Model Building Methodology for Multiphase Reaction Systems

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Model Building Methodology for Multiphase Reaction Systems Rameshwar Hiwale,† Sungwon Hwang,‡,* and Robin Smith† †

Centre for Process Integration, School of Chemical Engineering and Analytical Science, The University of Manchester, P.O. Box 88, Manchester, M60 1QD, U.K. ‡ Catalysts, Adsorbents and Specialities, UOP Ltd., Liongate, Ladymead, Guildford, Surrey, GU1 1AT, U.K. ABSTRACT: A new approach to reactor model building for two-phase absorption processes is developed by considering simultaneously mass and heat transfer phenomena, and chemical reaction mechanism and kinetics. In particular, the interaction of mass and heat transfer with chemical reaction over the reactor design is considered to improve the accuracy of the simulation results. A novel methodology is applied to identify suitable reaction mechanisms and kinetics based on limited experimental data. This methodology allows the engineer to develop feasible reaction mechanisms in a systematic approach. Importantly, the required scope for any further lab experiments is identified, especially when the modeling needs further clarification for the reaction kinetics or mechanisms. In this way, a more robust reactor design can be achieved by making full use of experimental information, saving unnecessary laboratory and pilot plant experiments. For a case study, chlorine absorption to oleic acid is applied to the modeling of a laminar jet absorber.

1. INTRODUCTION Most chemical reactions in industry involve multiple fluid phases, yet design of multiphase reactors remains a difficult task. Multiphase reactors are used in industries as diverse as the petrochemical, biological, and pharmaceutical industries. An appropriate reactor design with careful selection of reactor type and its optimum operating condition are key factors in defining the whole process configuration, including the downstream separation section and utility system. For this reason, it is central to the capital and operating cost of the process. Among the many different types of multiphase chemical reactions, some important chemical industrial processes involve mass transfer of one or more species from gaseous phase to liquid phase. Then, the transferred species from the gas phase chemically reacts with the liquid phase. Typical examples of this type of process are gas purification, oxidation, chlorination, hydrogenation, and hydroformylation processes.1 The absorption of gases in liquid solution accompanied by chemical reactions is an important industrial operation for the production of basic chemicals and for the removal of harmful substances from the gas streams. Compared with physical absorption, reactive absorption is able to cover high throughput with moderate partial pressures and without requiring large amounts of solvent.2 However, reactive absorption is a complex rate-controlled process that occurs far from thermodynamic equilibrium. Therefore, the equilibrium concept is often found to be inadequate to describe the whole absorption process. For this reason, development of accurate and reliable models with appropriate process kinetics and mass transfer coefficients is important. Furthermore, the accuracy of modeling is more important because process control and its optimization become strongly dependent on model predictions.2 Over the past few years, chemical engineers and scientists from both academia and industry have attempted to develop optimized reactive absorption systems. However, they have faced the following challenges. First, the complexity of multiphase reactor r 2011 American Chemical Society

modeling increases when mass and heat transfer phenomena between different phases such as diffusivity and solubility of the involved components are taken into account together with chemical reactions. Second, reaction mechanisms and kinetics have been developed from the lab experiments based on various experimental conditions. However, the results have not been confirmed by simulation results in many cases. The range of experimental conditions must cover the final conditions used in the reactor design. Finally, third, reactor design of the multiphase process system tends to be directly scaled up from small laboratory experiments without much detailed simulation of the chemistry and mass transfer. Furthermore, when a reactor design is developed and optimized, chemical engineers often face difficulties in obtaining enough required reaction data, since the data are developed in the early stage by chemists, without much consideration over the reactor design. Therefore, early involvement of reactor modeling and its optimization will bring the following benefits: (i) Kinetics and reaction mechanisms can be identified in a more systematic approach in line with reactor design. (ii) Mass transfer, chemical reactions and their mutual impact on a reactor design should be considered together with support from lab experimental data. (iii) More experiments can be executed when the reactor simulation results with developed kinetics require further clarification over the data obtained from experiments. Development of appropriate kinetics is crucial for the optimum reactor design. For these reasons, the following strategy has been adopted in this research. (1) Rigorous modeling is adopted to increase the

Received: June 3, 2011 Accepted: July 27, 2011 Revised: July 10, 2011 Published: July 27, 2011 10148

dx.doi.org/10.1021/ie201185y | Ind. Eng. Chem. Res. 2011, 50, 10148–10157

Industrial & Engineering Chemistry Research accuracy of the simulation results by considering the following issues simultaneously. • Physical properties of the major key components • Mass and heat transfer phenomena • Chemical reaction and its effect on mass and heat transfer coefficients (2) A novel methodology has been used to identify reaction mechanisms in multiphase systems, based on limited data over the reaction networks, and to obtain appropriate reaction kinetics which provides more accurate results. The methodology was originally developed by Zhang.3 However, it was limited to homogeneous reaction systems that were kinetically controlled and mass transfer did not play an important role. In this research, the methodology has been extended further to cover heterogeneous reaction systems. (3) Reactor modeling has been developed to predict simulation results and compare with laboratory experimental results. It allows an engineer to identify the scope for any further required data from lab experiments, especially when it requires further clarification for reaction kinetics or mechanisms. For example, multiple sets of kinetics can be developed to explain the same system behavior without much noticeable deviations. In such cases, the modeling provides more systematic guidelines as to what experimental data are required further under certain operating conditions to identify the most suitable kinetics among the rivals. By doing this, a more optimized reactor design can be achieved by making full use of experimental information, saving unnecessary laboratory and pilot plant experiments For a case study, a comprehensive model is developed for chlorine absorption to oleic acid, which reacts in the liquid phase. Experimental data are used to develop suitable reaction networks and kinetics through a stochastic optimization method, and a laminar jet absorber is modeled to provide the simulation results. To increase the accuracy of the system behavior, the model simultaneously takes into account the different aspects of chemical equilibrium, mass transfer, and chemical kinetics of feasible chemical reaction networks.

2. MODELING A significant effort has been devoted to develop rigorous kinetics, mass and heat transfer and hydrodynamics models that can be used to represent absorption systems with chemical reaction. Common industrial practice employs conventional design methodology based on past experience, qualitative and quantitative reasoning from pilot plant data, and development results obtained from other similar systems. Existing methods for reactor design and optimization can only be used after the reaction model has been obtained from laboratory experiments. In the process development, chemists and chemical engineers are typically working at different stages. Chemists aim to find reaction networks to obtain the desired product at an early stage, while chemical engineers focus on process design and reactor optimization at a later stage. The conventional approach to model building for reaction systems is generally step by step. First, several mechanisms or networks are proposed according to detailed identification of the reaction products and intermediates. Then, reaction rate data are obtained to develop the reaction rate law for a specific reaction mechanism through appropriate experimental planning, data collection, and analysis. Lastly, model reduction might be needed to simplify the models for engineering purposes. This

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conventional approach has often shown certain drawbacks, for example, experiments carried out without simultaneous analysis of the physical and chemical mechanisms. However, there are possible interactions between these mechanisms, and important factors relating to reactor design and optimization might be missed. In the worst case, the model might be based on ranges of conditions that are inappropriate for the final reactor design. An advanced reactor model which simultaneously considers all these mechanisms will provide detailed predictive information with high accuracy throughout the different stages of design, operation, and optimization. The main features that are applied to the modeling in this research are briefly explained in the next section. 2.1. Modeling of GasLiquid Reactions. 2.1.1. Mass Transfer Coefficient in Liquid Phase. The phenomenon of gasliquid mass transfer has been studied extensively. Chemical absorption and desorption are complex processes, involving chemical reaction kinetics, mass transfer processes, phase equilibrium at the interface, and fluid dynamics. Three major theories have been developed to describe the behavior of the highly complex absorption and desorption processes by using simplified models. These are film theory, penetration theory, and surface renewal theory. A detailed description on the background of each theory can be obtained from Hiwale.4 The film theory concept has been applied successfully since being developed. However, the penetration and surface renewal models have been preferred, since they are physically more realistic models.5 A laminar jet apparatus is well suited to the measurement of absorption especially when penetration theory is applied.6 Since experimental data that are used in this research are mainly obtained by using laminar jet apparatus, penetration theory will be applied in the simulation model. According to penetration theory with regard to jets in plug flow, if the radius of the laminar jet is large compared with the penetration depth of the solute, mass transfer coefficients can be described from the following equation:7 rffiffiffiffiffi D ð1Þ kl ¼ 2 πt where D is the diffusivity of gas in the liquid phase and t is the contact time of any element of the jet with gas. The contact time is calculated by assuming that the velocity profile of the liquid is always flat, and the surface velocity equals the average velocity. 2.1.2. Expression for Thickness of Mass Transfer Film. According to film theory, there exists a laminar film on both sides of the interface. Transport of material through these films then takes place by molecular diffusion alone. Film theory uses an effective film thickness of xf, whose resistance to mass transfer is as same as the sum of the resistances of the laminar, buffer, and turbulent zones combined.8 Allen reported an expression for the film thickness that could be inferred from Higbie’s penetration theory.9 Since mass and heat transfer processes are similar in respect of that the rate of transfer is directly proportional to mass or thermal concentration, the heat film depth can also be applied from Higbie’s theory. According the penetration theory, expression for film thickness with regard to mass transfer is described by the following equation.9 pffiffiffiffiffiffiffiffiffiffiffi xf ¼ πDA t ð2Þ where DA is the diffusivity and t is the contact time. 10149

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The corresponding heat transfer coefficient film thickness is described by the following equation.9 pffiffiffiffiffiffiffiffiffiffi xh ¼ πhG t ð3Þ where hG is the heat transfer coefficient and t is the contact time. 2.1.3. Enhancement Factor. When mass transfer is simultaneously accompanied by chemical reaction, it leads to more rapid and complete transfer of molecules from the gas phase to the liquid phase, compared with the case of pure physical mass transfer without chemical reaction. In the absorption process, diffusion and homogeneous chemical reaction cause similar effects and result in an increase in the overall mass transfer rate.10 To include the effect of chemical reaction on mass transfer, an enhancement factor E has been commonly used. It is basically defined as the ratio of mass transfer coefficient for absorption when chemical reaction occurs to mass transfer coefficient with pure physical absorption without chemical reaction.11 E¼

kL k0l

ð4Þ

where E is the enhancement factor, kL is chemical absorption (mass transfer) coefficient, m/s, and k0l is the physical absorption (mass transfer) coefficient, m/s; E is often expressed as a function of two dimensionless parameters. Alper12 has suggested an enhancement factor for instantaneous reactions, and Ei is calculated from following equation: rffiffiffiffiffiffi rffiffiffiffiffiffi DA C B DB Ei ¼ þ ð5Þ DB zCAi DA where DA and DB are the molecular diffusivities, and CA and CB are the concentrations of A and B in the liquid. The enhancement factor of a pseudo-first-order reaction, E1, is calculated from the following equations: pffiffiffiffiffiffiffi MH ð6Þ pffiffiffiffiffiffiffi E1 ¼ tanh MH

Figure 1. Laminar jet absorber.

the gas phase. Therefore, this type of arrangement can be considered to be a plug-flow arrangement. The interfacial area for the jet is given by the following expression:6 a ¼ πdL

From Higbie’s penetration model, physical mass transfer coefficients in the absorption process can be obtained from the following equation in the case of a laminar jet absorber.14,15 rffiffiffiffiffiffiffiffi 4 DQ 0 ð10Þ kl ¼ πd L Where, D is the diffusivity of the gas in the liquid, Q is the liquid flow rate, L is the liquid jet length, and d is the jet diameter The diffusion time is given by the following expression:6

where MH is the Hatta number and is given by DA k2 CB MH ¼ ðkl 0 Þ2

where k2 is the second order reaction rate constant, is the physical mass transfer coefficient. Yeramian et al.13 developed an enhancement factor, which was reported by Wellek et al.10 as an explicit expression given by E¼

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E1 2 ð 1 þ 4ðEi 1ÞEi =E1 2 1Þ 2ðEi 1Þ

t ¼

ð7Þ k0l

ð8Þ

2.1.4. Laminar Jet Apparatus. Most absorption reaction rates that are identified from the lab experiments are measured using a laminar jet apparatus, as it has been found to be one of the laboratory measurements that is able to produce most accurate results for gas absorption rates. The main reason for the use of this equipment is that the interfacial area is known accurately, and the physical absorption rates have been shown to agree with penetration theory predictions.6,14 A laminar jet absorber is shown in Figure 1. In the equipment, liquid flows downward, while it is continuously in contact with

ð9Þ

πd2 L 4Q

ð11Þ

Where, d is the diameter of the jet, L is the length of the jet, and Q is the liquid volumetric flow rate. 2.2. A New Approach to the Development of Reaction Mechanism and Kinetics. Detailed model building of chemical reaction systems and the corresponding reactor design present a challenge when chemical reaction processes are complex and the market window for new chemical products are short. A new methodology was developed by Zhang3 to build a model of chemical reaction systems by using minimum experimental measurements for the purpose of reactor design and optimization, based on limited information on the chemistry. A reaction scheme construction algorithm is used to provide all feasible reaction schemes via an optimization search, while reaction kinetics are obtained through the best fitting of experimental data.3 The overall mechanism is described in Figure 2. The methodology identifies all feasible reaction mechanisms based on two sets of reactions designated to be Class I and Class II. The basic principle of the approach is as follows:3 (1) As a constraint, all feasible reactions should satisfy an atomic balance. 10150



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Figure 3. Schematic diagram of reactor modeling compartments.

Figure 2. Reaction generation framework.3

(2) As an initial step in the algorithm, the reactions that involve only reactant materials are identified and they are allocated to Class I. (3) Further reactions that involve either products or combinations of reactant materials or products are allocated to Class II. (4) An iterative procedure constructs all feasible reactions between reactant materials and products. Further detailed description about the methodology can be obtained from the work of Zhang.3 The same methodology is applied to this research. However, Zhang3 applied the methodology only to homogeneous reactions where mass transfer did not play a significant role. In this work it is extended to heterogeneous reactions. Furthermore, an enhancement factor is applied to consider the interaction between mass-transfer through absorption or desorption and chemical reactions in order to increase the accuracy of model prediction. The methodology is applied to a case study of chlorine absorption to oleic acid in section 3. Model Discrimination. A simulated annealing algorithm is used for the search of feasible reaction mechanisms and kinetics.3 One of the major advantages of using the algorithm is to find multiple optimum solutions that satisfy specified constraints for the objective. In some cases, multiple individual kinetics were determined from the search to describe the same experimental results. In such a case, it is still required to identify further which model describes the reaction most accurately. Zhang developed the methodology to identify these model discriminations.3 Different ranges of operating conditions are applied to a reactor model, which are linked with different set of developed kinetics,

in order to find what condition provides maximum deviation among the results of the kinetic models developed. Then, the experimental study is executed under the same conditions. This methodology provides an effective guideline to find optimum kinetics through minimum pilot plant testing or experiments. The detailed procedure and algorithms can be found in the work of Zhang.3 2.3. Reactor Modeling and Simulation. A laminar jet laboratory apparatus is used to gain experimental information on the system (e.g., chlorine-oleic acid) as it allows accurate measurement of the liquid phase surface area and contact time.6 Forced convective mass transfer takes place from gas to liquid phase under conditions such that the whole film moves with the uniform velocity of the liquid jet. The solute is assumed to be sparingly soluble and to not disturb the physical properties of the liquid film. The contact time is very short, and the solute experiences uniform velocity profiles of the liquid jet. A mathematical model based on penetration theory will be adopted to describe the mass transfer of the solute gases into the interface. It is well-known that plug-flow operation can be modeled by using a number of mixed flow reactors (CSTRs) in series, as illustrated in Figure 3. The greater is the number of mixed flow reactors in series, the closer is the approach to plug flow operation. Kokossis and Floudas16 gave a more comprehensive representation in the form of a superstructure. The key advantage of such a representation is that only algebraic equations are sufficient for the mathematical description of a PFR unit. In addition, it has been demonstrated from the research of Hwang et al.17 that this approach enables a more flexible type of superstructure for reactor design and provides higher efficiency for the development of a novel type of reactor designs. A PFR has continuous feeds and products, the same as the corresponding CSTRs-inseries model. The mathematical representation of the reactor model with a multiphase reaction system includes the following equations: (1) Heat and mass balance for the compartments involved across the system. (2) Mass transfer rates of diffusing components and the equilibrium relations at the interface based on Henry’s law. (3) Hydrodynamic expressions for phase hold-ups, interfacial area between gas and liquid phase and mass transfer coefficients. Developing the simulation model requires extensive knowledge of the physicochemical properties of the fluids involved in the absorption process. These include density, viscosity, solubility, surface tension, and reaction rate constants. Components from one phase can transfer to another phase in the system through diffusion. At each compartment, the outlet molar flow of a component is calculated on the basis of the mass balance from the inlet molar flow of a component, reaction rate, 10151



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volumetric flow rate of each phase, molar concentration of a component, and diffusion rate of components. A component balance for each compartment is described below by the following equations: Vapor phase: outletflow ðkmol=sÞ ¼ inletflow ðkmol=sÞ ( masstransferflow ðkmol=sÞ þ reactionflow ðkmol=sÞ ð12Þ Liquid phase: outletflow ðkmol=sÞ ¼ inletflow ðkmol=sÞ ( masstransferflow ðkmol=sÞ þ reactionflow ðkmol=sÞ ð13Þ In the case of physical absorption only, the reaction flow becomes 0. The gas and liquid enters each compartment with specified temperature, molar flow rate, and composition. The specifications of feed streams are obtained from experimental data. In modeling, energy balances are not considered when physical gas absorption occurs without chemical absorption. Solute gas i crosses the interface into the liquid phase with a flux N i. The liquid film thickness varies along the length of the jet with respect to contact time. Concentration of any liquid reactant, i, is designated by Ci,bulk in the bulk liquid Ci,interface at interface. Both liquid and gas are assumed to be well mixed. Henry’s law is applied to relate the concentration of solute gas in bulk liquid phase to the concentration of the species in bulk vapor phase. For the solute gas, the physical equilibrium at the interface is expressed by Pi, interface ¼ HCi, interface

ð14Þ

Where H is Henry’s constant, Pinterface is the interfacial partial pressure, and Ci,interface is the interfacial molar concentration of the solute gas i. According to Treybal,18 the mass flux of an absorbed component, Ni across the gasliquid boundary at steady state can be presented in terms of mass transfer coefficient and driving force. Mass transfer flux of each species is a function of the driving force between concentrations in the bulk vapor and liquid phases. The general form of the transfer flux equation is shown in eq 15.18 Ni ¼ kg, i aðPi, out Pi, interface Þ ¼ kl, i 0 aðCi, interface Ci, bulk Þ

ð15Þ

where kg,i and kl,i are physical mass transfer coefficients of the solute gas i in the gas and liquid phase, respectively, a is interphase surface area, C is the molar concentration of species i, and P is the partial pressure. An enhancement factor, which was obtained from eq 8 in section 2.1.3, is used for reactor modeling in order to consider the effect of chemical reactions on diffusion mass transfer.

3. CASE STUDY—ABSORPTION OF CHLORINE IN OLEIC ACID USING LAMINAR JET ABSORBER 3.1. Introduction. Oleic acid is a fatty acid found in animal and vegetable oils. Oleic acid makes up about 5580% of olive oil, and 1520% of grape seed oil and sea buckthorn oil. It is also termed a monounsaturated fatty acid, because of single doublebonds between the carbons, which are the main reaction site for halogenation. Halogenation of fatty acids has been studied for many years, because many of the products provide useful intermediates for the preparation of other derivatives. For example, chlorination of fatty acids has received growing attention because the reaction produces vinyl ester, which is a potential comonomer in vinyl polymerization. In the case study, the modeling of the chemical reaction and mass-transfer between the gas and liquid phases will be applied to the simulation for the absorption process of chlorine into oleic acid. Experimental data will be used to identify feasible reaction mechanisms, and the kinetics will be developed on the basis of the two-stage method described previously in section 2.2. Once the required kinetics are developed and applied to a reactor model, the simulation results will be reviewed, together with experimental data with respect to both chemical conversion and absorption rate. On the other hand, the results of other studies will be compared, which considered only a single phenomenon rather than both reaction and mass-transfer. 3.2. Background. Roper studied chlorination of oleic acid dissolved in carbon tetrachloride in a flow reactor;19 the reactants were dissolved separately and mixed in the liquid phase at the inlet to the reactor. On the basis of the research results, Roper suggested that the kinetics could be described by a simple second order reaction rate. The amount of hydrogen chloride formation during chlorination of oleic acid reaction was not reported. Menting et al. studied the reaction between chlorine and oleic acid, and the reaction produced mainly 9,10-dichlorosteraic acid with other byproduct.20 The byproduct were the dimer 9(10)-(910-dichlorostearolyoxy)-10-9-chlorostearic acid and a few related products.20 Clegg and Winter studied kinetics of the reaction between chlorine and oleic acid in carbon tetrachloride solution.21 The process involves gas absorption with chemical reaction, which involves large heat generation. The reaction between chlorine and oleic acid is highly exothermic with negligible evaporation effect for the oleic acid. According to the work of Clegg and Winter, it was expected that interfacial turbulence would not be present in this system because of the high viscosity of the oleic acid.21 3.3. Modeling. Before numerical modeling for simulation and developing chemical kinetics based on the experimental data, it is required to obtain enough information about the physical properties of the fluids involved in the gasliquid absorption process. The important physical properties are diffusivity, solubility, density, and viscosity. These physical properties are required for the modeling of the reactor design, as discussed in section 2.3. The key physical properties and basic assumptions for the modeling are considered next. 3.3.1. Diffusivity. The molecular diffusivity of the absorbed Cl2 in oleic acid is important in the modeling of mass transfer. To understand the liquid film resistance to mass transfer, accurate measurements of molecular diffusivity in the liquid is required. Semiempirical methods have been reported so far, and the most widely used equation for estimating liquid diffusivity was 10152



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developed by Wilke and Chang.22 It features a correlation for nonelectrolytes in an infinitely dilute solution. It is an empirical correlation of the StokesEinstein equation.15 The diffusivity of Cl2 into oleic acid is calculated by using the following correlation:23 D ¼ 7:4 108

TðxMÞ0:5 μV 0:6

cm2 =sec

ð16Þ

where M is the molecular weight of the solvent, T is the temperature in K, μ is the viscosity of the solvent in cP, V is the molar volume of the solute at its normal boiling point in cm3/(g-mole), and x is an association factor of the liquid. Equation 16 shows that diffusivity is a function of temperature and viscosity. 3.3.2. Solubility. Solubility of the gas in the liquid, one of the most important physical properties, depends mainly on temperature and partial pressure of the gas over the liquid. Gas solubility is always limited by equilibrium between the gas and saturated solution of the gas. Therefore, it is required to calculate the diffusivity and the kinetics of the reaction between the absorbed gas and liquid in order to find solubility. When gas absorption is accompanied by chemical reaction, it becomes difficult to find the solubility since the reaction rate is greater than the rate of mass transfer. Therefore, an alternative material that has physical properties similar to those of oleic acid, but does not react with the solution, is used instead to find the solubility of the required substance. In this case, the solubility of chlorine in oleic acid could not be determined directly because of chemical reaction. Therefore, experimental data of another similar substance was used instead. In fact, n-hexoic acid and n-decoic acids have similar physical properties as oleic acid. Winter experimentally determined the solubility of chlorine in carbon tetrachloride, in hexoic acid [CH3 (CH2)4 COOH], and in decoic acid [CH3 (CH2)8 COOH].23 He also found that the solubility of chlorine in decoic acid was higher than that in hexoic acid. Winter calculated the solubility of chlorine in oleic acid, based on correlation given by Taylor and Hildebrand.23,24 The results showed that the solubility of the oleic acid lies between that of decoic and hexoic acid. Similarly, the solubility of hydrogen chloride in hexoic acid, in decoic acid, and in oleic acid was determined. The solubilities of chlorine and hydrogen chloride are given in Figure 4.23 The solubility is expressed in terms of Henry’s law, which relates the equilibrium concentration of the gas in the liquid phase as a function of its partial pressure. P i ¼ H i Ci

ð17Þ

where Hi is the Henry’s law constant for gas i, and Ci is the equilibrium concentration of the absorbed gas i in liquid. It is calculated based on total moles of gas, which physically absorb in a volume of liquid. 3.3.3. Density. Solution density is important in the modeling of mass transfer rate because it affects the liquid film coefficient for mass transfer. The density of oleic acid is reported as FOA = 887 kg/m3. It was reported by Winter that the density of oleic acid changed very slightly with variation of temperature.23 3.3.4. Viscosity. Viscosity is one of the important physical properties, especially for the modeling of mass transfer rate, because it affects the liquid film coefficient of mass transfer and the solubility of chlorine in oleic acid. The viscosity of oleic acid is sensitive to temperature. The viscosity of oleic acid is described

Figure 4. Solubility of chlorine and hydrogen chloride in oleic acid (experimental data from Winter)23.

by using the following correlation. μ ¼ 8:15104 expð3:1103 =TÞ

ð18Þ

where T is the absolute temperature in K and μ is viscosity in centipoises (cP) 3.3.5. Assumptions for the Modeling. For the mathematical modeling of a reactor, the following assumptions are applied. • The total volume is divided equally into elemental volumes. In each section, the gas and liquid enters with known temperature, molar flow rate, and composition. Solute gas i crosses the interface into the liquid phase with the flux Ni. • The film thickness is calculated by using the eq 2, and it varies along the length of jet with respect to contact time. • Both liquid and gas are assumed to be well mixed. • The reactions in the liquid phase take place in the liquid film only since it is a rapid reaction. • The chlorination of oleic acid is a highly exothermic reaction, and the reaction rate is very high. Therefore, the temperature inside a reactor plays an important role on the absorption of chlorine and desorption of hydrogen chloride from liquid to gas phase. In the research, the heat of reaction of each identified reaction network is applied to the modeling in order to take into account the temperature change throughout the reactor. The temperature is balanced through the reactor compartments within each time interval during simulation. Furthermore, heat transfer through the film thickness is included to the modeling. The effect of reaction temperature on the reactor performance is considered in the kinetic equations for each compartment. It is embedded into the mathematical formulation of the model. • In a reactor, viscosity and density vary with temperature. This ultimately leads to variation of the rate constants, solute concentrations at interface and diffusivity. These effects are considered in the modeling. • Penetration theory is adopted to describe the mass transfer of the solute gases at the interface. According to penetration theory with regard to jets in plug flow, if the radius is large compared with the penetration depth of the solute, the mass transfer coefficient can be calculated by using eq 1. 3.4. Development of Reaction Mechanisms and Kinetics. 3.4.1. Generation of Potential Reaction Mechanisms. A two-stage method is used to generate feasible reactions, following the procedure in Figure 2. The mechanism includes (1) classification of reacting species, 10153


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The reaction of chlorine with oleic acid was studied by Roper, and a second order model was used for kinetics of the reaction.19 Similarly, Winter performed experiments to determine the kinetics of reactions between chlorine and oleic acid.23 In the kinetic experimental study, the experiment for the reaction between chlorine and oleic acid was performed by using the capillary tube reactor, whereas the absorption of chlorine in oleic acid was performed in a laminar jet absorber. The study of the reaction between oleic acid and chlorine was conducted in order to find the kinetics under similar conditions by using a capillary tube. Since the experiments were carried out in the homogeneous phase by dissolving chlorine in carbon tetrachloride, mass transfer and its impact on reaction was eliminated in the kinetic experiments. In his research, two kinetic models were considered, and each model included different feasible reaction networks with their own kinetic parameters: (1) A model with independent parallel reactions: Model 1 is the simplest possible kinetic model. It takes into account substitution and the addition of molecules through the reactions as shown below. It was assumed that these two reactions occur independently. kA

s AP OAðAÞ þ Cl2 f

ð24Þ

where OA(A) is the concentration of oleic acid available for the addition reaction and AP is the addition product. kS

OAðSÞ þ Cl2 f s SP þ HCl

ð25Þ

where OA(S) is the concentration of oleic acid available for the substitution reaction and SP is the substitution product. (2) A model with interdependent parallel reactions: In Model 2, two parallel reactions were used to represent the reactions between chlorine and oleic acid. addition

OAðAÞ þ Cl2 s f AP substitution

ð26Þ addition

OAðSÞ þ Cl2 s f SP þ Cl2 s f AP

The results were compared with the reaction networks developed earlier by Roper, Menting et al., and Winter.19,20,23 The mechanisms above cover all potential mechanisms. The results are also in good agreement with Winter’s results.23 3.4.2. Development of Reaction Kinetics. To develop appropriate kinetics of the identified reaction networks, previous research work was reviewed to obtain experimental data.

ð27Þ

The kinetics of these two models are shown in Tables 1 and 2. First, the kinetics included in a reactor simulation model, which was illustrated in section 2.3. As shown in Figure 5, the results are compared against experimental data of Winter from a laminar jet absorber. Figure 5 shows rather poor agreement between experiment results and simulation predictions, with the kinetics determined by Winter.23 The main reasons for the deviations are the following: (1) Kinetic parameters. The kinetic parameters reported by Winter were not rigorously validated by experimentally measured data from the laminar jet absorber. (2) Jet lengths. In the absorption experiment with a laminar jet absorber, variation of jet length and the liquid flow rate may affect the physical absorption coefficient and the interfacial area. These effects were not considered in his reaction modeling since the experiments were performed in capillary reaction in the absence of absorption phenomenon. (3) Desorption of hydrogen chloride. Desorption of hydrogen chloride may affect the mass transfer rate of chlorine into oleic acid. However, it was not considered in his modeling. The simultaneous mass transfer and chemical reaction of a 10154



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Table 1. Kinetic Parameters of Kinetic Model 123 reaction

kinetic equation

kinetic parameters

1. OA+ Cl2 f AP (addition reaction)

r1 = A exp(Eact/(RT))COACCl2

2. OA + Cl2 f SP + HCl (substitution reaction)


A = 407.97 (m3/(mol 3 s))

Eact = 8577.15 (KJ/mol) n = 1 (OA, Cl2)

A = 153.787 (m3/(mol 3 s))

Eact = 8621.2 (KJ/mol) n = 1 (OA, Cl2)

Table 2. Kinetic Parameters of Kinetic Model 223 reaction

kinetic equation

kinetic parameters

1. OA + Cl2 f AP (addition reaction) 2. OA + Cl2 f SP + HCl (substitution reaction)

r1 = A exp(Eact/(RT))COACCl2 r2 = A exp(Eact/(RT))COACCl2

3. SP + HCl f AP (addition reaction)

r3 = A exp(Eact/(RT))CSPCHCl

Figure 5. Evaluation of the kinetic models based on experimental data and reported kinetic parameters from Winter23.

soluble solute in a two or three phase system has considerable impact on the modeling results. For these reasons, the methodology in section 2.2 is used to develop new parameters (i.e., activation energy and frequency factor) of the kinetics, based on both detailed reactor modeling and the experimental data from Winter.23 It should be noted that physical mass transfer phenomenon, chemical reactions, and their interactions are taken into account in order to increase the accuracy of the modeling for multiphase systems. The new kinetic parameters are summarized in Table 3, and the results are plotted against experimental data in Figure 6. The graph illustrates that model prediction results show good agreement with experimental data in various temperature ranges with an average deviation of 4.8%. As a next step, the same reactor model with reaction mechanisms developed and kinetics will be applied to the absorption process of chlorine to oleic acid. 3.5. Laminar Jet Absorber Experiments. The laminar jet absorber is the most flexible laboratory equipment for the absorption of gas into the liquid phase. The liquid jet is formed at an orifice and flows vertically downward in contact with the gas to be absorbed and is then collected in a receiver of suitable design.6 The laminar jet is the most suitable apparatus to use for obtaining experimental information on the system, as it allows accurate measurement of the liquid phase surface area and contact time. Varying the jet length and the liquid flow rate can change the physical absorption coefficient and the interfacial area. The hydrodynamics involved are extremely simple when an idealized rodlike cylindrical jet is assumed.6,2532

3

A = 223.289 (m /(mol 3 s)) A = 131.47 (m3/(mol 3 s)) A = 223.289 (m3/(mol 3 s))

Eact = 7162.44 (KJ/mol) n = 1 (OA, Cl2) Eact = 7166.18 (KJ/mol) n = 1 (OA, Cl2) Eact = 7162.44 (KJ/mol) n = 1 (SP, HCl)

Figure 6. Evaluation of the new kinetic model (optimized kinetic parameters given in Table 3), based on experimental data from Winter.23

Winter published experimental results for the absorption of chlorine into oleic acid obtained using a laminar jet absorber, and these data are applied to the reactor modeling.23 The data from Winter are shown in Table 4.23 The experimentally measured results at different jet lengths and gas and liquid flow rates were compared with the model predictions. Figure 7 compares experimental results with the predicted results from the model. The good agreement proves that the mathematical model developed for Cl2oleic acid with the laminar jet absorber provides much more accurate results in terms of chemical reaction and mass transfer.

4. SUMMARY An approach to reactor modeling has been developed to take into account mass-transfer (including major key physical properties) and chemical reactions simultaneously. A two-stage method developed by Zhang has been extended further to a multiphase reaction in order to identify all feasible reaction mechanisms and their kinetics.3 The methodology allows a chemical engineer to develop a reactor design at the early stage of lab experiments and to plan experimental measurements to suit the conditions in the final process design. It provides an opportunity to explore further required experiments in a systematic approach, if any further clarification about the identified kinetics is needed. For a case study, the absorption of chlorine into oleic acid and its reaction were used to demonstrate the approach. Experimental data was applied to a reactor model in order to develop appropriate reaction mechanisms and kinetics. Then, the prediction results of the model in various operating conditions were 10155



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Table 3. Feasible Reactions with New Kinetic Parameters reaction 1. OA + Cl2 f AP

kinetic equation r1 = A exp(Eact/(RT))COACCl2

2. OA + Cl2 f SP + HCl


3. AP f OA + Cl2

r3 = A exp(Eact/(RT))CAP

4. SP + HCl f OA + Cl2

r4 = A exp(Eact/(RT))CSPCHCl

kinetic parameters A = 91.990 (m3/(mol 3 s))

Eact = 2.85 104 (KJ/mol) n = 1 (OA, Cl2)

A = 46.27 (m /(mol 3 s))

Eact = 651.58 (KJ/mol) n = 1 (OA, Cl2)

3

A = 22.63 (m3/(mol 3 s)) A = 15.27 (m3/(mol 3 s))

Eact = 2657.93 (KJ/mol) n = 1 (AP) Eact = 656.59 (KJ/mol) n = 1 (SP, HCl)

Table 4. Experimental Data for Absorption of Chlorine into Oleic Acid23 experimental absorption sr. no

jet diameter (m)

jet length (m)

rate (kmol/s)

1

0.00168

0.0866

2.29 1010

2

0.00171

0.0757

2.14 1010

3

0.00179

0.0564

1.69 1010

4

0.00189

0.0386

1.40 1010

5

0.00168

0.0866

2.17 1010

6

0.00171

0.0757

2.09 1010

7

0.00179

0.0564

1.76 1010

8 9

0.00189 0.00169

0.0386 0.0866

1.26 1010 2.24 1010

10

0.00175

0.0668

1.91 1010

11

0.0018

0.0564

1.69 1010

12

0.00186

0.0451

1.44 1010

13

0.0019

0.0386

1.35 1010

14

0.00197

0.0289

1.03 1010

compared with experimental results in terms of both chemical reaction (e.g., conversion) and mass-transfer (e.g., absorption coefficient). It was demonstrated that the modeling results were in good agreement with both experimental measurements. By comparison, the results demonstrated that the reaction kinetics developed without considering mass-transfer provided much poorer prediction.

Figure 7. Experimental results vs model predicted results (experimental data are obtained from Winter)23.

P = total pressure (kPa) Pi = partial pressure of component i (kPa) Q = volumetric flow rate (m3/s) t = contact time (s) T = temperature (K, °C) V = molar volume (m3/mol) x = association factor of liquid xf, xh = film thickness (m) Greek Letters

’ AUTHOR INFORMATION Corresponding Author

*Tel. +44 1483 466251. Fax: +44 1483 466259. E-mail: [email protected].

’ NOMENCLATURE a = interfacial area (m2) Ci or CAe = concentration of component i, Interfacial concentration of component i (kmol/m3) d = diameter (m) Di or D = diffusivity of component i (m2/s) E = enhancement factor, Activation energy (, KJ/mol) E1 = enhancement factor for a pseudofirst order reaction () Ei = enhancement factor for Instantaneous reactions () Hi = Henry’s law constant of component I (kPa m3/kmol) hG = heat transfer coefficient (kcal/(s m2 K)) kl = mass transfer coefficient (m/s) kl0 = physical absorption (mass transfer) coefficient (m/s) k2 = second order reaction rate constant (m3/(kmol s)) kg or kG = gas phase mass transfer coefficient (Kmol/(m2 s) kPa) L = length (m) M, MH = molecular weight, Hatta Number (kg/kmol, ) Ni = mass transfer flux of component (Kmol/(s m2) interfacial area)

μ or η = viscosity (cP) F = density (kg/m3) Abbreviations

AP = addition product SP = substitution product

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Industrial & Engineering Chemistry Research (7) Higbie, R. The Rate of Absorption of a Pure Gas into a Still Liquid during Short Periods of Exposure. Trans. Am. Inst. Chem. Eng. 1935, 35, 36. (8) Whitman, W. Prelimininary Experimental Confirmation of The Two Film Theory of Gas Absorption. Chem. Metall. Eng. 1923, 29, 146. (9) Allen, J. Nonisothermal Mass Transfer with Chemical Reaction. MSc Thesis, University of Manchester Institute of Science and Technology, U.K., 1977. (10) Wellek, R. M.; Brunson, R. J.; Law, F. H. Enhancement Factors for Gas Absorption with Second Order Irreversible Chemical Reactions. Can. J. Chem. Eng. 1978, 56, 181. (11) Danckwerts, P. Significance of Liquid Film Coefficients in Gas Absorption. Ind. Eng. Chem. 1951, 43, 1460. (12) Alper, E. Absorption of a Gas into a Solution Containing More than One Reactant: Analytical Solutions of Instantaneous Reactions. Chem. Eng. Sci. 1973, 28, 1499. (13) Yeramian, A. A.; Gottifredi, J. C.; Ronco, J. J. Mass Transfer with Homogeneous Second-Order Irreversible Reaction: A Note on an Explicit Expression for the Reaction Factor. Chem. Eng. Sci. 1970, 25, 1622. (14) Astarita, G.; Savage, D.; Bisio, A. Gas Treating with Chemical Solvents; John Wiley & Sons; New York, 1983. (15) Danckwerts, P. V. Gas Liquid Reactions; McGraw-Hill: New York, 1970. (16) Kokossis, A. C.; Floudas, C. A. Optimisation of Complex Reactor Networks—I. Isothermal Operation. Chem. Eng. Sci. 1990, 45 (3), 595. (17) Hwang, S. Synthesis of Continuous Heterogeneous Catalytic Reactors. Ph.D. Thesis, University of Manchester Institute of Science and Technology, U.K., 2003. (18) Treybal, R. E. Adiabatic Gas Absorption and Stripping in Packed Towers. Ind. Eng. Chem. 1969, 61, 36. (19) Roper, G. H. Chlorination of Oleic Acid. Chem. Eng. Sci. 1953, 227. (20) Menting, J. E.; Grimm, R. A.; Weil, J. K.; Stirton, A. J. Chlorinated Alcohols: IV. The Chlorination of Oleic Acid. J. Am. Chem. Soc. 1969, 46 (2), 85. (21) Clegg, G. T.; Winter, P. Kinetics of the Reaction between Chlorine and Oleic Acid in Carbon Tetrachloride Solution. J. Am. Chem. Soc. 1972, 49, 433. (22) Wilke, C.; Chang, P. Correlation of Diffusion Coefficients in Dilute Solutions. AIChE J. 1955, 1, 264. (23) Winter, P. Mass Transfer with Chemical Reaction: The Absorption of Chlorine by Oleic Acid. Ph.D. Thesis, The Victoria University of Manchester, U.K., 1971. (24) Taylor, N. W.; Hilderbrand, J. H. Solubility VIII. Solubility Relations of Certain Gases. J. Am. Chem. Soc. 1923, 45, 682. (25) Sada, E.; Kumazawa, H.; Butt, A. Chemical Absorption Kinetics over a Wide Range of Contact Time: Absorption of Carbon Dioxide into Aqueous Solutions of Monoethanolamine. AIChE J. 1976a, 22 (1), 196. (26) Sada, E.; Kumazawa, H.; Butt, A.; Hayashi, D. Simultaneous Absorption of Carbon Dioxide and Hydrogen Sulfide into Aqueous Monoethanolamine Solution. Chem. Eng. Sci. 1976b, 31, 839. (27) Hagewiesche, D. P.; Ashour, S. S.; Al-Ghawas, H. A.; Sandall, O. C. Absorption of Carbon Dioxide into Aqueous Blends of Monoethanolamine and n-Methyldiethanolamine. Chem. Eng. Sci. 1995, 50 (7), 1071. (28) Rinker, E. B.; Ashour, S. S.; Sandall, O. C. Kinetics and Modeling of Carbon Dioxide Absorption into Aqueous Solutions of Diethanolamine. Ind. Eng. Chem. Res. 1996, 35, 1107. (29) Rinker, E. B.; Ashour, S. S.; Sandall, O. C. Absorption of Carbon Dioxide into Aqueous Blends of Diethanolamine and Methyldiethanolamine. Ind. Eng. Chem. Res. 2000, 39, 4346. (30) Aboudheir, A. Kinetic Modeling and Simulation of Carbon Dioxide Absorption into Highly Concentrated and Loaded Monoethanolamine Solutions, Ph.D. Thesis, University of Regina, Canada, 2002. (31) Aboudheir, A.; Tontiwachwuthikul, P.; Chakma, A.; Idem, R. Novel Design for the Nozzle of a Laminar Jet Absorber. Ind. Eng. Chem. Res. 2004, 43, 2568.

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(32) Ramachandran, N.; Aboudheir, A.; Idem, R.; Tontiwachwuthikul, P. Kinetics of the Absorption of CO2 into Mixed Aqueous Loaded Solutions of Monoethanolamine and Methyldiethanolamine. Ind. Eng. Chem. Res. 2006, 45, 2608.

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Model Building Methodology for Multiphase Reaction Systems

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