Evaluation of gas supply configurations for microbial product formation involving multiple gaseous substrates

Abstract

Background

Gaseous substrates such as O2 and CO2 are often required in fermentation processes. However, a simple methodology to compare different gas supply strategies using gaseous substrates from different sources is missing.

Results

In this study, we present a methodology to identify and theoretically compare different configurations to supply mixtures of gaseous compounds to fermentations that consume these gases. For the different configurations that were identified, all gas flow rates can be calculated in terms of other process parameters such as optimal concentrations of the gaseous compounds in the liquid phase, top pressures of the fermentation, and consumption/production rates. The approach is demonstrated for fumaric acid fermentation with Rhizopus delemar, which consumes O2 and can theoretically produce or consume CO2. Three different gas supply configurations were identified: Air supplemented with O2, a mixture of O2 and CO2, and air supplemented with CO2. All three configurations lead to gas supply costs in the same order of magnitude. O2 and CO2 prices and consumption rates determine which configuration is best. However, the overall production costs will not be dominated by the gas costs, but by the glucose costs.

Conclusions

The presented methodology enables a simple way to identify and compare different gas supply strategies for fermentations that require more than one gaseous substrate. This includes the costs for compression of gases. Other substrate costs are easily added for overall process optimization.

Husler et al. Bioresour. Bioprocess. (2016) 3:18 DOI 10.1186/s40643-016-0095-7

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Web End = Erik B. G. Husler, Luuk A. M. van der Wielen and Adrie J. J. Straathof*

Abstract

Background: Gaseous substrates such as O2 and CO2 are often required in fermentation processes. However, a simple methodology to compare dierent gas supply strategies using gaseous substrates from dierent sources is missing.

Results: In this study, we present a methodology to identify and theoretically compare dierent congurations to supply mixtures of gaseous compounds to fermentations that consume these gases. For the dierent congurations that were identied, all gas ow rates can be calculated in terms of other process parameters such as optimal concentrations of the gaseous compounds in the liquid phase, top pressures of the fermentation, and consumption/production rates. The approach is demonstrated for fumaric acid fermentation with Rhizopus delemar, which consumes O2

and can theoretically produce or consume CO2. Three dierent gas supply congurations were identied: Air supplemented with O2, a mixture of O2 and CO2, and air supplemented with CO2. All three congurations lead to gas supply costs in the same order of magnitude. O2 and CO2 prices and consumption rates determine which conguration is best. However, the overall production costs will not be dominated by the gas costs, but by the glucose costs.

Conclusions: The presented methodology enables a simple way to identify and compare dierent gas supply strategies for fermentations that require more than one gaseous substrate. This includes the costs for compression of gases. Other substrate costs are easily added for overall process optimization.

Keywords: Gasliquid mass transfer, Bioreactors, Modeling, Bioprocess design, Fumaric acid, Multiple gaseous substrates

Background

Biotechnological production of fuel and (bulk) chemicals from sustainable resources is a promising alternative for petrol-based processes. However, in many cases, petrochemical routes are economically more attractive. Often, the fermentation is one of the main contributors to the overall production cost, and much eort is spent to reduce the costs of this unit operation, for example utilization of lignocellulosic carbon sources (Straathof 2011). Another way to reduce fermentation costs is recycling of microbial mass, which decreases the consumption of substrate for the production of microbial mass.

High-density fermentation increases the volume-specic productivity and leads to smaller bioreactors, thus lower capital expenditures (CAPEX). In situ product removal is investigated for cases that product inhibition prevents high nal titers.

Next to substrates that can be supplied through a liquid feed, many fermentations need substrates that are gaseous at fermentation conditions, i.e., oxygen in countless aerobic fermentations. If possible, air is used for oxygen supply, because it is cheap, and the o-gas is generally vented after a single pass through the bioreactor. However, when using air the driving force for oxygen transfer from gas to liquid phase can become too small to sustain a sufficiently high oxygen transfer rate (OTR). This can be overcome by operating at higher top pressures

*Correspondence: [email protected] of Biotechnology, Delft University of Technology, Julianalaan 67, 2628 Delft, The Netherlands

2016 Husler et al. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/

Web End =http://creativecommons.org/licenses/by/4.0/ ), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Husler et al. Bioresour. Bioprocess. (2016) 3:18

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and/or increasing the oxygen mole fraction in the feed gas (van tRiet and Tramper 1991). The drawback of the rst method is that a higher top pressure leads to higher energy consumption, and of the second method that pure gases have to be purchased, or produced, which also introduces additional operational expenditures (OPEX).

The point concerning supply of gases becomes especially important when a fermentation requires a mixture of gaseous substrates, and when this mixture is not available as cost-free gas stream. Table1 shows several cases where this applies. For example, recent research showed that aerobic fumaric acid (FA) fermentations using Rhizopus delemar benet from increased partial CO2 pressures up to pCO2 = 0.1bar (Roa Engel etal. 2011). This eect is related to an anaplerotic reaction in the organisms metabolic network in which pyruvate carboxylase xes CO2. The need for a certain partial CO2 pressure was also reported for citric acid fermentations with Aspergillus niger (Papagianni 2007). The necessary CO2 is produced by the organism, but was stripped from the medium by increased aeration rates which led to lower product yields. McIntyre and McNeil (McIntyre and McNeil 1997) showed for this fermentation that 2% CO2 led to increased product concentration. Too high CO2 percentages can lead to lower product concentrations.

As stated before, air is usually vented after a single pass through the bioreactor. However, for other gas feeds, for example air enriched by O2, venting the o-gas after a single pass through the bioreactor would lead to losses of valuable gases. These losses can be reduced by recirculating the o-gas. A closed o-gas recycling when using pure O2 for aeration was presented by de Ory etal. (2004)

for vinegar production to avoid losses of ethanol via ogas, but the economic feasibility of the system compared to the conventional aeration method was not evaluated. Chang etal. (2010) presented such an evaluation for an industrial-scale poly(3-hydroxybutyrate) fermentation.

Their results showed that an o-gas recycle system including pressure swing adsorption for production of pure O2 leads to lower fermentation costs than conventional aeration with air.

This raises several questions: Will an o-gas recycle system generally lead to lower costs than aeration with air, even though the gaseous substrates would have to be bought? Would such a system also work when two or more gaseous compounds need to be controlled? Are there other alternative gas supply congurations which would lead to even lower costs? However, a systematic evaluation of dierent gas supply congurations for industrial fermentations is lacking. The questions are addressed by presenting a methodology to dene mathematically dened and physically feasible gas supply congurations based on a general case. For each of these cases, relations are derived to size all gas streams which enter or leave the bioreactor.

The methodology is illustrated for an FA fermentation with R. delemar, because it requires the presence of two gases, O2 and CO2, in the liquid phase. Still, the methodology enables a simple way to evaluate several gas supply congurations. First, a general case is dened which is mathematically underdetermined. Then three dierent and mathematically determined O2 and CO2 supply congurations for FA fermentation are derived from the general case: (1) CO2-enriched air with vented o-gas, (2) o-gas recycle with CO2 and O2 feed (zero gas emission), and (3) O2-enriched air with vented o-gas. All gas ow rates entering and leaving the system are derived for the three cases, and the cases are evaluated in terms of gas supply costs and overall production costs (including additional substrates and energy consumption).

Methods

A stirred tank reactor at steady state is used as a basis for the derivation of relations of the gas streams, and

Table 1 Examples ofmicrobial product formation involving multiple gaseous substrates

Organism Product(s) Gaseous substrate Gas feed Source

Rhizopus delemar Fumaric acid O2, CO2 Air, CO2 (Roa Engel et al. 2011)

Saccharomyces cerevisiae Malic acid O2, CO2 Air, O2, CO2 (Zelle et al. 2010)

S. cerevisiae Succinic acid O2, CO2 Air, O2 Jansen and van Gulik (2014) Corynebacterium glutamicum Cell mass O2, CO2 Air, O2, CO2 (Bumchen et al. 2007)

Clostridium carboxidivorans Ethanol CO, CO2, H2 CO, CO2, H2 (Hurst and Lewis 2010) Alkalibaculum bacchi and C. propionicum Alcohols CO, CO2, H2 Syngas (Liu et al. 2014)

Mycobacterium sp. Ethylene oxide Ethylene, O2 Ethylene, O2 (de Bont et al. 1983) Methylosinus sp. Propylene oxide Propylene, O2 Propylene, O2 (Hou 1984)

Methylosinus sp. 2-butanol Butane, O2 Butane, O2 (Patel et al. 1980) Brevibacterium sp. Glutamic acid O2, NH3 O2, NH3 (Nagy et al. 1995)

Husler et al. Bioresour. Bioprocess. (2016) 3:18

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gas and liquid phases are assumed to be ideally mixed except near the gasliquid interface. The gases are treated as ideal gases because fermentations are generally operated at relatively low pressures (ptot<10bar).

For example, Song etal. (2007) show the ideal behavior of Mannheimia succiniciproducens in terms of growth and succinic acid production up to a partial CO2 pressure of 1 bar. Therefore, non-ideal behavior can be neglected (Green and Perry 2007). When higher pressures are considered, a correction using the fugacity coefficient should be applied. Furthermore, the liquid phase is assumed to have the properties of pure water, a xed volume, and no pressure gradients due to height or so. The aim of the methodology is to calculate the gas inow rates as a function of the other process parameters.

Gas ow rates asa function ofproduction rates, total pressure, andpartial gas pressures

We start by dening steady-state mass balances for each component in the gas phase (see Eq.1):

The volume-specic production rate ri of component i by the bioreaction can be positive, negative in case of consumption, or zero in case of inert components such as N2 when air is used for O2 supply. Dierent from usual conventions, ow rates Fi and production rates ri are expressed in mole per m3 bioreactor liquid per second, because the absolute fermentor volume is not known. The ratio of partial pressures pi/pj of two components i

and j in the bioreactor equals the ratio of the gas outows of these two components (Eq. 3). The relation is easily derived: the mole fraction yi of component i in the gas phase equals the ratio of its partial pressure pi and the total pressure ptot. Similarly, it also equals the ratio of its partial molar outow Fouti and the total molar outow

Fouttot (Eq.2). If we divide the mole fractions of two components, we arrive at Eq.3.

Besides being present in a cheap gas stream, an inert gas in combination with the pressure in the bioreactor can also be used to adjust the partial pressures of multiple components i to a specic optimum.

All mass balances and pressureow relations are linear in terms of the gas ow rates, and this results in 2n1 linear equations with 2n unknowns, where n is the total number of components in the gas phase. The unknowns in the equations are the gas in- and outow rates of each component (Fini and Fouti). The partial pressures are known variables and their elimination from the system of equations is discussed in the next section. The total pressure is set by the process operator. There are several options to solve the resulting system of equations. First, one of the gas ow rates could be xed, thereby reducing the number of unknowns. Another option is to nd another independent equation without new unknowns. This can be achieved by xing the ratio of two components in the gas feed, which yields an additional pressureow relation. This is essentially the case when air is used as a single O2 source for an aerobic fermentation.

Now, the system of equations can be solved to express all ow rates Fi as a function of optimal partial gas pressures, the total pressure in the bioreactor, and the components production/consumption rates.

(1) Elimination ofpi throughmass transfer relation andHenrys law

Using the aforementioned relations, we can express all gas ow rates as a function of the production rates, total system pressure, and partial gas pressures. However, the microorganism senses the concentration of i in the liquid phase, not the partial pressure in the gas phase. To eliminate the partial gas pressures, we need the steady-state mass balance over the liquid phase (Eq.5), the mass transfer relation (Eq.6), and Henrys law (Eq.7).

Here, Ti is the mass transfer rate from gas to liquid phase [mol/(m3s)], kL,i is the mass transfer coefficient of i in the liquid phase, a is the specic gasliquid interface area [m2/m3], ci* is the concentration of i in the liquid phases [mol/m3] at the gasliquid interface, and ci is the concentration of i in the bulk of liquid phase [mol/ m3]. The interfacial concentration in the liquid phase is related to the partial pressure of i in the gas phase according to Henrys law. Hi is the Henrys law constant, and depending on its denition it has dierent units. Using the denition of Eq.7 where xi is the mole fraction of i

in the liquid phase at equilibrium, Hi has pressure units. The exact composition of the liquid is unknown, but by assuming that the bulk only consists of water, the molar

Fini = Fouti ri.

Ti + ri = 0

(5)

Ti = kL,i[notdef]c

(7)

i ci

(6)

pi = Hixi

yi = pi ptot

= Fouti Fouttot

(2)

Fouti

Foutj

= pi pj

(3)

pInert = ptot

~pi

(4)

Husler et al. Bioresour. Bioprocess. (2016) 3:18

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volume Vmol [m3/mol] of water can be used to express ci* as a function of xi.

Eliminating ci*, xi, and Ti from Eqs.58 and solving for the partial pressure yields

The nal step is substituting the partial pressures into the inow relations that were derived in the previous section. This yields the ow rates as a function of optimal concentrations in the liquid phase, Henrys constant, volume-specic production rates, mass transfer coefficients, and the total pressure in the bioreactor.

Energy forgas supply

Pumping gas into pressurized vessels demands energy for compression. The energy depends on the gas mass inow rate Finm [kg/(m3s)], the ratio of the gas pressure at its source psource, and the pressure ptot in the bioreactor.

The hydrostatic pressure in the vessel is neglected. The energy demand W [J/(m3s)] can be calculated by the general Bernoulli equation assuming adiabatic compression of an ideal gas while neglecting friction and changes in potential and kinetic energy (Sinnott 2005).

Kappa () equals the ratio of specic heats of the gas at constant volume (CV) and at constant pressure (Cp).

We must distinguish between dierent possible sources as some are pressurized and others are at ambient conditions. For example, air at ambient conditions must be compressed when the fermentation is operated at elevated pressures, but this is not necessary when the gas is already pressurized. For the rest of this study, it is assumed that purchased pure gases are pressurized.

Costs

To be able to select one of the gas supply congurations, we must determine the associated fermentation costs per kilogram product Gtot [$/kgP]. Here, investments are neglected for simplicity, and only the sum of gas costs Gi

[$/kgP] and energy costs for compression GW [$/kgP] is considered.

At this stage, all gas ows and production rates as well as energy demand and substrate consumption are

given as volume-specic quantities and they need to be converted into costs per kilogram product (Gi and GW).

Therefore, each rate is divided by the volume-specic rate rP,m [kg/(m3s)] of the product. This yields the amount of gas or associated energy demand per kilogram product, and multiplication by the associated prices (Pi [$/kgi] and

PW [$/J]) yields the costs per kilogram product. Molar substrate consumption rates ri [mol/(m3s)] are easily converted to mass-based rates ri,m [kg/(m3s)] by multiplication with the molar mass of the respective compound.

Results

The methodology has been applied to an FA fermentation with the fungus R. delemar, formerly known as R. oryzae. The fermentation is aerobic, but CO2 also plays an important role (Roa Engel et al. 2011), and it might even be consumed by the bioreaction instead of produced. The cause for this behavior is related to the metabolic network, and it is discussed during the derivation of the gas production/consumption rates in Derivation of gas production rates section. Nonetheless, this information was sufficient to dene three dierent gas supply congurations, and the gas inow relations were derived for all compounds of each separate case.

Gas supply congurations

The rst step is to identify the gas supply congurations that can maintain desired partial O2 and CO2

pressures (pO2 and pCO2) for this FA fermentation. The most general case is supply of both necessary gases (O2

and CO2) and an inert gas stream such as N2 in case ptot> pO2+ pCO2 (Fig.1a), and vent o-gas. So, we start by dening the O2, CO2, and N2 mass balances over the gas phase (Eqs. 1315) and the pressureow relations for O2 and CO2 on the basis of N2 (Eqs. 16 and 17). In total, there are ve equations with six unknowns (FinO2, FoutO2, FinCO2, FoutCO2, FinN2, and FoutN2) and therefore, as

discussed before, an additional relation is needed, or one variable has to be xed at a particular value.

c~i =

xi Vmol

(8)

pi = VmolHi

~(ri) kL,ia+ ci

.

(9)

Gi = ri,mrp,m (Pi) and GW

= Wrp,m (PW )

(12)

W = Finm

~pSource ~Source 1

ptot

pSource

1 1

(10)

FinCO2 = FoutCO2 rCO2

(13)

FinO2 = FoutO2 rO2

(14)

FinN2 = FoutN2

(15)

Gtot = GW +

~iGi

(11)

FoutCO2

FoutN2

= pCO2 pN2

(16)

Husler et al. Bioresour. Bioprocess. (2016) 3:18

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Fig. 1 Evaluated gas supply congurations: a general case, b case 1air enriched with CO2, c case 2o-gas recycle, and d) case 3

air enriched with O2

Next, the air inow rate needs to be determined. This ow is directly related to the O2 inow (Eq.21), which is derived similarly as the CO2 inow. Only the result is shown below. The relations for O2 and CO2 partial pressure are not substituted into this equation to reduce its complexity.

In addition to the gas cost, the energy for compression of gases to the desired top pressure needs to be taken into account, too. In case 1, air needs to be compressed from atmospheric to the desired top pressure. Pure CO2 is added from a pressurized source and therefore does not add to the energy requirements for compression.

Case 2: ogas recycle withO2 andCO2 feed (zero gas emission)

The second case is found when one of the gas outows is set to 0. By doing so, all other gas outows are removed as well. All the introduced gas can be kept in the biore-actor, but in practice it will be easier to use an o-gas recycle system (Fig. 1). Thus, the o-gas is fed to the bioreactor again, and only consumed amounts of gases have to be supplied. As indicated, the fermentation is operated at a given set of desired partial pressures. Pure O2 and CO2 are supplied to the bioreactor, and some N2

can be introduced during the start-up phase of the fermentation to achieve ptot. The costs for case 2 depend on the values of FinO2 and FinCO2, which are equal to rO2 and

rCO2, respectively, according to Eqs.23 and 24. FinO2 and FinCO2 are independent of the system pressure. It should be noted that this conguration implies that rCO20. Otherwise, a CO2 bleed stream would have to be introduced.

In this case, no additional energy is required for compression, because all gases are already pressurized.

Case 3: air supplemented withO2

The third case is a bioreactor that is aerated using air and additional pure O2 (Fig. 1d). The o-gas is vented after a single pass through the broth. The desired CO2 partial

Finair =

FinO2

0.21

(21)

FinO2 =

rO2

1 0.790.21 pO2pN

2

(22)

FoutO2

FoutN2

= pO2 pN2

(17)

Case 1: air supplemented withCO2

As proposed by Roa Engel et al. (2011), the bioreactor can be fed with air supplemented with CO2 (Fig.1b), and the o-gas is vented after a single pass through the biore-actor. This case is referred to as case 1. The mass balances over the gas phase and pressureow relations for O2 and

CO2 in terms of N2 are the same as for the general case (Eqs.1317), but we can add an additional pressureow relation for the O2 and N2 inow, because the ratio of the partial O2 and N2 pressures in the gas feed is known.

The costs of case 1 depend on FinCO2 and energy requirements to compress the air for FinAir. Therefore, we need to express both ow rates as a function of ptot, pi, and ri. The

CO2 inow is found by taking Eqs.1318 and eliminating all other ows (FinO2, FoutO2, FinN2, FoutN2 and FoutCO2).

Then, we substitute the partial pressure of the inert gas (Eq.4) and relations for the partial O2 and CO2 pressures (Eq.9) into the CO2 inow relation (Eq.19).

FinO2

FinN2

= pairO2 pairN2

= 0.210.79

(18)

FinO2 = rO2

(23)

FinCO2 = rCO2

(24)

rO20.79 pCO2

~0.21 pN2 0.79 pO2 rCO2

FinCO2 =

(19)

rO20.79HCO2Vmol

~(rCO2 )kL,CO2 a + cCO2

FinCO2 =

rCO2

(20)

~0.21ptot 0.21HCO2Vmol

~(rCO2 )kL,CO2 a + cCO2

HO2Vmol

~(rO2 )kL,O2 a + cO2

Husler et al. Bioresour. Bioprocess. (2016) 3:18

Page 6 of 12

pressure is sustained by CO2 produced by the bioreaction, implying that this conguration can only be applied when rCO20, because no CO2 is supplied (FinCO2 = 0).

In this case, the mass balances of O2 and CO2 are given by Eqs. 25 and 26, respectively. In contrast to the general case, there are two O2 sources: air and pure O2.

The pressureow relations remain unchanged. Looking at the system of equations, there are again six equations(three mass balances, Eqs.15, 25, and 26, and three pressureow relations, Eqs. 1618) and 6 unknowns (FinO2,pure, FoutO2, FinO2,air, FoutCO2, FinN2, FoutN2).

Similar to case 1, expressions for the pure oxygen inow FinO2,pure (Eq. 27) and the air inow FinAir (Eqs. 28 and 29) can be derived. As before, the relations are presented without substitution of the expression for partial pressures.

As in case 1, energy is required for compression of air, but the pure oxygen feed is already pressurized and does not add to the energy costs.

Derivation ofgas production rates

Next, we need to dene the gas consumption and production rates. FA can be produced from glucose (Glc) via two metabolic pathways (Roa Engel et al. 2008): (1) via the oxidative side of the citrate cycle which produces CO2 and consumes O2, and (2) via the reductive side of the citrate cycle using the anaplerotic route by carboxylation of pyruvate to oxaloacetate. The reaction stoichiometries per mole product of both pathways are given below, but the ratio at which both pathways contribute to the total FA production is not known. Therefore, it is not known whether the fermentation consumes or produces CO2. Available information on this topic is scarce, and when present, it is inconclusive. For simplicity, other reactions, such as cell growth and by-product formation, are neglected.

0.5 Glc CO2 + H2O + FA

(31)

So, it is not possible to identify the exact gas production rates for this fermentation. Still, the range of these rates can be derived from the metabolic pathways. First, we dene the mass-specic FA production rate, qP, as the sum of both pathways specic production rates. The oxidative and reductive pathways are dened as pathway 1 and 2 which run at the specic production rates qp1 and qp2, respectively. Next, the parameter b is dened as the fraction by which pathway 1 contributes to the total production rate. Therefore, the fraction by which pathway 3 contributes to qP is (1b).

Similarly, the total specic O2 and CO2 rates, qO2 and qCO2, respectively, are derived (see Fig. 2). The partial specic production rates run according to the stoichio-metric coefficients of each reaction multiplied by qp1 and qp2, respectively. Substitution of Eqs. 33 and 34 for qp1 and qp2 gives the following expressions for qO2 and qCO2 in terms of qP and b:

Finally, the specic production rates are multiplied by the microbial concentration, cX, which yields the gas production rates per m3.

This shows that O2 and CO2 rates (rO2 and rCO2, respectively) are functions of the organisms specic

FinO2,air + FinO2,pure = FoutO2 rO2

(25)

qP = qp1 + qp2

(32)

FoutCO2 = rCO2

(26)

qP1 = bqP

(33)

qP2 = (1 b)qP

(34)

FinO2,pure = rCO2

[notdef]

pO2

pCO2

pN2 pCO2

0.210.79

rO2

(27)

Finair =

FinO2,air

0.21

(28)

qO2 = 3bqP

(35)

FinO2,Air = rCO2

pN2

pCO2

0.210.79

(29)

qCO2 = (3b 1)qP.

(36)

ri = qicx

(37)

Fig. 2 Gas consumption and production rates per mole product versus pathway distribution b

Glc 3O2 + 2CO2 + 4H2O + FA

(30)

Husler et al. Bioresour. Bioprocess. (2016) 3:18

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fumaric acid production rate (qP), the chosen fraction of each pathways contribution to the total specic production rate (b value), and the microbial concentration in the fermentor. Concerning b values, it should be noted that they vary with microbial strain and fermentor condition. Measuring them is complicated because of the formation of side products and biomass, which grows as pellets or biolms for the most productive strains. From experimental overall yields of fumaric acid on glucose (Roa Engel etal. 2008), when neglecting that side products and biomass are formed, one can calculate b values in the range of 0.351. Research eorts aim to increase the yield of FA by shifting its production to the reductive side of the citrate cycle, thus moving b toward 0.

Economic evaluation ofgas supply strategies

After having dened the relations for relevant ow rates, which are related to costs, we can start the economic evaluation of the dierent gas supply strategies. The exact gas production rates are not known for FA fermentations; therefore, the three cases are compared over the contribution range of both pathways (b=01). Case 1 can be evaluated over the whole range of b values. Case 2 applies for b1/3, because the net CO2 production is negative up to this point. Case 3 applies for b1/3 for similar reasons. Furthermore, the evaluation is performed at several total pressures. The minimum pressure is taken as 1bar in order to prevent infections from the surroundings. The maximum pressure is taken as 2bar to prevent too high energy requirements for compression of air. Only cases with positive inow are considered. A negative inow of a component implicates that its inow is too high to maintain desired conditions in the bioreactor. For example, the amount of O2 in air could be too high. In this case, the feed could be altered either by removing O2 at the cost of an additional unit operation, or by increasing the amount of inert gas (i.e., N2). The second option would lead to additional gas costs.

Choice ofparameters

The values used for the parameters in the ow relations (kL,ia, ci, Hi, ptot, ri) are summarized in Table2. The gas

liquid mass transfer coefficients depend on several case-specic parameters such as geometry of vessel and stirrer, stirrer speed, temperature, bubble size, and composition of liquid phase. A comprehensive review on empirical relations for dierent reactor types to predict kL,ia was

presented by Garcia-Ochoa and Gomez (2009), and for O2 its value was shown to be in the range of 101104

s1 (Riet and Tramper 1991). For the ease of this evaluation, kL,ia is set to be constant. According to the lm theory (Cussler 2009), liquid mass transfer coefficients

of other compounds are estimated by the relationship between mass transfer coefficients and diusivities in the liquid phase.

The optimal CO2 concentration in the bulk of the liquid phase and the associated specic FA production rate are based on the study of Roa Engel et al. (2011). The dissolved CO2 concentration is calculated under the assumption of gasliquid equilibrium. This assumption is based on the results of the same study which indicated CO2 production rates close to 0. This implies that the concentration in the bulk liquid is close to the concentration at the gasliquid interface. However, this cannot be assumed for O2. In another study (Fu etal. 2010), it was shown that 3080% dissolved oxygen is benecial for FA production. Using the lower limit, CO2 is set to 30% of the equilibrium concentration between water and air at ambient conditions. The molar volume of the liquid was calculated from the density ( in kg/m3) of pure water at 308K and atmospheric pressure.

Chemical and energy prices used for the economic evaluation are also summarized in Table2. The indicated price ranges for CO2 and O2 are based on the following information and considerations. For O2, Monteiro et al. (2009) used 0.015$/kgO2 which is based on information of the company PRAXAIR. This seems to be relatively low price, because the same company stated in a presentation from 2005 a price range from 0.015 to 0.060$/kgO2 which depends on the type of process and the production scale. Accounting for ination from 2005 to 2014 gives a

kL,O2a

kL,CO2a

= DL,O2 DL,CO2

(38)

Table 2 Parameters used forFA example

Parameter Value Source

kL,O2a 6.0102 s1 (van t Riet and Tramper 1991)

CO2 6.0102 mol/m3 (Fu et al. 2010)

CCO2 1.6 mol/m3 (Roa Engel et al. 2011)

DO2 2.1109 m2/s (Cussler 2009)

DCO2 1.9109 m2/s (Cussler 2009)

qp 5.3102 kgP/(kgXh) (Roa Engel et al. 2011)

cX 50 kgX/m3 (Chang et al. 2014)

HO2 5.11109 Pa (Lide 2009)

HCO2 2.11108 Pa (Lide 2009)

Vmol 1.81105 m3/mol Calculated

~H2O 9.94102 kg/m3 (Lide 2009)

PO2 0.020.08 $/kgO2 (Sho Kobayashi and Hassel 2005)

PCO2 0.020.08 $/kgCO2 (Initiative 2012)

PGlc 0.68 $/kgGlc (United States Department of Agricul

ture 2014)

PW 0.094 $/kWh (Steelonthenet.com 2014)

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range from 0.02 to 0.08$/kgO2. For CO2, the situation is more complex. CO2 consumption comes at a certain price when it is purchased as a rened gas because capture and transportation costs have to be covered. However, one could also argue that consumption of CO2 could add additional income to a process since the nancial penalty for CO2 emission is set on CO2 emission in some countries.

In theory, a CO2-consuming process could be coupled to a CO2-emitting process. Therefore, the nancial penalty of the emitting process would be reduced and the savings can be counted as an income of the CO2-consuming process.

For this study, it was decided to purchase a rened gas. The other scenario has too many uncertainties because it depends on too many factors. The costs for CO2 capture and transportation are in the range of 0.0380.070$/kgCO2 according to a report of the National Enhanced Oil Recovery Initiative (NOERI). The range is close to the O2 price range, therefore it was decided to apply the same price range of 0.020.08 $/kg for both pressurized gases. Gas prices at the high end of this range were used to evaluate the impact of dierent top pressures.

Results ofeconomic evaluation

The resulting total costs Gtot per kg FA for b=01 under these conditions are in the range of 101103 $/kgFA

(see Fig.3) for both top pressures. For ptot=1atm, the lowest costs were calculated for cases 2 and 3 when the net CO2 production is 0 (b = 1/3). For both cases, the costs are equal at this b value, which is caused due to the fact that the CO2 outow of case 3 approaches 0 when no CO2 is produced. This reduces all other outows to 0 as well, which essentially turns this system into an o-gas recycle system with a pure O2 feed. For case 2, the costs increase linearly until b=0, and for case 3 they increase until b=1. The costs of cases 1 and 2 are the same when b=0. Case 1 reduces to case 2, because the O2 outow becomes 0 when rO2 = 0 at b=0, and this removes all other outow rates. For rO2>0, the costs of case 1 are at a minimum at b=0.19. The costs are only slightly higher in this range than for case 2. From this point on, the costs increase signicantly, and the curve has an asymptote at b=0.457, at which the costs become innitely high. This is caused by the fact that the optimal partial O2 pressure in the gas phase in the bioreactor increases as the O2 consumption rate increases, and as b approaches 0.457, the O2/N2 ratio in the outow approaches the O2/N2 ratio of the inow. This leads to an increase of all ow rates including the CO2 inow. It should be noted that most of the added CO2 is lost to the o-gas. The fact that the outow O2/N2 ratio approaches the inow ratio causes that case 1 cannot be used for b>0.457. How the b value of the asymptote of the cost curve of case 1 depends on pressure can be derived by substitution of Eqs.3537 and

the process parameters into the denominator of the rst term on the right-hand side of Eq.20, setting the resulting expression equal to 0, and solving it for b.

For ptot=2bar, the costs of case 2 are the same as for ptot=1bar, because they are independent of the top pressure (see Eqs. 23 and 24). Also the breakeven points of cases 1 and 2, and of cases 2 and 3 remain unchanged. Nonetheless, several dierences are observed for the results of cases 1 and 3. The most obvious ones are the gap in the cost curves of cases 1 and 3 between b=0.420.91 and their breakeven points at the start and end of the gap.

Furthermore, the curves of cases 1 and 3 are stretched and the costs of both cases are lower than for ptot=1atm.

The gap in both curves is present because optimal conditions in the gas phase cannot be maintained with these cases in this range because the O2/N2 ratio of the inow is too high. This is caused by the fact that the minimal O2/N2 ratio in the inow is the O2/N2 ratio of air. This leads to the problem that insufficient N2 is fed to the bio-reactor to strip sufficient CO2 from the liquid phase when aiming to maintain desired O2 pressures, which leads to

Fig. 3 Total gas supply costs of three dierent gas supply congu-rations: a ptot = 1 atm and b ptot = 2 bar. Gas prices were taken as

0.08 $/kg

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increased CO2 concentrations. On the other side, if one increases the N2 inow to maintain the desired CO2 pressure, there will be an overload of O2 supply. The only way to overcome this problem is to lower the O2/N2 ratio in the inow, for example by adding additional N2a conguration that is not considered here.

The breakeven points of cases 1 and 3 at the end and start of the gap occur because the ows of both cases are identical at these points. For case 1, the pure CO2 feed becomes 0, and for case 3, no pure O2 is added to the gas feed, which means that a pure air feed suffices to maintain the desired partial gas pressures within the vessel.

The stretching of the cost curve of case 1 is related to the fact that a higher top pressure increases the partial O2 pressure, and therefore higher transfer rates from gas to liquid phase can be achieved. Therefore, case 1 can be used up to b=1, when rO2 is at its maximal value, except for the range of the gap, and the limitation for case 1 at 1 bar is removed. Increasing the pressure even further (results not shown here) widens the gap. The end of the gap moves toward higher b values until the curves on the right-hand side of the gap are completely removed, and the start of the gap approaches b=1/3.

The total costs of both cases are lowered when ptot is

increased. For case 1, the costs become even slightly lower than those for case 2, and also loser than those of case 3 until their rst breakeven point. The costs are higher than for case 3 after the second breakeven point. The dierence between case 1 and the other two increases on the left-hand side of the gap when the pressure is elevated even further, and the dierence between cases 1 and 3 decreases on the right-hand side. For case 3, the costs decrease from b=1/3 to the rst breakeven point in case 1, in comparison to increasing from b=1/3 to 1. The overall lower costs of both cases is due to the fact that the amounts of pure gases which are lost in the o-gas decrease and therefore also the pure gas feeds decrease. For case 2, the pure O2 costs also decrease, because more O2 from air can be used.

Compression vs. gas costs

For case 2, compression costs are absent because no air is used. For cases 1 and 3 at ptot = 1 bar, the costs are completely governed by the pure gas prices in the present model, because in- and outside pressures are equal and friction and hydraulic pressure are neglected. The evaluation of ptot to 2bar shows an increasing trend for compression costs from b=0 to 1 for case 1 and 3, because the air inow increases. The compression costs become dominant near the breakeven points of cases 1 and 3, and they are the only costs at the breakeven points (Fig.4). Still, the general trend of the curves is governed by the gas costs.

Cost scenarios

As discussed before, the costs of gaseous substrates are variable and strongly depend on the production method, location, and production scale. Four cost scenarios were evaluated at ptot=1.5bar to estimate the impact of different O2 and CO2 prices on the gas costs per kg FA (see

Fig.5). The general trend of the curves is unaected by variations of O2 and CO2 prices except for cost scenario

B. Here, the costs for case 2 increase for large b, instead of decreasing. Furthermore, this case is the only one in which case 1 leads to lower costs than the o-gas recycle and case 3 for b>0. Still, the costs are higher than those in case 3 for high b values. Barely any dierences are seen between cases 1 and 2 for cost scenarios A and C, but the costs of case 3 are lower than those for case 1 for b=1/31. However, the dierences in costs of the three cases are less than 0.02$/kgFA in all scenarios, except for large b values.

Discussion

The presented methodology has not been validated by experiments. One can consider the situation in which microbial strains would be engineered in such a way that the dierent b values would be obtained at fermentation temperature, pressure, and composition such as proposed here. However, that would not make it possible to prove experimentally that full-scale fermentations show an economic optimum that agrees to our calculations.

Economic evaluation

Looking only at absolute costs which are directly related to gas supply, the dierences between the three cases are very moderate, especially for increased top pressures. Depending on the b value, either case 2 or case 3 should be used for low pressures. Only if O2 purchase costs are relatively low, such as in Fig.5b, there are situations that case 1 is favorable. However, case 1 has one

Fig. 4 Ratio of compression and total costs at ptot = 2 bar. Gas prices

were taken as 0.08 $/kg

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Fig. 5 Total costs for four dierent scenarios of high gas price (0.08 $/kg) and low gas price (0.02 $/kg) at p = 1.5 bar. a O2 high, CO2 high, b O2

high, CO2 low, c O2 low, CO2 low, d O2 low, CO2 high

major advantage over the other two cases, namely, it can be used for CO2-consuming and CO2-producing bio-reactions. The other two cases can only be used when either rCO20 (case 3) or rCO20 (case 2). Furthermore, the results indicate that a metabolism that operates the fermentation near b 1/3 can lead to the lowest costs in terms of gas supply. Energy costs for compression become relevant for elevated pressures. For b<1/3, compression costs are small compared to gas costs. However, they can take up to 100% of the total costs. This is the case when air does not need to be enriched with O2 and/

or CO2. Still, the general trend of the costs curves is governed by the gas costs. Increasing ptot lowers gas supply costs, but from a certain point on, too high pressures limit the application of cases 1 and 3, because desired conditions in the vessel cannot be maintained.

However, other costs than gas costs need to be considered to dene metabolic engineering targets and for optimal bioreactor design. When including the glucose costs, the lowest costs are achieved when all FA is produced by the reductive part of the citrate cycle (b=0), which means that only CO2 is consumed. This is caused by the fact that the costs for glucose per kg FA are one order of magnitude higher than gas supply costs, and

therefore the costs are dominated by the glucose costs. Even though other costs, in particular feedstock costs, are dominant, choosing the best gas supply conguration can still save about 0.01$/kg product, translating into a million dollars per year for a product that might be produced at a scale of 100,000 tonnes per year. The questions that remain are to which extent FA can be produced by the reductive pathway, and to which extent the oxidative pathway needs to contribute to provide ATP.

Methodology

This study only considered fermentations at steady state. However, many fermentations are operated as batch, or fed-batch, leading to changing production rates in time. This raises the question whether the methodology still can be used for these modes of operation. If the time course of the production rates is known, and if at each point in time an optimum steady state can be achieved with respect to the gas supply rates, the costs for different cases can be plotted over the time of the (fed-) batch and the methodology can still be used. The optimization of gas supply rates needs to be included when more detailed models are used for process analysis and optimization.

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Furthermore, during the cost calculations the eect of hydrostatic pressure was neglected, which is valid for small-scale bioreactors. For large-scale bioreactors, the hydrostatic pressure can lead to substantial pressure gradients between top and sparger levels, roughly 1bar per 10m, which leads to a higher power consumption. Additionally, the pressure drop along the bioreactor height implies that it will become more difficult to maintain the desired conditions in the liquid phase, because partial pressure in the gas phase will change from bottom to top.

Large-scale bioreactors also change the model to describe mass transfer between liquid and gas phases. In the current analysis, the bioreactor was considered to have a single compartment and both phases were assumed to be well mixed. This is valid for lab-scale bioreactors with a single impeller. However, the situation becomes more complex for larger vessels. According to van t Riet and Tramper (1991), the gas phase of large-scale vessels (typically three times larger height than width) is best modeled using compartmentalization. Modeling of the hydrostatic pressure and the question of how to achieve optimal conditions in large-scale vessels is not addressed here, but it still needs to be considered during actual fermentor design.

Other gases/fermentation

It has been mentioned that DSM uses case 3 for commercial succinic acid fermentation (Table 1) to be able to keep a relatively high CO2 concentration in the biore-actor(Jansen and van Gulik 2014). Details are not available. For other fermentations such as those mentioned in Table 1, the results may be very dierent, especially depending on the gas purchase prices. However, the methodology shown in this paper may be used in all cases.

Conclusions

The aim of this study was to compare dierent gas supply strategies for fermentations in which more than one substrate is a gaseous compound. A methodology to derive dierent gas supply strategies and subsequently calculate the size of each gas ow was presented. The methodology was applied to FA fermentation with R. delemar which needs O2 and CO2. Three dierent gas supply strategies were identied: (1) air supplemented with CO2 (vented o-gas), (2) o-gas recycled with pure CO2 and O2 feeds, and (3) air supplemented with O2. The costs directly related to gas supply are in the same order of magnitude for the three cases, but strongly depend on the O2 and

CO2 prices and consumption rates, which leads to the lowest costs. Compression costs only become relevant for large b values, and may exceed the gas purchase costs. However, the fermentation costs are dictated by the yield

on glucose which is highest when all FA is produced via the anaplerotic route. The results clearly show that an o-gas recycle strategy does not necessarily lead to lower overall production costs, and for each fermentation it must be evaluated which strategy is most benecial.

Nomenclature

a gasliquid interfacial area per bioreactor liquid volume [m2/m3]

c concentration in liquid phase [mol/m3]

Cp

specic heat at constant pressure [J/(kgK)]

CV

specic heat at constant volume [J/(kgK)]

Di

diusivity of i in liquid phase [m2/s]

F ow rate per fermentor liquid volume [mol/

(m3s)]

Gi

costs per kilogram product [$/kgP]

H Henrys law constant [Pa]kL mass transfer coefficient in liquid phase [m/s]

M molar mass [kg/mol]

P price [$/kgi] or [$/J]

p pressure [Pa]

q specic production rate [moli/(kgX])]

r production rate per bioreactor liquid volume

[mol/(m3s)]

T mass transfer rate per bioreactor liquid volume [mol/(m3s)]

Vmol molar volume [m3/mol]

W work [J/(m3s)]x mole fraction in liquid phase [moli/moltot]

y

mole fraction in gas phase [moli/moltot] density [kg/m3]

ratio of specic heats at constant volume and at constant pressure []

Subscripts

i, j for compounds i and j m for amounts in massP for producttot

for all components together W for workX for cell mass

Superscripts

out at outletin at inletmax maximum* at G/L interface

Husler et al. Bioresour. Bioprocess. (2016) 3:18

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Abbreviations

CAPEX: capital expenditures; FA: fumaric acid; OPEX: operation expenditures; OTR: oxygen transfer rate.

Authors contributions

EH conceived of this study and carried out the computations. AS participated in the study design and coordination and helped to draft the manuscript.

LW participated in the coordination and helped to draft the manuscript. All authors read and approved the nal manuscript.

Acknowledgements

This work was carried out within the BE-Basic R&D Program, which was granted an FES subsidy from the Dutch Ministry of Economic aairs, agriculture and innovation (EL&I). Henk Noorman is acknowledged for critically reading the manuscript.

Competing interests

The authors declare that they have no competing interests.

Received: 21 December 2015 Accepted: 21 March 2016

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