Initial-rate based method for estimating the maximum heterotrophic growth rate parameter (μHmax)

Bioresource Technology 116 (2012) 126–132

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Initial-rate based method for estimating the maximum heterotrophic growth rate parameter (lHmax) C. Fall a,⇑, C.M. Hooijmans b, M. Esparza-Soto a,1, M.T. Olguin c, K.M. Bâ a,1 a

Universidad Autonoma del Estado de Mexico (UAEM-CIRA), Apdo postal 367, Toluca, C.P. 50091, Estado de Mexico, Mexico UNESCO-IHE Institute for Water Education, Westvest 7, 2611 AX, Delft, The Netherlands c Instituto Nacional de Investigación Nuclear, Carr. Mexico-Toluca S/N, C.P. 52750, Ocoyoacac, Mexico b

a r t i c l e

i n f o

Article history: Received 6 January 2012 Received in revised form 27 March 2012 Accepted 29 March 2012 Available online 5 April 2012 Keywords: Activated sludge model ASM1 Heterotrophic growth rate Respirometry Seed varying method

a b s t r a c t Currently, the method most used for measuring the maximum specific growth rate (lHmax) of heterotrophic biomass is by respirometry, using growth batch tests performed at high food/microorganism ratio. No other technique has been suggested, although the former approach was criticized for providing kinetic constants that could be unrepresentative of the original biomass. An alternative method (seedincrements) is proposed, which relies on measuring the initial rates of respiration (rO2_ini) at different seeding levels, in a single batch, and in the presence of excess readily biodegradable substrate (SS). The ASM1-based underlying equations were developed, which showed that lHmax could be estimated through the slope of the linear function of rO2_ini(VWW + vML) vs vML (volume of mixed liquor inoculum); VWW represent the wastewater volume added. The procedure was tested, being easy to apply; the postulated linearity was constantly observed and the method is claimed to measure the characteristics of the biomass of interest. Ó 2012 Elsevier Ltd. All rights reserved.

1. Introduction The activated sludge Model No. 1 (ASM1; Henze et al., 2000) was developed on the basis of eight basic processes that involve two groups of microorganisms (heterotrophs and autotrophs) and 13 components (including chemical oxygen demand–COD– and N fractions, oxygen and alkalinity). The model include nearby 20 kinetic and stoichiometric parameters that need to be known, to be able to describe the performance of a specific activated sludge plant. Due to the very large number of constants included in the ASM models, there are some identifiability problems (LiwarskaBizukojc and Biernacki, 2010). In practice, only a very few number of the parameters are estimated or calibrated when modelling a wastewater treatment plant (WWTP), the majority being kept to its default values. It is important to have good methods that allow to accurately fix the default values. The first set of default values that was proposed for the ASM1 remains as the reference (Henze et al., 2000), but also some new mean values are often proposed in the literature (Cox, 2004; Hauduc et al., 2011) or by the software’s developers (Envirosim, 2006; Hydromantis Inc., 2006), on the basis of their own modelling experiences. Also, some experimental methods for measuring some of the parameters were presented in the ASM1 document, ⇑ Corresponding author. Tel.: +52 52 7222965550. 1

E-mail address: [email protected] (C. Fall). Tel.: +52 7222965550.

0960-8524/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.biortech.2012.03.102

but since then, some alternative experimental methods have been developed and are frequently used (Kappeler and Gujer, 1992; Vanrolleghem et al., 1999; Spanjers et al., 1999). The development of alternative methods is useful to facilitate the task of affirming or updating the default values, or to determine the values of the parameters for a particular WWTP. The maximum specific growth rate (lHmax) and the decay coefficient (bH) for the heterotrophic biomass are some of the most important parameters of the ASM1 model (Pollice et al., 2004). The value of the heterotrophic maximum growth rate is apparently very variable (3–12 d1 at 20 °C, Henze et al., 2000) and should be determined for each given effluent. Before the advent of ASM1, lHmax of a given wastewater (WW) was classically estimated on the basis of the relationship between the specific growth (or substrate removal) rates and the substrate concentration, usually reflected by a convenient linearized form of the Monod equation (Sözen et al., 1998). With the introduction of the dynamic mathematical models, the difficulties in the interpretation of the total COD, BOD, and VSS measurements encouraged the development of respirometric methods for assessing the kinetic constants. Today, the respirometric method most used for estimating lHmax is the one that was developed by Kappeler and Gujer (1992). The latter method consists in performing an aerobic exponential growth test in a batch at very high initial food/microorganism ratio (F/M), adding a small quantity of biomass (inoculum) to pre-settled wastewater sample that contains excess readily biodegradable substrate (SS). In such kind of experiment, the profile of the oxygen

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C. Fall et al. / Bioresource Technology 116 (2012) 126–132

uptake rate (rO2) might have a trend similar to the curve (a) on Fig. 1 (Fall et al., 2011). During the first period of the batch test, rO2 increases exponentially due to unlimited heterotrophic growth. Suddenly, the oxygen uptake rate will decrease because of limiting concentrations of SS. For the exponential growth phase, where neither substrate nor oxygen limitation exists, and without nitrification, the modified ASM1 model (with endogenous respiration) enables to calculate the oxygen uptake rate (rO2), as given by Eq. (1) (Kappeler and Gujer, 1992):

jr O2 ðtÞj ¼



 0 1  YH lH max þ ð1  f 0 pÞb0H X H0 eðlH max bH Þt YH

ð1Þ

where t is time; YH, the biomass yield; lHmax, the maximum specific growth rate; ´fp, fraction of the inert biomass residue (default va´ H, endogenous decay coefficient; and XH0, the initial biolue = 0.2); b mass concentration in the batch tests. Eq. (1) may be simplified, which yield Eq. (2). 0

Ln r O2 ðtÞ ¼ ðlH max  bH Þt þ Cte

ð2Þ

Representing the latter function yields a straight line, with ´H) as the slope, allowing to calculate lHmax, if b ´ H is (lHmax  b known. The constant or intercept (Cte) in the equation represents the initial oxygen consumption rate (rO2 at t0 = 0), by which the initial biomass present in the batch test may be calculated. Alternatively, Eq. (1) may be fit directly by an exponential function [y = b. exp (a.t)], where the constant a represents the difference ´H), while the constant b (oxygen uptake rate, rO2, at (lHmax  b t = 0) allows to calculate the initial biomass in the batch tests. As one advantage, in the method of Kappeler and Gujer (1992), it is not necessary to know the initial quantity of biomass in the system (XH0). However, some previous trials are often necessary to optimize the F/M ratio, and to achieve the desirable shape (a, Fig. 1) for the respirogram. Moreover, an aspect that was very criticized in the Kappeler and Gujer (1992) method is the high substrate/biomass (of about 4/1) ambient, which differs from the normally low-F/M conditions in the aeration tanks (Spanjers and Vanrolleghem, 1995; Ellis and Eliosov, 2004). There might be a change in the biomass population due to the experimental setup; the observed kinetics characteristics might no longer be representative of the original microbial population, but only of the fraction of organisms that grows selectively and becomes dominant during the experiment (Novák et al., 1994; Vanrolleghem et al., 1999). Before Kappeler and Gujer (1992), Ekama et al. (1986) proposed an initial-rate based method for measuring lHmax. The approach

consisted in running an aerated batch with suitable initial F/M ratio (e.g. 0.6 mg COD/mg VSS) that yield a respirogram similar to the trace b of Fig. 1. Indeed, with a moderate F/M and non-limiting SS, the oxygen uptake rate response will show a maximum plateau (rO2_max), (Sözen et al., 1998). Without nitrification, as predictable from the original ASM1 matrix (death-generation), the initial high oxygen uptake rate value will be proportional to the maximum specific growth rate, which can be written as:

jrO2

 max j ¼

 1  YH lH max X H0 YH

ð3Þ

In such a test, the biomass concentration in the batch (XH0) is considered as practically constant. Generally, the quantity of inoculum that is needed in this kind of test (moderate F/M) is much higher than in the previous high-F/M tests. In this case, only wastewaters with very high SS content will allow observing a durable and stable rO2 plateau. When the conditions are met and rO2_max is measured, Eq. (3) allows calculating lHmax, if XH0 is known. As drawbacks, the method is very sensitive to XH0 and relies on two individual measures (rO2_max and XH0) for the estimation of lHmax. Beside the now-classical method of Kappeler and Gujer (1992) for estimating lHmax, other alternative methods have not been reported in the literature, although there was a consensus that substantial biomass growth and a shift in biomass population may occur with the former procedure, and would result in kinetic parameters that are no longer representative of the original biomass. In the ASM calibration protocols and projects, the parameter lHmax is less and less measured (Hauduc et al., 2011). One of the reasons is probably the uncertainty in the representativeness of the values obtained by the conventional method. This also leads to uncertainties when attempting to actualize the proposed default values. Meanwhile, several approaches are still known in the field of chemical reaction engineering (Fogler, 2005) for measuring the kinetic parameters: initial-rate based methods, half-lives method, mass balancing, linearization of the rate laws, etc. The aim of the present study was to develop an alternative method for estimating the maximum specific growth rate of the heterotrophs (lHmax). The proposed method relies on measuring the initial rates of respiration, at different seeding levels, under the conditions of saturated SS. Instead of monitoring the rO2-time exponential growth curve (Fig. 1a) for a fixed initial quantity of seed, as performed traditionally, the volume of inoculum is stepwisely increased, while the corresponding initial oxygen consumption rates (rO2_ini) are measured at each step. The procedure was named as the method of Seed Increments (S.I. method). 2. Methods 2.1. Underlying equations and hypothesis of the S.I. method

(a) High F/M

(b) Low F/M

50

ro2 (mg/L.h)

40 30 20 10 0 0

1

2

3

4

5

6

7

8

9

Time (h) Fig. 1. Oxygen uptake rate (rO2) profiles: (a) High F/M growth test and (b) low F/M batch test.

Considering a batch test with SS in excess, the initial oxygen uptake rate (rO2_ini) is expected to increase proportionally to the quantity of inoculum present in the system. The quantity of biomass in the reactor may be varied, voluntarily at different moments, by adding a small initial quantum of mixed liquor in the WW, and then increasing it gradually by the addition of equal quantities of sludge at different stages. By measuring the initial oxygen uptake rate at each of the steps, lHmax can be extracted by model-interpreting the data. When a batch is run, the initial total concentration of heterotrophic biomass in the system (XH0, Eq. (4)) comes partly from the wastewater, and partly from the mixed liquor (ML) used to inoculate the reactor (‘‘seed’’).

X H0 ¼ ðV WW X H0

WW

þ v ML X H0

 ML Þ



1 V WW þ v ML

 ð4Þ

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VWW and vML represent the wastewater and mixed liquor volumes added in the reactor, while XH0_WW and XH0_ML are the biomass concentrations present in each of the stock mediums. By inserting Eq. (4) into Eq. (1), but now considering the original ASM1 matrix (death-generation, without nitrification), the initial oxygen uptake rate (rO2_ini, at t = 0) may be computed as it follows (Eqs. (5)–(7)):

r O2

ini

¼

1  YH lH max  ðV WW X H0 YH   1  V WW þ v ML

WW

þ v ML X H0

ML Þ

ð5Þ

which may be written as:

r O2

2.2. Experiments

1  YH lH max X H0 ML  v ML ini  ðV WW þ v ML Þ ¼ YH 1  YH þ lH max V WW X H0 WW YH

ð6Þ

or

r O2

ini

 ðV WW þ v ML Þ ¼ K  v ML þ C

ð7Þ

Eq. (7) stands as a linear form where the constants K (slope) and C (y-intercept) represent the following combinations of parameters (Eq. (8)).

K¼

1  YH lH max X H0 YH

ML

biomass in the WW vs in the ML). Otherwise, when a single lHmax value is hypothesized or proved, the data from the experiments allow determining the quantity of heterotrophic biomass (XH0_WW) in the wastewater. In such case, XH0_WW could be calculated from the value of the constant C (Eq. (8)), which may be found by measurement (batch test without seed) or by extrapolation. To perform well, the Method of Increments requires that SS remains high at least during the 4 to 5 gradual increases of the inoculum. Also, during the experiment, the overall quantity of biomass that results from the growth process must be insignificant, in comparison to the quantity of mixed liquor biomass that is directly added in the reactor.

and C ¼

1  YH lH max V WW X H0 YH

WW

ð8Þ

Eq. (7) shows that by varying the quantity of ML (‘‘seed’’) and by measuring the corresponding initial oxygen uptake rates in the different runs, one could estimate lHmax from the slope of rO2_ini (VWW + vML), function of vML. This is the basic principle of the seed varying method, called S.I. method (Seed Increments). The ideal linearity established from the model could be perturbed in practice by different causes introduced by the procedure used in the S.I. method. The main factors that may have an effect are: potential significant growth between the increments, possible biomass shift due to the high F/M ambient, and the 4- to 7-fold difference between the initial F/M ratios of the first and the last increments. The linear relationship between the oxygen uptake rate function [rO2_ini (VWW + vML)] and the seed volumes (vML) holds only if the fraction of biomass generated by growth, between the increments, is small compared to the quantity of biomass added by seeding. While the traditional exponential growth method is prone to substantial growth and shift of the initial culture, the dominant biomass in the S.I. tests will probably remain as the original mixed liquor added as seed increments at each of the different steps. To be able to extract the value of lHmax from the slope K, it is necessary to know the yield (YH, generally taken as the default value) and more importantly, XH0_ML, the quantity of heterotrophic biomass in the mixed liquor that is used for the inoculums. Several methods are known for estimating the mixed liquor biomass, one of which is by respirometry (Majewsky et al., 2011). For illustrative purposes, one may use typical values for the different parameters in Eq. (6) to graphically represent the theoretical relationship between rO2_ini (VWW + vML) and vML (Figure not shown): YH = 0.67, lHmax = 6 d1, VWW = 750 mL, XH0_ML = 1000 mg/L COD, XH0_WW = 50 mg/L COD. Typically, the quantity of inoculum (vML) in the different runs is from 0 to 70 mL (10-mL steps). There are two ways for estimating the initial oxygen uptake rate for the WW alone, when rO2_ini is measured for different seed volumes: firstly, by extrapolating the linear model (Eq. (7)), to vML = 0 and secondly, by measuring the initial respiration rate in a batch test performed without seeding (only WW). A significant deviation between the initial rO2 estimates would mean a difference between the kinetics of the two groups of biomass (different lHmax for the

2.2.1. Experimental plan For illustrating the application of the method and evaluate it, three series of trials were performed with the S.I. approach to estimate lHmax of different biomass. The three sets of sludge and wastewater used in the experiments were from different wastewater treatment plants. In the first two cases, while the method was in development, partial runs were performed to fine tune the procedures (pipetting, inoculum size) and resolve some limitations (get sufficient data points before substrate depletion). The third case was more comprehensive; it was used to illustrate and quantitatively evaluate the steps of the whole process, as well as to make some comparisons with the traditional methods. 2.2.2. Respirometer A respirometer with four sample chambers was used for all the experiments (2–3 replicates for each run; Fall et al., 2011). It was formed by four 1-L narrow-mouth bottles (reactors) equipped each with a magnetic stirrer, one-inch bar, two small porous diffusers connected to an aquarium air pump, a heating-refrigerating bath to control the temperature, as well as a dissolved oxygen probe (YSI 5739) and meter (YSI 57, Ohio, USA). Automatic data logging of the DO concentrations (2–5 s intervals) and control of the aeration pumps (ON/OFF at 5–6 mg/L O2) were performed via a computer, an interfaced hardware and a software (Microlink 752 and Windmill 3.0, Windmill Ltd., Manchester, UK). Globally, the respirometer was involved in four different kinds of tests, where the oxygen uptake rate always was the monitored parameter: (1) the first kind of runs was by the S.I. method for estimating lHmax; (2) the second kind of runs were to evaluate lHmax by the traditional method (exponential growth test); (3) thirdly, the readily biodegradable substrate concentration (SS) was tested in some of the WW samples and (4) fourth, in one case, some runs were performed to estimate the decay rate constant and/or the initial biomass concentration in the mixed liquor (XH0_ML) used to inoculate the reactors. 2.2.3. Tests for measuring lHmax For performing the tests of lHmax by the S.I. method, at the beginning, 600–650 mL of pre-settled WW and 10 mg/L Allyl thiourrea (ATU) were added to each reactor (2–3 replicates), and the oxygen uptake rate was continually monitored. A well-homogenized lot of 100–200 mL mixed liquor was side-prepared and carefully maintained in suspension to be able to provide repeatable 10-mL sub-samples, at the moment of seeding the reactors. As only the initial rO2 value was required at each step, no more than three ON–OFF aeration cycles were performed at each stage characterized by increasing quantities of seed added in the reactor. The first step was generally without inoculum, followed after by the addition of 10 mL well-homogenized mixed-liquor (ML). Further increments of 10 mL seed (ML) were then added to the WW in the reactor, at each of the subsequent steps (minimum of four in

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(b) 400 ro2_ini * Vi tot (mg/d)

ro2_ini * Vi tot (mg/d)

(a) 400 300

200

100

0 0.000

y = 7152x + 107 R2 = 1 0.020

0.040

0.060

300

y = 4881x + 125 R2 = 1

200

100

0 0.000

0.020

0.040

0.060

v_ML [ L]

v_ML [L]

Fig. 2. Respiration rates function of the mixed liquor volume added (case 1).

total). Because it is important to get precise and homogenized volumes of liquor, a 5-mL Eppendorf pipette was used to perform the shots. Where the classical exponential growth test was performed (lHmax, high F/M), it was done following the Kappeler and Gujer (1992) method. A small quantity of biomass (20 ml ML) was added once only at the beginning, to 600 mL of pre-settled WW with 10 mg/L ATU. The rO2-time profiles were followed until the end of the experiment. 2.2.4. Auxiliary measurements of SS, bH and XH0_ML When SS was occasionally measured, the low-F/M test procedure (Vanrolleghem et al., 1999) was followed, adding 400 mL of pre-settled WW sample to 300 mL freshly collected mixed liquor from the same WWTP, with 10 mg/L allyl thiourea (ATU). The respirograms were registered until reaching the endogenous respiration baseline. The readily biodegradable COD concentration was then calculated from the area under curve. As previously shown, to be able to estimate lHmax by the classical growth test method, it is necessary to know the value of the decay coefficient (bH). Similarly, to be able to calculate lHmax by the S.I. method, the quantity of biomass (XH0_ML, mgCOD/L) in the mixed liquor that is used as inoculum is needed. If bH is known (measured or taken as its default value), one way for determining XH0_ML is to measure the endogenous oxygen uptake rate (rO2 end ) of the mixed liquor lot (Majewsky et al., 2011). Based on ASM1 modified matrix that considers endogenous respiration, XH0_ML is given by Eq. (9),

X H0

ML

¼

r O2 end 0 ð1  fP0 ÞbH

ð9Þ

´H and ´fp are the endogenous decay coefficient (0.2 d1, by where b default) and the fraction of inert biomass residues (20%). The respi´H (or bH for original rometric method for the determination of b ASM1) is more thoroughly described elsewhere (Vanrolleghem et al., 1999). Briefly, it consists in measuring the endogenous respiration rate (rO2 end ) of the mixed liquor at many times over a period ´H is then obtained as the first order kinetic conof several days; b stant of the r O2 end -time function. 3. Results and discussion 3.1. First experimental trial In this case, a run was performed by the S.I. method, with 650 mL of WW at 20 °C. At the beginning, the test was initiated without any seed, before adding, latter, 10-mL mixed liquor (ML) increments. The initial oxygen uptake rate at each step was measured (average from three replicates) and represented as shown

in Fig. 2a. As expected, the respiration rate function ([rO2_ini (VWW + vML)] vs vML) was highly linear (coefficient of determination, R2 = 1.0), at least for the first three points. The plateau that occurred after was informing that SS was already depleted at the fourth and fifth increments. Fortunately, as with the traditional method for the measurement of lHmax by the procedure of Kappeler and Gujer (1992), the S.I. method also allows to detect and exclude the experimental points where SS is already depleted. For the S.I. method, the time variable is not involved when analyzing the data. However, it is important to carry out as quickly as possible the 4–5 increment steps needed, before the occurrence of any significant drop on SS; this was not the case in Fig. 2a. In the experiments performed latter, this kind of limitation was avoided by changing the set points of the ON/OFF aeration cycles (from 5– 6 mg O2/L to 5–5.5 mg/L), which allowed to reduce by a half the time required for completing the cycles, while keeping SS high until the end of the test. By doing so, more data points were obtained (Fig. 2b) and a very linear function resulted also from it (R2 = 1). Precise pipetting of well-homogenized aliquots when shooting the mixed liquor seeds is essential for obtaining high quality data. Data analysis of this run was not pursued until the end (i.e. until extracting the value of lHmax from the slopes), but it shows that the type of data needed by the S.I. method is easily obtainable ([rO2_ini (VWW + vML) vs vML). Also, the ideal linearity established from the model was not perturbed by any of the previously listed potential factors. Moreover, we need to pay some attention to a point that was previously emphasized, i.e. the significance of a possible difference between the initial rO2 directly measured in the unseeded WW, vs the initial rO2 obtained from extrapolating the data to v_ML = 0. In the case of Fig. 2, no difference was noted between those two estimates, which meant similar kinetics (similar lHmax values) for the indigenous biomass from the wastewater and for the biomass from the mixed liquor. The wastewater biomass is supposed to be from SS-rich ambient (WW), while the biomass from the mixed liquor represents a selected and acclimated microbial flora (activated sludge microcosm). 3.2. Second experimental trial This second example considers the case of a wastewater that was very poor in SS (approx. 35 mg/L COD), which limits the biomass growth and did not allow the direct measurement of lHmax by any of the methods (both the classical and the S.I. methods). It was necessary to increase the SS in the wastewater (synthetic readily biodegradable COD added as sodium acetate), to be able to test the methods. Fig. 3a shows the respirogram of a low-F/M batch test (standard procedure for measuring the readily biodegradable COD fraction)

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(a) 800

(b) 600 ro2_ini * Vi tot (mg/d)

ro2 (mg/L.d)

700 600 500 400 300 200 100

500

y = 3530.18x + 146.30 R2 = 1.00

400 300 200 100 0

0 0

1

2

3

4

5

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

Time (h)

v_ML [L]

Fig. 3. Oxygen uptake rates (rO2). (a) Low F/M respirogram and (b) rO2 function of the increments.

performed on acetate-spiked wastewater. With enough SS added in the reactor (300 mg/L COD) and a relatively high quantity of inoculum (300 mL mixed liquor seed + 400 mL fortified wastewater + ATU, 23 °C), a maximum and constant respiration rate (rO2 plateau) was sustained for more than 2.5 h. With acetate shots, sufficient time was then guaranteed to be able to perform several increments as required by the S.I. method, when running high F/ M batch tests. Fig. 3b shows the data from the batch test performed with acetate-spiked WW, by the S.I. method (at 20 °C). As expected, the rO2 function [rO2_ini (VWW + vML)] increased linearly (R2 = 1) with respect to the quantity of seed (vML), all along the 11 seed-increments performed. The linearity, as observed from all the data, reinforces the credibility of the main hypothesis (negligible biomass generated from the growth, compared to the biomass added by seeding). In this case, the decay rate of the sludge was known from a pre´ H = 0.122 d1, 20 °C). The endogenous respiration vious work (b (rO2_end = 167 ± 8 mg O2/L d) of the mixed liquor was measured during this campaign, which allowed estimating the quantity of biomass in the ML stock (XH0_ML = 1713 ± 80 mg/L COD, by Eq. (9)). By Eq. (8), the parameter lHmax, and complementarily XH0_WW (the native biomass present in the WW), were calculated from the constants K and C (slope and y-intercept) of Fig. 3b. The corresponding data and final results are presented in Table 1. The growth rate value estimated by this way was coherent with the wide ranges quoted in the literature (6 d1 by default, with a range from 2 to 12 d1, Henze et al., 2000; Cox, 2004; Sözen et al., 1998). The biomass content of the WW was relatively significant, being approximately 20% of the total COD. High values of XH0_WW (up to 25%) were already reported in many other wastewaters (Sperandio and Etienne, 2000; Gokcay and Sin, 2004). 3.3. Third experimental trial This was the most comprehensive evaluation performed on the method. Experiments were run in triplicate (20 °C) to estimate the growth rate parameter, both by the traditional method and by the increments approach (S.I. method). With respect to the Kappeler and Gujer (1992) method (traditional method), the respirometric growth curves were obtained, both with (+20 mL), and without (0 mL) adding a seed to the wastewater samples (600 mL). For the increment tests, each run was performed with 600 mL of WW to which was added multiples of 10-mL mixed liquor seeds (from 0 to 60 mL, in six steps). At the end, the values of lHmax (and accessorily, XH0_WW) from the three series of tests were compared. The knowl´ H is required by all the methods; the default value edge of b (0.2 d1, at 20 °C) was used when calculating lHmax.

Table 1 Estimation of lHmax and XH0_WW(case 2) by the method of increments. Replicates

K (mg/L d)

C (mg/d)

lHmax (d1)

XH0_WW mg COD/L

#1 (Fig. 3b) #2 #3

3530 4299 3280

146 108 151

4.2 5.1 3.9

118 85 131

YH = 0.67 (ASM1)

Mean ± Std. Dev. 4.4 ± 0.6 111 ± 24

Fig. 4 shows the kind of data obtained from the tests and their analysis. For the increments tests (Fig. 4a), the linear relationship between the total oxygen consumption rate [rO2_ini (VWW + vML)] and the seed volumes (vML) was drawn; then, the constants K and C (slope and y-intercept, Eqs. (7) and (8)) were extracted from the regression, and the parameters lHmax and XH0_WW were calculated (Table 2). The mixed liquor biomass needed to complete the calculations was estimated (XH0_ML = 1838 ± 200 mg/L COD), by measuring the endogenous respiration of the stock of inoculum (based on Eq. (9)). For the traditional Kappeler-and-Gujer method, the rO2-time series data (Fig. 4b, with vs without seed) were fit with exponential functions [y = bexp (at)], where the constant a represents the dif´H), while the constant b allows calculating the ference (lHmax  b initial biomass in the batch tests (based on Eqs. (1) and (2)). From b, the test performed without seed allows estimating XH0_WW (the quantity of biomass in the wastewater). Table 2 shows the values of the parameters calculated in triplicate for each of the three kinds of run (increments vs exponential growth methods). In average, the specific growth rate parameter was 4.4, 4.7 and 4.4 d1, respectively for each of the methods. Also, the initial biomass in the wastewater was 79 mg/L COD, from the increments method, against 64 mg/L COD, as estimated by the growth test without seed. Then, not any significant difference existed between the estimates provided by the different methods. However, this limited comparison could not be used to discard the fear that the growth method could provide kinetic constants that are no longer representative of the original biomass. A wider study is required to perform a more sound comparison between the methods. Additionally, as postulated before, the data provide two independent evidences that support a similar kinetic behavior for the indigenous biomass from the wastewater, vs the biomass from the mixed liquors. First of all, in Fig. 4a (increments), the initial rO2 directly measured for the run with 0 mL seed (square mark for v_ML = 0) was coinciding with the y-intercept of the line (model extrapolation to v_ML = 0). Secondly, as more direct evidence, the values of the maximum growth rate parameter (Table 2) were comparable for the native microorganisms in the wastewater (test without seed) and for the mixed liquor biomass (test with seed).

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(b)

y = 3601.44x + 110.82 R2 = 0.99

350 300

450 400 350

ro2 [mg/L.d]

ro2_ini * Vi tot (mg/d)

(a) 400 250 200 150 100 50

20 mL seed y = 209.75e3.94x R2 = 0.98

0 mL seed y = 163.95e4.38x R2 = 0.99

300 250 200 150 100 50

0 0.00

0.02

0.04

0.06

0.08

0 0.00

0.05

0.10

v_ML [L]

0.15

0.20

0.25

Time (d)

Fig. 4. Data analysis for estimating lHmax: (a) increments method and (b) traditional method.

Table 2 lHmax and XH0_WW from the different methods. Replicates

#1 (Fig. 4) #2 #3 Mean ± Std. Dev.

Method of increments

Growth without seed

Growth with seed

lHmax (d1)

XH0_WW mg COD/L

lHmax (d1)

XH0_WW mg COD/L

lHmax (d1)

4.2 4.2 4.8 4.4 ± 0.3

87 78 73 79 ± 7

4.6 4.8 4.8 4.7 ± 0.2

68 59 66 64 ± 5

4.1 4.6 4.6 4.4 ± 0.2

´ H to be able to calculate It is necessary to know the value of b

lHmax, both for the S.I. method as for the traditional method. However, contrary to Kappeler and Gujer (1992) method where lHmax is

´H, the increments approach not less sensitive to the exact value of b need a precise estimation of the quantity of biomass in the seed. This requires the knowledge of the decay rate coefficient and good measurements of the endogenous respiration for the mixed liquor seed. Based on the results from the three cases studies, the ideal linearity established from the model never was perturbed by any of the previously listed potential factors (significant growth between the increments, possible biomass shift, and the 4- to 7-fold difference between the initial F/M ratios). The experimental set-up of the S.I. method itself has the advantage of limiting the growth and shift of biomass, which were the main criticisms against the traditional exponential growth method. The dominant biomass in the system cannot be other than the biomass of the original mixed liquor added when incrementing the seed at each step. Moreover, although the S.I. method operates in the high F/M region, 5- to 7-fold differences on the F/M ratios may exist between the first and the last increments; this variation did not have an effect on the linearity of the data and model. Concordantly, Sözen et al. (1998) also outlined the absence of significant impact on the assessment of lHmax within 2- to 3-fold difference in the F/M ratios, when using exponential growth tests. The initial-rate based method developed is a viable alternative for measuring lHmax and the approach is potentially adaptable for measuring other kinetic parameters of the ASM models (e.g. the autotrophic growth rate). 4. Conclusions

The method of seed increments (S.I.), an initial-rate based method, was proposed for measuring the ASM1 growth rate parameter lHmax. The ASM1 underlying equations were derived, which put in evidence that varying the quantity of inoculum (vML) and measuring the corresponding initial oxygen uptake rates (rO2_ini) could allow estimating lHmax, through the slope of rO2_ini.(VWW + vML), function of vML. The practical applicability of the S.I. method was evaluated. High quality respirometric data were obtained and the postulated

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