CO 2 Mass Transfer in a Novel Photobioreactor
A thesis presented to
the faculty of the Russ College of Engineering and Technology of Ohio University
In partial fulfillment
of the requirements for the degree
Master of Science
Adam Mielnicki
August 2011
© 2011 Adam Mielnicki. All Rights Reserved.
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This thesis titled
CO 2 Mass Transfer in a Novel Photobioreactor
by
ADAM MIELNICKI
has been approved for the Department of Chemical and Biomolecular Engineering
and the Russ College of Engineering and Technology by
David J. Bayless
Loehr Professor of Mechanical Engineering
Dennis Irwin
Dean, Russ College of Engineering and Technology 3
Abstract
MIELNICKI, ADAM, M.S., August 2011, Chemical Engineering
CO 2 Mass Transfer in a Novel Photobioreactor
Director of Thesis: David J. Bayless
A novel carbon capture and storage (CCS) technology at the center of this investigation involves the biosequestration of CO 2 via cyanobacterial photosynthetic processes. A simulated flue gas stream introduces CO 2 into a temperature controlled photobioreactor where cyanobacteria are nourished with a flowing growth solution. Before the microorganism can fix carbon, CO 2 has to dissolve in the liquid growth solution. The absorption of CO 2 presents a potential limiting step in cyanobacterial growth and is therefore in need of quantification. In this study, the effects of growth solution flow rate on the liquid side mass transfer coefficient (k L) were observed and a model was selected for k L prediction. Both the model and experimental data showed that k L tends to increase with flow rate. Gaseous CO 2 concentration was manipulated as well and was shown to affect overall mass transfer but not k L. Higher gaseous
CO 2 concentration increased the CO 2 solubility limit, and therefore increased the rate of CO 2 absorption.
Approved: ______
David J. Bayless
Loehr Professor of Mechanical Engineering 4
Acknowledgments
I would like to sincerely thank my advisor, Dr. David J. Bayless, whose support and guidance has been invaluable in completing this thesis. His extensive engineering knowledge and unique insight on the best course of action have allowed me to overcome research obstacles on numerous occasions. Similarly, this work would not be possible without the help of
OCRC faculty and undergraduate members. In particular, I greatly appreciate Jesus Pagan and all his efforts in acquiring the AdeptOne robot. In addition, I would also like to thank the members of my thesis committee, Dr. Michael E. Prudich, Dr. Kevin Crist, and Dr. Morgan L. Vis. for contributing their time and effort towards helping me finish this work. I also want to thank all my friends and colleagues who were always there for me, throughout the good times as well as the bad. Finally, I want to thank my parents, Stanisław and Irena Mielnicki for their love, support, and most of all, having the courage to emigrate from Poland to provide me with more opportunities for success.
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TABLE OF CONTENTS
Page Abstract ...... 3 Acknowledgments ...... 4 List of Tables ...... 8 List of Figures ...... 9 Chapter 1 - Introduction ...... 12 1.1 Background ...... 12
1.1.1 CO 2 Sequestration Methods ...... 12 1.2 Biosequestration ...... 13 1.2.1 Photobioreactor Overview ...... 13 1.2.2 Obstacles to Commercialization ...... 14
1.2.3 Optimizing CO 2 Mass Transfer Rate ...... 14 1.3 Objectives ...... 15 Chapter 2 - Literature Review ...... 17 2.1 Falling Film Mass Transfer Models ...... 17 2.1.1 Falling Film Flow ...... 17 2.1.2 Hypothetical Models ...... 18 2.1.3 Empirical Models ...... 21 2.2 Film Depth Measurement Methods ...... 23 2.2.1 Introduction ...... 23 2.2.2 Needle Contact ...... 23 2.2.3 Drainage ...... 25 2.2.4 Hot-wire Anemometry ...... 25 2.2.5 Optical ...... 25 2.2.6 Capacitance ...... 26 2.2.7 Parallel-Wire Conductance ...... 26 Chapter 3 - Laboratory Equipment...... 28 3.1 TOC Analyzer ...... 28 3.1.1 Introduction and Sample Consideration ...... 28 6
Page 3.1.2 Inorganic Carbon Measurement ...... 28 3.1.3 Contamination Precautions ...... 30 3.1.4 Analyzer Calibration ...... 31 3.2 CRF-II ...... 32 3.2.1 Scope of Description ...... 32 3.2.2 Reaction Chamber and Flow...... 32 3.2.3 Gaseous Composition ...... 35 3.2.4 Temperature ...... 36 3.2.5 Light ...... 36 3.3 Safety ...... 36 3.3.1 TOC Analyzer ...... 36 3.3.2 CRF-II ...... 37 Chapter 4 - Results and Discussion ...... 38 4.1 Review of Objectives ...... 38 4.2 Film Thickness Measurement ...... 38 4.2.1 Offline Rig Design ...... 39 4.2.2 Parallel-Wire Conductance Probe Calibration ...... 47 4.2.3 Calibration Considerations ...... 50 4.2.4 Data Collection Method for Film Thickness Measurements ...... 57 4.2.5 Determination of Testing Conditions ...... 61 4.2.6 Film Thickness Data ...... 66 4.3 Experimental Mass Transfer ...... 74 4.3.1 CRF-II Modifications ...... 74 4.3.2 Data Collection Method for Experimental Mass Transfer ...... 77 4.3.3 Testing Conditions ...... 79
4.3.4 CO 2 Mass Transfer Data ...... 80 4.4 Mass Transfer Model Evaluation ...... 83
4.4.1 Experimental Liquid Side Mass Transfer Coefficient (k L exp ) ...... 84
4.4.2 k L exp Comparison with Mass Transfer Models ...... 89 Chapter 5 - Conclusions ...... 96 5.1 Review of Study ...... 96 7
Page 5.2 Effect of Flow Rate on Film Thickness and Mass Transfer ...... 96
5.2 Effect of CO 2 Concentration on Mass Transfer ...... 98 Chapter 6 - Recommendations ...... 100 6.1 Recommendations Overview...... 100 6.1.1 Improvement of Study ...... 100 6.1.2 Future Work...... 102 Symbols ...... 105 References ...... 106
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List of Tables
Page Table 4.1 Comparison of solution specific gravities and viscosities...... 56
9
List of Figures
Page Figure 1.1 Cyanobacteria cover the membrane, while growth solution flows vertically out of a thin opening between the membrane and the metal header...... 15 Figure 2.1 Flow regimes of a falling liquid film as characterized by Reynolds number (Zhang, 2003)...... 17 Figure 2.2 The needle contact method set up to measure the film depth of annular flow (Fukano, 1989)...... 24 Figure 2.3 Basic equipment for parallel-wire conductance method...... 27 Figure 3.1 Detailed view of TOC Analyzer components...... 29
Figure 3.2 Sample acidification leads to release of CO 2 in the digestion vessel...... 30 Figure 3.3 Reaction chamber and flow system...... 33 Figure 3.4 Cotton membrane and distribution header...... 34 Figure 3.5 Side view of distribution header showing shim flow mechanics...... 34 Figure 3.6 Heating and electrical components underneath the reaction chamber...... 35 Figure 4.1 Front view of Offline Rig...... 39 Figure 4.2 Adept MV-10 controller...... 40 Figure 4.3 Parallel wire conductance probe attachment fixture...... 41 Figure 4.4 Parallel wire conductance probe...... 42 Figure 4.5 AD5934 microchip on evaluation board...... 42 Figure 4.6 AD5934 evaluation board with parallel wire conductance probe...... 43 Figure 4.7 Offline Rig side view - flow and temperature controls...... 44 Figure 4.8 Modified distribution header inlets...... 45 Figure 4.9 Modified shim design...... 46 Figure 4.10 Calibration curve generated with a 470 ohm reference resistor...... 48 Figure 4.11 Impedance versus depth for solution calibration curve...... 49 Figure 4.12 Inverse of impedance readings results in linear conductivity versus depth relationship...... 49 Figure 4.13 Solution calibration set-up...... 50 Figure 4.14 Two identical calibrations producing different y intercepts...... 51 Figure 4.15 Solution calibration curve slopes before and after DI refills...... 53
Figure 4.16 Solution calibration curve slopes after evaporation using K 2PO 4 solution...... 54 Figure 4.17 Two sets of conductivities from Figure 4.16...... 54 10
Page
Figure 4.18 Solution calibration curve slopes before and after DI refills in K 2PO 4 solution...... 55 Figure 4.19 Close up view of two sets of conductivities from Figure 4.18...... 55 Figure 4.20 Solution calibration curves at different temperatures...... 57 Figure 4.21 Impedance measurements upon solution flow initiation...... 58 Figure 4.22 Impedance increased when flow was turned off...... 60 Figure 4.23 Locations evaluated for preliminary film depth measurements on Side 1...... 61 Figure 4.24 Preliminary flow rate versus film thickness measurements for locations defined in Figure 4.23...... 62 Figure 4.25 Parallel-wire probe resolution determination...... 63 Figure 4.26 Vertical film thickness variations...... 64 Figure 4.27 Horizontal film thickness variations...... 65 Figure 4.28 Locations of all measurements per membrane side...... 66 Figure 4.29 Film thicknesses across Side 2 of the membrane ...... 67 corresponding to locations outlined in Figure 4.28 at 1.70 GPM...... 67 Figure 4.30 Film thicknesses across Side 2 of the membrane at 1.00 GPM...... 67 Figure 4.31 Film thicknesses across Side 2 of the membrane at 0.50 GPM...... 68 Figure 4.32 Comparison of selected flow rates versus film thickness across Side 2 of the membrane...... 69 Figure 4.33 Comparison of selected flow rates versus film thickness down Side 2 of the membrane...... 70 Figure 4.34 Comparison of flow rate versus film thickness for columns 1 - 8 down Side 2 of the membrane at 1.70 GPM...... 70 Figure 4.35 Comparison of flow rate versus film thickness for columns 9-15 down Side 2 of the membrane at 1.70 GPM...... 71 Figure 4.36 Average film depth based on 90 measurements at each flow rate...... 71 Figure 4.37 Graph of empirically modeled versus actual film thickness...... 72 Figure 4.38 Close up view of cotton membrane...... 73 Figure 4.39 Front and side view of drainage trough...... 75 Figure 4.40 Schematic of CRF-II flow and sampling modifications...... 76 Figure 4.41 TIC concentration versus time...... 79
Figure 4.42 Flow rate effect on CO 2 absorption at a 10.0% CO 2 gas phase concentration...... 81
Figure 4.43 Effect of flow rate on CO 2 absorption at a 2.0% CO 2 gas phase concentration...... 82 11
Page
Figure 4.44 Effect of flow rate on CO 2 absorption at an ambient CO 2 gas phase concentration. . 83
Figure 4.45 Three CO 2 mass balances at different points in the CRF-II...... 84
Figure 4.46 TIC concentration data at 10.0% gaseous CO 2 and 1.70 GPM...... 86
Figure 4.47 CO 2 absorption data at 10.0% gaseous CO 2 and 1.70 GPM...... 87 Figure 4.48 Experimental liquid side mass transfer coefficients...... 88
Figure 4.49 Fick k L values compared with k L exp ...... 90
Figure 4.50 Koziol k L values compared with k L exp ...... 91
Figure 4.51 Henstock and Hanratty k L values compared with k L exp ...... 91
Figure 4.52 Yih and Chen k L values compared with k L exp ...... 92
Figure 4.53 Banerjee k L values compared with k L exp ...... 93
Figure 4.54 Davies k L values compared with k L exp ...... 94
Figure 4.55 All calculated and experimental k L values...... 95 12
Chapter 1 - Introduction
1.1 Background
1.1.1 CO 2 Sequestration Methods
In anticipation of CO 2 emission regulations, research has focused on methods of separating and storing CO 2 from flue gases. Such methods are collectively known as carbon capture and storage (CCS) techniques. CCS techniques include deep ocean storage, geo- sequestration, and mineral storage via a reaction with natural silicate minerals (Metz, 2005).
Although all three methods are potentially viable, commercialization has been slowed by high cost. First, all three approaches require an initial capture step that can take place either pre- or post-combustion. Pre-combustion methods depend on the power-plant producing syngas, such as an integrated gasification combined cycle (IGCC) plant, to partially oxidize coal and separate
CO 2. Post combustion methods include amine absorption, the use of polymeric membranes or oxy-fired systems which require manual separation of water from the CO 2 enriched flue gas.
These processes are energy intensive and therefore reduce the overall plant efficiency. Oxy-fuel firing relies on the use of pure oxygen for combustion instead of air, to produce an exit stream that consists almost entirely of CO 2 and water vapor. The water vapor is condensed out via cooling. As with the other post-combustion methods, the downside to oxy-fuel firing is a large energy requirement for high grade oxygen production, which results in reduced overall efficiency.
Once the CO 2 has been captured, the issue of transport arises. CO 2 can be shipped to its sequestration site via truck or rail but the most cost effective method would be via pipeline.
However, a suitable CO 2 pipeline network does not exist. Further, sequestration sites pose challenges of their own. Geo-sequestration sites consist of unmineable coal seams and saline 13
aquifers, both of which are possibly susceptible to the re-release of CO 2 during the injection process (Metz, 2005). Deep ocean storage provides the largest sink for CO 2 and works by injecting the gas deep enough so that the resulting pressure liquefies the CO 2 and keeps it relatively immobile. This method is only partially sustainable because modeling has shown that
50% of the stored CO 2 is expected to reemerge within 500 years (Metz, 2005). Lastly, mineral storage works by reacting CO 2 with naturally occurring minerals such as magnesium or calcium, to create inert carbonates. Although this method has no risk of CO 2 re-release, the necessary reactions are so energy intensive, that it is estimated a power plant utilizing a mineral storage technique would have to generate 60-180% more power (Metz, 2005).
1.2 Biosequestration
1.2.1 Photobioreactor Overview
CO 2 can be recycled via photosynthesis using an engineered photobioreactor, such as the one currently being investigated at the Ohio Coal Research Center (OCRC). This novel, bench-scale photobioreactor or carbon recycling facility II (CRF-II) consists of an artificially lit reaction chamber, wherein circulating flue gases are created by burning natural gas. Inside there are three vertical cotton membranes on which cyanobacteria grow; growth solution flows over the membrane forming a <1 mm falling liquid film. CO 2 diffuses through the solution to the microorganism (Bayless et al., 2006). The cyanobacteria separate CO 2 from the flue gas stream through absorption to carry on photosynthesis. This alleviates the initial capture step required for other CCS techniques. Secondly, once the cyanobacteria are harvested they can be used as a source of fuel or feed. Either way, a pipeline is not needed for transport, especially if conversion to bio-diesel (for example) takes place on site. Lastly, because the cyanobacteria itself serves as 14 a sequestration site, there are no concerns arising from where and how to store the captured emissions.
1.2.2 Obstacles to Commercialization
Although this technology holds a lot of promise, there are many challenges to resolve for it to be commercially viable. Such obstacles include optimization of light intensity or harvesting frequency, as well as key design issues such as determining which materials are most suitable for microorganism growth. This project is being done to characterize and improve the rate of CO 2 delivery to the cyanobacteria by identifying and manipulating nutrient solution flow rate and gas-phase CO 2 concentration. The faster the CO 2 makes contact with the cyanobacteria, the faster the microorganism will be able to fix carbon and grow, which in turn raises the overall algal productivity. A higher productivity will potentially yield greater return on investment since the photobioreactor would operate more efficiently. Also, reducing the CO 2 gas phase concentration to the necessary level to saturate the aqueous phase could aid in cost reduction. Untreated flue gas will not be permitted to enter the photobioreactor because waste products from the fossil-fuel combustion process may inhibit the growth or even kill the cyanobacteria, therefore treating the flue gas will be a cost.
1.2.3 Optimizing CO 2 Mass Transfer Rate
As described in Section 1.2.1, the cyanobacteria grow on a vertical membrane that is covered by a thin film of nutrient solution. The solution is pumped to, and dispersed via a metal distribution header located at the top of the membrane. The membrane is held in shape by a metal frame as shown in Figure 1.1. Circulating throughout the CRF-II and across the membrane is a CO 2 enriched gas stream. Therefore, the largest resistance to CO 2 transfer to the cyanobacteria is the nutrient solution. To determine the rate at which CO 2 penetrates the thin 15 film of nutrient solution and reaches the cyanobacteria, the use of falling film mass transfer models will be employed.
Figure 1.1 Cyanobacteria cover the membrane, while growth solution flows vertically out of a thin opening between the membrane and the metal header (OCRC, 2011).
1.3 Objectives
Falling film mass transfer models are mathematical models consisting of experimental parameters such as solution flow rate, viscosity, density, etc., developed to predict the liquid side mass transfer coefficient (k L). The rate of CO 2 absorption is affected by mass transfer coefficients on both the liquid and gaseous sides as seen in Equation 1.1,
# # # (1.1) - where K is the overall mass transfer coefficient and k G is the gas side mass transfer coefficient.
The CRF-II operating conditions are assumed to produce an environment where k G >>> kL, therefore only k L dictates the rate of gaseous mass transfer through the thin film. Such models were initially created to optimize industrial systems such as gas-liquid contacting columns, where saturation of a liquid with the gaseous species is critical to operation. Certain models also 16 take into account the thickness of the film, whose measurement posed a great challenge. To determine the best film mass transfer model for our system, the following objectives were proposed:
1. Design and validate a device to measure the falling film thickness using the arrangement
of film flow in the CRF-II. (This information was used to implement Objective 3.)
2. Measure experimental mass transfer rates of CO 2 from the gas phase into a falling liquid
film as a function of flow rate and CO 2 concentration. (These data was used to
determine experimental liquid side mass transfer coefficients (k L exp ).)
3. Select a useable film mass transfer model and implement it to calculate liquid side mass
transfer coefficients (k L) for comparison to the experimental results from Objective 2.
The scope of this study focused on the rate of mass transfer through the liquid film only.
As the carbon fixing mechanism of cyanobacteria would interfere with quantifying mass transfer solely through the growth solution, all experiments performed involved operating the CRF-II without cyanobacteria. Prediction of CO 2 transfer to the film served as the first step in future studies dealing with the formulation of more advanced models that will account for the CO 2 uptake rate of the cyanobacteria.
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Chapter 2 - Literature Review
2.1 Falling Film Mass Transfer Models
2.1.1 Falling Film Flow
A general knowledge of a falling film’s longitudal characteristics is required to understand falling film mass transfer. As seen in Figure 2.1, falling films exhibit four main flow regimes that can be categorized with the Reynolds number as defined by Equation 2.1,
& & (2.1) ˞˥ where Re is Reynolds number, d is film thickness, v is average liquid velocity, ρ is liquid density, is equivalent to the liquid mass flow rate per unit membrane width, and μ is the dynamic liquid viscosity.
Laminar flow Wavy laminar flow Transitional flow Re<25 25
The Reynolds number values denoting transition from one regime to another differ from author to author but their range is usually similar. Work performed by Portalski (1963), Koziol (1980), 18 and Yih and Chen (1982) all have contributed towards establishing these ranges. Up until a Re value of ≈25, the film exhibits smooth laminar motion. This regime is only present in the initial acceleration zone, near the top of the wetted wall. From 25 300 2.1.2 Hypothetical Models Mass transfer models for gas-liquid interactions fall into two basic categories, hypothetical and empirical models. Hypothetical models contain several adjustable or unknown parameters. Empirical models are generated by correlating dimensionless groups to empirical data. Hypothetical models date back to 1904, when Nernst postulated film theory for a gas- liquid interface (Seader, 2006). Nernst’s theory states that the entire resistance to mass transfer in a given phase is a thin, stagnant region at the interface, called a film. If only one gas is assumed present, the total pressure is equivalent to the partial pressure, which results in no resistance to mass transfer in the gas phase. In combination with Fick’s law of diffusion, the result is shown in Equation 2.2, (2.2) ˭ ˖˓ ˓˕ . ˕ ˫!˓˕ . ˕ 19 where m is the mass transfer rate, D is the diffusivity coefficient, A is area, δ is the boundary layer thickness, C Asat is the concentration of a species A at the interface and C Abulk is its concentration in the bulk flow. Generally the expression is treated as one term and called the liquid mass transfer coefficient, k L. However, there is no direct way to measure δ, only theoretical equations exist for predicting it. The equation implies that mass transfer varies directly with molecular diffusion but experiments have repeatedly indicated this dependency varies between D 0.5 and D 0.75 (Seader, 2006). In this study the diffusivity coefficient was calculated using the empirical Wilke-Chang equation for diffusion in binary liquid mixtures as seen in Equation 2.3: %" 1È. &'&(#" ,-./0-./ 3 (2.3) ˖"$$%$" 6' -./5/. where φ is an association factor for the solvent, μ is dynamic solvent viscosity, T is temperature, M is molecular solvent weight, and α is the liquid molar volume of the solute at its normal boiling point (Seader, 2006). Higbie improved upon Nernst’s work by proposing his penetration theory. Higbie replaced the concept of a stagnant film with a continuous series of Boussinesq eddies that move from the bulk flow to the interface where they remain for a short period of time during which molecular diffusion takes place (Seader 2006). Afterwards, they leave the interface and mix with the bulk, with another eddy taking its place at the interface. The mathematical relationship for this theory is given by Equation 2.4, (2.4) ˫! 85 where t C is the contact time of an eddy at the interface. An exponent of 0.5 on the diffusivity coefficient better correlates with experimental data. Although penetration theory more 20 accurately predicts mass transfer, the theory is difficult to implement because there is no easy way of measuring or even estimating the contact time. Also it is unreasonable to assume that all eddies have the same contact time (Seader, 2006). Penetration theory was further refined by Danckwertz (1951) by correcting the constant contact time assumption. Danckwertz’s surface-renewal theory replaced the constant contact time with a residence-time distribution, which ultimately resulted in Equation 2.5, (2.5) ˫! :˖; where s is the fractional rate of surface renewal. As with the t C in penetration theory, there are no proposed methods of measuring s. A theoretical mass transfer model that has been exclusively developed to deal with falling films has been created by Ruckentstein (1965) by integrating the Kaptiza vertical velocity profile. The Kaptiza profile solves for hydrodynamic parameters such as the film’s velocity and thickness (Kapitza, 1948). Ruckenstein’s model predicted that surface waves would increase mass transfer by only 15% from laminar flow. This has been proven to be inaccurate, with experiments showing a nearly 200% increase in mass transfer due to wave motion (Zhang, 2003). Banerjee (1967) has proposed eddy diffusivity models to determine mass transfer with Equation 2.6, "'&" (2.6) ˫! 1 ? %= =" where H is the average approach distance of an eddy to the interface and t E is the time between eddies. Both of these parameters were derived from theoretical equations describing wave velocity, length and liquid properties. 21 Davies (1969) performed research on how both smooth and rough surfaces affect mass transfer in falling films. His resulting theoretical relationship was based on Levich’s previous work on isotropic turbulence. The resulting equation, when adjusted for a smooth surface is given in Equation 2.7, "'' "'&' "'&' "'' $"'' (2.7) ˫! Ŵ'ŷŹ ( ˖ ˤ ˧ F G where g is gravity and σ is surface tension. Although Davies proposes Equation 2.7, his results do no agree with it. For smooth surfaces, his k L data exhibited an average increase of 4.5 times the predicted value. This factor of 4.5 will be applied to Equation 2.7 for the purposes of this study. The overall coefficient will therefore be 1.58 instead of 0.35. 2.1.3 Empirical Models Henstock and Hanratty (1979) developed their model by assuming that the mass transfer process is controlled by eddies whose length and velocity are characterized by bulk turbulence properties and that in a region of thickness that is close to the interface, the turbulence is dampened by viscosity. They note that falling film mass transfer can be related using Equation 2.8, (2.8) ˟˨˟J $"'' ˦˞˥ where Sh is the Sherwood number, given by Equation 2.9, (2.9) ˟˨ and Sc is the Schmidt number, given by Equation 2.10, (2.10) ˟J This theoretical model along with experimental data for sheared falling films gave rise to Equation 2.11. (2.11) ˟˨˟J $"'' Ŵ'ŴŴŻŻ Ŵ'ŻŴŻ˞˥ "'' $'' - Ŵ'ŴŷŻM˞˥ "'N $'' "'& #'' 22 As with Davies, the authors cite Equation 2.11 may underestimate k L values by up to a factor of 3. This factor was applied to the present study to achieve a better fit. Koziol (1980) used the same general relationship as Equation 2.8 and developed models that were correlated with particular Re ranges as given by Equations 2.12-2.14, "'' "'%N "'' U for 170 < Re < 335, (2.12) ˟˨O ŵ'źRR˞˥ ˟J ӘVә "'' "'$& "'' U for 335 < Re < 1080, (2.13) ˟˨O ŷ'RRŶ˞˥ ˟J ӘVә $& "'&# "'' for 1080 < Re < 2513, (2.14) ˟˨O R'MŶŷ ( ŵŴ ˞˥ ˟J where h is the height of the wetted wall, θ is an equivalent dimension defined by Equation 2.15 ? . (2.15) Y 8Z. and Sh m is a modified Sherwood number that does not utilize film thickness, as shown in Equation 2.16. U (2.16) ˟˨O Another approach of arranging a falling film mass transfer relationship is in terms of the * dimensionless mass transfer coefficient k L with the general relationship given in Equation 2.17, ( (2.17) ˫! ˦˞˥˟J˙\ where Ga is the Galileo number given in Equation 2.18, Z ? (2.18) ˙\ ]. * and k L is show in Equation 2.19, . #È% ( (2.19) ˫! Ә ә Ә Z ә where is the kinematic viscosity. Several researchers have correlated their data this way, with _ the most notable case being Yih and Chen (1982), who combined their data with ten other 23 authors, yielding a total of 846 data points. They concluded that the Galileo number is not significant and just as with Koziol, their models were correlated with the appropriate Re numbers as seen in Equations 2.20-2.22, ( $$ "'%N'' "'' for 49 < Re < 300, (2.20) ˫! ŵ'ŴMM ( ŵŴ ˞˥ ˟J ( $$ "'$#%& "'' for 300 < Re < 1600, (2.21) ˫! Ŷ'MMŹ ( ŵŴ ˞˥ ˟J ( $& "'`a"& "'' for 1600 < Re < 10500, (2.22) ˫! M'ŻŻŻ ( ŵŴ ˞˥ ˟J There has yet to emerge a uniformly accepted method for predicting such rates, therefore it is up to the researcher to determine which one best suits the system at hand. 2.2 Film Depth Measurement Methods 2.2.1 Introduction A review of literature revealed a number of custom-built instruments for measuring film thickness. The needle contact method and parallel wire conductance method appeared to hold the most promise, with the latter method being ultimately implemented. Accuracy was a top priority in implementation because the expected film thickness was <1mm, therefore an instrument error of ±0.01mm was desired. Most reviewed methods have been proven to discern such thicknesses, but until now, none has been used to measure flow depth over a flexible fabric. Suitability of these techniques depended on whether the proposed method could be augmented to fit and work with the membrane, as well as the simplicity of design. 2.2.2 Needle Contact A wide variety of alternative film depth measurement devices have been researched, but were deemed non-compatible, too complex or simply not sufficiently precise. One such method is the needle contact method. One of the first notable investigations into measuring falling film thickness using a needle probe was performed by Brauer (1956) with subsequent 24 improvements and analysis by Hewitt (1962) and Kirilov (1978). This method consists of a needle attached to a depth micrometer brought to the surface of the film. The needle itself serves as one of two electrodes in an electrical circuit. The other electrode is placed in a location that is in constant contact with the liquid film. When contact between the needle and the film occurs, the circuit is complete and the resulting voltage can be measured. The depth of the film is measured when contact is made, using the micrometer and a pre-defined zero position. One example of such a device is depicted in Figure 2.2. Figure 2.2 The needle contact method set up to measure the film depth of annular flow (Fukano, 1989). To determine the mean film depth, the contact frequency and duration have to be recorded. When a film falls vertically, waves form on its surface resulting in varying degrees of film depth with respect to the needle’s position. Methods for measuring contact frequency and duration have consisted of digital counters in conjunction with diodes and resistors. The biggest disadvantage of using this technique is that hysteresis occurs due to the needle obstructing the 25 flow of the film. As a wave passes over the needle, a liquid filament is drawn out, resulting in false contact duration readings. Although this is cited as a concern, the literature review has shown that results from the needle contact method closely correlate with more advanced measurement techniques, and therefore could be ignored for the purposes of this study. 2.2.3 Drainage The drainage technique that works by simultaneously stopping flow to the wetted wall while placing a container under the wall to capture the liquid layer (Portalski, 1963). Although simple, this method is difficult to implement because these two actions must occur simultaneously and water flow would has to be stopped at the top of the wetted wall. In our case, the membrane is attached to a header with a large volume that cannot be instantaneously stopped. The method is also manual, and therefore does not produce a continuous digital record that can be easily analyzed. 2.2.4 Hot-wire Anemometry Lyu and Mudawar (1991) used a hot-wire anemometer to measure film depth. Hot-wire anemometers are typically used for measuring fluid velocities, but the device can be augmented to also measure film depth (Lyu, 1990). The method works by applying a current to the anemometry probe, with the voltage signal becoming a function of thickness. The total electrical resistance depends on the length of wire immersed in the liquid film. Although applicable to our system, the literature review showed that this method has been seldom used in the past and was passed over due to a lack of detailed information. 2.2.5 Optical An optical method has been devised by Shedd and Newell (1998) wherein light is reflected from the surface of a falling film and projected back onto a transparent film wall, so 26 the image can be captured and digitized with a charge coupled device camera. Along with a computer equipped with a framegrabber card and the appropriate software, the depth of the film can be determined. This method was eliminated from consideration due to the necessity of a transparent wall. Some closely related optical methods have been devised by Barter and Lee (1994), where light attenuation is converted into film depth, as well as by Lorenecez (1997), who used a combination of photochromic dyes activated by lasers along with a high speed camera. Barter and Lee’s approach was deemed unsuitable as it also required that flow occur over a transparent surface. Lorenecez’s approach was removed from consideration as it required the flow to occur over an incredibly smooth surface. 2.2.6 Capacitance A capacitance probe can be used to measure the thickness of a film flowing over a metal wall (Ambrosini, 2002). As with the parallel wire conductance method, this technique consists of an electrical circuit, only here the film falls in between a metal wall and a capacitance probe. The measured capacitance is a function of film depth. This method was disregarded due to the requirement that flow must occur over a metal wall, which serves as an electrode itself. 2.2.7 Parallel-Wire Conductance The literature review revealed that one of the main purposes behind creating film depth measurement devices was to study the wave characteristics of a falling film. The needle contact method is suitable for determining the average film depth but, a continuous record of film depth was needed for quantifying wave behavior. One technique developed for solving this issue is the parallel wire conductance method, first constructed by Swanson (1966) with much refinement performed by Hanratty and his students Miya (1970), Laurinat (1982), Lin (1985) Andritsos (1986) and as well Karapanstsios (1989), (1995) and his colleagues. 27 The main components necessary for the parallel-wire conductance technique include a parallel-wire probe, a signal generator, an electronic analyzer, and a data acquisition system as shown in Figure 2.3. The probe consists of a set of short, chromel wires aligned in parallel and affixed to a base. The signal generator sends an electrical signal to one of the wires. Once the probe is immersed in the liquid film, conductance between the two wires occurs and the electrical analyzer receives a signal from the second wire. As more of the wires are immersed, the electrical resistance is lowered, therefore the relationship between depth and resistance is inversely proportional. The analyzer also converts the signal output into an analog signal, which then can be converted into a digital one and lastly, be read and recorded by the data acquisition system. Studies have shown that the resulting impedance output is inversely related to film depth (Karapanstsios, 1989). A modernized version of this method was utilized for film thickness measurements and elaborated upon in Section 4.2.1. Parallel wire conductance probe Function Electronic Computer/Data Generator Analyzer Acquisition System Figure 2.3 Basic equipment for parallel-wire conductance method. 28 Chapter 3 - Laboratory Equipment 3.1 TOC Analyzer 3.1.1 Introduction and Sample Consideration The proposed work involved measuring an experimental CO 2 mass transfer rate using an OI Analytical, Model 1010 Total Organic Carbon (TOC) Analyzer. The name is slightly misleading as it has the capability to measure both organic and inorganic carbon compounds. The experimental liquid side mass transfer coefficient was determined by measuring the inorganic carbon content of growth solution samples procured from the CRF-II over time and applying a mathematical treatment. The measurements assumed that CO 2 will be the source of all inorganic carbon detected. The growth solution nutrients did contain inorganic carbon compounds, therefore their amount was quantified and used as the initial inorganic carbon concentration. 3.1.2 Inorganic Carbon Measurement The TOC analyzer shown in Figure 3.1 begins performing measurements by pumping in the sample via a sipper tube connected to the “Sample In” inlet. The sample then enters the digestion vessel where a pre-defined amount of 5% phosphoric acid is added. Acidification causes all inorganic compounds to decompose into CO2. The acidified sample is heated and then sparged with a grade 5.0 (99.999) ultra high purity nitrogen gas which drives off the CO 2 towards a nondispersive infrared (NDIR) sensor. This process of CO 2 extraction from a sample volume is represented in Figure 3.2. The NDIR measures the inorganic carbon amount present by determining absorption of a certain wavelength of light. This information, along with the total volume of sample introduced, allows the TOC to calculate the inorganic carbon concentration. The TOC analyzer is 29 coupled with a computer using a software package called WinTOC provided by OI Analytical, which allows the user to automate this process, as well as adjust a variety of options that govern operation. Figure 3.1 Detailed view of TOC Analyzer components (OI Analytical, 1999). 30 Figure 3.2 Sample acidification leads to release of CO 2 in the digestion vessel (OI Analytical, 1999). 3.1.3 Contamination Precautions The instrument also takes several precautions to ensure that the measured inorganic carbon concentration is an accurate representation of the sample, and free of outside contaminants. Between each sample, all of the internal tubing that carries the sample fluid, acid, etc., is flushed with rinse water. The rinse water itself is continually purged with nitrogen gas to ensure it has as little inorganic carbon as possible. For the same reason, the acid is also continually purged with nitrogen. The nitrogen itself passes through a drying tube before being used as a purging gas. The drying tube contains a desiccant which removes moisture to reduce the amount of contaminants the gas may carry. Lastly, the digestion vessel is maintained just below 100˚C to aid the nitrogen and acid in driving off as much inorganic carbon as possible. Also a precaution, the user is to run a series of blanks before sampling. Running a blank causes the instrument to perform all the steps it normally would in measuring a sample, except for actually withdrawing the sample. This process yields an inorganic carbon concentration that represents the background noise associated with inorganic carbon that may be present in the 31 gas, rinse water, etc. This value is then averaged and automatically subtracted from measurements derived from the actual samples. 3.1.4 Analyzer Calibration Calibration of the TOC Analyzer consists of introducing samples of known inorganic carbon concentration and saving their respective NDIR responses for comparison with actual samples of unknown concentration. According to Henry’s law the expected maximum theoretical solubility of CO 2 in water at 50˚C and a 10% CO 2 atmosphere was 80 ppm, but because the instrument only reports the carbon element of the CO 2 molecule, the maximum concentration reported by the TOC analyzer was expected to be only 22 ppm. Calibration begins by making a 1000 ppm inorganic carbon stock solution by dissolving 8.826 grams of sodium carbonate in one liter of purified water. The WinTOC program allows calibration to be performed with up to five standards, therefore by using the appropriate pipettes, volumetric glassware and stock solution, standards containing 0, 5, 10, 20, and 25 ppm of inorganic carbon will be prepared. The program analyzes the standards the same way it does a normal sample as described previously, but instead of producing a series of concentration measurements, the software analyzes and saves the NDIR response. The user pre-defines how much inorganic carbon each standard contains. The NDIR response consists of area counts (area under the IR spectra) and varies linearly with inorganic carbon content. After the calibration procedure is completed, the WinTOC program calculates an R 2 value for the calibration curve, and if it is less than 0.999, then the calibration is repeated. Reasons for low R 2 values mainly stem from the user’s technique in preparing the standards. If care is not taken, the standards contain inaccurate amounts of inorganic carbon and this in turn becomes evident during calibration, when the area counts versus concentration relationship is not linear. 32 3.2 CRF-II 3.2.1 Scope of Description Samples evaluated by the TOC Analyzer were procured from the CRF-II. As mentioned in Chapter 1, the CRF-II is used for the experimental biosequestration of CO 2 from flue gases. Although the CRF-II is intended to operate with cyanobacteria, the organisms will not be used in this study and therefore aspects of the CRF-II that involve their cultivation and harvesting will be omitted. 3.2.2 Reaction Chamber and Flow The reaction chamber seen in Figure 3.3 holds three cotton membranes with distribution headers and light panels, and maintains a controlled environment where temperature, flow rate, light cycle and levels of CO 2, CO, and O 2 can be controlled. The membranes pictured in Figure 3.4 are the surface on which cyanobacteria grow with growth solution flowing over it. Currently the membranes are cotton but, studies are being done to identify the optimum fabric for this application. The distribution header receives growth solution from a holding tank via a Sandpiper diaphragm pump. The flow rate to each of the three headers is controlled with a separate King Instruments, 0.00-2.00 gallon per minute (GPM) variable area flow meter. Once the flow has traveled down the membrane, it drains into the holding tank where it re-circulates back into the reaction chamber. 33 Reaction chamber Cotton Light panels membrane Holding tank Growth solution flow meters Diaphragm pump Figure 3.3 Reaction chamber and flow system (Mielnicki, 2011). 34 Growth solution inlet Distribution header Cotton membrane Direction of flow Figure 3.4 Cotton membrane and distribution header (Mielnicki, 2011). The distribution header disperses growth solution uniformly on both sides of the cotton membrane as well as across the entire width of the membrane. As the growth solution enters the header in the center, an internal distribution shim directs flow to both sides of the membrane as shown in Figure 3.5. To aid the growth solution in reaching both ends of the membrane, the distribution shim’s plastic insert is cut in a serrated manner to throttle flow. Plastic insert Flow enters distribution header Flow splits Bar threaded through membrane Flow remains separated by membrane Figure 3.5 Side view of distribution header showing shim flow mechanics (Mielnicki, 2011). 35 The shim also serves a second purpose as a point of attachment for the cotton membrane by having a metal rod threaded through the membrane and inserted inside of the shim. This arrangement separates flow inside the header which results in an arrangement that allows flow to enter the distribution header via one inlet and exit on both sides of the membrane. 3.2.3 Gaseous Composition The reaction chamber is in the top section of the CRF-II with a gas burner and a fin strip heater located in the bottom as pictured in Figure 3.6. Reaction chamber Table Electrical ballast box Gas Fin -strip burner heater Figure 3.6 Heating and electrical components underneath the reaction chamber (Mielnicki, 2011). The burner maintains the temperature of the air inside the CRF-II and provides a simulated flue gas with up to 10% CO 2 by volume. The CO 2, CO, and O 2 levels are controlled by delivering the appropriate gas to air ratio to the burner using variable area flow meters. The composition of the gas is measured with a NOVA gas analyzer, which utilizes both infrared and electrochemical 36 sensors to detect levels of CO 2, O 2, and CO. The operator controls the flue gas composition using feedback from the NOVA gas analyzer. In cases where less than 10% CO 2 is needed, the burner is not used and instead CO 2 is delivered from a pressurized tank, while temperature is maintained by the fin-strip heater. 3.2.4 Temperature When using the fin-strip heater, temperature control of the air is automated using an on/off temperature controller, along with a temperature set-point pre-defined by the operator. The burner does not have a temperature controller. Instead, temperature is regulated by the amount of natural gas being fed to the burner. The temperature of the growth solution is controlled with a second on/off temperature controller that’s connected with an immersion heater. The holding tank shown in Figure 3.3 contains a 1000 W immersion heater and is insulated to minimize heat loss. Insulation also surrounds ducts that connect the burner/fin-strip heater to the acrylic test section. 3.2.5 Light The CRF-II has a total of four full spectrum fluorescent light panels. The panels deliver light to all six sides of the three growth membranes. The electrical ballast box for the lights is located directly above the burner, as show in Figure 3.6. The duration of lighting is controlled by an on/off timer switch. Light intensity is adjusted by either removing some of the bulbs or covering parts of the light panels with tape to block light. 3.3 Safety 3.3.1 TOC Analyzer Standard precautions taken while working with the TOC analyzer consist of wearing correct personal protective equipment and properly disposing of waste. Protective glasses must 37 be worn to shield the user from accidental contact with the phosphoric acid. Furthermore, when preparing the acidic reagent or dilution standards for calibration purposes, latex gloves must be worn. After a sample has been run, the analyzer ejects its analyzed sample, used reagent, and purge water into a 10 L waste beaker, whose contents are strongly acidic. When the beaker is almost full, the waste solution must be neutralized with a base, followed by dilution with water for disposal. Lastly care has to be taken when replacing the nitrogen cylinders. Once a nitrogen tank becomes empty, the tank valve must be shut off before the regulator can be removed. Similarly, when attaching the regulator to a new tank, the tank valve must not be opened prior to attachment of the regulator. When switching out tanks, ensure that the tank is properly fastened to a wall so that it will not fall over if pushed. Transporting tanks within the building must be done with the aid of a dolly. 3.3.2 CRF-II Carbon monoxide (CO) may be generated as an unwanted byproduct from burning natural gas. When inhaled, CO is extremely poisonous. While CO is produced in the CRF-II, the data acquisition and safety system ensures that harmful CO levels are not reached. If excessive levels of CO are detected by the NOVA gas analyzer (40> ppm), the safety system initiates a burner shut-down. There is also a Nighthawk CO alarm located in the room to assure space safety. The last precaution that’s taken to ensure dangerous levels of CO aren’t inhaled is a lab policy that requires the operator to wear a portable CO detector when running the CRF-II. 38 Chapter 4 - Results and Discussion 4.1 Review of Objectives The objectives achieved by this thesis have been the following: 1. Designed and validated a device to measure the falling film thickness using the arrangement of film flow in the CRF-II. 2. Measured experimental mass transfer rates of CO 2 from the gas phase into a falling liquid film using a Total Organic Carbon (TOC) analyzer as a function of flow rate and CO 2 concentration. 3. Selected a useable film mass transfer model and implemented it to calculate liquid side mass transfer coefficients (k L) for comparison to the experimental results from Objective 2. The first objective was achieved by constructing a modernized version of the parallel wire probe described in Section 2.2.7. Due to constraints, the conductance probe was integrated with a traversing device outside of the CRF-II reaction chamber. The second objective involved modifying the CRF-II to comply with mass transfer model assumptions and integrating the TOC analyzer to obtain a continuous record of CO 2 concentration measurements. The last objective combined data gathered from the previous two to model how k L behaved with respect to flow rate and gaseous CO 2 concentration and compare these results to experimental k L data. 4.2 Film Thickness Measurement Due to the lack of space inside the CRF-II reaction chamber, an Offline Rig was constructed to allow for falling film thickness measurements to be taken. The Offline Rig simulated conditions present inside the CRF-II by having one cotton membrane and distribution header combined with the appropriate flow and temperature controls. These controls were 39 further integrated with a parallel wire conductance probe as well as an AdeptOne robot that held the aforementioned probe and served as a precision positioning device. The AdeptOne robot allowed for film thickness readings to be taken across, down, and on both sides of the cotton membrane in a repeatable manner. 4.2.1 Offline Rig Design Integration of the cotton membrane and distribution header with the AdeptOne robot began by incasing the cotton membrane and distribution header in a custom frame made out of 80/20 aluminum extrusions as seen in Figure 4.1 . AdeptOne robot Metal barrier Custom 80/20 aluminum extrusion frame Robot base Pedestal Angle iron Figure 4.1 Front view of Offline Rig (Mielnicki, 2011). 40 The aluminum extrusion frame stabilized the cotton membrane and provided points of attachment for coupling with the AdeptOne robot. The AdeptOne robot was integrated with the aluminum extrusion frame via a robot base as seen in Figure 4.1. The AdeptOne robot sat in the center of the robot base, attached to a pedestal. Initially, there was a metal barrier that surrounded the pedestal on all sides. It was determined that placing the aluminum extrusion frame on the metal barrier would allow the robot arm to traverse both sides of the cotton membrane without any obstructions. To achieve this arrangement, a section of the metal barrier was cut out and angle iron welded in its place to hold the aluminum extrusion frame. The AdeptOne robot’s movements were programmed using an Adept MV-10 controller, as seen in Figure 4.2, and a PC. MCP Crossover ethernet cable connecting controller to PC Cables connecting controller to AdeptOne robot Figure 4.2 Adept MV-10 controller (Mielnicki, 2011). The PC came equipped with AdeptWindows software, a Windows 98 operating system and connected to the Adept MV-10 controller via an ethernet crossover cable. AdeptWindows ran a 41 V+ Version 13.0 programming language that utilized commands pre-defined by the manufacturer to control the AdeptOne robot’s movements. The MV-10 controller also came equipped with a manual control pendant (MCP) that was programmed to run the robot without the aid of the PC. The AdeptOne robot arm held the parallel-wire conductance probe via a custom built attachment fixture as seen in Figure 4.3 . The attachment fixture was machined to be bolted into the robot arm and held the conductance probe via a shaft collar. The shaft collar allowed for easy removal of the conductance probe for calibration purposes. Adept One robot arm Shaft collar Attachment fixture Parallel wire probe Figure 4.3 Parallel wire conductance probe attachment fixture (Mielnicki, 2011). The parallel wire conductance probe consisted of a micrometer head with a non- rotating spindle, a plastic shaft collar and two 24 A.W.G. chromel wires as seen in Figure 4.4 . The chromel wires were threaded through the shaft collar and glued in place. The ends of the wires facing away from the micrometer head were 1 cm in length, 2 mm apart, and used for impedance measurements. 42 Micrometer Chromel wires head Plastic shaft collar Figure 4.4 Parallel wire conductance probe (Mielnicki, 2011). The wire ends facing the micrometer head were connected with an Analog Devices AD5934 microchip that came pre-assembled on an evaluation board as seen in Figures 4.5 and 4.6. The AD5934 evaluation board connected to the parallel wire conductance probe via insulated copper wires with “gator grips” on both ends. A USB connection and a custom built Matlab graphical user interface (GUI) allowed the AD5934 evaluation board to communicate with the PC. 100 µF Capacitor Attachment 470 ohm sites for Calibration chromel wires Resistor 470 ohm USB Cord reference resistor AD5934 microchip Figure 4.5 AD5934 microchip on evaluation board (Mielnicki, 2011). 43 AdeptOne robot AD5934 evaluation arm board Insulated copper wires Parallel wire conductance probe Figure 4.6 AD5934 evaluation board with parallel wire conductance probe (Mielnicki, 2011). The AD5934 evaluation board allowed the user to send an A.C. signal to one of the chromel wires and once conduction between the two wires was established, the microchip was also capable of measuring the resulting impedance. The Matlab GUI was used for viewing impedance data in real time, as well as storing the impedance data in Excel form on the PC. The A.C. signal had a frequency of 24 kHz and impedances were recorded with a 20 Hz sampling rate. It was determined that the AD5934 evaluation board’s A.C. signal had a DC bias which could potentially result in unstable impedance measurements. To eliminate the DC bias, a high pass filter in the form of a 100 µF capacitor was installed on the board so the A.C. signal would pass through it before reaching the parallel wire conductance probe. Solution flow rate was controlled with two 1/8 hp centrifugal pumps, a 0.00 to 2.00 GPM variable area flow meter with an accuracy of ± 0.05 GPM, a 24 L solution tank, and a bypass gate valve as seen in Figure 4.7 . 44 Temperature controller Robot base Bypass valve Pump on/off switch Type K thermocouple Flow meter Immersion heater Pumps Solution tank Figure 4.7 Offline Rig side view - flow and temperature controls (Mielnicki, 2011). Initially a ½ hp pump was envisioned to circulate the solution but this pump introduced rust into the solution which resulted in faulty impedance readings. As a contingency plan, two readily available pumps with lower horsepower and plastic internal parts were used. Unfortunately this alternative arrangement could only generate a maximum stable flow rate of 1.70 GPM, instead of the desired 2.00 GPM. The solution flow path started in the solution tank, followed by entering the two pumps which delivered the solution to the distribution header via the flow meter. Once the solution traveled down the cotton membrane, it drained onto a catch tray and back into the solution tank. The other flow path after exiting the pumps consisted of the solution being re-rerouted directly into the solution tank via the bypass valve. The purpose of the bypass path was to reduce strain on the pump motors when low flow rates were needed. 45 Temperature was maintained at 50 ± 1 ° C and controlled with a Watlow EZ temperature controller connected to a Type K thermocouple and a 1500 Watt immersion heater as seen in Figure 4.7. The thermocouple resided inside the solution tank and the temperature reading displayed by the temperature controller was double checked using a handheld Fluke thermocouple reader. An infrared thermometer was used to ensure that the temperature on the cotton membrane surface was the same as in the solution tank. The distribution header was modified from its original design to achieve acceptable flowing film coverage across the entire width of the cotton membrane for a wide range of flow rates. The distribution header was altered so the solution would enter it via two inlets instead of one as seen in Figure 4.8. The dual inlet design allowed for better solution distribution across the width of the cotton membrane. The distribution header shim was also modified to accommodate for the change in inlet design. Modified dual inlets Original single inlet Figure 4.8 Modified distribution header inlets (Mielnicki, 2011). The modified shim design focused on throttling the flow of solution upon its entrance into the header and forcing it towards harder to reach areas across the width of the membrane as seen in Figure 4.9. 46 Distribution Inlets located above header shim these areas 0.5” Spacing 1.0” Spacing Figure 4.9 Modified shim design (Mielnicki, 2011). Throttling flow was performed by spacing cuts in the shim 1” apart below the solution inlets and reducing the spacing to 0.5” in the harder to reach areas of the center and ends of the membranes. Reduction in the spacing between cuts resulted in less resistance encountered by the solution on its way through the header and onto the cotton membrane. Several other inlet and shim cut arrangements were tested with the aforementioned configuration producing the best flowing film coverage for solution flow rates ranging from 0.50 to 2.00 GPM. Flow rates lower than 0.50 GPM were not evaluated because none of the shim arrangements tested was able to create acceptable coverage below it. Coverage was evaluated visually by rating each 1” of membrane width as having either a “present” or “absent” film for a given flow rate. 47 4.2.2 Parallel-Wire Conductance Probe Calibration The AD5934 evaluation board needed a resistor to have a constant impedance reference point for accurate impedance measurements. The resistor arrangement is shown in Figure 4.5. Upon initiation of the Matlab GUI interface with the AD5934 evaluation board, a calibration of the reference resistor took place with a second calibration resistor. The two resistors had the same measured resistance (470 ohms) for the all film thickness measurements reported. Once both resistors were installed correctly as seen in Figure 4.5, calibration took place by pressing a “Calibrate” button in the Matlab GUI and then removing the calibration resistor. Once the aforementioned calibration was completed, the accuracy of the AD5934 evaluation board was tested by measuring the resistance of known resistors. Initially, there were discrepancies between measured and actual resistances. This issue was mitigated by measuring several known resistances and generating a measured versus real impedance calibration curve as seen in Figure 4.10. A linear relation was derived, as shown in Equation 4.1, and was used to convert measured to real impedances for all film thickness measurements. Also, this calibration curve was assumed to be valid between 300 and 7000 measured ohms, therefore care was taken to ensure measured impedances stayed within these bounds. Ωr = 1.51Ωm – 270 (4.1) The calibration of the parallel wire conductance probe proceeded by generating a calibration curve for the liquid solution whose flowing film thickness was of interest. Because the AD5934 evaluation board could only measure impedance, a linear conductivity versus depth calibration curve was obtained. 48 12000 y = 1.51x - 269.99 10000 R² = 1.00 8000 6000 4000 Real Impedance (ohms) ImpedanceReal 2000 0 0 1000 2000 3000 4000 5000 6000 7000 Measured Impedance (ohms) Figure 4.10 Calibration curve generated with a 470 ohm reference resistor. Since the inverse of impedance is conductivity, this was done by taking the inverse of the measured impedance values as seen in Figures 4.11 and 4.12. This linear relationship, shown in Equation 4.2 determined how solution conductivity varied with respect to the depth of chromel wire immersion in a static, non-flowing environment. ef (4.2) ŵŸŵŹcd˟ Żźŷ'ŸŻ OO ( ŵ'Ÿc˭˭ - ŷŹM'ŵŶcd˟ 49 1000 900 800 700 600 500 400 300 Impednace (ohm) Impednace 200 100 0 0 0.5 1 1.5 2 2.5 3 3.5 Depth (mm) Figure 4.11 Impedance versus depth for solution calibration curve. 3000 2500 y = 763.47x + 359.12 R² = 0.9998 2000 1500 1000 Conductivity (µS) Conductivity 500 0 0 0.5 1 1.5 2 2.5 3 3.5 Depth (mm) Figure 4.12 Inverse of impedance readings results in linear conductivity versus depth relationship. This calibration consisted of placing the parallel wire conductance probe in the arrangement seen in Figure 4.13. It was imperative that the solution surface remain unperturbed during calibration as well as at a constant 50 °C. This was accomplished by filling a 250 mL flask with the 50 solution and attaching it to a ring stand so that most of the flask was surrounded by the heated solution in the solution tank. The parallel wire probe was then inserted into a sturdy calibration stand that positioned the chromel wires directly above the 250 mL flask. Each solution calibration curve consisted of five impedance measurements at depths of 1, 1.4, 1.8, 2.2 and 3.2 mm and each impedance measurement represented the average of a 20 second sampling duration, in which 400 readings were taken. Type K thermocouple Ring stand Parallel wire Conductance probe 250 mL flask Solution tank attached to ring stand Calibration stand Figure 4.13 Solution calibration set-up (Mielnicki, 2011). 4.2.3 Calibration Considerations Once the solution calibration curve was obtained, the parallel wire conductance probe was installed onto the Offline Rig as seen in Figure 4.6. Flowing film thicknesses were calculated by measuring the film’s impedance and converting it into thickness using the inverse of slope of the linear calibration curve seen in Figure 4.12. Only the calibration slope and not its y-intercept value were used for thickness calculations because although the slope always remained the same, the y –intercept varied as seen in Figure 4.14. 51 The y-intercept represents conductivity at the point of contact (POC) between the probe wires and the solution. Besides POC discrepancies experienced during calibration, it was also determined that the POC value varied between making contact with the solution and contacting the wet cotton membrane. Whereas the POC conductivities were around 400 µS during calibration, they were around 100 µS when contacting the wet membrane. 3000 2500 2000 Cal 1 -1y = 692.77x + 391.85 1500 Cal 1 -2y = 693.17x + 296.08 Conducitivity (µS) Conducitivity 1000 500 0 0 0.5 1 1.5 2 2.5 3 3.5 Depth (mm) Figure 4.14 Two identical calibrations producing different y intercepts. Because the POC value varied for every condition, the decision was made to measure its value for each point of interest on the membrane and use it in conjunction with the slope of the solution calibration curve for unknown film thickness calculations. A generalized form of the mathematical procedure used to calculate film thickness from impedance measurements is illustrated in Equation 4.3. ˦˩ˬ˭cˮ˨˩J˫j˥;;c˭˭ # OO (4.3) k lkmcn 'ccn o p Ә f ә ( ˦ˬq˱˩j˧c˦˩ˬ˭cJqjˤ' s˟ . ˭˥˭tu\j˥c˜˛˕cJqjˤ'ccs˟ 52 The initial intent was to use algal growth solution for film thickness measurements as well as during the CO 2 absorption trials outlined in Objective 2. Unfortunately the use of algal growth solution was not possible in the Offline Rig due to evaporation. Whereas the CRF-II is a closed system, with both solution and gaseous temperatures maintained at 50 °C, the Offline Rig was exposed to ambient air, resulting in evaporation rates as fast as 2 L/hr. Over the course of a testing period, enough growth solution would evaporate to cause an increase in solution conductivity. The change in conductivity over time invalidated the calibration curve. It was theorized that the change in conductivity occurred due to ion concentrations increasing as water evaporated. The first attempted resolution for stabilizing solution conductivity focused on this assumption by trying to maintain the original pre-evaporation concentration of ions. This was done by refilling the solution tank with de-ionized (DI) water for every 2 L that evaporated. After the first 2 L evaporated, this approach seemed promising as evidenced by the results shown in Figure 4.15. However, the subsequent refills did not produce the same effect. This method was deemed ineffective because the latter refills had a less predictable effect on conductivity and more importantly, the change between refills would produce large errors in thickness calculations. 53 80 70 60 50 Initial Pre-Evap. (26 L) 40 Pre 1st Refill (24 L) Post 1st Refill (26 L) 30 Conductivity (uS) Pre 2nd Refill (24 L) 20 Post 2nd Refill (26 L) 10 0 0 0.2 0.4 0.6 0.8 Depth (mm) Figure 4.15 Solution calibration curve slopes before and after DI refills. A second approach for maintaining stable solution conductivity consisted of increasing the ionic content to a point where a further increase in ion concentration caused by evaporation did not result in a noticeably higher conductivity. This was achieved by adding 90 g of K 2PO 4 into 26 L of reverse osmosis (RO) water instead of using 26 L of algal growth solution. K 2PO 4 was chosen due its relatively neutral pH when dissolved in water and because 90 g resulted in an almost 10 fold increase in conductivity over the algal growth solution. In comparison, the algal growth solution had around 9 g of various ionic constituents per 26 L. This method turned out to be much more effective at maintaining constant solution conductivity as can be seen in Figures 4.16 and 4.17. Figure 4.16 shows that as evaporation continues to increase the ion concentration, conductivity remains somewhat stable, but upon closer inspection in Figure 4.17, it can be seen that conductivity increases slightly with evaporation. 54 400 350 300 250 Initial (26 L) 200 1st Evap. (24 L) 150 2nd Evap. (22 L) Conducitivty (µS) Conducitivty 100 3rd Evap. (20 L) 4th Evap. (18 L) 50 0 0 0.2 0.4 0.6 0.8 Depth (mm) Figure 4.16 Solution calibration curve slopes after evaporation using K 2PO 4 solution. 350 340 330 320 Initial (26 L) 310 1st Evap. (24 L) 300 2nd Evap. (22 L) Conducitivty (µS) Conducitivty 290 3rd Evap. (20 L) 280 4th Evap. (18 L) 270 0 0.2 0.4 0.6 0.8 Depth (mm) Figure 4.17 Two sets of conductivities from Figure 4.16. This conductivity drift was further reduced using the DI refill method, and this time the combination of the two methods proved to minimize the conductivity changes, as seen in Figures 4.18 and 4.19. 55 600 500 Initial Pre -Evap. (26 L) 400 Pre 1st Refill (24 L) 300 Post 1st Refill (26 L) Pre 2nd Refill (24 L) 200 Conductivity (µS) Post 2nd Refill (26 L) 100 Pre 3rd Refill (24 L) 0 26L Post 3rd Refill (26 L) 0 0.2 0.4 0.6 0.8 Depth (mm) Figure 4.18 Solution calibration curve slopes before and after DI refills in K 2PO 4 solution. 520 500 Initial Pre -Evap. (26 L) 480 Pre 1st Refill (24 L) 460 Post 1st Refill (26 L) Pre 2nd Refill (24 L) 440 Conductivity (µS) Conductivity Post 2nd Refill (26 L) 420 Pre 3rd Refill (24 L) 400 26L Post 3rd Refill (26 L) 0 0.2 0.4 0.6 0.8 Depth (mm) Figure 4.19 Close up view of two sets of conductivities from Figure 4.18. Each film thickness testing period took about 10 hours to complete and it was determined that although conductivity drift was minimized by increasing the solution conductivity with K 2PO 4 and DI water refills, a slight drift was still present. To further reduce this 56 discrepancy, solution calibration curves were taken at the before and after of each film thickness testing period and averaged. To ensure that the K 2PO 4 solution created a film thickness profile that accurately represented the one created by the algal growth solution, specific gravity and viscosity measurements showed that there was no difference in these physical properties, therefore the K2PO 4 was considered an acceptable substitute. These physical properties were measured using a hydrometer and a viscometer and Table 4.1 shows how these values compared for both solutions as well as RO water at 20 °C. Table 4.1 Comparison of solution specific gravities and viscosities. Growth RO Trial K PO Solution 2 4 Water 1 995 995 995 Specific 2 995 995 995 Gravity 3 995 995 995 1 1.0 1.0 1.0 Viscosity (cP) 2 1.0 1.0 1.0 3 1.0 1.0 1.0 Because the physical properties of the K 2PO 4 solution were similar to RO water, ionic content in the amounts used for film thickness measurements did not have a measureable effect on such properties. A second consideration was ensuring that a ±1 °C fluctuation in temperature did not adversely affect film depth measurements. This was checked by generating solution calibration curves over a range of temperatures as seen in Figure 4.20. From this information it was 57 estimated that a 1 °C change in temperature (as regulated by the Watlow EZ controller) would result in about a 2% change in conductivity. 50 45 40 35 30 52.5 °C 25 20 49.9 °C 15 Conductivity (µS) Conductivity 47.2 °C 10 44.9 °C 5 0 0 0.2 0.4 0.6 0.8 Depth (mm) Figure 4.20 Solution calibration curves at different temperatures. 4.2.4 Data Collection Method for Film Thickness Measurements After all necessary calibration procedures were completed, the parallel wire conductance probe was attached to the AdeptOne robot arm and film thickness measurements were performed in a repeatable manner as outlined with the following steps: First, the AdeptOne robot arm holding the parallel wire conductance probe was brought close to the membrane surface and an Adept V+ program was initiated to traverse the cotton membrane in a pre-defined pattern. Note that the Adept V+ program caused the robot arm to pause at each location of interest on the cotton membrane and only proceeded to the next one when prompted by the user. Next, the Offline Rig pumps were turned on for 1 minute to wet the cotton membrane. 58 The micrometer was used to bring the parallel chromel wires in contact with the wet membrane until electrical contact was established between the two wires. Once electrical contact was made, the micrometer was used to carefully pull the wires away from the cotton membrane, until electrical contact was lost. This was necessary because electrical contact does not occur until the cotton membrane was visibly depressed. Pulling the parallel wires away from the membrane until contact was lost ensured that the cotton membrane surface was not being disturbed. Reducing surface disturbances was necessary for creating a film thickness that accurately represented film depth conditions encountered inside the CRF-II. Once the pumps were turned on, the flow rate was set to the desired value, and the film depth was allowed to develop for 60 seconds. It was repeatedly observed that after the solution was introduced onto the cotton membrane, impedance measurements tended to become less scattered over time, as seen in Figure 4.21. The 60 second time interval was chosen as a safe time beyond which measurements were assumed to be stable. 2500 2000 1500 1000 Impedance (ohm) Impedance 500 0 0 20 40 60 80 100 120 140 160 Time (sec) Figure 4.21 Impedance measurements upon solution flow initiation. 59 For data recording, a 30 second impedance sample was recorded and averaged. The averaged impedance value was used for film depth calculations for the particular location on the membrane. The pumps were then turned off and impedance measurements were taken for 30 seconds. As the flowing film leaves the cotton membrane, impedance measurements were taken for POC determination. Measurements were taken for 30 seconds because after this time interval, the flowing film was considered to be completely gone. Also, waiting for the solution to drain off the cotton membrane eliminates the possibility that solution would “stick” to the chromel wires as they are being pulled away from the cotton membrane in the subsequent location. The chromel wires were pulled away from the cotton membrane and the robot arm was moved to the next location on the membrane using the robot controller. The number of locations was pre-defined by the user in the AdeptOne program. At each location, this procedure of approaching and withdrawing from the membrane and taking samples for the specified amount of time would be repeated. Although a 30 second sample was taken to determine the POC conductivity, further testing was performed to determine which impedance value accurately represented the impedance at POC. An example of such a data obtained is shown in Figure 4.22. The increase in impedance was caused by both a decrease in film thickness between the two probe wires, as well as a decrease in the temperature of the wet cotton membrane. To determine which impedance measurement in Figure 4.22 represented the POC, it was necessary to establish how 60 long it took for the flowing film to disappear from the cotton membrane after the pumps were shut off, as well as how long it took for the membrane surface temperature to drop below 45°C. 14000 12000 10000 8000 6000 Impedance (ohm) Impedance 4000 2000 0 0 5 10 15 20 25 30 35 Time (sec) Figure 4.22 Impedance increased when flow was turned off. The temperature 45 °C was chosen as the cut-off temperature because data in Figure 4.20 showed that conductivity at this temperature was similar to that of a 50 °C environment. The disappearance of flowing film from the cotton membrane was evaluated visually and was found to occur at around 5 seconds after the flow was shut off for all flow rates tested. The surface temperature was measured with an infrared thermometer and was found to decrease to 45 °C at 7 seconds after pump shut off for all tested flow rates. To accommodate for both of these effects, the POC impedance reading consisted of a 2 second average from 6 to 8 seconds after the pumps were shut off. 61 4.2.5 Determination of Testing Conditions Preliminary testing was carried out to determine which flow rates should be evaluated for flowing film thickness measurements. This testing consisted of measuring film thickness at 3 locations down the length off Side 1 of the cotton membrane as seen in Figure 4.23. Location 1 Location 2 Location 3 Location 4 Figure 4.23 Locations evaluated for preliminary film depth measurements on Side 1 (Mielnicki, 2011). Side 2 of the membrane faced the AdeptOne robot and was not investigated during preliminary testing as it was assumed findings would be similar due to the symmetrical nature of the distribution header. Film thickness at each location was evaluated at flow rates ranging from 0.50 to 1.70 GPM, in 0.10 GPM increments. This range was chosen because 1.70 GPM is the upper output limit of the Offline Rig flow system and 0.50 GPM is the lowest flow rate at which an acceptable flowing film was observed as described during the header modification testing. The results of this testing showed that film depth tends to increase from 0.50 to 0.90 GPM, levels off around 1.00 GPM and then increases and levels off again past 1.00 GPM as 62 shown in Figure 4.24. Film depths at flow rates below 1.00 GPM were investigated more thoroughly as it appeared they experienced more variation than film depths beyond 1.00 GPM. Based off these preliminary findings, the following flow rates were chosen for a full investigation of how film depth behaves across the entire cotton membrane with respect to flow rate: 0.50, 0.60, 0.80, 0.90, 1.00, 1.30, 1.50, and 1.70 GPM. 0.60 0.50 0.40 0.30 Location 1 Depth(mm) 0.20 Location 2 Location 3 0.10 0.00 0.40 0.90 1.40 Flow rate (GPM) Figure 4.24 Preliminary flow rate versus film thickness measurements for locations defined in Figure 4.23. The uncertainty in these measurements was low at ± 4.9% and calculated using Equation 4.4. 1 $ $ $ . (4.4) ˯yl O z˯op{ - ˯op - ˯n | Urep was ±0.19 mm and it represents the uncertainty from repetition. It was obtained by calculating the 95 th percentile confidence interval from five film thickness measurements at Location 2 and a flow rate of 1.00 GPM. The flow rate was fluctuated between repetitions to take into account as much variation as possible. U res was ±0.01 mm and it was obtained by 63 determining the minimal increase in thickness that would produce a discernable change in conductance. This was achieved by performing a calibration in increments of 0.01 mm as seen in Figure 4.25. Lastly, u cal was ±0.005 mm and was taken to be the precision of the micrometer with which all solution calibrations were performed. 710 700 690 680 670 660 Conductivity(µS) 650 640 0.98 1 1.02 1.04 1.06 1.08 1.1 1.12 Depth (mm) Figure 4.25 Parallel-wire probe resolution determination. To determine how many film thickness measurements would be necessary to produce an accurate picture of how it behaves across the entire cotton membrane, another preliminary study was performed. This time film depth was measured with respect to its vertical and horizontal positions on the membrane. Ten measurements were taken from Location 1 to 3 (Figure 4.23) for the vertical evaluation and ten measurements were taken from Location 2 to 4 for the horizontal evaluation. The increment of length between evaluated locations was 16.7 mm from Location 1 to 3 and 20 mm from Location 2 to 4. For the horizontal evaluation, only half of the width of the cotton membrane was evaluated because it was assumed that due to 64 the modified header design (Figures 4.8 and 4.9), the film depth profile on the membrane half not measured would be a mirror image of the measured half. As can be seen in Figure 4.26 and 4.27, film thickness variation was much more pronounced in the horizontal measurements, rather the vertical ones. To get a quantitative idea of how much the measurements varied, standard deviation was calculated for all vertical and horizontal measurements. Vertical measurements had a mean of 0.46 mm and a standard deviation of 0.03 mm, whereas horizontal measurements varied by almost a factor of three more with a mean of 0.45 mm and a standard deviation of 0.09 mm. 0.60 0.50 0.40 0.30 Depth(mm) 0.20 0.10 0.00 0 50 100 150 200 Vertical Distance (mm) Figure 4.26 Vertical film thickness variations. Another constraint in performing film thickness measurements was the desire to evaluate one flow rate in one measurement session. The motivation behind this was to minimize error that may have been introduced from Offline Rig start-up and shut-down procedures. To reduce such variation in flow rate measurements, the length interval between locations was increased. Measurement results showed there is less variation between horizontal readings than vertical 65 ones, therefore more flexibility existed in increasing the length interval between vertical measurements. 0.70 0.60 0.50 0.40 0.30 Depth(mm) 0.20 0.10 0.00 0 50 100 150 200 Horizontal Distance (mm) Figure 4.27 Horizontal film thickness variations. Using these results, the measurement grid was decided to be three rows of measurements across the membrane with each row consisting of 15 measurements for each flow rate, as seen in Figure 4.28. This arrangement resulted in 45 measurements per each side of the cotton membrane and therefore a total of 90 measurements for each flow rate evaluated. 66 Figure 4.28 Locations of all measurements per membrane side (Mielnicki, 2011). 4.2.6 Film Thickness Data Film thickness measurements revealed that although a flowing film appears across the entire membrane, its thickness can vary considerably. The data shown in Figure 4.29 indicates that at 1.70 GPM, film thickness is largest in the center and towards the edges of the membrane, and the areas between those are the smallest. At 1.70 GPM, the film went from 0.26 mm at its thinnest depth to beyond 0.50 mm. The trend in thicknesses across the membrane correlates with the flow regime created by the modified header design described in Section 4.2.1. Columns 4 and 12 represent the film thickness right below the inlets on the header, which is also where the flow was throttled to produce more even coverage. Columns 1, 8, and 15 represent the areas of the membrane furthest away from the header inlets, which is where flow was diverted. 67 0.80 0.70 0.60 0.50 0.40 Row 1 0.30 Depth(mm) Row 2 0.20 Row 3 0.10 0.00 0 5 10 15 Column Position Figure 4.29 Film thicknesses across Side 2 of the membrane corresponding to locations outlined in Figure 4.28 at 1.70 GPM. As the solution flow rate decreases, the overall thickness across the membrane decreases as seen in Figure 4.30. At 1.00 GPM, although film thicknesses had a similar range (0.17 and 0.47 mm) as the 1.70 GPM data, the overall trend shows that most of the measured depths have decreased, while the variation across the membrane is similar. 0.80 0.70 0.60 0.50 0.40 Row 1 0.30 Depth(mm) Row 2 0.20 Row 3 0.10 0.00 0 5 10 15 Column Position Figure 4.30 Film thicknesses across Side 2 of the membrane at 1.00 GPM. 68 When the flow rate is reduced, both the overall thickness as well as the variation in thickness across the membrane decrease as can be seen in Figure 4.31. 0.80 0.70 0.60 0.50 0.40 Row 1 0.30 Depth(mm) Row 2 0.20 Row 3 0.10 0.00 0 5 10 15 Column Position Figure 4.31 Film thicknesses across Side 2 of the membrane at 0.50 GPM. At the lowest flow rate evaluated, 0.50 GPM, the distinct variation seen at higher flow rates across the membrane has almost disappeared and overall the thicknesses dropped to the mid 0.20 mm range. A comparison of measured depths for all three flow rates is seen in Figure 4.32. Each point in Figure 4.32 represents the average of the three measurements taken the length of each column. 69 0.80 0.70 0.60 0.50 0.40 1.70 GPM 0.30 Depth(mm) 1.00 GPM 0.20 0.50 GPM 0.10 0.00 0 5 10 15 Column Number Figure 4.32 Comparison of selected flow rates versus film thickness across Side 2 of the membrane. Film thicknesses moving down each column tended to begin with relatively thin measurements at Row 1, which is the inception of the flowing film. At Row 2, the film thickness increased slightly and upon reaching Row 3, the film thickness generally decreased back to the values observed at Row 1. These trends can be seen in Figure 4.33, and as with Figure 4.32, each point is the average of 15 readings taken across each row. Although thickness decreased with a decrease in flow rate as was observed in the data sorted by rows, the variation amongst columns did not change noticeably from higher to lower flow rates. It should also be noted that the trends observed across rows were much more predictable than the ones observed down columns. 70 0.80 0.70 0.60 0.50 0.40 1.70 GPM 0.30 Depth(mm) 1.00 GPM 0.20 0.50 GPM 0.10 0.00 1 1.5 2 2.5 3 Row Number Figure 4.33 Comparison of selected flow rates versus film thickness down Side 2 of the membrane. The trends seen in Figure 4.33 tended to occur in the majority of columns, but some columns exhibited trends where measured thicknesses were larger at the inception of flow rather than at the bottom of the membrane, as seen in Figures 4.34 and 4.35. 0.70 0.60 Column 1 Column 2 0.50 Cloumn 3 0.40 Column 4 Depth(mm) Cloumn 5 0.30 Column 6 Column 7 0.20 1 1.5 2 2.5 3 Cloumn 8 Horzontal Position Figure 4.34 Comparison of flow rate versus film thickness for columns 1 - 8 down Side 2 of the membrane at 1.70 GPM. 71 Figure 4.35 Comparison of flow rate versus film thickness for columns 9-15 down Side 2 of the membrane at 1.70 GPM. For a comprehensive determination of how film depth was affected by the flow rate, all 90 film thickness measurements were averaged for each flow rate and graphed in Figure 4.36. 0.60 0.50 0.40 0.30 Depth(mm) 0.20 0.10 0.00 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 Flow Rate (GPM) Figure 4.36 Average film depth based on 90 measurements at each flow rate. 72 The trend observed in Figure 4.36 is similar to the one produced by preliminary testing as shown in Figure 4.24. However, the preliminary film thickness measurements did not account for the large difference between 0.50 and 0.60 GPM, or for the drastic increase between 1.00 and 1.30 GPM. The data indicated in Figure 4.36, that the film thickness ranged from 0.18 mm at 0.50 GPM to 0.49 mm at 1.30 GPM. Besides the dip in film thickness observed at 0.90 GPM, the final data agreed well with preliminary testing. The empirical film thickness equation developed by Karapantsios (1995) and supported by Takahama and Kato (1980) predicted values that were lower than the ones obtained experimentally with the Offline Rig as seen in Figure 4.37. This discrepancy might be due to several factors such as surface roughness, distribution header design, and inaccurate parallel wire conductance probe readings. It is important to note that only smooth surfaces were used for film thickness measurements by other researchers to present the least disturbance to flow. Reynolds Number 157 257 357 457 557 657 0.60 0.50 0.40 Exp. 0.30 Karapantsios Depth(mm) 0.20 0.10 0.00 0.40 0.90 1.40 Flow Rate (GPM) Figure 4.37 Graph of empirically modeled versus actual film thickness. 73 This study differed from most of the review literature because the surface used for testing was not smooth. The cotton membrane was weaved with fibers that were ~0.20 mm thick and exhibited a networked pattern as shown in Figure 4.38. The observed surface roughness may have introduced turbulence which increases film thickness. The distribution header itself may have introduced turbulence as well. Previous researchers ensured that flow was introduced onto their surface with as little disturbance as possible (Karapantsios 1989, 1995; Takahama and Kato, 1980). The header was designed for even distribution, but not for smooth inception of flow onto the cotton membrane. Figure 4.38 Close up view of cotton membrane (Mielnicki, 2011). It was assumed that all measured conductivity was due to the flow between the length of the wires and flow on the other side of the permeable cotton membrane did not result in much additional impedance. In literature, the probe was usually threaded through a pipe where annular film thickness around the inside of the pipe was measured. This arrangement resulted in the tips of the wires never coming into contact with the liquid. In the Offline Rig, the probe wires were pressed against the surface of the cotton membrane. The membrane was a permeable surface that absorbed solution, so there was a chance that the additional surface area of the tips of the wires combined with flow on the other side of the membrane contributed to a greater 74 than actual conductivity. Because electricity takes the path of least resistance and it was shown that POC conductivity of the wet membrane was lesser than that of the K 2PO 4 solution (Section 4.2.3), this effect was considered negligible for the purposes of this study. The combination of such effects may also have contributed to thinner thicknesses at higher flow rates. The expectation was that the film thickness should steadily increase with flow, but 0.90 GPM and flow rate beyond 1.30 GPM the measured thicknesses contrast this theory. It is possible that the velocity of the falling film increased, therefore generating a thinner film. The reasons for fluctuation in velocity stem directly from the same reasons for variation in film thickness. 4.3 Experimental Mass Transfer Experimental mass transfer curves were generated via data collected from the CRF-II and a TOC analyzer. A constant gaseous CO 2 atmosphere was maintained within the CRF-II, while the TOC analyzer sampled the circulating growth solution over time until TIC saturation was reached. Parameters that varied between trials were gaseous CO 2 concentration and growth solution flow rate. The data was used to calculate experimental liquid side mass transfer coefficients (k L exp ) values for comparison with k L values predicted by mass transfer models. 4.3.1 CRF-II Modifications Before the CRF-II could be used for CO 2 absorption data collection, several modifications were required. These modifications were done to allow for direct comparison with the mass transfer models in literature and account for changes applied during film thickness measurements. The critical falling film mass transfer model assumption is that all CO 2 absorption takes place over the area where the flowing film falls. This conflicts with the conventional operation of 75 the CRF-II, because the flow path exposed the solution to gaseous CO 2 in several other locations, namely while pooling at the bottom of the reaction chamber before draining back into the holding tank. Other important surface areas of exposure included the space inside the distribution header and within the piping connecting the reaction chamber to the holding tank. After modification of the experimental set-up, the falling film area consisted almost exclusively of the cotton membrane surface. The unnecessary surface area created by the distribution headers was reduced by using only one of the three CRF-II cotton membranes. To prevent solution from pooling at the bottom of the reaction chamber, a drainage trough was constructed as seen in Figure 4.39. Membrane placed in between splash guards Splash guards Trough drains directly to holding tank piping Figure 4.39 Front and side view of drainage trough (Mielnicki, 2011). The drainage trough was placed underneath the membrane and routed the solution directly from the membrane into the drainage plumbing. The splash guards ensured solution was not lost as it fell from the membrane and onto the trough. To maintain the same film thickness coverage area observed during film thickness measurements, the same modified distribution header and inlet configuration described in Section 4.2.1 was used. This set-up limited the mass 76 transfer area to both sides of one cotton membrane which had an effective surface area of 3273 cm 2. The diaphragm pump used for circulating the solution through the CRF-II introduced fluctuations in flow rate readings. This instability was more pronounced at lower flow rates and could vary as much as ±1.0 GPM. To reduce this source of error, a surge suppressor was integrated on the discharge end of the diaphragm pump as seen in Figure 4.40. Single CRF-II Flow of Growth Membrane Solution TOC Analyzer Flow Holding Tank Air Re -circulation Air to Drainage Surge Pump Diaphragm Trough Suppressor Pump Figure 4.40 Schematic of CRF-II flow and sampling modifications (Mielnicki, 2011). The surge suppressor acted as a shock absorber by having the solution pass through a chamber where an air filled pouch absorbs flow pulsations created by the diaphragm pump. Although only one membrane was being used for experimentation, all three flow lines remained in operation. Instead of connecting to distribution headers, the unused lines were re-routed back into the holding tank. Maintaining flow in all three lines further contributed to a reduction in 77 flow rate fluctuation. Both flow modifications resulted in a flow rate accuracy of ±0.05 GPM, which was on par with the Offline Rig flow system. The TOC analyzer did not have the sensitivity to accurately measure the differential in TIC between fluid sampled at the top and bottom of the membrane, so it was integrated with the holding tank and assumed that TIC concentration was uniform throughout the CRF-II at any given time. To ensure this assumption could be safely applied, it was necessary to keep the holding tank well mixed. Mixing and TIC sampling was achieved by integrating the TOC analyzer and holding tank with a re-circulation pump, as shown in Figure 4.40. The recirculation pump was a 1/8 hp centrifugal pump that drew solution from the bottom of the holding tank and discharged into the top at a flow rate of about 10 GPM. 4.3.2 Data Collection Method for Experimental Mass Transfer Once the modified distribution header, cotton membrane, and drainage trough were installed, the CRF-II was sealed with the CRF-II cover. The data collection method for each CO 2 absorption experiment is outlined in the following steps: First, the fin strip heater and blower were turned on and the gaseous temperature was set to 50 °C using a Watlow temperature controller. Next the light panels were turned on. This step was implemented to simulate conventional CRF-II usage as well as assist in gas phase heating. The NOVA gas analyzer was turned on and before connecting it to the CRF-II, room air was sampled. If it read 0.0% CO 2, the CO 2 sensor was assumed to work properly. The CO 2 cylinder was opened and the CO 2 concentration was set to the desired level. The reaction chamber was separated from the holding tank with a gate valve which remained closed to prevent the CO 2 gas from contacting the growth solution. For trials not requiring elevated levels of CO 2, this step was skipped. 78 The holding tank was filled with 16 gallons of growth solution and heated to 50 °C using a 1000 W immersion heater. A valve located at the bottom of the holding tank remained closed during filling and ensured the growth solution volume was 16 gallons for each trial. Once the desired temperatures and CO 2 concentration have been reached, the re-circulation pump was turned on and the gate valve above the holding tank is opened. Next the TOC analyzer sequence was initiated, and the first TIC concentration was taken up. It was assumed that the time between the opening of the gate valve and TOC analyzer sequence initiation did not result in any measureable CO 2 absorption. As the TOC analyzer takes up the first sample, the diaphragm pump was turned on by setting a pressure regulator to 70 psi and flow rate was set to the desired level. About 5 seconds separate TOC analyzer sequence initiation and diaphragm pump commencement, but the difference was considered negligible and they were assumed to begin simultaneously. This assumption implied that the first TIC reading is the initial concentration and subsequent ones accurately represent increases in concentration during TIC sampling intervals. The TOC analyzer measured TIC concentration every ~6 minutes until the dissolved TIC saturation concentration was reached. Saturation was considered to be reached after TIC measurements stopped increasing and fluctuated around a maximum due to instrument error. This usually occurred after the highest measured concentration was followed by three consecutive measurements with concentrations within ±0.10 ppm of this maximum, as seen in Figure 4.41. The average of the last four concentrations measured was considered to be the TIC saturation concentration. Shutdown began with turning off flow rate and the holding tank immersion heater and draining growth solution. Next, the holding tank was filled with 8 gallons of RO water and the CRF-II was purged of TIC-saturated growth solution. The RO purge water was subsequently 79 drained. Such a procedure of heating the liquid and gaseous phases and sampling TIC content until saturation was reached was repeated for all pre-defined CO 2 concentrations and flow rates. 35 30 25 20 15 10 TIC Concentration TIC (ppm) 5 0 0 20 40 60 80 100 Time (min.) Figure 4.41 TIC concentration versus time. 4.3.3 Testing Conditions All experimental CO 2 absorption tests took place at 50 °C and at CO 2 mole fractions of 10.0%, 2.0% and ambient (approximately 400 ppm). 10.0% CO 2 was chosen because it is similar to the CO 2 content of flue gases from coal-fired power plants. A CO 2 concentration of 2% was chosen to help determine how mass transfer is affected by CO 2 concentration. 2.0% CO 2 was chosen as it was the lowest concentration that could be reliably measured by the NOVA gas analyzer. Ambient CO 2 levels were evaluated as a control, where an increase in TIC concentration was not expected. The flow rates evaluated were 0.50, 0.60, 0.80, 0.90, 1.00, 1.30, 1.50, and 1.70 GPM, which produced film depths of interest as determined during film thickness measurements with the Offline Rig. 80 The NOVA gas analyzer was calibrated with a 10.0 ± 0.2% CO 2 calibration gas before testing and was checked weekly. Preliminary testing showed that the growth solution saturated at ~30.0 ppm TIC when using 10.0% CO 2, ~10.0 ppm TIC for 2.0% CO 2, and ~4.0 ppm when using ambient air. The range of saturation concentrations required the TOC analyzer be calibrated for the appropriate ranges. For 10.0% CO 2, the TOC calibration range was from 0 to 100 ppm TIC. For 2.0% CO 2 and ambient CO 2 levels, the calibration range was lowered to 0 to 20 ppm. The calibration range was dictated by internal mechanics of the TOC analyzer. Uncertainty in TIC concentration data was again calculated using Equation 4.4. For testing involving 10.0% CO 2, the uncertainty was ±2.5% and increased to ±5.5% for 2.0% CO 2. Five RO water samples assumed to have a constant TIC concentration were used to calculate a urep of ±1.1% for all tests. U cal was related from the calibration gas used for the NOVA gas analyzer, which was accurate to within ±2.0% and applied to both 10.0% and 2.0% CO 2 tests. U res was related to the resolution of the NOVA gas analyzer, which produced readings that could be discerned to within ±0.1% of the gas phase CO 2 concentration. This resulted in a u res of ±1.0% at 10.0% CO 2 and a u res of ±5.0% at 2.0% CO 2. For ambient conditions, the NOVA gas analyzer could not produce reliable readings so the uncertainty for these trials was ±1.1% and stemmed exclusively from u rep . 4.3.4 CO 2 Mass Transfer Data With 10.0% CO 2 and a maximum growth solution flow rate of 1.70 GPM, TIC saturation concentration required about 1.5 hours to reach and stabilized around 30.0 ppm as can be seen by the data shown in Figure 4.42. Tests with lower flow rates tended to require about the same time to reach saturation and generally did not increase beyond 30.0 ppm of TIC. However, the incremental increases in TIC concentrations were different. From Figure 4.42, it can be observed 81 that the change in TIC concentration from 0 to 6 minutes at 1.00 GPM is larger than that of 0.50 GPM. This would imply that the k L value increased with flow rate, but no conclusions were drawn until the k L values were calculated. 35 30 25 20 1.7 GPM 15 1.0 GPM 10 0.5 GPM TIC Concentration TIC (ppm) 5 0 0 20 40 60 80 100 Time (min.) Figure 4.42 Flow rate effect on CO 2 absorption at a 10.0% CO 2 gas phase concentration. For all flow rates, the initial TIC concentration of the growth solution ranged between 3.0 to 5.0 ppm and was accounted for when performing k L calculations. At 2.0% CO 2, a 9.0 ppm TIC saturation concentration was observed, which took almost 2 hours to reach. This is shown by the data presented in Figure 4.43. 82 12 10 8 1.70 GPM 6 1.00 GPM 4 0.50 GPM TIC Concentration TIC (ppm) 2 0 0 50 100 150 Time (min) Figure 4.43 Effect of flow rate on CO 2 absorption at a 2.0% CO 2 gas phase concentration. The ± 5.5% uncertainty made preliminary conclusions about the variation of kL with flow rate challenging, as was done with the 10.0% CO 2 data. Although these tests were conducted for a greater time duration than at 10.0% CO 2, it should be noted that the extra time was spent to attain saturation. This implied that the difference in trial length between the 10.0% and 2.0% CO 2 may be due to instrument error. Solubility theory dictates that at lower CO 2 partial pressures, the TIC saturation concentration should be lower, which is supported by the data. The TIC saturation concentration of ~30.0 ppm and ~9.0 ppm for 10.0% and 2.0% CO 2 respectively also agrees with predicted values generated using advanced solubility models being currently developed (Dasaard, 2011). Testing conducted with an ambient concentration of CO 2 resulted in no overall absorption of CO 2, as seen in Figure 4.44. For every flow rate evaluated, a pattern emerged where the TIC concentration increased between 0 and 5 minutes and then slowly headed back to its original concentration. It was thought that the initial concentration may not necessarily 83 represent the TIC saturation concentration at ambient CO 2 levels and exposure of growth solution to ambient CO 2 as a thin flowing film allowed it to reach its true saturation level. This would explain the initial increase in TIC concentration. The eventual decrease may have been due to mechanical mixing of the growth solution producing a slight degasification effect. Due to a lack of observed CO 2 mass transfer, only the flow rates shown in Figure 4.44 were tested at ambient CO 2 conditions. 5.0 4.5 4.0 3.5 3.0 1.70 GPM 2.5 2.0 1.00 GPM 1.5 0.50 GPM 1.0 TIC Concentration TIC (ppm) 0.5 0.0 0 10 20 30 40 50 Time (min) Figure 4.44 Effect of flow rate on CO 2 absorption at an ambient CO 2 gas phase concentration. 4.4 Mass Transfer Model Evaluation Once data for experimental CO 2 mass transfer rates was gathered, a mathematical treatment was applied to obtain the kL exp values, which were then plotted for comparison with kL values predicted from literature, as described in Chapter 2. The model that best represented the experimental mass transfer coefficients was further optimized to reduce error. 84 4.4.1 Experimental Liquid Side Mass Transfer Coefficient (k L exp ) All evaluated falling film mass transfer models either predict for kL, or can be easily manipulated to yield this parameter. To obtain an experimental liquid side mass transfer coefficient for comparison, an overall mass balance along with the CO 2 absorption data and several assumptions were utilized. A series of equivalent mass balances that relate the concentration in the holding tank to Fick’s Law is seen in Equation 4.5: ~ (4.5) ˭ ˢ ˕# . ˕" ˫!cp{ ˓˕ . ˕ where m is the mass transfer rate, V is the tank volume, C tank is CO 2 concentration in the holding tank, t is time, γ is the volumetric flow rate, C 0 is CO 2 concentration before the membrane, C 1 is CO 2 concentration after the membrane, C sat is the saturation concentration of CO 2 at the film’s surface and C bulk is the average CO 2 concentration in the bulk of the film. Figure 4.45 graphically represents the mass transfer process. Membrane Expanded View of Membrane (1 side) C0 Csat Holding Tank (dC tank /dt) Cbulk Direction of Flow C1 ν Figure 4.45 Three CO 2 mass balances at different points in the CRF-II (Mielnicki, 2011). 85 The TOC analyzer was not able to detect concentration changes between the top and bottom of the membrane, therefore at any given time the concentration present in the tank was assumed to be approximately equivalent to all other concentrations within the CRF-II (besides the saturation concentration), as shown in Equation 4.6. Ctank ≈C 1≈C 0≈C bulk (4.6) As the mass balance around the membrane could not be evaluated, an approximate mass balance was used that relates Fick’s Law directly to the changes in concentration observed over time in the tank, as shown in Equation 4.7 . ~ (4.7) ˢ ˫!cp{ ˓˕ . ˕m Rearrangement, integration and simplification of this relationship yields Equation 4.8 c= ~ $~cő~ $ (4.8) ˥ ~ $~ where dt was integrated from 0 to t and C initial is the initial CO 2 concentration in the holding tank. An exponential regression was then applied to Equation 4.8 yielding the relationship seen in Figure 4.46. The -0.067 exponential value in Figure 4.46 represented c= so membrane . area and holding tank volume were factored out to obtain kL exp . 86 1.2 1.0 ) initial -C 0.8 -0.067t sat y = e )/(C 0.6 R² = 0.9964 tank@t 0.4 -C sat (C 0.2 0.0 0 5 10 15 20 25 Time (min.) Figure 4.46 TIC concentration data at 10.0% gaseous CO 2 and 1.70 GPM. Although TIC concentration data was measured until saturation was achieved, the regressions were performed using concentration data that represented 80% of the concentration change between C initial and C sat . This is illustrated in Figure 4.47. Using only the initial concentration data yield much higher R 2 values than when all the data was used for regression analysis. 87 35 30 80% of change 25 between 3.6 and 30.6 ppm 20 reached at 23 15 minutes 10 TIC Concentration TIC (ppm) 5 Data range 0 used for regression 0 20 40 60 80 100 Time (min.) Figure 4.47 CO 2 absorption data at 10.0% gaseous CO 2 and 1.70 GPM. Uncertainties in the kL exp value were ±4.4% and ±12.1% for a 10.0% and 2.0% gaseous CO 2 atmosphere respectively and were again calculated using Equation 4.4. For a 10.0% gaseous th CO 2 environment, u rep was ±3.8% and was obtained by calculating the 95 percentile confidence interval for five kL exp values from CO 2 absorption data gathered at 1.00 GPM. The u rep increased to ±10.9% for the 2.0% CO 2 atmosphere and was determined in the same way. U cal and u res were not gathered directly so instead the values used for uncertainty calculations in the TIC concentration data were again assumed. The kL exp values increased with flow rate for the 10.0% gaseous atmosphere, and the 2.0% CO 2 data tended to follow a similar trend, although the larger error made it more difficult to make the same observation as seen in Figure 4.48. The error in the 2.0% CO 2 data caused the kL exp values to overlap which suggests that gaseous CO 2 concentration did not affect k L exp under these testing conditions. Because the two sets of data are indistinguishable, all subsequent 88 discussion focuses on the trends observed with the 10.0% CO 2 data. The range of flow rates evaluated corresponded to a range of Re numbers from 197 to 670. Reynolds Number 157 257 357 457 557 657 0.025 0.020 0.015 2%CO2 (cm/s) 10%CO2 0.010 L exp L k 0.005 0.000 0.40 0.90 1.40 Flow Rate (GPM) Figure 4.48 Experimental liquid side mass transfer coefficients. The Re range coincided with a wavy laminar flow regime from 197 to 300 (0.50 to 0.90 GPM) and with a transitional flow regime from 300 to 670 (0.90 and 1.7 GPM) as defined in Section 2.1.1. The k L exp values remained somewhat constant from 0.50 to 0.80 GPM at ~0.014 cm/s. From 0.90 to 1.30 GPM, k L exp increased and reached a maximum of ~ 0.021 cm/s. The increase in kL exp after 0.90 GPM coincides with the falling film flow regime changing from wavy laminar to transitional flow, which begins at a Re of 300. After 1.30 GPM, k L exp stabilized again, this time around the maximum k L exp value reached at 1.30 GPM. The general trend in k L exp versus flow rate was similar to the one observed in film thickness versus flow rate as seen in Figure 4.36. 89 4.4.2 k L exp Comparison with Mass Transfer Models Uncertainty for all k L values calculated with falling film mass transfer models was completed using a propagation of error method that utilized partial derivatives and parameter uncertainty. Assuming a generic mass transfer model where k L=f(x,y,z…), the propagation of error equation would be described with Equation 4.9: ! $ ! $ ! $ (4.9) 8 ˯E2 Ә ˯ә -Ә ˯ә -Ә ˯ә - where ux, u y, and u z are known uncertainties in parameters x, y, and z, and u kL is the calculated the uncertainty in kL. For each mass transfer model evaluated, parameters x, y, and z were replaced with their respective physical properties (density, viscosity, Schmidt number, etc.). The value for density, viscosity, surface tension, and gravity were all procured from literature at 50 °C and assumed to have an uncertainty of ±1.0%. Measurements of length and area had an uncertainty of ±1/8” and the flow rate had an uncertainty of ±0.05 GPM. The diffusivity coefficient was calculated using Equation 2.3 as described in Section 2.1.2. The diffusivity coefficient was determined for a CO 2-H2O system and assumed valid for use with the growth solution. The uncertainty in intermediate parameters for k L calculation such as Sc, Re, etc. was determined using the propagation of error method as well and all model uncertainty was evaluated at 1.00 GPM. Fick’s law (Seader, 2006)serves as the most basic interpretation of k L, where it consists of dividing the diffusivity coefficient with film thickness. The model was not considered to accurately predict k L values for the experimental conditions. However, it was evaluated to confirm this assumption. The comparison of predicted and measured k L values is shown in Figure 4.49. While the calculated Fick k L values had an uncertainty of ±5.0%, the data indicates that FIck’s law under-predicted k L by about an order of magnitude. 90 0.030 0.025 0.020 0.015 Exp. (10% CO2) kL (cm/s) kL 0.010 Fick 0.005 0.000 0.40 0.90 1.40 Flow rate (GPM) Figure 4.49 Fick k L values compared with k L exp . The Fick k L values reached a maximum with 0.0013 cm/s at the slowest flow rate, 0.50 GPM and decreased to 0.00077 cm/s at 1.70 GPM. The Fick relationship was an inverse function of film thickness, so as flow rate increase, the trend in kL was the opposite of what was observed with film thickness in Figure 4.36. Koziol models (1980), described in Section 2.1.3, for both laminar and transitional flow were evaluated and had respective uncertainties of ±5.6% and ±5.3%. The two flow regimes were divided at 0.90 GPM with the transitional model having a greater rate of change in k L, as seen in Figure 4.50. Both the laminar and transitional Koziol k L values increased with increasing flow rates, and went from a minimum of 0.020 cm/s to a maximum of 0.028 cm/s. The Koziol models over-predicted the k L by about 50% and did not exhibit the same trend observed in the kL exp data. 91 0.030 0.025 0.020 Exp. (10% CO2) 0.015 Koziol Lam. kL (cm/s) kL 0.010 Koziol Trans. 0.005 0.000 0.40 0.90 1.40 Flow rate (GPM) Figure 4.50 Koziol k L values compared with k L exp . The Henstock and Hanratty model (1979), as described in Section 2.1.3, produced k L values that were within the same range as k L exp , but again, the overall trend did not mimic the experimental data as seen in Figure 4.51. 0.030 0.025 0.020 Exp. (10% CO2) 0.015 Henstock and kL (cm/s) kL 0.010 Hanratty 0.005 0.000 0.40 0.90 1.40 Flow rate (GPM) Figure 4.51 Henstock and Hanratty k L values compared with k L exp . 92 Henstock and Hanratty’s model had an uncertainty of ±6.8% and exhibited a trend where k L values would alternate between high and low as the flow rate increased. Although the model fluctuated, overall, k L increased with flow rate. The maximum k L value of 0.024 cm/s was reached at the fastest flow rate, whereas the minimum did not coincide with the slowest flow rate and instead occurred at 0.60 GPM with a value of 0.014 cm/s. As with Koziol, two Yih and Chen models (1982), as described in Section 2.1.3, were evaluated. The first model was governed by laminar flow and the other was used for a transitional regime which again began at 0.90 GPM. The results of the comparisons of k L are seen in Figure 4.52. 0.030 0.025 0.020 Exp. (10% CO2) 0.015 Yih and Chen Lam. kL (cm/s) kL Yih and Chen 0.010 Trans. 0.005 0.000 0.40 0.90 1.40 Flow rate (GPM) Figure 4.52 Yih and Chen k L values compared with k L exp . The laminar Yih and Chen model exhibited a greater slope than the transitional model and both models had relatively low uncertainties of ±2.5% and ±1.8% respectively. Both models predicted 93 higher k L values at higher flow rates and went from a minimum of 0.013 cm/s to a maximum of 0.017 cm/s. The laminar Yih and Chen model coincided better with the respective experimental data whereas the transitional model slightly under-predicted k L. The overall trend was similar to the Koziol models. The Banerjee model (1967), as described in Section 2.1.2, had an uncertainty of ±4.1% and predicted that k L values were on average within 10% of the k L exp values. The comparison is plotted graphically in Figure 4.53. The model results displayed a trend similar to the one observed in Koziol and Yih and Chen where an increase in flow rate resulted in an increase in k L. The minimum k L coincided with the k L exp at .015 cm/s as did the maximum with a k L value of .021 cm/s. With an average percent difference of 10%, the k L values were very close to the experimental ones, but again the overall trend did not match what was observed in the experimental data. 0.030 0.025 0.020 Exp. (10% 0.015 CO2) Banerjee kL (cm/s) kL 0.010 0.005 0.000 0.40 0.90 1.40 Flow rate (GPM) Figure 4.53 Banerjee k L values compared with k L exp . 94 The Davies model (1969), described in Section 2.1.2, yielded k L values that approximated the experimental kL values very well and displayed a trend that best represented the one observed in the experimental data. The comparison is graphically illustrated in Figure 4.54. The Davies model had an uncertainty of 3.9% and a minimum k L value of 0.10 cm/s at 0.50 GPM. It reached a maximum of 0.21 cm/s at 1.30GPM. As with the k L exp values, the Davies k L values were stable from 0.60 to 0.90 GPM and began increasing after 0.90 GPM. Both the model and k L exp reached a maximum at about 1.30 GPM and stayed close to the value as flow rate increased to 1.70 GPM. Slight discrepancies occurred at 0.50 and 0.90 GPM, where the Davies model under- predicted k L, but overall it still had a low average percent difference of 10%. 0.030 0.025 0.020 Exp. (10% CO2) Davies 0.015 kL (cm/s) kL Modified 0.010 Davies 0.005 0.000 0.40 0.90 1.40 Flow rate (GPM) Figure 4.54 Davies k L values compared with k L exp . The combination of a similar trend and k L values that were within the k L exp range is why the Davies model was considered to be the best model for predicting k L values in the CRF-II. The Davies model coefficient was set arbitrarily by the authors to match empirical data, so a percent 95 difference minimization was undertaken with the experimental data of this work. The result was a modification of the Davies model as represented by Equation 4.10 and is graphed in Figure 4.52. "'' "'&' "'&' "'' $"'' (4.10) ˫! ŵ'Żŵ ( ˖ ˤ ˧ F G Note that exponents in the Davies model were theoretically derived and therefore not manipulated for this optimization. Comparing all models simultaneously shows that the k L exp values are bounded by all the models evaluated as seen graphically in Figure 4.55. 0.030 Exp. (10% CO2) 0.025 Yih and Chen Lam. Koziol Lam. 0.020 Yih and Chen 0.015 Trans. Davies kL (cm/s) kL 0.010 Koziol Trans. Henstock and 0.005 Hanratty Fick 0.000 0.40 0.90 1.40 Banerjee Flow rate (GPM) Figure 4.55 All calculated and experimental k L values. The fact that k L exp values lay between k L values predicted by several previous researchers provides a small sense of assurance that the experimental data may be valid. From this perspective, it is also clearer to see that the Davies model is a better fit for the experimental data than any of the other models evaluated. 96 Chapter 5 - Conclusions 5.1 Review of Study The goal of this study was to model CO 2 mass transfer in a novel photobioreactor as a function of gaseous CO 2 concentration and solution flow rate. Experimental liquid side mass transfer coefficients (k L exp ) were determined from CO 2 absorption curves generated with the CRF-II and compared to k L values predicted by falling film mass transfer models. Average film thickness was an input parameter to many mass transfer models, so an Offline Rig was constructed to help quantify film thickness values with respect to flow rate at 50 °C. After a comparison of all predicted k L values with the experimental values, the Davies model appeared to be the best fit for the experimental data. The Davies coefficient was adjusted for an optimized fit. 5.2 Effect of Flow Rate on Film Thickness and Mass Transfer With respect to flow rate, CO 2 absorption curves produced two zones of stability from 0.50 to 0.80 GPM and from 1.30 to 1.70 GPM where the liquid side mass transfer coefficient was around 0.014 and 0.020 cm/s respectively as seen in Figure 4.48. The two stable regions were connected via a transitional region where k L exp increased abruptly at 0.90 GPM with highest kL exp being 0.021 cm/s observed at 1.30 GPM. This shows that as the falling film experiences more turbulence, mass transfer coefficients increase, which is a trend supported by the mass transfer models reviewed. The calculated Reynolds number at 0.90 GPM was 354 and the flow regimes transition from wavy laminar to transitional flow at around this value which according to Koziol and Yih and Chen should result in a decreased mass transfer rate rather the increased one that was observed. Because the experimental mass transfer coefficients were within the bounds of the 97 models found in literature and increased with increasing Re, confidence in the experimental results is warranted. The empirical equations presented by Koziol and Yih and Chen, were least squares fits to their collected data and therefore obscure what occurred between individual data points. The exact same phenomena of a decreasing k L rate at the inception of a transitional flow regime may not have always occurred, which is the case with the results of this study. The modified theoretical Davies model was the best fit for k L exp data. This was expected because the model was a function of film thickness, which followed the same trend as k L exp . As with k L exp , film thickness experienced similar regions of stability with respect to flow rate, separated again by an increase around 0.90 GPM. The resulting adjusted Davies model can predict k L values that have only a ±10% difference from the true value. The implications of this study are that a desired mass transfer rate can be achieved by setting the flow rate to an appropriate corresponding value and growth solution pump usage can be therefore optimized. Because the ultimate mass transfer rate will be dictated by the inorganic carbon uptake rate of the algal species cultivated within the CRF-II, knowing the approximate mass transfer rate assures that the microorganism’s growth rate will not be limited by the rate of CO 2 absorption from the flue gas into the growth solution. Further, setting the flow rate to the appropriate value ensures that the pump does not circulate growth solution faster than necessary. Such an optimal pump usage results in lower power consumption and maintenance costs associated with pump operation. The regions of mass transfer stability also contribute to efficient pump usage by showing that mass transfer rates are somewhat independent of flow rate below 0.90 GPM and above 1.30 GPM. 98 5.2 Effect of CO 2 Concentration on Mass Transfer The large error associated with the 2.0% CO 2 data caused it to overlap with the 10.0% CO 2 data and therefore the two sets were considered indistinguishable. This leads to the likely conclusion that liquid side mass transfer coefficients are independent of gaseous CO 2 concentration between 2.0% and 10.0% CO 2. Therefore, at gaseous CO 2 concentrations as low as 2.0%, mass transfer is dominated by CO 2 diffusion into the liquid growth solution and gaseous diffusion effects are therefore not limiting in comparison. The theoretical mass transfer models support this conclusion by their lack of model parameters that account for a gas phase concentration of the species being absorbed. The empirical models were obtained from data gathered at 100% gaseous CO 2 conditions so the fact that the k L exp data collected in this study is bounded by such models indicates that the models are just as applicable at lower CO 2 concentrations. Although k L is unaffected by CO 2 concentration, the mass transfer rate is affected, as seen in Equation 2.2. The mass transfer rate is a function of the CO 2 saturation concentration in the growth solution which is dependent upon the partial pressure of CO 2 in the gaseous phase. According to Henry’s Law, higher gaseous partial pressures result in higher liquid mole fractions. This phenomenon was observed during the study because growth solution in the 2.0% gaseous environment saturated at ~9.0 ppm, and the 10.0% CO2 atmosphere yielded a ~30.0 ppm saturation concentration. Mass transfer is a direct function of saturation concentration, so a threefold increase as seen in the 2.0% and 10.0% data would result in a threefold increase in mass transfer as well. Therefore, mass transfer rates can be controlled via the gas phase CO 2 concentration. Again, the desired mass transfer rate will be dictated by the algal species being cultured. 99 Although a ~10.0% CO 2 flue gas stream would be available in industry, the gas would have to be processed before entering the CRF-II to ensure it will not destroy the algal species. Knowing the minimum gas phase CO 2 concentration necessary for optimal algal growth would also reduce operational costs associated with CRF-II operation. 100 Chapter 6 - Recommendations 6.1 Recommendations Overview Although the study achieved all three of its objectives, in retrospect, measures could have been taken to reduce uncertainty as well yield even more useable data. A review of what steps should be taken in the future to maximize the use of this study’s results will also be reviewed. 6.1.1 Improvement of Study After a complete picture was generated of how film thickness behaves with respect to flow rate, it was apparent that the preliminary film thickness studies were not enough information for basing off which flow rates to investigate. As seen in Figure 4.36, there is a large increase in film thickness between 1.00 and 1.30 GPM which was not visible in the preliminary data seen in Figure 4.24. Flow rates at the higher end of the flow meter range may be too abrasive for algal species to adhere to the cotton membrane, so it would be worthwhile to investigate film thickness as well as k L exp between 1.00 and 1.30 GPM. This would elucidate whether 1.30 GPM is indeed the highest film thickness/mass transfer coefficient as well if the region of stability occurring beyond 1.30 GPM extends towards lower flow rates. The major drawback of using the Offline Rig was evaporation of growth solution. Although the problem was circumvented with a highly conducive solution, the ideal scenario would utilize growth solution. A way of addressing this problem would be to maintain the growth solution as well as the air around it at the same temperature in an enclosed chamber, much like the CRF-II set up. Theoretically, once the air saturates with growth solution, no more evaporation should occur and film thickness testing could begin. Ideally, an enclosure could be built to surround the cotton membrane and distribution header, as well as allow for the robot 101 arm to make contact with the membrane and traverse it. The integration of the enclosure with the robot arm could be done via rubber gaskets that accommodate motion. It was assumed that the flow on the other side of the membrane being measured did not result in noticeable additional conductivity between the two wires of the conductance probe. Although the wire tips are pressed against the cotton membrane where conductivity is relatively low with respect to when flow is initiated, an investigation could ensure that ignoring the effect of double sided flow on a permeable membrane was a safe assumption to make. Such a study would require the probe wires be threaded through and flush with a material that is non-permeable and at the same time exhibits the same conductivity as a wet membrane. On the side of the material where the probe wires are flush, a falling film would exist with control over the film thickness, perhaps again via flow rate. Another way of mitigating this problem could have possibly been piercing the cotton membrane with the wires so that the wire tips never make contact with the solution and film thicknesses on both sides of the membrane are measure simultaneously. This would require an evaluation of a suitable replacement for chromel that exhibits the same high conductivity as well as an increased hardness that would allow for the wire to pierce the cotton membrane without deforming. It was also assumed that the cotton membrane surface roughness did not affect film depth or k L exp readings. With an average fiber thickness around 0.02 mm, it is possible that the chromel wires were not the same distance away from the membrane, which could have resulted in inaccurate film thickness measurements. This could have been investigated by attaching a smooth surface to the membrane header and measuring the film thickness. If discrepancies arose, perhaps a correlation for film thickness between a smooth surface and a rough cotton membrane could be developed. For k L exp , a similar approach could have been undertaken and a 102 comparison made as well. Davies (1969) and Koziol and Broniarz (1980) both have performed studies showing surface roughness increases mass transfer, but their results were not applicable to this study because the cotton fibers (or turbulence inducing “ridges”) created a cross- sectional matrix with little space between ridges, whereas the researchers had a uniform surface with ridges space much further apart. Davies cites that the closer the ridges are, the more the rough surface behaves like a smooth one indicating that the increase may be negligible as assumed. Lighting within the CRF-II was thought not to play a role in mass transfer and was kept on for all trials. In actual algal growing conditions, the CRF-II cycles the light between periods of on and off to simulate natural algal growth conditions. Trials could have been conducted with the CRF-II lights off to eliminate the possibility that they affect mass transfer. 6.1.2 Future Work Some of the recommended future work revolves around the use of a much more sensitive gas phase analyzer than the NOVA gas analyzer used in this study. An analyzer that could accurately measure gaseous CO 2 concentration from 0% to 2% should be used to repeat the 2% CO 2 trials performed in this study. Repeating the trial with a more sensitive instrument would lower the ±12.1% uncertainty in k L exp that mainly stemmed from poor repeatability. It also may be the case that the current method of CO 2 injection into the CRF-II does not produce a uniform gaseous composition at low CO 2 concentrations. The proposed gas analyzer would also be capable of detecting this by showing that measurements vary relatively drastically over short periods of time. Studies at concentrations below 2.0% CO 2 should also be conducted. This data would reveal at which concentration, if at all, the gas phase CO 2 concentration has an impact on the 103 liquid side mass transfer coefficient. This would be valuable information in that it would produce a CO 2 concentration which the CRF-II should be operated above to ensure a gas side mass transfer coefficient does not inhibit mass transfer. Such a study may also help explain the discrepancy observed during experiments conducted at ambient CO 2 gas phase concentrations. Another way of increasing mass transfer without manipulating the flow rate or CO 2 gas phase concentration would be to alter the growth solution. A major factor in establishing a solution CO 2 saturation point is pH. In this study, the growth solution had a slightly basic pH between 7.5 and 8.0. Creating a more basic environment via buffers would allow the growth solution to hold more inorganic carbon, which would have the same mass transfer enhancing effects as an increase is gas phase CO 2. An investigation of how temperature affects the liquid side mass transfer coefficient should also take place. A preliminary study of how temperature affects film thickness revealed little fluctuation occurs within ±5 °C of 50 °C, but it is unlikely the same would be observed with kL exp . Temperature affects most of the parameters that the mass transfer models are composed of as well as the CO 2 saturation concentration. At lower temperatures a variety of conflicting affects would occur such as the growth solution being able to absorb more CO 2 to increase mass transfer or a decrease in the diffusivity coefficient which leads to slower mass transfer. At higher temperatures, these phenomena would have the reverse effect. Although the CRF-II is intended to operate at 50 °C, a temperature imposed by an industrial flue gas stream, the temperature most likely will not be exact and therefore knowing how mass transfer is affected by perturbations in temperature would reveal how algal growth will alter. Once the effect of all algal growth conditions on mass transfer has been characterized, the inorganic carbon uptake rate by the algal species itself should be determined. Quantifying 104 the rate at which the microorganism fixes carbon would show whether CRF-II growth conditions are adequate or if they are inhibiting algal growth. If growth inhibition occurs, such information as the mass transfer model developed in this study would indicate whether the appropriate mass transfer rate can be achieved. 105 Symbols A = area AC = cross sectional area C0 = concentration after membrane C1 = concentration before membrane Cbulk = concentration in bulk flow Csat = saturation concentration at film interface Ctank = concentration in tank D = diffusivity coefficient d = film thickness g = gravity H = Henry’s constant He = interfacial eddy approach distance kL = liquid mass transfer coefficient * kL = dimensionless mass transfer coefficient m = mass transfer rate p = partial pressure s = fractional rate of surface renewal t = time tC = eddy contact time te = time between eddies v = average velocity V = volume x = liquid mole fraction = mass flow per unit membrane width µ = dynamic viscosity Ω = electrical impedance γ = volumetric flow rate δ = boundary layer film thickness θ = equivalent dimension ρ = density σ = surface tension = kinematic viscosity _ Ga = Galileo number Re = Reynolds number Sc = Schmidt number Sh = Sherwood number 106 References Ambrosini, W., Forgione, N., & Oriolo, F. 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Chemical Engineering Communication , 17 , 123-136. Zhang, Huying. (2003). Falling liquid film flow. Proposal (Unfinished) (pp. 1-18). ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! Thesis and Dissertation Services ! !