Metabolic modeling of synthesis gasfermentation in bubble column reactors

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Citation Chen, Jin, Jose A. Gomez, Kai Hoffner, Paul I. Barton, and MichaelA. Henson. “Metabolic Modeling of Synthesis Gas Fermentationin Bubble Column Reactors.” Biotechnology for Biofuels 8, no. 1(December 2015).

As Published http://dx.doi.org/10.1186/s13068-015-0272-5

Publisher BioMed Central

Version Final published version

Citable link http://hdl.handle.net/1721.1/97554

RESEARCH ARTICLE Open Access

Metabolic modeling of synthesis gasfermentation in bubble column reactorsJin Chen1, Jose A. Gomez2, Kai Höffner2, Paul I. Barton2 and Michael A. Henson1*

Abstract

Background: A promising route to renewable liquid fuels and chemicals is the fermentation of synthesis gas (syngas)streams to synthesize desired products such as ethanol and 2,3-butanediol. While commercial development of syngasfermentation technology is underway, an unmet need is the development of integrated metabolic and transportmodels for industrially relevant syngas bubble column reactors.

Results: We developed and evaluated a spatiotemporal metabolic model for bubble column reactors with the syngasfermenting bacterium Clostridium ljungdahlii as the microbial catalyst. Our modeling approach involved combining agenome-scale reconstruction of C. ljungdahlii metabolism with multiphase transport equations that govern convectiveand dispersive processes within the spatially varying column. The reactor model was spatially discretized to yield alarge set of ordinary differential equations (ODEs) in time with embedded linear programs (LPs) and solved using theMATLAB based code DFBAlab. Simulations were performed to analyze the effects of important process and cellularparameters on key measures of reactor performance including ethanol titer, ethanol-to-acetate ratio, and CO andH2 conversions.

Conclusions: Our computational study demonstrated that mathematical modeling provides a complementary tool toexperimentation for understanding, predicting, and optimizing syngas fermentation reactors. These model predictionscould guide future cellular and process engineering efforts aimed at alleviating bottlenecks to biochemical productionin syngas bubble column reactors.

Keywords: Metabolic modeling, Bioprocess engineering, Microbial fermentation, Ethanol production

BackgroundThe development of alternative, renewable sources of fuelsand chemicals to reduce our dependence on petroleumhas emerged as a paramount challenge for maintainingthe economic security and environmental wellbeing of theUSA. An essential component of this quest is to developrenewable, environmentally friendly sources of biochemi-cals via the conversion of readily available plant biomassand waste streams that represent a significant quantity ofreduced carbon feedstock. An emerging conversion routewith wide feedstock versatility is direct fermentation ofwaste gas streams and synthesis gas (syngas; mainlycomprised of H2/CO/CO2) by specialized CO fermentingmicrobes. Because syngas can be produced relativelycheaply from a wide variety of biomass feedstocks [1, 2],

the bottleneck in this route is the syngas fermentationstep. Key considerations are the metabolic capabilities andperformance of the microbial catalyst that converts syngasinto the desired biochemical, gas–liquid mass transfercharacteristics that determine the availability of solublegas components for microbial conversion and the bio-reactor design that affects all aspects of the conversionprocess.

Gas fermentation for production of fuels and chemicalsA model syngas-consuming organism is Clostridiumljungdahlii, a rod-shape anaerobic bacterium that wasdiscovered in 1987 and found to have the ability to fer-ment CO and H2 into ethanol and acetate [3]. This dis-covery initiated a wave of research and developmentefforts aimed at understanding and optimizing syngas fer-mentation for ethanol production [4]. Several other bac-teria including C. aceticum [5], Acetobacterium woodii [6],and C. carboxidivorans [7] also have been studied for

* Correspondence: henson@ecs.umass.edu1Department of Chemical Engineering, University of Massachusetts, Amherst,MA 010003, USAFull list of author information is available at the end of the article

© 2015 Chen et al. This is an Open Access article distributed under the terms of the Creative Commons Attribution License(http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium,provided the original work is properly credited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.

Chen et al. Biotechnology for Biofuels (2015) 8:89 DOI 10.1186/s13068-015-0272-5

syngas fermentation. All these mesophilic bacteria syn-thesize ethanol through the reductive acetyl-CoA meta-bolic pathway, a non-cyclic, fermentative pathway whichis active under anaerobic conditions [8]. Electrons re-quired in the pathway are supplied by the syngas com-ponents CO and H2. Optimal growth conditions forC. ljungdahlii have been reported as 37 °C and pH of 6.0[9], but at least one study claims that ethanol synthesiswas increased at lower pH values where growth was sig-nificantly reduced [10].One of the most challenging problems in syngas fer-

mentation is to establish culture conditions which offerfavorable gas–liquid mass transfer characteristics suchthat the syngas is readily dissolved and available for mi-crobial conversion. A variety of reactor types includingstirred tank reactors, trickle bed reactors, packed bedreactors, monolithic biofilm reactors, membrane-basedreactors, and bubble column reactors have been investi-gated [9]. While more advanced designs based on bubblecolumn reactors are being developed for large-scale pro-duction [8], most academic research has been performedin stirred tank reactors with continuous liquid and syn-gas flows. Stirred tank reactors can have CO mass trans-fer coefficients over 100 h−1 through the use of speciallydesigned impellers, high agitation rates, and microspar-gers that create small gas bubbles [9, 11]. However, sub-stantially enhanced syngas mass transfer can be achievedin bubble column reactors due to higher average masstransfer driving forces caused by favorable gas compos-ition spatial profiles and longer gas–liquid contact times.Another potential strategy for increasing syngas solu-bility is the use of elevated operating pressures [12]. Thisapproach has not been widely studied because gas com-pression at the industrial scale is costly.Because the syngas feed is introduced into the bottom

of the bubble column (Fig. 1), CO and H2 concentra-tions decrease as the gas flows up the column due tocellular consumption. Therefore, the column has spa-tially varying dissolved gas concentrations that affect cel-lular growth and product synthesis. In principle, highdissolved CO concentrations throughout the column aredesirable since CO is the primary carbon source forgrowth. Previous experimental studies [8, 13] have sug-gested that high dissolved CO levels can inhibit both COand H2 uptake rates (Fig. 2). Therefore, column opti-mization requires that dissolved CO concentrations aresufficiently high near the top of the column to promotegrowth, but CO concentrations near the bottom of thecolumn are not so high as to significantly inhibit gas up-take rates. The relative amounts of dissolved CO and H2

have a strong impact on the split between the desiredproduct ethanol and the undesired byproduct acetate[14, 15]. While ethanol synthesis is promoted at high H2

concentrations, the ratio of ethanol to acetate increases

with increasing H2 concentration. Therefore, the objec-tive is to establish desirable H2 and CO concentrationprofiles along the column such that the ethanol pro-duction is maximized and the acetate production isminimized. The design and operation of bubble columnreactors to achieve a suitable compromise between thesecompeting objectives has proven to be a difficult chal-lenge that has limited commercial syngas fermentationtechnology. We believe that the development of model-based techniques for simulating and optimizing syngasbubble column reactors is essential to advance thistechnology.

Spatiotemporal modeling of microbial metabolismSteady-state [16] and dynamic [17–20] flux balance ana-lysis techniques based on genome-scale metabolic re-constructions have become standard tools for analyzingmicrobial metabolism. Recently, the first genome-scalemetabolic reconstruction of a CO fermenting organismwas introduced for the bacterium C. ljungdahlii [21].The iHN637 model includes an extensive reaction net-work of central metabolism, including the pathways in-volved in carbon fixation and energy conservation. Themodel was shown to be capable of producing acetate, etha-nol, and 2,3-butanediol under conditions consistent with

Fig. 1 Bubble column reactor for microbial syngas fermentation

Chen et al. Biotechnology for Biofuels (2015) 8:89 Page 2 of 12

experimental data. While a few very simple unstructuredgrowth models of syngas fermentation have been de-veloped [22, 13], we are not aware of any dynamicmodels based on FBA and/or genome-scale metabolicreconstructions.Dynamic modeling of syngas bubble column reactors

poses an additional challenge not encountered in well-mixed stirred tank reactors. Namely, spatial gradients arepresent because the dissolved CO and H2 concentrationsdecrease as the gas flows up the column due to cellularconsumption [8]. The cellular growth and product syn-thesis rates along the column are determined by theselocal dissolved gas concentrations. While spatiotemporalmodels that account for both spatial and temporalvariations in the extracellular environment have been con-structed, these studies utilized table lookups of precom-puted FBA solutions [23–25] or heuristic lattice-baseddescriptions of nutrient diffusion [23–25]. We propose ageneral methodology for spatiotemporal metabolic mo-deling based on combining genome-scale reconstructionswith fundamental transport equations that capture therelevant convection and/or diffusional processes. Add-itional details on the numerical solution procedure will beavailable in a forthcoming publication. The model solutionprocedure involved spatially discretizing the partial dif-ferential equations (PDEs) to generate an ordinary dif-ferential equation (ODE) system with embedded linearprograms (LPs) that was integrated with DFBAlab [26], aMATLAB code that performs reliable and efficient dy-namic FBA simulations. We demonstrated the capabilitiesof our approach by performing dynamic simulations withthe syngas bubble column reactor model presented below.The contributions of the present study include the follow-ing: (1) a detailed presentation of the bubble columnmodel including experimentally derived parameters and

(2) an extensive investigation into the effects of processand cellular parameters on bubble column performance.

Results and discussionImpact of design and operating parameters on bubblecolumn performanceThe model was used to predict the effects of importantdesign and operating parameters on bubble columnperformance, as measured by the liquid and gas phaseconcentrations exiting the reactor under steady-stateconditions. Due to the lack of accurate dissolved gas up-take kinetic parameters and directly comparable experi-mental data for model validation, the model predictionsshould be viewed as qualitative rather than quantitative.This capability was deemed sufficient for predictingtrends with respect to key parameters. Each predictionwas generated by simulating bubble column startup withN = 100 node points and a final time of 1000 h to obtainthe steady-state solution. Typically 5–10 simulationswere performed for each parameter, and plots showingparameter trends were generated by linearly inter-polating the cases ran (indicated by asterisks) withinMATLAB.We first investigated the impact of the feed compos-

ition by varying the CO mole fraction with the H2 molefraction adjusted such that the mole fractions summedto unity. Experimental studies [27] have shown thatethanol synthesis is favored relative to acetate synthesisat high H2/CO feed ratios. We observed the same trendin our bubble column simulations (Fig. 3). The ethanoltiter was predicted to achieve a maximum of 120 g/L ata CO mole fraction of 0.45, which represents a H2 richfeed. As the mole fraction was increased beyond thisvalue, the ethanol concentration was predicted to de-crease and acetate synthesis began. The ethanol and

Fig. 2 The effects of CO and H2 mass transfer and cellular uptake on biomass production and the distribution of metabolic products by C. ljungdahlii.The lines with arrows represent positive/activating effects and the lines with bars represent negative/inhibitory effects

Chen et al. Biotechnology for Biofuels (2015) 8:89 Page 3 of 12

acetate concentrations were approximately equal at amole fraction of 0.55. Thereafter, the acetate titer in-creased rapidly, the ethanol titer decreased rapidly, andCO2 synthesis began due to low dissolved H2 levels.Interestingly, the acetate concentration decreased at COmole fractions beyond 0.75, presumably due to reducedbiomass production. A maximum biomass concentrationof about 35 g/L was predicted for a 50/50 CO/H2

mixture.Next we explored the impacts of the superficial gas

velocity (uG) reactor performance. Increasing uG alsocaused the gas volume fraction εG to increase accordingto Eq. 9. High uG values were predicted to increase dis-solved CO and H2 concentrations at the expense of re-duced CO and H2 conversions in the gas phase (Fig. 4).Due to enhanced dissolved H2 concentrations, high uGvalues produced more favorable ethanol/acetate splits.

For example, uG = 300 m/h produced an ethanol/acetateratio of 10:1 but CO and H2 conversions of only 7 and19 %, respectively. Conversely, low uG values producedmore favorable conversions but high acetate concentra-tions as well as substantial CO2 synthesis.Many experimental studies have argued that the effi-

ciency of syngas fermentation is limited by gas–liquidmass transfer [28]. To explore this claim, we varied theCO gas–liquid mass transfer coefficients km,C to cover arange of values reported in the literature [9]. As withour nominal values, we set the H2 mass transfer coeffi-cient km, H to be 250 % larger than the CO value and theCO2 mass transfer coefficient km,D to be equal to the COvalue. As expected, the primary value of high masstransfer coefficients was predicted to increase dissolvedCO and H2 concentrations, with CO much more stronglyaffected (Fig. 5). Below our nominal value km,C = 80 h−1,

Fig. 3 Effect of the feed CO mole fraction on steady-state concentrations in the exiting liquid and gas streams. The dashed lines indicate thenominal feed CO mole fraction used in the other simulations

Fig. 4 Effect of the superficial gas velocity on steady-state concentrations in the exiting liquid and gas streams. The vertical dashed lines indicatethe nominal superficial gas velocity used in the other simulations. The horizontal dashed lines indicate the inlet gas concentrations of CO and H2

Chen et al. Biotechnology for Biofuels (2015) 8:89 Page 4 of 12

acetate was the primary byproduct and no CO2 wassynthesized. Above this nominal value, the acetatetiter decreased rapidly and the ethanol titer increasedrapidly such that the ethanol/acetate ratio was 5.75 atkm,C = 500 h−1. Such high mass transfer coefficients canbe achieved in bubble column reactors through the use ofsyngas microsparging and/or internal packing to increasegas–liquid contact [9]. Enhanced gas–liquid mass transferalso improved syngas consumption, with the CO and H2

conversions increased to 34 and 89 %, respectively, atkm,C = 500 h−1.Most column operating conditions investigated in this

study were predicted to produce low syngas conversionsdue to limited gas–liquid mass transfer and cellular up-take rates. For example, our nominal conditions resultedin 62 % H2 conversion and 29 % CO conversion. One

method for increasing these conversions is partial re-cycle of unconsumed gas exiting the top of the column(Fig. 1). We explored the effects of gas recycle by allow-ing a fraction α of the gas exiting the column to berecycled and mixed with the fresh syngas feed. Whilesyngas conversion was predicted to be improved as ex-pected, gas recycling had the undesirable effect of sub-stantially reducing the ethanol titer and the ethanol/acetate ratio (Fig. 6). This behavior seemed to be causedby decreasing dissolved H2 concentrations as the recycleratio was increased.

Impact of gas uptake parameters on bubble columnperformanceThe model was used to predict the effects of importantgas uptake parameters on bubble column performance, as

Fig. 5 Effect of the CO gas–liquid mass transfer coefficient km,C on steady-state concentrations in the exiting liquid and gas streams. The H2

and CO2 mass transfer coefficients were set to be 2.5km,C and km,C, respectively. The dashed lines indicate the nominal km,C value used in theother simulations

Fig. 6 Effect of the gas recycle ratio on steady-state concentrations in the exiting liquid and gas streams. No gas recycle was used in theother simulations

Chen et al. Biotechnology for Biofuels (2015) 8:89 Page 5 of 12

measured by steady-state concentrations at the columnexit as before. Because our nominal CO and H2 maximumuptake rate values had substantial uncertainty, we variedthese maximum rates to investigate their impact. Both up-take rate parameters were predicted to have substantial ef-fects on biomass production, with small rates insufficientto meet the ATP maintenance requirements of the celland generating no growth (Fig. 7). The maximum rate pa-rameters also affected both the amount and distributionof metabolic byproducts. For a H2 maximum uptake ratevmax, H = 10 mmol/gDW/h, the model predicted that noethanol would be synthesized regardless of the CO uptakerate. In this case, increasing amounts of acetate and CO2

were produced as the CO maximum uptake rate vmax, Cwas increased. For larger H2 maximum uptake rates,increasing amounts of ethanol were synthesized up tovmax, C = 25 mmol/gDW/h, at which point the ethanoltiter began to drop while the acetate titer continued to in-crease. We also varied the saturation constants in the COand H2 uptake rate expressions (Eq. 2) to examine theirimpacts. The main effect of increasing the CO saturationconstant was to decrease the acetate titer and increase theethanol titer by establishing more favorable ratios of thetwo gas uptake rates (results not shown). Decreasing theH2 saturation constant had the same effect.Previous experimental studies [8, 13] have suggested

that high dissolved CO levels can inhibit the uptake of

CO and/or H2. To explore the impact of such inhibitoryeffects, we modified the uptake rate expressions asfollows:

vC ¼ vmax;CC

Km;C þ C þ C2.

KI;C

1

1þ E þ AKI

vH ¼ vmax;HCKm;HþH

1

1þ E þ AKI

1

1þ CKI;H

ð1Þ

where KI, C and KI, H are parameters that account for COinhibition of CO uptake and H2 uptake, respectively. Eachparameter was varied independently to obtain three valuesthat corresponded to no inhibition (KI, C = KI, H = 106 g/L),moderate inhibition, and strong inhibition. As expected,inhibition of either CO or H2 uptake was predicted toreduce steady-state biomass production throughout thecolumn (Fig. 8). CO inhibition had the interesting effect ofsubstantially reducing acetate synthesis but having verylittle impact on the exiting ethanol titer due to the estab-lishment of more favorable intracellular CO/H2 levels. Atthe highest level of inhibition, no acetate was producedand the ethanol titer was over 60 g/L. Conversely, CO in-hibition of H2 uptake shifted the product distributionstrongly towards acetate with no ethanol produced at thehighest inhibition level.

Fig. 7 Effect of the CO and H2 maximum uptake rate parameters on steady-state biomass and byproduct concentrations at the top column.The dashed lines indicate the nominal CO maximum uptake rate used in the other simulations. The nominal H2 maximum uptake rate wasvmax, H = 70 mmol/gDW/h

Chen et al. Biotechnology for Biofuels (2015) 8:89 Page 6 of 12

ConclusionsBubble columns are the preferred reactor technology forindustrial production of fuels and chemicals from synthe-sis gas. A number of experimental studies have been per-formed to investigate the effects of the microbial catalyst,the column design parameters, and the column operatingconditions on syngas fermentation performance [9]. Be-cause the effect of cellular and process parameters oncolumn performance are complex, mathematical model-ing provides a complementary tool to experimentation forunderstanding, predicting, and optimizing syngas fer-mentation reactors. We developed a spatiotemporal meta-bolic model for bubble column reactors by combining agenome-scale metabolic reconstruction of the syngas fer-mentating bacterium C. ljungdahlii with multiphase trans-port equations that govern convective and dispersiveprocesses within the spatially varying column. To obtain acomputationally tractable model, we performed spatialdiscretization to yield a large set of ordinary differentialequations (ODEs) in time with embedded linear programs(LPs). Our initial attempts to solve the discretized modelwithin MATLAB using a straightforward combination of

built-in ODE solvers and the MOSEK LP solver provedunsuccessful. We found the recently developed MATLABbased code DFBAlab [26] to be a critical enabling tool,without which this study would not have been possible.Model translation into the DFBAlab format required min-imal work.Column startup was dynamically simulated with dif-

ferent process parameters to generate steady-state col-umn profiles for analysis of parameter trends. Becausethe liquid product stream was removed from the top ofthe column, we focused our analysis on liquid and gasphase concentrations at this point. Our analysis waslimited to syngas feed streams containing only CO andH2. We predicted the following trends that could guidecolumn design and operation for maximization of etha-nol production:

� A maximum ethanol titer of 120 g/L and no acetateproduction were achieved at a CO mole fraction of0.45 (Fig. 3). The ethanol concentration decreasedrapidly, CO2 synthesis occurred and acetate quicklybecame the dominant byproduct at higher CO mole

Fig. 8 Effect of CO inhibition of CO uptake (left) and H2 uptake (right) on steady-state biomass and byproduct production throughout the column.The nominal case corresponds to no inhibition (KI, C = KI, H = 106 g/L)

Chen et al. Biotechnology for Biofuels (2015) 8:89 Page 7 of 12

fractions, suggesting that H2 augmentation ofCO-rich syngas feeds may be beneficial.

� High superficial gas velocities enhanced the ethanoltiter and ethanol/acetate split at the expense of lowCO and H2 conversions (Fig. 4), indicating thepossible benefit of recycling unconsumed gas toachieve higher conversions.

� Partial recycling of unconsumed gas showed thepotential to substantially improve CO and H2

conversions at the expense of increased gascompression costs (Fig. 6). Because recycling hadthe negative effect of reducing the ethanol titer andthe ethanol/acetate ratio due to depleted H2 levels,H2 augmentation may be necessary to achieveacceptable process economics.

� Enhanced ethanol titer and ethanol/acetate splitwere achieved with increasing liquid velocity up to acritical value at which the column was washed out(results not shown). The development of reactormonitoring and control strategies would benecessary to stably operate near this critical value.

� Increasing reactor length enhanced both theethanol titer and the ethanol/acetate split(results not shown). Because taller reactorsrequired more syngas feed compression, aneconomic analysis would be needed to determinethe optimal length.

� Efficient gas–liquid mass transfer was found to becritical to achieve high ethanol production and highconversions (Fig. 5). A CO mass transfer coefficientof 500 h−1 was predicted to produce an ethanol titerof 130 g/L, an ethanol/acetate ratio of 6, and COand H2 conversions of 34 and 89 %, respectively, fora syngas feed containing 60 % CO. These resultsdemonstrate the need for continued development ofadvanced bubble column designs that achieve veryhigh gas–liquid mass transfer rates.

� The bubble column model also was used toinvestigate the effect of CO and H2 uptakeparameters on reactor performance. The followingtrends were observed that could guide theengineering of bacterial syngas uptake kinetics forethanol overproduction:

� Enhanced H2 uptake rates achieved either byincreasing the maximum uptake rate or by reducingthe uptake saturation constant substantiallyincreased the ethanol titer and the ethanol/acetateratio (Fig. 7). Consequently, C. ljungdahliiengineering efforts should focus on increasing H2

uptake rates.� Ethanol and/or acetate inhibition of growth modeled

as inhibition of the CO and H2 uptakes reducedbiomass production but increased the ethanol titerand the ethanol/acetate ratio (results not shown).

Therefore, cellular engineering efforts aimed atreducing byproduct inhibition may have limitedeffectiveness.

� Inhibition of CO uptake at high CO levels reducedbiomass production but had almost no effect on theethanol titer while reducing acetate synthesis (Fig. 8).Conversely, CO inhibition of H2 uptake reducedgrowth and shifted the product distribution stronglytowards acetate. Consequently, C. ljungdahliiengineering efforts should focus on alleviatingCO inhibition of H2 uptake.

Future work on syngas bubble column modeling couldinclude the incorporation of more realistic columnhydrodynamics [29] to improve model fidelity.

MethodsModel formulationThe bubble column model was formulated by combininga genome-scale metabolic reconstruction of C. ljungdahliiwith uptake kinetics for dissolved gases and reaction-convection-dispersion type equations for gaseous and dis-solved substrates and synthesized metabolic byproducts.The C. ljungdahlii iHN637 reconstruction accounts for637 genes, 698 metabolites, 690 intracellular reactions,and 95 exchange reactions that capture the primary meta-bolic pathways involved in synthesis gas fermentation[21]. The model has been shown to produce growth onseveral known substrates including CO and CO2/H2 mix-tures as well as to provide good agreement with experi-mentally determined growth and acetate production rateson fructose. Our preliminary flux balance calculationswith the typical maximum growth objective showedthat the primary metabolic byproducts for growth onCO/H2 mixtures were ethanol, acetate, and CO2. We as-sumed that the extracellular pH was maintained constantthroughout the reactor such that the intracellular pHcould be assumed constant at the value used for chargebalancing of the metabolic reconstruction [21].Uptake kinetics were specified for the dissolved gas-

eous substrates CO and H2 as well as for the dissolvedgaseous byproduct CO2 that could be reassimilated. Up-take kinetics were assumed to follow inhibited Monodexpressions of the form,

vi ¼ vmax;iSiKm;i þ Si

1

1þ EþAKI

ð2Þ

where vi is the uptake rate (mmol/gDW/h) of the i-thsubstrate, Si is the dissolved concentration (mmol/L) ofthe i-th gaseous substrate, vmax,i is the maximum uptakerate, Km,i is the saturation constant, and KI is an inhi-bition constant. A combined term involving both theconcentrations of ethanol (E) and acetate (A) was used

Chen et al. Biotechnology for Biofuels (2015) 8:89 Page 8 of 12

to account for the known inhibitory effects of these twoproducts on C. ljungdahlii growth [22, 30]. To reducethe number of model parameters, the two products wereassumed to induce equal inhibition of all substrate up-take rates such that only a single KI value was needed tomodel inhibition of growth due to high ethanol and/oracetate concentrations. Equation (2) was used to estab-lish bounds on the possible uptake rates with the actualuptake rates being determined by the solution of theintracellular flux balance problem. Both vmax,i and Km,iwere important parameters due to the large dissolvedgas concentration gradients in the bubble column re-actor (see Results).Despite synthesis gas fermentation being an active re-

search area, we found a dearth of literature for deter-mining the parameter values needed to calculate uptakerates for the three possible substrates (CO, H2, CO2).Parameter values for the CO maximum uptake rate andsaturation constant were obtained from a recent expe-rimental study [13]. Based on our own limited expe-rimental data (unpublished), we assumed that the H2

maximum uptake rate was double the CO value. Becausedata was lacking for determination of the remaining pa-rameters, the CO2 maximum uptake rate and the H2

and CO2 saturation constants were taken to be equal tothe corresponding CO values. The value of the inhib-ition constant was chosen based on our previous model-ing efforts involving uptake inhibition by ethanol andother toxic byproducts (Hanly and Henson 2014). Dueto the large uncertainties associated with these param-eter values (Table 1), we explored the sensitivity of ourmodel predictions to the dissolved gas uptake kinetics.The genome-scale reconstruction of intracellular metab-

olism and the substrate uptake kinetics were combinedwith reaction-convection-dispersion type equations forthe bubble column transport processes. Because our focuswas describing spatially varying cellular metabolism ratherthan detailed modeling of the potentially complex columnhydrodynamics [29], we assumed ideal plug flow for thevapor phase and plug flow plus axial dispersion for theliquid phase. These assumptions represent reasonablesimplifications given the gas superficial velocities withinthe bubbly flow regime (<5 cm/s; [29]) and the very smallliquid velocities (<0.02 cm/s) used in our simulations.Convection and dispersion were assumed to occur only in

the axial direction of the bubble column reactor suchthat spatial variations could be captured with a singlevariable z.The mass balance of C. ljungdahlii biomass had the

form,

∂X z; tð Þ∂t

¼ μX−uLεL

∂X∂z

þ DA∂2X∂z2

uLX 0; tð Þ−εLDA∂X 0; tð Þ

∂z¼ 0

∂X L; tð Þ∂z

¼ 0 X z; 0ð Þ ¼ X0

ð3Þwhere X is the biomass concentration (g/L), μ is cellulargrowth rates (h−1) obtained from the flux balance calcu-lation, uL is the liquid phase velocity, εL is the liquidphase volume fraction, and DA is the axial dispersion co-efficient of the liquid phase. A typical Danckwertsboundary condition was imposed at the reactor entrance(z = 0), while a zero slope boundary condition was ap-plied at the reactor exit (z = L). A uniform biomass con-centration profile within the reactor was used as theinitial condition.Mass balances of the dissolved gaseous substrates had

the form,

∂CL z; tð Þ∂t

¼ vCX þ km;C

εLC�−CLð Þ− uL

εL

∂CL

∂zþ DA

∂2CL

∂z2

uLCL 0; tð Þ−εLDA∂CL 0; tð Þ

∂z¼ 0

∂CL L; tð Þ∂z

¼ 0 CL z; 0ð Þ ¼ CL0

∂HL z; tð Þ∂t

¼ vHX þ km;H

εLH�−HLð Þ− uL

εL

∂HL

∂zþ DA

∂2HL

∂z2

uLHL 0; tð Þ−εLDA∂HL 0; tð Þ

∂z¼ 0

∂HL L; tð Þ∂z

¼ 0 HL z; 0ð Þ ¼ HL0

ð4Þwhere CL and HL are the liquid phase CO and H2 con-centrations (mmol/L), vC and vH are the CO and H2 up-take rates (mmol/gDW/h) obtained from the fluxbalance calculation, km, C and km, H are the correspon-ding gas–liquid mass transfer coefficients, and C* andH* are the saturated liquid concentrations (mmol/L) cal-culated from the corresponding gas phase concentra-tions using Henry’s law at the specified temperature andpressure. Constant gas–liquid mass transfer coefficientswere used for simplicity despite their known dependenceon various factors including gas bubble size [31], whichwas not modeled in this study. The Danckwerts boun-dary conditions imposed at the reactor entrance as-sumed the form shown since dissolved gases were notfed to the reactor, while zero slope boundary conditionswere applied at the reactor exit. Uniform concentrationprofiles calculated from the initial gas phase concentra-tions using Henry’s law were imposed as initial condi-tions, which was consistent with the liquid phase beingsaturated with the feed gases prior to inoculation.

Table 1 Nominal dissolved gas uptake parameters

Substrate vmax (mmol/gDW/h) Km (mmol/L) Source

CO 35 0.02 [13]

H2 70 0.02 Specified

CO2 35 0.02 Specified

Substrate KI (g/L) Source

All 10 Specified

Chen et al. Biotechnology for Biofuels (2015) 8:89 Page 9 of 12

Mass balances of the two substrates in the gas phasehad the form,

∂CG z; tð Þ∂t

¼ −km;C

εGC�−CLð Þ− uG

εG

∂CG

∂zCG 0; tð Þ ¼ CGFCG z; 0ð Þ ¼ CG0

∂HG z; tð Þ∂t

¼ −km;H

εGH�−HLð Þ− uG

εG

∂HG

∂zHG 0; tð Þ ¼ HGFHG z; 0ð Þ ¼ HG0

ð5Þwhere CG and HG are the gas phase CO and H2 concen-trations (mmol/L), εG = 1-εL is the gas phase volumefraction, and uG is the superficial gas velocity. The gasconcentrations at the reactor entrance CGF and HGF

were calculated from the partial pressures of the feedgas using the ideal gas law. Uniform initial conditionswere specified by setting CG0 = CGF and HG0 = HGF ,which again was consistent with the liquid phase beingsaturated with the feed gases prior to inoculation.Mass balances on the two major metabolic byproducts

ethanol and acetate had the form,

∂EL z; tð Þ∂t

¼ MEvEX−uLεL

∂EL

∂zþ DA

∂2EL

∂z2

uLEL 0; tð Þ−εLDA∂EL 0; tð Þ

∂z¼ 0

∂EL L; tð Þ∂z

¼ 0 EL z; 0ð Þ ¼ EL0

∂AL z; tð Þ∂t

¼ MAvAX−uLεL

∂AL

∂zþ DA

∂2AL

∂z2

uLAL 0; tð Þ−εLDA∂AL 0; tð Þ

∂z¼ 0

∂AL L; tð Þ∂z

¼ 0 AL z; 0ð Þ ¼ AL0

ð6Þwhere EL and AL are the concentrations of liquid phaseethanol (g/L) and acetate (g/L), vE and vA are the corre-sponding fluxes (mmol/L) calculated from the flux bal-ance model, and ME and MA are the correspondingmolecular weight (g/mmol). Gas phase balances on etha-nol and acetate were omitted under the assumption oflow volatility at column conditions. Danckwerts bound-ary conditions were imposed at the reactor entrance andzero slope boundary conditions were applied at the re-actor exit as before. Uniform ethanol and acetate con-centration profiles were used as initial conditions.Mass balances on liquid and gas phase carbon dioxide

had the form,

∂DL z; tð Þ∂t

¼ vDX þ km;D

εLD�−DLð Þ−uL

εL

∂DL

∂zþ DA

∂2DL

∂z2

uLDL 0; tð Þ−εLDA∂DL 0; tð Þ

∂z¼ 0

∂DL L; tð Þ∂z

¼ 0 DL z; 0ð Þ ¼ DL0

∂DG z;tð Þ∂t ¼ −

km;D

εGD�−DLð Þ−uG

εG

∂DL

∂z

DG 0; tð Þ ¼ DGF DG z; 0ð Þ ¼ DG0

ð7Þwhere DL and DG are the concentrations of liquid phaseCO2 (mmol/L) and gas phase CO2 (mmol/L), vD is theCO2 flux (mmol/L) calculated from the flux balance

model, km,D is the CO2 gas–liquid mass transfer coeffi-cient, and D* is the saturated liquid CO2 concentration(mmol/L) calculated from the corresponding gas phaseconcentration using Henry’s law. For liquid phase CO2,Danckwerts and zero slope boundary conditions wereapplied at the reactor entrance and exit as before. TheCO2 concentration at the reactor entrance DGF was cal-culated from the CO2 partial pressure of the feed gasusing the ideal gas law. This formulation allowed CO2 tobe a feed component and/or a metabolic byproduct. Auniform liquid phase CO2 concentration profile calcu-lated from the initial CO2 gas phase concentration usingHenry’s law was imposed as an initial condition. A uni-form initial condition for gas phase CO2 was specifiedby setting DG0 = DGF.The reactor was assumed to be isothermal, while the

pressure profile was calculated from the liquid head as,

P zð Þ ¼ PL þ ρLg L−zð Þ ð8Þ

where L is the length of the column, ρ is the liquidphase density assumed to be equal to the density ofwater, and PL is the pressure (Pa) at the top of the col-umn, which was assumed to be atmospheric pressure.Accordingly, gaseous substrates were modeled to dis-solve more readily in the lower portion of the column.Calculation of gas and liquid volume fractions in bubblecolumn reactors is notoriously difficult, as the volumefractions are known to depend on a number of operatingparameters [29]. The effect of the gas flow rate is knownto be particularly important. Therefore, we fit gas flowrate versus gas volume fraction data [32] to a simplemodel [33] to derive the following relationship:

εg ¼ εG;maxuGKG þ uG

ð9Þ

where εG, max is the maximum achievable gas volumefraction and KG is a type of saturation constant.Parameter values for the bubble column reactor model

were obtained from the literature to the extent possible(Tables 1 and 2). The reactor length and cross-sectionalarea were chosen to represent an industrial scale reactorwith volume of 125,000 l and a typical length-to-diameter ratio of 10 [29]. The liquid and superficial gasvelocities were chosen to achieve a liquid residence timeof 100 h to maintain the gas flow in the homogeneous,bubbly regime (<5 cm/s) where dispersion effects wouldbe small and to achieve a high gas-to-liquid velocity ra-tio of 300 [29]. A small value of the liquid phase disper-sion coefficient was specified to improve numericalstability of the model (see “Model solution”) while en-suring that the liquid flow would be convection con-trolled. A feed stream with a 1.5:1 CO:H2 ratio anddevoid of CO2 was used to model a CO-rich syngas

Chen et al. Biotechnology for Biofuels (2015) 8:89 Page 10 of 12

mixture [9]. A very wide range of CO gas–liquid masstransfer coefficients that differ according to the reactorconfiguration, gas sparging method, and agitation ratehave been reported [9]. We conservatively selected theCO mass transfer coefficient to be consistent with abubble column without microsparging and internalpacking. Based on the limited literature available [34],we chose the H2 gas–liquid mass transfer coefficient tobe 250 % larger than the CO value. The CO2 mass trans-fer coefficient was specified to be equal to the CO valuedue to lack of data. Due to the large variability asso-ciated with these parameter values, we explored the sen-sitivity of our model predictions to the mass transfercoefficients. The initial conditions were chosen to mimica newly inoculated reactor with saturated liquid compo-sitions and no spatial gradients.

Model solutionThe bubble column reactor model is consisted of a setof PDEs for multiphase transport processes with em-bedded linear programs that described intracellular me-tabolism. We spatially discretized the PDE model usingthird-order finite differences for the convection termsand second-order central differences for the diffusionterms. The resulting ODE system with embedded LPswas solved with DFBAlab [26], a MATLAB code specific-ally designed for large-scale dynamic FBA simulations,combined with the LP solver Gurobi and the stiff ODEsolver ode15s. DFBAlab requires the specification of lexico-graphic optimization objectives to avoid the common prob-lem of non-unique exchange fluxes that render the ODEsystem impossible to integrate. The objectives were sequen-tially applied in the following order: (1) maximization ofthe growth rate, (2) maximization of the CO uptake rate,(3) maximization of the H2 uptake rate, (4) minimizationof the CO2 synthesis rate, (5) minimization of the acetatesynthesis rate, and (6) minimization of the ethanol synthe-sis rate. The ordering of these objectives had no effect onmodel predictions. We found that 100 spatial node points(900 ODEs, 600 LPs) provided a suitable compromisebetween solution accuracy and computation time. Add-itional details on the numerical solution procedure areavailable in the forthcoming publication.

AbbreviationsDFBAlab: Dynamic flux balance analysis laboratory; FBA: Flux balance analysis;LP: Linear program; ODE: Ordinary differential equation; PDE: Partialdifferential equation.

Competing interestsThe authors declare that they have no competing interests.

Authors’ contributionsJC and MAH conceived the study and developed the model. JC, JAG, KH,and PIB developed the model solution method. JC performed thesimulations and analyzed the results. JC, JAG, KH, and MAH prepared themanuscript. All authors read and approved the final manuscript.

Table 2 Nominal parameter values for the synthesis gas bubblecolumn reactor

Parameter Symbol Value Source

Reactor length L 25 m Specified

Reactor cross-sectional area A 5 m2 Specified

Superficial gas velocity uG 75 m/h Specified

Liquid phase velocity uL 0.25 m/h Specified

Liquid phase dispersioncoefficient

DA 0.25 m2/h Specified

Temperature T 37 °C [3]

Pressure at top of column PL 1.013×105 Pa Specified

CO mole fraction in feed gas xC 0.6 Specified

H2 mole fraction in feed gas xH 0.4 Specified

CO2 mole fraction in feed gas xD 0 Specified

CO Henry’s law constant HC 8×10−4 mol/L/atm [35]

H2 Henry’s law constant HH 6.6×10−4 mol/L/atm [35]

CO2 Henry’s law constant HD 2.5×10−2 mol/L/atm [35]

CO gas–liquid mass transfercoefficient

km, C 80 h−1 [9]

H2 gas–liquid mass transfercoefficient

km, H 200 h−1 [34]

CO2 gas–liquid mass transfercoefficient

km, D 80 h−1 Specified

Maximum gas volume fraction εG, max 0.53 Fit to data

Gas volume fraction saturationconstant

KG 540 m/h Fit to data

Gas volume fraction εG 0.0646 Calculated

CO concentration at reactorentrance

CGF 80.64 mmol/L Calculated

H2 concentration at reactorentrance

HGF 53.76 mmol/L Calculated

CO2 concentration at reactorentrance

DGF 0 mmol/L Calculated

Initial biomass concentration X0 0.1 g/L Specified

Initial gas phase COconcentration

CG0 80.64 mmol/L Calculated

Initial gas phase H2

concentrationHG0 53.76 mmol/L Calculated

Initial gas phase CO2

concentrationDG0 0 mmol/L Calculated

Initial liquid phase COconcentration

CL0 1.642 mmol/L Calculated

Initial liquid phase H2

concentrationHL0 0.903 mmol/L Calculated

Initial liquid phase CO2

concentrationDL0 0 mmol/L Calculated

Initial liquid phase ethanolconcentration

EL0 0 mmol/L Specified

Initial liquid phase acetateconcentration

AL0 0 mmol/L Specified

Chen et al. Biotechnology for Biofuels (2015) 8:89 Page 11 of 12

AcknowledgementsJC and MAH wish to acknowledge the financial support from the ReCommunityRecycling and assistance from the Harish Nagarajan (UCSD) with the C. ljungdahliigenome-scale metabolic reconstruction.

Author details1Department of Chemical Engineering, University of Massachusetts, Amherst,MA 010003, USA. 2Process Systems Engineering Laboratory, Department ofChemical Engineering, Massachusetts Institute of Technology, Cambridge,MA 02139, USA.

Received: 22 March 2015 Accepted: 9 June 2015

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Chen et al. Biotechnology for Biofuels (2015) 8:89 Page 12 of 12