ARTICLE pubs.acs.org/est
Advanced Control for Photoautotrophic Growth and CO2-Utilization Efficiency Using a Membrane Carbonation Photobioreactor (MCPBR) Hyun Woo Kim, Andrew K. Marcus,* Jeong Hoon Shin, and Bruce E. Rittmann Swette Center for Environmental Biotechnology, The Biodesign Institute at Arizona State University, P.O. Box 875701, Tempe, Arizona 85287-5701, United States
bS Supporting Information ABSTRACT: A membrane carbonation (MC) module uses bubbleless gas-transfer membranes to supply inorganic carbon (Ci) for photoautotrophic cyanobacterial growth in a photobioreactor (PBR); this creates the novel MCPBR system, which allows precise control of the CO2-delivery rate and minimal loss of CO2 to the atmosphere. Experiments controlled the supply rate of Ci to the main PBR by regulating the recirculation rate (QR) between the module of MC chamber and the main PBR. The experiments evaluated how QR controls the CO2 mass transport in MC chamber and how it connects with the biomass production rate, Ci concentration, pH in the PBR, and CO2-utilization efficiency. The biomass production rate and Ci concentration increased in response to the Ci supply rate (controlled by QR), but not in linear proportion. The biomass production rate increased less than Ci due to increased light limitation. Except for the highest QR, when the higher Ci concentration caused the pH to decrease, CO2 loss to gas ventilation was negligible. The results demonstrate that this MCPBR offers independent control over the growth of photoautotrophic biomass, pH control, and minimal loss of CO2 to the atmosphere.
’ INTRODUCTION Carbon dioxide (CO2) is the major greenhouse gas contributing to global climate change; thus, efforts to reduce CO2 discharge are needed to minimize and ultimately reverse climate change.1 Biofuel production from photoautotrophic biomass, a biomass-derived product, or both is a promising energy solution, since CO2 fixation makes the biofuels carbon neutral.2 Among phototrophic microorganisms, the cyanobacterium Synechocystis sp. strain PCC6803 is a promising candidate, as it can achieve a high biomass yield and is robust for a wide range of temperature, salinity, and pH conditions.38 With PCC6803, biofuel production can target whole cells or a biomass-derived product, because genetically modified strains of PCC6803 can excrete energy-rich chemicals like fatty acids.9 Maintaining high productivity by PCC6803 in a photobioreactor (PBR) requires matching the nutrient supply rates with the rate of biomass synthesis.10 Past research, focusing on the natural environment, has emphasized the effects of light, nitrogen, and phosphorus for preventing algal blooms. A key phenomenon that must be understood is the rate at which the cyanobacterium acquires nutrients, so that its growth can be precisely controlled during photosynthesis. Among the nutrients, inorganic carbon (Ci) presents the largest demand for photoautotrophic growth, since carbon (C) constitutes approximately 50% of biomass dry weight (DW).11 Particularly in large-scale PBR applications, the Ci supply rate is massive and must be accomplished efficiently. CO2-gas aeration is the normal approach for supplying Ci to the liquid phase, where it partitions among aqueous CO2 r 2011 American Chemical Society
(i.e., CO2(aq), HCO3, and CO32) according to the pH.12 Thus, the pH and the total Ci concentration can become significant limiting factors for photoautotrophic growth in a PBR. Because PCC6803 can take up Ci only from CO2(aq) and HCO3,13,14 Ci speciation in the PBR affects how Ci is made available to PCC6803 and how rate limitation by Ci occurs. Experiments show that the optimal pH for PCC6803 is between pH 7.5 and 9.0;15 thus, PCC6803, in general, prefers slightly alkaline pH, as do other cyanobacteria,16 although the kinetics of PCC6803 under pH limitation needs better quantification. With Ci-limiting conditions, in which other nutrients were provided in excess, recent research demonstrated that PCC6803 has a Monod half-maximum-rate concentration for Ci of KS = 0.5 g C/m3 (or 0.5 mg C/L).17 Often, the CO2-delivery rate controls the pH, total Ci, and the Ci speciation inside PBRs. A challenge, therefore, is finding an efficient CO2-delivery method to control the growth of PCC6803 in a scalable photobioreactor for producing a range of renewable bioproducts.1822 The same principles apply to the wide range of microbial phototrophs besides PCC6803. Bubbleless gas-transfer membranes are widely used in environmental engineering and food industries.2325 One key environmental engineering example is the membrane biofilm reactor (MBfR), which utilizes hollow-fiber membranes (HFM) to Received: December 17, 2010 Accepted: May 4, 2011 Revised: April 25, 2011 Published: May 10, 2011 5032
dx.doi.org/10.1021/es104235v | Environ. Sci. Technol. 2011, 45, 5032–5038
Environmental Science & Technology
ARTICLE
Figure 1. Schematic of a membrane carbonation photobioreactor (MCPBR): (a) designation of its flows, concentrations, and dimension; and (b) longitudinal cross-section of a hollow fiber.
deliver a gaseous substrate directly to a biofilm attached to the surface of the membranes’ outer wall. The MBfR technology has been used to deliver hydrogen or oxygen gas to either reduce oxidized contaminants or oxidize reduced contaminants.2628 HFMs are an effective way to deliver gaseous substrates because their high specific surface area maximizes the diffusion of target substance.2931 Because the gas-transfer mechanism is diffusion, the rate of gas transfer can be controlled by adjusting the partial pressure inside the fiber.32,33 In particular for PBRs, using membrane delivery by diffusion should minimize any wasting of CO2 to the atmosphere by off-gassing, which can be significant with aeration.34,35 For practical HFM applications, the input CO2 source may be the atmosphere or combustion gases, and they may need to be pretreated to remove aerosols that could foul the membrane. Thus, HFMs have been used to supply CO2 for cyanobacteria and algae-based nutrient removal and biomass production,3641 and they should be able to achieve efficient and controlled delivery of CO2 to suspended PCC6803 biomass in either closed or open PBR system. Here, we evaluate a membrane carbonation photobioreactor (MCPBR), which uses HFMs pressurized with pure CO2 to deliver Ci to a PBR growing PCC6803. We employed HFMs manufactured with a dense polyurethane inner layer as an example of a bubbleless gas-transfer membrane that ensures that CO2 transfer occurs by diffusion. We tested a MCPBR system consisting of two compartments: a main PBR and a membrane carbonation (MC) module. For controlling the CO2 transfer-rate into the main PBR, we placed the MC module within the internal recycling system. The MC module receives Ci depleted recycling liquid from the main PBR. Within the module, the CO2 partialpressure difference between the inside and the outside of each membrane drives the diffusion of gaseous CO2 (i.e., CO2(g)) into the recycling liquid to elevate the Ci concentration. The rate of CO2 delivery by the membrane module depends on the surface area of the HFMs and on the hydrodynamic conditions surrounding the membrane (the Reynolds number). For the MC module, the overall Ci supply rate is ultimately determined by the recycling rate of carbonated liquid containing an elevated Ci concentration and the CO2 concentration inside the main PBR (“the demand”).
Inside the PBR, the Ci concentration depends on a balance of the rate of CO2 and HCO3 utilization by PCC6803 and the Ci supply rate from the MC. Proper control of the Ci delivery rate from the module should enable efficient transfer of CO2 for growing PCC6803 biomass in the main PBR, controlling the pH, and minimizing CO2 off-gassing. This study evaluates the concept of the MCPBR through continuous operation of an MCPBR with a fixed surface area of HFMs. To build the MCPBR, we integrated a benchtop PBR with a small module of hollow-fiber membranes, similar to that used for a bench-scale MBfR. We evaluated our ability to control the delivery of CO2 via the hollow fibers and, consequently, the growth performance of PCC6803 and the CO2-utilization efficiency based on Ci delivery to the MCPBR.
’ MATERIALS AND METHODS Experimental Setup of the MCPBR. Figure 1a is a schematic of the MCPBR used in this study, and Figure 1b shows a longitudinal cross-section of a hollow fiber membrane installed in the module of MC chamber. Physical characteristics of MCPBR are in Table 1. The MCPBR consisted of a tubular main reactor made of glass (KIMAX, Germany), a MC chamber, a magnetic stirrer with a spin bar (300 rpm), two peristaltic pumps for influent/effluent and recirculation, two light panels for irradiation, connection tubing including sampling ports, and a gas (O2) exchange membrane filter to prevent pressure buildup. We modified a laboratory-scale MBfR reactor28,32,42 to be the MC. The glass tube of MC contained a main bundle of three-layer composite HFMs (model MHF 200TL, Mitsubishi Rayon), for which nonporous thin polyurethane membrane is sandwiched between two porous polyethylene layers. We chose composite HMFs with dense polyurethane inner layer as our means for bubbleless CO2 delivery by diffusion. The MC fibers were connected to a CO2-supply tank with Norprene tubing (Masterflex, USA), plastic barbed fittings, and gastight rubber seals in both ends to guarantee a gastight condition. The CO2 pressure was constantly controlled by two regulators (3471-A, Matheson Tri-Gas Inc.; Victor HPT100-80-20-BV, Thermadyne Inc.). 5033
dx.doi.org/10.1021/es104235v |Environ. Sci. Technol. 2011, 45, 5032–5038
Environmental Science & Technology
ARTICLE
Table 1. Physical Characteristics of the MCPBR item
unit
value
MC number of hollow fibers
25
membrane surface area, AM
cm2 (104 m2)
44
specific surface area, a
m1
14,285
membrane mass transport
g C/m2/atm/d
2,880 (240)
(mol/m2/atm/d) working volume of MC, VMC
103 m3 (L)
0.008
recirculation flow rate of MC, QR
103 m3/d (or L/d)
24, 50, or 73
working volume of PBR, V
103 m3 (L)
5.5
height and diameter
102 m (cm)
31 and 18
influent and effluent flow
103 m3/d (or L/d)
1.1
rpm
300
PBR
rate of PBR, QI and QE mixing rate of PBR
Based on our previous experience with MBfRs,43 fouling by precipitation, such as CaCO3, can be a problem with a high pH, e.g., > 8. Because CO2 is an acid and is used to lower pH for precipitate control, the likelihood of CaCO3 formation on the membrane was not high in our application. Consistent with this analysis, we observed no fouling during the 40-day operation of our MCPBR. Two light panels with white-fluorescent lamps (F15T8-RSCW, General Electric) were placed on both sides of the PBR to supply photosynthetically active radiation (PAR) with a constant illumination level of 44 W/m2 each to the exterior PBR surface. A sampling port was installed in the effluent tubing line. The MC was exposed to room light, which had an intensity of approximately 3 W/m2 as PAR. The MCPBR had a continuous influent and effluent flow rate that was independent of the internal recirculation rate. Inoculum and Culture Media. We inoculated the MCPBR with PCC6803 taken from a mother culture grown in a 10-L glass reservoir bottle (KIMAX, Kimble Chase) aerated with filtered air (2 Lair/Lliquid/min). We continuously illuminated the bottle using fluorescent lamps (20 W/m2 on the exterior) in the photoincubator chamber (TC30, Conviron Inc.) maintained at 30 °C. We supplied nonlimiting inorganic nitrogen (Ni), phosphorus (Pi), and other nutrients using a modified BG-11 medium11 that contained 5 times the Pi concentration of the original recipe.44 To ensure that the MC was responsible for all delivery of inorganic C, we removed all sources of Ci for the medium. The medium’s total alkalinity was 1.8 meq/L (= 90 g/m3 as CaCO3), and its pH was 8.0 ( 0.2. For all the medium solutions, we used ultrapure deionized water (18.2 MΩ 3 cm) produced by the Purelab ultra (ELGA lab water, USA) and autoclaved them before use. Startup and Operating Procedures of the MCPBR. We inoculated the MCPBR with 5.5 L of inoculum with a 730-nm optical density (OD) of 1.6 and then supplied pure CO2 gas to the MC at a pressure of 15 psi (= 103 kPa =1 atm) and began liquid recirculation at 24 L/d. We operated the MCPBR with continuous flow and a hydraulic retention time (HRT) of 5 d for all experiments; the corresponding flow rate of BG-11 medium was 1.1 L/d. At least two volumes of HRT turnover were allowed before we changed the liquid recirculation rate to 50 and then 73 L/d.
Sampling and Analytical Methods. We monitored the operating performance of the MCPBR by analyzing samples taken from the effluent according to a set sampling plan. For the continuous experiments, we took one sample per day. All physical, chemical, and biological analyses were determined in duplicate and expressed as average values after appropriate pretreatment and storage at 4 °C. To represent global steady state at each flow rate, we averaged the last three days of data for all the parameters. After filtering samples through a 0.2-μm membrane filter (GD/X, Whatmann, USA), we analyzed the filtrate for anions (NO3, SO42, and PO43) and cations (Naþ, Kþ, Ca2þ, Mg2þ, and NH4þ) using an ion chromatograph (ICS-3000, Dionex, USA) equipped with an IonPac AS18 (Dionex, USA) anion exchange column or a CS18 (Dionex, USA) cation exchange column, respectively. We measured OD, pH, total Ci, and the concentrations of all carbonate species (i.e., CO2(aq), HCO3, and CO32) according to the methods of our previous study.11,45 We calculated total alkalinity of modified BG-11 using the analytical definition of alkalinity,12 which includes HCO3, CO32-, HPO42, Hþ, and OH, and we converted the equivalents to mg as CaCO3. Mass Balances for Ci and Biomass in MCPBR. To analyze the result of all experiments, we developed steady-state mass balances for Ci and biomass in the MCPBR according to eqs 14, which are based on the volumes and flows in Figure 1. Equation 1 describes the steady-state mass balance for Ci in an MCPBR: Ci supplied from the HFMs is balanced by the Ciuptake reaction for biomass synthesis and Ci loss to the effluent and loss by ventilation
J Ci, T 3 AM ¼ λ 3 r b 3 V þ Q E 3 Ci, T þ Q G 3 Ci, G
ð1Þ
where JCi,T is the total Ci flux transferred from the membrane into the liquid (g C/m2/d), AM is the membrane surface area (0.0044 m2), λ is the stoichiometric uptake ratio of Ci to biomass as dry weight (0.51 g C/g DW), rb is the volumetric net biomass production rate as dry weight (g DW/m3/d), V is the volume of the reactor (0.0055 m3), QE is the effluent flow rate (= QI) (m3/d), QG is the ventilation gas flow rate (m3/d), Ci,G is the total concentration of Ci species in the ventilating gas (g C/m3), and Ci,T is the total concentration of Ci species (g C/m3). An influent mass flow is not included, because the medium contained no inorganic C. The steady-state mass balance for PCC6803 biomass in a completely stirred tank reactor (CSTR) is described by eq 2 Q E 3 X R ¼ rb 3 V
ð2Þ
where XR is the biomass concentration in the MCPBR and its effluent (g DW/m3). The gradient of CO2 between inside the membrane and the liquid in the MC promotes diffusion by Fick’s law J Ci, T ¼ K 3 ðPM PL Þ
ð3Þ
where K is the CO2 mass-transport coefficient for the Mitsubishi HFM 200 L membranes (g C/m2/atm/d),46 PM is the CO2(g) in the HFM module inside (atm), and PL is the CO2(aq) in equilibrium with Ci in the liquid (atm). We developed a separate mass balance for steady-state Ci transfer from the membrane to the PBR using two-film theory of gas transfer to a liquid.47 We assumed that the difference of partial pressure between CO2(g) inside the membrane and CO2(aq) in the liquid drives the mass transport of CO2 across the membrane wall. 5034
dx.doi.org/10.1021/es104235v |Environ. Sci. Technol. 2011, 45, 5032–5038
Environmental Science & Technology
ARTICLE
Figure 3. Biomass production rate, CO2 flux (JCi,T), and pH in MCPBR according to QR.
Figure 2. Dynamics of biomass as DW (lower), pH (lower), and Ci species (upper) in the MCPBR as QR was increased from 24 to 73 L/d. Fixed were the CO2 pressure of 1 atm, HRT of 1 d, AM of 44 cm2, and light irradiance (LI) of 44 W/m2 as PAR.
The liquid circulating through the MC gains the maximum amount of Ci possible for a given pH, and the transfer rate from the HFM is not limiting. Because recirculation transfers newly supplied CO2(aq) to the main PBR, the transfer rate is the same as the rate at which CO2(aq) (= H2CO3*) diffuses through membrane, as shown in eq 4 ΔCi, T 3 Q R ¼ K 3 AM 3 ðPM PL Þ ¼ K 3 AM 3 ðPM R0 3 Ci, T 3 K H, pc Þ
ð4Þ
where QR is the recirculation flow rate passing through MC (m3/ d), ΔCi,T is the difference between influent and effluent Ci,T of MC, KH,pc is the Henry’s Law constant (0.0294 m3 3 atm/mol or 0.00245 m3 3 atm/g C), and R0 is the fractional ionization constant 12 for CO2(aq) depending on liquid pH, as shown in Equation S1 in Supporting Information. Equation 1 equals eq 4 at global steady-state, because CO2(g) that diffuses through the membrane is balanced by Ci invested for biomass synthesis and lost in the effluent and ventilation, keeping the Ci,T concentration stable. The uptake of CO2(aq) and HCO3 for synthesis is related to the rate of biomass synthesis by stoichiometry (i.e., in eq 1), which is derived in Supporting Information (Equations S4 and S5). We calculated the CO2utilization efficiency by calculating the terms in eq 1 as shown in Supporting Information.
’ RESULTS AND DISCUSSION We operated the MCPBR in a continuous mode for harvesting biomass and recharging with fresh medium. Based on daily samples,
Figure 2 shows the concentrations of biomass and soluble components for the three recirculation flow rates: QR = 24, 50, and 73 L/d. Increasing QR from 24 to 73 L/d led to higher biomass concentrations: from 420 to 528 g DW/m3. Each QR achieved a steady biomass concentration within about 10 days, and this gave a common specific growth rate (μ = Q/V) of 0.2 d1, assuming that all the biomass was suspended. Thus, increasing QR provided a higher Ci-delivery rate that allowed more biomass accumulation. Figure 2 also presents the Ci, CO2(aq), HCO3, CO32, and pH values. For days 0 to 16, when QR was 24 L/d, total Ci averaged 29 g C/m3, except for a transient increase to 49 g C/m3 on day 9. The average pH of 9.1 made HCO3 the dominant Ci species at 27 g C/m3; CO32 was only 2 g C/m3, and CO2(aq) was negligible. From day 16, we approximately doubled QR (to 50 L/d), and this led to an increase of average Ci to ∼59 g C/m3. Since the average pH declined to 7.6, HCO3 became ∼95% of Ci, with CO2(aq) approximately 5% and CO32 negligible. When we further increased the QR to 73 L/d, the steady-state Ci reached as high as 117 g C/m3, and the average Ci was 98 g C/m3, which is 1.7-fold higher than for 50 L/d. With the pH declining to 6.8, the molar ratio between CO2(aq) and HCO3 increased to 3:7. Our previous work revealed that KS for Ci, including CO2(aq) and HCO3 (2% and 98% for those conditions), is about 0.5 g C/m3 for PCC6803 at pH 8;17 therefore, PCC6803 in the MCPBR should have experienced no Ci limitation. In addition, Figure S1 in Supporting Information shows that none of NO3, SO42, and PO43 was present at a rate-limiting concentration. The clear correlation of Ci and pH to QR (Figure 2) demonstrates that the MCPBR achieved the goal of managing the rate of photosynthesis by controlling the Ci-delivery rate. The relationship was not linear, as Ci proportionally increased more than did QR: for the QR ratios of 1.0:2.1:3.0, the Ci ratios at steady-state were 1.0:2.4:4.6. Figure 3 compares the CO2 flux, the biomass production rate, and the pH at each operating condition. The flux was computed using the effluent flow rate, the measured Ci concentration, and the stoichiometric utilization of Ci according to eqs 1 and 2. The biomass production rate was computed from eq 2. Increasing QR from 24 to 73 L/d improved the total delivery of CO2(g) to the liquid from 61 to 97 g C/m2/d, and that resulted in increases of the biomass production rate: from 84 g DW/m3 3 d with QR = 24 L/d to 106 g DW/m3 3 d for QR = 73 L/d. This supports our premise that the biomass production rate can be managed by 5035
dx.doi.org/10.1021/es104235v |Environ. Sci. Technol. 2011, 45, 5032–5038
Environmental Science & Technology
ARTICLE
Table 2. Membrane Mass Transport, CO2-Transfer Efficiency, and CO2-Utilization Efficiency Based on Mass Balance during Continuous Operation of the MCPBR item
unit
value
independent variable 103 m3/d (or L/d)
QR
24
50
73
fixed operating conditions QE
103 m3/d (or L/d)
1.1
1.1
1.1
V
103 m3 (L)
5.5
5.5
5.5
AM
104 m2 (cm2)
44
44
44
PM KH,pc
atm m3 3 atm/g C (m3 3 atm/mol)
1.02 0.00245 (0.0294)
1.02 0.00245 (0.0294)
1.02 0.00245 (0.0294)
60
124
180
g C/g DW
0.51
0.51
0.51
Ci
g C/m3
29.3
59.0
97.6
Ci,T
mol C/m3
2.4
4.9
8.1
XE
g DW/m3
420
480
528
λ XE
g C/m3 mol C/m3
215 18
246 20
270 23
9.1
7.6
6.8
Rea stoichiometry λ experimental measures
pH estimated variables K
g C/m2/atm/d
60
75
95
JCi,T
g C/m2/d
61
77
97
JCi,T AM/V
g C/m3/d
R0
49
61
78
0.0014
0.0454
0.2311
CO2 captured and lost biomass (λ 3 rb 3 V) effluent (QE 3 Ci,T)
g C/d (%) g C/d (%)
0.24 (88) 0.03 (12)
0.27 (80) 0.06 (19)
0.30 (69) 0.11 (25)
ventilation (QG 3 Ci,G)
g C/d (%)
0.00 (0)
0.00 (1)
0.02 (6)
Reynolds number (Re) for the flow in the MC = QRDH/νA. We assumed that the kinematic viscosity (ν) is the same as for water (0.8 106 m2/s) at 30 °C, and the hydraulic diameter (DH) and cross-sectional area of the MC were 0.006 m and 2.8 105 m2, respectively. a
adjusting QR when other conditions are held constant (i.e., CO2 pressure = 1 atm, AM = 44.0 cm2, μ = 0.2 d1, and LI = 44 W/m2 as PAR for this set of experiments). In the MCPBR, the high pH at QR = 24 L/d resulted from relatively insufficient CO2 delivery from the MC compared to photoautotrophic consumption of HCO3 and CO2(aq). As QR increased to 50 and 73 L/d, however, total Ci-delivery improved from 61 g C/m2/d (QR = 24 L/d) to 77 and 97 g C/m2/d, respectively, resulting in greater steady-state Ci and a pH decrease inside the MCPBR (Figure 3). Thus, proper adjustment of QR (from 24 to 50 L/d) provided a superior pH, since PCC6803 prefers slightly alkaline pH.7 The bottom part of Table 2 shows estimated values for the CO2(aq) fractional ionization constant (R0), mass-transfer flux, volumetric mass-transfer rate, K-estimates, and CO2-utilization efficiency for each experimental condition; these values were computed using mass balance eqs 1 4 and the operating and measured values given in the upper parts of the table. The estimated values in Table 2 reveal significant and related trends. First, K increased from 60 to 95 g C/m2/atm/d as QR increased, but not in linear proportion to QR. The literature indicates that increasing the water velocity past the fibers
promotes CO2 mass transport in HFMs due to improved liquid-side mass-transport.38,40 The increase in liquid-side transport normally is proportional to Reynolds number (Re).46,48 In our experiment, the Re in MC chamber increased from 60 to 180 (Table 2). This increase in mass-transport kinetics in the MC is an extra benefit from increasing QR. Due to the increased advection of Ci and faster mass transport, higher Re (and QR) improved the volumetric Ci delivery rate to the PBR (up to ∼78 g C/m3/d). Second, the higher Ci delivery rate allowed the Ci concentration in the PBR to increase, lowered the pH, and caused R0 to become larger. This underscores that adjusting QR is a means to maintain adequate Ci and pH. The relationship between Ci and pH depends on the alkalinity in the medium, 90 g/m3 as CaCO3 in these experiments. With alkalinity fixed in the influent, the MC allowed us control over pH by delivering different amounts of Ci. A different total alkalinity would change the relationship among JCi,T, Ci, and pH. Third, the availability of light irradiance, the sole energy source for photosynthetic activity, eventually controlled the degree to which the biomass concentration could be increased by increasing QR.11 For example, increasing QR 1.5-fold (50 to 73 L/d) 5036
dx.doi.org/10.1021/es104235v |Environ. Sci. Technol. 2011, 45, 5032–5038
Environmental Science & Technology gave an increase in the biomass concentration of only 1.1-fold, while Ci,T increased 1.7-fold. Since nutrient limitation was not playing a role in these experiments, light limitation mainly controlled the growth kinetics. With the biomass synthesis rate increasing proportionally less than the increase in Ci delivery rate, Ci increased (from ∼29 to ∼98 g C/m3), pH decreased (from ∼9.1 to ∼6.8), and R0 increased (from ∼0.001 to ∼0.23). We had a fixed light irradiance in our experiments; increasing the light irradiance in proportion to JCi,T may counteract the three effects. Finally, the biomass captured λ 3 rb 3 V = 0.24 g C/d (88%), 0.27 g C/d (80%), and 0.30 g C/d (69%) of the CO2 supplied by the fibers at QR = 24, 50, and 73 L/d, respectively. Thus, the CO2utilization efficiency had an inverse relationship with QR. For low QR values, the loss of carbon to the ventilation was negligible (
