/l） 8500 7600 6950 14500

（*For the measurement of the activate microbe in the activate sludge is unsolved, the X₀ was expressed by MLVV that was measured by weight method）

Calculate the HRT separately by put the dataes into formula 2.18 which get from tab.4.1and 4.2,and then compare with the HRT get by the testing ,it will prove the veracity and reliability of the formula 2.18.the outcome of the HRT show in tab. 4.4,fig.4.1 and 4.2.

Tab.4.4　 HRT get by formula calculation

Time（d） _T =6h T =5h _T =4h _T =3h 1 6.2 5.0 4.7 3.0 2 6.2 4.9 3.6 3.0 3 6.0 5.1 4.2 3.2 4 6.0 5.4 4.0 3.0 5 5.9 5.1 4.1 3.0 6 6.0 5.1 4.0 3.1 7 6.2 5.1 4.0 3.0 8 6.2 5.1 4.1 3.2

Fig.4.1 compare measurement by experiment with calculate by formul _T=6h

Fig.4.2 compare measurement by experiment with calculate by formula _(T=4h)

From the figure 4.1 and 4.2,the outcome is inosculate ，there are only few errors in this dependance. The calculation results are in agreement with the experiment data according to the dependance in case of the first and second day of the experiment are respectively 4.7h and 3.6h in addition to the error ratio are 17.5%and10%.in conclusion, the dependance has its own validity and dependability which lead to a impressive guidance to the MBR’s design.

4.Conclusions

4.3 The experiment verify that：the HRT that calculate through the formula inosculate with measurement by the experiment.

References:

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