BIOTECHNOLOGY TECHNIQUES Volume 10 No.6 (June 1996) p.425430 Received (1s revised 9rlr April.

A FAST KINETIC MODEL DISCRIMINATION APPLIED TO THE CONTINUOUS TWO-PHASE ANAEROBIC DIGESTION OF

FRUIT AND VEGETABLE WASTES

A. h&z.-Viturtia and I. Mata-Alvarez*

University ofBarcelona - Dept. of Chemical Engineering - Marti i Franques 1/6plt - E-08028 - Barcelona - Spain

SUMMARY

A simple method to fit the constants of first order, Monod and Chen and Hashimoto modeis usiug only one single linear regression, is presented. The method can be applied to continuous operated systems. As au example, the kinetic behaviour of the anaerobic digestion of a mixture of fruit and vegetable wastes is studied. Chen and Hashimoto model yields the best fit.

INTRODUCTION

An understandiig of the kinetics of the biodegradation processes enables predictions of the

performance of reactors and assists in design. Kinetics can also contribute to the

understanding of the mechanisms regulating anaerobic digestion processes (Cecchi et d,

1990). From a review of the diierent models proposed for methanization of complex

substrates @Iata-Alvarez & Cecchi, 1990), three, quite known have been selected and tested

in this investigation: first-order, Monod and Chen-IIashimoto model.

The first order kinetic model has been applied to systems involving complex wastes. It is

simple and useful. The basic equation for the substrate utilization rate r (g 1-i day) is:

r=-kS 0) where k (day-‘) is the first-order kinetic constant and S (g 1-r) represents the biodegradable

reactor substrate concentration.

’ To whom all correspondence should be addressed

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Lawrence and McCarty (1969) applied the Monod model to anaerobic digestion processes.

Since then, it has been widely used, especially with soluble substrates. The basic equation is:

CL = l-hux s@G+s) (2)

where ~1 (day -‘)is the specific micro-organism growth rate, h (day -‘) the maximum specific

micro-organism growth rate and K, (g I-‘) the saturation kinetic constant.

The Chen-Hashimoto model (1978) is an application of that of Contois adapted to anaerobic

digestion processes. It is an expanded form of the Monod model which takes into account

mass transfer limitations that may cause the specitic growth rate to vary with population

density. The basic equation is:

p = b (S/S,) / pc + (1-K) S/S,] (3)

where M is the Chen-Hashimoto kinetic constant and S, (g 1-l) the biodegradable influent (or

initial) substrate concentration.

The biodegradable substrate concentration S (‘g l-r), is a difficult parameter to be measured.

Usually it is preferable to use the accumulated methane production per unit of volatile solid

added (the specific methane production), B (m3 C& kg-’ VS). This parameter is related to

the biodegradable substrate concentration as follows:

(B,-B)/B, = S/S,

where B, (m’ C& kg-’ VS )is the ultimate methane yield (Chen & Hashimoto, 1978).

(4)

Application to a steady-state continuous system

Assuming a completely mixed continuous flow system, the rates of change of the micro-

organism and substrate concentration are given as follows:

dX/dt = PX - (XERT) (5)

dS/dt = r + (S,-S)/HRT (6)

where X (g 1-l) is the effluent microorganism concentration and HRT (day), the hydraulic

retention time).

Under steady state conditions, equations 5 and 6 yield:

p= l/HRT

r = (S-S,)/HRT

For the First order model, equations 1, 8 and 4 give:

HRT = l/k [B/($,-B)]

(7)

(8)

(9)

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For the Monod model equations 2,7 and 4 give:

HRT = HK~~IN + FRTMBI WS,) @34(RrB)l (10)

where HRTm = ~/PM. This equation can be arranged as a function of B/@&,-B) as follows:

HRT = J3RTm (1 + K$S,,) + HRTm Q&/S,) [B/@&,-B)] (11)

In the same way, for the Chen-Hashimoto model, results:

HRT = 13RTm + ElRTm K [B/&,-B)] (12)

Looking at equations 9, 11 and 12 it is clear that all of them have the same structure:

HRT = a + b ~/(B,-B)] (13)

This fact provides an easy method to estimate the constants of the three models, using a

simple and single linear regression of HKT vs. B/@-B). The intercept and the slope, will give

the constants of each model, provided that a previous estimate of the ultimate methane yield,

B, , is available. If the regression is satisfactory, it means that the experimental behaviour fits

mathematically to all the three models. The lack of fit will be the same for the three models,

so that discrimination among them will be done on the basis of the values of the constants

fitted.

MATERIALS AND METHODS

Experiments were carried out at laboratory scale in two parallel, two-phase systems, one consisting of a hydrolyser (1.3 1 working volume) and a me&miser (hybrid type reactor of 0.5 1 workipg volume) coupled by means of a peristaltic pump. Both reactors were maintained at 35 f O.S’C. The lower section of methanisers consisted of an upflow anaerobic sludge blanket reactor. Above this was an anaerobic filter using polyurethane foam as a support. More details of this

device can be found in literature (Mtz.-Viturtia et al., 1995).

Four different feed flow rates of substrate, simulating the wastes of Barcelona Central Market (see Table 1 for composition) were used, until steady-state performance was achieved. Resulting hydrolyser hydraulic retention times are shown in Table 2.

Table 1. Basic characteristics of the substrate fed to the hydrolisers, (Mtz.-Viturtia et al., 1995)

Parameter Value

Total Solids, TS (g I?) 64

Volatile Solids, VS (g 1-l) 56.7

Total Nitrogen (mg I-‘) 1322

Total Phosphorous (mgf’) 300

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Total Solids (TS), Volatile Solids (VS), Total Nitrogen and Total Phosphorous analysis were carried out in accordance with the Standard Methods (1985) and Bond & Straub (1986). Biogas production was measured using a displacement device equipped with an optical cell (Mata- Alvarez et al., 1986).

RESULTS

Table 2 shows the main results obtained with the continuous two-phase anaerobic digestion

of f?uit and vegetable wastes. They are presented in a form suitable for fitting purposes.

Estimation of S, and B, values

The value of S, required by the Monad model, is assumed to be equal to the volatile solids

concentration at the influent stream. Then, Tom Table 1, S, = 56.7 g 1-l. At the same time

and before the constants of the three models can be established, B, is also required. This

value was estimated in a previous paper (Mata-Alvarez et a1.,1993) following the method

reported by Cben & Hashimoto (1978). The value obtained was B, = 8.517 m3 CT% kg-’ VS

add.

Model fitting

Plotting the values of HRT against B/(%,-B) (Table 2), a straight line is obtained. The best fit

with a regression coefficient of 0.9996 is:

HRT = 3.464 + 4.252 B/(&,-B) (14)

This equation, will be the basis for the fitting analysis.

The first-order model is rejected because equation 9 predicts a zero origin ordinate, and

equation 14 has a value of 3.464.

Applying the values of equation 14 to the Monad equation 1 P results that HRTm= -0.7873 day and %= -305.1 g I-‘. These negative values have not significance, Thus the Modod model is also rejected.

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Table 2. Experimental results observed in the four hydraulic retention times tested. Results are given in terms of

the specific methane production. The ratio B/&B) is provided for fitting purposes..

Working in the same way and using the Chen-Hashimoto equation 12, the following

constants are fitted:

HRTa = 3.464 day

K = 11.227

~MAX = UHRTMN = 0.2887 day-’

These values of the Chen-Hashimoto kinetic constants are within the range referenced by

diierent authors, fi-om 0.11 to 0.79 day-’ for PM, and from 0.17 to 9.04 for JX, (Pfeffer,

1974; Bryant et al., 1976; varel et al., 1977; Brito et al, 1987). As a consequence this

model is the one presenting the best fit and the constants obtained are the most appropriate

for this system.

CONCLUSIONS

Discrimination of the best kinetic model to fit the behaviour of a continuous anaaerobic

digsetion of f?uit and vegetable wastes has been carried out using only a single linear

regression. Results show clearly that the best model corresponds to the Chen and Hashimoto

one.

ACKNOWLEDGEMENT

Authors gratefidly acknowledge the support of CICYT Spanish project AMB93-0658

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