Chemical Engineering & Processing: Process Intensification 124 (2018) 174–185
Contents lists available at ScienceDirect
Chemical Engineering & Processing: Process Intensification journal homepage: www.elsevier.com/locate/cep
Rigorous design of multiphase reactors: Identification of optimal conditions for mass transfer limited reactions Mingquan Xie, Hannsjörg Freund
T
⁎
Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Lehrstuhl für Chemische Reaktionstechnik, Egerlandstrasse 3, 91058 Erlangen, Germany
A R T I C L E I N F O
A B S T R A C T
Keywords: Reactor design Multiphase system Mass transfer Carbon dioxide Chemical absorption Process intensification
Multiphase reaction systems are often complex due to the interaction of reaction and transport processes. To design optimal reactors for such systems, a rigorous optimization is necessary. In this regard, this work proposes extensions of a reactor design methodology based on rigorous optimization. Each phase is represented by one fluid element, subject to different mass and energy fluxes. While the unlimited external fluxes are optimally provided along the reaction route, sensitivity analysis of the parameters related to the limited external fluxes is performed. The extended methodology is applied in the reactor design for chemical absorption of CO2 as an example for complex multiphase reaction systems with severe mass transfer limitation. An accurate model which is also numerically suitable for optimization has been set up and validated with pilot plant data from literature. Optimal temperature profiles which result from balancing the different temperature-dependent phenomena are identified for cases with different inlet conditions, and tailor-made heat control strategies are shown for these cases. The potential of the developments in improving mass transfer rates by, e.g., structural design or solvent design has been quantified. This model-based design methodology is generally applicable to different multiphase reaction systems with severe mass transfer limitation.
1. Introduction In literature, many different reactor design methods exist including heuristics, attainable region approaches (e.g. [1,2]) and superstructure optimization (e.g. [3–5]). These design methods can be applied to single phase as well as multiphase reaction systems. For multiphase systems, Krishna and Sie [6] developed a strategy to choose between different multiphase reactors based on heuristics and with the aid of certain characteristics of the reaction systems. Mehta and Kokossis applied superstructure schemes to multiphase reactors [7] and eventually obtained homogeneous and multiphase reactor networks [8]. Kelkar and Ng [9] aggregated reactor attributes and constituent parts to form a reactor for the specific reaction under consideration. Comprehensive descriptions of these reactor design methods can be found in previous works for homogeneous systems [10] and for multiphase systems [11]. These methods have in common that they are intended to guide the optimal selection from existing reactors or networks of existing reactors/reactor parts. It is then difficult with these methods to systematically include novel process intensification options in the design and to obtain tailor-made reactors. In order to allow for both, the identification of the maximum potential of the reaction system as well as the design of innovative reactor concepts, based on
⁎
the concept of elementary process functions (EPF) [12] Freund, Peschel and Sundmacher recently proposed a new multi-level reactor design (MLRD) methodology [10,13]. The idea is to track a fluid element during the process, which travels through the reactor and changes its state within. On level 1, by continuously providing the fluid element with the optimal fluxes which are adjusted such that optimal states of the fluid element are achieved at all times, the optimal reaction conditions in the reactor can be identified. The most suitable fluxes to be further considered are determined by comparing the results of different cases including different combinations of fluxes, each representing different concepts for process intensification. On level 2, these fluxes obtained from level 1 are approximated by the optimal profiles of control variables such as the coolant temperature and the tube diameter by introducing the mass and heat transfer mechanisms, thereby checking the feasibility of realization of the most promising process intensification options. On level 3, the suitable control variables are further approximated using the detailed technical design. This methodology has been successfully applied to different systems, including gas phase reaction systems [10,13–15] and multiphase reaction systems [11,16–19] (Table 1 except for CO2 absorption). In those previously investigated systems, mass transfer limitations either can be completely neglected or have no significant influence. However,
Corresponding author. E-mail address:
[email protected] (H. Freund).
https://doi.org/10.1016/j.cep.2017.11.012 Received 29 April 2017; Received in revised form 16 October 2017; Accepted 19 November 2017 Available online 22 November 2017 0255-2701/ © 2017 Elsevier B.V. All rights reserved.
Chemical Engineering & Processing: Process Intensification 124 (2018) 174–185
M. Xie, H. Freund
Latin symbols a A c cp D H J k K L M p q r R t T u w X z Z
Greek symbols ϵ δ ν ρ
specific area [m2/m3] cross-sectional area [m2] concentration [mol/m3] heat capacity [J/(kg K)] diffusion coefficient [m2/s] Henry's law constant [Pa] mass transfer rate [mol/(m3 s)] reaction rate coefficient, various units equilibrium constant, various units thickness of liquid film [m] molar mass [kg/mol] pressure [Pa] specific heat flux [W/m3] reaction rate [mol/(m3 s)] gas constant [J/(mol K)] time [s] temperature [K] velocity [m/s] mass fraction [–] mole fraction [–] length [m] total length [m]
hold up [–] thickness of liquid segments [m] stoichiometric coefficient [–] density [kg/m3]
Abbreviations EPF MEA MLRD RMSE
elementary process functions monoethanolamine multi-level reactor design root-mean-square error
Indices C for g gl in l rev tot 0
carbon forward gas phase gas–liquid interface inlet liquid phase reverse total operating point
2. The influence of transfer limitations and the extensions of the methodology
this assumption is of course not generally applicable since in many multiphase reaction systems severe mass transfer limitations exist. In these systems, one or more reactants diffuse from one phase into another phase where the reaction takes place, and the mass transfer rate is rather small compared to the reaction rate. Thus, a large concentration gradient is present. In order to consider the influence of the limited mass flux, the methodology is further extended for such systems in this present contribution. More specifically, it is the goal to rigorously consider multiphase reaction systems based on the EPF concept, by describing the system with fluid elements and fluxes as well as analyzing and optimizing different fluxes. For this, the tools of rigorous optimization and sensitivity analysis are applied, in order to obtain an optimal reactor design. The extended methodology is applied to the chemical absorption of CO2 with monoethanolamine (MEA) as example. Although based on the function of a CO2 absorber in a chemical process the CO2 absorber is a separator rather than a reactor, the design of CO2 chemical absorber can represent the design of multiphase reactors. This system is chosen not only because it can represent the multiphase reaction systems with severe mass transfer limitation (see Table 1), but also because it is highly industrially relevant and many data are available. However, it should well be noted that the extended methodology is generally applicable to different multiphase reaction systems with severe mass transfer limitation, since it is only based on the balance equations, reaction kinetics, transfer kinetics, thermodynamics and system inherent boundaries.
To apply the MLRD methodology to the multiphase system in which mass fluxes are limited, the types and influences of flux limitations need to be reviewed and discussed in the EPF framework. 2.1. The influence of transfer limitations According to the EPF concept, when a fluid element is passing through a reactor, the state of the fluid element is changed by different types of fluxes. If each flux can be freely controlled, then each state in the operating range of the thermodynamic state space can be reached and kept in the reactor, i.e., possible species concentrations and temperature for the reaction are all attainable. The thermodynamic state determines the performance of the reaction (e.g. reaction rate or differential selectivity), and at least one state leading to maximum performance exists in the operating range of the state space. To keep this state, the corresponding fluxes of energy and all relevant components, which depend on the nature of the intrinsic reaction, need to be provided to counteract the effect of the reaction flux at this state (Fig. 1).
Table 1 Summary of the reaction systems to which the MLRD methodology has been applied and comparison to the CO2 absorption system in this work. System
Phase
Mass flux intensity
SO2 oxidation [10,13] EO synthesis [14,15]
Pseudo-homogeneous gas Pseudo-homogeneous gas
Negligible Negligible with constraints Considerable Decisive
Hydroformylation [11,16–19] Liquid and gas CO2 absorption, this work Liquid and gas
Fig. 1. The state in a fluid element (circle) leading to maximum performance and the corresponding fluxes (arrows).
175
Chemical Engineering & Processing: Process Intensification 124 (2018) 174–185
M. Xie, H. Freund
each phase with one fluid element in order to rigorously describe the multiphase system. Previous examples for the application of the MLRD methodology treated the fluid element as homogeneous due to the minor limitation of the mass and energy transfer in the fluid element. A further important extension in this contribution is the consideration of possible gradients of concentration and/or temperature resulting from the mass and/or energy transfer limitation inside a fluid element, when such gradient strongly affects the system. This leads to the treatment of an inhomogeneous fluid element. The systematic extensions of the methodology towards the rigorous description of multiphase systems are exemplified for the optimal design for the chemical absorption of CO2.
At a first view this concept may seem like an ideal CSTR, however, it can hardly be realized by a traditional CSTR since the output of the traditional CSTR is dependent on the state in the reactor. A more appropriate comparison of this concept would be a biological cell, with membranes separating and controlling different material fluxes and mechanisms maintaining optimal temperature. In reality, the realization of such an ideal case for chemical reactors is always too optimistic. Different transfer limitations affect the mixing of different components and energy. Some common types of mixing processes, including mixing of reactants and products, of different reactants, of desired products and undesired products, and of heat are listed in the supplementary material. Depending on the current development of different technologies, not all of these limitations are always possible to be fully removed. These limitations can come from different aspects. For example, there could be no good solvent discovered for certain gas–liquid reaction systems to provide high gas solubility so that mass transfer would not pose limitation to the performance. Another example could be that for certain gases, no suitable membrane known so far can separate them selectively. Thus, the change of state is often unavoidable in a reactor as the reaction continuously takes place. The limited fluxes are limiting the reactor performance. An optimal route through different states in the whole process, subject to such limited fluxes and other unlimited fluxes, is needed to achieve an overall optimal process (Fig. 2). The optimal extent of the unlimited fluxes can be calculated by solving a dynamic optimization problem, which is formulated based on the apparatus-independent model equations including balance equations, reaction kinetics, transfer kinetics, thermodynamics and design bounds. This has already been shown in previous works [10,14,11]. The limited fluxes are further discussed in the following section on the methodology extensions.
3. Case study: chemical absorption of CO2 with MEA Absorption is one of the most important methods to treat gas streams in order to change the gas composition [20]. Chemical absorption has a larger absorption potential than physical absorption due to the consumption of the absorbed gas component by the reaction. However, the advantage from the reaction involves higher complexity regarding apparatus design. Despite the popularity of the application of chemical absorption in many different sections of chemical industry, it is still no easy task to rigorously model a chemical absorption apparatus [21,22]. The reaction system often consists of a complex reaction network with multiple reversible reactions, and considerable amount of heat is generated within. The reactions should be fast in order to have a high efficiency of absorption, which makes the consideration of mass transfer unavoidable. The simultaneous consideration of complicated reaction kinetics and mass transfer under non-isothermal conditions results in a complex problem. Many models of different complexity have been proposed for chemical absorption, depending on whether the reaction and mass transfer are considered to be at equilibrium or kinetically controlled, and how detailed they are described [23–25]. The relative simple models are easy to adopt and thus have been widely used for design for many years. However, it has been shown that such models are physically inconsistent and may yield results that are in conflict with data from experimental studies [23]. The design based on the complex models is still largely based on repeated forward simulation studies, which is inefficient, difficult to take process intensification into account and may lead to non-optimal design. Chemical absorption of CO2 with aqueous chemical solvents such as alkanolamines is a well established technology for CO2 removal in order to reduce greenhouse gas emission which becomes more and more important nowadays. Aqueous MEA solvent has been widely studied and applied for such purpose due to its high reactivity and absorption capacity. However, this absorption process is still inefficient, especially with regard to energy utilization. For example, the energy consumption for this kind of CO2 absorption is estimated to be 15–30% of the net power production of a coal-fired power plant [26]. Different attempts were made to improve the efficiency. One of these attempts is by process (heat) integration, especially by intercooling [27]. For example, in
2.2. Methodology extensions With the above concept in mind, it can be concluded that the identification and quantification of material and energy flux limitations is an important first step necessary for optimal reactor design. So far, the MLRD methodology [10] has not dealt with such limited fluxes. In this contribution, the MLRD methodology is extended in a way that the limited fluxes are at their limits and the other fluxes are optimally provided along the route. This should be performed at the early stage of design, which is on level 1 of the MLRD methodology. The reason is that if the limitations are considered later on level 2 and result in a significant reduction of the objective performance, then the decisions made on level 1 including the selection between different combinations of optimal fluxes are not guaranteed to be correct. For example, one combination of optimal fluxes can result in the maximum performance on level 1, yet lead to lower performance than another combination on level 2. Sensitivity analysis can be performed on the parameters related to the limited fluxes to quantitatively predict the optimal performance achievable in the future due to the technology development that allows for breaking through today's technical limitations regarding the magnitude of fluxes. The unlimited/optimal fluxes can further be approximated with the previous design methodology in a multi-level approach in order to lead to a detailed design. Also, the previous methodology tracks only one fluid element which represents the one reacting phase. It simplifies the multiphase reactor design by treating the other phases as service phases only, for which the state variables can be freely controlled and the change in this phase is not related to the overall performance. However, this becomes less suitable when dealing with more complicated multiphase reaction systems. For example, some of the main reactants may only be provided to the reacting phase from other phases. Another example is that there could be two reacting phases coupled in one system. Due to this reason, we present an extension of the previous methodology by representing
Fig. 2. The optimal reaction route (an example process with no simultaneous product separation and with optimal reactant and energy fluxes).
176
Chemical Engineering & Processing: Process Intensification 124 (2018) 174–185
M. Xie, H. Freund
K 4 = c l,RNH2 c l,H3O+/ c l,RNH+3
the simulation by Freguia and Rochelle [28], the reboiler duty was reduced by 3.8% from intercooling in the middle of the absorption column. Plaza et al. [29] investigated the effect of intercooling on systems with variable CO2 lean loading, different solvent rate and different intercooling positions. This design approach based on variation of process parameters requires large amount of simulation work, and usually results in sub-optimal cases due to the complex and simultaneous influence of temperature on different aspects of the system such as reaction kinetics, solubility and mass transfer kinetics. In this work, the above mentioned rigorous optimization is performed to determine the optimal state profile of the reactor. Model equations are first established and validated by literature data. Then, the fluxes which can be freely integrated are optimized rigorously. Finally, the effect of enhancing limited fluxes is explored by means of sensitivity analysis.
The equilibrium constants are adopted from Aboudheir et al. [30] and summarized in Appendix A (Table A4). CO2 absorption takes place at moderate liquid phase loads mainly via direct reaction with MEA (Eq. (6)) [21], and thus the absorption via reaction with H2O (Eq. (7)) can be neglected. Among various reaction mechanisms in literature – zwitterion, termolecular and base-catalyzed hydration – the reaction of CO2 with primary, secondary and sterically hindered amines is usually described by the zwitterion mechanism [31]. In this work, the kinetics (Eq. (13)) are adopted from Kucka et al. [32] with the parameters shown in Appendix A (Eq. (A.1)).
r = k for c l,CO2 c l,RNH2 − k rev c l,RNHCOO- c l,H3O+
In this chemical absorption system, two continuous fluid phases contact counter-currently. One fluid phase is the gas phase containing CO2, H2O and other gaseous species which are treated in this work as one gaseous inert component, i.e., they have no influence on the reaction and do not diffuse into the liquid phase. The other fluid phase is the liquid phase containing MEA, CO2, H2O and resulting ionic species. In the reactor, the CO2 in the gas phase dissolves into the liquid phase and reacts with it.
K2
HCO−3 + H2 O ⇋ CO32 − + H3 O+ K3
RNHCOO− + H2 O ⇋ RNH2 + HCO−3
ctot,MEA = c l,RNH2 + c l,RNH+3 + c l,RNHCOO−
(14)
ctot,C = c l,CO2 +
(15)
RNH+3 + H2 O ⥪ ⥭ RNH2 + H3 O+
+ c l,CO2 − + c l,RNHCOO− 3
Additionally, the charge balance is derived: (16)
3
3.1.2. Solubility Many rigorous models exist to describe the phase behavior of electrolyte systems such as the generalized electrolyte non-random twoliquid model [33]. However, the focus of this work is not on investigating the implementation of an advanced thermodynamic model in the large-scale optimization, which has already been demonstrated in a previous work [17]. Also, in the present contribution it was important to keep the optimization problem numerically suitable to solve. Thus, Henry's law adopted from Austgen et al. [34] is used in our model (parameters in Table A5):
(1) (2) (3)
* 2= Xl,CO
K4
c l,HCO−3
c l,RNH+3 + c l,H3O+ = c l,HCO−3 + c l,OH− + 2 c l,CO2 − + c l,RNHCOO−
3.1.1. Reaction network and kinetics When the vapor–liquid equilibrium is reached, several reversible reactions exist at equilibrium (R = HOCH2CH2): K1
(13)
To determine this system with eight species and five reactions, three balance equations are required. Since the species originate from MEA and CO2, the total amount of MEA and carbon are calculated for balancing:
3.1. Model
2H2 O ⇋ OH− + H3 O+
(12)
(4)
pCO2 HCO2
(17)
ln HCO2 = a0 − a1/ Tl − a2 ln Tl + a3 Tl
K5
CO2 + 2H2 O ⇋ HCO−3 + H3 O+
3.1.3. Further thermodynamic relations The gas phase is described by the ideal gas law:
When the partial pressure of CO2 is larger than at equilibrium, the reaction of CO2 directly with MEA
pi = cg, i RTg,
kfor
CO2 + RNH2 + H2 O ⇄ RNHCOO− + H3 O+ k rev
(6)
p=
and the reaction of CO2 with H2O ′ k rev
(7)
(20)
(21)
3.1.4. Mass transfer According to the above model description, only CO2 mass transfer is taken into account in the interphase mass transfer. In the liquid phase, diffusion of different species is assumed to follow a Fickian diffusion approach with the diffusion term Di(∂2cl,i/∂x2), in which the diffusivity of CO2 is obtained from Hiwale et al. [22] (see Table A5 for parameters).
(8)
(9)
(
2 DCO2= (a0 + a1 ctot,MEA + a2 ctot,MEA )exp −
K2 = c l,CO2 − c l,H3O+/ c l,HCO−3
(10)
K3 = c l,RNH2 c l,HCO−3 / c l,RNHCOO−
(11)
3
∑ pi
Other relations regarding the total concentration of the liquid phase cl,tot and mole fraction of each species Xi are given in Appendix A.
With the assumption that the water concentration is constant due to its large amount in the liquid phase, the reaction equilibrium can be written as:
K1 = c l,OH− c l,H3O+
(19)
ln pH2O = a0 − a1/ Tl − a2 ln Tl + a3 Tla4
are kinetically controlled, while the other reversible reactions (Eqs. (1)–(4)) can still be considered to reach equilibrium instantaneously. Reaction (6) can be seen as the combination of reaction (3) and (5), and thus
k for K = 5 k rev K3
i = CO2 , inert, H2 O
The water vapor is considered to be saturated and its partial pressure is a function of temperature [35] (parameters in Table A5):
k for ′
CO2 + 2H2 O ⇄ HCO−3 + H3 O+
(18)
(5)
a3 + a 4 ctot,MEA Tl
) × 10
−6
(22)
The diffusivities of other species are assumed constant, which are estimated using the Nernst–Hartley electrolyte model and are 177
Chemical Engineering & Processing: Process Intensification 124 (2018) 174–185
M. Xie, H. Freund
neglected. The fluid elements are considered to feature a homogeneous temperature distribution.
summarized in Appendix A (Table A6). 3.1.5. Balance equations For this system, the reactor design methodology is extended to enable the tracking of two fluid elements simultaneously over length. This extension is necessary for the here considered system since the reaction takes place in the liquid phase, while the key reactant CO2 stays mainly in the gas phase. Thus, one fluid element is required to represent each phase. Since the mass and energy transfer between two fluid elements can only take place at a same location, the tracking of the two fluid elements should be performed over length. In this system, due to the large mass transfer limitation the reaction between CO2 and MEA mainly takes place near the gas–liquid interface, and its rate changes rapidly with the distance to the interface, which makes the homogeneous consideration of the fluid element inadequate. A new length dimension in the liquid fluid element is introduced in this work and the mass balance equations are formulated accordingly. The liquid phase in the CO2 absorber can be divided into the film region where the main reaction between the absorbed CO2 and MEA takes place, and the bulk region where the concentration of the CO2 from the inlet loading changes only due to the shift of the reaction equilibrium caused by the change of the liquid temperature. CO2 diffuses from the gas–liquid interface through the film region into the bulk region, in the direction which is defined as x direction (see Fig. 3). It is assumed that the liquid phase has a constant superficial velocity ul (ul > 0). Then, the steady-state mass balances of CO2, carbon and MEA in the liquid phase are
∂2c l,CO2 ul ∂c l,CO2 + νCO2 r = DCO2 ∂x 2 ϵl ∂z ul ∂ctot,C = ϵl ∂z
∑ Di i
ul ∂ctot,MEA = ϵl ∂z
∂2c l, i , ∂x 2
∑ Di i
∂ 2c
i ∈ CO2 , CO32 −, HCO−3 , RNHCOO−
l, i
∂x 2
,
i ∈ RNH2 , RNH+3 , RNHCOO−
d dT ul cp,l ρ l dzl
ug cp, v,g
∂c l,CO2 =0 ∂x
(27)
dz
= −Jgl, i ,
i = CO2 , inert
∫0
L
rΔr Hdx
dTg dz
= (Tl − Tg ) agl hgl
(32)
• Balance equations: Eqs. (16), (23)–(32) • Reaction kinetics: Eqs. (8)–(13) • Thermodynamics: Eqs. (17)–(21), (A.2)–(A.4) • Design parameters: see Table 2, except for the outlet condition • Inlet temperature • Absorber height
The boundary x = L is chosen at a location in the liquid bulk so that the concentration gradient near the gas–liquid interface is well described. If this location is too close to the interface, Eq. (27) is not satisfied. If this location is too far away from the interface, the number of grid points in the region with concentration gradient can be too small to accurately approximate the gradient. However, this location does not have to be exactly at the interface of the film region and bulk region. A value of L as 2 × 10−5 m is used in this work. The fluid element representing the gas phase is considered as homogeneous. Then, the mass balance in the gas phase is
d (ug cg, i )
gl
3.2.1. Model validation The above described model is validated with external pilot plant data from literature [36], for three experiments with different inlet conditions, more specifically different liquid to gas ratios and different inlet compositions. In all these experiments, the inlet liquid temperature is 313.15 K. The inlet gas temperature for cases 1 and 2 is 321.15 K, and for case 3 it is 313.76 K. The height of the packing is 4.2 m. The inlet conditions of these different experimental cases are summarized in Table 2. Further details of the pilot plant are given in the respective reference by Notz [36]. The characteristics of the absorber depend on the design and the inlet conditions. The specific gas–liquid interfacial area agl is set to 250 m2/m3 according to the packing Mellapak 250Y used in the experiments. The heat transfer coefficient is assumed constant as 31 W/ (m3 K) (estimated from the Chilton–Colburn analogy [37]). The liquid hold up is estimated with a model from Stichlmair et al. [38], and a mean value is used for each case. For model validation, heat control is not considered. Then, the following model equations are solved in the simulation:
(25)
x = L,
) −a
3.2. Simulation and optimization
with the boundary conditions at the x coordinate as (26)
RTg
dz
The values of the parameters for substance properties including heat capacity cp,l, reaction heat ΔrH, latent heat of water λ H2O and gas phase volumetric heat capacity cp, v,g can be found in Appendix A.
(24)
* 2 Xl,CO2 = Xl,CO
ug pH2 O
(31)
(23)
x = 0,
= − (Tl − Tg ) agl hgl − λ H2O
(
The comparison of simulation results and experimental data is shown in Fig. 4. The liquid temperature in each case rises after the liquid enters the column. At different locations in different cases, the liquid temperature reaches a maximum and is then continuously decreasing towards the outlet. The gas temperature is close to the liquid temperature due to the heat transfer between these two phases. The mass fraction of CO2 in the liquid increases due to the absorption. The root-mean-square error (RMSE) is summarized in Table 3. Although a
(28)
with the interphase mass transfer Jgl,i as
∂c l,CO2 ⎞ agl Jgl,CO2 = −DCO2 ⎛ ⎝ ∂x ⎠ x = 0
(29)
Jgl,inert = 0
(30)
⎜
⎟
The energy balance in temperature form for the liquid phase (Eq. (31)) includes reaction heat, heat transfer between gas and liquid, and latent heat from the phase change of water, while the energy balance in temperature form for the gas phase (Eq. (32)) only includes heat transfer between gas and liquid. Heat loss to the environment is
Fig. 3. CO2 concentration profile in the liquid phase of the CO2 absorber. The change of the location of the boundary between film region and bulk region as the absorption progresses (z direction) is shown. For illustrative purposes, an isothermal case is shown.
178
Chemical Engineering & Processing: Process Intensification 124 (2018) 174–185
M. Xie, H. Freund
Table 2 Design parameter of the CO2 absorber.
Table 3 Root-mean-square error of simulation results compared to pilot plant data.
Design parameter
Case 1
Case 2
Case 3
Inlet condition Inlet CO2(g) flow rate [mol/s] Inlet CO2(g) mole fraction (water free) [–] Ratio of inlet CO2(g) to MEA [–] Lean solvent CO2 loading [–] Weight fraction of MEA [–]
0.0540 6.48% 0.406 0.0950 0.292
0.0534 6.44% 0.132 0.245 0.255
0.0250 3.84% 0.0959 0.232 0.287
Absorber characteristics Liquid hold up [–] Specific interfacial area [m2/m3] Heat transfer coefficient [W/(m3 K)] Pressure [Pa]
0.037 250 31 105
0.11 250 31 105
0.047 250 31 105
Outlet condition CO2 removal [–]
86.80%
76.42%
87.30%
Variable
Case 1
Case 2
Case 3
RMSE of liquid temperature RMSE of mass fraction of CO2 in liquid ×102
1.68 K 0.878
2.14 K 0.0622
1.80 K 0.102
simple fluid element model is used, it could well be validated with external pilot plant data. Thus, the model proposed in the present contribution can be considered reliable and can further be used for optimization. Fig. 5. The balanced fluid elements in the absorber.
3.2.2. Optimization As stated before, to design a reactor, the material and energy flux limitations need to be determined first. Regarding the mixing of different reactants, CO2 and MEA are unavoidably separated by the phase split. In this work, the dosing of reactants is not investigated. Regarding the mixing of reactants and products, the ionic species are difficult to be selectively removed. Regarding the mixing of heat, it is possible to control the temperature by, e.g., aforementioned intercooling. Thus, the optimal reactor is obtained with an optimal temperature profile, which can be deducted from the following optimization.
In order to reach the optimal temperature profile in each fluid element, optimal heat fluxes are provided to the fluid elements. The energy balance is derived by adding a free heat flux q for each fluid element.
d dT ul cp,l ρ l dzl
= ql − (Tl − Tg ) agl hgl − λ H2O
(
ug pH2 O RTg
dz
) −a
gl
∫0
L
rΔr Hdx (33)
Fig. 4. Temperature profiles in both phases (left) and mass fraction profile of CO2 in the liquid phase (right) of different cases. Solid line: liquid phase; dashed line: gas phase. Square symbol: experimental data of the liquid phase; circle symbol: experimental data of the gas phase.
179
Chemical Engineering & Processing: Process Intensification 124 (2018) 174–185
M. Xie, H. Freund
ug cp, v,g
dTg dz
= qg + (Tl − Tg ) agl hgl
With this formulation, the results from the previous model validation serve as references where qg = ql = 0. Then, the scenario with no limitation on the additional heat fluxes applied to both phases is investigated, which means optimal temperatures are obtained at all the positions along the absorber. Furthermore, the scenarios where the additional heat flux is applied to only one phase, i.e. ql = 0 or qg = 0 are considered. In these scenarios, the other parts of the optimization problem OP1 remain unchanged. The results of these scenarios indicate the importance of each flux, which is particularly useful when a certain heat flux would be difficult to be realized in practice. The optimization problem OP1 is solved and the optimal temperature profiles (Fig. 6) are obtained. These temperature profiles provide optimal reaction conditions at any place of the reactor. If temperatures are lower, the solubility of CO2 is higher but the reaction rate and diffusion rate are lower (and vice versa). The optimality of the temperature profiles results from the balance of reaction rate, solubility and diffusion rate. For different cases, the initial temperatures of the liquid feature quite different optimal values. In the reactor, for cases 1 and 2, the optimal liquid temperature continuously decreases. Unlike the temperature decrease in the previous simulation (Fig. 4), which is due to the cooling from the gas phase, the decrease here is freely controlled by the external heat flux according to the liquid's state. In case 3, the optimal liquid temperature is increasing along the liquid flow, which seems to contradict the common sense that low temperature promotes absorption. The explanation for this behavior is that with increased temperature, although the solubility of CO2 is reduced, the reaction and diffusion coefficients are increased, which can overall promote the chemical absorption. In these cases, the optimal liquid temperatures are not at the bound of the temperature range, so there is no need to investigate the kinetics in a different temperature range. For the gas phase, the low temperature decreases the volumetric gas flow rate and henceforth increases the residence time of the gas phase.
(34)
The balance of the fluid elements including considered fluxes in this process can be regarded as illustrated in Fig. 5. At each location, limited material and heat fluxes occur between the gas and the liquid fluid elements, and an additional heat flux is provided to each element. The heat control can reduce the regeneration duty by increasing the CO2 cyclic carrying capacity. In this way, the length is kept the same when the removed fraction of CO2 is maximized. Another scenario is to reduce the absorber column height and thereby the capital cost by optimal heat control while maintaining a same CO2 absorption capacity. The choice between these two optimization objectives would lead to different results, and it should be made according to the economic evaluation and the design task. The MEA process benefits more from the latter [39]. Thus, in this example the length should be minimized via optimal heat fluxes and initial conditions under the constraint that the removed fraction of CO2 is kept the same as for the benchmark case. The flow rates of the components in the flue gas are kept the same as in the experimental cases shown in Table 2. The lean solvent CO2 loading is also kept the same, meaning that a same desorber can be applied. The total MEA amount is fixed to the experimental value instead of fixing the liquid flow rate and MEA mass fraction. Then, the optimization problem to be solved is:
Obj =
min
(OP1)
Z
T l,in, ql (z ), Tg,in, qg (z ), w MEA, ul
s.t.
• Balance equations: Eqs. (16), (23)–(30), (33)–(34) • Reaction kinetics: Eqs. (8)–(13) • Thermodynamics: Eqs. (17)–(21), (A.2)–(A.4) • Design parameters: see Table 2, except for weight fraction of MEA • Temperature: 298.15 K ≤T ≤ 363.15 K, 298.15 K ≤T ≤ 363.15 K l
g
Fig. 6. Optimal temperature profile (left) and heat flux profile (right) of different cases. Solid line: liquid phase; dashed line: gas phase.
180
Chemical Engineering & Processing: Process Intensification 124 (2018) 174–185
M. Xie, H. Freund
To maintain this optimal temperature profile, an optimal heat flux profile needs to be provided to each phase as seen in Fig. 6. In every case, heat needs to be removed from the gas phase to keep the gas temperature low. In cases 1 and 3, additional heat needs to be supplied to the liquid phase to keep liquid temperature optimal. In case 2, the liquid phase is heated at the beginning and cooled later on. This shows that the heat control strategy should be tailor-made for each absorber to achieve optimal performance. To achieve selective heating or cooling to the individual phases, some process intensification options are available. For example, separation coupled with intercooling or interheating at multiple locations of the column can be applied to approximate the optimal flux profiles. The continuous cooling or heating via a jacket outside the column wall acts mostly on the gas phase, since the average liquid hold up is small, and the liquid hold up near the wall is even smaller [40]. Microwave heating can also be applied to selectively heat the liquid phase in the packed column [41,42]. The choice between different options involves the consideration of technical feasibility, safety and cost, which is not further discussed in the current contribution. When heat control is applied to only the liquid phase, different heat flux profiles are also needed for different cases as shown in Fig. 7. In case 1, heating is applied near both inlet and outlet of the absorber, while cooling is applied to the middle part. The resulting temperature in the middle part is approximately the mean temperature of optimal gas and liquid phase temperatures in Fig. 6. This is a compromise so that the gas is not overheated and the liquid temperature is still high enough. In cases 2 and 3, cooling is applied first, followed by heating near the end. And the resulting temperature again is between the optimal gas and liquid phase temperatures. When heat control is applied to only the gas phase, cooling is applied in each case. However, in case 2 the gas inlet temperature is at its lower bound, while in the other cases higher gas inlet temperatures are needed to prevent liquid phase from being cooled down too much
(Fig. 8). The resulting lengths from different heat control options of all cases are plotted in Fig. 9. An improvement of more than 20% in each case (up to 38%) compared to the reference case is obtained when both liquid and gas phases have optimal temperature profiles. Heat control only in the liquid phase leads to less improvement compared to only in the gas phase. In case 2, heat control only in the gas phase leads to almost the same performance as heat control in both phases. In short, with the option where both phases are optimally controlled, each phase can be manipulated by its own external flux and is linked to each other by the fluxes in between the two phases. Different process intensification options can be directly considered in the design and quantitatively compared in order to obtain the optimal strategy, which can be non-intuitive and therefore hard to be derived on the basis of heuristics and/or pure forward simulation studies. 3.2.3. Sensitivity analysis It is important to reveal the influence of certain parameters on the optimal result for future improvement of the absorbers. For example, a different packing could provide a better specific gas–liquid interfacial area, and a different solvent could provide better solubility or diffusivity of CO2. With the methodology provided, the sensitivity of the system with regard to the individual parameters can be analyzed to guide ongoing research for process intensification and to reveal the effect of the parameter uncertainty on the objective. This was performed by systematically varying the studied parameters and performing optimizations while keeping all the other parameters and the optimization problem the same as in the original optimization OP1. The studied parameters are the gas–liquid interfacial area agl, liquid hold up ϵl, Henry's law constant HCO2 and diffusivity DCO2 . The gas–liquid interfacial area and liquid hold up are changed when a different packing is applied, and the Henry's law constant and diffusivity are changed when a different solvent is used. The variation of Henry's law constant Fig. 7. Heat control only in liquid phase: optimal temperature profile (left) and heat flux profile (right) of different cases. Solid line: liquid phase; dashed line: gas phase.
181
Chemical Engineering & Processing: Process Intensification 124 (2018) 174–185
M. Xie, H. Freund
Fig. 8. Heat control only in gas phase: optimal temperature profile (left) and heat flux profile (right) of different cases. Solid line: liquid phase; dashed line: gas phase.
full potential of future developments regarding packing structure and/ or solvent system can be revealed. For example, for a reactor with a gas–liquid interfacial area the same as in Table 2 and another one with an increase of 10% in the interfacial area, the resulting optimal temperature profiles are different (see Fig. 11). It can be seen that the change of gas–liquid interfacial area affects the section with relatively low temperature more largely, since in this section the mass transfer, which is directly related to the gas–liquid interfacial area, dominates the absorption behavior.
3.3. Numerical solution approach In order to solve the dynamic optimization problems, the differential algebraic equation system is discretized with the method of orthogonal collocation on finite elements [45] on the z coordinate (along the reactor), and with the finite difference method on the x coordinate
Fig. 9. Optimal total lengths of the CO2 absorbers with different heat control options in different cases.
HCO2 and diffusivity DCO2 is realized by introducing a multiplication factor in the definitions. This analysis is performed for case 2 with heat control in both phases as example. Different sensitivities of the reactor performance on the different parameters are compared in Fig. 10. The increase of the gas–liquid interfacial area agl results in smaller performance change compared to the decrease of the agl. The increase and decrease of other parameters result in similar performance changes. The comparison between the sensitivities on different parameters shows that in the investigated range the influence of different parameters has a sequence of “gas–liquid interfacial area agl ≥ Henry's law constant HCO2 > diffusivity DCO2 > liquid hold up ϵl”. This sequence is in accordance with the results from Huepen and Kenig [43] and Toennies et al. [44]. However, in this work instead of fixing the operating conditions for varied parameters, the reactor is optimized for each varied parameter so that the
Fig. 10. Parameter sensitivity.
182
Chemical Engineering & Processing: Process Intensification 124 (2018) 174–185
M. Xie, H. Freund
in a column. The model has been successfully verified with experimental pilot plant data from literature. Based on this model, the optimal temperature profiles of gas and liquid phases, and the corresponding optimal external heat flux profiles are calculated by dynamic optimization for three cases with different inlet conditions using various heat control options. The optimal temperatures result from balancing reaction rate, mass transfer rate and solubility. The optimal external heat flux profiles can be totally different for different cases. Thus, to design an optimal CO2 absorber a tailor-made strategy should be applied, which can be derived from the optimization methodology in this work. The limited mass flux between gas phase and liquid phase and the diffusive flux within the liquid phase can be described with certain parameters including interfacial area, Henry's law constant, diffusion coefficient and liquid hold-up. Sensitivity analysis on these parameters quantitatively show the effect of improving structure and solvent design on this system, provided that optimal heat fluxes are always enforced.
Fig. 11. Different optimal temperature profiles (liquid phase) for the CO2 absorbers with different gas–liquid interfacial areas.
(into the liquid bulk). The equation system is thereby converted into a system of nonlinear algebraic equations and then solved using the stateof-the-art nonlinear programming solver CONOPT 3.15 C under AMPL on a PC (Intel® Core™ i7-2600 CPU (3.40 GHz), 16 GB memory). CONOPT is a generalized reduced-gradient (GRG) algorithm for solving large-scale nonlinear programs involving sparse nonlinear constraints [46]. The z coordinate is uniformly discretized with 30 finite elements and 4 collocation points per finite element. The grid distribution in the numerical discretization of the x coordinate can largely influence the simulation results. This has been shown in similar models for CO2 absorbers [47,44]. Here, the thickness of the jth segment δj is calculated as follows:
δj =
⎧L × ⎨L × ⎩
1 m (n − m + 1) m m (n − m + 1)
4. Conclusion It is a challenge to rigorously design multiphase reactors with severe mass transfer limitations. In the present contribution, extensions of a recent optimal reactor design methodology [10] are proposed. The major extension is to treat technically limited and unlimited fluxes differently. While the unlimited fluxes are optimally provided along the reaction route, sensitivity analysis of the parameters which are related to the limited fluxes is performed, provided that the optimality of unlimited fluxes is always enforced. Furthermore, the previous methodology has been extended in other aspects in order to rigorously consider multiphase systems. Each phase is represented by one fluid element, and each fluid element is subject to its own internal fluxes, transfer fluxes between two elements and external fluxes. The external fluxes for each fluid element can be separately optimized. Also, fluid elements can feature internal gradients due to the transfer limitations. The extended methodology has been applied to the example system of chemical absorption of CO2 with MEA based on a two-dimensional model proposed in this contribution. Up to 38% performance improvements were obtained for the investigated cases, with optimal external heat fluxes which vary between different cases. The potential of future developments regarding solvent design and structure design were quantitatively identified in the sensitivity analysis.
if j ≤ m if j > m
(35)
where n is the number of segments and m is a grid distribution factor. The value of n should be chosen based on the balance between computing time and accuracy, while m is used to distribute grid points according to the gradients. In this work, n = 30 and m = 20 were identified as suitable values. Another technique applied in this optimization is the careful scaling, which is especially important to this work since some variables such as concentrations of ionic species and concentration gradients have very different orders of magnitude. Scaling of the optimization variables promotes the convergence of the nonlinear optimization problem. The variables which need to be scaled depend on the implementation. With the units as in the Nomenclature, the magnitudes of the variables c l,H3O+ , ∂c l,CO2/ ∂x and ∂2c l,CO2/ ∂x 2 are in the order of 10−6, 104 and 109.
Acknowledgements The authors gratefully acknowledge funding from the German Research Council (DFG), within the framework of its ‘Excellence Initiative’ (Cluster of Excellence ‘Engineering of Advanced Materials’ at Friedrich-Alexander-Universität Erlangen-Nürnberg). The authors also thankfully acknowledge financial support from the Helmholtz Association within the frame of the Helmholtz Energy Alliance “Energy Efficient Multiphase Chemical Processes”.
3.4. Summary of the case study A rigorous rate-based model both accurate and numerically suitable for optimization is proposed for chemical absorption of CO2 with MEA Appendix A. Additional equations and parameters Reaction rate coefficient with unit of [m3/(mol s)] is
k for = 4.495 × 108 exp(−44 940/(RT))
(A.1)
Since the major components in the liquid phase are water and MEA, of which the total amounts barely change in the absorber, the total concentration of the liquid phase cl,tot can be assumed constant and approximately related to the mass fraction of total MEA w MEA .
c l,tot ≈ ctot,MEA + c tot,H2O ≈ ρ l w MEA / MMEA + ρ l (1 − w MEA )/ MH2O
(A.2)
The change of the liquid phase density ρl in this investigated system is found to be rather small (< 2%) [48], and therefore assumed constant as 1022 kg/m3. Then, the mole fraction of each species can be calculated: 183
Chemical Engineering & Processing: Process Intensification 124 (2018) 174–185
M. Xie, H. Freund
Table A4 Reaction equilibrium constants as lnK = a1/T + a2 lnT + a3. Equilibrium constant K1 K2 K3 K4 K5
[(mol/dm3)2] [mol/dm3] [mol/dm3] [mol/dm3] [mol/dm3]
a1
a2
a3
T, range [K]
−13 445.9 −12 431.7 −3090.83 −5851.11 −12 092.1
−22.4773 −35.4819 0.0 0.0 −36.7816
140.932 220.067 6.69425 −3.3636 235.482
273–498 273–498 298–413 298–413 273–498
Table A5 Parameters for substance properties. Variable
a0
a1
a2
a3
a4
HCO2 (Eq. (18)) pH2O (Eq. (21))
170.7126 73.649
8477.711 7258.2
21.95743 7.30374
0.005781 4.1653 × 10−6
– 2
DCO2 (Eq. (22))
2.35
4.01 × 10−4
1.29 × 10−7
2119
0.0934
Table A6 Diffusion coefficients. Species
Diffusion coefficient [m2/s]
RNH2 H3O+ OH− HCO − 3 CO 32 −
1.2859 × 10−9 9.9507 × 10−9 5.6362 × 10−9 1.549 × 10−9 9.8484 × 10−10
RNH+ 3 RNHCOO−
1.4211 × 10−9
1.4211 × 10−9
Xl, i = c l, i/ c l,tot
(A.3)
Xg, i = cg, i/ ∑ cg, i
(A.4)
The liquid phase heat capacity cp,l changes only slightly (< 3% for this system) with respect to temperature and composition when the amount of MEA and CO2 is small [49,50], so a fixed value of 3.656 × 103 J/(kg K) is used in this work. The reaction heat ΔrH only takes the direct reaction of CO2 with MEA into account and also a fixed value of 84 431 J/mol [22] is used. And the latent heat of water takes the value of 45 × 103 J/mol [22]. The gas phase volumetric heat capacity cp, v,g is 1.17 × 103 J/(m3 K) [51]. Other parameters for calculating the reaction equilibrium constants, Henry's law constants, partial pressure of water vapor and diffusion coefficients are given in Tables A4–A6. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.cep.2017.11.012.
[11] A. Peschel, B. Hentschel, H. Freund, K. Sundmacher, Design of optimal multiphase reactors exemplified on the hydroformylation of long chain alkenes, Chem. Eng. J. 188 (2012) 126–141. [12] H. Freund, K. Sundmacher, Towards a methodology for the systematic analysis and design of efficient chemical processes. Part 1. From unit operations to elementary process functions, Chem. Eng. Process. 47 (12) (2008) 2051–2060. [13] H. Freund, A. Peschel, K. Sundmacher, Model-based reactor design based on the optimal reaction route [Modellgestützter Reaktorentwurf auf Basis der optimalen Reaktionsführung], Chemie-Ingenieur-Technik 83 (4) (2011) 420–426. [14] A. Peschel, F. Karst, H. Freund, K. Sundmacher, Analysis and optimal design of an ethylene oxide reactor, Chem. Eng. Sci. 66 (24) (2011) 6453–6469. [15] A. Peschel, A. Jörke, K. Sundmacher, H. Freund, Optimal reaction concept and plant wide optimization of the ethylene oxide process, Chem. Eng. J. 207–208 (2012) 656–674. [16] B. Hentschel, H. Freund, K. Sundmacher, Model-based determination of the optimal reaction route for integrated multiphase processes [Modellbasierte ermittlung der optimalen reaktionsführung für integrierte mehrphasenprozesse], ChemieIngenieur-Technik 86 (7) (2014) 1080–1087. [17] B. Hentschel, A. Peschel, M. Xie, C. Vogelpohl, G. Sadowski, H. Freund, K. Sundmacher, Model-based prediction of optimal conditions for 1-octene hydroformylation, Chem. Eng. Sci. 115 (2014) 58–68. [18] B. Hentschel, A. Peschel, H. Freund, K. Sundmacher, Simultaneous design of the optimal reaction and process concept for multiphase systems, Chem. Eng. Sci. 115 (2014) 69–87. [19] B. Hentschel, G. Kiedorf, M. Gerlach, C. Hamel, A. Seidel-Morgenstern, H. Freund, K. Sundmacher, Model-based identification and experimental validation of the
References [1] D. Hildebrandt, D. Glasser, C.M. Crowe, Geometry of the attainable region generated by reaction and mixing – with and without constraints, Ind. Eng. Chem. Res. 29 (1990) 49–58. [2] M. Feinberg, D. Hildebrandt, Optimal reactor design from a geometric viewpoint – I. Universal properties of the attainable region, Chem. Eng. Sci. 52 (1997) 1637–1665. [3] L.K.E. Achenie, L.T. Biegler, A superstructure based approach to chemical reactor network synthesis, Comput. Chem. Eng. 14 (1990) 23–40. [4] A.C. Kokossis, C.A. Floudas, Optimization of complex reactor networks. 2. Nonisothermal operation, Chem. Eng. Sci. 49 (1994) 1037–1051. [5] M. Hillestad, A systematic generation of reactor designs. II. Non-isothermal conditions, Comput. Chem. Eng. 29 (2005) 1101–1112. [6] R. Krishna, S. Sie, Strategies for multiphase reactor selection, Chem. Eng. Sci. 49 (24 (Part A)) (1994) 4029–4065. [7] V. Mehta, A. Kokossis, Development of novel multiphase reactors using a systematic design framework, Comput. Chem. Eng. 21 (Suppl. 1) (1997) S325–S330. [8] V. Mehta, A. Kokossis, Nonisothermal synthesis of homogeneous and multiphase reactor networks, AlChE J. 46 (11) (2000) 2256–2273. [9] V. Kelkar, K. Ng, Screening multiphase reactors for nonisothermal multiple reactions, AlChE J. 46 (2) (2000) 389–406. [10] A. Peschel, H. Freund, K. Sundmacher, Methodology for the design of optimal chemical reactors based on the concept of elementary process functions, Ind. Eng. Chem. Res. 49 (21) (2010) 10535–10548.
184
Chemical Engineering & Processing: Process Intensification 124 (2018) 174–185
M. Xie, H. Freund
[20]
[21] [22]
[23] [24] [25] [26] [27]
[28] [29] [30]
[31] [32] [33] [34]
[35]
[36] R.J. Notz, CO2-Abtrennung aus Kraftwerksabgasen mittels Reaktivabsorption, Logos Berlin, 2010 ISBN 3832523863. [37] T.H. Chilton, A.P. Colburn, Distillation and absorption in packed columns – a convenient design and correlation method, Ind. Eng. Chem. Res. 27 (3) (1935) 255–260. [38] J. Stichlmair, J. Bravo, J. Fair, General model for prediction of pressure drop and capacity of countercurrent gas/liquid packed columns, Gas Sep. Purif. 3 (1) (1989) 19–28. [39] K. Li, W. Leigh, P. Feron, H. Yu, M. Tade, Systematic study of aqueous monoethanolamine (MEA)-based CO2 capture process: techno-economic assessment of the MEA process and its improvements, Appl. Energy 165 (2016) 648–659. [40] M. Fourati, V. Roig, L. Raynal, Experimental study of liquid spreading in structured packings, Chem. Eng. Sci. 80 (2012) 1–15. [41] R. Cherbański, Numerical simulations of heat transfer in a packed column: comparison of microwave and convective heating, Heat Mass Transf. 51 (5) (2015) 723–733. [42] T. Durka, T. Van Gerven, A. Stankiewicz, Microwaves in heterogeneous gas-phase catalysis: experimental and numerical approaches, Chem. Eng. Technol. 32 (9) (2009) 1301–1312. [43] B. Huepen, E. Kenig, Rigorous modeling and simulation of an absorption-stripping loop for the removal of acid gases, Ind. Eng. Chem. Res. 49 (2) (2010) 772–779. [44] I. Tönnies, H. Mangalapally, H. Hasse, Sensitivity study for the rate-based simulation of the reactive absorption of CO2, Energy Proc. 4 (2011) 533–540. [45] J.S. Logsdon, L.T. Biegler, Accurate solution of differential–algebraic optimization problems, Ind. Eng. Chem. Res. 28 (11) (1989) 1628–1639. [46] A. Drud, CONOPT: a GRG code for large sparse dynamic nonlinear optimization problems, Math. Program. 31 (2) (1985) 153–191. [47] N. Asprion, Nonequilibrium rate-based simulation of reactive systems: simulation model, heat transfer, and influence of film discretization, Ind. Eng. Chem. Res. 45 (6) (2006) 2054–2069. [48] A. Hartono, E. Mba, H. Svendsen, Physical properties of partially CO2 loaded aqueous monoethanolamine (MEA), J. Chem. Eng. Data 59 (6) (2014) 1808–1816. [49] L.-F. Chiu, H.-F. Liu, M.-H. Li, Heat capacity of alkanolamines by differential scanning calorimetry, J. Chem. Eng. Data 44 (3) (1999) 631–636. [50] R. Weiland, J. Dingman, D. Cronin, Heat capacity of aqueous monoethanolamine, diethanolamine, N-methyldiethanolamine, and N-methyldiethanolamine-based blends with carbon dioxide, J. Chem. Eng. Data 42 (5) (1997) 1004–1006. [51] C.L. Yaws, Yaws’ Handbook of Thermodynamic Properties for Hydrocarbons and Chemicals, Knovel, 2009.
optimal reaction route for the hydroformylation of 1-dodecene, Ind. Eng. Chem. Res. 54 (6) (2015) 1755–1765. Ö Yildirim, A. Kiss, N. Hüser, K. Leßmann, E. Kenig, Reactive absorption in chemical process industry: a review on current activities, Chem. Eng. J. 213 (2012) 371–391. E. Kenig, L. Kucka, A. Górak, Rigorous modeling of reactive absorption processes, Chem. Eng. Technol. 26 (6) (2003) 631–646. R. Hiwale, S. Hwang, R. Smith, Model building methodology for multiphase reaction systems – modeling of CO2 absorption in monoethanolamine for laminar jet absorbers and packing beds, Ind. Eng. Chem. Res. 51 (11) (2012) 4328–4346. E. Kenig, R. Schneider, A. Górak, Reactive absorption: optimal process design via optimal modelling, Chem. Eng. Sci. 56 (2) (2001) 343–350. R. Taylor, (Di)still modeling after all these years: a view of the state of the art, Ind. Eng. Chem. Res. 46 (13) (2007) 4349–4357. C. Kale, A. Grak, H. Schoenmakers, Modelling of the reactive absorption of CO2 using mono-ethanolamine, Int. J. Greenh. Gas Control 17 (2013) 294–308. M. Jassim, G. Rochelle, Innovative absorber/stripper configurations for CO2 capture by aqueous monoethanolamine, Ind. Eng. Chem. Res. 45 (8) (2006) 2465–2472. M. Wang, A. Lawal, P. Stephenson, J. Sidders, C. Ramshaw, Post-combustion CO2 capture with chemical absorption: a state-of-the-art review, Chem. Eng. Res. Des. 89 (9) (2011) 1609–1624. S. Freguia, G. Rochelle, Modeling of CO2 capture by aqueous monoethanolamine, AlChE J. 49 (7) (2003) 1676–1686. J. Plaza, E. Chen, G. Rochelle, Absorber intercooling in CO2 absorption by piperazine-promoted potassium carbonate, AlChE J. 56 (4) (2010) 905–914. A. Aboudheir, P. Tontiwachwuthikul, A. Chakma, R. Idem, Kinetics of the reactive absorption of carbon dioxide in high CO2-loaded, concentrated aqueous monoethanolamine solutions, Chem. Eng. Sci. 58 (23–24) (2003) 5195–5210. P. Vaidya, E. Kenig, CO2-alkanolamine reaction kinetics: a review of recent studies, Chem. Eng. Technol. 30 (11) (2007) 1467–1474. L. Kucka, I. Müller, E. Kenig, A. Grak, On the modelling and simulation of sour gas absorption by aqueous amine solutions, Chem. Eng. Sci. 58 (16) (2003) 3571–3578. C.-C. Chen, Y. Song, Generalized electrolyte-NRTL model for mixed-solvent electrolyte systems, AlChE J. 50 (8) (2004) 1928–1941. D. Austgen, G. Rochelle, P. Xiao, C.-C. Chen, Model of vapor–liquid equilibria for aqueous acid gas–alkanolamine systems using the electrolyte-NRTL equation, Ind. Eng. Chem. Res. 28 (7) (1989) 1060–1073. T.E. Daubert, R.P. Danner, Physical and Thermodynamic Properties of Pure Chemicals: Data Compilation, Taylor & Francis, Washington, 1989 ISBN 1560321555.
185
