Kinetics of organic carbon removal by a mixed culture in a membrane bioreactor

Biochemical Engineering Journal 3 (1999) 61±69

Kinetics of organic carbon removal by a mixed culture in a membrane bioreactor C. Wisniewski*, A. Leon Cruz, A. Grasmick

Laboratoire des MateÂriaux et ProceÂdeÂs Membranaires (LMPM), CC 024 ± Universite de Montpellier II, Place EugeÁne Bataillon, 34095, Montpellier cedex 05, France Received 11 September 1998; accepted 16 December 1998

Abstract The aim of this work was to model the biological activity and anticipate the kinetic behaviour of microorganisms and the overall performance of the process according to a speci®c model and running parameters. The bacterial inoculum used in these experiments was a mixture of cultures taken from the wastewater treatment plant in Montpellier. The fermentor, used in association with an ultra®ltration separation stage (with a ®ltration area of 0.2 m2) had a working volume of 15.8 l. For various working conditions (different solid retention times, different hydraulic retention times and substrate concentrations), the biomass concentration and the residual substrate concentration, expressed in terms of dry weight and chemical oxygen demand, respectively, were measured. The basic idea of modelling was related to the concept of maintenance. The coef®cient of maintenance, E, and the theoretical conversion yield, y, were therefore calculated. The values of E and y, measured for total cell recycling experiments and for experiments with various solid retention times, remained similar and were found to equal 0.040 mgCOD mgVSS hÿ1 and 0.36 mgVSS mgCODÿ1, respectively. Determining these two constants and modelling the treatment process made it possible to anticipate the optimal biomass concentration for a de®ned removal ef®ciency under different steadystate operating conditions. # 1999 Elsevier Science S.A. All rights reserved. Keywords: Membrane bioreactor; Organic carbon removal; Biokinetics; Modelling

1. Introduction In the ®eld of wastewater treatment, biological processes constitute one of the basic treatment tools as these give optimal ef®ciency whilst minimising energy consumption and concentrates production. In France, the most commonly used intensive systems are activated sludge processes used in association with downstream separation via decantation. This last stage is only possible when the bacterial culture remains ¯occulated, that is, in the form of agglomerates, a result of physico-chemical interaction between microorganisms (mainly bacteria), mineral particles (silicates, iron oxides, etc.), exocellular polymers and multivalent cations [1]. In particular, with activated sludge processes, whose ¯ocs may reach several hundred microns in size, the substrate must go through the ¯occulated biological mass via diffusion before reaching the active sites. Hence the particular transfer mechanism from within the ¯oc is added to the traditional transfer and reaction mechanisms and this *Corresponding author.

may limit the overall reaction, a phenomenon observed with very structured biomasses (thick bio®lm), Fig. 1 [2]. The introduction of membrane bioreactors, which associate downstream separation with the biological contactor by setting up a porous, calibrated barrier, gives us an excellent biological quality of treated wastewater without it being necessary to ¯occulate the biomass beforehand. In order to decrease the hydraulic resistance of the membrane ®ltration system, strong hydrodynamic restrictions are generally imposed, and these consequently break up the macro¯ocs via super®cial erosion due to the ¯uid's movement and the appearance of small aggregates. This corresponds to the fragmentation of ¯oc resulting from the breakage of the ®lamentous network [3]. This destructuration of the suspension and the reduction in size of the particles would appear to limit the importance of diffusional transfer within the ¯oc and increase the apparent reaction [4,5]. In this way, with a system such as a membrane bioreactor, one may suppose that the assimilation of a simple, soluble and quickly biodegradable substrate essentially integrates the permeation and metabolism stages within the active sites, the latter becoming the limiting stage in the process.

1369-703X/99/$ ± see front matter # 1999 Elsevier Science S.A. All rights reserved. PII: S1369-703X(98)00046-1

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Fig. 1. Transfer and reaction mechanisms in a flocculated system.

The aim of this work consisted, ®rstly, of suggesting a model for the process of degrading a carbon substrate, taking into account the particular conditions imposed by the membrane bioreactor. This model was inspired by the works of Pirt [6,7] and Bouillot et al. [8] and has helped us to arrive at two parameters, named E and y, which represent the coef®cient of maintenance and the theoretical conversion yield, respectively. Modelling should help us to anticipate the way the membrane bioreactor is running and its performances notably in relation to the main operational parameters: the hydraulic retention time , the solid retention time  p and the in¯uent's concentration in polluants, S0. 2. Suggested kinetic model

The relationships between the different functional parameters (Fig. 2) were found from the mass balances governing the evolution of the substrate and the biomass within the system.  Mass balance on the substrate Q0 S0 ˆ …Qp ‡ Qe †S ‡ rS Vr ‡ Vr dS=dt in which Q0 ˆ Qp ‡ Qe and  ˆ Vr =Q0 so that rS ˆ …S0 ÿ S†= ÿ dS=dt:

(4)

 Mass balance on the biomass

The assimilation of the substrate may be described very simply using a model which takes into account (i) the synthesis of new elements (synthesis of new cells, synthesis of substances in reserve), which bring about an increase in the weight of the biomass present (anabolism), and (ii) the freeing of biologically useable energy which makes it possible to uphold and maintain these cells (catabolism). The consumption of the substrate may therefore be expressed from two parameters P and E which correspond, respectively, to the quantity of substrate eliminated per unit of biomass in view of ensuring the synthesis of new elements and the quantity of substrate eliminated per unit of biomass in view of ensuring the maintenance. In a constant environment, E is supposed as being stable for a given strain of microorganisms developing on a de®ned substrate [6,7]. The consumption rate of the substrate rS, the production of the biomass rX and the real conversion rate observed yobs (biomass produced/substrate eliminated) are given according to X (biomass concentration) and y (theoretical conversion yield), via the following equations: rS ˆ PX ‡ EX;

(1)

rX ˆ Py X;

(2)

yobs ˆ rX =rS :

(3)

rX Vr ˆ Qp X ‡ Vr dX=dt in which p ˆ Vr =Qp so that rX ˆ X=p ‡ dX=dt:

(5)

In the steady state, it is therefore possible to express P and E by simplifying Eqs. (1)±(4) so that P ˆ 1=…p y†;

(6)

E ˆ …S0 ÿ S†=…X† ÿ 1=…p y†:

(7)

Fig. 2. Diagram of the membrane reactor.

C. Wisniewski et al. / Biochemical Engineering Journal 3 (1999) 61±69

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Now that we know ,  p and S0, the operational parameters imposed by running conditions and having measured S, the substrate residual concentration, and X, the biomass concentration at the steady state, it is thus possible to calculate E and y, then to deduce P by tracing rS/X (or (S0ÿS)/(X)) as a function of 1/ p. E is therefore the ordinate at the origin and y is the inverse of the slope to the right. 3. Experimental 3.1. Materials and methods 3.1.1. Cultivation media and substrates The bacterial inoculum used in these experiments was a mixture of cultures taken from the wastewater treatment plant in Montpellier (France). The mixed culture was acclimatised to the hydrodynamic and biological conditions before the experiments took place. The operation was carried out on denitri®cation experiments. We used a synthetic substrate of potassium nitrate and ethanol as sources of oxygen and carbon, respectively. The substratum was prepared for working with a COD/N ratio of 4.8. 3.1.2. Experimental unit and operating conditions 3.1.2.1. Fermentor. The fermentor, used in association with a tubular membrane model, had a working volume of 15.8 l. The system was maintained at 258C. Anoxic conditions were ensured during the experimental work by regularly checking to make sure that the dissolved oxygen concentration was less than 0.2 mg lÿ1. The pH was adjusted to 8.8. A schematic diagram of the membrane bioreactor is given in Fig. 3. 3.1.2.2. Filtration unit. The filtration unit consisted of a ceramic membrane. The mineral membranes used were formed of 19 channels, 4 mm in diameter and 850 mm long. The membranes had a filtration area of 0.2 m2 and an average pore size of 0.05 mm. The initial permeate flow measured with tap water was 1000 l hÿ1 mÿ2 bÿ1. The clogged membrane was regenerated by chemical means and before each run the water permeability was brought up to within 10% of the initial value. The experiments were run at a pressure of 1±1.35 bar and a crossflow velocity of 1.32 m sÿ1. The experimental hydrodynamic conditions are given in Table 1. The hydraulic retention times chosen were

Fig. 3. The membrane bioreactor unit.

between 2 and 10 h, corresponding to a permeate flow ranging from approximately 8 to 40 l hÿ1 mÿ2 bÿ1. 3.1.3. Experimental procedure The supply of substrate and ®ltration were ensured continuously. Different trial campaigns were carried out: (i) by imposing a hydraulic retention time of 2 h and total retention of the biomass within the system; (ii) by imposing a hydraulic retention time ranging from 2 to 10 h for a biomass retention time of 3±9 days. For the whole of the trials, the substrate concentration in the permeate, S, and the biomass concentration, X, within the system were followed over the time. For each of the trial campaigns the coef®cient of maintenance and the conversion rate were calculated working from balance equations. 3.1.4. Analytical methods Substrate concentration, S, and biomass concentration, X, were expressed as chemical oxygen demand (COD) concentration and volatile suspended solids (VSS) concentration, respectively (APHA [10]). 4. Results and discussion 4.1. Results obtained with total cell recycling regimes The ®rst trial campaign was carried out without biomass extraction during the experiments and so the system was

Table 1 Hydrodynamic conditions Flow rate (l hÿ1)

Linear velocity in the membrane module (m sÿ1)

Reynolds number

Shear stress in the membrane module (N mÿ2)

Kolmogoroff microscale (mm) [9]

1135

1.32

5280

8

55

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Fig. 4. VSS concentration and effluent COD concentration values during the different experiments.

running with total cell recycling. For each of the three experiments, the hydraulic retention time was maintained at 2 h and the substrate concentration in the in¯uent, named S0, equalled approximately 1000 mgCOD lÿ1. Fig. 4 shows the evolution of the VSS concentration in the system and the evolution of the COD concentration in the permeate during each of the three experiments. For each one, the initial value of the biomass concentration, X0, equalled 4620 (trial a), 3920 (trial b) and 3400 mg lÿ1 (trial c), respectively. In all these cases the ef¯uent COD concentration, named S, evens out very quickly. We may therefore suppose that S is constant during the experiment and therefore write (Eq. (4)) that the term dS/dt is zero and the substrate assimilation rate remains identical throughout the whole operation and equals (S0ÿS)/. As the assimilation rate of substrate rS is constant, the part of the substrate eliminated per unit of biomass in order to ensure synthesis (represented by parameter P), would therefore become lower as X increases, due to the fact that E is a constant parameter (Eq. (1)). As the experiment progresses, the synthesis of new cells should therefore decrease progressively until it reaches a value of zero for which the biomass concentration would then remain constant. From then on, the substrate would only be consumed in order to

ensure the maintenance requirements of the cells present. Fig. 4, which shows the progressive evolution of the biomass concentration in the system, illustrates the variation in synthesis rates. Considering that the assimilation rate of substrate rS remains constant, and that recycling of the biomass is complete, the balance equations give the following: ‰…S0 ÿ S†= ÿ EXŠy ˆ dX=dt:

(8)

After integration, the expression of X as a function of time is given by the following: X ˆ …S0 ÿ S†=…E† ÿ ‰…S0 ÿ S†=…E† ÿ X0 Š exp…ÿyEt†: (9) The theoretical and experimental evolutions of the biomass concentration are shown in Fig. 5. The values obtained for E and y are given in Table 2. Fig. 6 shows, as an example, the evolution of parameters P and E during one trial (trial a): E, by de®nition, is a constant parameter and P is an inverted function of time. The average values determined for E and y are 0.040 mgCOD mgVSS hÿ1 and 0.33 mgVSS mgCOD, respectively. The values for E are very close to each other (typical deviation of 0.0033 mgCOD mgVSS hÿ1 representing approximately 8% of the average value), the values of y

Fig. 5. Experimental and theoretical VSS concentration values during the different experiments.

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Table 2 Values obtained for E and y in total biomass recycling experiments  (h)

X0 (mgVSS lÿ1)

S0 (mgCOD lÿ1)

rs (mgCOD lÿl hÿ1)

E (mgCOD VSS hÿ1)

y (mgVSS mgCODÿ1)

2 2 2

4620.00 3920.00 3400.00

1040.00 1020.00 990.00

336.50 344.00 346.50

0.038 0.045 0.038

0.35 0.40 0.25

0.040

0.33

Average values

Fig. 7. Experimental and theoretical VSS concentration values during the experiments carried out by Bouillot [12]. Fig. 6. Evolution of P and E during experiment (a).

lead to a typical deviation of 0.062 mgVSS mgCOD representing approximately 20% of the average value. Pitter and Chudoba [11] give an average conversion rate y of 0.34 mgVSS mgCOD for ethanol. However, the literature does not allow us to check the validity of the values obtained for y and E in more detail. Indeed, these values correspond to a perfectly de®ned substrate and bacterial culture. Nevertheless, with a membrane bioreactor and total biomass recycling, works of Bouillot [12] (on a culture of Pseudomonas ¯uorescens and a synthetic substrate based mainly on acetate, sucrose and peptone) have made it possible to measure a coef®cient of maintenance equalling about 0.034 mgCOD mgVSS hÿ1, working from the steady state. The modelling (working from Eq. (9)) of the bacterial growth observed throughout this work gave a value for E of around 0.030 mgCOD mgVSS hÿ1, which corresponds to the values determined by Bouillot. Fig. 7 shows that the modelling suggested by this work is in perfect keeping with the results obtained by this author during the experiments. 4.2. Results obtained for different hydraulic retention times and biomass breeding rates The second trial campaign was carried out with biomass extraction by imposing different hydraulic retention times and different solid retention times. The different working conditions (,  p, S0) are shown in Table 3. For each trial, the values of X (biomass concentration) and S (residual substrate concentration), as taken at the steady state, are also

featured. Rates rS (substrate consumption rate) and rX (biomass formation rate) were directly deduced from Eqs. (4) and (5). The different parameters yobs (experimental conversion yield), Cm (mass organic load) and  (removal ef®ciency) were deduced from the following equations: yobs ˆ rS =rX ˆ X=…S0 ÿ S†p ;

(10)

Cm ˆ S0 =…X† ˆ 1=…yp †;

(11)

 ˆ …S0 ÿ S†=S0 :

(12)

The results obtained make it possible to outline certain conclusions of a general nature. For example, we may note that the longer the hydraulic ¯ow time, the better the reduction in pollution. We may also note that for an imposed reduction in pollution and an imposed biomass retention time, the increase in the hydraulic retention time corresponds to a decrease in X. For a constant reduction in pollution and an imposed hydraulic retention time, the increase in  p imposes an increase in the stabilised biomass concentration. These two latter points will be taken up again later on. It is possible to determine E and y from the experimental results obtained with a ®xed  and  p, by tracing rS/X as a function of l/ p according to the following relationship taken from Eq. (7): rS =X ˆ …l=y†…l=p † ‡ E:

(13)

The two lines represented in Fig. 8 correspond to (i) the linear regression obtained from all the experimental points measured with biomass extraction, (ii) the straight line obtained from parameters E and y determined during the

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Table 3 Steady-state values of the main parameters for different solid and hydraulic retention times  (h)

 p (d)

X (mgVSS lÿ1)

S0 (mgCOD lÿ1)

10.00 10.00 10.00 10.00 7.50 5.00 5.00 5.00 5.00 5.00 5.00 5.00 2.00 2.00

6.00 6.00 3.00 3.00 3.00 9.00 4.50 3.50 3.00 6.00 6.00 6.50 6.00 5.00

2318.00 2662.00 1613.00 1080.00 1400.00 6450.00 2170.00 2950.00 1930.00 2500.00 3500.00 6200.00 5800.00 4009.00

1063.00 1047.00 1081.00 1058.00 1053.00 1009.00 1021.00 1998.00 1029.00 1055.00 2260.00 3205.00 1022.00 1036.00

S (mgCOD lÿ1) 10.50 23.00 129.00 225.00 306.00 175.50 243.00 580.00 313.00 345.00 709.00 1030.00 313.00 374.50

rS rX yobs Cm  (mgCOD lÿ1 hÿ1) (mgVSS lÿ1 hÿ1) (mgVSS mgCODÿ1) (mgCOD mgVSS dÿ1) 105.25 102.40 95.20 83.30 99.60 166.70 155.60 283.60 143.20 142.00 310.20 435.00 354.50 330.75

16.10 18.49 22.40 15.00 19.44 29.86 20.09 35.12 26.81 17.36 24.31 39.74 40.28 33.41

0.15 0.18 0.24 0.18 0.20 0.18 0.13 0.12 0.19 0.12 0.08 0.09 0.11 0.10

1.10 0.94 1.61 2.35 2.41 0.75 2.26 3.25 2.56 2.02 3.10 2.48 2.11 3.10

0.99 0.98 0.88 0.79 0.71 0.83 0.76 0.71 0.69 0.67 0.69 0.68 0.69 0.64

Fig. 8. rS/X versus l/ p.

campaigns carried out with total cell recycling. Fig. 8 shows us a great dispersion in the experimental points as compared with the linear regression. Pirt [13] emphasised that the linear relationship between rS/X and l/ p (Eq. (13)) has not always been checked. He also noted a large difference between the experimental points and the linear regression when the dilution rate imposed on the biomass (l/ p) was below 10% of the speci®c maximum growth rate. Indeed, low dilution rates would seem to cause a decrease in maintenance energy requirements (which would seem to give a lower value for E) due to the presence of dormant or ``non-valid'' cells. Although we were working with suitable dilution rates (l/ p taken between 0.005 and 0.14 hÿ1) above 10% of the speci®c maximum growth rate determined for ethanol (0.008 hÿ1 [11]), it is possible to envisage that the cells present within our suspension do not all have the same physiological

condition and thus the same maintenance requirements. Indeed, within any one biological culture, Mason et al. [14] suggested separating the total population into four different categories: (i) viable cells which assimilate the substrate, biodegrade, and multiply, (ii) ``dormant'' cells which are momentarily inactive (an intermediate condition for cells which may still be divided or go into the next category, (iii) non-valid cells which no longer have the capacity to reproduce but may use the substrate, (iv) dead cells which no longer have any activity but still possess a wall and whose morphology has not changed. However, in order to simplify things, the bacterial population is often assimilated to a group of cells, whose physiological condition is similar, so that they react in the same way to the categories of nutrition or culture imposed on them, although it is not the case. Indeed, it is dif®cult to appreciate the validity of cells and the means of measuring used (measur-

C. Wisniewski et al. / Biochemical Engineering Journal 3 (1999) 61±69

ing the INT activity, differential centrifuging, ATP measuring, the immuno¯uorescence or ¯uorescence method) give uncertain results. So, generally, as with our trials, the bacterial population X is quanti®ed by measuring the concentration of volatile matter in suspension. This method does not take into account the different physiological states of the cells. It is so very possible that, during experiments carried out on long periods (as with our trials), the different physiological states of the cells evolve during the experiments, which can cause scatter when estimating maintenance requirements. This may explain the differences observed between the experimental results and the linear regression during the second trial campaign (long experiments) and the good adequation between the model and the experimental values obtained in the ®rst campaign (total cell recycling regime) with short trials. 4.3. Use of the model for controlling the membrane bioreactor's performance Nevertheless, the average values obtained for parameters E and y, working from the linear regression deduced from the latest trials are 0.04 mgCOD mgVSS hÿ1 and 0.36 mgVSS mgCODÿ1, respectively. They are very close to those obtained during the ®rst trial campaign carried out without biomass extraction. These results therefore seem to show that the value of the coef®cient of maintenance E remains constant and may be reproduced whatever the working conditions imposed. This point is extremely interesting as it allows us to associate a characteristic parameter with the suspension, regardless of working conditions, and

67

this may be useful for the management and control of the biological process, that is to say, the whole process. Indeed, going from Eq. (14), it is possible to describe the system whatever the working conditions and thus anticipate sludge production for example, or the stabilised value of biomass concentration X within the process, resulting from the modi®cations or evolutions of ,  p or S0. rS =X ˆ …S0 ÿ S†=…X† ˆ 0:04 ‡ 2:90…l=p †

(14)

where rS is in mgCOD lÿ1 hÿ1, X in mgVSS lÿ1, ,  p in h, and S0 is in mgCOD lÿ1. We wanted to con®rm this phenomenon by imposing different working conditions on the system (by modifying ,  p or S0 successively) and by comparing the experimental values obtained with those anticipated by the model, at the steady state. Fig. 9 illustrates examples of the evolutions in the concentration of X following these modi®cations to the working conditions. Two phases were observed: they correspond to a transitory state, relative to the variation in the parameter chosen, and then a steady state. The evolutions observed in this graph con®rm Eq. (7) that is (i) for an imposed reduction in pollution (S0ÿS) and an imposed biomass retention time, the increase in the hydraulic retention time corresponds to a decrease in X, (ii) the increase in  p, for constant reduction in pollution and a constant hydraulic retention time, imposes an increase in the concentration of stabilised biomass. Table 4 lists the experimental and theoretical values of the biomass concentration obtained for all the experiments at the steady state. The deviations between the experimental values and the theoretical values are variable. However,

Fig. 9. Experimental and anticipated VSS concentration values during the different experiments.

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C. Wisniewski et al. / Biochemical Engineering Journal 3 (1999) 61±69

Table 4 Experimental and theoretical biomass concentration values  (h)

 p (d)

Experimental X (mgVSS lÿ1)

Theoretical X (mgVSS lÿ1)

Deviation (%)

10.00 10.00 10.00 10.00 7.50 5.00 5.00 5.00 5.00 5.00 5.00 5.00 2.00 2.00

6.00 6.00 3.00 3.00 3.00 9.00 4.50 3.50 3.00 6.00 6.00 6.50 6.00 5.00

2318.00 2662.00 1613.00 1080.00 1400.00 6450.00 2170.00 2950.00 1930.00 2500.00 3500.00 6200.00 500.00 4009.00

1775.00 1727.00 1211.00 1060.00 1267.00 3154.00 2368.00 3881.00 1822.00 2395.00 5232.00 7525.00 5979.00 5238.00

23 35 25 2 9 51 9 31 5 4 49 21 3 31

Average value

apart from certain speci®c cases, the biomass concentration X, corresponding to the steady state, may be estimated at approximately 20% of its true value. This disparity may seem large but, as we have seen previously, it is probably related to the fact that maintenance requirements are so dif®cult to estimate. Whatever the reason, these results con®rm that, during the likely variations in working conditions, it is possible, for example, to estimate the optimal biomass concentration value required in order to maintain a given reduction. 5. Conclusion The aim of this work consisted of (i) modelling biological activity and (ii) anticipating the kinetic behaviour of microorganisms and the overall performance of the process according to a speci®c model and running parameters. The basic idea of this modelling was related to the concept of maintenance. The values for E and y, measured for the total recycling experiments and for experiments with various solid retention times, remained similar and were found to equal 0.040 mgCOD mgVSS hÿ1 and 0.36 mgVSS mgCODÿ1, respectively. The working conditions imposed on the biological suspension, therefore, would not seem to modify the culture's maintenance requirements. Although this point may be particularly interesting, especially with regard to managing the system, it is, however, necessary to point out that the physiological explanation of the maintenance concept is delicate to formulate, and may be subject to much controversy. The complex phenomena related to the physiological condition of the culture (mortality, lyse, cryptic growth, for example) should be taken into account as these are likely to modify requirements. Nevertheless, this work has shown that, thanks to simple data, it is not only possible to anticipate the way the membrane bioreactor will run, and its performance, but

21

also to correct any possible malfunctioning within the system. Apart from the process's compactness and the excellent quality of the treated water, the membrane bioreactor therefore has another major advantage: the possibility of managing the system very simply, working from the operational parameters ,  p and S0. 6. Nomenclature Cm E P Q0 Qe Qp rS rX S0 S Vr X yobs y t

mass organic load (Tÿ1) quantity of substrate eliminated per unit of biomass in view of ensuring maintenance (Tÿ1) quantity of substrate eliminated per unit of biomass in view of ensuring the synthesis of new compounds (Tÿ1) influent flow rate (L3 Tÿ1) effluent flow rate (L3 Tÿ1) purge flow rate (L3 Tÿ1) substrate consumption rate (M Lÿ3 Tÿ1) rate at which biomass is formed (M Lÿ3 Tÿ1) inlet substrate concentration (M Lÿ3) substrate concentration at t or residual substrate concentration at the steady state (M Lÿ3) overall reactional volume (L3) biomass concentration at t or residual biomass concentration at the steady state (M Lÿ3) observed or experimental conversion yield (biomass produced/substrate eliminated) theoretical conversion yield time (T)

Greek letters   p

removal organic efficiency hydraulic retention time (T) solid retention time (T)

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[7] S.J. Pirt, Maintenance energy: a general model for energy-limited and energy sufficient growth, Arch. Microbiol. 133 (1982) 300± 302. [8] P. Bouillot, A. Canales, A. Pareilleux, A. Huyard, G. Goma, Membrane bioreactors for the evaluation of maintenance phenomena in wastewater treatment, J. Ferment. Bioeng. 69(3) (1990) 178±183. [9] K. Van't Riet, J. Tramper, Basic Bioreactor Design, Marcel Dekker, New York, 1989. [10] American Public Health Association, Standard Methods for Examination of Water and Wastewater, 18th ed., 1992. [11] P. Pitter, J. Chudoba, Biodegradability of Organic Substances in the Aquatic Environment, CRC Press, Boca Raton, 1990. [12] P. Bouillot, BioreÂacteurs aÁ recyclage des cellules par proceÂdeÂs membranaires: application aÁ la deÂpollution des eaux en aeÂrobiose, Ph.D. Thesis, INSA, Toulouse, 1988. [13] S.J. Pirt, The energetics of microbes at slow growth rates: maintenance energy and dormant organisms, J. Ferment. Technol. 65 (1987) 173±177. [14] C.A. Mason, J.D. Bryers, G. Hamer, Activity, death and lysis during microbial growth in chemostat, Chem. Eng. Commun. 45 (1986) 163±176.