Intensification potential of hollow fiber membrane contactors for CO2 physical absorption using methanol as solvent

UNIVERSITY OF VALLADOLID SCHOOL OF INDUSTRIAL ENGINEERS Master in Chemical Engineering MASTER THESIS Intensification potential of hollow fiber membrane contactors for CO2 physical absorption using methanol as solvent Author: Álvarez Escalante, Iván Supervisors: Rode, Sabine Belaissaoui, Bouchra ENSIC Nancy, January 2021 TFM REALIZADO EN PROGRAMA DE INTERCAMBIO TÍTULO: Intensification potential of hollow fiber membrane contactors for CO2 physical absorption using methanol as solvent ALUMNO: Iván Álvarez Escalante FECHA: 29-01-2021 CENTRO: École nationale supérieure des industries chimiques UNIVERSIDAD: Université de Lorraine TUTORAS: Sabine Rode y Bouchra Belaissaoui INTENSIFICATION POTENTIAL OF HOLLOW FIBER MEMBRANE CONTACTORS FOR CO2 PHYSICAL ABSORPTION USING METHANOL AS SOLVENT Student: Ivan ALVAREZ ESCALANTE Supervisors: Sabine RODE Bouchra BELAISSAOUI January 2021 ABSTRACT: Integrated Gasification Combined Cycle (IGCC) produces syngas through the gasification of carbonaceous fuels. Removing CO2 for storage from the hydrogen gas is a key step in the process for the IGCC power plant for both the power generation and mitigation of greenhouse gas emissions. RectisolTM is a commercial process which is applied to syngas physical absorption using methanol as solvent and packed contactor technology. This study investigates the intensification potential of using dense layer hollow fiber membrane contactors (HFMC) instead of packed contactors (PC), which have additional design constraints due to flooding. Moreover, it has been considered pressure drop restrictions in the HFMC design. The research is based on previous simulation work with Aspen HYSYS taken out under different operating conditions of inlet temperature, inlet pressure and inlet CO2 concentration. It was obtained an intensification potential such that the volume of the contactor could be reduced as minimum 100 times if PC are substituted by HFM. In addition, a parametric study revealed that for HFMC contactor, the volume is not notably affected by methanol inlet temperature, whereas for PC is reduced at higher liquid inlet temperatures. Moreover, it is decreased at higher inlet pressures and at higher concentrations of CO2 in the gas inlet. KEYWORDS: Syngas purification, intensification, physical absorption, hollow fiber membrane contactor, methanol ACKNOWLEDGMENTS In the first place, I would like to express my gratitude to my supervisors, Professor Sabine Rode and Assistant Professor Bouchra Belaissaoui, for their guidance and patience during my research project. I am extremely grateful for their friendly meetings and for their personal support. Next, I would like to thank to Dayra, this work would not have been possible without her unconditional support. And to my parents, for their love and encouragement, without them I would never have enjoyed so many opportunities. I NOMENCLATURE Latin symbols Symbol Definition Units A Cross section area m2 a Specific area m2solid m-3contactor aLG Gas-liquid interfacial area. m2 interface gas-liquid m-3contactor B Pore geometry efficiency dimensionless C Concentration mole m-3 D Diffusion coefficient m2 s-1 d Diameter m Ea Permeation activation energy J mol-1 FLG Flow factor dimensionless Fp Packing factor of the packed column dimensionless FMC Function to integrate in the membrane contactor m6 kmole-1 FPC Function to integrate in the packed column m4 kmole-1 Fr Froude number dimensionless g Constant of acceleration due to gravity m s-2 G Gas molar flow through the cross section mole s-1 H Henry constant of component Pa HET Height of a theoretical stage m HUT Height of a transfer unit m k Individual mass transfer coefficient m s-1 K Global mass transfer coefficient m s-1 L Liquid molar flow through the cross section mole s-1 M mol Molar mass of component g mol-1 m Partition coefficient gas-liquid m3 gas m-3 liquid N Molar flow in the interphase mole m-2 s-1 NET Number of theoretical stages dimensionless NUT Number of transfer units dimensionless P Pressure Pa R Mass transfer resistance s m-1 RLG Ratio liquid-gas m3 liquid m-3 gas Rg Universal gases constant J K-1 mole-1 Re Reynolds number dimensionless r Radius m Sh Sherwood number dimensionless T Temperature K u Superficial velocity m s-1 v Interstitial velocity m s-1 V Total volume of the contactor m3 V󰇗 Volumetric flow m3 s-1 Vmol Molar volume cm3 mole-1 We Webber number dimensionless Y Dimensionless capacity dimensionless x Molar fraction in the liquid phase mol mole-1 y Molar fraction in the gas phase. mol mole-1 z Axial coordinate m z* Normalized axial coordinate dimensionless Z Total length of the contactor m II Greek symbols Symbol Definition Units ΔH0abs Heat of absorption at standard conditions J mole-1 ΔH0dis Heat of dissolution at standard conditions J mole-1 δ Thickness m ε Porosity dimensionless η Recovery of a compound in the contactor dimensionless θ Contact angle between liquid absorbent and the membrane surface dimensionless κ Kozeny equation constant dimensionless λ Extraction ratio dimensionless µ Viscosity Pa s Ρ Permeability mole m-1 s-1 Pa-1 Р0 Pre-exponential factor in permeability equation mole m-1 s-1 Pa-1 σc Wettability of the used material in the packed column kg s-2 σ Surface tension of phase N m-1 τ Tortuosity of the membrane dimensionless ν Diffusion volume cm3 mole-1 ρ Density kg m3 Φ Association factor dimensionless φ Fiber volume fraction dimensionless ω Acentric factor dimensionless Subscripts and superscripts Symbol Definition A Carbon dioxide abs Relative to the absorption process ax Relative to the axial direction * Relative to normalized length B Methanol or Hydrogen crit Critical d Dense layer dis Relative to the dissolution eq Related to equilibrium state ext External flood Relative to flooding G Relative to the gas phase lm Logarithmic mean L Relative to the liquid phase nom Nominal i Relative to a component if Relative to the interface gas-liquid int Internal in Relative to an inlet stream of the contactor j Relative to a phase (gas or liquid) k Relative to an equilibrium stage MC Relative to the hollow fiber membrane contactor out Relative to an outlet stream ov Overall III Subscripts and superscripts (cont.) Symbol Definition p Microporous support PC Relative to the Packed column red Reduced Abbreviations Abbreviation Definition ACM Aspen Custom Modeler bmim TCM 1-Ethyl-3-methylimidazolium tricyanomethanide bmim BF4 1-butyl-3-methylimidazolium tetrafluoroborate CCS Carbon Capture and Storage CPA Cubic-Plus-Association DEPG Dimethyl Ether of Polyethylene Glycol (SelexolTM) ENSIC École nationale supérieure des industries chimiques HFMC Hollow fiber membrane contactor IGCC Integrated Gasification Combined Cycle LRGP Laboratoire Réactions et Génie des Procédés MEA Monoethanolamine. NASA The National Aeronautics and Space Administration NMP N-Methyl-2Pyrrolidone, Purisol PC Packed contactor PEG-300 Polyethyleneglycol-300 PSRK Predictive Soave–Redlich–Kwong RMT Relative Membrane Thickness SRK Soave-Redlich-Kwong TEG Triethylene glycol. UNIFAC UNIQUAC Functional-group Activity Coefficients IV LIST OF FIGURES Figure 1. Evolution of global mean surface temperature over the period of instrumental observations (Allen et al., 2018) ...................................................................................................... 1 Figure 2. Carbon dioxide historic indirect measurements by reconstruction from ice cores and Mauna Loa CO2 record (NASA, 2020) ............................................................................................ 2 Figure 3. Global greenhouse gas emissions by economic sector (IPCC, 2014) ............................... 3 Figure 4. Diagram of possible CCS systems (IPCC, 2005) ............................................................. 7 Figure 5. CO2 capture and storage from power plants (IPCC, 2005) ............................................... 8 Figure 6. Typical IGCC and pre-combustion carbon capture scheme (Belaissaoui and Favre, 2018) ................................................................................................................................................. 9 Figure 7. RectisolTM process for CO2 removal (Rackley, 2017a) .................................................... 9 Figure 8. Partition coefficient vs Temperature compared to literature references (Nanyonjo, 2020) ........................................................................................................................................................ 11 Figure 9. Solubility of CO2 in methanol at low temperatures (Nanyonjo, 2020) .......................... 12 Figure 10. Countercurrent packed column (Asendrych et al., 2013) ............................................. 13 Figure 11. Hollow fiber membrane module and SEM cross section of an hollow fiber (Belaissaoui et al., 2016). ............................................................................................................... 14 Figure 12. Representation of a hollow fiber membrane contactor for the gas-liquid absorption (Chabanon et al., 2014). ................................................................................................................. 14 Figure 13. Screenshot of the absorber column in Aspen HYSYS® ............................................... 17 Figure 14. VLE of CO2-methanol system at -40degC (Nanyonjo, 2020). ..................................... 18 Figure 15. Temperature as a function of the stage in the Aspen HYSYS absorption column (baseline case) ................................................................................................................................ 20 Figure 16. Molar flows of the liquid and the gas phase as a function of the stage in the Aspen HYSYS absorption column (baseline case) ................................................................................... 20 Figure 17. Equilibrium and operating curve in the Aspen HYSYS absorption column (baseline case) ................................................................................................................................................ 21 Figure 18. Scheme of the simulation and modeling methodology ................................................. 22 Figure 19. Screenshot of Wolfram Alpha® .................................................................................... 24 Figure 20. Scheme of the axial coordinate calculation .................................................................. 27 Figure 21. Concentration gradients near a gas-liquid interface. .................................................... 30 Figure 22. Representation of the hollow fiber membrane contactor (HFMC) used for absorption of CO2 in methanol (Villeneuve et al., 2018a) .............................................................................. 32 Figure 23. Scheme of the partition coefficient in stage 0 ............................................................... 38 Figure 24. Flash drum simulation in Aspen Plus® ......................................................................... 38 Figure 25. Variation of outlet CO2 mole fraction, outlet temperature of gas and outlet temperature of liquid with varying inlet liquid molar flowrate (baseline case) (Mckechnie, 2020) .................. 43 Figure 26. VLE of CO2-methanol and operating line (for simulation 5 and 8, respectively) (Mckechnie, 2020) ......................................................................................................................... 44 Introduction 2 Figure 2. Carbon dioxide historic indirect measurements by reconstruction from ice cores and Mauna Loa CO2 record (NASA, 2020) According to IPCC (2014), if there are not supplementary efforts to reduce global greenhouse emissions, they will grow up much more rapidly due to increase of human population and its activities. Scenarios without extra mitigation would lead the earth to a surface temperature increase from 3.7 to 4.8 degC in 2100, taking as reference the preindustrial levels. Thus, it is crucial to reduce the emissions of CO2 and other greenhouse gases. It is observed in Figure 3 that the main source of CO2 in the world are electricity and heat production, with coal, natural gas, and oil as the main fuels, consequently it will be critical to apply carbon capture technologies in that sectors. Carbon Capture and Storage (CCS) is a promising technology to reduce the impact of continued hydrocarbon energy production. CCS firstly isolates the carbon dioxide emissions then stores them in deep geological formations to prevent them escaping back into the atmosphere (Lockwood, 2017). Introduction 3 Figure 3. Global greenhouse gas emissions by economic sector (IPCC, 2014) Post-combustion carbon capture is a well-established and commonly employed CCS technology (Dennis et al., 2014); however, it poses environmental and energy related problems such as significant energy penalties from carbon dioxide compression and amine scrubbing. Oxy-fuel combustion is another promising technology, however with it is limited to pilot-scale operations, no full-scale operations and costly air separation unit (ASU), it remains an under researched area (Theo et al., 2016). Pre-combustion carbon capture within an integrated gasification combined cycle (IGCC) separates hydrogen from the fuel before the energy generation step by firstly gasifying the fuel to produce a syngas, which after a water gas shift reaction, comprises of predominantly hydrogen and carbon dioxide (30-40% CO2) at high temperature (190-210 degC) and pressure (20-70bar) with trace impurities (Scholes et al., 2010). Currently the process requires a high energy consumption (Shen Yang et al., 2016) with the most energy intensive step of the process being the water gas shift reaction (responsible for 44% of the total efficiency), however the removal of carbon dioxide prior to the hydrogen being suitable as a fuel still contributes a large proportion of the energy usage (21% of the total efficiency). (Belaissaoui and Favre, 2018). This is the area of focus for this research. Currently the prominent method for carbon dioxide removal within an IGCC is by a packed column absorber (Sun and Smith, 2013). Previous studies for post-combustion carbon capture have demonstrated the intensification benefits of using membrane contactors as a promising alternative to packed columns (Rode et al., 2012) due to their larger interfacial surface area (5000 to 20 000 m-1) and decreased diffusion distances due to submillimeter hydraulic diameters in comparison to a packed column (500 m-1) (Favre and Svendsen, 2012). The membrane separates physically the gas and the liquid streams, thus preventing liquid entrainment or flooding which can cause operational constraints for the packed bed (Villeneuve et al., 2018b). Being able to demonstrate the intensification benefits of membrane contactors has a wide-reaching implication within the Introduction 4 energy sector, where compact, lightweight equipment can have dramatic consequences such as in offshore environments However, their benefits might be balanced by an increased mass transfer resistance due to the presence of the membrane itself and the possible occurrence of porous membrane wetting (Belaissaoui and Favre, 2018). 1.2.Previous work 1.2.1. Physical, transfer and thermodynamic properties of gas and liquid mixtures of hydrogen, carbon dioxide and methanol in view of the modelling of physical absorption processes In this work, carried out by Alice Nanyonjo, an ENSIC intern, the physical properties of a H2 – CO2 gas mixture, a CO2 – methanol liquid mixture and the liquid-vapor equilibrium of a CO2 – methanol system were studied as applied to physical absorption of CO2 in methanol at high pressure (20 – 50 bars) and low temperatures (-60, -40°C). Calculations were made at both 1 bar and 30 bars in a temperature range of -60 – 25°C and a H2 – CO2 gas mixture containing 39% CO2, pure methanol being the solvent. The first objective was to validate the estimation of the diffusion coefficient and the dynamic viscosity of the components of different fluids for them to be used directly from a simple procedure in Aspen Custom Modeler (ACM) instead of having to rewrite the correlations in a membrane contactor model, as would be the case in Matlab®. The second was to choose a thermodynamic model that described the liquid – vapor equilibrium of the CO2 – methanol system. Different correlations were used to estimate the physical properties and the deviation from those made by Aspen were calculated. For the diffusion coefficient of hydrogen and carbon dioxide into methanol, a 4% average deviation was observed. For H2 diffusing into CO2, a 5% average deviation was observed while for methanol diffusing into the H2 – CO2 gas mixture, an average 20% deviation was observed. These deviations remain acceptable. For the gas dynamic viscosity, an average 10% deviation was noted for pure H2. 1.3% was noted for pure CO2 and 20% methanol for the original gas mole fraction. Moreover, as the mole fraction of CO2 in the gas reduces, the deviation increases but this is because of the choice of the mixing rules used. For the liquid dynamic viscosity, no deviation was noted for pure components and the CO2 – MeOH binary solution. whose CO2 mole fraction was varied from 0.1 to 0.3. In fact, Aspen neglected the binary interactions between the two components. In literature, experimental data of the VLE of CO2 – MeOH was compiled and compared to estimations made by 4 models: CPA (Cubic-Plus-Association), SRK (Soave-Redlich-Kwong), PSRK (Predictive Soave–Redlich–Kwong ) and UNIFAC (UNIQUAC Functional-group Activity Coefficients) with Henry’s Law. CPA was found to best characterize the VLE of the system. Introduction 5 1.2.2. Evaluation of membrane contactors for CO2 capture from syngas mixtures using physical absorbents: simulation study This thesis completed by Ewan Mckechnie, another ENSIC intern, looked for to continue previous research completed into the intensification potential of dense hollow fiber membrane contactors, compared to the industry favored packed contactor for carbon dioxide absorption. Using Aspen HYSYS®, a parametric study was completed to understand the optimal operating conditions for physical absorption of carbon dioxide into methanol as well as an investigation into the fluid dynamics within the column to allow further work to be completed into the intensification potential of hollow fiber membrane contactors. The parametric study looked at optimizing the conditions for absorption to occur as well as developing a database of information as to which the intensification potential could be determined over. The fluid dynamics investigation determined the likelihood of flooding and the operability of the equipment. Flooding can happen at any point within the column and to give a comparable metric, the gas inlet velocity was used. It was found that there was minimal variation in limiting gas inlet velocity within the column. 1.3.Literature review A few number of articles about the process of CO2 physical absorption in hollow fiber membrane contactors have been developed in the literature. It is remarkable that not all the articles used methanol as solvent; two of them applied Polyethylene Glycol (PEG) variants, like PEG-300 (Kartohardjono et al., 2017) or Dimethyl Ether of Polyethylene Glycol (DEPG), also known as SelexolTM (Belaissaoui and Favre, 2018). Other articles have selected ionic liquids as physical solvents, like Butyl-3-methlyimidazolium tricyanomethanide (bmim TCM) (Usman et al., 2018) or Pahlavanzadeh et al. (2020), in which it has been utilized 1-butyl-3-methylimidazolium tetrafluoroborate (bmim BF4). However, only two articles have used methanol as solvent, Mahdavian et al. (2011) and Scholes et al. (2013). In relation with the inlet gas, most of the processes are about CO2 removal from syngas, assuming that syngas components are CO2 and H2, with the CO2 molar fraction in syngas around 0.4 (Scholes et al., 2013) (Usman et al., 2018) (Belaissaoui and Favre, 2018). Moreover, for some processes the gas inlet contains a mixture of CH4 and CO2, for example Mahdavian et al. (2011) and Kartohardjono et al. (2017) and other include a mixture of air and CO2. However, it is important that the CO2 molar fraction is around 0.4 for all the processes found in the literature. Concerning the pressure conditions, most of the papers are high pressure processes like the process of this report. In found articles the operating pressure goes from 20 bar (Usman et al., 2018), 26 bar (Scholes et al., 2013) and 36 bar in the case of Belaissaoui and Favre. (2018). However, for Pahlavanzadeh et al. (2020) the operating pressure is atmospheric as maximum for an absorption of CO2 from air. Mahdavian et al. (2011) and Kartohardjono et al. (2017) do not even specify the operating pressure. Introduction 6 Regarding the temperature of the processes, in the articles which involve methanol as solvent the temperature goes from 0 to 30 degC (Mahdavian et al., 2011). In general, it can be stated that the temperature of the literature processes is within the operating temperature interval of this report, except for Scholes et al. (2013) and Kartohardjono et al. (2017), in which the temperature has not been specified. Concerning the volumetric flow of the liquid, for most of the articles the liquid volumetric flow is not within the industrial domain (Mahdavian et al., 2011) (Kartohardjono et al., 2017) (Pahlavanzadeh et al., 2020), as occurs in this report. However, Usman et al. (2018) and Belaissaoui and Favre (2018) have solvent volumetric flow close to industrial conditions. Scholes et al. (2013) does not specify the volumetric flows. In relation to the geometrical parameters used in the literature, the ratio δM/rM-ext is between 0.27 and 0.55 for all the papers; concerning the internal diameter of the membrane, its value oscillates between 235 and 607 µm, excluding Scholes et al. (2013), in which the authors have not specified the geometrical parameters of the membrane. Regarding the length of the membrane contactor, it fluctuates from 0.065 m for small contactors to 1-1.5 m, which is a typical length of industrial membrane contactors. Table 1 presents the geometrical parameters and operational domain of the papers found in the literature. Table 1. Overview of operational parameters in HFMC CO2 physical absorption studies reported in the literature: A) Mahdavian et al. (2011), B) Scholes et al. (2013), C) Kartohardjono et al. (2017), D) Usman et al. (2018), E) Belaissaoui et al. (2018), F) Pahlavanzadeh et al. (2020) Ref. Operational conditions Membrane ηCO2 % Gas Solvent T degC P bar VL,in m3/h VG,in m3/h VL,in VG,in-1 (-) yco2,G (-) δM/rM-ext (-) dM-int µm Z m A ~90-97 CH4 CO2 Methanol 0 20 30 NS 0.018 0.036 0.06 0.3 0.6 Not clearb 0.33 607 0.30 B 90 CO2 H2 Methanol NS 26 NS Not clearc NS 0.40 NS NS NS C Not cleara CH4 CO2 5%wt PEG-300 NS NS 0.006 0.036 NS NS 0.36 0.55 235 0.25 D 90 CO2 H2 bmim TCM 50 20 1337 1.49E+06 9E-04 0.45 0.51 430 1.50 E 94.6 CO2 H2 SelexolTM 35 36 9.16 116.9 0.078 0.38 0.29 370 1.00 F ~45-80 Air CO2 Ionic liquid Water 30 0-1 0.0012 0.012 0.0024 0.5 5 0.35 0.27 275 0.065 NS: Not specified. a Incorrect CO2 recovery formula b 8 mol m-3 c 642.4 tonnes h-1 Introduction 7 1.4.Background theory 1.4.1. Carbon dioxide capture and storage Carbon capture and storage (CSS) is a process which involve the separation of CO2 from industrial and energy sources, transport to a storage location and finally long-term isolation in geological formations in the ocean or used in other processes, thus it is not emitted to the atmosphere. Extensive application of CCS technology could be capable of reducing mitigation costs and enhance adaptability in emissions reductions (IPCC, 2005). Figure 4. Diagram of possible CCS systems (IPCC, 2005) The reductions of emissions to the atmosphere with this system is restricted by the fraction of carbon dioxide captured, since an increase of CO2 production implies a worse efficiency of power plants or industrial processes because of the energy needed to capture CO2, as well as leakages in transport and in long-term storage. In the case of a power plant with CCS system, it is estimated a CO2 emissions reduction of 80-90% compared to a plant without CCS (IPCC, 2005). In Figure 5 it can be observed that there is an increase of CO2 production in plants with CCS, this is due to the extra energy required to capture, transport and storage, so it is essential to understand the process along its life cycle. Introduction 8 Figure 5. CO2 capture and storage from power plants (IPCC, 2005) Thus, carbon capture and storage technology could decrease the global greenhouse emissions of fossil fuel power plants, it is a truly promising strategy, but it has not yet used at large scale and in commercial fossil plants (IPCC, 2014). Other choices of mitigating climate change could be improving the efficiency of the processes, use less carbon-based fuels and to utilize more nuclear power as well as renewable energies (IPCC, 2005). 1.4.2. Integrated Gasification Combined Cycle Integrated Gasification Combined Cycle (IGCC) produces synthesis gas (syngas) through the gasification of carbonaceous fuels. Removing carbon dioxide for storage from the hydrogen gas is a key step in the process for the IGCC power plant for both the power generation and mitigation of greenhouse gas emissions. Conventionally, packed columns are used to absorb carbon dioxide from the syngas through pressurized physical solvents such as methanol or Dimethyl Ether of Polyethylene Glycol (DEPG) (SelexolTM). In IGCC pre-combustion carbon capture, syngas is treated to capture CO2 before to combustion, in order to mitigate the emissions of greenhouse gases (Belaissaoui and Favre, 2018). In Figure 6 it is observed a scheme of the IGCC process with pre-combustion carbon capture, in which block of interest is the one of CO2 removal. Introduction 9 Figure 6. Typical IGCC and pre-combustion carbon capture scheme (Belaissaoui and Favre, 2018) 1.4.3. RectisolTM process RectisolTM is a commercial process developed in the 1950s and it is applied mainly to syngas purification using methanol as solvent, this process comprises physical and chemical absorptions as well as membrane separation, hence it is valuable to do research about membrane intensification potential in this technology (Sun and Smith, 2013). In Figure 7 it can be observed a blocks diagram of RectisolTM process. Figure 7. RectisolTM process for CO2 removal (Rackley, 2017a) Physical absorption processes are more economically efficient at higher pressures and lower temperatures. Moreover, methanol absorption power for CO2 is greater than other solvents like water or N-Methyl-2Pyrrolidone, Purisol (NMP). This solubility characteristic implies less solvent flowrate and regeneration. Thus, it is important to know the relative solubility of CO2 in methanol compared to H2, in the following table it is checked that CO2 solubility is around 435 times H2 solubility in methanol at -40 degC (Sun and Smith, 2013). Introduction 10 Table 2. Relative solubility in methanol at -40 degC (Sun and Smith, 2013) Component H2S COS CO2 CH4 CO N2 H2 Relative solubility 5.9 3.6 1 0.027 0.012 0.0058 0.0023 1.4.4. Absorption using a physical solvent Carbon dioxide can be captured from syngas mixture mainly by two ways: chemical absorption, where there is a reaction between the liquid solvent and the solute, and physical absorption, which is based on change temperature and pressure in order to favor the absorption. This report will be focused on physical absorption. Thus, regarding physical absorption, the velocity at which a solute in a gas mixture can be dissolved in a certain liquid solvent depends on the deviation from equilibrium. Assuming an ideal gas, vapor-liquid equilibrium can be defined by Henry’s law, which states that the partial pressure of a specie Pi is directly proportional to its liquid-phase mole fraction xi (Smith, Van Ness and Abbott, 2001). yiP=Hixi [1] Where Hi is the Henry constant and can be obtained experimentally. Moreover, Henry’s law also can be expressed as a volumetric parameter by a partition coefficient mi, which is a function of composition, temperature and pressure of the system. mi=CiL CiG [2] In the following graph it is shown a simulation of the variation of the partition coefficient of CO2 with the temperature in order to obtain a comparison of Aspen HYSYS® estimation to literature references (Nanyonjo. 2020). It is important to remark that this partition coefficient is only valid for diluted systems (in this case xCO2<0.3). Introduction 11 Figure 8. Partition coefficient vs Temperature compared to literature references (Nanyonjo, 2020) Another important parameter in this process is the heat of absorption, which can have an influence on the gas solubility and the diffusion coefficients. It is well-known that if there is not chemical reaction the heat of absorption is equal to the heat of dissolution (equation 3). ∆Habs 0=∆Hdis 0 [3] In addition, heat of absorption can be expressed as the enthalpy change from a VLE data using the standard Clausius equation (Jonassen et al., 2014). [∂lnPi ∂(1/T)]P,x=∆Habs 0 Rg [4] Low temperatures and high pressures help the carbon dioxide to be better absorbed without requiring a chemical reaction, as it can be observed in Figure 9. Consequently, physical absorption is ideal to apply to pre-combustion carbon capture, since it is industrially favored, due to its conditions of temperature and pressure (Nanyonjo, 2020). 0 10 20 30 40 50 60 70 210 230 250 270 290 310 mi (-) T (K) Aspen S1 S2 S3 S4 S5 Simulation and operational domain 18 2.2. Selection of the thermodynamic package Cubic-Plus-Association (CPA) equation of state was chosen, based on association theory, it is a combination of the well-known Soave-Redlich-Kwong (SRK) EoS and Wertheim’s association term. The publication of that equation was completed in 1996, after that, it has been applied to diverse equilibrium systems with a remarkable success (Kontogeorgis et al., 2006). The reason why it has been selected CPA EoS is because, according to Aspen simulations, it is the property method which best describes the VLE of carbon dioxide-methanol system in relation to experimental data, better than Soave-Redlich-Kwong (SRK), Predictive Soave–Redlich–Kwong (PSRK) and UNIFAC, models which have been used for this system previously in the literature (Nanyonjo, 2020). Certainly, Figure 14 supports the affirmation that CPA is the most accurate model, with the VLE of experimental curve for a system CO2-methanol. In that figure is represented a comparison with experimental data of the models employed to simulate the VLE of CO2-methanol (Poling et al., 2006), where yCO2 and xCO2 are the molar fraction of CO2 in the vapor and in the liquid, respectively. Figure 14. VLE of CO2-methanol system at -40degC (Nanyonjo, 2020). Finally, in Table 4 below gives a summary of the conclusions, concerning the accuracy of Aspen HYSYS® at estimating some physical properties. 0,0 0,3 0,6 0,9 0,0 0,2 0,4 0,6 0,8 1,0 P (MPa) xCO2, yCO2 (-) CPA x PSRK x SRK x UNIFAC x CPA y PSRK y SRK y UNIFAC y S5 x S5 y Simulation and operational domain 19 Table 4. Summary of average deviations of physical properties estimated by Aspen, taking as reference values calculated by correlations (Nanyonjo, 2020) Physical property Symbol Average deviation Diffusion coefficient of H2 into Methanol DH2,MeOH 4,00% Diffusion coefficient of H2 into CO2 DH2,CO2 5,00% Diffusion coefficient of methanol into H2-CO2 mixture DMeOH, H2+CO2 20,00% Dynamic viscosity of pure H2 µH2 10,00% Dynamic viscosity of pure CO2 µCO2 1,30% 2.3. Operational domain Simulations were performed varying the CO2 composition of the inlet gas, operating pressure, temperature of the liquid inlet and temperature of the gas inlet. In Table 5 can be observed the operational parameters of the baseline case. It is important to remark that liquid inlet molar flow was adjusted until reaching 95% of CO2 recovery. Table 5. Baseline operating parameters on Aspen HYSYS® simulation Operating conditions Value Units Number of stages 10 dimensionless Gas molar inlet flowrate, NG,in 1.00 kmole h-1 Liquid inlet composition, xCO2,in 0.997 (MeOH) 0.003 (CO2) mole mole-1 Carbon dioxide recovery, ηCO2 95±1 % Liquid inlet molar flowr, NL,in 1.68 kmole h-1 Inlet pressure, PG,in=PL,in 40.00 bar Liquid inlet temperature, TL,in -50.00 degC Gas inlet temperature, TG,in -20.00 degC Gas inlet CO2 composition, yCO2,in 0.40 mole mole-1 Where CO2 recovery was calculated with the following equation: ηCO2=NCO2,G,in−NCO2,G,out NCO2,G,in [6] In this report, first of all it is going to be studied the simulation 1, which is the baseline case. The parameters changed for the rest of simulations are presented in Table 6. Table 6. Parameters varied in the simulated points with Aspen HYSYS® Variable Values Units Inlet pressure, PG,in=PL,in 20, 40, 50 bar Liquid inlet temperature, TL,in -30, -20, -10, 0, 10, 20 degC Gas inlet temperature, TG,in -30, -20, -10, 0, 10 , 20, 30 degC Gas inlet CO2 composition , yCO2,in 0.3 and 0.4 mole mole-1 Simulation and operational domain 20 2.3. Simulation outputs In the following figures, it is presented the profiles along the column given by Aspen HYSYS® for the baseline case input parameters of Table 5. These profiles illustrate that the properties and flows change along the column, in addition, there is a pinch point in stage 9 (Figure 17), where the driving force is minimum and the temperature has a peak. Figure 15. Temperature as a function of the stage in the Aspen HYSYS absorption column (baseline case) Figure 16. Molar flows of the liquid and the gas phase as a function of the stage in the Aspen HYSYS absorption column (baseline case) Simulation and operational domain 21 Figure 17. Equilibrium and operating curve in the Aspen HYSYS absorption column (baseline case) Design basis and modeling approach 22 3. DESIGN BASIS AND MODELING APPROACH Figure 18. Scheme of the simulation and modeling methodology In the scheme of Figure 18 is presented the steps followed in this work in order to obtain the intensification potential of hollow fiber membrane technology. In this section will be explained the third step, the mass balance of an element of volume of a contactor. 3.1.Design basis 3.1.1. Mass balance of a contactor The mass balance in contactor of specie i in the gas phase is presented in the following equation, considering the axial diffusion negligible. ugdCiG dz +KiG aLG(CiG−CiL mi)=0 [7] It is remarkable that the mass balance of Equation 7 can be rearranged in order to integrate the differential equation and calculate the length of a certain contactor (Rode, 2019). Thus, if the rearranged differential equation is integrated, it is obtained the following expression: Z=∫dz Z 0=∫ uG aLG∙KiG∙dCiG CiG−CiL mi=∫ F dCiG [8] CiG,out CiG,in CiG,out CiG,in Design basis and modeling approach 23 Where: F= uG aLG∙KiG∙1 CiG−CiL mi [9] In order to compute the volume of a contactor, it must multiply the length of the contactor by its cross-section area (Equation 10). V=A ∙ Z=∫A dz Z 0=∫ V󰇗G aLG∙KiG∙dCiG CiG−CiL mi [10] CiG,out CiG,in It should be noted that for our system F is stiff function in a certain range of CiG, so it will be harder to integrate numerically because it should be considered different fitting functions and its precision would not be appropriate. Consequently, the first option selected was to evaluate the inverse of this function and integrate it by parts by a numerical method. There are two key differences between finding the length of the packed contactor and the length membrane contactor; the global mass transfer coefficient, KiG and also aLG which differs depending on the technology as this favours the membrane contactor due to it being more compact. The global mass transfer coefficient has an increased resistance to mass transfer for the membrane contactor and is calculated differently to account for the geometry of the membrane contactor in comparison to the packed contactor. Finally, it is important to underline that the design of the volume of the HFMC has some restrictions, mainly related to pressure drop and technology available, that constraints will be exposed at the point 4 of this report. 3.1.2. Design of a contactor by numerical integration 3.1.2.1. Integration by Tchebychev method There is an integration rule adequate the integration of the F function, although usually is applied to cooling towers, it is the Tchebychev method (Perry, 2008) (Rode, 2020), this rule is suitable because it only requires to estimate the function in four points and evaluates the inverse, so it will not introduce many errors, which is an advantage compared to other methods, like trapezoidal rule. In equation 11 is presented Tchebychev approximation for a function F(CiG) between two points. Z=∫ F(CiG) dCiG CiG,out CiG,in ≈CiG,in−CiG,out 4 (F1+F2+F3+F4) [11] Where: F1=1 F (CiG,in+0,1(CiG,in−CiG,out)) [12] Design basis and modeling approach 24 F2=1 F (CiG,in+0,4(CiG,in−CiG,out)) [13] F3=1 F (CiG,out− 0,4 (CiG,in−CiG,out)) [14] F4=1 F (CiG,out− 0,1 (CiG,in−CiG,out)) [15] 3.1.2.2.Integration by Wolfram Alpha® Wolfram Alpha® is a computational knowledge engine created by Wolfram Research, it consists of a massive store of expert-level knowledge and algorithms to response questions automatically. This language can calculate definite integrals of one or more variables and do a graphic representation of the solution, provided that a fitting function is available for the curve to be integrated (Wolfram Research, 2020). Figure 19. Screenshot of Wolfram Alpha® Furthermore, this language can be applied to a varied areas of knowledge such as physics, chemistry, engineering, money and finance, etc. In addition, the syntax is very easy and intuitive, for example, for the definite integral of function f(x) between x=a and x=b it would be as follows: integrate f(x) from x=a and x=b. Design basis and modeling approach 25 To finish, it is important that the integration of the fitting functions was performed analytically, however the results precision depends on the precision of the polynomial fitting. 3.1.3. Design of a contactor by HUTOG method On the one hand, it can be defined the local height of a unit transfer of a contactor taking as reference the gas phase (HUTOG) by the following equation, for a certain axial coordinate of the contactor (Rode, 2020): HUTOG=uG KAG aLG [16] In case that KAG does not depend on the superficial velocity, Equation 16 can be expressed also as the product of A and HUTOG: A∙HUTOG=V󰇗G KAG aLG [17] For the membrane contactor the interfacial area, aLG, is constant, as it has been stated previously, however for the packed column is variable. On the other hand, other important parameters are HET, which is defined as the height of a theoretical stage, and NET, the number of theoretical stages. If Z is the total length of the contactor, HET is given by the following expression: HET= Z NET [18] To simplify the calculation of Z and V of the contactors can be used the Colburn’s relation, which is applied to linear equilibrium and operating curves, it gives a relationship between HET and HUTOG (Rode, 2019). NUTOG NET =HET HUTOG=lnλi λi−1 [19] Where λ𝑖 is the extraction ratio and it is defined in equation 20, for a certain local axial coordinate of the contactor and for a component i: λi=V󰇗G V󰇗L mi [20] Nevertheless, in this case the curves are not linear, thus in order to check if the mentioned condition is achieved along the axial coordinate, it is going to be defined the average λi along the contactor: λ=1 N∑λ𝑛 N n=1 [21] Design basis and modeling approach 26 Therefore, if 0,8<λ<1,25, equation 19 can be simplified (Rode, 2019) and the assumption of equation 22 can be made. This situation usually is reached in systems with a very high capture of CO2 within typical industrial conditions, as the case studied. HET≅HUTOG→Z≅HUTOG∙ NET [22] Consequently, it is admitted implementing a discrete sum of every transfer unit in order to calculate Z and V, for the packed column and the membrane, respectively. Nonetheless, it is important to remark that it is the sum of average HUTOG of every transfer unit, which is equivalent to the following expressions for Z and V: Z=HUTOG1 2+∑HUTOGk 10 k=2 +HUTOG11 2 [23] V=A∙HUTOG1 2+∑(A∙HUTOGk) 10 k=2 +A∙HUTOG11 2 [24] 3.1.4. Calculation of the axial coordinate In order to represent properties along the column as a function of the axial coordinate without knowing previously the value of the length, it is defined the normalized axial coordinate, z*, as following: z∗=zZ→dz=Z∙dz∗ [25] If we consider axial coordinate as a set of discrete values, it is obtained the following equation in order to compute z*, depending on whether it known the length (equation 26) or the volume of the contactor (equation 27). zk∗=zk−1∗+HUT       OGk,k−1 Z [26] zk∗=zk−1∗+A∙HUT       OGk,k−1 V [27] Where z0∗=0 and: HUT       OGk,k−1=HUTOGk+HUTOGk−1 2 [28] A∙HUT       OGk,k−1=A∙HUTOGk+A∙HUTOGk−1 2 [29] In Figure 20 is presented a scheme of the mentioned calculation. Design basis and modeling approach 27 Figure 20. Scheme of the axial coordinate calculation 3.2.Model features It was supposed a one-dimensional model, since it is not essential to simulate a two-dimensional model: a 1-D adiabatic model works with a suitable precision in order to simulate membrane contactors in industrial conditions, according to Albarracin et al. (2016). Consequently, it was applied a steady-state adiabatic (i.e. no heat losses) one dimensional model to simulate the absorption the carbon dioxide in methanol. In Table 7, it is detailed the model assumptions, depending on the contactor, in order to perform the simulation and the calculations. Table 7. Model features Domain Technology Feature Fluids Packed contactor and hollow fiber membrane contactor - Gas phase consists of a mixture of CO2 and H2 - Liquid phase contains methanol and traces of CO2 Thermal conditions Packed contactor and hollow fiber membrane contactor - Gas-liquid flow is not isothermal. Flow conditions Packed contactor - Counter-current operation - Steady state in both phases Hollow fiber membrane contactor - Counter-current operation - Steady state in both phases - 1-D model - Plug flow with axial dispersion negligible Design basis and modeling approach 34 3.4.2. Global mass transfer in the membrane Mass conservation law states that in a steady state process there is an equality of molar fluxes for the system considered (Villeneuve et al., 2018a), as it is stated in equation 44. Ni,G dint=Ni,MC−p dMC−lm−p=Ni,MC−d dMC−lm−d=Ni,L dext [44] Where: Ni,G=kiG(CiG−Ci,MC−int) [45] Ni,MC−p=ki,MC−p(Ci,MC−int−Ci,MC−dp) [46] Ni,MC−d=ki,MC−d(Ci,MC−dp−Ci,MC−ext) [47] Ni,L=kiL(mi Ci,MC−ext−CiL) [48] Thus, molar flow of specie i can be expressed as follows: Ni=KiG(CiG−CiL mi) [49] Where KiG is the global mass transfer coefficient respect to the gas phase, expressed in cylindrical geometry: 1 KiG=dMC−ext dMC−lm−p∙1 ki,MC−p+dMC−ext dMC−lm−d∙1 ki,MC−d+dMC−ext dMC−int∙1 kiG+1 mi kiL [50] It is easier to express every term of Equation 50 as a resistance to mass transfer, in order words, the inverse of the mass transfer coefficient, as it has been done for the mass transfer coefficients in the packed contactor. Thus, assuming that global mass transfer coefficient in the gas phase as sum of the mass transfer resistances in the microporous support, the dense layer, the gas phase and in the liquid phase (Villeneuve et al., 2018a), it is obtained the following equation: RiG,ov=Ri,MC−p+Ri,MC−d+RiG+RiL [51] 3.4.3. Liquid side and gas side mass transfer In both phases it is going to admit a laminar flow and a fully developed profile of CO2 concentration, so the Sherwood number (Sh) is considered as 3.66 (Villeneuve et al., 2018a). The stated non dimensional number is defined by the following equation: Shij=kij dh Dij [52] Design basis and modeling approach 35 Therefore, the mass transfer coefficient of the component i can be deduced from Equation 52 as follows for the liquid and gas phase: kiL=ShiL DiL dh,ext ; kiG=ShiG DiG dh,int [53] Where, diffusion coefficients, DiL and DiG, are computed with correlations mentioned the following points. 3.4.4. Dense layer mass transfer According to Villeneuve et al. (2018a), permeability of component i in the dense layer is expressed as Equation 54: Ρi=Ρi,0exp(−Ea,i R T) [54] Where, Ρi,0 and Ea,i depend on the type of membrane and the specie i.. Hence, the mass transfer coefficient of component i in the dense layer is expressed in equation 55 (Villeneuve et al., 2018a). ki,MC−d=Ρi(RT δMC−d) [55] 3.4.5. Microporous support mass transfer Mass transfer coefficient for a specie i in the microporous support ki,MC-p is a function of the porosity of the membrane ε, its tortuosity τ, the thickness of the microporous support δMC-p and the diffusion coefficient of i in the gas phase DiG (equation 56) (Villeneuve et al., 2018a). ki,MC−p=ε DiG τ δMC−p [56] However, for the same support ε, τ and δM-p are constant and ki,M−p only is a function of DiG, which only depends on the specie i. Therefore, this mass transfer coefficient can be expressed as a function of the mass transfer coefficient and the diffusion coefficient of a reference, in this case CO2 at 21 degC (Villeneuve et al., 2018a). ki,MC−p=kCO2,MC−p,21degC(DiG DCO2,G,21degC) [57] kCO2,MC−p,21degC is given at Villeneuve et al. (2018a) and DCO2,G,21degC was calculated with the correlation of diffusion in the gas phase of equation 58. Design basis and modeling approach 36 3.5. Correlations of transport properties In this section will be presented the correlations used in order to compute the transport properties since they are required in order to calculate the mass transfer coefficients in both contactors. All the correlations were validated with Aspen by Nanyonjo (2020) for the operating conditions of pressure and temperature and for the range of concentration of CO2 of this report. 3.5.1. Diffusion coefficient in the gas phase Initially, it is defined the diffusion coefficient of a component i on the gas phase, it has been applied the Fuller-Schettler-Giddings’ (FSG) correlation for a binary diffusion, for components A and B the equation is the following (Fuller et al., 1966) (Poling et al., 2006). DAB= 0,001T1.75(1 Mmol−A+ 1 Mmol−B)0.5 P[vA1 3+vB1 3 ]2 [58] In our particular case, A: CO2, B: H2 and P must be introduced in atm. Table 12. Parameters used in FSG correlation Parameter CO2 H2 Units νi 26,9 7,07 cm3 mole-1 Mmol−i 44,0098 2,0159 g mole-1 Despite this correlation of diffusion coefficient in the gas phase is for low pressures (<10 bar), it can be checked that it works with a suitable precision compared with experimental data at high pressures and in the temperature range along the contactor. 3.5.2. Diffusion coefficient in the liquid phase. In the case of the diffusion coefficient of specie A, in our case CO2, in a solvent B, methanol, Wilke-Chang correlation for a binary diffusion has been used, which is presented in equation 59 (Wilke and Chang., 1955) (Poling et al., 2006). DAB μB T=7.410−8(ϕB∙Mmol−B)0.5 V0.6mol−A(eb) [59] Vmol−A(eb)= Mmol−A ρA,eb [60] In the following table is exposed the parameters used in order to calculate the diffusion coefficient in the liquid phase, for carbon dioxide and methanol. Design basis and modeling approach 37 Table 13. Parameters for CO2 and methanol CO2 Parameters Parameter Value Units M_CO2 44,01 g mole-1 ρCO2_éb 1178,40 kg m-3 VCO2_éb 37,35 cm3 mole-1 3.5.3. Surface tension It is essential to calculate the surface tension at the liquid inlet because it is not included in the simulation results, there is no experimental data either, so it must be estimated by Aspen HYSYS®. Thus, this transport property has been simulated using CPA property package and, according to Aspen Properties® Help, it was computed by the Hakim-Steinberg-Stiel submodel for pure component surface tension (Hakim et al., 1971), that expression is presented in equation 61. σj=4,60104∙10−7Pcrit,j2 3 Tcrit,j1 3Qpj(1−Tred,j 0,4 )mj [61] Where: Qpj=0,1574+0,359ωj−1,769Χj−13,69Χj2−0,510ωj2+1,29ωjΧj [62] mj=1,210+0,5385ωj−14,61Χj−32,07Χj2−1,656ωj2+22,03ωjΧj [63] Tred,j=Tj Tcrit,j [64] Where, parameter Χj is the Stiel polar factor, its value is 0 by default. Lastly, it is observed that the calculation of the surface tension for other conditions would be difficult as in the case of the partition coefficient, also it has been decided to use an extrapolation curve. 3.6. Partition coefficient As it has been stated previously, partition coefficient is function of concentration in gas and liquid phase and the temperature, also it appears in the global mass transfer calculation. The value of this parameter is given by the simulations in Aspen HYSYS® for every equilibrium stage, but it is unknown for the liquid input stream. The reason is that, thermodynamically for the liquid input, it would represent the ratio of concentrations in the liquid phase and gas phase, but the concentration of CO2 in the gas phase which would be in equilibrium with a known concentration of CO2 in the liquid inlet, so in this case the concentration in the gas phase which would go out from stage 0, thus it would be hypothetic. Methanol parameters Parameter Value Units M_MeOH 32,04 g mole-1 φB 1,90 dimensionless Design basis and modeling approach 38 Figure 23. Scheme of the partition coefficient in stage 0 In order to calculate this coefficient, it has been simulated a ternary equilibrium in a flash drum with the software Aspen Plus® (Aspentech, 2020b), which provides a specific flash drum block (Figure 24). Figure 24. Flash drum simulation in Aspen Plus® The procedure is as follows: the composition of the feed stream is changed until the liquid stream has a CO2 fraction of 0,003 (composition of CO2 in the liquid inlet), choosing the property package CPA in Aspen Plus®. In order to reach a CO2 fraction of 0,003, the sensitivity analysis tool of Aspen Plus® has been used. After that, it is obtained the CO2 concentration in the vapour phase, so it is possible to calculate the partition coefficient. Finally, it is important that this calculation is difficult to automatize, therefore, for a parametric analysis changing the operational conditions, an extrapolation curve will be applied. FLASH FEED LIQUID VAPOR Study of the pressure in the hollow fiber membrane contactor 39 4. STUDY OF THE PRESSURE IN THE HOLLOW FIBER MEMBRANE CONTACTOR The design of the membrane contactor must include simultaneously the study of the mass transfer and the study of the pressure of the liquid and the gas phase along the membrane, both domains will determine the feasibility of the membrane contactor. The aim of the study of the pressure along is to have a design which leads to a good distribution of both phases in the contactor. Indeed, as it will be shown in subsequent sections, the pressure drop in the contactor is a limiting factor in the design because it determines the flow distribution of the two phases. If the flow distribution is uniform it means that the gas and the liquid are in perfect plug flow, so maldistribution situation can be ignored (Rode et al., 2012) Moreover, the pressure drop is conditioned by the geometry of the membrane, its dimensions, the fluid flow and its properties. Therefore, it is a problem of optimization in which the geometry of the membrane and the dimensions of the contactor must be adjusted to obtain the desired pressure drop in both the gas and the liquid. Finally, it is important to note that in the case of the packed contactor, this study was not carried out since the results in terms of mass transfer did not lead to a feasible tower design, so it is useless to perform a study of the pressure. 4.1. Pressure drop in the liquid phase In order to calculate the pressure drop in the liquid phase per meter of contactor, it is applied a Kozeny-type equation for axial external flow of the liquid in the membrane contactor, with a Kozeny constant κ adjusted to the fiber geometry (Happel, 1959) (Rode et al. 2012). −dPL dz=4 κ μL (rM−ext)2 φ2 (1−φ)3 uL [65] κ=5,5φ2−7,87φ+7,43 [66] 4.2.Pressure drop in the gas phase In the case of the axial internal flow, the gas phase, it has been used the Hagen-Poiseuille equation in order to calculate the pressure drop in the gas phase per meter, equation 67, for pipe flow (Rode et al. 2012), because the flow is assumed to be laminar. −dPG dz =8 μG (rMC−ext−δM)2 uG εG=8 μG (rMC−ext)2(1− δMC rMC−ext)4φuG [67] Study of the pressure in the hollow fiber membrane contactor 40 Where: δMC=δMC−d+δMC−p [68] 4.3. Distribution considerations and pressure constraints 4.3.1. Pressure drop ratio It is possible to compute the ratio of these two pressure drops directly without knowing the velocities in the liquid and in the gas phase, since, instead of velocities, it depends on the ratio of volumetric flows. That ratio is obtained dividing equation 67 and 65, it is expressed in the following expression (Rode et al. 2012): dPG dPL=2(1−φ)3 (5,5φ2−7,87φ+7,43)φ3 (μG μL)1 (1− δMC rMC−ext)4 V󰇗G V󰇗L [69] To know the value of this ratio is truly important in order to perform a preliminary analysis of the difference in terms of order of magnitude between the pressure drop in the gas and the liquid. In addition, this parameter is necessary to check if there is a similar distribution in both phases. Thus, the first constraint of this system is that this pressure drops ratio is one (in other words, the average value, since it is variable), in order to ensure the statement of similar distributions. 4.3.2. Relative pressure drop Another significant indicator is the relative pressure drop. The inlet pressure in both phases is 40 bar in the baseline case, nevertheless in order to compare pressure drops at different inlet pressures it is defined the relative pressure drop as following, for the gas and the liquid, respectively: ∆PG,rel=PG,in−PG,out PG,in ∆PL,rel=PL,in−PL,out PL,in [70] This parameter is important because it must have a certain value in order to have an ideal distribution in the contactor, then it is the second restriction. Furthermore, since PG,in=PL,in, which is given usually in packed contactors, then the relative pressure drops in both phases will tend to be similar, which indicates that the pressure drop ratio will tend to one. 4.3.3. Inertial pressure drop Regarding the design of membrane contactors, as it has been said, it is essential to have a minimum pressure drop in both phases so that there is a good distribution throughout the contactor, in other words, that minimum is a function of the inertial pressure drop. Study of the pressure in the hollow fiber membrane contactor 41 Hence, it is required to calculate a reference pressure drop to get an idea of the minimum pressure necessary for an acceptable distribution, this minimum depends on the inertial pressure drop, which is defined with the following equation for the liquid and the gas phase, respectively: ΔPG,inertial=ρGvG2 2 ΔPL,inertial=ρLvL2 2 [71] Normally, the minimum pressure drop in the gas and the liquid phase for the contactor is around ten times the inertial pressure drop. Consequently, there is another constraint in the system, which is that the pressure drop in both phases must be over a minimum. However, it is also necessary not to have an excessive pressure drop, since we would lose efficiency and also the operational costs that this would entail, so there is also a constraint of the maximum pressure drop. 4.3.4. Operational constraints for membrane contactor design The overall constraints of the problem on the design of the contactor are reflected in the following table: Table 14. Restrictions of the optimization problem Restrictions ΔPG ΔPL≅1 ΔPG,min≤ΔPG≤ΔPG,max ΔPL,min≤ΔPL≤ΔPL,max ∆PG,rel=x Z consistent with actual technology Where x is a value between 0 and 1, a typical value for conventional packed contactors is 0.05 at atmospheric pressure (Villeneuve et al., 2018a), but probably for HFMC is a little different, thus a research on pressure drop of commercial HFMC is required. The final constraint of the problem is the technology available, certainly the membrane design must be consistent with dimensions of industrial membranes and scientific literature. To conclude, in order to solve the optimization problem, the easiest way is to change geometrical parameters such as Z/A and relative membrane thickness, RMT. The objective function can be to minimize the volume of the hollow fiber membrane contactor or to increase the intensification factor. Study of the pressure in the hollow fiber membrane contactor 42 4.3.5. Pressure profile calculation Previously, it has been demonstrated that the length of the membrane contactor will not be known, since the volume is obtained directly. In order to obtain the pressure drop profile, it is essential to estimate the velocity profile, so cross section area A is required, but also A must be computed to calculate the length of the contactor Z and this last one is needed in order to have the pressure drop profile, consequently there is a degree of freedom in the equations, as it was commented before. Certainly, A is a constant and it is proportional to the pressure drop, so the curve shape of pressure drop will not change with A, just its magnitude. Thus, it is observed that it is possible to make a rearrange of the terms and a change of variable of equations 65 and 67, then it is obtained the following expressions, equations 72 and 73, for the liquid and the gas, respectively. A Z(−dPL dz∗)= 4 κ μL (rMC−ext)2 φ2 (1−φ)3 V󰇗L [72] A Z(−dPG dz∗)= 8 μG (rMC−ext)2(1− δMC rMC−ext)4φuG [73] Where z* is the normalized axial coordinate. Now, all the values of this functions along coordinate z* are known, so it is possible to assign a fitting function and integrate it respect to z* and once we give a value of A/Z it can be obtained the pressure profile. This procedure is illustrated in the following equations for a pressure in the gas and in the liquid in a certain point along the axial coordinate of the contactor, it will be integrated locally, in order to obtain the profile, using the trapezoidal rule. PG(zn)=PG(zn−1)+[1 2(A Z(−dPG dz∗)|z=zn+A Z(−dPG dz∗)|z=zn−1)∙(zn−zn−1)]∙(Z A) [72] PL(zn)=PL(zn+1)+[1 2(A Z(−dPL dz∗)|z=zn+A Z(−dPL dz∗)|z=zn+1)∙(zn+1−zn)]∙(Z A) [73] The boundary conditions are: PG(z0=0)=PG,in and PL(zN=Z)=PL,in, N is the number of intervals along the axial coordinate. Absolute axial coordinate z is obtained giving a value of Z/A, which implies that Z can be calculated and then z=z∗∙Z In addition, it is important to remember that in the case of HFMC, there is not flooding restrictions, so it can be chosen the ratio Z/A in order to change the magnitude of the pressure drop, once that ratio is selected it is possible to get the Z and obtain pressure profile. Results and discussion 43 5. RESULTS AND DISCUSSION 5.1.Case study simulations Figure 25 below shows an example of the preliminary case studies run to determine the inlet liquid molar flow for 95% of CO2 recovery. For an absorption column within Aspen HYSYS®, the recovery could not be set as a fixed variable and hence the case study function allowed for a range of inlet liquid molar flowrates (Mckechnie, 2020). Figure 25. Variation of outlet CO2 mole fraction, outlet temperature of gas and outlet temperature of liquid with varying inlet liquid molar flowrate (baseline case) (Mckechnie, 2020) The change in carbon dioxide molar fraction is unsurprising as the increased liquid flow leads to reduced carbon dioxide outlet molar gas fraction as more carbon dioxide is absorbed. The trend shows a negative logarithmic curve until the molar fraction reaches approximately 0, after which increasing the liquid molar flow has no observable effect on the carbon dioxide removal from the syngas. The outlet gas temperature shows a similarly predictable curve, decreasing in a more pronounced negative logarithmic curve until the gas outlet temperature equates to the liquid inlet temperature, -50 degC. Finally, the liquid outlet temperature gradually increases until no more observable carbon dioxide is seen to be absorbed then proceeds to decrease as there is no more generation of heat from the carbon dioxide being absorbed and decreases towards the liquid inlet temperature as the entire column cools (Mckechnie, 2020). A pinch point defines the point in the contactor which is limiting the absorption of carbon dioxide. This correlates to the warmest point within the contactor where the absorption of carbon dioxide into methanol is at its lowest. In fact, in some cases, the inlet gas temperature can be that much higher than the temperature within the contactor that there is a significant increase of temperature on the final stage that carbon dioxide can desorb. 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 -60 -50 -40 -30 -20 -10 0 0 2 4 6 8 10 yCO2,out T (degC) NL,in (kmol h-1) TG,out TL,out yCO2,out Results and discussion 50 5.2.4. Intensification potential as a function of the method The results in terms of the contactor volume reduction (i.e. intensification factor) that were for the baseline case are exposed in Table 16, as a function of the different methods implemented in this report. Table 17. Overall intensification results Volume Method PC HFMC Units Intensification factor HUTOG 3,43E-01 2,23E-03 m3 154,26 Tchevychev 3,25E-01 2,06E-03 m3 157,70 Wolfram Alpha® 3,80E-01 2,46E-03 m3 154,30 5.2.5. Pressure in the contactors First, it is necessary to emphasize that the results obtained in terms of intensification potential are not complete without first carrying out an analysis of the pressure along the contactor, in addition to making a comparison with current industrial technology. In Figure 34 is presented the ratio between pressure drop in the gas and in the liquid phase. As it can be observed, there is a high difference between the pressure drop in both phases along the contactor for the baseline case, the average value of this ratio must be one, as it has been shown in point 4. Figure 34. Pressure drop ratio among the gas and liquid vs z* in the baseline case (RMT=0.47) On the other hand, as it has been presented in point 4, in order to obtain the absolute value of the pressure profile, the ratio A/Z must have a value because of the geometry degree of freedom. Furthermore, dPG/dz and dPL/dz must be integrated locally to obtain the profile, the method applied in this case was Trapezoidal method, since the curves are continuous, it is easy to implement it. 0 0,05 0,1 0,15 0,2 0,25 0 0,2 0,4 0,6 0,8 1 dPG/dPL(-) z* (-) Results and discussion 51 A common gas relative pressure drop in order to have a uniform distribution reducing compression costs in conventional packed columns, is 5% (Villeneuve et al., 2018), however, according to Favre and Svendsen. (2012), it must not be far above 7%, whereas Chu et al. (2019) stated that 1% is sufficient for most of applications. Indeed, that value depends on whether the process is at high pressure or at atmospheric pressure. In Figure 35 can be appreciated the pressure profile assuming A/Z such that a relative pressure drop (ΔPG,rel) is equal to 5%, for the baseline case. Moreover, it is important to remark that this pressure profile has the same shape, independently of A/Z, but the absolute value of the pressure profile is proportional to A/Z. Figure 35. Pressure profile in the gas and in the liquid phase in the baseline case (RMT=0.47) with Z/A such that a relative pressure drop (ΔPG,rel) is equal to 5% However, as it can be observed in Figure 35, an excessive pressure drop is perceived in the liquid phase, which would make the process unfeasible. However, that pressure drop was calculated assuming a relative pressure drop in the gas phase of 5% (200 kPa). Then, if the inertial pressure drop in the gas phase is computed it is obtained a maximum of 0.153 kPa. As it has been commented previously, the minimum pressure drop is around 10 times the inertial pressure drop, which is 1.53 kPa, truly small value, since it would represent a relative pressure drop in the gas phase of 0,038%. According to Lee et al. (2020a), for a long-term operating conditions, it is achieved a relative pressure drop in the gas phase of 4.49% for a pressure of the gas inlet of 1 bar and a fiber length of 13 cm, a result consistent with this study, but the process of this report is a high pressure process. In addition, Dalane et al. (2018) determines, for a fiber length of 1 m and a ceramic HFMC, around 0.06% of relative pressure drop in the gas phase, for a dehydration of natural gas at 80 bar. In the case of another high pressure process (Chu et al., 2019), it was determined a ΔPG,rel of less than 0 10 20 30 40 0 0,2 0,4 0,6 0,8 1 P (bar) z* (-) Pl (bar) Pg(bar) Results and discussion 52 0.5% for a CO2 removal from natural gas without solvent. Moreover, Belaissaoui and Favre (2018) achieved 1.75% of pressure drop at 36 bar. Those results are similar to an industrial HFMC (3M™ Liqui-Cel™ EXF-2.5×8) at 7.2 bar. Nevertheless, as stated by Hoff et al. (2013), the result is 49.2% of pressure drop at 1 bar of gas inlet, truly very high pressure drop which could imply the unfeasibility of the contactor. Therefore, Hoff et al. (2013) will not be taken as reference in the discussion. Table 17 summarizes the results in terms of pressure drop found in the literature and for a commercial HFMC. Apparently, the relative pressure drop in the gas phase must be less than 1% for high pressure processes. Table 18. Results obtained by different sources in terms of pressure drop and contactor dimensions Source Process PG,in ΔPG,rel Z bar % m 3M™ Liqui-Cel™ EXF-2.5×8 General purpose. Liquid side 7,2 <1 0,28 Hoff et al. (2013) CO2 absorption in MEA1 in post combustion 1,00 49,2 3 Villeneuve et al. (2018a) CO2 absorption in aqueous ammonia in post combustion 1,00 5,00 0,25 Belaissaoui and Favre (2018) CO2 absorption from syngas using Selexol® 36 1,75 1 Dalane et al. (2018) Subsea natural gas dehydration by absorption in TEG2 80,00 0,06 1 Chu et al. (2019) CO2 removal from natural gas (without solvent). Outside fibers. 60,00 <0,5 1 Lee et al. (2020a) CO2 absorption in MEA1 with ceramic HFMC 1,09 4,49 0,13 1Monoethanolamine. 2Triethylene glycol. In terms of length of the contactor, the mentioned profile (Figure 35) implied a length of 7.80 m. Therefore, it is too large compared to contactors from the literature and commercial contactors. Since, as stated by McKeen (2012), hollow fiber membrane modules should have typically a fiber length from 1 to 1.6 m, which agrees with Rackley (2017b), who indicates that typical fiber lengths Results and discussion 53 are usually around 1 m. In the case of commercial HFMC, and their lengths goes from 50 to 140 cm (Lenntech, 2020). As a conclusion, it is necessary to perform an optimization by changing geometric parameters. In that analysis it must be considered typical geometries and pressure drops of the literature and commercial membrane contactors, in order to have a design adjusted to reality. 5.2.6. Optimization problem In the first place, it is important to do a sensitivity analysis before solving the optimization problem. The easiest way to do it is to modify the geometry of the membrane fibers (see equation 69), in other words, relative membrane thickness (RMT). The reason why RMT has been chosen to be changed is because if φ, fiber volume fraction, was altered, for example, the volume of the contactor would be modified excessively, the aim is to optimize the pressure drop without interfere in the intensification result. Therefore, changing relative membrane thickness does imply only an unimportant change in the contactor volume. Thus, in next figure it is presented the sensitivity analysis of the variable pressure drop ratio changing the relative membrane thickness, using equation 69. Figure 36. Sensitivity analysis of ΔPG/ ΔPL vs z*, changing relative membrane thickness (RMT) In Figure 36 it can be observed that there is a large sensitivity of pressure drop ratio to positive changes in RMT, whereas there is a small sensitivity when this parameter is decreased. The range of variation was between 0.4 and 0.76, but it is useless to decrease this variable below 0.4, since there is not sensitivity in that range; also it does not make sense to increase above 0.76, since it is 0 1 2 3 4 5 6 00,2 0,4 0,6 0,8 1 dPG/dPL (-) z*(-) RMT=0,4 RMT=0,47 RMT=0,6 RMT=0,65 RMT=0,7 RMT=0,73 RMT=0,76 Results and discussion 54 not desirable that the value is far from one. Moreover, it is significant that this sensitivity obtained is consistent with a similar analysis taken out by Chu et al. (2019) in a simulation of CO2 capture from natural gas. Thus, the optimum point, pressure drop ratio one, is found for relative membrane thickness of 0.67, it is not necessary to perform more iterations in order to gain precision, since this work is based on simulations and approximations. The next step it to change Z/A ratio, maintaining the relative membrane thickness of 0.67. On the other hand, concerning the relative pressure drop requirement, it must not be considered the value of 5%, since as it has been checked previously, it is too large for a high-pressure process. In addition, as stated by Lee et al. (2020a), it is expected that HFMC are a good alternative to PC because of its high performance, even at low pressure drops. Furthermore, according to typical values of shell and tubes heat exchangers and the values of the literature (Table 17), a pressure drop of 1 bar must be met as maximum in both phases, therefore it has been decided that this new constraint replace the restriction of 5% of pressure drop, as an upper limit to have a good distribution in the HFMC. Consequently, in the following figure is presented the pressure drop results and the pressure profile meeting all restrictions, the optimized case. Figure 37. Pressure profile in the gas and in the liquid phase (optimized case), RMT=0.67, Z=2.18 m Moreover, in the following table is exposed the overall results of the optimization of the hollow fiber membrane contactor compared to the baseline case. 38,8 39,0 39,2 39,4 39,6 39,8 40,0 0 0,2 0,4 0,6 0,8 1 P (bar) z* (-) PL PG Results and discussion 55 Table 19. Global results of the optimization problem compared to the baseline case Inputs Outputs Case Parameters Value Units Parameters Value Units Baseline RMT 0,47 - Volume1 2,23E-03 m3 Z 7,80 m ∆PG,rel 5,00 % Intensification factor 154,26 - ∆PL,rel 33,92 % ∆PG 2,00 bar ∆PL 13,57 bar Optimized problem RMT 0,67 - Volume1 2,36E-03 m3 Z 2,18 m ∆PG,rel 2,27 % Intensification factor 145,60 - ∆PL,rel 2,50 % ∆PG 0,90 bar ∆PL 1,00 bar 1Volume calculated by HUTOG method. As it can be appreciated in Table 18, the volume barely changes if we compare the optimized result with the baseline case; besides the intensification factor it is still very high (the volume of the hollow fiber membrane contactor would be 145.60 times smaller compared to the packed contactor at the same conditions), which represents a huge intensification potential. This intensification result is certainly optimistic if it is taken into account results obtained by Hoff et al. (2013), in a CO2 capture in post combustion process, who obtained only a 75% of volume reduction compared to a conventional packed column at 1 bar. Finally, a sensitivity analysis was performed varying the length Z in order to see how important it is relating to the variation of the length in the relative pressure drop for different values of RMT. It is observed also a large sensitivity to higher RMT, it makes sense since the pressure drop in the gas phase is a function of RMT to the fourth power, as it has been shown in the pressure drop equations. Results and discussion 56 Figure 38. Sensitivity analysis of ΔPG,rel vs Z changing RMT for baseline case 5.3. Parametric analysis: effect of liquid inlet temperature, inlet pressure and CO2 gas inlet concentration It is necessary to underline that in previous steps it has been optimized only the baseline case, which is one of the 90 simulations taken out originally by Mckechnie (2020), and 18 additional simulations performed by the author of this report, with Aspen HYSYS®, varying operational parameters. Therefore, it is essential to check how the optimization results are affected by the change of some parameters as liquid inlet temperature, inlet pressure and gas inlet CO2 concentration. Regarding the flow factor (FLG) at the liquid inlet, which will be affected since, since it varies with the liquid inlet temperature, TL,in, The flow factor fluctuates from 1.94 to 7.35 along the simulations and the inlet liquid temperature varies from -50 to 20 degC, in function of the 95% of CO2 recovery requirement in every simulation. In the baseline case FLG is equal to 2.33. In Figure 39 it is shown a comparison of the flow factor at the inlet. The flow factor is slightly affected by the inlet molar fraction of CO2, but there is a significant variation of it with the change of temperature of the liquid inlet, TL,in 0 2 4 6 8 10 12 14 16 18 012345 ΔPG (bar) Z (m) RMT=0.4 RMT=0.47 RMT=0.6 RMT=0.65 RMT=0.7 RMT=0.73 RMT=0.76 Results and discussion 57 Figure 39. FLG vs temperature of the liquid inlet and for different pressures, and for yco2=0,3 and 0,4, respectively (Mckechnie, 2020) Table 20. FLG vs temperature of the liquid inlet and for different pressures legend: shapes TG,in (degC) Shape -30 Square -20 Square rotated 45° -10 Triangle 0 Cross (x) 10 Dash 20 Cross (+) 30 Circle Certainly, the higher temperature of methanol absorbent at the inlet, it implies an increase in the methanol flowrate required to meet the 95% of CO2 recovery. Moreover, it is favorable to work at a higher temperature of the liquid, since we will be closer to the isothermal behavior (it maximizes the absorption capacity), but this would involve that it will be necessary a higher methanol flow. The main interrogation is whether the observed variation of the flow factor with temperature of the liquid inlet would involve a substantial change in the volume of the contactors, thus in the intensification factor. The volume for other simulations will be computed by HUTOG method, since it is the easiest and most accurate among the methods exposed in this report, moreover its requirement is met for all the simulations. 1 2 3 4 5 6 7 8 -50 -40 -30 -20 -10 0 10 20 FLG (-) TL,in (degC) 20 bar 40 bar 50 bar 1 2 3 4 5 6 7 8 -50 -40 -30 -20 -10 0 10 20 FLG (-) TL,in (degC) 20 bar 40 bar 50 bar Results and discussion 58 Thus, a sensitivity analysis changing inlet liquid temperature, inlet pressure and inlet gas CO2 concentration (which implies that FLG would change) is necessary in order to figure out how the volume of the contactors would be affected, and therefore the intensification factor. This analysis has been carried out for a gas inlet temperature of 10 degC, although the aim was to perform it for the least favorable temperature for the system, in other words, the most restrictive (30 degC), however, there are not enough available simulations to perform a parametric analysis under these conditions, not even at 20 degC. Table 21. Variation range of the variables and the value of fixed parameters for the pressure drop optimization Variable parameters Fixed parameters Optimization parameters TL,in PG,in=PL,in yCO2, in TG,in RMT Z degC bar (-) degC (-) m -50 -40 -30 -20 -10 0 10 20 20 40 50 0.3 0.4 10 * * * The value which must verify the pressure drop constraints of Table 13. Therefore, the results in terms of volume of the contactors and intensification factor are presented in Figures 40 and 41 for the pressures of 20, 40 and 50 bar, for the molar fraction of CO2 in the inlet gas of 0.3 and 0.4, also varying the temperature of the inlet liquid (TL,in). Furthermore, it should be noted that these results have been calculated solving simultaneously the pressure optimization problem. Figure 40. Parametrical analysis of the volume of the contactors for TG,in=10 degC 0,E+00 2,E-01 4,E-01 6,E-01 8,E-01 -30 -20 -10 0 10 20 VPC (m3) x 1 TL,in (degC) 0,E+00 2,E-03 4,E-03 6,E-03 8,E-03 -30 -20 -10 0 10 20 VHFMC (m3) x 1 TL,in (degC) Results and discussion 59 Figure 41. Parametric analysis intensification factor for TG,in=10 degC Table 22. Parametric analysis graphical representation legend Table 23. Numerical values of the parametrical analysis for TG,in=10 degC yCO2,in Pin TL,in Sim VHFMC VPC FLG IF 𝛌  RMT L ΔPG ΔPL mole mole-1 bar degC - m3 m3 - - - - m bar bar 0,3 20 -30 52 5,19E-03 7,43E-01 3,053 142,980 0,838 0,6896 2,194 0,965 1,000 -20 56 5,16E-03 6,99E-01 3,484 135,361 0,822 0,6945 2,137 0,982 1,000 -10 60 5,11E-03 6,49E-01 4,027 126,987 0,801 0,6991 2,070 0,994 1,000 0 91 5,04E-03 5,96E-01 4,724 118,284 0,770 0,6991 1,991 1,001 1,000 10 92 4,94E-03 5,41E-01 5,636 109,446 0,722 0,6991 1,891 1,005 1,000 20 93 4,76E-03 4,72E-01 7,353 99,095 0,605 0,6991 1,700 1,000 1,000 40 -30 67 2,63E-03 3,72E-01 2,631 141,348 0,857 0,6850 2,145 0,942 1,000 -20 71 2,63E-03 3,58E-01 2,919 136,211 0,846 0,6892 2,111 0,963 1,000 -10 75 2,60E-03 3,40E-01 3,363 130,456 0,814 0,6954 2,047 0,978 1,000 0 94 2,59E-03 3,21E-01 3,677 123,757 0,819 0,6954 2,022 0,993 1,000 10 95 2,58E-03 3,01E-01 3,998 116,780 0,827 0,6954 1,998 1,005 1,000 90 100 110 120 130 140 150 -30 -20 -10 0 10 20 IF (-) TL,in (degC) Legend yCO2,in Triangle 0,3 Circle 0,4 Legend Pin (bar) blue 20 orange 40 grey 50 References 66 Happel, J., 1959. 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Journal of Membrane Science, vol. 511, pp. 180206, http://dx.doi.org/10.1016/j.memsci.2016.03.051 3MTM, 2018. Data sheet of 3MTM Liqui-CelTM membrane contactors [online] Available at: <www. 3M.com/Liqui-Cel> [Accessed 16 November 2020]. 3MTM, 2019. Data sheet of 3MTM MembranaTM OXYPLUSTM, Capillary Membrane, PMP 90/200 [online] Available at: <www.3m.com/membrana> [Accessed 11 November 2020]. Annexes 71 8. ANNEXES 8.1. Commercial tower packings Figure 43. Common tower packings. (a) Rashig rings; (b) metal Pall ring; (c) plastic Pall ring; (d) Berl saddle; (e) ceramic Intalox saddle; (f) plastic Super Intalox saddle; (g) metal Intalox saddle (McCabe, 2007) Table 24. Features of different packings (Rode, 2019) Annexes 72 8.2.Specification data sheet of 3MTM MembranaTM OXYPLUSTM Figure 44. Data sheet of 3MTM MembranaTM OXYPLUSTM, Capillary Membrane, PMP 90/200 (3M, 2019) 8.2. Specification data sheet of other membranes Table 25. HFMC parameters as a function of different articles. Value Units Specification Chu et al. (2020) Dalane et al. (2018) Lee et al. (2020a) Number of fibers 6,00E+04 9,20E+06 200 - Fiber external diameter, dMC-ext 250 704 208 µm Fiber internal diameter, dMC-int 200 600 127 µm Packing density 6000 1500 na m-1 Annexes 73 8.3.Commercial hollow fiber membrane contactors Table 26. Lenntech® hollow fiber membrane contactors (Lenntech, 2020). Hollow fiber membrane Length Diameter Units Housing 45 50,3 10,8 cm Housing 65 73,2 10,8 cm Housing 85 131 10,8 cm Housing 152M 81,3 16,8 cm Housing 154M 139 16,8 cm Table 27. 3MTM Liqui-CelTM hollow fiber membrane contactors on countercurrent flow (3M, 2020) Hollow fiber membrane contactor Length Diameter Units EXF-2.5x8 Series 277 77 mm EXF-4x28 Series 889 85 mm EXF-8x40 Series 1502 255 mm EXF-8x80 Series 2518 255 mm 8.4. Raw simulation data Table 28. Raw simulation data from Aspen HYSYS (Mckechnie, 2020) Case study YCO2,G,in Pin Stages TL,in TG,in NL,in Tpeak Stage Tpeak FLG ηCO2 Tdif (-) mole mole-1 bar - degC degC kmole h-1 degC (-) (-) (-) degC 1 0,4 40 10 -50 -20 1,68 -0,52 8 2,33 95,26% 49,48 2 0,4 20 10 -50 -20 2,60 -13,70 9 2,58 95,20% 36,30 3 0,4 50 10 -50 -20 1,46 3,88 8 2,26 95,32% 53,88 4 0,4 40 10 -50 -10 1,70 0,07 8 2,26 94,31% 50,07 5 0,4 20 10 -50 -10 2,65 -13,04 10 2,64 95,22% 36,96 6 0,4 50 10 -50 -10 1,50 4,59 8 2,33 95,38% 54,59 7 0,4 40 10 -50 -30 1,64 -1,15 8 2,29 95,35% 48,85 8 0,4 20 10 -50 -30 2,55 -14,09 8 2,53 95,19% 35,91 9 0,4 50 10 -50 -30 1,35 1,68 8 2,09 95,32% 51,68 10 0,4 40 10 -40 -30 1,80 2,06 8 2,47 95,24% 42,06 11 0,4 20 10 -40 -30 2,90 -10,11 8 2,89 95,52% 29,89 12 0,4 50 10 -40 -30 1,48 4,82 8 2,27 95,33% 44,82 13 0,4 40 10 -40 -10 1,90 3,16 8 2,71 95,94% 43,16 14 0,4 20 10 -40 -10 3,00 -9,34 9 3,00 95,60% 30,66 15 0,4 50 10 -40 -10 1,63 7,49 8 2,51 95,37% 47,49 16 0,4 40 10 -40 0 1,90 3,73 9 2,49 94,25% 43,73 17 0,4 20 10 -40 0 3,00 -8,31 10 2,81 94,18% 31,69 18 0,4 50 10 -40 0 1,66 8,10 8 2,51 95,00% 48,10 19 0,4 40 10 -30 -10 2,10 6,79 8 2,96 95,92% 36,79 20 0,4 20 10 -30 -10 3,40 -4,78 9 2,39 95,14% 25,22 21 0,4 50 10 -30 -10 1,80 10,87 8 2,82 95,91% 40,87 22 0,4 40 10 -30 0 2,10 7,36 9 2,75 94,39% 37,36 23 0,4 20 10 -30 0 3,45 -4,20 10 3,35 95,22% 25,80 Annexes 74 Table 29. Raw simulation data from Aspen HYSYS (Mckechnie, 2020) (cont.) Case study YCO2,G,in Pin Stages TL,in TG,in NL,in Tpeak Stage Tpeak FLG ηCO2 Tdif (-) mole mole-1 bar - degC degC kmole h-1 degC (-) (-) (-) degC 24 0,4 50 10 -30 0 1,80 11,50 8 2,61 94,28% 41,50 25 0,4 40 10 -30 10 2,16 7,98 10 2,94 95,24% 37,98 26 0,4 20 10 -30 10 3,50 -3,14 10 3,42 95,35% 26,86 27 0,4 50 10 -30 10 1,86 12,12 9 2,83 95,32% 42,12 28 0,4 40 10 -20 0 2,36 11,48 9 3,19 95,32% 31,48 29 0,4 20 10 -20 0 3,96 0,71 9 3,79 95,18% 20,71 30 0,4 50 10 -20 0 2,00 15,33 8 2,96 94,98% 35,33 31 0,4 40 10 -20 10 2,40 11,99 9 3,26 95,43% 31,99 32 0,4 20 10 -20 10 4,00 1,55 10 3,81 95,10% 21,55 33 0,4 50 10 -20 10 2,04 15,90 9 3,05 95,15% 35,90 34 0,4 40 10 -20 20 2,40 13,04 10 3,07 94,12% 33,04 35 0,4 20 10 -20 20 4,00 2,52 10 3,65 94,15% 22,52 36 0,4 50 10 -20 20 2,08 16,66 10 3,15 95,36% 36,66 37 0,4 40 10 -10 10 2,70 16,62 9 3,72 95,95% 26,62 38 0,4 20 10 -10 10 4,70 6,89 10 4,67 94,69% 16,89 39 0,4 50 10 -10 10 2,26 20,25 9 3,35 95,20% 30,25 40 0,4 40 10 -10 20 2,70 17,18 10 3,54 94,90% 27,18 41 0,4 20 10 -10 20 4,70 7,77 10 4,53 95,67% 17,77 42 0,4 50 10 -10 20 2,30 20,76 9 3,45 95,44% 30,76 43 0,4 40 10 -10 30 2,74 18,47 10 3,62 95,05% 28,47 44 0,4 20 10 -10 30 4,70 8,64 10 4,40 95,00% 18,64 45 0,4 50 10 -10 30 2,30 21,96 10 3,26 94,24% 31,96 46 0,3 20 10 -50 -10 2,50 -17,35 10 2,39 95,94% 32,65 47 0,3 20 10 -50 -20 2,45 -18,69 9 2,33 95,78% 31,31 48 0,3 20 10 -50 -30 2,40 -19,24 9 2,27 95,66% 30,76 49 0,3 20 10 -40 0 2,87 -12,33 10 2,65 95,28% 27,67 50 0,3 20 10 -40 -10 2,85 -13,65 10 2,69 95,96% 26,35 51 0,3 20 10 -40 -20 2,80 -14,56 9 2,63 95,78% 25,44 52 0,3 20 10 -30 10 3,35 -6,90 10 3,05 95,35% 23,10 53 0,3 20 10 -30 0 3,30 -8,05 10 2,98 95,11% 21,95 54 0,3 20 10 -30 -10 3,25 -9,24 10 2,91 94,89% 20,76 55 0,3 20 10 -20 20 3,95 -1,02 10 3,56 95,40% 18,98 56 0,3 20 10 -20 10 3,90 -2,02 10 3,48 95,20% 17,98 57 0,3 20 10 -20 0 3,85 -3,04 10 3,42 95,00% 16,96 58 0,3 20 10 -10 30 4,65 5,42 10 4,05 94,88% 15,42 59 0,3 20 10 -10 20 4,65 4,48 10 4,10 95,22% 14,48 60 0,3 20 10 -10 10 4,60 3,62 10 4,03 95,04% 13,62 61 0,3 40 10 -50 -10 1,63 -5,93 9 2,13 95,31% 44,07 62 0,3 40 10 -50 -20 1,60 -6,78 8 2,12 95,70% 43,22 63 0,3 40 10 -50 -30 1,55 -7,50 8 2,01 95,23% 42,50 64 0,3 40 10 -40 0 1,83 -1,76 10 2,35 95,21% 38,24 65 0,3 40 10 -40 -10 1,80 -2,73 9 2,34 95,49% 37,27 66 0,3 40 10 -40 -20 1,75 -3,50 8 2,23 94,98% 36,50 67 0,3 40 10 -30 10 2,07 3,28 10 2,63 95,20% 33,28 68 0,3 40 10 -30 0 2,05 1,74 9 2,66 95,77% 31,74 69 0,3 40 10 -30 -10 2,00 1,12 9 2,61 95,22% 31,12 70 0,3 40 10 -20 20 2,35 8,62 10 2,95 95,18% 28,62 71 0,3 40 10 -20 10 2,32 7,08 10 2,92 95,26% 27,08 72 0,3 40 10 -20 0 2,30 6,05 9 2,94 95,66% 26,05 73 0,3 40 10 -10 30 2,70 14,29 10 3,40 95,60% 24,29 74 0,3 40 10 -10 20 2,65 12,94 10 3,27 95,09% 22,94 Annexes 75 Table 30. Raw simulation data from Aspen HYSYS (Mckechnie, 2020) (cont.) Case study YCO2,G,in Pin Stages TL,in TG,in NL,in Tpeak Stage Tpeak FLG ηCO2 Tdif (-) mole mole-1 bar - degC degC kmole h-1 degC (-) (-) (-) degC 75 0,3 40 10 -10 10 2,65 11,47 9 3,36 95,83% 21,47 76 0,3 50 10 -50 -10 1,43 -1,86 9 2,08 95,36% 48,14 77 0,3 50 10 -50 -20 1,40 -2,77 8 2,06 95,66% 47,23 78 0,3 50 10 -50 -30 1,35 -3,62 8 1,94 95,06% 46,38 79 0,3 50 10 -40 0 1,60 2,02 9 2,32 95,52% 42,02 80 0,3 50 10 -40 -10 1,56 1,14 9 2,24 95,25% 41,14 81 0,3 50 10 -40 -20 1,52 0,31 8 2,16 95,07% 40,31 82 0,3 50 10 -30 10 1,80 6,71 10 2,59 95,69% 36,71 83 0,3 50 10 -30 0 1,75 5,52 9 2,45 94,93% 35,52 84 0,3 50 10 -30 -10 1,72 4,70 9 2,42 95,12% 34,70 85 0,3 50 10 -20 20 2,01 11,94 10 2,80 95,05% 31,94 86 0,3 50 10 -20 10 2,00 10,18 10 2,87 95,84% 30,18 87 0,3 50 10 -20 0 1,95 9,55 9 2,72 95,16% 29,55 88 0,3 50 10 -10 30 2,30 17,45 10 3,26 95,89% 27,45 89 0,3 50 10 -10 20 2,25 15,91 10 3,12 95,27% 25,91 90 0,3 50 10 -10 10 2,22 14,81 9 3,07 95,24% 24,81 91 0,3 20 10 0 10 5,50 9,99 10 4,72 94,94% 9,99 92 0,3 20 10 10 10 6,70 17,04 10 5,64 94,90% 7,04 93 0,3 20 10 20 10 8,90 24,41 10 7,35 95,01% 4,41 94 0,3 40 10 0 10 3,00 17,24 9 3,68 95,25% 17,24 95 0,3 40 10 10 10 3,40 23,82 9 4,00 94,46% 13,82 96 0,3 40 10 20 10 4,00 30,66 9 4,75 95,21% 10,66 97 0,3 50 10 0 10 2,50 20,11 9 3,40 95,06% 20,11 98 0,3 50 10 10 10 2,80 26,30 9 3,65 94,23% 16,30 99 0,3 50 10 20 10 3,20 33,02 9 4,12 94,35% 13,02 100 0,4 20 10 0 10 5,40 13,35 9 5,02 95,25% 13,35 101 0,4 20 10 10 10 6,30 20,56 9 5,69 95,01% 10,56 102 0,4 20 10 20 10 7,40 28,29 9 6,51 94,96% 8,29 103 0,4 40 10 0 10 3,00 22,05 9 3,89 94,93% 22,05 104 0,4 40 10 10 10 3,40 28,07 9 4,36 95,06% 18,07 105 0,4 40 10 20 10 3,90 34,64 9 5,07 95,66% 14,64 106 0,4 50 10 0 10 2,50 25,28 9 3,56 94,61% 25,28 107 0,4 50 10 10 10 2,80 30,96 9 3,93 94,58% 20,96 108 0,4 50 10 20 10 3,20 37,14 9 4,65 95,62% 17,14