TA918C(1s2024) - Aula 8 - PROCESSO CONTINUO

Prévia do material em texto

Prof. Andreas K. Gombert
TA918C - Microbiologia 
e Fermentações
Aula 8 - 09/05/2024 
BIOPROCESSOS CONTÍNUOS
constant physico-chemical conditions. Furthermore, chemostat cultures
enable studies on the growth of micro-organisms at specific growth rates
below their mmax. Thus, even when microbial strains or growth conditions
are compared that have or cause a different mmax, chemostat cultivation
enables a comparison of their physiology at an identical specific growth rate
chosen and set by the researcher.
A chemostat (Fig. 2) can be defined by five key elements: (i) an ideally
mixed fermentation vessel (bio-reactor), (ii) a continuous inflow of fresh
growth medium, (iii) a medium composition in which a single nutrient of
choice limits biomass formation and in which all other nutrients are present
in excess, (iv) a continuous outflow of culture broth with an identical
chemical composition and biomass concentration to that in the bio-reactor
and (v) a constant ratio between effluent flow rate and culture volume in the
bio-reactor. The unique option of chemostats to ‘‘dial in’’ a specific growth
rate can best be understood by combining these five defining elements with a
mass balance of the biomass:
dðVcxÞ=dt ¼ jincx;in $ foutcx;out þ mcx;bioreactorV
Figure 2 Experimental setup for chemostat cultivation. Panel A, early design by
Monod (from Monod, 1950) where N indicates the medium reservoir; B the bio-
reactor in which cells are grown; P the effluent reservoir; E the inoculation flask and
M the stirring engine. Panel B, photograph of a current chemostat setup where 1
indicates the medium reservoir, 2 the bio-reactor, 3 the effluent reservoir, 4 the
inoculation flask and 5 the stirring engine. Adapted from Monod (1950) with
permission from Institut Pasteur.
MICRO-ARRAY ANALYSIS IN BAKER’S YEAST 265
Author's personal copy
FORMAS DE CONDUÇÃO DO PROCESSO: 
- BATELADA (= descontínuo) 
- BATELADA-ALIMENTADA (=descontínuo-alimentado) 
- CONTÍNUO
SCRIT
Processo contínuo 
(=continuous)
X
 
The CONTINUOUS reactor 
Compounds are 
constantly fed and 
being removed along 
the process
TYPICAL AIM IS TO CALCULATE THE VOLUME.
Flow/volume = residence time-1 
V.C. = Volume de Controle
EQUAÇÃO GERAL DO BALANÇO DE MASSA 
ACÚMULO = ENTRA - SAI + PRODUÇÃO 
Produção ≠ 0 quando o componente é consumido ou gerado numa reação 
Produção = 0 quando não houver reação ou quando o B.M. total 
Acúmulo = 0 quando a situação for de regime permanente (=estado estacionário) 
Acúmulo ≠ 0 quando a situação for de regime transiente 
Balanço de massa de células: 
d(X.V)/dt = FE.XE - FS.XS + μ.X.V [massa de células/tempo] 
Batelada: FE = FS = 0 
Batelada-alimentada: FS = 0 
Contínuo: normalmente, FE = FS e estado estacionário: d(XV)/dt = 0 
Normalmente, XE = 0 (alimentação de meio estéril). 
Hipótese de mistura perfeita: XS = X 
0 = -FS.X + μ.X.V = X*(μ.V - FS) 
• Balanços de massa em biorreatores
FE 
XE
FS 
X
Veloc. espec. de crescimento 
μ = (1/X)*(dX/dt) 
Veloc. espec. de consumo de S 
μS = (1/X)*(-dS/dt) 
Veloc. espec. de formação de P 
μP = (1/X)*(dP/dt) 
X
• Balanços de massa em biorreatores
FE FS
V.C. = Volume de Controle
EQUAÇÃO GERAL DO BALANÇO DE MASSA 
ACÚMULO = ENTRA - SAI + PRODUÇÃO 
Balanço de massa de substrato: 
d(S.V)/dt = FE.SE - FS.SS - μS.X.V [massa de substrato/tempo] 
Batelada: FE = FS = 0 
Batelada-alimentada: FS = 0 
Contínuo: normalmente, FE = FS e estado estacionário: d(SV)/dt = 0 
Hipótese de mistura perfeita: SS = S 
0 = FE.SE - FS.S - μS.X.V
Veloc. espec. de crescimento 
μ = (1/X)*(dX/dt) 
Veloc. espec. de consumo de S 
μS = (1/X)*(-dS/dt) 
Veloc. espec. de formação de P 
μP = (1/X)*(dP/dt) 
V.C. = Volume de Controle
EQUAÇÃO GERAL DO BALANÇO DE MASSA 
ACÚMULO = ENTRA - SAI + PRODUÇÃO 
Balanço de massa de produto: 
d(P.V)/dt = FE.PE - FS.PS + μP.X.V [massa de produto/tempo] 
Batelada: FE = FS = 0 
Batelada-alimentada: FS = 0 
Contínuo: normalmente, FE = FS e estado estacionário: d(PV)/dt = 0 
Normalmente, PE = 0 (alimentação de meio estéril). 
Hipótese de mistura perfeita: PS = P 
0 = - FS.P + μP.X.V
• Balanços de massa em biorreatores
FE FS
V.C. = Volume de Controle
Veloc. espec. de crescimento 
μ = (1/X)*(dX/dt) 
Veloc. espec. de consumo de S 
μS = (1/X)*(-dS/dt) 
Veloc. espec. de formação de P 
μP = (1/X)*(dP/dt) 
Balanço de massa de células: 
d(X.V)/dt = FE.XE - FS.XS + μ.X.V (XE = 0, V = cte, XS = X) 
V.dX/dt = - FS.X + 𝜇.X.V (defino vazão específica D = F/V) 
dX/dt = (-D + 𝜇).X (em estado estacionário, dX/dt = 0) 
D = F/V = 𝜇 (desde que 𝜇 < 𝜇MAX) O QUE ISTO SIGNIFICA? 
Processo contínuo
9
Description of the Chemostat
Author(s): Aaron Novick and Leo Szilard
Source: Science, New Series, Vol. 112, No. 2920 (Dec. 15, 1950), pp. 715-716
Published by: American Association for the Advancement of Science
Stable URL: http://www.jstor.org/stable/1678964 .
Accessed: 10/02/2011 06:03
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QUIMIOSTATO
10
Monod, J. (1950) La technique de culture continue theorie et applications. Annales de l’Institut Pasteur 79, 390–410. 
constant physico-chemical conditions. Furthermore, chemostat cultures
enable studies on the growth of micro-organisms at specific growth rates
below their mmax. Thus, even when microbial strains or growth conditions
are compared that have or cause a different mmax, chemostat cultivation
enables a comparison of their physiology at an identical specific growth rate
chosen and set by the researcher.
A chemostat (Fig. 2) can be defined by five key elements: (i) an ideally
mixed fermentation vessel (bio-reactor), (ii) a continuous inflow of fresh
growth medium, (iii) a medium composition in which a single nutrient of
choice limits biomass formation and in which all other nutrients are present
in excess, (iv) a continuous outflow of culture broth with an identical
chemical composition and biomass concentration to that in the bio-reactor
and (v) a constant ratio between effluent flow rate and culture volume in the
bio-reactor. The unique option of chemostats to ‘‘dial in’’ a specific growth
rate can best be understood by combining these five defining elements with a
mass balance of the biomass:
dðVcxÞ=dt ¼ jincx;in $ foutcx;out þ mcx;bioreactorV
Figure 2 Experimental setup for chemostat cultivation. Panel A, early design by
Monod (from Monod, 1950) where N indicates the medium reservoir; B the bio-
reactor in which cells are grown; P the effluent reservoir; E the inoculation flask and
M the stirring engine. Panel B, photograph of a current chemostat setup where 1
indicates the medium reservoir, 2 the bio-reactor, 3 the effluent reservoir, 4 the
inoculation flask and 5 the stirring engine.Adapted from Monod (1950) with
permission from Institut Pasteur.
MICRO-ARRAY ANALYSIS IN BAKER’S YEAST 265
Author's personal copy
QUIMIOSTATO = Cultivo contínuo em estado 
estacionário, com um nutriente limitante do 
crescimento no meio de alimentação.
Criado simultaneamente por Monod ;-)
Balanço de massa de células: 
d(X.V)/dt = FE.XE - FS.XS + μ.X.V (XE = 0, V = cte, XS = X ou mistura perfeita) 
V.dX/dt = - FS.X + 𝜇.X.V (defino vazão específica D = F/V) 
dX/dt = (-D + 𝜇).X (em estado estacionário, dX/dt = 0) 
D = 𝜇 O QUE ISTO SIGNIFICA? 
Balanço de massa de substrato: 
d(S.V)/dt = FE.SE - FS.SS - μS.X.V (FE = FS = F, V = cte, SS = S ou mistura perfeita) 
V.dS/dt = F(SE - S) - μS.X.V (em estado estacionário, dS/dt = 0) 
0 = D(SE - S) - μS.X (lembrando que YX/S = 𝜇/μS) 
0 = D(SE - S) - (𝜇/YX/S)*X (D = 𝜇, do B.M. de células acima) 
0 = D(SE - S) - (D/YX/S)*X 
0 = D(SE - S - X/YX/S) 
X = YX/S*(SE - S) —> X dentro do reator, no estado estacionário 
Quimiostato
• Por que um cultivo contínuo tende ao estado estacionário?
dX/dt = (-D + 𝜇).X imaginemos que por algum motivo 𝜇 > D, então X cresce 
X = YX/S(SE - S) se X cresce, então S tem que diminuir, pois Y e SE são ctes 
𝜇 = 𝜇MAX.S/(KS + S) equação de Monod* —> 𝜇 diminui e o sistema tende a 𝜇=D 
(pode-se fazer o raciocínio inverso, 𝜇 < D, e chega-se à mesma conclusão) 
* considera apenas o fenômenos de limitação por S, ou seja, 𝜇 é somente função de 
uma eventual limitação por S e não também função de outros fenômenos, como 
por exemplo inibição por S ou inibição por P
sempre se inicia como um cultivo em batelada, mas…
Modelo cinético de Monod
https://www.cs.montana.edu/webworks/projects/stevesbook/contents/chapters/chapter002/section002/black/page001.html
SCRIT
forma da equação é idêntica à de 
Michaelis & Menten, para 
cinética enzimática. Mas, enquanto 
a primeira é baseada 
num mecanismo de reação (modelo 
fenomenológico), a de 
 Monod é baseada 
em observação experimental 
somente (modelo empírico)!
14
GROWTH OF BACTERIAL CULTURES 383
situation is very improbable and, in general, the maximum growth
rate should be expected to be controlled by a large number of
different rate-determining steps. This makes it clear why ex-
ponential growth rate measurements constitute a general and
sensitive physiologic test which can be used for the study of a wide
variety of effects, while, on the other hand, quantitative inter-
pretations are subject to severe limitations. Even where the condi-
tion or agent studied may reasonably be assumed to act primarily
on a single rate determining step, the over-all effect (i.e., the growth
rate) will generally remain an unknown function of the primary
effect.
Although very improbable, it is of course not impossible that
the exponential growth rate could in certain specific cases actually
~1o5
3:
~1.0
Fx6. 4.~Growth rate of E. col¢ in synthetic medium as a function of glucose
concentration. Solid line is drawn to equation (2) with RK = 1.35 divisions per hour,
and Ct =0.22 M X10-4 (11). Temperature ° C.
be determined by a single master reaction. But such a situation
could hardly be assumed to prevail, in any one case, without direct
experimental evidence. Some recent attempts at making use of the
master reaction concept in the interpretation of bacterial growth
rates are quite unconvincing in that respect (19).
Rate-concentration relations.--Notwithstanding these difficul-
ties, relatively simple empirical laws are found to express conven-
iently the relation between exponential growth rate and concentra-
tion of an essential nutrient. Examples are provided in Figs. 4 and
5. Several mathematically different formulations could be made to
fit the data. But it is both convenient and logical to adopt a
hyperbolic equation:
CR = RK ........................ [21Ct+C
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15
384 MONOD
similar to an adsorption isotherm or to the Michaelis equation.
In the above equation C stands for the concentration of the
nutrient. RK is the rate limit for increasing concentrations of. C.
Cz is the concentration of nutrient at which the rate is half the
max~mumo
The constant RK is useful in comparing efficiency in a series of
related compounds as the source of an essential nutrient. So far
extensive data are available only with respect to the organic
source (11). The value of R~ may vary widely when different
0.035
~o.o~o
~0.o2 s
-~ 0.o~o
o.o|o
! t I
O.1 O~. O.~
GLUCOSE (Mx)
FI~. 5.~C-rowth rate of M. tuberculosis in Dubos’ medium, as a function of
glucose concentration. So|id llne drawn to eqt~ation (2) wil~ RK=0.037 and
~--~/~5 (20~.
organic sources are compared under otherwise identical conditions.
There is no doubt that it is related to the activity of the specific
enzyme systems involved in the breakdown of the different com-
pounds, and it can be used with advantage for the detection of
specific changes (e.g., hereditary variation) affecting one or an-
other of these systems (30).
The value of C~ should similarly be expected to bear some
more or less distant relation to the apparent dissociation constant
of the enzyme involved in the first step of the breakdown of a
given compound. Furthermore, since a change of conditions affect-
ing primarily the velocity of only one rate-determlning step will,
in general (but not necessarily), be only partially reflected in the
www.annualreviews.org/aronline
Annual Reviews
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7
Equação de Monod p/ diferentes Ks
aumentando KS
8
Ks corresponde à S na qual µ=µmax/2
O modelo de Monod 
explica todas as situações?
• Somente leva em conta o fenômeno de limitação por 
substrato! 
• Não descreve p.ex. a fase lag. Por que?
𝝁 = 𝝁MAX*S/(KS + S)
Descreve bem as fase log, desaceleração e estacionária (desde 
que o único fenômeno relevante seja limitação por S)
• Se houver outros fenômenos importantes na situação de 
interesse, p. ex. inibição por substrato ou inibição pelo 
produto, preciso usar outros modelos!
 Diferentes Modelos de Crescimentos
Linearização p/ obtenção dos 
parâmetros KS e 𝜇MAX
Coef. linear
Coef. angular
(Equação de Lineweaver-Burk)
S k
S
s
max +
= µµ
Monod
Linearização
Diferença entre SE e S
33 Continuous culture
remembered that nongrowth related secondary metabolites are produced only under 
certain physiological conditions—primarily under limitation of a particular substrate 
so that the biomass must be in the correct “physiological state” before production 
can be achieved. The elucidation of the environmental conditions, which create the 
correct “physiological state” is extremely difficult in batch culture and this aspect is 
developed in a later section.
Thus, batch fermentation may be used to produce biomass, primary metabolites, 
and secondary metabolites. For biomass production, cultural conditions supporting 
the fastest growth rate and maximum cell population would be used; for primary 
metabolite production conditions to extend the exponential phase accompanied by 
product excretion and for secondary metabolite production, conditions giving a short 
exponential phase and an extended productionphase, or conditions giving a decreased 
growth rate in the log phase resulting in earlier secondary metabolite formation.
CONTINUOUS CULTURE
Exponential growth in batch culture may be prolonged by the addition of fresh me-
dium to the vessel. Provided that the medium has been designed such that growth 
is substrate limited (ie, by some component of the medium), and not toxin limited, 
exponential growth will proceed until the additional substrate is exhausted. This ex-
ercise may be repeated until the vessel is full. However, if an overflow device was 
fitted to the fermenter such that the added medium displaced an equal volume of cul-
ture from the vessel then continuous production of cells could be achieved (Fig. 2.5). 
If medium is fed continuously to such a culture at a suitable rate, a steady state is 
FIGURE 2.5 A Schematic Representation of a Continuous Culture
SE
S
SE eu escolho! 
e portanto defino X! 
S vem p.ex. de Monod: 
S = 𝜇.KS/(𝜇MAX - 𝜇) 
depende da combinação 
entre microrganismo, meio 
de cultivo e condições 
ambientais!
Quimiostato
• Escolho 𝜇 —> 𝜇 = D = F/V (limitado a 𝜇 < 𝜇MAX) 
• Escolho X —> X = YX/S*(SE - S), lembrando que S << SE
37 Continuous culture
increase in s and a decrease in x as D approaches Dcrit. Fig. 2.8 illustrates the effect 
of increasing the initial limiting substrate concentration on x and s . As SR is in-
creased, so x increases, but the residual substrate concentration is unaffected. Also, 
Dcrit increases slightly with an increase in SR.
The results of chemostat experiments may differ from those predicted by the fore-
going theory. The reasons for these deviations may be anomalies associated with the 
equipment or the theory not predicting the behavior of the organism under certain 
x¯
s¯
x¯
FIGURE 2.7 The Effect of Dilution Rate on the Steady-State Biomass and Residual Substrate 
Concentrations in a Chemostat of a Microorganism with a High Ks Value for the Limiting 
Substrate, Compared with the Initial Substrate Concentration 
______, Steady-state biomass concentration; — — —, Steady-state residual substrate 
concentration.
FIGURE 2.8 The Effect of the Increased Initial Substrate Concentration on the Steady-State 
Biomass and Residual Substrate Concentrations in a Chemostat 
______, Steady-state biomass concentration; — — —, Steady-state residual substrate 
concentration. SR1, SR2, and SR3 represent increasing concentrations of the limiting 
substrate in the feed medium.
lavagem = “wash-out” 
quando D > 𝝁MAX
Produtividade no quimiostato 45 Continuous culture
in Fig. 2.11. Thus, maximum productivity of biomass may be achieved by the use of 
the dilution rate giving the highest value of Dx .
The output of a batch fermentation described by Eq. (2.27) is an average over the 
period of the fermentation and, because the rate of biomass production is dependent 
on initial biomass (dx/dt = µx), the vast proportion of the biomass is produced toward 
the end of the fermentation. Thus, productivity in batch culture is at its maximum 
only toward the end of the process. For a continuous culture operating at the optimum 
dilution rate, under steady-state conditions, the productivity will be constant and al-
ways maximum. Thus, the productivity of the continuous system must be greater 
than the batch. A continuous system may be operated for a very long time period 
(several weeks or months) so that the negative contribution of the unproductive time, 
tiii, to productivity would be minimal. However, a batch culture may be operated for 
only a limited time period so that the negative contribution of the time, tii, would be 
very significant, especially when it is remembered that the batch culture would have 
to be reestablished many times during the time-course of a continuous run. Thus, 
the superior productivity of biomass by a continuous culture, compared with a batch 
culture, is due to the maintenance of maximum output conditions throughout the 
fermentation and the insignificance of the nonproductive period associated with a 
long-running continuous process.
The steady state achievable in a continuous process also adds to the advantage of 
improved biomass productivity. Cell concentration, substrate concentration, product 
concentration, and toxin concentration should remain constant throughout the fer-
mentation. Thus, once the culture is established the demands of the fermentation, in 
terms of process control, should be constant. In a batch fermentation, the demands 
of the culture vary during the fermentation—at the beginning, the oxygen demand is 
low but toward the end the demand is high, due to the high biomass and the increased 
viscosity of the broth. Also, the amount of cooling required will increase during the 
process, as will the degree of pH control. In a continuous process oxygen demand, 
Dx¯
FIGURE 2.11 The Effect of Dilution Rate on Biomass Productivity in Steady-State 
Continuous Culture
Produtividade = D.X [g/(L.h)]
opera-se normalmente em 
0,85*DCRIT, para evitar 
risco de lavagem!
P
Processo descontínuo (batelada): Vantagens
▪ Maior segurança (contaminação - assepsia) 
▪ Sistema Fechado – Batelada – Industria de Alimentos 
▪ Flexibilidade (produtos) 
▪ Fases sucessivas (mesmo recipiente) 
▪ Controle da estabilidade genética do Micro-organismo 
▪ Identificação de todos materiais do mesmo lote 
DESVANTAGENS 
▪ Menores rendimentos/produtividades (Tempo “morto”) 
▪ Maior necessidade de mão-de-obra humana 
▪ (↓) Tempos Mortos: (↑) Produtividade 
▪ Obtenção de Caldo Fermentado Uniforme
(Bom p/ etapa de Downstream)
▪ Manutenção das células em mesmo estado fisiológico
▪ Associação de outras Operações contínuas 
▪ Facilidade de Controles Avançados 
▪ (↓) Mão de Obra
Processo Contínuo: VANTAGENS
▪ (↑) Investimento 
▪ Mutações espontâneas (longos períodos)
▪ (↑) Contaminação – sistema aberto
DESVANTAGENS
Como "projetar" meu processo?
• Preciso partir de uma meta de produção! Pode ser p.ex. determinada 
por uma demanda de mercado.
• Exemplo: 10 ton de massa seca de levedura por mês.
• Supondo que Pr = 2,5 g X/(L.h), 10*106/30/24/2,5 = 5555 L é o volume 
de reator necessário!
• Pr = D.X —> Uso D = 0,85*DCRIT
• Se DCRIT = 0,4 1/h —> D = 0,34 1/h —> F = D*V = 1888 L/h
• X = Pr/D = 2,5/0,34 = 7,35 g/L
• SE = S + X/YX/S = 0 + 7,35 g/L / 0,5 g/g = 14,7 g/L
P
 Contínuo múltiplos estágios Contínuo
 Batelada Alimentada
 Batelada Simples
não abordamos neste curso, 
mas é muito utilizado na 
indústria 
de bioprocessos! 
(útil por exemplo para 
manter a concentração 
de nutrientes baixa no 
biorreator ou para controlar 𝝁)