Multiphase partitioning airlift bioreactors: An alternative for hydrocarbon biodegradation in contaminated environments

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Multiphase partitioning airlift bioreactors: An alternative for hydrocarbon biodegradation in contaminated environments
nezb, Sergio Valdivia-Riveraa, Manuel Alejandro Lizardi-Jime Sergio Alejandro Medina-Morenoc, Victor Sánchez-Vázquezd,*

a Centro de Investigacio´n y Asistencia en Tecnologı´a y Disen˜o del Estado de Jalisco A.C., Unidad Sureste, Merida, Mexico b CONACYT-Universidad Auto´noma de San Luis Potosı´, San Luis Potosi, Mexico c Universidad Polit
ecnica de Pachuca, Zempoala, Mexico d Departamento de Biotecnologı´a, Universidad Auto´noma Metropolitana-Iztapalapa, Iztapalapa, Mexico *Corresponding author: e-mail address: [email protected]

Contents 1. An overview of hydrocarbon pollution 2. Microbial uptake by direct contact and emulsified forms 3. Bacterial routes of hydrocarbon degradation 4. Fungal hydrocarbon uptake 5. Airlift bioreactor as remediation alternative 6. Immobilized microorganisms 7. Mathematical modeling 8. Conclusions References Further reading

2 3 4 7 8 12 14 20 21 23

Abstract Airlift bioreactor (ALB) is a multiphasic pneumatic system agitated with gas phase bubbles that break toward the liquid phase, resulting in an isothermal expansion that keeps pseudo-homogeneity within the bioreactor. ALBs are extensively used in biotechnology. However, scarce information is available about environmental purposes, e.g., hydrocarbon biodegradation. This chapter is focused on describing the applicability of the airlift bioreactors for hydrocarbon biodegradation, considering some advantages and disadvantages; these could be evaluated by experimental way or via mathematical modeling and simulation. This chapter reviews: (i) an overview of hydrocarbon pollution, (ii) microbial uptake by direct contact and emulsified forms, (iii) bacterial uptake, (iv) fungal uptake, (v) airlift bioreactors as hydrocarbon remediation alternative, (vi) immobilized microorganisms in airlift bioreactors and (vii) mathematical modeling.

Advances in Chemical Engineering ISSN 0065-2377 https://doi.org/10.1016/bs.ache.2019.01.006

#

2019 Elsevier Inc. All rights reserved.

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1. An overview of hydrocarbon pollution Due to the global energy needs of the oil sector, it has grown rapidly (Gonza´lez, 2009). Pollution from oil spills is a problem derived from its transport, which has affected the planet for decades (Mironov, 1968). However, despite technological advances, it is a problem that continues, since the hydrocarbons industry is of vital economic importance for industrialized and developing countries (Soto-On˜ate and Caballero, 2017). So some of the spills, or environmental disasters, most important that have occurred in the world, have occurred in the territory of countries benefited from the hydrocarbons industry. Some examples of spills around the world are: France with 19,800 tons in the year 1999; France and Portugal with 63,200 tons in the year 2002; Philippines with 2100 tons in the year 2006; Republic of Korea with 10,900 tons in the year 2007 (Soto-On˜ate and Caballero, 2017). In the year 2016, 5500 tons of oil was spilled into the sea in Veracruz, Mexico (ITOPF, 2017). Oil spills affect the marine life, birds, ecosystems and human health due to their toxic, carcinogenic and mutagenic properties (Abha and Swaranjit, 2012). The direct impacts on the environment are related to the death and loss of vitality of species within an ecosystem, as some hydrocarbons, especially the lighter ones, are easily absorbed in the organs and cellular tissues, promoting lethal toxic effects (ITOPF, 2017). In Mexico, the presence of oil and gas pipelines is recognized, among others that cross the entire Mexican Republic (Orozco, 2010); these pipelines are often deteriorated causing spills (Schmidt-Etkin, 2010). Some frequent causes of spills are exploitation of oil wells and inadequate procedures of hydrocarbon disposal, both of them resulted in water and soil pollution (Saval, 2000). Oil spilled in water and soil is susceptible to microbial degradation processes (Lizardi-Jim
enez et al., 2012, 2015) generating a great industrial and research interest for the development of technologies able to recover water and soil contaminated with oil; such as: excavation and confinement, steam extraction, stabilization and solidification, soil washing, chemical precipitation, vitrification, incineration, among others (Skladany and Metting, 1993). Many of these treatments do not destroy the polluting hydrocarbons; they only transfer them from one to another, and moreover some of these methods are expensive and generate byproducts that could be more toxic than initial hydrocarbons. An attractive

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biotechnological alternative, presented in this chapter, refers to the use of petroleum-degrading microorganisms, which could be cultured (as free suspended or immobilized cells) in airlift bioreactors to degrade the hydrocarbons in contaminated environments. So this chapter is focused on describing the applicability of the airlift bioreactors for hydrocarbon biodegradation, considering some advantages and disadvantages; these could be evaluated by experimental way or via mathematical modeling and simulation.

2. Microbial uptake by direct contact and emulsified forms Some of the most common biotechnological options related to the bioremediation of water and soil contaminated by oil and its derivatives are based on the use of microorganisms. It has been reported that direct contact with oil pollutants acts as a selective pressure that selects consortia with greater degrading capability within a native microbial community (R€ oling et al., 2002) improving the efficiency of oil removal in soils and the cleaning and decontamination of aqueous effluents. Microbial hydrocarbon degrading consortia can be isolated from the roots of some plants that grow naturally in oil contaminated sites, since the microenvironment developed in the rhizosphere of these plants promotes the growth of microbial populations with potential hydrocarbon degradation activity (Dı´az-Ramı´rez et al., 2003). (a) Consumption by direct contact The adhesion of cells to the hydrocarbon droplets can minimize the diffusion distance facilitating the transport of the hydrophobic substrates into the microbial cells. The high cellular hydrophobicity is a prerequisite for the removal of alkanes by direct contact. (b) Consumption via emulsified forms Emulsification consists in increasing the surface area of the hydrocarbon phase by forming microscopic droplets in stable emulsions. Some studies state that the consumption of emulsified forms is preponderant over direct contact (Medina-Moreno et al., 2013). The main difference is while in direct contact cells add to droplets, maybe macroscopic, in emulsified way microdroplets or nanodroplets add to cells.

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3. Bacterial routes of hydrocarbon degradation Oil-derived hydrocarbons can be divided into four classes according to their structure and molecular configuration: • Aliphatics. • Aromatics. • Asphaltenes: phenols, fatty acids, ketones, esters and porphyrins. • Resins: pyridines, quinols, carbazoles, sulfoxides and amides. The use of hydrocarbons has increased in daily activities, leading to a constant pollution problem. However, there are microorganisms which have developed the ability to degrade this type of compounds, this being a practical method that could be effective to reduce the problem in contaminated sites. The extraordinary versatility of bacteria to use different hydrocarbons as the sole source of carbon and energy was evidenced due to its potential to oxidize different xenobiotic compounds. These compounds are naturally or chemically synthesized by human-industrial activities; however, they are discharged daily into the environment, generating a large contamination problem. The presence of aromatic compounds in the biosphere through history explains why microorganisms have developed different metabolic pathways using these compounds as a substrate and a source of energy for their growth, thus getting a variety of microorganisms that can mineralize the compounds of interest (Widdel and Rabus, 2001). To reduce the contamination of these aromatic compounds, bacteria use a wide variety of catabolic routes. Therefore, biodegradation is defined as the process by which microorganisms transform or alter the chemical structure of pollutants in the environment through oxidation-reduction reactions. Several factors are known that affect the degradation of hydrocarbons but one of the most important is its low bioavailability for microorganisms; this is defined as the degree of interaction of compounds or contaminants with microorganisms (Harms et al., 2010). Petroleum hydrocarbons biodegradability is function on the chemical structure and follows the next trend: Linear alkanes > branched alkanes > small aromatics > cycle alkanes > polycyclic aromatic hydrocarbons. It should be noted that the high molecular weight hydrocarbons such as polycyclic aromatic are not completely mineralized. Alkanes are saturated hydrocarbons and also are among the main constituents of oil (20–25%) are more biodegradable (Tzintzun-Camacho et al., 2012).

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H2O

O2 Aerobic chemotrophs

Anoxygenic photoautotrophic

CO2

Biomass

Light Hydrocarbons CnHm

Biomass CO2

Anaerobic chemotrophs

NO3+

N2

Fe(III)

Fe(II)

SO42–

H2S

CO2 Biomass

CH4

Fig. 1 Systems that use microorganisms to degrade hydrocarbons. Modified of LizardiJim
enez MA: Degradación microbiana de hidrocarburos. In Peralta-P
erez R, RochaGutierrez A, Zavala J, editors: Topicos selectos de bioquímica, Universidad Autónoma de Chihuahua, 60–86, 2015.

In Fig. 1, systems that use microorganisms to degrade different types of hydrocarbons are presented. Some microorganisms are able to form or “synthesize” biomass by using oxygen as the final electron acceptor in oxide-reduction reactions (aerobic chemotrophs) by which they degrade or consume hydrocarbons. Others, on the other hand, use different final electron acceptors (anaerobic chemotrophs). These two types of microorganisms generate carbon dioxide as the final product of degradation. Finally, another group of microorganisms are able to incorporate carbon dioxide for the formation of biomass (Anoxygenic phototroph). Bacteria genera Roseococcus and Rhodobacter are examples of anoxygenic phototrophs (Yurkov and Csotonyi, 2009). Fig. 2 shows the route of terminal oxidation (oxidation of a terminal carbon) of the alkanes and the route of subterminal oxidation (oxidation of a subterminal carbon). The short chain alkanes are also metabolized by a subterminal oxidation, where the secondary alcohol is transformed to a ketone, to be later oxidized by a Baeyer-Villager type monooxygenase until obtain an ester. The ester is hydrolyzed by an esterase to an alcohol and a fatty acid. In some cases both ends of the alkane are oxidized and a dicarboxylic acid is produced; generally this reaction is carried out in yeasts and bacteria (Tzintzun-Camacho et al., 2012).

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Fig. 2 Main metabolic pathways in the degradation of alkanes. Modified of LizardiJim
enez MA: Degradación microbiana de hidrocarburos. In Peralta-P
erez R, RochaGutierrez A, Zavala J, editors: Topicos selectos de bioquímica, Universidad Autónoma de Chihuahua, 60–86, 2015.

Most aerobic microorganisms could easily degrade long-chain hydrocarbons. So it can say that the microorganisms that are capable of degrading alkanes must first oxidize the last carbon of the molecule with the help of the multienzyme complex that does not do more than incorporate an oxygen molecule. Thus, a hydrocarbon with an alcohol group is obtained, which is more reactive. Through other enzymes this alcohol group is oxidized to aldehyde and finally to a carboxylic acid. Thus a molecule similar to a fatty acid is obtained and can be degraded to acetyl-CoA by β-oxidation. This oxidation process can also occur in nonterminal carbons, giving rise to two fatty acids that will be processed by β-oxidation as shown in Fig. 3 (Ashraf et al., 1994) where alkane is oxidized to secondary alcohol to suffer a dehydrogenation to methyl ketone which is oxidized to acetyl ester to produce acetic acid and a primary alcohol. Acetic acid is first oxidized to aldehyde and then to carboxylic acid which in turn enters β-oxidation. The most studied genre in the field is Pseudomonas.

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Fig. 3 Oxidation of alkanes to carboxylic acids for entry into the β-oxidation. Modified of Lizardi-Jim
enez MA: Degradación microbiana de hidrocarburos. In Peralta-P
erez R, RochaGutierrez A, Zavala J, editors: Topicos selectos de bioquímica, Universidad Autónoma de Chihuahua, 60–86, 2015.

4. Fungal hydrocarbon uptake The development of chromatographic techniques coupled to mass spectrometry has allowed to study the mechanisms of catabolic hydrocarbon breakdown. Filamentous fungi strains can metabolize alkanes by the insertion of molecular oxygen by alkane monooxygenases (Rehm and Reiff, 1981). The involved enzyme array involves cytochrome P450 (Gallo et al., 1971). Following the alkane oxidation to primary alcohol, further oxidation to fatty acid via aldehyde occurs; these reactions involve NADPH yielding dehydrogenases specific for long chain alcohols and aldehydes. Finally, further catabolic route for fatty acids is the β-oxidation producing the corresponding acyl-CoA ester (Lindley and Heydeman, 1985). Polycyclic aromatic hydrocarbons (PAH) are contaminants which are known as carcinogenic and mutagenic compounds. Filamentous fungi

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H

H

H

ase

0 -45 en t P xyg Cy noo o M

R

H R

O O2

O

tic ma nzy ment e e n No rrang rea

H

H2 O Epox hydr ide olase s

OH OH H R

Pero

xida

R

ses

PAH-Quinones

Ring fission products

CO2

Fig. 4 Pathways for the fungal metabolism of polycyclic aromatic hydrocarbons. Edited of Cerniglia CE: Fungal metabolism of polycyclic aromatic hydrocarbons: past, present and future applications in bioremediation, J Ind Microbiol Biotechnol 19:324–333, 1997.

can also degrade PAH. Several peroxidase activities have been observed as responsible of aromatic rings rupture and first oxidation step (Wang et al., 2009). In comparison with bacteria, filamentous fungi are better able to colonize soil and to compete with autochthonous microbiota (Novotny et al., 1999). Some fungi strains have been reported as degraders of macromolecular organic matter with which the target pollutants have been combined (Wang et al., 2009). The biodegradation of PAH by fungi depends on the catalytic activity of extracellular enzymes. Two of the main routes of PAH oxidation are via peroxidases and Cyt P-450 monooxygenase, as shown in Fig. 4. Anaerobic degradation could take place in core of fungal pellets. The principal mechanistic characteristics of the anaerobic biological activation of hydrocarbons, particularly of alkanes, come to be manifest by formation of functionalized products from alkanes, as the least reactive hydrocarbons and requires very harsh conditions or special catalysts for activation (Widdel and Rabus, 2001).

5. Airlift bioreactor as remediation alternative Airlift bioreactor (ALB) is an example of multiphasic partitioning bioreactors. ALB is a pneumatic agitation equipment which is characterized by the energy supply to maintain the homogeneity inside by means of gas flow (Chisti, 1989). The gas phase velocity generates an isothermal expansion that can promote three different regimes depending on the state of gas phase in a downcomer zone: (i) no air bubbles, (ii) bubbles remain stationary and

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(iii) bubbles flow downward and into the riser; the regime as well as the generated hold up is directly related by the superficial gas velocity (van Benthum et al., 1999). ALB has important advantages over other bioreactors configurations such as less cell damage, exhibiting higher aeration rates and lower energy costs (Chisti and Ja´uregui-Haza, 2002). One of the main advantages of the ALB is the low operation costs and energy consumption since the aeration and the mixing are caused by the same device: a gas sparger. In the ALB, the fluidization of solids is not a direct consequence of the gas bubbling but rather is due to the circulation of the liquid inside of the bioreactor. Due to the above, ALB offers the possibility of a very simple fluidization of solids, high efficiency, and allows to establish internal environments with approximately constant cutting forces along the bioreactor, because of the distribution of the energy supplied for agitation and mixing is not by kinetic energy of a stirrer. Therefore, morphological and metabolic changes in the culture cells are avoided; for this reason ALB is widely used in bioprocesses (Chisti and Ja´uregui-Haza, 2002) and for bioremediation of a variety of contaminant compounds (Table 1). Compared with agitated tanks, the advantages of the ALB are that their construction is simple because they do not have moving mechanical parts to carry out the agitation (Chisti, 1989), costs are reduced by energy supply, since the air it accomplishes the functions of aeration and agitation (Chisti and Ja´uregui-Haza, 2002). ALB has disadvantages, for example, the hydrodynamic is scarcely studied in comparison with stirred tank reactor and for this reason control could be difficult. On the other hand, air bubble diameter, from the sparger, is a key factor due to very small bubbles could be trap in oil phase, at the top of volume operation of reactor, in multiphasic systems and consequently a lot of foam is produced. A specific design of gas sparger, take into account the orifice diameter, is mandatory (Lizardi-Jim
enez, 2007). In the ALB there are four zones that allow a recirculation of the liquid in the bioreactor. The first zone, in which the gas is supplied, is known as the riser zone and has the highest gas phase retention coefficient (εg) in the bioreactor and is where most of the transfer of oxygen gas occurs. There are two basic configurations of the ALB: external circulation and internal circulation (Fig. 5). The fluid flow pattern in an ALB is very simple than other reactor configurations even more than a bubble column, generating a perfect mixing (Wu and Merchuk, 2004). The ALB with external circulation has at least one “loop” or arm with a diameter generally smaller than that of the main body of the bioreactor; on the other hand the internal circulation has a concentric tube that separates

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Table 1 Use of airlift bioreactors in bioremediation processes. Contaminant Objective Highlight

Diesel

Mass transfer study

High concentration (130 g L
1) of initial diesel was used and degraded

Reference

Dutta et al. (2018)

Total Adsorptionpetroleum degradation hydrocarbons simultaneous phenomena study in continuous operation

Aerobic granules able to Corsino et al. degrade total petroleum (2018) hydrocarbons in an airlift bioreactor, performance and stability

Ammonium

Ammonium partial nitration

Study of short-term effects of heavy metals and antibiotics on nitrifying bacterial activities

Petroleum and CO2

Restore wastewater and control CO2 emission

Microalgae airlift Abid et al. photobioreactor coupled to (2017) a bacterial ALB

Endocrine disrupting chemicals

Contaminant removal

Use of white-rot fungi without nutrients

CO2

Hydrodynamic study Effect of high gas superficial Sadeghizadeh velocity on CO2 biofixation et al. (2017) in microalgae ALB

Xing and Jin (2018)

Pezzella et al. (2017)

Hexadecane, Hydrocarbon phenanthrene degradation and pyrene

An electric field pretreatment was used to improve mass transfer for hydrocarbon degradation

Sa´nchezVa´zquez et al. (2017)

Toluene

Algal-bacterial airlift photobioreactor

Lebrero et al. (2016)

Hydrocarbon degradation

Lubricants in Automotive Continuous internal loop wastewater lubricants removal in airlift bioreactor emulsified wastewater

Khondee et al. (2012)

the main body of the bioreactor. In both cases, external and internal circulation, the liquid circulating in the ALB enters an oxygen release zone, which functions as a gas-liquid separator. The gas-free liquid then flows to the descent zone (downcomer) and travels to the bottom of the column, in which it completes the cycle and re-enters the ascent zone. This circulation is an effect caused by the difference between the εg of the riser and

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Fig. 5 Airlift bioreactor configurations: Internal (A) and external (B) circulation. Modified of Lizardi-Jim
enez MA: Degradación microbiana de hidrocarburos. In Peralta-P
erez R, Rocha-Gutierrez A, Zavala J, editors: Topicos selectos de bioquímica, Universidad Autónoma de Chihuahua, 60–86, 2015.

downcomer and determined, among other things, by the geometric relationships in the design of the ALB. Fig. 6 shows the geometric relationships that are considered fundamental in the design of a BAL with internal recirculation: concentric tube height (H2), operating height (H1), concentric tube diameter (D2), ALB diameter (D1), distance from the base of the ALB to the concentric tube (Bottom) and distance from the concentric tube to the operating height of the ALB (gas-liquid separator) (Chisti and Ja´uregui-Haza, 2002; Lizardi-Jim
enez et al., 2012). Some authors agree (Lizardi-Jim
enez et al., 2012) that the H2/H1 ratio should fluctuate between 0.6 and 0.9, D2/D1 between 0.66 and 0.74, Bottom/H1 between 0.04 and 0.08 and Liquid gas separator/H1 between 0.06 and 0.22. The geometric relationships that are established in the ALB determine to a large extent the hydrodynamic characteristics (type and flow patterns) in the bioreactor and therefore have an influence on mass transfer phenomena that limit bioprocesses. Recent work (Lizardi-Jim
enez et al., 2012) produced microbial petroleum-degrading consortia using the geometric relationship H1/D1 ¼ 5 D2/D1 0.65 and H2/H1 ¼ 0.77 and the hydrocarbon and oxygen transfer rates as a criterion of operation.

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Fig. 6 Airlift bioreactor. H2 concentric tube height, H1 operating height of the liquid, D2 concentric tube diameter, D1 ALB diameter. Modified of Medina-Moreno SA, Jim
enezGonzález A, Guti
errez-Rojas M, Lizardi-Jim
enez MA: Hexadecane aqueous emulsion characterization and intake by an oil-degrading microbial consortium, Int Biodeterior Biodegrad 84:1–7, 2013.

6. Immobilized microorganisms Hydrocarbon biodegradation using ALB could be limited due to their low solubility and bioavailability. Lizardi-Jim
enez et al. (2012) found that hexadecane (HXD) consumption by an oil-degrading consortium was limited by the hydrocarbon transfer rate rather than the oxygen transfer rate. Even though a good degrader microorganism could be immobilized on a good hydrocarbon sorbent support (Khondee et al., 2012). If a microorganism is immobilized on a porous support, internal and external mass transfer resistances could generate a great influence on the biodegradation

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kinetics. Internal mass transfer resistances are highly related with the porous particle size and its effectiveness (Al-Muftah and Abu-Reesh, 2005). The relationship between particle size and mass transfer resistance can be represented by the Thiele modulus, which reflects the combined effects of particle diameter, the maximum reaction rate and the diffusivity of the reactants into the pores of the catalyst (Liu et al., 2005). For heterogeneous reaction systems, it is necessary to experimentally evaluate the mass transfer resistances in catalytic particles, especially in biological catalysts, due to their dependency on complex biochemical reaction mechanisms. A particle size might exist at which the effectiveness factor is maximal and, therefore, the immobilized biocatalyst performance is optimal ( Jeison et al., 2003). On the two main hydrocarbon uptake mechanisms, it was found that predominant microbial hydrocarbon uptake mechanism is by direct contact (A´ngeles et al., 2017). This is related to oil-water interface adhesion microbial capabilities (Abbasnezhad et al., 2011); however, when an immobilized microorganism is used as hydrocarbon degrader, the external cells could present high biodegradation rates in contrast to starved cells into the pores, i.e., low effectiveness biodegradation (Dzionek et al., 2016). In that context, Sa´nchez-Va´zquez et al. (2017) observed two alternatives able to enhance effectiveness: (i) the particle size diminishment and (ii) the hydrocarbon degradation assisted by a bioemulsifier agent. In the abovementioned work, A. brasiliensis attached to perlite and pretreated with an electric field was visualized as a fungal whole cell biocatalyst (BC). The BC was proposed as a promising method to remediate contaminated water in an ALB, due to its HXD sorbent-degrader capability (Sa´nchez-Va´zquez et al., 2015). The BC was capable of degrading a hydrocarbon blend composed of HXD, PHE and PYR. The application of the electric field as an electrochemical pretreatment during BC production promoted surface changes in BC and production of an emulsifier protein in the ALB. Surface changes enhanced the affinity between BC and hydrocarbons, improving hydrocarbon uptake by direct contact. The resulting emulsion was associated with decreased internal and external mass transfer resistances and consequently, an effectiveness factor close to unity for all three hydrocarbons, even for larger BC diameters (Sa´nchez-Va´zquez et al., 2017). All this information is important because it could be used into mathematical models to predict hydrocarbon degradation rates with different microorganisms and operational conditions of the bioreactor.

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7. Mathematical modeling Mathematical modeling is a basic tool of research which consists of abstracting and mathematically representing a studied phenomenon. For this, it is required a solid knowledge and understanding of the theory related to the phenomenon or object of study, as well as skills in algebra or calculus, in function of the complexity of the model. Mathematical models are used in a wide range of sciences, such as anthropology, finances or biochemistry among many others; because of their use it is possible to understand the variables present in a phenomenon and the way they affect it, as well as make predictions about their behavior at a point of time, generally in the future (Lokhandwala et al., 2013). In the field of biotechnology, a useful application is observed in growth kinetics of microorganisms and consumption or conversion of substrates (Okpokwasili and Nweke, 2005). The application or development of a model in these biological systems allows to know some intrinsic characteristics of the microorganisms, such as their specific growth rate or the duration of their growth phases with great accuracy, in addition to the response they could have under different conditions of temperature, pH, humidity, among other variables (Zwietering et al., 1990). Some classical models used in the growth of microorganisms are the Logistic (Ricker, 1979), Gompertz (Zwietering et al., 1990) and Von Bertalanffy (Von Bertalanffy, 1938) models. These models share some common assumptions. The first is that the population grows to a point of saturation in which the rate of growth decreases and a constant mortality rate appears over short to moderate time periods, as long as there are enough resources in broth culture, although the death phase is not considered in the equations. The second is the use of the logarithm of the relative size of the population against time (y), where N and N0 are the concentrations of microorganisms during the kinetics and in the initial time, respectively (Eq. 1).


N y ¼ ln N0

 (1)

The reparameterized equations of Gompertz (Eq. 2), Von Bertalanffy (Eq. 3) and Logistic (Eq. 4) describe “y” in terms of mathematical parameters “a,” “b” and “c,” which represent the specific maximum growth rate (μm) defined as the tangent at the point of inflection; the lag phase (λ) defined

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as the intercept of the x-axis on the tangent; and the asymptote [A ¼ ln (N∞/N0)] which is the maximum value reached. y ¼ ae
e

b
ct

(2)

y ¼ a =3
eb
ct a y¼ 1 + eb
ct 1

(3) (4)

In order to obtain the inflection point, where the specific rate of growth is maximum, the second derivative of “y” is calculated with respect to time in some of the equations to be used, for example, the Gompertz equation (Eq. 5). y0 ¼ ace
e eb
ct b
ct

  b
ct y00 ¼ ac 2 e
e eb
ct eb
ct
1

(5)

Applying the criterion of the second derivative, where the equation is equal to 0, it is obtained that the inflection time is b/c. From the first derivative, and relating to biological parameters, it is possible to obtain Eqs. (6) and (7) in order to calculate the specific maximum growth rate and the lag phase, respectively. ac e b
1 λ¼ c μm ¼

(6) (7)

where a ¼ A, substituting (6) and (7) in (2), (3) and (4), Eqs. (8), (9) and (10) are obtained, respectively. μm e



ðλ
t Þ + 1
e A

y ¼ Ae  μm e  1 y ¼ A =3
e A ðλ
tÞ + 1 y¼ 1+e

A μm e



A ðλ
tÞ + 1

(8) (9) (10)

However, classical models do not consider some external variables to microorganisms, such as the medium in which the microorganism is found, the behavior of the substrate in the media, the mass transport from the media

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to the microorganisms or the effects derived from a couple kinetic, factors that are important to consider when working with more complex conditions (e.g., hydrocarbons as substrate). On the other hand, some complex models take into account hydrodynamic (Sikula et al., 2007) and mass transfer parameters such as volumetric mass transfer coefficients (kLa) and transfer rates ( Jia et al., 2006; Uraizee et al., 1998) to explain consumption more precisely. In particular, a model that has been proposed, validated and used in multiphasic partitioning bioreactors such as ALB, taking into account both types of parameters to explain hydrocarbon consumption through particle size diminution (i.e., the quantity of hydrocarbon transferred from oilliquid interface followed by liquid phase diffusion transport to the cells), is the Vilca´ez model (Denis et al., 2016; Vilca´ez et al., 2013). This model will be explained, in this chapter, due to hydrocarbon uptake through direct interfacial contact is highlighted (additional to more classical emulsified uptake considerations). However, in advanced modeling books, it is necessary to consider that this mathematical model does not adequately represent the behavior of the airlift reactor (it has limitations as all models). The hydrodynamic phenomenon is very complex, and at least ordinary differential equations must be handled in the balances of the carbon source, dissolved oxygen, biomass and oxygen in the gas phase. The Vilca´ez model is based on the degradation of hydrocarbon droplets, considering the reduction in droplet size, until a particle size where the effectiveness factor is maximal, due to consumption by microorganisms in the water-oil interface and the different droplet sizes based on a range distribution function (Fig. 7); therefore, the model integrates two sub-models that are connected to each other, the shrinking core model (SCM) which explains the biodegradation of a single oil drop and the fractional conversion model (FCM) to explain the biodegradation of all the drops in the system (Vilca´ez et al., 2013). According to Vilca´ez et al. (2013) and Denis et al. (2016), the SCM states that the shrinking rate of droplets is related to microorganisms’ oxygen consumption and can be controlled by the ratio of hydrocarbon mass transfer from the particle surface and the degradation rate at the oil surface, due to that the internal diffusion usually limits the overall rate of reaction, as is established by the Thiele modulus. Therefore, the biodegradation rate is as follows:


1 dN oil h dN O2 ¼
S dt S dt

(11)

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Fig. 7 Scheme of Vilcáez model for CO2 and biomass conversion in function of droplet size reduction on an airlift bioreactor.

where S is the oil droplets total interfacial area, NO2 and Noil are the oxygen and oil mass, respectively, and h is the hydrocarbon biodegraded mass per oxygen consumed. Additionally, the oxygen consumption rate per surface unit is as follows:


1 dN O2 μ ¼ BS S dt YO2

(12)

where YO2 is the relation between the new microbial biomass and the mass of oxygen consumed, and BS stands for the microbial concentration at the oil droplet surface. The oil mass in function of droplet density and oil droplet diameter can be written as: π dN oil ¼ ρoil D2 dD 2

(13)

where ρoil is the oil density and D is the oil droplet diameter. By substituting Eqs. (12) and (13) into (11) and considering S ¼ πD2 and YO2 ¼ hYoil, it is possible to represent the rate of change in droplet diameter in terms of microbial concentration at the oil droplet surface: dD 2 μ ¼ BS dt ρoil Yoil

(14)

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After integrating Eq. (14), the oil conversion fraction into CO2 and new cells for a single oil droplet (X1-drop), as a function of time, is given by:
 krn 3 (15) X1
drop ðtÞ ¼ 1
1
t D where krn ¼

2 μ BS ρoil Yoil

(16)

Eq. (15) is the final equation of the sub-model. The equation describes the biodegradation of single oil droplet with diameter D at time t by direct interfacial contact. At this point, it is important to note that hydrocarbon consumption sometimes can be limited by inhibition at high concentration of oil (Lizardi-Jim
enez et al., 2012, 2015). Therefore, in order to represent this inhibition, other kinetic models can be integrated to the sub-model through the parameter μ. Here are some classical examples: CS Monod (1949): μ ¼ μm K S + CS CS Andrews (1968): μ ¼ μm C2 KS + CS + S Ki CS Yano and Koga (1969): μ ¼ μm C2 C3 K S + CS + S + S Ki Ki K where Ki, KS and CS are the inhibition constant, the half saturation constant and substrate concentration, respectively. It is interesting to note that other models, like Gompertz, Logistic and Von Bertalanffy, could also be integrated at this point, through the μm parameter. In the other hand, the FCM is needed in order to describe the probability of appearance of a certain size of oil droplet in the bioreactor and to know the fraction (X) of biodegraded oil. Due to the assumption that biodegradation is controlled by the reaction at the surface, by integrating Eq. (15) with respect to the size of oil droplets it is possible to obtain the fraction of conversion X: ∞  ð
krn t 3 X ¼1
1
P ðDÞdD (17) D 0

where P(D) is the distribution of oil droplet size and, when biosurfactants are presented in the media to produce an emulsion, can be represented

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Airlift bioreactors for hydrocarbon degradation

by the gamma distribution in order to obtain an approximation of the droplet size distribution: P ðDÞ ¼

D 1 α
1
β e D βα ΓðαÞ

According to Eq. (17) the smallest particle is completely biodegraded at certain time. Including a variable integration limit Dt it is possible to know the droplet diameter at the time of complete degradation: D ðt

X ¼1
0

D 1
0 α Dα
1 e β dD β ΓðαÞ

Dð max


krn t 1
D

3

Dt

D 1
Dα
1 e β dD β ΓðαÞ α

(18) Eq. (18) indicates that any droplet of diameter less than Dt is completely converted with a value equal to 1. Therefore, the final equation for FCM sub-model is as follows: Dð max


krn t 1
D

X ¼1


3

Dt

D 1
D α
1 e β dD β ΓðαÞ α

(19)

In order to link SCM and FCM sub-models it is important to take into account the Sauter mean droplet diameter (d32) and assume that oil droplets are homogeneous in the operational volume. Therefore, total interfacial area is represented as: S ¼ 6V0/d32, where d32 is given by: Dð max

X d32 ¼ X

P ðDÞD3 dD nj D nj

3

D2

j

D

¼D0 ðmax j

ð1
X Þ

(20)

P ðDÞD2 dD

D0

Therefore, BS can be expressed as: BS ¼

BV d32 6V0

(21)

where V stands for bioreactor operational volume, V0 for oil volume and B for cell biomass concentration.

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Finally, at the water-oil interface the maximum microbial density (BS,max) is limiting BS, so the function of microbe concentration at oil surface is given by the accumulation rate of microbial cells in ALB operational volume: dB S ¼ μBS dt V

(22)

The Vilca´ez model has been used with experimental data to the better understanding of hydrocarbon consumption in ALB (Denis et al., 2016). However, there is still a long path to walk in order to understand hydrocar´ ngeles et al., 2017; Dutta et al., bon mass transfer phenomena in ALB (A 2018; Tec-Caamal et al., 2018) but one thing for sure is that the use of mathematical modeling will have a key role to play.

8. Conclusions Multiphase partitioning airlift bioreactors could represent an alternative for hydrocarbon biodegradation in contaminated environments due to important advantages over other types of bioreactors as bubble column or stirred tanks: low cost and higher mass transfer rates. Several studies regarding bacterial and fungal growth with oil as sole carbon source were successfully performed in recent years. Furthermore, a wide knowledge about mechanisms of uptake, considering math modeling, of oil phases by emulsified droplets or interfacial direct contact with macroscopic droplets is available. Because mathematical modeling is a basic tool of research which consists of abstracting and mathematically representing a studied phenomenon we can suggest that a solid knowledge and understanding of the theory related to the studied phenomenon is now included in this chapter about the use of partitioning airlift bioreactors with environmental purposes for nonsoluble pollutants; however, it should be mentioned that experimental validation of the mathematical models is nowadays poor, so it is necessary to develop integral works which contain both experimental and mathematical modeling scope. In this way, the use of airlift bioreactors for environmental remediation could be successfully applied in field scale. In an uncontrolled spill scenario oil could tap a surface that is big as Texas state surface, i.e., deep water horizon, 2010. Then, large scale bioreactors are relevant for this purpose and the largest reactors around the world are airlift. Air compressors to agitate these largest reactors are commercially available and they are cheaper than correspondingly impeller to stirred tank.

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21

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Further reading Va´zquez-Va´zquez JL, Ortega-de la Rosa ND, Huerta-Ochoa S, Gimeno M, Guti
errezRojas M: Novel exopolysaccharide produced by Acinetobacter bouvetii UAM25: production, characterization and PAHs bioemulsifying capability, Rev Mex Ing Chim 16(3):721–733, 2017.