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Hindawi Publishing CorporationInternational Journal of Chemical EngineeringVolume 2012, Article ID 984827, 12 pagesdoi:10.1155/2012/984827

Research ArticleEffect of Mixing on Microorganism Growth in Loop Bioreactors

A. M. Al Taweel, 1 Q. Shah, 2 and B. Aufderheide 2

1 Department of Process Engineering and Applied Sciences, Dalhousie University, Halifax NS, Canada B3J 2X4 2Process Engineering Programme of The University of Trinidad and Tobago, Point Lisas Campus, Brechin Castle, Couva,

Trinidad and Tobago

Correspondence should be addressed to A. M. Al Taweel, [email protected]

Received 27 January 2012; Accepted 24 May 2012

Academic Editor: Shaliza Binti Ibrahim

Copyright 2012 A. M. Al Taweel et al. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The impact of mixing on the promotion of microorganism growth rate has been analyzed using a multiphase forced-circulationpipe-loop reactor model capable of identifying conditions under which it is possible to convert natural gas into Single-Cell Protein.The impact of mixing in the interphase mass transfer was found to exert a critical role in determining the overall productivity of the bioreactor, particularly at the high cell loadings needed to reduce the capital costs associated with the large-scale productionneeded for the production of relatively low-value SCP in a sustainable manner.

1. Introduction

Industrial biotechnology uses living cells or cellcomponents(yeast, moulds, bacteria, plants, and enzymes) to synthesizeproducts that are easily degradable, require less energy toproduce, and create less waste during their production, allof which helps to decrease the environmental impact of thispromisingmanufacturingapproach. It is already used to gen-erate large quantities of biobased products in sectors such as:chemicals, food and feed, detergents, pulp and paper, healthcare, textiles, bioenergy (e.g., biofuels, biogas), photocat-alytic algae production, wastewater treatment, bioleaching,and biological site remediation. It also holds the promiseof being a credible method for the sustainable developmentof many other products because it uses renewable raw materials and is capable of achieving very high effi ciencieswhile converting nonrenewable resources to nal productswith minimum generation of undesirable byproducts/waste.Nevertheless, the shift to the bioprocessing route will happenonly if the economic process and market demands justify thetransition. However, the growing environmental pressurescombined with the rapid developments in the sciencesupporting biotechnology (sequencing of industrial bacterialand yeast genomes, metabolic engineering, bioinformatics

and computer-based modeling, and process optimization)are opening up opportunities for new products and costreductions.

One of the main factors a ff ecting the economic viability of many of the aforementioned operations is the rate atwhich interphase mass transfer can take place since it is oftenthe parameter limiting the growth rates of microorganismsencountered in many of these biotechnological processes[15]. The use of forced-circulation loop reactors holdsthe promise of overcoming such limitations in a cost-eff ective fashion particularly for large-scale operations [ 611]. Whereas the achievement of high productivity is usually not a high priority issue in the production of high-valuebiotechnological products such as medical therapeutics andpharmaceuticals, the relatively low value of the productsencountered in industrial biotechnology necessitate thathigh utilization e ffi ciencies for capital and raw materials beachieved to ensure sustainability [ 4, 5].

The objective of this study is to develop a mathematicalmodel that is capable of quantifying the role that mixingand interphase mass transfer play in the overall performanceof pipe-loop bioreactors. Particular emphasis is placed onidentifying the value of kLa needed to achieve high overallreactor productivity under di ff erent design and operating


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2 International Journal of Chemical Engineering

conditions (e.g., biomass loading, bioconversion rates, feedgas composition, supercial liquid velocity, and gas to liquidratios). Judicious selection of mixing devices can then bemade in order to achieve optimal conditions. A case study in which natural gas is converted into Single-Cell Proteinis used to illustrate the capabilities of this approach and

to identify a range of optimal conditions necessary forsustainable operations. Interest in this technology is drivenby the promise of meeting the rapidly increasing worldwidedemand for protein-rich nutrition in an energy-e ffi cient andcost-eff ective fashion [2].

2. The Role of Mixing in Bioreactors

Bioreactors are characterized by a complex three-phase ow (liquid, gas, and biomass) and the interaction betweenmixing and biological reactions is complicated by the factthat such interactions take place simultaneously at themacro-, meso-, and micromixing scales.

Macromixing thus dictates the ow pattern prevalent inthe bioreactor and ensures that the nutrients are reasonably well distributed throughout its volume. Large-scale biore-actors have been shown to exhibit heterogeneous hydro-dynamic and concentration elds with the cells circulatingthrough such reactors being submitted to an extracellulaructuating environment [ 12]. Insuffi cient macromixing canconsequently induce modications of the cell metabolism,leading to the formation of byproducts and decreasing theoverall reactor performance with large-scale cultivationsexhibiting lower carbon conversion yields than expectedfrom lab-scale experiments [ 13]. In the case of the photo-bioreactors used for algae production, macromixing is used

to ensure proper exposure to high-intensity light and toprovide alternate durations in light and dark regions, anenvironmental requirement for some microorganisms toachieve high growth rates and to produce the desirableproduct quality [ 1416].

On the other hand, the Kolmogorov microscales fortypical bioreactor congurations vary from 50 to 300 m,which is far larger than the size of bacterial or yeast cells(2 and 10 m, resp.). Microbial cells, which usually havedensities very close to the aqueous environment into whichthey are suspended, are therefore usually engulfed by theliquid stream in which molecular di ff usivity becomes themain mechanism responsible for providing substrate to the

cells [13]. It is however well accepted that the size of bubblespresent in turbulently owing liquid (a factor which strongly aff ects the rate of gas exchange) is inversely related to thelocal energy dissipation rate or the local microscale [ 1720].The same requirements apply to facilitating interphase masstransfer in the liquid-liquid dispersions encountered duringthe biodegradation of hydrophobic substrates, or when animmiscible liquid phase is introduced to facilitate oxygentransfer [ 21].

High levels of microscale turbulence are therefore nec-essary to improve mass transfer between the phases butattention must be given to ensure that shear-sensitive cellsare not damaged [ 19, 22]. On the other hand, recent ndings

Liquid feed

Gaseousefuents

Concentratedmicroorganism

slurry

Gaseous feed

Startupmicroorganisms StartupStartup

Figure 1: Schematic representation of a pipe-loop bioreactor sys-tem.

suggest that, contrary to the commonly accepted idea, abenecial eff ect on the growth rate of animal cells can beachieved at moderately elevated agitation rates [ 23].

2.1. Forced-Flow Pipe-Loop Bioreactors.The overwhelmingmajority of the information dealing with the impact thatmixing has on the performance of bioreactors focused onmechanically agitated tanks, bubble columns, and airliftreactors [ 24], with very limited attention being given tothe case of pipe-loop bioreactors although they hold thepromise of being used for large-scale industrial bioprocessingbecause of their uniform plug ow characteristics, ease of control, and low capital and operating costs. To redress thisdeciency, attention in the following sections will be focusedon analysing the performance of tubular loop bioreactorsin which the biochemical reaction rate is usually controlledmainly by mixing and its ability to promote interphase masstransfer. A case study in which natural gas is converted intoSingle-Cell Protein is used to illustrate the capabilities of thisapproach.

The operation of a typical pipe-loop bioreactor is sche-matically represented in Figure 1 in which diff erent reactorcongurations can be used:

(i) horizontal, inclined, and vertical closed-loop reactorsystems in which the ow is mechanically inducedusing pumps and static-mixing elements are usedto develop the desired ow patterns, gas dispersion,and local energy dissipation rates needed to maintaingood contact [ 3, 2527],

(ii) vertical U-loop reactors [ 8, 11], in which axial ow mixers/pumps are used to induce the desired ow while static mixers are used at several locations alongthe loop to redisperse the gas and improve contactbetween the phases,

(iii) combinations of the above [ 7].

Regardless of the method used to induce uid ow (pumps, inline axial ow mixers, or airlift), the processperformance of the bioreactor can be described by the samemodel.

2.2. Interphase Mass Transfer in Forced-Flow Pipe-Loop Biore-actors. Static mixers have become an integral and basiccomponent of the multitude of equipment used in thechemical process industries. Because of their simplicity and


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International Journal of Chemical Engineering 3

the absence of any moving parts, these mixers are beingincreasingly used in a wide range of applications [ 28]. They are thus used for laminar and turbulent mixing of miscibleliquids, in enhancing the performance of heat exchangersand tubular reactors, for laminar and turbulent homogeniza-tion, to promote coagulation and occulation under well-

controlled hydrodynamic and chemical environment as wellas for the dispersion of immiscible phases.The only source for energy dissipation that is associated

with the use of static mixers is that related to the loss of pressure energy as the uid passes through the static-mixingelements. This is usually supplied by the pump used tocirculate the fermentation broth through the reactor loop.The major disadvantage of using static-mixing elements inbioreactors therefore stems from the direct coupling betweenthe local energy dissipation rate within the mixing elements(which controls the rate of interphase mass transfer) and thevelocity at which the two phases pass through such elements.This limits, to some extent, the operational exibility of thesystems but the use of multiple mixers operating in parallelcan be used to overcome this di ffi culty.

A typical static mixer is composed of a series of identical,motionless inserts that are installed in tubular structures(pipes, columns, or reactors) with the purpose of redistribut-ing the uid in a direction transverse to the main ow (i.e., inthe radial and tangential directions). The e ff ectiveness of thisredistribution is a function of the specic design and numberof elements. On the other hand, the recently introducedscreen/grid mixing elements can be considered as means formodifying the turbulent characteristics (turbulence scalesand intensity) of the pipe ow, thereby providing a highdegree of control on the performance of the gas/liquidcontact [ 20, 29, 30].

Although the patent literature pertinent to static mixersandtheir usegoes back to the 1930s, systematic investigationsconcerning the various factors a ff ecting gas/liquid contactingand interphase mass transfer in such units are somewhatlimited [ 20, 3134]. However, the work conducted by Heyouni et al. [ 17] presents a very systematic investigationof the various factors aff ecting gas/liquid contacting in staticmixers and compared their ndings with the performance of other commonly used contactor types such as mechanically agitated tanks, bubble columns, and airlift reactors. They reported that the use of Lightning static mixers can enhancethe interfacial area of contact between the phases by afactor of 1025 with the value of the interphase masstransfer coeffi cient increasing with increasing liquid andgas velocities. Volumetric mass transfer coe ffi cients as highas 2.5s 1 were obtained at local energy dissipation ratesof about 100 kW/tonne. Similar results were also reportedby several other investigators [ 20, 33, 34] at somewhatsimilar rates of energy dissipation within the volume of the mixer. The impact that various constituents present infermentation broths have on bubble breakage/coalescenceand mass transfer was simulated by Azizi and Al Taweelby adding trace quantities of a cationic surfactant (up to20 ppm of SDS). In spite of the well-known adverse e ff ectthat surfactants have on the value of the liquid-side masstransfer coeffi cient kL, [24, 35], volumetric mass transfer

U = 0.85 m/s

U = 0.5 m/s

Figure 2: Axial variation in local interphase mass transfer coe ffi -cient.

coeffi cients as high as 4.0 s 1 were obtained thanks to theabilityof screens/sieves to e ffi ciently generate large interfacialareas of contact.

It is however very interesting to note that whereasstatic mixers are typically characterized as having very high local energy dissipation rates (with values of up to1,000 kW/tonne being reported), the power needed to pumpthe fermentation broth through the bioreactor can be ratherlow. Thus whereas Azizi and Al Taweel [34] obtained masstransfer coeffi cients as high as 4.0 s 1 using average energy dissipation rateswithin the contactor volume, , of320W/kg,the amount of energy used to pump a unit mass of the liquidthrough the 560 mm long static mixer, E M , was found tobe as low as 0.02 kWh/tonne. This is mainly attributable tothe low residence times spent within the static mixer. Muchsmaller values of E M were obtained by Lemenand et al., [ 36],while using high-effi ciency vortex static elements to disperseimmiscible uids.

The aforementioned very high volumetric mass transfercoeffi cients were obtained by using relatively small inter-screen spacing (70 mm) and high supercial velocities, fac-tors which resulted in reducing thee ffi ciencyby which energy is utilized to promote mass transfer between the phases (0.10.6 kgO2/kWh, depending on the operating conditions andthe interfacial characteristics of the system). These values arean order of magnitude smaller than those reported by AlTaweel et al. [9] using similar mixing elements placed farapart (with interscreen spacing of 7001,200 mm) where theemphasis was on achieving high oxygen transfer e ffi cienciesby taking advantage of the coalescence retardation e ff ect of the contaminants.

In the present analysis, it is envisaged that the approachrecommended by Turunen and Haario [ 32] will be adopted.Short sections containing a relatively small number of static-mixing elements will be used to disperse the gas into smallbubbles. Each of these sections will then be followed by relatively long sections of empty pipes which are used toprovide the loop reactor with the desired residence time.Unfortunately, the ne bubbles formed by the static mixerswill tend to coalesce into bigger ones as the dispersion owsinto the regions of lower local energy dissipation rates. Theoverall outcome of these processes is schematically depictedin Figure 2 which presents the axial variation of the localmass transfer coeffi cient predicted by CFD simulation fortwo supercial velocities.

The achievement of high interphase mass transfer ratesallows for supplying the high oxygen demands associatedwith the use of high cell loadings, and for the stripping of


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the CO 2 that tends to dissolve in the broth particularly atelevated pressures.

3. Converting Hydrocarbons into SCP

In this section, the impact of multiphase mixing (andthe associated impact on interphase mass transfer) onthe performance of forced-ow pipe-loop bioreactors isillustrated using the important industrial biotechnology casewhere hydrocarbons and hydrocarbon-based products areconverted into single-cell protein. This technology is well-established and has been practiced for many years [ 37].Initially, attention focused on the use of waxy n-para ffi ns,a byproduct from oil reneries with the primary use of the product being poultry and cattle feed. Because of theabundance of relatively low-cost natural gas, and the fastconversion rates achievable at lower hydrocarbon molecularweights, emphasis has recently shifted towards using severalmethanotrophic microorganisms in a continuous process

that simply uses methane, oxygen, ammonia, minerals, andwater as raw materials. This approach was so successfulthat a joint venture between Statoil and DuPont (NorfermA/S) constructed a 10,000 tpa plant in Norway that uti-lized circulating loop reactors with both horizontal andvertical sections in which static mixers were introduced toenhance gas/liquid mass transfer. Commercial-scale produc-tion began in May 2003, but was shut down after 3 yearspresumably because of the low production rate per unit vol-ume of the reactor and the relatively high cost of natural gassupply.

3.1. Pipe-Loop Bioreactors for SCP Production. The contin-

uous manufacture of proteins by the biochemical oxidationof gaseous hydrocarbons in the presence of a nitrogenousnutrient has been achieved using horizontal and verticalclosed-loop reactors, vertical airlift reactors, as well as verticalU-loop reactors [ 10, 11, 27, 38]. These investigations, aswell as many others, identied that the productivity of this process is inuenced by a wide range of parameterssuch as the liquid phase concentration of oxygen, methaneand CO2, the biomass concentration, temperature, andpH.

Although the process is relatively simple, the reactordesign methodology is rather complex as it deals with amultiphase system (gas/liquid/solid) in which the gaseous

reactants have to dissolve into the aqueous medium where ahighly exothermic heterogeneous biochemical reaction takesplace.

The model presented in this paper takes into accountthe most critical components a ff ecting the various processestakingplace within the bioreactor used for converting naturalgas into SCP. It can be used to design and evaluate theperformance of vertical and horizontal tubular loop reactors,as well as the riser section of an Air-Lift Reactor wheremost of the interphase mass transfer takes place. The modelcalculates the spatial variation in biomass production as themultiphase reacting mixtures ow along the length of thepipe-loop reactor and can therefore be used for

(i) identifying the operating conditions under which theoverall production rate is mass transfer limited orreaction rate limited,

(ii) identifying the optimum design and operating condi-tions such as reactor length, supercial liquid velocity and the gas to liquid ow ratio, and optimumbiomass concentration in the recycle stream,

(iii) determining the impact of promoting interphasemass transfer by preconcentrating the oxygen in thegas stream (by switching from air to cryogenic oxy-gen), operating at elevated pressures, and the inser-tion of static mixers at various locations along thereactor length,

(iv) calculating the impact of the variousdesign and oper-ating conditions on the energy dissipation rates in thevarious components of the process, thereby enablingthe identication of the optimum balance betweencapital and operating costs,

(v) identifying the optimum oxygen to methane ratioand the conditions under which it is necessary torecycle and reuse unconsumed raw materials (naturalgas, methanol, oxygen, and ammonia).

Better understanding of the interaction between thoseparameters is needed in order to develop sustainable meansfor converting natural gas and methanol into SCP.

3.2. Specic Conditions for M. capsulatus SCP Production.Bioreaction stoichiometry can vary signicantly dependingon the value of a host of parameters that include growthmedia optimization, temperature, and pressure of the reac-

tion. The SCP produced by the biooxidation of natural gasusing mostly M. capsulatus contains about 70% crude pro-tein, 10% crude fat, 10% nucleic acid, and 7% ash and can berepresented by the elemental analysis CH 1.8O0.5N0.2. Nielsenet al. [39] presented the following stoichiometry for thebiooxidation of natural gas (mainly methane) with ammoniaand oxygen using the aforementioned microorganism:

CH4 + 0.104NH 3 + 1.45O2 0.52CH1.8O0.5N0.2

+ 0.48CO2 + 1.69H2O(1)

The corresponding reaction yield coe ffi cients are given inTable 1.

According to Joergensen and Degn [ 40] the specicgrowth rate of M. capsulatus, S, during the biooxidation of methane at 45 C, can be described by the following Monod equation with the saturationconstant valuesgiven in Table 1:

S =max C S,l

K SM + C S,l . (2)

4. Modeling the Performance of Forced-Circulation Loop Bioreactors

Analysis of a bioreactor performance requires a model forthe ow eld, a model for the biomass reactions taking


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Table 1: Baseline parameters used in simulations.

Parameter Value Units Parameter Value Units

max 0.37 hr 1 T STP 25 CK S 1.3 e 6 mol CH 4/L P T 3 atmY SX 1.93 (mol CH 4/mol Cell) P STP 1 atm

Y OX 2.80 (mol O2/mol Cell) U G,0 0.043 m/sY CX 0.92 (mol CO 2/mol Cell) U L 0.5 m/sH CH4 1,000.9 L atm/mol y CH4,0 0.40 []H O2 1,100.81 L atm/mol y O2,0 0.58 []H N2 2,023.6 L atm/mol y N2,0 0.02 []H CO2 47.39 L atm/mol y CO2,0 0.00 []T 45 C Z 15 m

place in the liquid phase, and a model for the mass transferbetween phases (from gas to liquid and from the liquidto biomass). Despite the fact that biological reactions areconditioned by the mass transfer between the liquid andthe biomass, hydrodynamics and bioreactions are generally coupled through conservation equations for the dissolvedspecies.

For properly designed forced-circulation loop reactorsoperating at the relatively high Reynolds numbers encoun-tered in large-scale operations, the tendency of bubblesto segregate under the action of gravity can be neglectedparticularly when static mixers are inserted to counteractthe tendency for phase segregation and to redisperse thegas phase into ner bubbles [ 33, 41, 42]. The bioconversiontaking place in such reactors can then be well represented by the simple plug-ow multiphase reactor loop in which the

microorganisms can be considered as fully dispersed into theliquid phase ( Figure 3).

The rate of interphase mass transfer that can be achievedin such a reactor depends on the type of static mixer used, thespacing between mixing elements, the supercial velocity of the liquid, the interfacial characteristics of the system, andthe volume fraction occupied by the gas in the two-phaseowing system [17, 20, 27, 3134]. In this investigation,emphasis is therefore placed on developing better under-standing of the role that interphase mass transfer plays indetermining the overall bioreaction rate, and how it interactswith diff erent design and operating conditions. Subsequentpublications will address means by which optimum mixing

conditions can be achieved in pipe-loop bioreactors.The characteristics of the bubbly ow system passing

through the control element depicted in Figure 3 is deter-mined by the physical properties of the two phases, theirrespective ow rates, and the extent to which the gasphase is dispersed through the liquid. The microorganismssuspended in the liquid phase usually have a density that isclose to that of water and their volumetric ow rate can, atpresent, be incorporated as a part of the liquid phase. Atrelatively low volumetric concentrations (up to 30 g cells/Ldry weight) the presence of bacteria in water will exertlittle inuence on its characteristics but, the rheology of the microbial suspensions can become more complex at

v

CO2

CH4

O2

CO2CH4O2

V

Figure 3: Schematic representation of the bubbly ow and inter-phase mass transfer, taking place in pipe-loop bioreactor.

high-volumetric solid loadings of interacting and occulatedmicroorganisms [ 43].

The operational characteristics of the multiphase biore-actor are usually based on the volumetric ow rate of theliquid phase to be processed (which includes the suspendedmicroorganisms as an integral part of it) and the gas to liquidvolumetric ow ratio, G/L. The latter is usually taken at STP(25 C, Pressure 1 atm) and does therefore not necessarily reect the actual conditions present in the reactor which canoperate over a wide range of temperatures and pressures.

The total number of gaseous molecules introduced to thereactor is therefore given by

N G0 =i= n

i= 1

F G,iP STPRT STP

, (3)

where F G,i is the gas ow rate (at STP) for each of the ithgases introduced to the reactor and n is the total number of

gaseous species encountered in the bioreactor.Consequently, the volumetric ow rate of the gas phaseat any particular point along the reactor length, QG, can bedetermined from

QG =N G0RT

P T . (4)

And the supercial velocity of the gas phase owing throughthe control element, U G, can be expressed by,

U G =QG Ac

, (5)

where Ac is the cross-sectional area of the loop reactor.


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Similarly, the supercial velocity of the liquid phase ow-ing through the element, U L, can be expressed by

U L =QL Ac

. (6)

The supercial velocity of the two-phasesystemcan thereforebe expressed as

U T = U G + U L. (7)

Neglecting the slip velocity between the phases, a reasonableassumption in nely dispersed bubble ows, the volumefraction of the gas phase (i.e., the gas holdup) can beexpressed as

G =QG

QG + QL. (8)

The total number of gas molecules owing through the

control element is determined by the ow rate of thevariousgaseous constituents fed into thereactor, minus thosequantities that have been transferred into the liquid phase,as well as by the various gaseous products that evolve as aresult of the biochemical reaction taking place. Parts of thelatter gases dissolve into the liquid phase with the remainderbeing transferred into the bubbly ow gas phase (includingwater vapour which can play a signicant role at relatively high operating temperatures).

Since there is no biochemical reaction taking place in thegas phase, the axial evolution of the reactant concentrations(in the gas and liquid phases) along the length of the reactorcan be described by

dC CH4 ,Gdz

=

(kLa/ G) C CH4 C CH4 ,LU T

, (9)

dC CH4 ,Ldz

=(kLa/ (1 G)) C CH4 C CH4,L Y SX C X

U T ,

(10)

dC O2,Gdz

=

(kLa/ G) C O2 C O2,LU T

, (11)

dC O2 ,Ldz

=(kLa/ (1 G)) C O2 C O2,L Y OX C X

U T , (12)

dC CO2 ,Gdz

=

(kLa/ G) C CO2 C CO2 ,LU T

, (13)

dC CO2 ,Ldz

=(kLa/ (1 G)) C CO2 C CO2 ,L + Y CX C X

U T .

(14)

The values of the yield coeffi cients Y SX ,Y OX , and Y CX aregiven in Table 1 for the case when Methylococcus capsulatusis used to convert methane into SCP.

In addition to the reactants, the gases introduced to thebioreactor usually contain an amount of inerts (nitrogen and

rare gases) the value of which depends on the composition of the oxygen source as well as that of the natural gas. Althoughthese gases do not take part in the biooxidation reaction, they partially dissolve in the liquid stream circulated through theloop reactor and their presence in the gas phase results inreducing the concentration of the reactants present in that

phase and can, therefore, adversely aff

ect the mass transferrates. The same applies to the case of the CO 2 produced as aresult of the biochemical reaction.

The axial variation of the inert gas concentration in thegaseous and liquid phases is given by

dC Inert, Gdz

= (kLa/ G) C Inert C Inert,L

U T , (15)

dC Inert,Ldz

=(kLa/ (1 G)) C Inert C Inert,L

U T . (16)

Although the mass transfer coe ffi cient for the various gasescan be signicantly diff erent, they are assumed to be equal

for the purpose of this investigation. The equilibriumconcentrations present at the gas/liquid interface used in ( 9)(16) were computed using Henrys law,

C i = y i P

H i, (17)

where the values of Henrys constant for the various gasesare based on the standard values reported in Table 1 butcorrected for the bioreactor operating temperature using avant Hoff equation. The vapour pressure of water present atthe interface was estimated using the Antoine equation.

5. Results and DiscussionThe system of nonlinear ODE describing the fermentationof M. capsulatus in a single pass, (3)( 17), was solved usingMATLABs ODE solvers. The impact of various design andoperating parameters on the performance of the reactor wasnumerically determined with the objective of identifyingoptimum design and operating conditions using the produc-tivity per unit volume as a preliminary indicator. Pressurelosses due to the ow through the static mixers and alongthe reactor length was neglected at this stage of analysis.

Throughout the present investigation, the oxygen tomethane ratio was kept at the stoichiometric value of 1.45.The 15 m long loop bioreactor was assumed to operateat the optimum temperature of 45 C by providing meansfor removing the heat released through the biooxidationreaction. The oxygen stream is also assumed to be fromcryogenic distillation (97% O 2 with 3% inerts) except wherethe eff ect of using diff erent oxygen enrichment methodswas assessed. In cases where the methane and oxygen arecompletely consumed prior to leaving the tubular reactor,the set of diff erential equations reduces to only the liquidphase for the remainder of the reactor. This was necessitatedbecause a singularity in the gas phase equations occurs as thegas fraction approaches zero.

To reduce the computational e ff ort associated with theanalysis of this complex process at this early stage of process


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0 5 10 150

5

10

15

20

25

Distance (m)

C o n c e n

t r a t

i o n

i n l i q

u i d

( m g /

L )

CH4O2CO2

(a) Broth concentrations

0 5 10 150

0.5

1

1.5

2

2.5

C o n c e n

t r a t i o n

i n g a s

( g / L

)

Distance (m)

CH4O2CO2

(b) Bubble concentrations

Figure 4: Startup concentration proles in the liquid and gas phases ( P T = 3 atm, kLa = 0.05 s

1, C X 0 = 5 g/L,G/L = 0.20, and U L = 0.5 m/s).

assessment, it was assumed that the dissolved gases areushed out from the recycled liquid stream which is thenreturned to the reactor after it is presaturated by the reac-tants (95% of max achieved at the operating temperaturespressures).

5.1. Startup Operations. In the liquidphase,where the bioox-idation reaction takes place, the axial variation of thereactants (CH 4 and O 2) and product (CO 2) concentrationsis controlled by the relative magnitude of the rate at whichthe reactants are supplied to the liquid phase (throughinterphase mass transfer) and the rate at which they are con-sumed through the biooxidation microbial activity. Duringthe startup stage, the bioreaction is initiated by introducing asmall amount of the bacterial inoculums to the recirculatingliquid followed by the introduction of the reactant gases atthe desired pressure. To accurately simulate this transientstage, the concentration of the reactants in the liquid phaseentering the loop was set at zero but was found to increasealong the reactor length due to the absorption and/or gasevolution associated with the microbial growth ( Figure 4).

On the other hand, the concentration of the reactants inthe gas phase decreases as the dispersion progresses along thereactor length with very low concentrations of CO 2 appear-ing in the gas phase due to its progressive accumulation inthe liquid phase where it is very soluble at the relatively highpressures used in this case. Due to the low biomass loadingsused at startup, the gaseous reactants (CH 4 and O 2) are notfully consumed in the bioreactor and large quantities of thegaseous reactants may need to be ared or recirculated untilsuffi cient biomass loadings have been built up.

This transit situation continues with complete recircu-lation of the liquid at progressively higher concentrationof the microorganisms until a quasi-steady state is reachedin which the SCP can be harvested. Since harvesting istypically conducted at atmospheric pressure, most of the

gases dissolved in that liquid stream will ash out before theliquid is returned back to the reactor ( Figure 1).

5.2. E ff ect of Mixing and Promotion of Interphase Mass Trans- fer. The relative importance of interphase mass transfer andreaction rates is clearly shown in Figure 5. At relatively low volumetric mass transfer coe ffi cients, the average productiv-ityof the bioreactor is limited by the rate at which the gaseousreactants are transported into the liquid phase. On the otherhand, the reactor productivity is controlled by the intrinsicbiooxidation rate at high mass transfer coe ffi cients with thetransition point between the two regimes being a function of the diff erent design and operating conditions.

The length of reactor needed to achieve >99% utilizationof the reactants was found to decrease as the value of theinterphase mass transfer coe ffi cient and biomass loadings areincreased. This suggests that the process can be operated atsomewhat higher gas/liquid ratios, or that shorter reactorlengths can be used, in order to ensure maximum utilizationof the reactor volume. Both of these options can have signif-icant impact on enhancing process sustainability.

The importance of using a combination of high cell load-ing and high volumetric mass transfer coe ffi cients is demon-strated in Figure 6. For the design and operating conditionstested, the fraction of reacting gases that get converted ina single pass through the loop was found to increase fromabout 20% up to about 100% as the cell loading is increasedfrom 3 to 15 g/L provided that the mixing intensity is highenough to supply the microorganisms with the nutrientsthey need to grow. The overall complexity of the conversionprocess becomes much simpler if practically all the reactantsare consumed within a single pass, thus avoiding need for thecomplex andcostlyoperationsneededto separate and recyclethe unused reactants. There is, however, some indicationsthat it is necessary to maintain a minimum level of oxygen


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0 0.05 0.1 0.15 0.21

1.5

2

2.53

3.5

4

4.5

5

5.5

P r o

d u c t

i v i t y

( k g /

h r / m

3 )

k L a (s 1)

C x 0 = 3 g/L C x 0 = 6 g/LC x 0 = 9 g/L C x 0 = 15 g/L

Figure 5: Eff ect of the volumetric mass transfer coe ffi cient on the reactor productivity ( P T = 3 atm, G/L = 0.20, and U L = 0.5 m/s).

0 0.05 0.1 0.15 0.2

0

0.5

1

1.5

2

2.5

k L a (s 1)


O 2 c o n c e n

t r a t

i o n

i n g a s

( g / L

)

(a) Bubble oxygen concentration

0 0.05 0.1 0.15 0.2

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

k L a (s 1)


C H 4 c o n c e n

t r a t

i o n

i n g a s

( g / L

)

(b) Bubble methane concentration

Figure 6: Eff ect of the volumetric mass transfer coe ffi cient on the concentration of oxygen and methane in the gas phase exiting the reactor( P T = 3 atm, G/L = 0.20, and U L = 0.5 m/s).

concentration within the reactor to maintain a vigorous andhealthy microorganism population.

The high-mass transfer coe ffi cients needed to maintain ahigh level of reactor productivity cannot always be achieved,particularly in the case of shear-sensitive microorganisms.The use of high-operating pressures to promote masstransfer has been proposed as a mean for overcoming suchdiffi culties. As can be seen from Figure 7, the production-rateper unit volume of the reactor was found to increase linearly with increasing operating pressure but tends to atten o ff beyond a certain pressure the value of which depends on thecell loading. Operating the reactors at pressures higher thanthose optimal values is wasteful of energy, whereas the fullproductivity potential of the reactor will not be achieved by operating at pressures lower than the optimal. It is, however,

important to remember that the volumetric ow rate of thegases owing through the reactor decreases in proportionto the operating pressure, thereby making it more di ffi cultto achieve and maintain elevated volumetric mass transfercoeffi cients at high pressures.

An extensive analysis of the results obtained revealedthat productivity of the pipe-loop bioreactor is controlledmainly by the magnitude of the interphase mass transferand the cell loading in the fermentation broth beingintroduced into the reactor. The combined e ff ect of thesetwo highly interactive parameters is given in Figure 8 whichclearly illustrates the regions of mass transfer limitations,regions where the kinetics of microbial growth controls theoverall performance, and the conditions where both of theseparameters play an important role.


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1 1.5 2 2.5 3 3.5 4 4.5 50.5

1

1.5

2

2.5

3

3.5

4

4.5

Pressure (atm)

P r o

d u c t

i v i t y

( k g /

h r / m

3 )


Figure 7: Eff ect of pressure on the reactor productivity for di ff erentcell loadings (kLa = 0.025s 1, G/L = 0.20, and U L = 0.5 m/s).

0

1 0

2 0

3 0

0

0 . 1

0 . 2

0

2

4

6

I n i t i a l c e l l

l o a d i n g (

g / L )k L a ( s 1 )

P r o

d u c t

i v i t y

( k g /

h r / m

3 )

Figure 8: Eff ect of initial cell loading and volumetric mass transfercoeffi cient on the productivity of the bioreactor ( P T = 3 atm, G/L =0.20, and U L = 0.5 m/s).

A plateau in reactor productivity was observed to occurunder conditions where both high biomass loadings, and ele-vated interphase mass transfer coe ffi cients, can be achieved.In this region, an increase in the value of either parameterdoes not appear to enhance the productivity of the loop-bioreactor mainly because the reactants are exhausted beforereaching the end of the xed length bioreactor (15 m). On theother hand, one can use shorter bioreactor length to matchthat where the bioactivity takes place, thereby reducing thecapital cost of the bioreactor and increasing the productivity of the bioactive parts of the reactor.

Figure 8 clearly shows that bioreactor productivity ashighas 4 kg/hm 3 can be achieved using average mass transfercoeffi cients as low as 0.05 s 1, a feat that can be easily achieved using pipe-loop bioreactors that are equipped withappropriately designed static mixers. However, considering

0. 3 0. 4

0. 5 0. 6

0. 7

0

0 . 1

0 . 2

0

2

4

6

k L a ( s 1 )

P r o

d u c t

i v i t y

( k g /

h r / m

3 )

U L ( m/ s )

Figure 9: Eff ect of supercial liquid velocity and mass transfercoeffi cient on the productivity of the bioreactor ( P T = 3 atm, C x 0 =15 g/L, and U G,0 = 0.043m/s).

that there are in excess of 40 commercially available staticmixers designs that can be used for that purpose, the detailedanalysis/design of the gas liquid contact in such units isbeyond the scope of the present investigation.

One of the most commonly used means for controllingthe level of the interphase mass transfer coe ffi cient in thecase of gas/liquid dispersions owing through static mixersis by increasing the supercial velocity of the liquid phase.The impact of such action on the productivity of the loopbioreactor is shown in Figure 9 for a xed biomass loading of 15 kg/m3 and a constant inlet supercial gas velocity of U G =0.043 m/s.

Since we are dealing with a xed length reactor, anincrease in supercial gas velocity will lead to reducing theresidence time in the bioreactor. It is therefore interesting tosee that for kLa values 0.08s 1, a plateau in the bioreactorproductivity was observed to occur for supercial liquidvelocities of 0.4 m/s or higher. Under such conditions, all thereactants are converted within the specied reactor lengthand any changes in the residence time, kLa, and G/L ratioare not reected in the productivity but in the length of thereactor needed to achieve conversion. The slight reductionin productivity observed at U L values lower than 0.4 m/s iscaused by the incomplete conversions of the reactants at theelevated G/L ratios associated with the low liquid supercialvelocities.

Under conditions where low kLa values are expected toprevail, it was found that the use of high liquid supercialvelocities results in increasing the productivity of the reactorto some extent. This unexpected nding stems from theincreased importance of the reactant feed rates associatedwith the elevated inux of presaturated liquid feed. This, inturn, resulted in the average concentration across the reactorlength being higher the larger the liquid supercial velocity is, with the consequent increase in average bioreaction rate.It is, however, not desirable to operate the bioreactor outsideof the plateau region because of the large reactant fractionthat remains unutilized at the end of the reactor, and


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the consequent need to establish a costly reactant recovery system to maintain the sustainability of the operation.

6. Conclusions and Recommendations

The impact that mixing has on the productivity of growingmicroorganisms in loop bioreactors has been investigatedusing the bioconversion of natural gas into Single-CellProtein as a case in point. A computer-aided design andsimulation model capable of analyzing the factors a ff ectingthis process was developed which is capable of accountingfor the impact that a wide range of operating and designconditions can have on the productivity of the tubular loop-reactors used in industry.

The results obtained in this investigation suggest thatit is possible to operate the process in a manner by whichmore than 99% of the reactants can be utilized in a once-through operation provided that proper biomass loadingsand reactor lengths are used, and adequately high interphasemass transfer coeffi cients are achieved. Average bioreactorproductivities in excess of 4 kg/h m 3 are predicted to beachieved using average mass transfer coe ffi cients as low as0.05s 1, a feat that can be easily achieved using pipe-loopbioreactors that are equipped with appropriately designedstatic mixers.

However, that model does not yet address the physicalmeans by which the desired interphase mass transfer coef-cients can be achieved, a deciency that is presently beingaddressed.

Nomenclature

a: Interfacial area of contact [m 2 / m3] Ac: Cross-sectional area of the loop reactor

pipe [m 2]C : Bulk concentration [mol/L] and Constant in

Vant Ho ff equation [L atm/mol]C : Equilibrium concentration at the interface

[mol/L]D: Pipe diameter [m]E: Energy consumption rate [kW]Em: Energy consumed per unit mass of the liquid

[kW/tonne]H : Henrys constant [L atm/mol]kL: Mass transfer coeffi cient in liquid phase

[m s 1]kLa : Volumetric mass transfer coe ffi cient [s 1]L: Pipe length [m]P : Pressure at any particular point along the

reactor length [atm]Q: Volumetric ow rate [m 3/s]R: Universal gas constant [L atm/K mol]Re: Pipe Reynolds numbert : Residence time [s]T : Temperature [ C]U : Supercial velocity [m/s]V : Volume [m3] y : mole fraction in gas phase

Y i j : Stoichiometric yield coeffi cient of component i relative to component j (e.g.,Y SX , mol CH 4/mol Cells)[mol i/mol j].

Greek Symbols

: Local turbulent kinetic energy dissipationrate [kW/tonne]

G: Volumetric fraction of dispersed phase [] : Density [kg/m 3] : Surface tension [N/m] : Total residence time in the reactor [s]: Viscosity [cP] and Specic growth rate of the

microorganisms [h 1]: Volumetric fraction of dispersed phase [].

Subscript

0: Initial conditionsCH4: MethaneCO2: Carbon dioxideG: GasH2O: Water vapouri: Component i in yield coeffi cient either

produced or consumed (e.g., S for substrateor C for carbon dioxide)

Inert: Nonreactive gases j: Component j in yield coeffi cient (e.g., X )L: LiquidMax: Maximumref: Reference conditionsSTP: Standard temperature and pressure (25 C,

1atm)T : Total X : Cell biomass.

Acknowledgment

The nancial support of BGTT and NSERC is gratefully acknowledged.

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