Overall volumetric mass transfer coefficient in solid foam packing

Transcription

1 Eindhoven University of Technology MASTER Overall volumetric mass transfer coefficient in solid foam packing Veltman, A Award date: 2006 ink to publication Disclaimer This document contains a student thesis (bachelor's or master's), as authored by a student at Eindhoven University of Technology. Student theses are made available in the TU/e repository upon obtaining the required degree. The grade received is not published on the document as presented in the repository. The required complexity or quality of research of student theses may vary by program, and the required minimum study period may vary in duration. General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. Users may download and print one copy of any publication from the public portal for the purpose of private study or research. You may not further distribute the material or use it for any profit-making activity or commercial gain

2 Overall Volumetric Mass Transfer Coefficient in Solid Foam Packing A. Veltman April 2006 Graduation report Graduation committee Ir. C.P. Stemmet Dr. ir. J. van der Schaaf Dr. ir. B.F.M. Kuster Prof. dr. ir. J.C. Schouten Ir. J.G. Wijers Direct supervisor Project supervisor Project supervisor Graduation professor External committee member aboratory of Chemical Reactor Engineering Department of Chemical Engineering and Chemistry Eindhoven University of Technology

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4 Summary This report outlines the 7 month graduation project that was performed at the aboratory of Chemical Reactor Engineering. The focus of the graduation project was on the gas-liquid mass transfer coefficient in solid foam. This project is part of the STW funded research project Gas-iquid Solid Foam Reactors: a study of reaction engineering aspects. Solid foam is a new type of structured packing that is currently assessed. Gas-liquid mass transfer is often found to be the rate-limiting step in gas-liquid-solid reactions. Knowledge on the overall volumetric mass transfer coefficient, k a, is therefore essential in the design of a multiphase reactor. The overall volumetric mass transfer coefficient consists of the liquid film coefficient, k, and the specific surface area, a. High values for k a are expected due to the very large specific surface area of solid foam. Mass transfer experiments have been performed by measuring the absorption of carbon dioxide in water. This method was evaluated by also determining the overall volumetric mass transfer coefficient for the absorption of oxygen in water. Mass transfer coefficients were calculated with a dispersed plug flow model with mass transfer. Oxygen mass transfer k a results ranged from 0.15 to 0.22 s -1 for countercurrent low liquid holdup experiments with 10 ppi aluminum foam. The obtained k a values in the current study for trickle flow are significantly higher than values obtained from literature for structured Mellapak packings. The specific surface area of solid foam is significantly higher than for the other types of packing which probably explains the high k a values. Measuring k a with carbon dioxide absorption poses some significant drawbacks. The concentration of carbon dioxide is measured indirectly with ph-sensors and therefore assumed to be in equilibrium with hydronium ions. Chemical reactions are involved in the absorption of carbon dioxide in water that should be taken properly into account in order to calculate k a. Furthermore, the reaction rate constant of the reaction between water and carbon dioxide is known to be slow and needs to be included in the model. The model for carbon dioxide was shown to be incapable of calculating a value for the overall mass transfer coefficient. Axial dispersion, or backmixing, was demonstrated to have an influence on the value of the overall mass transfer coefficient. This was done by a comparison of a mass balance assuming an ideally mixed liquid phase and a mass balance assuming an ideal plug flow liquid phase. An example of oxygen results showed a variation of k a values from 0.15 to 0.41 s -1, for negligible axial dispersion and maximum axial dispersion respectively. It is necessary to evaluate axial dispersion when assessing gas-liquid mass transfer in multiphase reactors. 3

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6 Contents SUMMARY... 3 CONTENTS INTRODUCTION MUTIPHASE REACTORS Flow configurations and flow regimes Types of packings Important reactor design parameters MASS TRANSFER Mass transfer Modeling mass transfer Modeling steady state mass transfer EXPERIMENTA METHOD Experimental setup Dynamic and steady state measurements RESUTS AND DISCUSSION Determining the overall volumetric mass transfer coefficient The influence of dispersion on k a Results for oxygen mass transfer Results for carbon dioxide mass transfer Conclusions FINA CONCUSIONS AND RECOMMENDATIONS NOMENCATURE REFERENCES APPENDIX... I 5

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8 Introduction 1 Introduction Equation Chapter 1 Section 1 Mass transfer between the gas and liquid phase is often the rate-limiting step in multiphase reactors. Generally, mass transfer is enhanced by a reactor packing that increases the interfacial area between two phases. This packing can be dumped in the reactor with random orientation. Another type of packing is structured packing which can fit the reactor dimensions exactly. The trend in the development of packing materials is towards well-defined open structures with a low solid holdup and a high specific surface area. Open reticulated solid foam is a new type of structured packing which is already commercially available. Typically, the solid holdup is low (3%), with a specific surface area up to 4500 m 2 /m 3. This would imply significantly reduced operational and investment costs because reactor volumes can be reduced and pressure drop over the packing is low. The PhD project of C.P. Stemmet is an STW (Dutch Technology Foundation) funded project in which solid foam is investigated as a new type of structured packing. This project is a cooperation between the Eindhoven University of Technology and industrial partners ABB-ummus, Shell Global Solutions, DSM and Engelhard. The objective of the PhD project is to develop a generic design methodology for structured gas-liquid reactors using solid foam as catalyst support for optimum mass transfer and hydrodynamics, enabling intensified chemical processes. The performance of a packing can be quantified by the overall volumetric mass transfer coefficient. The mass transfer coefficient is influenced by parameters such as gas and liquid velocity, gas and liquid holdup, porosity and surface area of the packing, as well as physical properties of the gas and liquid, e.g. viscosity, surface tension and density. The aim of this graduation project is to investigate the overall volumetric mass transfer coefficient in solid foam packing as a function of foam properties and gas-liquid flow conditions. The effect of the surface area on mass transfer will be investigated by using foams with different specific surface areas. Furthermore, flow conditions (gas and liquid flows); and the direction of gas and liquid flow (cocurrent down, co-current up and countercurrent) will be varied. The overall volumetric mass transfer coefficient will be determined from a fit of a plug flow reactor model to the experimentally determined inlet and outlet concentrations of the absorbed gaseous component in the liquid phase. In Section 2 multiphase reactors and important hydrodynamic and mass transfer parameters are discussed, as well as flow configurations and flow regimes. Mass transfer from the gas to the solid surface is explained in Section 3 and a model to characterize mass transfer is introduced. In Section 4 the experimental method and the necessary calculations are shown, preceded by a description of the experimental setup. Experimental and modeled results are given in Section 5. Finally, conclusions will be drawn in Section 6, including recommendations for further research. In the appendices elaborate calculations are shown. Furthermore, a new possibility of experimentally determining the overall mass transfer coefficient with conductivity sensors is demonstrated. 7

9 G G Figure 1. Flow configurations in multiphase reactors. From left to right: co-current up, co-current down and countercurrent gas-liquid flow. G Figure 2. Flow regimes in solid foams for a countercurrent configuration. Two different high liquid holdup regimes (I bubble regime and II pulse regime) as well as one low liquid holdup regime (III trickle regime) can be observed. The flooding point is also indicated. (Stemmet et al. (2005)) 8

10 Multiphase Reactors 2 Multiphase Reactors Equation Chapter (Next) Section 1 Gas-liquid-solid reactors are frequently used in industry. Two of the most commonly used multiphase reactors are the slurry bubble column and the fixed bed reactor. In the following section only fixed bed reactors are discussed. The solid phase in these reactors has a large interfacial surface area and can be used as catalyst support. These large surface areas enhance mass transfer between the separate phases. One way of characterizing the performance of a packing material is its gas to liquid mass transfer. In the following section the different flow regimes in multiphase reactors are described. Furthermore, different types of packing are described, followed by an explanation of the main design parameters in the characterization of solid foam packing. 2.1 Flow configurations and flow regimes For the reactor considered in this project, three different flow configurations are possible. These are shown in Figure 1. Gas and liquid move in the same direction, either upwards (co-current up) or downwards (co-current down). Another possibility is that gas and liquid move in opposite directions, viz countercurrent. iquid will move downwards through the column and gas will flow upwards. The flow configuration in combination with the gas and liquid flow rates will define a flow regime. For a countercurrently operated solid foam reactor these have been previously studied by Stemmet et al. (2005). In the column that is used for this project two different high liquid holdup regimes as well as one low liquid holdup regime can be distinguished, as is depicted in Figure 2. More information on holdup is given in Section In the low liquid holdup regime liquid flows over the packing in trickle flow. The column was initially gas filled causing a thin liquid film to be created on the packing. The liquid film covers the complete packing resulting in a large gas-liquid contact area. Increasing the gas velocity does not influence the holdup significantly until the flooding point is reached, which can also be seen in Figure 2. Under flooding conditions the liquid can not flow down over the packing but is pushed back out of the column due to the high gas flow rate, this is the operating limit for the reactor. In the high liquid holdup regime, a gas flow is introduced to a completely liquid filled reactor. Gas will move through the column in bubbles, this is called the bubble regime. As the gas velocity is increased, the bubbles will eventually stretch over the complete width of the column, resulting in a pulsing flow. Waves of gas will move upward through the column while a net liquid down flow is maintained. Eventually, the flooding point is reached when the gas velocity is so high that the liquid is incapable of flowing down the reactor. Flow regimes for solid foams in co-current configuration have not been previously assessed. The main advantage of using a co-current configuration is that flooding issues do not play a role and that it is therefore possible to use higher velocities and foam types with smaller pore sizes, i.e. higher specific areas. The co-current up configuration resembles the high liquid holdup regime in countercurrent situation. The co-current down configuration shows resemblance with the low liquid holdup regime in a countercurrent configuration. 2.2 Types of packings Industry strives towards reactor packing that satisfies the requirements of a large gas-liquid interfacial area per unit volume and a low pressure drop per unit height. Pressure drop has to be low because pumps and compressors generally contribute to a large part of the investment and operational costs. A lower pressure drop will result in a less energy-consuming process. Furthermore, reactor volumes can be substantially decreased if larger specific surface areas can be achieved. This will also decrease the 9

11 Figure 3. Conventional packing. eft: Berl saddles. Right: Raschig rings. Figure 4. Structured packing. eft: A monolith reactor (ebens et al. (1999)). Right: Sulzer Mellapak packing (Sulzer website). Figure 5. A new type of structured packing: solid foam. Solid foam is available in different pore sizes. A smaller pore size results in a higher specific surface area. 10

12 Multiphase Reactors initial investment costs (Billet (1995)). Reactor packings can be manufactured from many types of materials and are available in different sizes and shapes. Two different types of column packing are available for fixed bed reactors: conventional and structured packing. These types of packing will be discussed below Conventional packings In Figure 3 some examples of random packings are shown. In general these types of packings show a moderately high surface area per unit volume; however solid holdup can be quite large. This results in a high pressure drop over the column. The packing is randomly dumped in a reactor. It is difficult to have a uniform flow distribution due to this random orientation in the reactor. Channeling likely occurs in this type of packing, possibly resulting in dead zones in the reactor. This will give a poor reactor efficiency. A major advantage of using conventional packing is that the production cost of this type of packing is relatively low (Billet (1995)) Structured packing It can be concluded that there is a need for well defined structured packing with a low solid holdup. Some well known examples are shown in Figure 4. Structured packing generally shows a lower solid holdup and an improved flow distribution compared to conventional packing. Redistributors can be included in the design to maintain an optimum flow distribution. Even though production costs are generally higher for this type of packing, energy costs can be significantly reduced by the lower pressure drop (Billet (1995)). The solid foam that is currently researched in this project is a new type of structured packing, as shown in Figure 5. This solid foam has great potential because it combines a high porosity with a large specific surface area. These foams are available in different pore sizes, varying from 5 to 100 pores per linear inch (PPI). Solid foam can be manufactured in any shape. The potential of solid foam as a new type of structured packing is discussed in the sections below more elaborately. 2.3 Important reactor design parameters Flow distribution There are two important aspects in the distribution of the flows in the reactor: external factors and properties of the packing itself. External factors are e.g. the gas and liquid distributors, the column design and support plates that might be present. Uniform flow in the packing itself is a necessity, otherwise channeling will occur. Channeling results in an inefficient use of the packing and it will increase the risk of hotspot formation within the reactor, dead zones and by-passing. Solid foam has very uniformly defined cells and it is therefore expected that flow distribution is uniform Holdup Holdup is defined as the fraction of volume that either the gas, liquid or solid occupies. This implies that the sum of gas, liquid and solid holdup must be equal to one. ε + ε + ε = 1 (2.1) G S The voidage, or porosity, is defined as the fraction of volume where gas and liquid can flow through compared to the total reactor volume. The solid holdup of the solid foam used in this graduation project is low, at 7%. This results in a voidage of 93%. Vr VS ε = = 1 ε S = 0.93 (2.2) V r 11

13 Figure 6. Different residence time distributions, resulting from an ideal pulse. 12

14 Multiphase Reactors Pressure drop A fluid flowing through a packing generally looses some of its initial pressure by friction, height changes and variable velocities. A higher pressure drop will demand larger pump capacities and require more energy. This will lead to higher operational and investment costs. The high porosity of solid foam will result in much lower pressure drops than for conventional packing types which generally have a lower voidage (Richardson (2003)) Axial dispersion In an ideal plug flow reactor molecules that are introduced to the column at a certain time, will all leave the reactor at the same time as well. These molecules all have the same residence time. However, this is generally not the case; backmixing causes some molecules to speed up and some to slow down, resulting in a residence time distribution. It is important to research mixing effects in solid foams because otherwise reactor performance can be overestimated. A residence time distribution can be measured by injecting an amount of tracer at the inlet and by measuring the outlet concentration. In Figure 6 an example of two different output curves with axial spreading are shown resulting from an ideal pulse. In Section 5 the effect of axial dispersion, or backmixing, on mass transfer will be assessed. Backmixing in solid foams appears to be comparable to other types of structured packing as was previously studied by Doornenbal (2005) for a countercurrent configuration in the high liquid holdup regime. However, further research on dispersion effects is necessary for all configurations Mass and Heat Transfer Temperature within a reactor should be controlled at all times to prevent undesired side-reactions, catalyst deactivation etc. It is therefore necessary to have optimal heat transfer in the reactor. Heat transfer is expected to be very good compared to conventional packings and monolith reactors. Monolith reactors consist of a block with a large number of thin parallel channels in which gas and liquid are brought into contact. The risk of hotspot formation is large in case of an exothermic reaction for monolith reactors and for less uniformly distributed conventional packings. In gas-liquid-solid reactions mass transfer from the poorly soluble gaseous component to the catalytic site is generally the rate-limiting step compared to the reaction rate. Mass transfer therefore needs to be quantified to give an optimum reactor design. In Section 3 gas-liquid-solid mass transfer and gasliquid mass transfer will be described in further detail. 13

15 Gas gas-liquid film Iiquid-solid film P C * iquid C S Solid C C S Figure 7. Resistances in gas-liquid-solid mass transfer. (Gangwal et al. (2004)) Gas gas film liquid film iquid p CO2 * C C Figure 8. Gas-liquid mass transfer, the resistance to mass transfer is assumed to be entirely present in the liquid film layer. The relation between the gas phase concentration and liquid phase concentration is described by Henry s aw, with C * (Sherwood (1975)). Figure 9. Gas-liquid equilibrium showing Henry s aw (Basmadjian (2004)). 14

16 Mass Transfer 3 Mass Transfer Equation Chapter (Next) Section 1 In this section gas-liquid-solid mass transfer will be briefly discussed followed by a description of gas-liquid mass transfer. A model for gas-liquid mass transfer is introduced that will allow for an evaluation of the overall volumetric mass transfer coefficient. 3.1 Mass transfer Gas-liquid-solid mass transfer In gas-liquid-solid mass transfer the gaseous component has to be absorbed in the liquid phase at the gas-liquid interface. Then it has to diffuse from the gas-liquid interface to the bulk liquid and finally it has to diffuse to the catalytic site on the solid phase. This is schematically shown in Figure 7. These separate steps can all be considered as a resistance to mass transfer. The largest resistance is the limiting step in the operation of the reactor. In order to increase the reactors efficiency, this resistance has to be decreased as much as possible (until another resistance becomes limiting). Over the years, catalyst activity has been optimized resulting in rapid reaction at the catalyst surface; the transfer of reactants to the surface becomes rate-limiting. Two resistances to mass transfer remain: gas-liquid and liquid-solid resistance. It is assumed that internal diffusion limitations are negligible in the solid foam because the catalyst is located at the outer surface of the solid foam. Furthermore, by increasing the liquid-solid interfacial area the liquid-solid mass transfer resistance can be minimized. iquid-solid mass transfer will not be further considered in this report. This leaves the mass transfer between the gas and liquid phase as the rate limiting step. This will be discussed in the next section Gas-liquid mass transfer Gas-liquid mass transfer is very often the rate limiting step in gas-liquid-solid reactions. It is therefore an important parameter to quantify in order to draw conclusions on the packing performance. A schematic of the two film theory is shown in Figure 8 where a gas and liquid phase are in mutual contact. The gas-liquid interface is depicted to be separated from the bulk gas phase and the bulk liquid phase by two thin film layers. It is assumed all resistance is located in the film layers. The overall coefficient for gas-liquid mass transfer, K o, is a combination of the two separate film coefficients, k G and k = + (3.1) K H k k o G The process is liquid film controlled. The gas film resistance can be neglected because the Henry coefficient, H, is moderately high. The overall mass transfer coefficient can therefore be assumed to be well described by the liquid film coefficient, k, as shown in equation (3.2). 1 1 (3.2) K k o A typical curve for a gas-liquid equilibrium is shown in Figure 9. The concentration in the liquid phase is shown here in relation to the gas pressure, i.e. the gas concentration. For low concentrations and low pressures the plot becomes linear and can be described with Henry s aw. * p = H C (3.3) G Henry s law implies that the amount of gas dissolved in the liquid is directly proportional to the partial pressure of the gas over the liquid. Henry s coefficients are a function of temperature and possibly dissolved ions in the solution. 15

17 C D A ax z z C,φ z v z+dz Gas iquid * ( C ) k a C C D A ax z z + dz C z+ dz,φ v z Figure 10. Illustrating the derivation of the liquid-side mass balance for countercurrent gas and liquid flow. The ingoing and outgoing convection terms are shown, as well as the dispersion term and the overall transfer term between the gas and liquid phase. 16

18 Mass Transfer The partial pressure of carbon dioxide can by expressed as a function of the concentration carbon dioxide in the gas phase. p = C RT (3.4) G G The following expression for the equilibrium liquid phase concentration is obtained (3.5). * CG RT C = (3.5) H In Figure 8 the driving force for gas to liquid mass transfer was shown to be expressed by (C * -C ). In the absence of a concentration gradient, equilibrium is reached. The net mass transfer stops if C is equal to C * ; the liquid in contact with the gas phase is completely saturated with the gas. In the presence of a reaction in the system, this concentration difference can be greatly influenced. The driving force will be enhanced by removal of the reaction product causing more gas to dissolve in the liquid. Two main parameters in gas to liquid mass transfer have been discussed: the intrinsic liquid mass transfer coefficient, k, and the driving force, (C * -C ). The surface area available for gas-liquid mass transfer, the effective gas-liquid interfacial area, a, is also important. Reactor packings such as the currently investigated solid foam, aim at increasing the effective area and thereby greatly enhancing mass transport. In the current mass transfer study the product k a is determined, instead of determining k and a separately, as is done in the Danckwerts-plot technique (Cents et al. (2005)). The overall resistance to gas-liquid mass transfer is therefore completely described by the overall volumetric mass transfer coefficient k a. 3.2 Modeling mass transfer Mass transfer can be quantified by making a mass balance over the reactor. A mass balance for the liquid phase and a similar balance for the gas phase can be derived. These balances are linked by the mass transfer between the two phases. This is done by solving an envelope over a small piece of a countercurrently operated reactor; this is graphically depicted in Figure 10. In this figure the convective terms going in and out of the envelope are shown, as well as the dispersion term showing the deviation from ideal plug flow. In a dynamic measurement an accumulation term is required as well. The transfer from gas to liquid phase is described by the concentration gradient and the overall volumetric mass transfer coefficient. The derivation of the gas and liquid phase mass balances is demonstrated in the appendix. The final equations for the dispersed plug flow model are shown in (3.6) and (3.7). 2 C i C C CG RT = u + D ax, + k 2 a C t z z H (3.6) C C C C RT ε t z z H 2 G i G G G = ug + Dax, G k 2 a C εg (3.7) A system of partial differential equations can only be solved if the boundary conditions and initial conditions are known. This will be discussed in the next two sections. The gas that is absorbed in the liquid phase might also undergo a chemical reaction. A reaction term needs to be included in the mass balance if this occurs. This will be further explained in Section 4 and 5 for the absorption of carbon dioxide in water. 17

19 0 0 Figure 11. eft: closed-closed boundaries, showing plug flow behavior immediately left and right of the boundary and dispersed flow between 0 and. Right: open-open boundaries, showing undisturbed flow at the boundaries. Experimental data - gas concentration IN - liquid concentration IN and OUT ε, εg Matlab Model 2 ug, u C C C ka (guess) = u + Dax 2 p, t z z G H, R, T DG, D (guess) ka CGRT + C ε H Modeled output in liquid phase ka Good match Compare model data to experimental data No match Figure 12. Schematic of the model that is used to give an estimate on the overall mass transfer coefficient. 18

20 Mass Transfer Initial conditions The initial conditions at the reactor inlet for both gas and liquid are required to solve the partial differential equations. The inlet and outlet concentrations of the liquid phase are measured in the experimental setup. Furthermore, the ingoing gas concentration is measured at the inlet as well. The outgoing gas concentration is not measured but can be calculated by making a mass balance over the complete reactor. C C u = C C u (,, ) (,, ) in out G out G in G u C = C C + C ( ) G, out, in, out G, in ug Boundary conditions Several different boundary conditions can be used for solving a system of partial differential equations. Two well known examples are closed-closed boundaries and open-open boundaries. Combinations are also possible, namely closed-open and open-closed. Closed-closed implies that ideal plug flow behavior is assumed upstream of the inlet (z=0) and downstream of the reactor outlet (z=). Open-open boundaries assume dispersed flow upstream and downstream the reactor outlet. These two situations are visualized in Figure 11. The model considered in this report assumes closedclosed boundaries. This is because during the experiments the gas phase is injected at the immediate inlet of the system, and backmixing at the distributors is assumed to be negligible. The same assumption is used for the outlet of the system. The derivation of the boundary conditions is included in the appendix The dispersed plug flow model The mass balances for the gas and liquid phase, combined with their initial and boundary conditions together make up the dispersed plug flow model with mass transfer. In this model non-steady state mass transfer and axial dispersion for the gas and liquid phase can be accounted for properly. The dispersed plug flow model with mass transfer can be translated into a Matlab script to determine the performance of the solid foam. In Figure 12 a schematic of the model is shown. During the experiments the gas concentration and the liquid phase concentration at the inlet are measured. This experimental data serves as an input for the model. As can be seen in the mass balance (3.6) for the liquid phase, the only unknown parameters in this equation are the dispersion coefficient and the mass transfer coefficient. Holdup values for solid foam were previously determined (Jongmans (2004), Doornenbal (2005)). The pressure and temperature of the system can be measured and Henry coefficients are tabulated. Hence, when the experimentally measured ingoing gas concentration is used as an input, a modeled output for the outgoing liquid concentration can be generated by assuming a certain value for the overall mass transfer coefficient. This modeled output can be compared to the experimentally measured outlet concentration of liquid. Varying the guessed value for k a will ultimately lead to the best estimate for the overall mass transfer coefficient. The comparison is currently done visually but the Matlab script can be extended to automatically minimize the sum of squares of the modeled and experimental output. 3.3 Modeling steady state mass transfer It is also possible to measure mass transfer by steady state measurements. The previously described model can be used for these experiments as well. It is also possible to give an indication of k a by setting the concentration change over time (3.6) to zero. Furthermore, for trickle flow experiments the axial dispersion term is assumed to be negligible. Equations (3.6) and (3.7) will then simplify to the following equations. (3.8) 19

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22 Mass Transfer i C CGRT 0 = u + ka C z H i CG CGRT ε 0 = ug ka C z H ε G (3.9) (3.10) The solution of the differential equation for negligible axial dispersion is presented in equation (3.11), the exact derivation is shown in the appendix. CG,out RT CG,in RT ln C,in C,out H H ka = RTε ε + s s HuG u (3.11) However, if axial dispersion is high the overall mass transfer coefficient will be affected. The maximum mass transfer coefficient will be obtained by assuming ideal mixing for the liquid phase and plug flow for the gas phase. The solution of the gas phase plug flow balance is presented in equation (3.12). In the appendix the exact derivation is shown. CH CH ln CG,out CG,in RT RT ka = ε RT u H s G (3.12) It is now possible to compare k a values for steady state situations with maximum axial dispersion and without axial dispersion. 21

23 Figure 13. Schematic of setup in countercurrent high liquid holdup regime. Figure 14. Schematic of setup in countercurrent low liquid holdup regime. 22

24 Experimental Method 4 Experimental Method Equation Chapter (Next) Section 1 In this section the experimental method that was used to obtain the overall volumetric mass transfer coefficient is explained. First the absorption of carbon dioxide in water will be discussed, followed by an explanation of desorption experiments. Finally, the influence of temperature on the carbon dioxide in water equilibrium will be demonstrated. The experimental setup for countercurrent experiments that was used to obtain this data is explained in further detail. The type of experiments that are possible to measure k a will also be addressed. 4.1 Experimental setup Three different flow configurations are possible for a multiphase reactor, viz co-current up, co-current down and countercurrent. The experimental setup can be operated in two different countercurrent modes, in low liquid holdup and high liquid holdup. The high liquid holdup regime was first reported by Stemmet et al. (2005). The countercurrent configurations will be discussed below Countercurrent high liquid holdup The experiments were performed in a rectangular 2D-column. The height of the column can be varied; 30, 60 and 90 cm modules can be installed. In these modules pieces of solid foam can be mounted, with dimensions of 30x30x1 cm each. Mass transfer experiments were performed at 30 and 60 cm height. A schematic of the setup is shown in Figure 13 for the high liquid holdup regime. iquid is fed to the top of the column by pump P51 and circulated through the main supply vessel. The ph-sensors and conductivity sensors are located at the liquid inlet and liquid outlet of the column. Pump P51 is operating at a constant flow rate. The heat exchanger will control the temperature at 30 o C. Gas is introduced at the bottom of the column. The gas leaves through the top of the column towards the gas-liquid separator. A small liquid stream is fed to the column by pump P92B from the gas-liquid separator to maintain the stability of the system. Gas and liquid are fed through five distributor blocks to guarantee proper distribution of the fluids. The distributor blocks have to be cleaned regularly due to fouling. The pipelines to the gas and liquid distributors are all equal in length Countercurrent low liquid holdup The column can also be operated in a low liquid holdup regime, as schematically shown in Figure 14. A low liquid holdup regime can be established by filling up the column through pump P51. The column is then drained with pump P92A, leaving a thin liquid film on the packing. Continuously, the same amount of liquid is drained from the bottom as is fed to the top. The amount of liquid in the column therefore remains low. The gas distribution is similar to the high liquid holdup regime. 4.2 Dynamic and steady state measurements In Section 3 two methods for determining the overall volumetric mass transfer coefficient in gasliquid systems were shown: dynamic and steady state measurements. Dynamic measurements have the advantage that it is also possible to draw conclusions on the axial dispersion in the solid foam. Steady state measurements only give information on the overall mass transfer coefficient, but are easier to perform experimentally. In Section 5 both types of experiments are demonstrated and explained in more detail Absorption of CO 2 Mass transfer data is generally obtained from dynamic oxygen measurements (Chaumat (2005)). However, the fairly low solubility of oxygen in water can cause problems when measuring high mass transfer coefficients. Data interpretation becomes difficult due to a slow response from the oxygen sensors in the experimental setup. It was therefore chosen to characterize mass transfer by absorption of carbon dioxide in water. 23

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26 Experimental Method The absorption of carbon dioxide in water involves several chemical reactions. The amount of carbon dioxide dissolved in water influences the concentration of hydronium ions. Hydronium ions can be quantified with both the ph-sensors and the conductivity sensors that are present in the setup. The amount of carbon dioxide that is absorbed from the gas phase to the liquid phase is a measure for the total mass transfer capacity of the solid foam packing. When carbon dioxide is absorbed in water first the gaseous carbon dioxide will be solvated according to equation (4.1). CO (g) CO (aq) (4.1) 2 2 A small fraction of the solvated carbon dioxide reacts with water to give carbonic acid through the following equilibrium reaction (4.2). CO (aq)+h O(l) H CO (aq) (4.2) The rate at which carbonic acid is formed is important because it controls the formation of hydronium ions (as indicated by reaction (4.3)). In Section 3 it was explained that chemical reactions need to be included in the overall mass balance as well. In Section 5 the mass balance including the reaction rate will be shown. The amount of H 2 CO 3 is assumed to be negligibly small because it rapidly dissociates as soon as it is formed. Therefore the reaction of carbon dioxide and water is often described in one step, as shown in equation (4.3). Carbonic acid is a weak acid that dissociates in water to give hydronium ions and bicarbonate ions. - + CO (aq)+2h O(l) HCO (aq) + H O (aq) (4.3) The net equilibrium constant, or K a value, resulting from combining equation (4.2) and the first dissociation step (4.3) is given by (4.4). - + HCO 3 H3O = pk 1 K 1 10 a a = (4.4) CO [ ] 2 The equilibrium reactions mentioned above are dominating in the experimental ph-range (4~6). Equilibrium reaction (4.5) also takes place, but is usually assumed to be negligible at ph-values lower than HCO (aq) + H O(l) CO (aq) + H O (aq) (4.5) The corresponding equilibrium constant, K a2, is equal to (4.6) CO 3 H3O pk 2 K - = 2 10 a a = HCO 3 The water constant, or autoprotolysis constant, is defined by equation (4.7) H O OH + H O 2 3 = = + - pkw H3O OH K w 10 (4.6) (4.7) Taking equation (4.4), (4.6) and (4.7) into account, there are now four unknowns left in three equations. To calculate the concentration of carbon dioxide an extra equation is required in the form of the electro-neutrality equation. This equation implies that the total amount of negative charge present in the solution has to be equal to the total positive charge in the solution, in order for the solution to be neutral. 25

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28 Experimental Method CO 3 + HCO 3 + OH = H3O (4.8) Combining equations (4.4), (4.6), (4.7) and (4.8) will eventually lead to the equation (4.9) where the carbon dioxide concentration is given as a function of the concentration hydronium ions. The exact derivation is found in the appendix. [ CO ] 2 + Kw H3O + H3O = K a1 2K a H3O H3O The concentration of hydronium ions is known exactly, because it is detected with a ph-sensor. The ph of the solution can be converted to the concentration of H 3 O + with equation (4.10). ph = log H O + (4.10) 10 3 Equation (4.9) and (4.10) can be combined to convert experimental data from mass transfer experiments to a carbon dioxide concentration. Ions have the ability to conduct an electrical current. The concentration of hydronium ions in the solution can therefore be monitored with the available conductivity sensors. This is only possible as long as the concentration of hydronium ions lies in the detectable range of the conductivity sensor. The relation between conductivity and the amount of hydronium ions present in the solution is included in the appendix. (4.9) Desorption of CO 2 Mass transfer can also be characterized by desorption experiments, the opposite of absorption. Desorption, or stripping, is a process in which the carbon dioxide is removed from the solution by using nitrogen gas. inek et al. (1984) showed that it does not matter whether mass transfer coefficients were obtained in absorption or desorption experiments. Desorption will give similar information on the mass transfer coefficients in the solid foam. All mass balances and equations that were previously shown, still apply, only the gas concentration at the inlet will be zero Influence of temperature on solubility and equilibrium constants Generally, the solubility of a gas in water decreases when temperature rises. Kinetic energy is higher at elevated temperatures causing more motion between the molecules present in the solution which will then escape more easily. The equilibrium constants in equation (4.4), (4.6) and (4.7) are all temperature-dependent. Hence, when evaluating the solubility of carbon dioxide in water, the temperature has to be taken into account. Equilibrium constants are usually tabulated for a temperature of 25 o C. The first dissociation constant of carbonic acid, pk a1, has a value of 6.37 at this temperature (Atkins (1998)). pk a1 is equal to 6.33 at the steady state temperature of the setup, which is approximately 30 o C. The temperature dependency of K a1 is shown by equation (4.11) (Danckwerts (1966)) log10 Ka 1 = T (4.11) T The second dissociation constant, pk a2, has a value of at 30 o C. This is derived from equation (4.12) (Danckwerts (1966)). 27

29 Plot of Henry Coefficients vs Temperature H [Pa m 3 mol -1 ] T [ C] Figure 15. Graph showing temperature dependency of concentration based Henry coefficients. (Janssen (1987)) 28

30 Experimental Method log10 Ka2 = T (4.12) T The previously shown temperature dependencies for K a1 and K a2 are valid for a temperature range from 0 o C to 50 o C. The carbon dioxide that is converted to bicarbonate ions and hydronium ions is controlled by reaction (4.3). The reaction rate, k r, rate is shown by the expression below (Danckwerts (1966), Pinsent (1956)). For 30 o C the reaction rate is equal to s log10 kr = log10 T (4.13) T The water constant, pk w, is 14 at 25 o C and has a value of at 30 o C. The Henry coefficient is also dependent on temperature. In literature the Henry coefficient is found in many different forms, either based on mole fraction, molality or concentration. A concentration based Henry coefficient is required for the dispersed plug flow model that was introduced in Section 3. The mole fraction based Henry coefficient can easily be converted by equation (4.14) (Devoe (2001)). M w, water 3-1 H = H x Pa m mol ρ water (4.14) This coefficient also shows a temperature dependency, as is depicted in Figure 15 for the temperature range of 10 to 70 o C. The temperature dependency is also demonstrated by equation (4.15) (Sander (2005)). 0 Hsoln 1 1 H = H exp 0 R T T soln H = 2400 [ K ] R 0 T = H 0 [ K ] mol = kg bar (4.15) Influence of salt on solubility The solubility of carbon dioxide is also dependent on the amount of salt present in the solution. Pure demineralized water was used for the mass transfer experiments. Pulses of potassium chloride were introduced to the reactor by other users of the setup, for axial dispersion measurements. This means that traces of KCl could be present in the solution despite the change to fresh demineralized water for mass transfer experiments. Weisenberger (1996) has researched the effect of different concentrated salt solutions on the solubility of gases. In general the gas solubility decreases with increasing salt concentration, this is called salting out. The effect can be described by the Sechenov equation. In this equation C G,0 and C G represent the concentration of gas in pure water and in the salt solution respectively, C s is the total concentration of the salt. log C / C = K C (4.16) (,0 ) G G s K is the Sechenov constant, which is given by the equation (4.17). It can be calculated with the model parameters h i and h G. K can also be measured experimentally; in this report the modeled values will be used. 29

31 30

32 Experimental Method ( ) K = Σ h + h n (4.17) i G i Values for h i are tabulated. The parameter h G can be calculated with equation (4.18), which shows a slight temperature dependency. Values for h G,0 and h T are also tabulated model parameters. The model parameters can be used in a temperature range from K. hg = hg,0 + ht ( T K) (4.18) These equations can be used to give an estimate for the carbon dioxide solubility in water when salt is present. In the axial dispersion experiments the maximum pulse concentration used was 6 mmol/l. When the total salt concentration in the system is assumed to be equal to the maximum pulse concentration (more likely it will be in a far lower range, viz 10-5 mol/l) the deviation in gas solubility will be in the order of 10-3 percent. Therefore it is concluded that the effect on gas solubility from traces of salt present in the system can safely be neglected. This is also confirmed by experiments, as shown in the appendix. 31

33 Concentration [mol.m -3 ] CO 2 gas IN/100 (exp) H + liquid IN (exp) H + liquid OUT (exp) Concentration [mol.m -3 ] CO 2 gas IN/100 (exp) H + liquid IN (exp) H + liquid OUT (exp) Time [s] Figure 16. Dynamic experiment ( ) for 10 ppi aluminum foam, gas velocity 0.3 m/s, liquid velocity 0.02 m/s, high liquid holdup Time [s] Dynamic experiment ( ) for 10 ppi aluminum foam, gas velocity 0.3 m/s, liquid velocity 0.02 m/s, high liquid holdup CO 2 gas IN/100 (exp) H + liquid IN (exp) CO 2 gas IN/100 (exp) H + liquid IN (exp) Concentration [mol.m -3 ] H + liquid OUT (exp) Concentration [mol.m -3 ] H + liquid OUT (exp) Time [s] Figure 17. Dynamic experiment 1 ( ) for 10 ppi aluminum foam, gas velocity 0.05 m/s, liquid velocity 0.02 m/s, high liquid holdup Time [s] Dynamic experiment 2 ( ) performed directly afterwards experiment 1 for 10 ppi aluminum foam, gas velocity 0.05 m/s, liquid velocity 0.02 m/s, high liquid holdup CO 2 gas IN/100 (exp) H + liquid IN (exp) CO 2 gas IN/100 (exp) H + liquid IN (exp) Concentration [mol.m -3 ] H + liquid OUT (exp) Concentration [mol.m -3 ] H + liquid OUT (exp) Time [s] Figure Second step experiment for 10 ppi aluminum foam, gas velocity 0.1 m/s, liquid velocity 0.02 m/s, high liquid holdup Time [s] Similar 50 second step experiment for 10 ppi aluminum foam, gas velocity 0.1 m/s, liquid velocity 0.02 m/s, high liquid holdup. 32

34 Results and Discussion 5 Results and Discussion Equation Chapter (Next) Section 1 In order to find the best method of determining the overall volumetric mass transfer coefficient various experiments were performed. These experiments will be assessed in the next section. Carbon dioxide absorption was used for the determination of the overall mass transfer coefficient. Oxygen absorption experiments were also performed to validate this method. In the following section first the oxygen results will be presented. This is followed by an explanation of the influence of axial dispersion on the overall mass transfer coefficient. Furthermore, the model used for the carbon dioxide experiments will be validated. 5.1 Determining the overall volumetric mass transfer coefficient There are several ways of determining the overall volumetric mass transfer coefficient, e.g. dynamic experiments and steady state experiments. These will be briefly discussed below Dynamic experiments Dynamic mass transfer experiments were performed only for countercurrent configurations, for both the high liquid holdup and low liquid holdup regime. A nitrogen flow was introduced to the column and instantaneously switched to a fixed CO 2 /N 2 -ratio for 10 seconds; this is called a step experiment. The advantage of using a dynamic measurement is that it gives information on mass transfer and on the axial dispersion in the solid foam; this was previously shown in the derivation of the dispersed plug flow mass balance in Section 3. In Figure 16 two identical experiments that were performed on different days are shown. These experiments were performed at the same gas and liquid velocities and were done in the high liquid holdup regime. In this figure the gas step of carbon dioxide that was introduced (blue) and the response of hydronium ions in the liquid (black) are shown. There is a great difference between the heights of the two peaks, indicating that more mass was transferred to the liquid phase in the second experiment. The experiments in Figure 16 are not reproducible. Furthermore, in the first experiment the bulk concentration was not measured and the concentration of hydronium ions was assumed to remain stable, as indicated by the black dotted line. In the second experiment the concentration of hydronium ions was measured at the inlet. The hydronium ion concentration of the bulk solution does fluctuate slightly, as is depicted in the second graph of Figure 16. This is due to the fact that the liquid flow is recycled. The outlet liquid concentration of hydronium ions increases when carbon dioxide is introduced to the column, eventually the bulk concentration will respond to this step as well. The changing inlet concentration of hydronium ions should be taken into account if a series of experiments is performed. A number of experiments were performed on the same day to test the reproducibility of step experiments. Two high liquid holdup experiments at the lowest gas velocity (0.05 m s -1 ) are shown in Figure 17. It was observed that the first experiment of a series of experiments generally shows a great deviation with an equal experiment, performed directly afterwards. The exact cause of the deviation between two similar experiments has not been investigated. To find out precisely what happens in these experiments, it is required that the inlet and outlet gas concentrations are measured too. The inlet gas concentration could be dispersed by the system before it is introduced to the solid foam causing the steps not to look as well defined as the ones previously shown in Figure 17. Several tests were performed to find a more reliable method of measuring the overall volumetric mass transfer coefficient. Instead of a 10 second step a 50 second step of carbon dioxide was introduced to the reactor. In Figure 18 two examples of 50 second step experiments are shown; these were performed for the same gas and liquid velocity and were measured in the high liquid holdup regime. The graphs in Figure 18 seem more reproducible than the experiments with a shorter step time. This is concluded by visual comparison of the two graphs. The rate at which the hydronium ion concentration increases and decreases is comparable. The heights of the peaks are comparable, therefore it can be concluded that the total amount of hydronium ions that was added to the solution is approximately equal. 33

35 0.16 Concentration [mol.m -3 ] O 2 gas IN (Exp) O 2 liquid IN (Exp) O 2 liquid OUT (Exp) O 2 liquid OUT (Model) Time [s] Figure 19. Example of a steady state oxygen desorption experiment. The gas velocity is 0.2 ms -1 and the liquid velocity is 0.01 ms -1. The oxygen outlet concentration is modeled with a k a value of 0.15 s -1. Table 1. The modeled mass transfer coefficient for different values of the axial dispersion coefficient. The gas velocity is 0.2 m s -1 and the liquid velocity is 0.01 m s -1. iquid axial dispersion coefficient (D ax,, m 2 s -1 ) Mass transfer coefficient (k a, s -1 ) iquid phase completely mixed 0.41 Table 2. Oxygen mass transfer countercurrent, trickle flow experiments for 10 ppi foam. Axial dispersion was set to 10-4 m 2 s -1. Gas velocity (m s -1 ) iquid velocity (m s -1 ) iquid holdup (-) Mass transfer coefficient (s -1 ) Table 3. Oxygen mass transfer countercurrent, high liquid holdup for 10 ppi foam. Gas velocity (m s -1 ) iquid velocity (m s -1 ) Gas holdup (-) Mass transfer coefficient (s -1 )

36 Results and Discussion Steady state experiments The overall volumetric mass transfer coefficient can also be determined with a steady state experiment. In a steady state experiment the ph of the solution is first lowered by introducing carbon dioxide to the system. The solution is then stripped with nitrogen gas at a constant gas and liquid velocity. The operation will be at steady state after a period of time, this implies that there is a fixed concentration difference between the inlet and outlet concentration of hydronium ions. However, this is not truly steady state as fresh liquid is continuously recycled through the reactor. This fixed difference will remain constant as long as there still is a driving force for mass transfer. Eventually the inlet and outlet concentration will go to the same value; the bulk solution that was recycled will then be completely saturated. Steady state experiments were performed for oxygen desorption and carbon dioxide desorption. Initially, experiments for desorption of carbon dioxide were performed. Oxygen is less soluble in water than carbon dioxide. This implies that the liquid phase will become saturated faster in oxygen experiments. It is not possible to quantify k a when the solution is saturated at the outlet because it is not known at which point in the reactor this has happened. Experiments always need to be performed in the range of the driving force for mass transfer. Carbon dioxide is therefore a more promising method because it has a higher solubility in water, oxygen will saturate sooner in water. However, several issues were encountered in this method. These will be addressed later in this section. The experiments with oxygen desorption will be discussed first to validate the model that was developed in Section 3. In Figure 19 an example of a steady state experiment is shown. This experiment was performed in a countercurrent configuration, in the trickle flow regime. The oxygen concentration at the reactor inlet was measured (green), as well as the oxygen concentration at the reactor outlet (black). The red dotted line shows the modeled oxygen output. Axial dispersion was assumed to be low in this regime. The value for k a was varied until a match was found between the experimental oxygen concentration and the modeled oxygen concentration. The modeled liquid outlet concentration first shows a dip because the model requires an initial concentration in order to generate an output. The outlet experimental concentration at time equal to zero was chosen as the initial concentration for the model. 5.2 The influence of dispersion on k a The values of the axial dispersion coefficient can be varied to test the influence of dispersion on k a in the dispersed plug flow model that was derived in Section 3. Frequently, k a is determined by neglecting the axial dispersion term. The overall volumetric mass transfer coefficient can also be calculated by assuming the gas phase to be in plug flow and the liquid phase to be ideally mixed. Complete mixing implies the maximum dispersion coefficient, D ax. Derivations for expressing k a, based on a steady state assumption, were previously discussed in Section 3. In Table 1 modeled values for the overall mass transfer coefficient are shown for different values of the dispersion coefficient. All parameters in the mass balances, including the concentrations, were fixed except k a and D ax. The maximum overall mass transfer coefficient is obtained for an ideally mixed liquid phase. The minimum overall mass transfer coefficient is obtained when axial dispersion is neglected. If the dispersion coefficient is increased, the overall volumetric mass transfer coefficient will also increase. When doing mass transfer calculations it should therefore always be checked whether it is justified to neglect axial dispersion in the system. The mass transfer coefficient for zero axial dispersion matches with the value for D ax = 10-4 (Table 1, both have a value of 0.15 s -1 for k a). This means that the Matlab model is capable of calculating the same mass transfer coefficient that was also calculated with the simplified derivation that neglects axial dispersion and assumes steady state. 5.3 Results for oxygen mass transfer Results for the overall volumetric mass transfer coefficient obtained from oxygen desorption measurements are shown in Table 2 and Table 3. Tests were performed for 10 ppi foam in a 35

37 Figure 20. A gas bubble in the high liquid holdup regime with solid foam packing. It is assumed that there is a thin liquid layer covering the foam inside the gas bubble. This increases the surface area compared to a bubble column. The red arrows indicate the direction of liquid flow. Figure 21. Comparison of k a vs liquid velocity, B, for different types of packing. aso (1995) investigated structured Mellapak packing, Norman (1961) and Mohunta et al. (1969) investigated 25-mm Raschig rings, Billet (1989) investigated 50-mm Hiflow rings. Graph obtained from aso (1995). 36