Pressure swing adsorption for hydrogen purification

PRESSURE SWING ADSORPTION FOR THE PURIFICATION OF HYDROGEN CLÁUDIA RUBINA SPÍNOLA FRANCO DISSERTAÇÃO DE MESTRADO APRESENTADA À FACULDADE DE ENGENHARIA DA UNIVERSIDADE DO PORTO EM ENGENHARIA QUÍMICA M 2014 Master in Chemical Engineering Pressure Swing Adsorption for Hydrogen Purification Master Thesis Of Cláudia Rubina Spinola Franco Developed within the course Dissertation Carried out at Process System Enterprise Supervisor at FEUP: Dr. Ana Mafalda Ribeiro Supervisor at Process Systems Enterprise: Dr. Maarten Nauta Department of Chemical Engineering October, 2014 “Tenho em mim todos os sonhos do mundo” Fernando Pessoa “Insanity: Doing the same thing over and over again and expecting different results” Albert Einstein Pressure Swing Adsorption for Hydrogen Purification Acknowledgments I would like to acknowledge my dearest parents for being responsible for who I am today. For always standing by me, supporting my decisions, either good or bad, for being my biggest support in life and for believing and encourage me through every journey of my life. To my little sister and my best friend, thank you for admiring me and look at me as a role model. That certainly made me always try to be better than what I was. To my family in London, for having me and making me feel like I was at home despite the fact of being in London. Thank you for all your help in the first weeks, for all the family events and for all the good times that made the months I spent in London unforgettable. To André, thank you for listening to all my “engineering dramas” without knowing anything about it but pretending to understand every little thing. Thank you for always encourage me to do better and to make me believe that I could do it. I want to acknowledge my dear friend and colleague Rómulo Oliveira for all the help studying, for all the time spent with me, for being an exceptional colleague and friend since my first day at FEUP. Thank you Eva Neves for all the time we spent together, for always being available for helping me, for providing your amazing notes but most of all for being the friend that you are. To my friend and colleague Catarina Marques, for all your kind words, for all your drawings that could be used to explain any complicated chemical process and for sharing this adventure in London with me. Words cannot express how comfort was to have a familiar face in PSE every day. To all of you my partners in this challenging journey of engineering, I’m pretty sure my journey wouldn’t be as amazing as it was without you. As I read somewhere “if you want to go faster go alone. If you want to get far, go together”. With you I’m sure I went faster and far at the same time. To my dear friends Hugo Nunes, Raquel and Gomes for being the same friends you always were although we’re all different persons now. Thank you to the IST interns Mariana Marques, Artur Andrade and Renato Wong. Can’t possible imagine this internship without you, without your support, help, pub days, for being so welcoming and for including me in your “Lisbon cycle”. It was a pleasure and a privilege working with you, discussing engineering with you and learning with you. I would like to acknowledge Professor Costas Pantelides and PSE London for giving me this amazing opportunity, for the wonderful work environment and conditions and, also for the financial support. Pressure Swing Adsorption for Hydrogen Purification To my supervisor at PSE, Maarten Nauta, your gPROMS® training sessions were fundamental for the work done through this internship and also thank you for all your help, time and for everything you transmitted to me through the entire internship. To my supervisor at FEUP, Ana Mafalda Ribeiro, thank you for being always available, for revising everything and for all your help with the theory. I’m pretty sure you’ll be a wonderful teacher very soon. I would also like to acknowledge my former supervisor Diogo Narciso, Charles Brand and Mayank Patel for all your help and support through the entire process. To Professor Alírio Rodrigues, thank you for your amazing classes and for being the engineer that I can only dream to be one day. To Professor Adélio Mendes, for teaching engineering but most of all, for teaching me lessons about life. Thank you for being an inspiration and for making me feel proud after each lab class. To Professor Luís Madeira and Miguel Loureiro, thank you for your support through this Erasmus Program and for all that you transmitted to me through my journey at FEUP. To all the teachers and professors that somehow had an impact in my life, either by teaching or making my life hard. Both ways of teaching sure were important and had a huge impact in who I am today. Pressure Swing Adsorption for Hydrogen Purification Abstract Hydrogen has been extensively explored in the past years as an alternative source of energy due to environmental concerns and economical motivations. The properties of the considered component and, the fact that it is obtained and employed in the course of several industrial chemical processes, increased the motivation for the purification of hydrogen. In this work, gPROMS® tool is going to be employed for the simulation of the adsorption step from a Pressure Swing Adsorption process used to purify hydrogen. Two isotherm models are being introduced to the adsorption libraries of this tool with the aim of validating the multilayer adsorption bed model, recently added to the adsorption libraries present in gPROMS®. The validation of the Langmuir-Freundlich multilayer isotherm model is done by using breakthrough experiments with binary mixtures of H2/CH4, H2/CO and H2/CO2 and, a five component mixture composed by H2/CH4/CO2/CO/N2. Breakthrough simulations are performed with this model for different feed pressures, feed flow rates and different activated carbon ratios. The results are then compared with experimental data from the literature. The Multisite Langmuir multilayer isotherm model is added the Adsorption libraries present in gPROMS and simulations with a five component mixture of H2/CH4/CO2/CO/N2 are performed. The loading profile of CH4 as well as the temperature through the adsorption bed, at the end of the feed step, is analyzed and the simulation results are compared with data from the literature. The Parameter Estimation tool is also employed in this work with the aim of estimating the Linear Driving Force coefficients as well as the parameters of the Multisite Langmuir isotherm. These estimations are performed with the purpose of evaluating the ability of this tool in predicting the desired parameters and also, the quality of the parameters provided by it. Pressure Swing Adsorption for Hydrogen Purification Pressure Swing Adsorption for Hydrogen Purification Resumo O hidrogénio tem sido explorado nos últimos anos devido a motivações ambientais e económicas. As propriedades deste componente, e, o facto de poder ser obtido no curso de vários processos químicos industriais incentivaram à sua purificação. Este trabalho tem como objetivo o uso da ferramenta gPROMS® para a simulação do passo relativo à adsorção num processo de PSA para a purificação de hidrogénio. Dois modelos de isotérmicas são adicionados às bibliotecas da ferramenta de simulação mencionada, com o objetivo de validar uma coluna de adsorção com n camadas de adsorvente, coluna esta recentemente adicionada às bibliotecas de adsorção do gPROMS®. A validação da isotérmica Langmuir-Freundlich para colunas de adsorção, que contemplam várias camadas de adsorvente, é efetuada através de simualações de breakthrough, recorrendo para tal a misturas binárias de H2/CH4, H2/CO e H2/CO2, bem como, misturas de 5 componentes constituídas por H2/CH4/CO2/CO/N2. A isotérmica Multisite Langmuir é também adicionada às bibliotecas de adsorção presentes na mesma ferramenta de simulação, e simulações de breakthrough são realizadas recorrendo a uma mistura de cinco componentes, H2/CH4/CO2/CO/N2, com o objetivo de comparar os perfis de quantidade adsorvida do metano e o perfil de temperatura ao longo da coluna, no fim do passo de adsorção, sendo os resultados obtidos comparados com os resultados presentes na literatura. Parâmetros como os coeficientes de LDF e os parâmetros da isotérmica Multisite Langmuir são estimados com recurso à ferramenta de estimação de parâmetros presente no gPROMS®, com o objetivo de avaliar a capacidade desta ferramenta na previsão dos parâmetros, bem como avaliar a qualidade dos resultados obtidos. Pressure Swing Adsorption for Hydrogen Purification v Figure 4.17 – Experimental data and major iterations performed by gPROMS® for the parameter estimation ................................................................................................................. 40 Figure 4.18 – Comparison of the experimental data with the simulation results employing the LDF coefficients obtained through the parameter estimation ........................................................ 41 Figure 4.19 - Experimental data and major iterations performed by gPROMS® for the parameter estimation for a constant variance of 0.01 ......................................................................... 43 Figure 4.20 – Major iterations for the Multisite Langmuir isotherm parameter estimation for a constant variance of 0.05 .......................................................................................................... 45 Figure 5.1 – Adsorption bed dialog box .............................................................................. 54 Figure 5.2 –Multilayer Langmuir-Freundlich isotherm dialog box ............................................... 55 Figure 5.3 – Simulation and experimental breakthrough data comparison for a five mixture at a feed pressure of 10 atm and a feed flow rate of 8.6 SLPM for a 0.5 cr .............................................. 59 Figure 5.4 - Simulation and experimental breakthrough data comparison for a five mixture at a feed pressure of 10 atm and a feed flow rate of 8.6 SLPM for a 0.32 cr ............................................. 60 Figure 5.5 - Simulation and experimental breakthrough data comparison for a five mixture at a feed pressure of 10 atm and a feed flow rate of 8.6 SLPM for a 0.65 cr ............................................. 60 Figure 5.6 – Simulation and experimental breakthrough curves for a column filled with activated carbon at 6.5 bar and 5.0 SLPM ................................................................................................ 61 Figure 5.7 - Simulation and experimental breakthrough curves for a column with two layers of adsorbent at a feed pressure of 6.5 bar and feed flow rate of 5 SLPM ........................................ 61 Figure 5.8 - Simulation and experimental breakthrough curves for a column with two layers of adsorbent at a feed pressure of 8 bar and 5 LSPM ................................................................. 62 Figure 5.9 – Multisite Langmuir dialog box .......................................................................... 63 Figure 5.10 – Loading profiles for t = 40 s ........................................................................... 66 Figure 5.11 – Loading profiles for t = 100 s ......................................................................... 66 Figure 5.12 – Loading profiles for t = 1000 s ........................................................................ 66 Figure 5.13 – Measured data and major iterations for a relative constant variance of 0.05 ............... 70 Pressure Swing Adsorption for Hydrogen Purification vi List of tables Table 3.1 – Coefficients for the different types of mass transfer ............................................... 15 Table 3.2 – Parameters of the existing isotherms in gML libraries .............................................. 16 Table 4.1 - Connection between equal variables present in the multilayer and isotherm models ....... 20 Table 4.2 – Scheme of the relations between variables in the multilayer model ............................ 21 Table 4.3 – Input conditions ........................................................................................... 23 Table 4.4 – Initial values for the LDF coefficients ................................................................. 39 Table 5.1 – PSA Milestones, adapted from Pressure Swing Adsorption [10] ................................... 52 Table 5.2 – List of models present in the adsorption libraries of gPROMS® ................................... 53 Table 5.3 – Specifications made through the dialog box ......................................................... 53 Table 5.4 – Langmuir-Freundlich isotherm parameters ........................................................... 56 Table 5.5 – LDF coefficients and heat of adsorption for the Langmuir-Freundlich isotherm validation . 57 Table 5.6 – Adsorbent properties employed in the Langmuir-Freundlich isotherm validation ............. 57 Table 5.7 – Adsorption bed properties for the validation of the Langmuir-Freundlich isotherm .......... 58 Table 5.8 – Molar fractions and feed conditions for the five component mixture ........................... 59 Table 5.9 – Conversion of the provided parameters to the LDF coefficient ................................... 64 Table 5.10 – Multisite Langmuir isotherm parameters ............................................................ 64 Table 5.11 - Properties of the adsorbent and feed conditions for the simulation performed using the Multisite Langmuir isotherm ........................................................................................... 65 Table 5.12 – gPROMS® output for the parameter estimation performed considering a constant variance of 0.05 ..................................................................................................................... 67 Table 5.13 – Upper and lower bounds for the 0.05 constant variance parameter estimation ............. 68 Table 5.14 - Estimated parameters for a constant variance of 0.05 and different upper and lower bonds for each component ..................................................................................................... 69 Table 5.15 - gPROMS® parameter estimation output with the final values obtained for the LDF coefficient for a variance of 0.01 ..................................................................................... 71 Table 5.16 – Lower and Upper bounds for the Multisite Langmuir isotherm parameter estimation ...... 72 Table 5.17 – Final values obtained for the parameter estimation of the Multisite Langmuir isotherm in the activated carbon layer ............................................................................................. 73 Table 5.18 - Final values obtained for the parameter estimation of the Multisite Langmuir isotherm in the zeolite layer ......................................................................................................... 74 Pressure Swing Adsorption for Hydrogen Purification vii Notation and glossary 𝑎𝑖 number of neighbouring sites occupied by the adsorbate molecule in the multisite Langmuir isotherm, dimensionless 𝐴 Bed area [m2] 𝐶𝑝,𝑎𝑑𝑠 Heat capacity of adsorbent material [kJ/kg∙K] 𝐶𝑝,𝑤 Heat capacity of the wall material [kJ/kg∙K] 𝑑𝑏 Bed diameter [m] 𝑑𝑝 Adsorbent particle diameter [m] 𝐷𝑎𝑥 Dispersion coefficient [m2/s] ℎ Fluid mass specific enthalpy [kJ/kg] ℎ𝑎𝑑 Enthalpy of adsorbed component [kJ/mol] ℎ𝑖∅(𝑇) Pure component enthalpy at the bed temperature and standard pressure (1 bar). [kJ/mol] 𝑘1 Langmuir-Freundlich isotherm parameter [mol/kg] 𝑘2 Langmuir-Freundlich isotherm parameter [mol/(kg∙K)] 𝑘3 Langmuir-Freundlich isotherm parameter [atm−1] 𝑘4 Langmuir-Freundlich isotherm parameter [K] 𝑘5 Langmuir-Freundlich isotherm parameter, dimensionless 𝑘6 Langmuir-Freundlich isotherm parameter [K] 𝐾𝑖 Equilibrium constant in the Multisite Langmuir [bar] 𝑘𝑇,𝑏𝑤 Heat transfer coefficient from bed to wall [W/(K∙m2)] 𝑘𝑇,𝑤𝑎 Heat transfer coefficient from wall to ambient [W/(K∙m2)] 𝑙𝑤 Bed wall thickness [m] 𝑀𝑊 Molecular weight [kg/mol] 𝑃 Bed pressure [bar] Pressure Swing Adsorption for Hydrogen Purification viii 𝑞 Concentration of gas phase components adsorbed on solid phase [mol/kgsolid] 𝑞𝑒𝑞 Equilibrium concentration of gas phase components adsorbed on solid phase [mol/kgsolid] 𝑇 Temperature of both fluid and solid phase [K] 𝑇𝑎 Ambient temperature [K] 𝑇𝑤 Wall temperature [K] 𝑢 Fluid superficial velocity [m/s] 𝑈𝑏 Bed internal energy density [kJ/mbed 3] 𝑣 Fluid dynamic viscosity [Pa.s] 𝑥 Component mass fraction [kg/kg] Greek Letters 𝜀𝑏𝑒𝑑 Bed void fraction [mvoid 3/mbed 3] 𝜀𝑡𝑜𝑡 Total void fraction [mvoid 3/mbed 3] 𝜆 Fluid thermal conductivity [kW/mK] 𝜆𝑎𝑑 Adsorbent thermal conductivity [kW/mK] 𝜌 Bed fluid density [kgfluid/mbed 3] 𝜌𝑏𝑒𝑑 Bed density [kgadsorbent/mbed 3] 𝜌𝑤 Wall density [kg/m3] 𝜔 Mass transfer coefficient [s−1] Ω LDF factor, dimensionless Index i Component Pressure Swing Adsorption for Hydrogen Purification ix Abbreviations CFDM Centered Finite Difference Method cr Carbon ratio gML gPROMS model libraries IAS Ideal Adsorbed Solution Theory LDF Linear Driving Force PSA Pressure Swing Adsorption TSA Temperature Swing Adsorption VPSA Vacuum Pressure Swing Adsorption VSA Vacuum Swing Adsorption Pressure Swing Adsorption for Hydrogen Purification Introduction 1 1 Introduction 1.1 Relevance and Motivation In the last years, the need for alternatives to fossil fuel has been explored due to environmental concerns. In order to be significant, an alternative fuel has to be technically feasible, economically competitive, environmentally satisfactory and readily accessible. Plenty potential alternative fuels have been suggested, comprising methanol, ethanol, hydrogen, biodiesel, natural gas, liquefied petroleum gas (LPG), Fischer-Tropsch fuel p-series, solar fuels, electricity (Meher LC et al. ,2006) [1]. Lately, hydrogen has been extensively explored as an alternative source of energy due to its features. Hydrogen is the most abundant element in the universe, it has a higher specific energy content, when compared with the other fuels and, is widely used in numerous chemical process industries as hydrocracking, hydrogenation of fats and oils, methanol production, manufacture of silicon, among others [2]. This component can be obtained in the course of several chemical and industrial processes by the conversion of hydrocarbons and methanol on a reforming process to produce a synthesis gas [3]. Despite all the methods for obtaining hydrogen, catalytic reforming of natural gas bound with a water gas shift reaction step is mainly the utmost profitable process for hydrogen production at a commercial scale [4]. In this process, hydrogen is obtained mixed with a high proportion of impurities, such as water vapour, carbon dioxide, methane, carbon monoxide, and in some cases, nitrogen. Hydrogen is also obtained mixed with impurities in off-gases from many processes, such as catalytic reforming of naphta, ethylene production, and ammonia production. Reducing the content of impurities in hydrogen is essential for its applications [5]. 1.2 Process System Enterprise Process System Enterprise is the world’s leading supplier of Advanced Process Modelling technology and related model-based engineering and innovation services to the process industries. PSE helps customers to apply advanced models based on their gPROMS® platform technology, enabling these customers to explore the process decision space rapidly, reducing uncertainty and make better, faster and safer design and operating decisions through deeper understanding of their processes. Pressure Swing Adsorption for Hydrogen Purification Introduction 2 1.3 Objectives and Outline The purpose of the present work is to provide a breakthrough model that could be used in PSA processes employing columns with more than one layer of different adsorbents. Two different isotherm models are being incorporated in gPROMS® libraries, with the purpose of being employed in simulations concerning multilayer adsorption columns. With the aim of validating the models, data from the literature present in chapter two is going to be used in the breakthrough simulations. A tool present in gPROMS, parameter estimation tool, is going to be employed with the purpose of estimating the Linear Driving Force parameters, as well as, isotherm parameters in order to evaluate the capacity of this tool in predicting parameters related with a breakthrough simulation with multilayer adsorption bed. This work is outlined as follow: In chapter two a brief introduction of the main concepts of Pressure Swing Adsorption is presented along with some concepts of the adsorption process. Several industrial and Lab scale processes concerning multilayer PSA systems are described. Chapter three contains the main equations of the mathematical model inserted in gPROMS® adsorption libraries and, a brief description on gPROMS® tool is made. In chapter four the modelling done is presented as well as the breakthrough simulations and validations. Parameter Estimation of the LDF coefficients and isotherm parameters using the developed models is also performed and presented in this chapter. Pressure Swing Adsorption for Hydrogen Purification Contextualization and state of art 3 2 Contextualization and state of art Several separation processes could be employed for gas separation, such as extraction, distillation and adsorption. Although distillation is simpler, the costs associated with energy became a problem that worked as a driving force to more research in adsorption [6]. The adsorption processes, mostly Pressure Swing Adsorption (PSA), are the most commonly used for this purpose due to its characteristics for the separation of gases mixtures [2]. 2.1 Pressure Swing Adsorption and its Milestones Although the establishment of PSA processes is frequently attributed to Skarstrom and Guerin de Montgareuil and Domme in 1957-1958, several of the crucial aspects of this process were established earlier in the work of Kahle. In the patent dated from 1953, Kahle states an adsorption process for the separation and purification of gas mixtures. A process composed by two adsorbent columns is described with the purposes of improvement of the process and particularly, accomplish a more economical consumption of the quantities of heat and cold employed [7]. Later, in 1957, Skarstrom presents a process for the drying of the air, or other gases materials, without the need of external heat to regenerate the adsorbent, which reduces the requirement for adsorbent material and provides equipment that allows the production of effluent streams rich, in at least, one component. The process was composed by two adsorbing beds [8]. Pressure Swing Adsorption systems were the first technology created using the Skarstrom’s cycle [9]. Some of the milestones as well as relevant papers and patents of Pressure Swing Adsorption evolution are gathered in Appendix 1. 2.2 Adsorption Adsorption is based on the interaction that occurs between gas molecules when nearby a solid surface, resulting in a reduction in potential energy. In order to maintain the molecular density in the surroundings of the surface greater than in the free-gas phase, the molecules tend to concentrate in the solid region. The attributes of the solid and sorbate are very crucial in determining the strength of the surface forces. If the interactions between gas and solid are weak, involving only van der Waals forces the phenomena described will be physical adsorption. Different molecules will interact differently with the surface, and, the nature of the surface involved will also affect the nature of the interaction. These factors define the “selectivity” of the process which is the substance for adsorption separation processes. Due to the small capacities attainable in the chemisorption processes, most feasible adsorption processes, including PSA, rely on physical adsorption. The behaviour of a PSA process is highly determined by equilibrium and kinetic aspects, however, the relative significance of each of Pressure Swing Adsorption for Hydrogen Purification Contextualization and state of art 4 these factors varies from system to system. In the great number of PSA processes the selectivity depends on differences in the equilibrium but there are also some PSA processes in which the separation depends on the differences in the adsorption rate [10]. 2.3 Isotherms In order to obtain a perception of the adsorption mechanism, adsorption isotherms are employed. They consist in curves that relate the holding of a substance from a fluid phase in the solid-phase at equilibrium. Due to adsorption complexity, several models of isotherms have been developed [11]. The shape of the isotherm is very important when deciding on the sorbate that will be used in a process. Isotherms can be categorized as linear, favourable or unfavourable. When the isotherm has a convex upward curvature it is entitled as favourable, and the dimensionless adsorbed phase is always higher than the dimensionless fluid phase concentration. When an isotherm is favourable in the adsorption step it is unfavourable in the desorption, once that the initial and final states are reversed and vice-versa [12]. Figure 2.1 – Dimensionless equilibrium isotherm showing the meaning of “favorable”, “linear” and “unfavorable” Several isotherms can be found in the literature and each can produce a better fitting for a specific situation. The Langmuir isotherm approaches the Henry’s Law for low concentrations and a saturation limit at high concentrations. The Langmuir-Freundlich isotherm combines the form of the Langmuir isotherm with the form of the Freundlich isotherm. This isotherm can be employed for several different systems and in a wide range of conditions; however, it does not reduce to Henry’s Law in the low-concentration limit [10]. Other isotherm models can be found in the literature. For example, in the work of BastosNeto et al. for the study of the breakthrough curves of methane, the adsorption equilibrium is described by the Toth model [13]. In 2012 Filipe Lopes et al. employed the Virial adsorption isotherm model in their work on fast-cycling VPSA for hydrogen purification [14]. q c Linear Favorable Unfavorable Pressure Swing Adsorption for Hydrogen Purification Contextualization and state of art 5 2.4 Adsorbents Adsorbents play a very important role in the adsorption process and their selection determines the performance of the separation. Several factors are accounted for when selecting an adsorbent for a particular process, such as the multicomponent adsorption equilibrium capacities, selectivity’s, available surface area, among others [15]. The most common adsorbents employed in Pressure Swing Adsorption for hydrogen purification include activated aluminas, silica gels, activated carbons (ACs), and zeolites [16]. Silica Gel and Activated Alumina are both useful desiccants but, while silica gel has high capacities at low temperatures, activated alumina has at high temperatures [6]. Activated carbons exhibit higher CO2 adsorption capacities when compared with the other adsorbents and they are very competitive due to their low cost, high surface area and amenability to pore structure modification, and surface functionalization (Wang et al., 2011) [17]. In the other hand, zeolites are porous crystalline aluminosilicates. The fact that its structure is a combination of SiO4 and AlO4 tetrahedra, connected in several regular arrangements through shared oxygen atoms, forming an open crystal lattice which determines the micropore structure precisely uniform, with no distribution of pore size. This characteristic of zeolites distinguishes them from the other adsorbents [6]. 2.5 PSA basic cycles A Pressure Swing Adsorption process requires an adsorbent that preferentially adsorbs one component from a mixed feed. Two main steps characterize this process: adsorption, during which the preferentially adsorbed species are gathered from the feed, and desorption (or regeneration) step, where species are taken out from the adsorbent [10]. The basic PSA system proposed by Skartstrom in 1957 still is the basis of the actual PSA processes (Figure 2.2). This specific process entailed two adsorbing beds and each bed was submitted to four different steps: Pressurization, Adsorption (Feed), Countercurrent Blowdown and Countercurrent Purge [10],[18]. When operating, a PSA process produces at least two streams. In the adsorption step, a stream rich in the less adsorbed species is formed and it is usually named as “light product” or raffinate stream. In the desorption step, a stream rich in the strongly adsorbed species is obtained and is often called as “heavy product” or extract stream [19]. Pressure Swing Adsorption for Hydrogen Purification Modelling Tool and Mathematical Model 12 Models with the particulars of a dynamic simulation activity is done in a Process Entity. A Process performs two key roles:  to instantiate a generic Model: this is done by providing specifications for all the Model’s Parameters, Input Variables (degrees of freedom), Selectors and Initial Conditions that have not been given values directly in the Model. Any specifications given in Specification dialogs from the topology of a flowsheet Model will appear as un-editable text in the Process Entity.  to define an operating procedure for a process model in the form of a Schedule; a Schedule may simply specify the execution of an undisturbed simulation for a period of time or a more complex scenario such as Modelling the start-up of a complex Process with multiple external disturbances to the system. 3.1.2 gPROMS® Libraries To model Pressure Swing Adsorption (PSA) or Temperature Swing Adsorption (TSA) the Separation part of the gPROMS® Model Libraries (gML) are required. The gML libraries are a set of libraries that can be used to model processes in the chemical and petrochemical industries. The list of models related to the PSA modelling are showed in Appendix 2 and they can be combined with other gML models to model a PSA system as a part of a full plant model. 3.2 Component and mathematical model Models describing the phenomena taking place in the adsorption bed, source, sinks, valves, stream analyzer and PID controller are all connected and are all required for the simulations of the PSA process. Taking into consideration the number of equations employed in all the models related with the PSA process only the main equations used in the adsorption bed model is presented in the present section of this work. All the information on the models and equations being used in the present work were obtained from the gML manual from gPROMS®. 3.2.1 Adsorption bed model In this model a 1-dimensional axially distributed bed in terms of the mass and the energy transport through the bed as well as the mass and energy transport between the gas phase and the adsorbent material, including also the momentum balance in the bed which depends on the mass flow rate is described. This model has an interface with different tabs including the design, the fluid, the wall, the isotherm, dynamics and numeric which allows the user to Pressure Swing Adsorption for Hydrogen Purification Modelling Tool and Mathematical Model 13 specify some parameters (see Appendix 2). This model comprises a number of models whose equations are described below. 3.2.2 Mass balance In describing these equations it is assumed that the mass transfer driving force is on a solid coverage basis instead of on a concentration or partial pressure basis. The continuity equation for each species in the fluid phase is given by: 𝜀𝑡𝑜𝑡𝜕𝜌𝑥𝑖 𝜕𝑡 +𝜕𝜌𝑢𝑥𝑖 𝜕𝑧 =𝜀𝑏𝑒𝑑𝜕 𝜕𝑧(𝜌𝐷𝑎𝑥𝜕𝑥𝑖 𝜕𝑧)−𝜌𝑏𝑒𝑑𝑀𝑊𝑖𝜔𝑖(𝑞𝑒𝑞,𝑖−𝑞𝑖) (3.1) The subscript 𝑖 refers to the components in the feed mixture. For the mass balance the boundary conditions for the inlet and outlet are: 𝑖𝑛𝑙𝑒𝑡∶ 𝐹𝑖𝑛𝑤𝑖𝑛 𝐴=𝐹𝑖𝑛𝑥𝑖 𝐴−𝜀𝑏𝑒𝑑𝜌𝐷𝑎𝑥𝜕𝑥𝑖 𝜕𝑧 (3.2) 𝑜𝑢𝑡𝑙𝑒𝑡: 𝜀𝑏𝑒𝑑𝜌𝐷𝑎𝑥𝜕𝑥𝑖 𝜕𝑧=0 (3.3) The mass balance for the adsorbed phase is given by: 𝜕𝑞𝑖 𝜕𝑡=𝜔𝑖(𝑞𝑒𝑞,𝑖−𝑞𝑖) (3.4) 3.2.3 Energy Balance Equation (3.5) denotes the energy balance for the bed used in the PSA simulations. 𝜕𝑈𝑏 𝜕𝑡 = 𝜀𝑏𝑒𝑑𝐷𝑎𝑥𝜕 𝜕𝑧(𝜌𝜕ℎ 𝜕𝑥)−𝜕𝑢𝜌ℎ 𝜕𝑧 + 𝜕 𝜕𝑧 ( (𝜀𝑏𝑒𝑑𝜆+ (1−𝜀𝑏𝑒𝑑) 0.22𝜀𝑏𝑒𝑑2 𝜆+2 3𝜆𝑎𝑑)𝜕𝑇 𝜕𝑧 ) −𝑘𝑇,𝑏𝑤 4 𝑑𝑏(𝑇−𝑇𝑤) (3.5) For this equation, the boundary conditions are: 𝑧=0: 𝐹𝑖𝑛ℎ𝑖𝑛/𝐴=𝑢𝜌ℎ−𝜀𝑏𝑒𝑑𝐷𝑎𝑥𝜌𝜕ℎ 𝜕𝑧−(𝜀𝑏𝑒𝑑𝜆+ (1−𝜀𝑏𝑒𝑑) 0.22𝜀𝑏𝑒𝑑2 𝜆+2 3𝜆𝑎𝑑)𝜕𝑇 𝜕𝑧 (3.6) 𝑧=1: 𝜕𝑇 𝜕𝑧=0 (3.7) Pressure Swing Adsorption for Hydrogen Purification Modelling Tool and Mathematical Model 14 When calculating the internal energy of the bed, the contributions of both the fluid and the solid phases have to be considered, therefore, equation (3.8) is used for that purpose. 𝑈𝑏=𝜀𝑇(𝜌ℎ−𝑃)+𝜌𝑏𝑒𝑑(∑𝑞𝑖ℎ𝑎𝑑,𝑖 𝑖+𝐶𝑝,𝑎𝑑𝑠(𝑇−𝑇𝑟𝑒𝑓)) (3.8) The mass specific enthalpy of an adsorbed species is given by: ℎ𝑎𝑑,𝑖=ℎ𝑖∅(𝑇,𝑃)+𝛥𝐻𝑎𝑑,𝑖+𝛥𝐶𝑝,𝑎𝑑,𝑖(𝑇−𝑇𝑟𝑒𝑓) (3.9) The heat transfer through the wall of the bed needs to be taken into account so the energy balance model is completed. Equation (3.10) gives the energy balance to the wall. ((𝑑𝑏+2𝑙𝑤)2−𝑑𝑏2) 𝑑𝑏2𝜌𝑤𝐶𝑝,𝑤𝜕𝑇𝑤 𝜕𝑡 =((𝑑𝑏+2𝑙𝑤)2−𝑑𝑏2) 𝑑𝑏2𝜕 𝜕𝑧(𝜆𝑤𝜕𝑇𝑤 𝜕𝑧)+𝑘𝑇,𝑏𝑤4 𝑑𝑏(𝑇−𝑇𝑤)−𝑘𝑇,𝑤𝑎4(𝑑𝑏+2𝑙𝑤) 𝑑𝑏2(𝑇𝑤 −𝑇𝑎) (3.10) 3.2.4 Momentum balance The static pressure drop is determined from the Ergun equation as follows. 𝜕𝑃 𝜕𝑧−150𝜐(1−𝜀𝑏𝑒𝑑)2𝑢 𝜀𝑏𝑒𝑑3𝑑𝑝2−1.75(1−𝜀𝑏)𝜌|𝑢|𝑢 𝜀𝑏3𝑑𝑝=0 (3.11) 3.2.5 Linear Driving Force Equation (3.4) used to describe the mass transport between the fluid and an adsorbed phase requires a mass transfer coefficient. The following general correlation is used to describe the pressure and temperature dependence resulting from different types of diffusion processes taking place: 𝜔𝑖=𝜔0,𝑖(𝑇 𝑇𝑟𝑒𝑓)𝑛𝑇(𝑃 𝑃𝑟𝑒𝑓)𝑛𝑃 (3.12) Depending on the type of mass transfer chosen in the bed configuration dialog the coefficients are set to the values presented in Table 3.1. This correlation can be adapted to user requirements. The mass transfer coefficient relation can be edited directly and any relation between the temperature, pressure, mass fraction, density and the mass transfer coefficient can be introduced. For the purposes of this work no changes were made to this correlation. Pressure Swing Adsorption for Hydrogen Purification Modelling Tool and Mathematical Model 15 Table 3.1 – Coefficients for the different types of mass transfer Mass transfer type nT nP Constant 0 0 Bulk 1.81 -1 Knudsen 0.5 0 Custom - - 3.2.6 Fluid properties The physical properties of the fluid are calculated through relations for density, thermal conductivity, viscosity, enthalpy and pure component molar enthalpy. In the template “fluid properties” calls to a Physical Properties package implemented as gPROMS Foreign Object are made. This model can be customized by the user implementing custom correlations for physical properties or modify the names of the Foreign Object physical properties calls to conform to other types of physical property packages. gPROMS® contains a physical properties package named Multiflash that supports all commonly-used thermodynamic and transport properties, including a wide range of equation and state activity coefficient thermodynamic models. Multiflash is specifically designed for equation-orientated modelling, providing tight convergence of internal iterations and analytical partial derivatives with respect to temperature, pressure and composition. 3.2.7 Dispersion model The dispersion model is used to calculate the axial dispersion coefficient from the component diffusivities and the fluid condition at each point in the bed. However, this model can be customised by the user and the correlation used can be also modified. gPROMS® also provides the option of using a constant axial dispersion coefficient. When this option is considered, the user introduces the desired value for this coefficient in the dialog box concerning the mass transfer and then, this value is constant through the entire adsorption column. 3.2.8 Isotherms The isotherms are used by the model to predict the amount of material that is adsorbed for each component when the gas phase and the surface are in equilibrium. In gML library there are four options available to specify the adsorption for a multicomponent mixture: Pressure Swing Adsorption for Hydrogen Purification Modelling Tool and Mathematical Model 16  Langmuir: 𝑞𝑒𝑞,𝑖=𝑞0,𝑖𝑏𝑖𝑝𝑖, 1+∑𝑏𝑗𝑝𝑗 𝑛𝑗=1 𝑏𝑖=𝑏1,𝑖𝑒1000𝑏2,𝑖(1𝑇−1 𝑇𝑟𝑒𝑓) (3.13)  Langmuir-Freundlich 𝑞𝑒𝑞,𝑖=(𝑞𝑒𝑞,𝑖 0+𝑞𝑒𝑞,𝑖 1𝑇)𝑏𝑖𝑝𝑖1 𝑛1+𝑛2 𝑇 1+∑𝑏𝑗𝑝𝑗1 𝑛1+𝑛2 𝑇 𝑗 , 𝑏𝑖=𝑏1,𝑖𝑒𝑏2,𝑖(1𝑇−1 𝑇𝑟𝑒𝑓) (3.14)  Ideal Adsorbed Solution (IAS) Theory Temperature dependence of the mass transfer constant in line with Knudsen-type diffusion in pores. Table 3.2 – Parameters of the existing isotherms in gML libraries Parameter Symbol Description Adsorption constant preexponential factor 𝑏1 Pre-exponential part of the purecomponent adsorption equilibrium constant. Adsorption constant activation energy 𝑏2 Activation part of the pure-component adsorption equilibrium constant. Saturation loading 𝑞0,𝑏1 Pure component Henry’s law constant Inhibition constants 𝛼 Inhibition constants to describe the effect of each adsorbed component k on the adsorption of a particular component i  Custom model gPROMS® allows the use of a custom isotherm that is written by the user in the custom model isotherm present in gPROMS® libraries. Pressure Swing Adsorption for Hydrogen Purification Modelling and Simulation 17 4 Modelling and Simulation In this chapter all the adjustments and improvements made to some of the current models in gPROMS® libraries’ are presented as well as the results obtained and the motivations to do so. The new models are tested with data from the literature presented in chapter 2 of this work, providing the possibility of comparing the simulation results with experimental data. 4.1 Breakthrough model validation A model that allows the prediction of the breakthrough time in a PSA process is very important for the industries in use of this technology. Recently, a multilayer adsorption bed model was added to gPROMS® libraries, however this model was validated using a custom isotherm. The standard Langmuir and Langmuir-Freundlich isotherms were not yet used for a multilayer process simulation. As it was mentioned before in chapter 3 of the present work (section 3.2.8), different isotherm models exist in gPROMS® libraries and could be employed for adsorption processes employing one layer of adsorbent. Considering that breakthrough simulations concerning an adsorption bed with more than one layer of adsorbent are going to be performed, these models need to be improved in order to be applied to multilayer processes. The breakthrough process used for all the simulations (see Figure 4.1) consists in one source, one sink, two reversible valves and one multilayer adsorption bed. In the source, the composition of the feed is specified as well as the feed temperature, feed pressure and feed flow rate. The valves allow maintaining the desired pressure inside the column while the sink is where the product’s composition specification is defined as well as the product pressure and temperature. In the adsorption bed dialog box it is also possible to define the initial composition inside the column, the initial temperature and the pressure inside the column. It is also in the mentioned dialog box that the properties of the bed and the adsorbent are specified. Likewise, the isotherm being employed in the process is chosen and its parameters are defined. The tabs present in the dialog box associated with the adsorption bed can be seen in Figure 4.1. In order to have the new isotherm models working properly, it was required to add some changes to some of the existing models needed for the PSA process simulation. The models profiting from these changes, the changes made and reasons for it are mentioned below in this section, as well as the results from the simulations performed resorting these models. Pressure Swing Adsorption for Hydrogen Purification Modelling and Simulation 18 Figure 4.1 – Adsorption bed layout on the left and dialog box on the right 4.1.1 Axial dispersion model As it was mentioned in the previous chapter, the axial dispersion coefficient could be either calculated through a correlation already included in gPROMS® or it could be calculated through any other correlation preferred by the user through the custom dispersion model. The original dispersion model calculates the axial dispersion coefficient for each component by means of the correlation suggested by Edwards and Richardson. Nevertheless, a correlation involving a fewer number of equations was suggested in the literature presented in the chapter 2 of this work. The correlation proposed by Wakao and Funazkri (1978), characterized by equation (4.1) was then incorporated in gPROMS® libraries replacing the original dispersion correlation. 𝜀𝑏𝑒𝑑𝐷𝑎𝑥 𝐷𝑚=20+0.5𝑆𝑐𝑅𝑒 (4.1) As the original dispersion model, the one employing the Wakao and Funazkri correlation allows to calculate the axial dispersion coefficients for every component of the feed mixture, being the diffusivities the only parameter required. The other variables are calculated through variables from the adsorption bed. The Wakao and Funazkri correlation requires a Pressure Swing Adsorption for Hydrogen Purification Modelling and Simulation 19 smaller number of equations due to the minor number of variables, leading to the reduction of the time needed for the simulation to be completed. For each layer, the axial dispersion coefficient is assumed to depend on the fluid properties in the same way. 4.1.2 Multilayer model The multilayer model allows the exchange of information between the adsorption bed model and the isotherm model, as can be seen in Figure 4.2. Also, the multilayer model lets the user choose the isotherm model intended to be used for the simulation. Although there are different isotherm models present in the gPROMS® library, only one isotherm can be applied for each simulation. It is not possible yet to employ different isotherms according to the adsorbent, for example. Figure 4.2 – Connections between isotherm model, adsorption bed model and multilayer model Different sections compose the multilayer model. A first section, where the connection with the variables provided by the adsorption bed is formulated, is followed by a section for each existing isotherm model. In the section corresponding to each isotherm model the connection between the variables used in both models takes place. The different isotherms models existing in gPROMS® libraries are defined by different equations and, each of it with different parameters. For this reason, each isotherm corresponds to a different model and all these isotherm models are connected to the multilayer model. Pressure Swing Adsorption for Hydrogen Purification Modelling and Simulation 20 When considering a process with a multilayer adsorption bed, the number of parameters being considered for the isotherm changes. While in a column filled with one layer of adsorbent the parameters of the isotherm are the same throughout the entire column, in a multilayer adsorption bed these parameters have different values for each different layer present. Also, the heat of adsorption undergoes a different distribution domain. In a one layer column the heat of adsorption for each component is constant for the whole process. In a multilayer process this variable varies according to the layer of adsorbent and, for this reason, the distribution of this variable as an array of components needs to be altered to a variable with a distribution in the components and the number of layers. A relation between the variables being exchanged between models is needed so that the values of those are correctly used for the respective models. When a column is composed for a single layer of adsorbent equality between the variables in the dimension z is sufficient for the correct linkage of these values. However, this relation is no longer valid when the column in the process is composed by layers of different adsorbents. Table 4.1 - Connection between equal variables present in the multilayer and isotherm models Connection between bed and multilayer models for one layer column For z = 0 to 1 qeq=isotherm.qeq heat od adsorption=isotherm.heat of adsorption For a multilayer process these variables are calculated separately for each layer preventing the use of the relation above. A relation between these variables and the layers of the column is then of extreme importance to assure that the exchange between models is correctly done and, also that the variables are being calculated for the right layer of the column. Therefore, a variable that relates the length of the column with the layers needs to be introduced in order to ease the implementation and calculation of the variables being sent to bed in the different layers of adsorbent. This variable corresponds to an array of the number of layers + 1. This variable provides the correct use of the parameters for the calculation of the variables in the isotherm model in each layer, despite the number of layers that compose the adsorbing bed. With the introduction of this new variable a connection between the first point of the column is calculated in a FOR DO cycle and in a second FOR DO cycle the remaining calculations are Pressure Swing Adsorption for Hydrogen Purification Modelling and Simulation 21 incorporated. A relation between the axial dimension and the fraction of this dimension corresponding to a certain layer of the bed is obtained with the introduction of this variable and it can be seen below (Table 4.2). Table 4.2 – Scheme of the relations between variables in the multilayer model Relation between variables for a multilayer column For z = 0 to domain boundary per layer cum(1) qeq=isothermport.qeq heat of adsorption(1,)=isotherm.heat of adsorption(1,) For n = 1 to number of layers For z = domain boundary per layer cum (n) to domain boundary per layer (n+1) qeq=isothermport.qeq heat of adsorption(n,)=isotherm.heat of adsorption(n,) The previously mentioned changes were applied to the sections of the Langmuir and Langmuir-Freundlich isotherms present in the multilayer model considering that these two models were also being improved with the purpose of being used in multilayer PSA processes. 4.2 Langmuir-Freundlich multilayer isotherm Taking into account the literature [31], a Langmuir-Freundlich isotherm was chosen to be included in gPROMS® libraries. Considering that all the data required for the simulation could be accessed, a comparison between the results from the simulation with the model and the experimental data could be done. The selected literature for the validation of the Langmuir-Freundlich multilayer isotherm refers to a process where the adsorption column contains two layers, being the adsorbents employed, from the feed to the product end, activated carbon and zeolite. The effect of the feed flow rate and feed pressure were studied for mixtures of two, three and five components as well as the temperature profiles for each situation. In the mentioned work, the effect of the ratio of adsorbents used is also studied with breakthrough experiments performed for three different arrangements of the adsorbent layers. The mathematical model suggested in the considered literature assumes that the gas phase behaves as an ideal gas mixture, radial concentration and temperature gradients are Pressure Swing Adsorption for Hydrogen Purification Modelling and Simulation 28 analysed considering that the temperature profile for the binary mixture of hydrogen and carbon dioxide was not provided by the literature [31]. According to the loading profile on Figure 4.8, carbon dioxide was not adsorbing in the zeolite layer, which explains the earlier breakthrough of this component. Taking this into consideration, the values of the variables involved in the calculation of the 𝑞𝑒𝑞𝑖 of carbon dioxide were evaluated for the zeolite layer. Figure 4.8 – Breakthrough of the H2/CO2 mixture at 10 atm and a feed flow rate of 6.8 SLPM and respective loading profile for t = 1400 s According to the output provided by gPROMS® in the end of each simulation, the loading of CO2 in the zeolite is zero due to the calculation of the parameter 𝑏𝐶𝑂2,2. A value of zero was being calculated for the parameter 𝑏𝐶𝑂2,2 for the zeolite layer, resulting in a loading equal to zero in this layer. With the aim of understanding the reasons for the zero value associated with this parameter, the calculations related with 𝑏𝐶𝑂2,2 were analysed. The fact that carbon dioxide was adsorbing only in the activated carbon layer lead us to consider that the issues of the zeolite layer could be related to the parameters used for the CO2 in this layer. With the purpose of confirming it, and after some analysis of the parameters from similar isotherms, it was noticed that the order of magnitude of 𝑘3 for the CO2 in the zeolite layer wasn’t in agreement with the observations made in the literature. It was decide therefore to use 𝑘3=1.578(1 atm ) for the next simulation, rather than 𝑘3 = 1.578× 10−4(1 𝑎𝑡𝑚 ) in order to observe the impact of this change in the breakthrough time of hydrogen. This value was obtained from a work from the same author of the considered literature [38]. The results presented on Figure 4.9 showed that the breakthrough time is now much closer to the experimental data. However, a higher deviation of the simulation results for the H2/CO2 mixture is observed when compared with the other mixtures used in the previous simulations. 0,7 0,75 0,8 0,85 0,9 0,95 1 0400 800 1200 molar fraction (H2) time (s) gPROMS simulation's result Experimental data 0 0,5 1 1,5 2 2,5 3 3,5 00,2 0,4 0,6 0,8 1 qCO2(mol/kg) z Pressure Swing Adsorption for Hydrogen Purification Modelling and Simulation 29 Despite this difference between experimental and simulation data, for the following simulations of the present work, it will be considered that 𝑘3,CO2=1.578(1 atm ) for the zeolite layer. Figure 4.9 – Comparison of the results between the simulation with gPROMS and experimental data for the breakthrough of the H2/CO2 mixture at 10 atm and 6.8 SLPM The simulations with the binary mixtures showed that good predictions are obtained with the gPROMS® breakthrough model for the feed pressures of 4 and 10 atm. However, when the pressure is increased to 16 atm a considerable deviation between the simulation and experimental results takes place. This deviation is also prominent for the binary mixture of hydrogen and carbon dioxide. In respect to the shape of the breakthrough curve it can be observed that for the experimental results a slightly steepest curve is observed when compared with the results obtained with gPROMS®, although the approximation of the molar fraction to the feed molar fraction takes much longer than in the simulation results. 4.2.2.2 Five component breakthrough simulation A five components mixture was used as feed in order to investigate the influence of the activated carbon ratio of the adsorption bed in the breakthrough curve for each component. In the following simulations three different carbon ratios are employed in a process with a feed flow rate of 8.6 SLPM and a feed pressure of 10 atm. The same assumptions considered for the binary mixtures are made for the five component simulations, as well as the temperatures. In the first simulation the column is considered to have the same length of each adsorbent. The molar fractions of each component in the feed mixture are provided in the literature and can be seen in Appendix 3 (see section 3.3) 0,7 0,75 0,8 0,85 0,9 0,95 1 01000 2000 3000 molar fraction (H2) time (s) Experimental data Simulation Pressure Swing Adsorption for Hydrogen Purification Modelling and Simulation 30 For an equal length layer of activated carbon and zeolite the first component leaving the adsorption bed is nitrogen, followed by methane and carbon monoxide. Carbon Dioxide is the last component to break through the column, as can be observed in the Figure 4.10. A logarithmic scale is employed for the time axis considering that the same was done in the work being used for the present validation. The results from this simulation are in agreement with the experimental data and the comparison is presented in Appendix 3 (see section 3.3). Figure 4.10 – Breakthrough curve for a 0.5 activated carbon ratio with the time axis in logarithmic scale The effect of increasing and decreasing the ratio of the activated carbon layer (cr) in the column can be seen through the results obtained from the following simulations. A comparison between activated carbon ratios of 0.32 with 0.65 is made and presented in the following Figure 4.11. As previously mentioned in chapter two of this work, the activated carbon layer is responsible for the removal of the methane and the carbon dioxide from the product stream, while the zeolite layer removes mainly the nitrogen and carbon monoxide. From Figure 4.11 can be observed that, when decreasing the length of the activated carbon layer the breakthrough of methane occurs earlier when compared to the bed having a higher length of activated carbon. The opposite situation takes place when increasing the layer of activated carbon. Figure 4.11 shows that the breakthrough of carbon dioxide is visibly affected by the proportions of adsorbent employed. However, when the fraction of zeolite employed is higher, this component takes longer to break through when compared with the situation where activated carbon is the adsorbent with a higher fraction. Although zeolite adsorbs carbon dioxide this is not practical because carbon dioxide adsorbs very strongly in this adsorbent leading to the need of extremely low pressures when it comes to the desorption step. 0 0,2 0,4 0,6 0,8 1 10 100 1000 molar fraction time (s) H2 CH4 CO2 CO N2 Pressure Swing Adsorption for Hydrogen Purification Modelling and Simulation 31 Figure 4.11 – gPROMS® results: on the left breakthrough for a 0.32cr and on the right breakthrough for 0.65 cr Relatively to the nitrogen and carbon monoxide, the time required for these two components to breakthrough of the adsorption bed is considerably higher when the length of the zeolite layer is increased. However, the impact is not as visible as it is for the components adsorbing in the activated carbon layer. This can be explained due to the molar fraction of the components being removed in the zeolite layer being smaller than the molar fraction of the components adsorbing in the activated carbon. A comparison between the experimental and simulation breakthrough curves for the five component mixture is made and presented in the Appendix 3 (see section 3.3). In this comparison is shown that gPROMS® model can be used for the prediction of the breakthrough time in the conditions of the considered simulations. 4.2.3 Validation of the Langmuir-Freundlich multilayer isotherm with different data The Langmuir-Freundlich isotherm modelled previously is now going to be employed in a process that originally used a different isotherm model. The present literature was considered taking into consideration that the feed and operating conditions were similar with the ones employed in the validation section of the Langmuir-Freundlich isotherm. A column with the same dimensions is used in the process; however, the molar fractions of the components present in the feed mixture are different from the simulations performed above. The feed flow rate and pressures are contained in the range of pressures where the gPROMS® simulations results provided good predictions of the breakthrough time. The following simulations are performed with the purpose of having an insight on the capabilities of the new model in predicting the breakthrough for different situations besides the ones employed for its validation. Four different simulations are being executed for the analysis of the breakthrough of a five component mixture, first with one layer of activated carbon, then with a column filled with zeolite and the last simulation considers a column with two layers of adsorbent, activated carbon layer followed by a zeolite layer. 0 0,2 0,4 0,6 0,8 1 10 100 1000 molar fraction time (s) H2 CH4 CO2 CO N2 0 0,2 0,4 0,6 0,8 1 10 100 1000 molar fraction time (s) H2 CH4 CO2 CO N2 Pressure Swing Adsorption for Hydrogen Purification Modelling and Simulation 32 For these simulations a temperature of 298 K was assumed for the feed and for the initial temperature of the column, considering that, in the literature a range of temperature of 293298 K was stated [38]. A total of 80 discretization points were employed in the following simulations. The properties of the adsorbents employed in the literature considered for the following simulation have the same properties as the ones employed in the simulations from the previous section, as well as the properties of the adsorption bed. The first simulation performed consisted in a process operating an adsorption bed with only one layer of adsorbent employed, allowing confirming the functionality of the model for processes with one layer of adsorbent. The breakthrough curve presented below was obtained from a process where the column is filled with one layer of activated carbon. Figure 4.12 – gPROMS simulation a bed containing activated carbon at 6.5 bar and feed flow rate of 5 SLPM The comparison of gPROMS® simulation with the experimental data from the considered literature shows that the model in use can predict the breakthrough time for the conditions employed in the simulation in Figure 4.12, although with some deviation between the profiles, mainly due to the earlier breakthrough of nitrogen in the gPROMS® simulation. However, a good prediction for the breakthrough of carbon dioxide and carbon monoxide is obtained (see Appendix 3, section 3.4). Afterwards, the same mixture was used as feed for a process with two adsorbent layers, activated carbon and zeolite, with a cr of 0.7. The effect of pressure was studied in the following simulations and the results compared with the experimental data provided in the considered literature [38]. 0 0,2 0,4 0,6 0,8 1 0500 1000 1500 2000 molar fraction time (s) H2 CH4 CO2 CO N2 Pressure Swing Adsorption for Hydrogen Purification Modelling and Simulation 33 Figure 4.13 - Breakthrough of a 5 component mixture with a 0.7 layer of activated carbon and 0.3 layer of zeolite: on the left, feed pressure of 6.5 bar and on the right feed a feed pressure of 8 bar When increasing the feed pressure a higher capacity of the adsorption bed is observed when compared with lower feed pressures, resulting in a latter breakthrough of the components of the feed mixture. The comparison between the feed pressures of 6.5 and 8.0 bar show a difference of 200 seconds in the breakthrough of nitrogen, for example. A deviation to the right in the breakthrough profiles can be observed and also the fact that a large width in the curves is verified for higher pressures. The analysis of the breakthrough for a feed pressure of 6.5 bar in Figure 4.13 provides a contrast with Figure 4.12, showing the impact of the addition of a layer of zeolite in the adsorption bed. By including this layer in the adsorption bed a latter breakthrough of nitrogen and carbon monoxide can be observed when comparing with a bed employing only one layer of activated carbon. This situation takes place due to the visible increase in the bed capacity of adsorbing nitrogen and carbon monoxide. The comparison of the experimental and simulation breakthrough curves for a feed pressure of 6.5 bar shows that the prediction obtained with gPROMS® model is good but, the breakthrough of carbon dioxide takes place considerably earlier when compared with the experimental results (see Appendix 3, section 3.4). The prediction of the breakthrough for methane can be considered good; however, due to the small molar fraction of this component in the feed mixture the breakthrough profile concerning this component is not visible in the mentioned graphical representation. 4.3 Multisite Langmuir isotherm A Multisite Langmuir isotherm for multilayer processes was intended to be introduced to gPROMS® libraries. A Multisite Langmuir isotherm, employed in a PSA process for the 0 0,2 0,4 0,6 0,8 1 01000 2000 molar fraction time (s) H2 CH4 CO2 CO N2 0 0,2 0,4 0,6 0,8 1 0500 1000 1500 2000 molar fraction time (s) H2 CH4 CO2 CO N2 Pressure Swing Adsorption for Hydrogen Purification Modelling and Simulation 34 purification of hydrogen, from a five component mixture in a column with two layers of adsorbent was chosen. A layer of activated carbon followed by a layer of zeolite is used for a process consisting in 9 steps with 1 or 4 beds. The considered literature studied the employment of two different mathematical models, a complete and a reduced one, and the impact of these in the results of the simulations. Loading, concentration and temperature profiles in the cyclic steady state and for some steps of the PSA process are shown in the mentioned work [39]. The mathematical model employed in the considered literature assumed that gas phase behaviour was described by the ideal gas law, no gradients in the radial direction, axial dispersed plug flow, macropore and micropore mass transfer resistances described by the LDF model, no temperature gradients inside each particle, the column wall interchanges energy with the gas phase inside the column and with the external environment, constant porosity along the bed and that the Ergun equation is valid locally. 4.3.1 Multisite Langmuir isotherm modeling The multisite Langmuir isotherm, described by equation (4.4) will then be introduced in gPROMS® library, replacing the Langmuir isotherm mentioned in chapter 3 (Equation (3.13)) with the aim of being used in PSA processes involving a multilayer adsorption bed. (𝑞𝑖 𝑞𝑖,𝑚𝑎𝑥)=𝑎𝑖𝐾𝑖𝑝𝑖[1−∑(𝑞𝑖 𝑞𝑖,𝑚𝑎𝑥) 𝑖]𝑎𝑖 (4.4) where 𝐾𝑖=𝐾∞exp(−∆𝐻 𝑅𝑇). This equation was introduced and calculated in the same two FOR DO cycles mentioned in the multilayer and Langmuir-Freundlich models. Heat of adsorption is, once again, assumed to be a parameter for the present isotherm model and, the model was written with the same assumptions used in the other isotherm model. As it was done for the Langmuir-Freundlich model, the parameters of the isotherm were assumed to have a distribution in the components and in the axial direction due to the variation of these parameters with the temperature in the adsorption bed. The variables used to obtain these parameters were considered as arrays of the components and number of layers. During the modelling period an error occurred due to the negative values being assumed by the term raised to the parameter 𝑛𝑖, preventing gPROMS® from running the simulation with the present isotherm. In order to avoid this situation, the absolute value of the said term was used instead, with the purpose of resolving this numerical problem. Pressure Swing Adsorption for Hydrogen Purification Modelling and Simulation 35 4.3.2 Multisite Langmuir simulations Taking into account the data provided by the paper chosen, some calculations needed to be done in order to have the parameters required by gPROMS®. For the present simulations it was assumed that the adsorbent particles were spherical, implying that Ω𝑐=15 for the calculation of the LDF factor, being this factor constant through the entire adsorption bed. The diffusivity was assumed to vary inversely with the pressure. Since gPROMS® requires the bed density instead of the particle density, those values were obtained through equation (4.5). The values obtained for the LDF parameter are presented in Appendix 4, Table 5.9. 𝜌𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒(𝑘𝑔𝑎𝑑𝑠𝑜𝑟𝑏𝑒𝑛𝑡 𝑚𝑎𝑑𝑠𝑜𝑟𝑏𝑒𝑛𝑡 3)= 𝜌𝑏𝑒𝑑 (1−𝜀𝑏𝑒𝑑) (4.5) A total of 180 points of discretization (90 points per layer) were used in the simulations concerning the Multisite Langmuir isotherm. Although the breakthrough time was not provided by the mentioned work, it was agreed to simulate the breakthrough for the considered process, since the mass balance of the column as well as the loading profiles could be observed and analysed, considering that the mentioned models provide important information on the process. The breakthrough model employed in the simulations performed in the previous section of this work is going to be used in the following simulations but with the Multisite Langmuir isotherm instead of the Langmuir-Freundlich isotherm. Figure 4.14 – Breakthrough curve obtained with gPROMS® model employing the Multisite Langmuir isotherm The analysis of the breakthrough curve displayed in Figure 4.14 shows that nitrogen is the first component to break through of the adsorption column, followed by methane, carbon monoxide and then, carbon dioxide. The data from the present breakthrough curve is going to be employed later in this work, with the purpose of estimating the isotherm parameters. 0 0,2 0,4 0,6 0,8 1 01000 2000 3000 mass fraction time (s) H2 CH4 CO2 CO N2 Pressure Swing Adsorption for Hydrogen Purification Modelling and Simulation 36 Two simulations are being performed with the purpose of comparing the temperature profile through the entire column and the loading profile of methane, both at the end of the feed step. The following simulations are going to be carried until 𝑡=40 s which corresponds to the end of the feed step. Figure 4.15 – On the left: temperature profile of the column and on the right the loading profile of methane both at the end of the feed step Despite the fact that a match was obtained for the comparison between the results gotten with gPROMS® and the data provided for the temperature profile, the same can’t be said when referring to the loading profile. As we can observe from Figure 4.15, a considerably deviation exists, mainly at the feed end of the column. In order to have some insight on what was happening inside the adsorption bed, the loading profile throughout the column for different times was analysed and can be seen in Appendix 5 (section 4.2). The analysis of the loading profile for 𝑡=40 s (Appendix 4, Figure 5.10) shows that the loading fronts have reached already the first 10 % of the adsorption bed. The experimental results (Figure 4.15) showed that at the feed end of the column the amount adsorbed of methane is lower when compared with the amount adsorbed a little further ahead in the adsorption bed. Further ahead in the adsorption bed the amount adsorbed of methane is higher, due to the absence of competition with the carbon dioxide. With the aim of verifying if the competition between carbon dioxide and methane took place latter, the loading profile for 𝑡=100 𝑠 was investigated (see Appendix 4, Figure 5.11). The competition between carbon dioxide and methane is still not visible, however it is possible to see that competition between carbon dioxide and carbon monoxide takes place. The loading of the carbon monoxide is higher in the fraction of the adsorption bed where there is no carbon dioxide. This situation gets more prominent when the loading fronts arrive to the 300 305 310 315 320 325 330 335 340 345 00,2 0,4 0,6 0,8 1 Temperature (K) z gPROMS Experimental data 0 0,04 0,08 0,12 0,16 0,2 00,2 0,4 0,6 0,8 1 qi, CH4(mol/kg) z Experimental data Obtained with gPROMS Pressure Swing Adsorption for Hydrogen Purification Modelling and Simulation 37 zeolite layer and can be observed in the loading profile for 𝑡=1000 s (see Appendix 4, Figure 5.12). Given that the shape of the adsorbent particles was not provided by the literature, affecting the LDF coefficient due to Ω parameter, it was agreed to perform simulations considering different shapes for the adsorbent particles and, therefore, different LDF coefficients. Taking into consideration the information provided in other literature from the same authors and with the aim of correcting the deviation observed between the simulation and experimental results, it was agreed to perform a different simulation assuming that the particles of activated carbon were slab micropores (Ω𝑐=3) and the zeolite particles were cylinders (Ω𝑐=8) [40]. Figure 4.16 – Comparison of the loading profiles with different adsorbent geometries The loading profiles obtained for particles with a spherical shape show that changing the LDF factor, Ω, does not provide a better resemblance with the literature data. Decreasing the LDF factor decreases the LDF coefficient, causing a higher mass transfer resistance. This results in a lower loading for methane, as can be observed in Figure 4.16. Taking this into consideration, it was agreed to assume that both particles had a LDF factor equal to 8 and perform a new simulation. Results in Figure 4.16 show that the loading of methane at the feed end of the column still is higher than what is obtained in the literature [39]. Considering that the packages regarding the properties of the components provided by gPROMS® are made with the purpose of being applied in simulations of a wide range of industrial processes, like it was mentioned in chapter three of the present work, some of the deviations verified between simulation and literature data might be related with the 0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16 0,18 00,2 0,4 qCH4(mol/kg) z Ω(AC)=3,Ω(Z) = 8 Ω(AC and Z) = 15 Literature 0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16 0,18 00,2 0,4 qCH4(mol/kg) z Ω(AC and Z)=8 Ω(AC and Z) = 15 Literature Pressure Swing Adsorption for Hydrogen Purification Modelling and Simulation 44 is 0.01. However, the estimation of the hydrogen LDF coefficients is the one with the higher level of uncertainty. When comparing the estimated values per layer of adsorbent, the data obtained from the estimation shows that predictions with a higher level of certainty are obtained for the zeolite layer. The final values obtained are now going to be used as initial guess for a new simulation with the aim to investigate if the results are again the same as it happened with the simulation for a constant variance of 0.05 or if better estimations are being obtained. The use of the final values from the simulation present in Figure 4.19 as initial guesses for a new parameter estimation showed that the values obtained were not the optimal values, as happened for the constant variance of 0.05. gPROMS® performed 7 major iterations and the process was interrupted due to a numeric error. With the aim of avoiding this error the bounds of molar and mass fraction as well as the bounds of velocity were changed. The valves coefficients were also increased considering that gPROMS® provided information related with problems in maintaining the desired pressure inside the adsorption bed. Six major iterations were again required to obtained new values which lead us to conclude that the final results from the first simulation with a constant variance of 0.01 were not the optimal ones. The results obtained for the previously mentioned parameter estimation shows that gPROMS® provides estimations with high levels of uncertainty. The LDF coefficients of hydrogen are the ones with the higher level of uncertainty, which could be related with the fact that this is the less strongly adsorbed, and therefore, the effect of the LDF coefficient of this component in the control variable is weaker when compared with the other components. Due to this reason, it is harder to gPROMS® to provide a better estimation. From all the estimations above the parameter estimated with a higher level of certainty was the LDF coefficient for carbon dioxide in the zeolite when considering a constant variance of 0.01. This component is the one which adsorbs more strongly in the considered adsorbent which could explain the fact of this being the better estimation obtained, due to the fact that a slightly change in the parameter being estimated affects strongly the control variable. 4.4.2 Multisite Langmuir parameters estimation With the aim of having more information about the model developed for the Multisite Langmuir isotherm, the model employing this isotherm is going to be used for parameter estimation. For this purpose, breakthrough data obtained in previous simulations presented in this work (see Figure 4.14) are going to be subjected to some treatment with Microsoft Excel, Pressure Swing Adsorption for Hydrogen Purification Modelling and Simulation 45 as previously done for the estimation of the LDF coefficients. To obtain the noise to be introduced to the breakthrough curve a mean of zero, a standard deviation of 0.05 and a random probability were considered for NormInv function of Microsoft Excel. The following simulations are being performed in order to estimate the parameters for the Multisite Langmuir isotherm. A constant variance of 0.05 is being considered and the initial guesses for each parameter, component and adsorbent are presented in Appendix 5 (see Table 5.16). A total of 30 parameters are going to be estimated simultaneously. Some problems arise when trying to perform the present parameter estimation related with some discontinuities in the calculation procedures. The analysis of the gPROMS® output suggested that the problems in the parameter estimation were related with the valves so it was agreed to increase the valve coefficients from 105 to 106. A total of 38 major iterations were required in order to obtain the desired parameters and they are showed in Figure 4.20. As we can see, the number of major iterations required to obtain the estimation for each parameter increased when compared with the number of major iterations required to obtain estimation for the LDF coefficients. However, when the parameters being estimated were the LDF coefficients only 10 parameters were being estimated simultaneously. Through the major iterations shown in Figure 4.20 it is possible to observe the path transverse by gPROMS® in order to find the estimations for the considered parameters. It is visible that the iteration curve tends to be more dispersive as the number of iterations increases. Figure 4.20 – Major iterations for the Multisite Langmuir isotherm parameter estimation for a constant variance of 0.05 The final values obtained for the Multisite Langmuir isotherm parameters are gathered in Appendix 5 (see Table 5.17 and Table 5.18). The analysis of these results shows that the 0 0,2 0,4 0,6 0,8 1 0500 1000 1500 mass fraction (H2) time (s) Initial Iteration 1: Major Iteration 4: Major Iteration 7: Major Iteration 10: Major Iteration 15: Major Iteration 20: Major Iteration 25: Major Iteration 30: Major Iteration 35: Major Iteration 38: Major Iteration Pressure Swing Adsorption for Hydrogen Purification Modelling and Simulation 46 estimated parameters are obtained with an extremely high level of uncertainty despite the fact that the final values attained are quite close to the values suggested in the literature [39]. When comparing the estimated parameters in the activated carbon layer with the estimated parameters obtained for the zeolite layer, it is possible to verify that, although in both situations the parameters are estimated with very high levels of uncertainty, the parameters obtained for the zeolite layer have a lower level of certainty, as was observed when estimating the LDF coefficients in the previous section of this work. The high level of uncertainty obtained when estimating the isotherm parameters can be related with the fact that a slightly change in one of the parameters has a considerable impact in the control variable, and, therefore in the prediction of the breakthrough. Several combinations of values for the parameters for each component can be made and provide a good prediction of the measured data, resulting in a high level of uncertainty in the estimated parameters. Pressure Swing Adsorption for Hydrogen Purification Conclusions 47 5 Conclusions 5.1 Accomplished goals A breakthrough model, using the multilayer Langmuir-Freundlich isotherm, was validated in the course of the present work, providing good predictions for the breakthrough time. However, for higher pressures the deviation between the simulation and experimental data increases, leading to the consideration that 𝑞𝑒𝑞 might be over-estimated. Although the shape of the curves obtained through gPROMS® simulation have some deviation compared to the experimental data, it was assumed that the validation of the considered model was accomplished. Considering that the physical properties present in Multiflash are provided with the purpose of being employed in a wide range of industrial processes can affect the prediction of the breakthrough profiles. This fact could explain the differences between experimental and simulation results, when binary mixtures were employed as feed. The employment of the multilayer Langmuir-Freundlich isotherm in other situations present in the literature showed that good predictions are obtained when only one layer of activated carbon is used. Satisfactory predictions are obtained for a process with two layers of adsorbent, activated carbon and zeolite, for a feed pressure of 6.5 bar. However, a considerable deviation between experimental and simulation results takes place when the feed pressure is increased to 8 bar. A Multisite Langmuir isotherm was successfully added to the gML libraries and a validation of the temperature profile through the entire bed was accomplished. The comparison between the literature and simulation loading profiles for methane showed that an over prediction of 𝑞𝑒𝑞 also takes place when using this isotherm model. The Parameter Estimation tool present in gPROMS® was employed with the purpose of estimating the LDF coefficients in the process concerning the validation of the LangmuirFreundlich isotherm and the isotherm parameters of the Multisite Langmuir model. Two different variance models were applied in these estimations: constant variance and relative constant variance. However, results showed that for the process being considered the use of the relative constant variance model did not provide good approximations between the measured and predicted values. In the simulations using the constant variance, variances of 0.05 and 0.01 were applied. The results provided by gPROMS® show that, in the situations considered for the parameter Pressure Swing Adsorption for Hydrogen Purification Conclusions 48 estimation, final values with a higher level of certainty were obtained for a constant variance of 0.01 and equal lower and upper bounds for all the components in both adsorbents. When the parameters being estimated were the isotherm parameters, a higher number of iterations were required to obtain the wanted estimation and a higher level of uncertainty took place. This results can be explained by the high number of parameters being estimated, the complexity of the breakthrough model and the fact that, a slightly change in one of the parameters has a huge impact in the control variable and, therefore, in the breakthrough curve. The values obtained in the parameter estimation simulation are strongly affected by the model and the measured data being given to gPROMS®. Results with a high level of uncertainty can indicate that the model being used for simulating the process is not robust, that great errors are associated with the measured data or, that the amount of measured data given to gPROMS® is not enough to provide the desired estimations. gPROMS® is not able yet to produce estimations with a high level of certainty, however this tool is in a development and improvement stage. 5.2 Limitations and future work Taking into consideration that the adsorption is different from adsorbent to adsorbent, and from component to component, the possibility of using different isotherms for different adsorbents could become useful. When it comes to the parameter estimation tool, making the simulation faster would be extremely important since it would be possible to perform several attempts of estimating the parameters, testing different bounds and initial guesses without spending a considerable amount of time in each simulation. Pressure Swing Adsorption for Hydrogen Purification References 49 References 1. Balat, M., Potential importance of hydrogen as a future solution to environmental and transportation problems. International Journal of Hydrogen Energy 2008, 33, (15), 4013-4029. 2. Rahimpour, M. R.; Ghaemi, M.; Jokar, S. M.; Dehghani, O.; Jafari, M.; Amiri, S.; Raeissi, S., The enhancement of hydrogen recovery in PSA unit of domestic petrochemical plant. Chemical Engineering Journal 2013, 226, (0), 444-459. 3. Towler, G. P.; Doshi, K. J.; Vanden Bussche, K. M.; Senetar, J. J., Process for providing a pure hydrogen stream for use with fuel cells. Google Patents: 2001. 4. Silva, B.; Solomon, I.; Ribeiro, A. M.; Lee, U. H.; Hwang, Y. K.; Chang, J.-S.; Loureiro, J. M.; Rodrigues, A. E., H2 purification by pressure swing adsorption using CuBTC. Separation and Purification Technology 2013, 118, (0), 744-756. 5. Delgado, J. A.; Águeda, V. I.; Uguina, M. A.; Sotelo, J. L.; Brea, P.; Grande, C. A., Adsorption and Diffusion of H2, CO, CH4, and CO2 in BPL Activated Carbon and 13X Zeolite: Evaluation of Performance in Pressure Swing Adsorption Hydrogen Purification by Simulation. Industrial & Engineering Chemistry Research 2014. 6. Ruthven, D. M., Principles of Adsorption & Adsorption Processes. A Wiley – Interscience 1994. 7. Heinrich, K., Process for the purification and separation of gas mixtures. Google Patents: 1953. 8. Skarstrom, C. W., Method and apparatus for fractionating gaseous mixtures by adsorption. Google Patents: 1960. 9. Cruz, P.; Santos, J. C.; Magalhães, F. D.; Mendes, A., Cyclic adsorption separation processes: analysis strategy and optimization procedure. Chemical Engineering Science 2003, 58, (14), 3143-3158. 10. Ruthven, D. M.; Farooq, S.; Knaebel, K. S., Pressure swing adsorption. VCH Publishers: 1994. 11. Foo, K. Y.; Hameed, B. H., Insights into the modeling of adsorption isotherm systems. Chemical Engineering Journal 2010, 156, (1), 2-10. 12. Barros, M. A. S. D.; Arroyo, P. A.; Silva, E. A., General Aspects of Aqueous Sorption Process in Fixed Beds. 2013. 13. Bastos‐Neto, M.; Möller, A.; Böhm, J.; Gläser, R.; Staudt, R., Breakthrough curves of methane at high pressures for H2 purification processes. Chemie Ingenieur Technik 2011, 83, (1‐2), 183-190. 14. Lopes, F. V. S.; Grande, C. A.; Rodrigues, A. E., Fast-cycling VPSA for hydrogen purification. Fuel 2012, 93, (0), 510-523. 15. Sircar, S.; Golden, T. C., Purification of Hydrogen by Pressure Swing Adsorption. Separation Science and Technology 2000, 35, (5), 667-687. 16. Banu, A.-M.; Friedrich, D.; Brandani, S.; Düren, T., A Multiscale Study of MOFs as Adsorbents in H2 PSA Purification. Industrial & Engineering Chemistry Research 2013, 52, (29), 9946-9957. 17. García, S.; Gil, M. V.; Pis, J. J.; Rubiera, F.; Pevida, C., Cyclic operation of a fixedbed pressure and temperature swing process for CO2 capture: Experimental and statistical analysis. International Journal of Greenhouse Gas Control 2013, 12, (0), 35-43. Pressure Swing Adsorption for Hydrogen Purification References 50 18. Biswas, P.; Agrawal, S.; Sinha, S., Modeling and simulation for pressure swing adsorption system for hydrogen purification. Chemical and Biochemical Engineering Quarterly 2010, 24, (4), 409-414. 19. Lopes, F. V. S. New Pressure Swing Adsorption Cycles for Hydrogen Purifation from steam reforming off-gases University of Porto Porto, 2010. 20. Malek, A.; Farooq, S., Study of a six‐bed pressure swing adsorption process. AIChE journal 1997, 43, (10), 2509-2523. 21. Berlin, N. H., Method for providing an oxygen-enriched environment. Google Patents: 1966. 22. Chahbani, M. H.; Tondeur, D., Predicting the final pressure in the equalization step of PSA cycles. Separation and Purification Technology 2010, 71, (2), 225-232. 23. Hedin, N.; Andersson, L.; Bergström, L.; Yan, J., Adsorbents for the post-combustion capture of CO2 using rapid temperature swing or vacuum swing adsorption. Applied Energy 2013, 104, (0), 418-433. 24. Grande, C. A., Advances in pressure swing adsorption for gas separation. International Scholarly Research Notices 2012, 2012. 25. Liu, Z.; Grande, C. A.; Li, P.; Yu, J.; Rodrigues, A. E., Multi-bed Vacuum Pressure Swing Adsorption for carbon dioxide capture from flue gas. Separation and Purification Technology 2011, 81, (3), 307-317. 26. Thomas, W. J.; Crittenden, B. D., Adsorption technology and design. ButterworthHeinemann: 1998. 27. Cavenati, S., Separação de misturas CH4/CO2/N2 por processos adsorptivos. 2012. 28. Ribeiro, A. M.; Santos, J. C.; Rodrigues, A. E., PSA design for stoichiometric adjustment of bio-syngas for methanol production and co-capture of carbon dioxide. Chemical Engineering Journal 2010, 163, (3), 355-363. 29. Baksh, M. S. A.; Simo, M., Six bed pressure swing adsorption process operating in normal and turndown modes. Google Patents: 2013. 30. Chlendi, M.; Tondeur, D., Dynamic behaviour of layered columns in pressure swing adsorption. Gas Separation & Purification 1995, 9, (4), 231-242. 31. Jee, J.-G.; Kim, M.-B.; Lee, C.-H., Adsorption Characteristics of Hydrogen Mixtures in a Layered Bed: Binary, Ternary, and Five-Component Mixtures. Industrial & Engineering Chemistry Research 2001, 40, (3), 868-878. 32. Casas, N.; Schell, J.; Pini, R.; Mazzotti, M., Fixed bed adsorption of CO2/H2 mixtures on activated carbon: experiments and modeling. Adsorption 2012, 18, (2), 143-161. 33. Baksh, M. S. A.; Ackley, M. W.; Notaro, F., multilayer adsorber beds, used for removing impurities including water, carbon dioxide, methane, carbon monoxide and nitrogen from a gas stream containing hydrogen. Google Patents: 2009. 34. Gittleman, C.; Appel, W.; Winter, D.; Sward, B., Hydrogen purification process using pressure swing adsorption for fuel cell applications. Google Patents: 2005. 35. Papadias, D. D.; Ahmed, S.; Kumar, R.; Joseck, F., Hydrogen quality for fuel cell vehicles – A modeling study of the sensitivity of impurity content in hydrogen to the process variables in the SMR–PSA pathway. International Journal of Hydrogen Energy 2009, 34, (15), 6021-6035. 36. Majlan, E. H.; Wan Daud, W. R.; Iyuke, S. E.; Mohamad, A. B.; Kadhum, A. A. H.; Mohammad, A. W.; Takriff, M. S.; Bahaman, N., Hydrogen purification using compact pressure swing adsorption system for fuel cell. International Journal of Hydrogen Energy 2009, 34, (6), 2771-2777. Pressure Swing Adsorption for Hydrogen Purification References 51 37. Cho, S. H.; Bhat, S. G. T.; Han, S. S.; Park, J. H.; Kim, J. N.; Jung, H., Pressure swing adsorption apparatus and method for hydrogen purification using the same. Google Patents: 2011. 38. Ahn, S.; You, Y.-W.; Lee, D.-G.; Kim, K.-H.; Oh, M.; Lee, C.-H., Layered twoand four-bed PSA processes for H2 recovery from coal gas. Chemical Engineering Science 2012, 68, (1), 413-423. 39. Ana M. Ribeiro, C. A. G., Filipe V.S. Lopes, José M. Loureiro, Alírio E. Rodrigues, A parametric study of layered bed PSA for hydrogen purification Chemical Engineering Science 2008, 63, (5258-5273). 40. Lopes, F. V.; Grande, C. A.; Ribeiro, A. M.; Loureiro, J. M.; Evaggelos, O.; Nikolakis, V.; Rodrigues, A. E., Adsorption of H2, CO2, CH4, CO, N2 and H2O in activated carbon and zeolite for hydrogen production. Separation Science and Technology 2009, 44, (5), 1045-1073. Pressure Swing Adsorption for Hydrogen Purification Pressure Swing Adsorption Milestones 52 Pressure Swing Adsorption Appendix 1 Milestones Table 5.1 – PSA Milestones, adapted from Pressure Swing Adsorption [10] 1930 - 1933 First PSA patents issued to Finlayson and Sharp (U.K. 365,092) 1953 - 1954 Papers by H. Kahle outlining the principle of PSA (including heat storage) and giving details of a PSA process for removal of CO2, hydrocarbons and water vapor from air. 1955 - 1956 Synthetic zeolites produced commercially 1957 - 1958 French patent 1,223,261, P. Guerin de Montgareuil and D. Domine (Air Liquide): the “vacuum swing” PSA cycle is described. U.S. Patent 2,944,627, C. W. Skarstrom (Esso Research and Engineering): the low-pressure purge is introduced, and the importance of containing the thermal wave in the bed is emphasized. 1960 - 1965 Development and commercialization of the “Heatless Drier” for smallscale air drying and early versions of the “Isosiv” process for separation of linear hydrocarbons. 1965 - 1970 Development and commercialization of PSA for hydrogen purification 1970 – 1972 First large-scale PSA processes for O2 production 1972 – 1973 O2 selective carbon sieves produced commercially 1976 PSA nitrogen production process using CMS adsorbent 1976 – 1980 Small-scale medical oxygen units 1982 Large-scale vacuum swing processes for air separation (Adapted from Ruthven PSA) Pressure Swing Adsorption for Hydrogen Purification gPROMS Adsorption Models 53 gPROMS® Adsorption Models Appendix 2 2.1 List of models and specifications Table 5.2 – List of models present in the adsorption libraries of gPROMS® List of models Adsorption bed Source Sink Valve Header/storage tank Schedule model Recovery reporting model Mass balance reporting model Stream analyser PID controller Table 5.3 – Specifications made through the dialog box Design Fluid (mass transfer) Fluid (heat transfer) Wall Isotherm Dynamics Numerics Number of layers Mass transfer coefficient correlation Thermal operation mode Metal density Isotherm model Composition basis Flow mode Layers length Metal heat capacity Reference temperature Feed and product inert section pressure Number of discretizati on points Bed diameter Mass transfer basis Wall thickness Bed void Heat transfer coefficient bed-wall Bed density Ambient temperature Isotherm parameter Particle void Dispersion coefficient Particle diameter Wall specific heat capacity Mass fraction Particle thermal conductivity Mass transfer coefficient Initial temperature Particle heat capacity Thermal conductivity of the material Product and feed inert section volume Diffusivities Pressure Swing Adsorption for Hydrogen Purification Langmuir-Freudlich Isotherm 60 Figure 5.4 - Simulation and experimental breakthrough data comparison for a five mixture at a feed pressure of 10 atm and a feed flow rate of 8.6 SLPM for a 0.32 cr Figure 5.5 - Simulation and experimental breakthrough data comparison for a five mixture at a feed pressure of 10 atm and a feed flow rate of 8.6 SLPM for a 0.65 cr 0 0,2 0,4 0,6 0,8 1 10 100 1000 molar fraction time (s) sim. H2 exp. H2 sim. CH4 exp. CH4 sim. CO2 exp. CO2 sim. N2 + CO exp. N2 + CO 0 0,2 0,4 0,6 0,8 1 10 100 1000 molar fraction time (s) sim. H2 exp. H2 sim. CH4 exp. CH4 sim. CO2 exp. CO2 sim. N2 + CO exp. N2+CO Pressure Swing Adsorption for Hydrogen Purification Langmuir-Freudlich Isotherm 61 3.4 Validation of the Langmuir-Freundlich multilayer isotherm with different data Figure 5.6 – Simulation and experimental breakthrough curves for a column filled with activated carbon at 6.5 bar and 5.0 SLPM Figure 5.7 - Simulation and experimental breakthrough curves for a column with two layers of adsorbent at a feed pressure of 6.5 bar and feed flow rate of 5 SLPM 0 0,2 0,4 0,6 0,8 1 0500 1000 1500 2000 molar fraction time (s) sim. H2 exp. H2 sim. CH4 exp. CH4 sim. CO2 exp. CO2 sim. N2 + CO exp. N2 + CO 0 0,2 0,4 0,6 0,8 1 0500 1000 1500 2000 molar fraction time (s) sim. H2 exp. H2 sim. CH4 exp. CH4 sim. CO2 exp. CO2 sim. N2 + CO exp. N2 + CO Pressure Swing Adsorption for Hydrogen Purification Langmuir-Freudlich Isotherm 62 Figure 5.8 - Simulation and experimental breakthrough curves for a column with two layers of adsorbent at a feed pressure of 8 bar and 5 LSPM 0 0,2 0,4 0,6 0,8 1 0500 1000 1500 2000 molar fraction time (s) sim. H2 exp. H2 sim. CH4 sim. CO2 sim. N2 + CO exp. CH4 exp. CO2 exp. N2 + CO Pressure Swing Adsorption for Hydrogen Purification Multisite Langmuir Isotherm 63 Multisite Langmuir Isotherm Appendix 4 4.1 Multisite Langmuir isotherm modelling Figure 5.9 – Multisite Langmuir dialog box Pressure Swing Adsorption for Hydrogen Purification Multisite Langmuir Isotherm 64 Table 5.9 – Conversion of the provided parameters to the LDF coefficient Activated carbon Zeolite Components 𝐷𝑐 𝑟𝑐2(𝑠−1) gPROMS 𝜔𝑖(𝑠−1) 𝐷𝑐 𝑟𝑐2(𝑠−1) gPROMS 𝜔𝑖(𝑠−1) H2 8.89×10−2 1.3335 9.23×10−2 1.3845 CH4 3.96×10−3 5.94×10−2 1.04×10−2 0.156 CO2 1.24×10−2 0.186 1.87×10−4 0.002805 CO 2.11×10−2 0.3165 4.22×10−3 0.0633 N2 2.29×10−2 0.3435 2.13×10−2 0.3195 Table 5.10 – Multisite Langmuir isotherm parameters Components qmax (mol∙kg−1) ai (-) 𝐾∞×1011( Pa−1) (−∆H)(kJ.mol−1) Activated Carbon CO2 7.8550 3.0 2.125 29.084 H2 23.565 1.0 7.233 12.843 CH4 6.7329 3.5 7.904 22.701 CO 9.0634 2.6 2.680 22.577 N2 5.8913 4.0 23.46 16.263 Zeolite CO2 4.525 2.2 11.11 35.965 H2 9.954 1.0 50.76 9.2309 CH4 4.976 2.0 35.65 20.643 CO 3.828 2.6 3.937 29.773 N2 4.148 2.4 30.83 20.413 Pressure Swing Adsorption for Hydrogen Purification Multisite Langmuir Isotherm 65 Table 5.11 - Properties of the adsorbent and feed conditions for the simulation performed using the Multisite Langmuir isotherm Feed conditions Pressure (bar) 7 Temperature (K) 303 Flow rate (Nm3/h) 12.2 Adsorbent properties Activated carbon Zeolite Particle porosity 0.566 0.503 Particle density (kg/m3) 842 1126 Particle specific heat (J/kg·K) 709 920 Particle radius (m) 1.17×10−3 0.85×10−3 Pressure Swing Adsorption for Hydrogen Purification Multisite Langmuir Isotherm 66 4.2 Loading Profiles Figure 5.10 – Loading profiles for t = 40 s Figure 5.11 – Loading profiles for t = 100 s Figure 5.12 – Loading profiles for t = 1000 s 0 0,5 1 1,5 2 00,2 0,4 0,6 0,8 1 qi (mol/kg) z H2 CH4 CO2 CO N2 0 0,5 1 1,5 2 2,5 00,2 0,4 0,6 0,8 1 qi (mol/kg) z H2 CH4 CO2 CO N2 0 0,5 1 1,5 2 2,5 00,2 0,4 0,6 0,8 1 qi (mol/kg) z H2 CH4 CO2 CO N2 Pressure Swing Adsorption for Hydrogen Purification Parameter Estimation 67 Parameter estimation Appendix 5 5.1 LDF coefficients estimation 5.1.1 Variance of 0.05 Table 5.12 – gPROMS® output for the parameter estimation performed considering a constant variance of 0.05 Original ω Final value, 𝜔 Confidence interval 90% 95% 99% Activated Carbon H2 0.700 0.665 477.4 568.9 748 CH4 0.195 0.167 11.69 13.93 18.32 CO2 0.035 0.027 0.5692 0.6783 0.8919 CO 0.15 0.108 23.27 27.73 36.47 N2 0.261 0.23 21.74 25.91 34.07 Zeolite H2 0.700 0.665 166.8 198.7 261.3 CH4 0.147 0.185 0.5071 0.6043 0.7946 CO2 0.0135 0.0599 0.2978 0.355 0.4667 CO 0.063 0.045 0.08414 0.1003 0.1318 N2 0.099 0.14 0.6762 0.8059 1.06 Pressure Swing Adsorption for Hydrogen Purification Parameter Estimation 68 Table 5.13 – Upper and lower bounds for the 0.05 constant variance parameter estimation Components Lower bound Upper bound Activated carbon H2 0.5 0.9 CH4 0 0.4 CO2 0 0.2 CO 0 0.4 N2 0.1 0.5 Zeolite H2 0.5 0.9 CH4 0 0.4 CO2 0 0.2 CO 0 0.2 N2 0.1 0.5 Pressure Swing Adsorption for Hydrogen Purification Parameter Estimation 69 Table 5.14 - Estimated parameters for a constant variance of 0.05 and different upper and lower bonds for each component Original ω Final value, 𝜔 Confidence interval 90% 95% 99% Activated Carbon H2 0.700 0.6 358 426.6 560.8 CH4 0.195 0.3 - - - CO2 0.035 0.1 9.728 11.59 15.24 CO 0.15 0.09 8.039 9.581 12.59 N2 0.261 0.15 5.552 6.616 8.698 Zeolite H2 0.700 0.6 138.2 164.7 216.5 CH4 0.147 0.15 0.153 0.1823 0.2396 CO2 0.0135 0.1 0.7814 0.9313 1.224 CO 0.063 0.1 0.25 0.2979 0.3917 N2 0.099 0.15 0.515 0.6138 0.8068