A STUDY OF PRESSURE DROP AND FLOW CHARACTERISTICS IN PACKED BED REACTORS (PBRs) USING A DEVELOPED VIRTUAL EXPERIMENT
ABSTRACT
PBRs are reactors that are tubular and filled with the solid catalyst particles which help in catalyzing gas reactions. They are known to offer higher conversion per weight ratios compared to the existing catalytic reactors. The advantage offered by the PBRs is that the conversion rates are based on the catalyst amount and not the reactor volume. There is a realization that it helps in improving the contact between two chemical phases. PBRs are used in chemical reactors, as a scrubber, distillation process and storing heat in some chemical plants. The pressure drops and flow characteristics in the PBRs can be studied under different simulations. For this research, there is the development of a virtual experiment to study the flow characteristics and pressure drops in the PBRs. There is an explanation of the operation of the PBRs and the introduction of the COMSOL Multiphysics software program.
ACKNOWLEDGMENT
I would like to give my sincere thanks and gratitude to my Project Advisor who guided me through this research. If it were not for her, this work would not have reached this level. The amount of motivation and energy that she gave me is unmatchable and I really appreciate her. Secondly, I would like to thank my reading committee for his advice and contribution towards this work. Their immense contribution and direction at some points of this work played a long way to the realization of a completion. I would also like to thank my parents and siblings for their support all through my academic journey.
TABLE OF CONTENTS
List of Tables vii
List of Figures viii
Chapter 1 – Introduction…………………………………………………………………1-7
Chapter 2 – Literature Review…………………………………………………………8-44
Chapter 3 – Research Objective…………………………………………………………45
Chapter 4 – Materials and Methods…………………………………………………46-53
References……………………………………………………………………………54-56
LIST OF TABLES
Table
Title
Page
1
A comparison data outcome of cold flow and CFD simulations
33
2
Kinetics parameters of the catalytic methane combustion (CMC)
38-39
LIST OF FIGURES
Figure
Title
Page
1
The diagram of the packed bed bioreactor
2
2
Effect of (a) Flow rate, (b) Bad height, (c) Inlet concentration of 4-CP,
(d) Porosity of bed on 4-CP degradation in packed bed reactor
17
3
Effects of a Gradual Temperature Increase in a PBR
19
4
CFD PBR simulation
24
5
MATLAB simulations
28
6
Cold Flow simulations
33
7
The depiction of conversion of HCl into Cl2
36
8
Correlation between the temperature and reaction rate
41
9
Inverse proportionality between space velocity/residence time and conversion
42
10
Mechanism of the packed bed reactor and gas chromatograph
48
11
Cross-sectional layout of the cylindrical reactor
49
CHAPTER ONE
INTRODUCTION
The world cannot progress without an efficient and reliable chemical industry. The global population relies on chemical industries for operations such as water cleaning and manufacturing of pharmaceutical goods. The number of world citizens is increasing exponentially and progressively [1]. Humanity will continue demanding clean water for drinking. At the same time, the population will need medical products. The stated demands pressure chemical industries to be effective and meet the needs of consumers. The stakeholders must identify how to cater to the wants of humanity while creating profits for themselves [2]. Chemical industrial players can accomplish the objective by advancing packed bed reactors (PBRs). The stakeholders ought to focus on efficient pressure drop and fluid flow. The two factors are essential for a high rate of chemical conversions [3]. Pressure drop is the decrease of pressure in a packed bed reactor (PBR), allowing an increase in the fluid volume and a high rate of chemical reactions [1]. Fluid flow is the movement of fluids within a PBR whenever pressure is low to enable increased chemical reactions and a high conversion rate [1]. The design, simulation, and optimization of PBRs must be considered to continue revolutionizing the chemical industry.
Packed-bed bioreactors comprise cylindrical vessels that contain catalysts such as enzyme concentration or microbial organisms. For immobility, many approaches including as encapsulating, cross-links, bond formation, and adsorption are commonly utilized. Since packed-bed bioreactor processes are heterogeneity, enzymatic biochemical processes and permeation barriers may play a larger role in regulating reaction conditions. As a result, reactions in these bio-processers can take place in either a weight transmission or a reaction-controlled mode. Below is a diagrammatic representation of a PBR.
Figure 1. The diagram of the packed bed bioreactor
Operating PBRs could cause adverse environmental effects. The reactors can release chemicals in the surroundings, affecting flora and fauna [3]. The reason is chemicals interact with physical and biophysical elements in surroundings. Animals could die because of the harmful chemicals reaching their respiratory system [6]. It is the same case with human beings. The chemicals can interfere with the ordinary life of communities surrounding the reactors. It is the responsibility of operators to ensure the PBRs are safe and have no negative environmental ramifications. The environmental ethics should prompt proprietors of PBRs to design the reactors as required. A better design means less leakage of chemicals into the environment [2]. The pressure and fluid flow must be appropriate to guarantee the safer operation of PBRs. Therefore, better design, simulation, and optimization of the PBR structures encourage surrounding communities to support the facilities.
Mitigating adverse effects on the environment has favorable economic outcomes for the stakeholders. It means PBR facilities operate without causing chemical leakage into the environment. The leakages, as indicated, destroy plants and animals. Likewise, the chemical release could contaminate the atmosphere and drinking water, leading to health care crises among people [7]. Such scenarios demand the chemical industry stakeholders take social and economic responsibility. Chemical industries should compensate community members and pay heft legal penalties. The best way to prevent negative ramifications on the environment should be the advanced design of PBRs. Improved chemical systems produce demanded products making sufficient profits for stakeholders. Everyone benefits because owners and managements shun spending resources in rectifying the degradation of the surroundings [3]. The money is for the reinvestment in the business. As such, PBRs business has sufficient capital to meet the pharmaceutical and clean water demands.
PBR is almost like fluid bed reactors but differs based on the number of catalysts used. Thus, the two share a similar history and application. The genesis of the technology was in 1920 in Germany [8]. The pioneer was a chemical engineer known as Fritz Winkler. The US first applied the technology in 1942 [9]. The US chemical engineers used the Catalytic Cracking Unit to manufacture petroleum. The Standard Oil Company benefitted from the technology, leading to more development. The developers wanted the technology to assist in preparing oil and petroleum for global consumption [9]. The advancement led to the creation of PBRs, which used fewer number of catalysts compared to FBRs. The catalysts were crucial for the cracking process. It reduced elements like petroleum into smaller particles [10]. Developing the industry has contributed to the mass production of oil, petroleum, pharmaceutical products, and clean water [10]. The technology is cleaner and effective. Hence, it will continue benefitting the current world.
Chemical industry stakeholders must continue to develop PBRs because of their economic and social benefits. The industry players can do so by focusing on the structures of the systems. In particular, engineers ought to consider the tubular elements essential for hosting catalysts. The parts of the PBRs should be large enough to allow fluid movement and prevent the increase of volumetric flow rate [1]. The volumetric flow rate causes a pressure drop, leading to slowing chemical reactions. As a result, the system must consume an enormous amount of energy. In ordinary situations, PBRs relies on the gravitational pull to speed the chemical reactions and collection of the products. However, an increased volumetric flow rate prevents reactants and catalysts from interacting efficiently because of friction [5]. PBR makers must eliminate the problem because it negates the sustainable development agendas. It is the responsibility of industries to mitigate the level of natural resource use.
The world has many problems, and they increase progressively. One of the issues affecting the world is the lack of clean water and enough pharmaceutical products [6]. The globe needs solutions for the mentioned and other problems. Chemical industries are crucial stakeholders in the eradication of the social and economic issues affecting humanity. However, the chemical sector cannot assist in the elimination of the challenges without being proactive.
Pressure drop is a negative phenomenon because it slows the rate of chemical reactions. Subsequently, pressure drop augments volumetric flow rate within the bed reactors. The augmenting volumetric flow rate reduces concentration of reactants [9]. The rate of reaction lowers. Operators have to utilize significant resources in artificial energy. It is through simulations that chemical engineers can determine the best PBR designs. The modeling process ensures chemical engineers plan and establishes efficient PBRs. The meaning of productive PBRs is they can balance pressure and fluid flow. The liquid movement should be free of frictions within the tubular reactors. The reason is friction lowers the rate of flow, leading to pressure drop. Different methods of simulating PBRs exist. Chemical engineers can utilize computation fluid dynamics [18]. Also, the experts can use MATLAB in modeling PBRs with accuracy.
Grounded theory constitutes the theoretical framework that informs this study. Uncovering the association of optimum performance and underlying considerations include the used approach for this study. Therefore, there is an accurate and detailed understanding of the association of paramount factors and existing dynamics, such as underlying causes of altered optimal functioning of PBRs. Optimization is more of the considerations because it guarantees efficiency and sufficient production of chemicals. The research explores the stated elements, including pressure drop and fluid flow [4]. Also, the study utilizes a literature review formula in understanding the concepts and the implication they have in modern chemical and water treatment operations. Availability of relevant materials expedites the realization of the objectives of the research. The resources ought to include articles, texts, and online sites. The criterion is the materials to be recent and contain necessary data. To be specific, the materials should contain details on the design. Other information should relate to the optimization and simulation of PBRs. Equally, the resources should consist of details on pressure drop and liquid movement characteristics. Theoretically, the pressure decreases down the length of the reactor, and thus the volumetric flow rate increases. As a result, the concentration of the reactant decreases (in addition to the decrease due to conversion), which lowers the rate of reaction [11].
The Ergun equation for pressure drop in a PBR is:
Equation 1
P: pressure, z: PBR length, : void fraction, : volumetric flow rate, : viscosity
: diameter of catalyst particle, : cross-sectional area of the PBR, m: mass flow rate
B: laminar flow term, G: turbulent flow term
Having talked much at length on the flow rate, it is also important to highlight other important parameters as far as PBR systems are concerned. Particle sizes are determined by their dimeters in the PBR. This is a dominate parameter in in the systems because large diameters mean large particle sizes, which causes a reduced conversion rate. On the other hand, large particle sizes are known to increase voltage breakdown causing a partial discharge in the system [12]. The result of the partial discharge is the reduction in the overall system’s performance.
In summary, as this study seeks to develop a virtual experiment so that PBRs can be studied by students to learn how to operate them and why they work the way they do. The implications of PBR on the chemical industry highlight its relevance. Specifically, this study explores the dynamics of pressure drop and fluid movement in PBR. All in all, studying pressure drop and fluid movements in PBRs is advantageous as it highlights its connection to the streamlined and highly functional chemical industry. Therefore, this study seeks to demonstrate to students the dynamic of PBRs. COMSOL Multiphysics is the online platform that will be used to conduct simulations of the experiment.
CHAPTER TWO
LITERATURE REVIEW
The principal purpose of the research proposal is to develop an online simulation using COMSOL Multiphysics software program. Multiple studies have been conducted on this topic. According to Daniels and Thistlethwaite, chemical industrial players must focus on the design of the PBRs for them to benefit the global population. Also, the stakeholders should consider the simulation of PBRs. Chemical engineers can apply simulation approaches like Computational Fluid Dynamic (CFD) [4]. The technology offers accurate simulations for the design of PBRs. Thus, CFD is vital for the establishing efficient PBRs for various applications.
The global population cannot thrive and progress without controlling the chemical sector. The industry contributes to the production of essentials like clean water for drinking. Also, the sector provides pharmaceuticals for various uses around the world [1]. People should remember without chemical industries, driving their vehicles and cooking in their homes would be impossible. The cars use products like petroleum, and homesteads require gas for preparing meals. The contributors should understand the purpose of pressure drop in a PBR. Likewise, the industrial players should fathom the need for flowing fluid in a PBR. The understanding prompts stakeholders to focus on the advanced design of the PBRs. The processes assisting in better designs are simulations and optimizations. The two factors guarantee the productivity of the PBR facilities.
The following points summarize the specific objectives of the research:
The study should explain the gains the global population receives from the operations of chemical industries, particularly PBRs.
The research accounts for the pressure drop. It explains the implication the pressure drop has on the operations of PBRs and potential mitigation measures.
The other element the study accounts for is fluid movement. The research explains the ramifications of fluid movement and the realization of chemical reactions.
The study focuses on the consumption of energy by PBRs. It is imperative to understand when PBRs consume much energy and when it does the opposite.
The research offers explanations on how PBR engineers can improve the performance of the facilities. It will guarantee the accomplishment of economic and social objectives in the business.
The study highlights how simulation and optimization contribute to the advancement of PBRs.
2.1 Chemical Industries
The world is changing rapidly, and the changes require advanced solutions. One of the areas the globe needs feasible solutions is the chemical industry. The sector is crucial because it is involved in meeting the dynamic needs of the global population. The trend will continue because of the availability of sufficient food, shelter, and clean water. Other factors contributing to the increase of the masses are economic opportunities and better health care in considerable parts of the world [1]. Chemical industries play a significant role in the preparation and distribution of essentials products. For instance, packed bed reactors expedite waste management. Also, the PBRs enabled manufacturing pharmaceutical and purifying drinking water. The stakeholders in chemical industries must advance PBRs [2]. It is the only way to continue benefiting the global population and accumulating profits for shareholders.
The advancement of PBRs is crucial because chemical industries have enabled the agriculture sector to develop over time. Growers rely on numerous forms of chemicals to realize their farming objectives. Farmers use fertilizers, pesticides, insecticides, and fungicides [3]. The chemicals allow the agriculturalists to protect their crops and augment their farm produce. Therefore, chemical industries are one of the backbones of the agricultural sector. Stakeholders provide chemicals that ensure sustainable farming and profits. The growers do not have to expend much energy because they only need minimal amounts of fertilizers [1]. The chemical components facilitate the growth of crops and augment harvest. Another reason for advancing PBRs is the chemical products decrease runoff. It means the use of fertilizers does not contaminate water systems. Hence, the decrease in runoff prevents the spread of nitrous oxide [3]. The outcomes indicate how chemical industries are crucial in the advanced method of growing crops.
PBRs have endless benefits in agriculture because they provide chemicals that transform crops for the better. One of the benefits is the rearing of crops resistant to drought and pests. Rearing drought-resistant and pesticide-tolerant plants expedite the elimination of green practices such as till farming [3]. The ramification is the chemicals contribute to increased yields in farms. It means the chemicals mitigate the loss of plants agriculturalists used to experience. PBRs produce pharmaceutical products with the potential of eliminating fungi and bacteria [1]. As a result, many farms are free of increased natural toxins. One of the criteria used in chemical industries is the assessment of chemicals produced. The evaluations ascertain whether the chemical products are harmful or beneficial [3]. If the products have detrimental effects, the evaluators propose their destruction. Chemical engineers need to establish reliable PBRs because they will prevent unwanted business outcomes.
Chemical industries have impacts on the environment through the products their release in the markets. Scientist suggests that biological, physical, and chemical components interact within surroundings [1]. The interaction tends to occur within the molecular level, covering any adverse outcomes. However, the mixing of chemicals and other elements in the environment leads to phenomenon like climate change. Other undesirable ramifications are contamination of natural resources and biodiversity [4]. Still, chemical products undermine the conservation of soil and groundwater. More of the negativities are an increase in waste and air pollution. The unwanted ramifications of PBRs should prompt chemical engineers to consider how to improve them. Improving PBRs implies the surroundings will be safer. The chemical, physical, and biological interactions will support life rather than destroy it. Chemical industry players should be proactive in mitigating global-scale loss of natural resources [3]. Also, the stakeholders should be active in stopping negative health impacts and environmental pollution.
PBRs are part of the scientific development plans in understanding different diseases like cancer. It means scientists must fathom the genesis and effects of all diseases. The objective is to find a cure for health care conditions. However, a solution is not possible without understanding how PBRs are crucial in producing chemical medication. The entire system of PBRs should be efficient [5]. It allows scientists to accomplish their objective of healing diseases. Chemical engineers should realize the globe in the 21st century rely on it for better lives. The global population demands chemical products with limited ramifications on their health and environment. People use chemical products like soaps and medicine to improve their health status [3]. Only productive PBRs can continue meeting the chemical needs of the augmenting populations. Efficient PBRs should produce reliable and harmless products to cater to the needs of consumers.
PBRs should be part of the global vision of using sustainable energy sources. The world is at risk of global warming because of increased fossil fuel combustion. Also, the greenhouses gases like carbon dioxide augment progressively. Human beings should be proactive in mitigating the levels of carcinogens released in the atmosphere [3]. The mitigation efforts will ensure sustainable development and the protection of the environment. PBRs should be productive because the world depends on them to halt the use of fossil fuels. PBRs are crucial for producing gases used in cooking and other industrial activities [6]. However, PBRs are part of the problem, particularly when they are inefficient. As an illustration, a PBR with a poor design utilizes much energy [6]. As such, the PBR contributes to the over-exploitation of natural sources of energy. PBR engineers should consider the system and ensure it serves the intended purposes efficiently.
2.2 Packed Bed Reactors
The invention of PBRs contributed to the transformation of oil and gas processing. The PBRs brought efficiency to chemical industries. Typically, a PBR entails cylindrical equipment with curved heads. Engineers prefer PBRs to be vertical to save the energy needed for converting chemicals into different forms. A vertical PBR relies on gravity to permit the flow of reactants in the cylindrical equipment [7]. The reactions occur faster or slow based on the number of immobilized or static catalysts. If the catalysts are adequate, the chemical reactions occur faster. Quite the reverse if the catalyst is insufficient, chemical reactions take a long time to complete. Stakeholders in chemical industries should ensure catalyst is appropriate and sufficient [8]. As such, chemical engineers can allow many chemical reactions intended to produce essentials. The goods include gasoline, medicine, diesel, and many others as petroleum [8]. The stated items allow human beings to meet their economic and homestead needs.
PBRs are varied chemical reaction systems, meaning stakeholders have sufficient options to realize their economic objectives. The systems could entail cylindrical, circular, or rectangular tubes. Reactants enter through the curved heads of various equipment shapes [8]. The reactants must flow via the cylindrical, rectangular, and circular tubes. It is in the stated tubes where the reactants pass over or through fixed catalysts [9]. The catalysts tend to be small indissoluble particles. It means the reactants do not affect the catalysts as they transform. The contact between the reactants and the catalysts allows chemicals to transform to produce intended products [8]. The goods produced within the chemical reactions must exit on the bottom part of the system. The collection sections should be secure to ensure limited leakage of harmful chemicals [9]. The safety relies on the concentration gradient through the reactor.
Engineers designing PBRs must consider the life span of catalysts. If the active life of chemical agents is shorter, the designer should consider the fact. The implication is the designer must design a PBR with an efficient mechanism to regenerate catalysts. It should be the opposite if the chemical agents have a long-life span. Planning is a crucial phase in designing PBRs [10]. It is in the stage where engineers determine the level of reactants and catalysts. Likewise, the designers decide the purpose of PBRs and their inherent benefits to stakeholders. Engineers should create PBRs with a durable active life. A viable strategy to expedite the objective is choosing a long-life span catalyst [11]. Durable fixed-bed chemical pellets allow numerous reactions without the need to regenerate other catalysts. As such, the PBRs are profitable to shareholders.
The primary characteristic of catalysts used in PBRs is fixed granular pellets. The chemical agent particles entail a diameter between 1 and 5 mm [12]. Loaders can utilize varied techniques to load the pellets in the chemical reaction tubes. Loaders can load the particles as one bed or separate sectional beds [8]. Alternatively, the loaders can insert the chemical agents in tubes. The purpose of loading catalysts using various techniques is to ensure efficiency through the preservation of energy. Loaders intend gravity to allow the free flow of reactants in PBRs [12]. As a result, the process requires limited artificial energy needed for producing various products. Catalysts produce desired results if manufactured from appropriate raw materials. In particular, rhodium, nickel, and osmium are relevant resources for making chemical agents [8]. Other raw materials are copper and platinum.
Apart from using suitable raw materials, PBRs are effective when using the right sizes of catalysts. The recommended size should entail around 3.175 mm [8]. The particle is large enough to allow chemical reactions to take place. Ceramic beads are provided as excellent examples of recommended chemical agents with the right sizes [5]. Ceramic beads consist of metal materials. Also, the pellets have a 3.75mm diameter [8]. The ceramic beads enable the chemical reactions occurring within an electric catalytic oxidizer. The purpose of the system is to treat air streams. In particular, an electric catalytic oxidizer removes volatile organic compounds from the reactants [5]. The VOCs are harmful elements found in streams of gases. The particles can cause adverse health care effects. Better designs of PBRs guarantee secure chemical reactions because everything is in the right sizes [5]. The entrance, the tubes, and chemical agents should be appropriate to produce wanted products without negative ramifications.
One undeniable fact about PBRs is they are considerably versatile. The versatility allows the chemical reactors to process various products. PBRs enable the absorption of chemicals [13]. The elements facilitate manufacturing pharmaceutical products. Distillers rely on PBRs to manufacture alcoholic products like spirits. Other processes requiring PBRs are catalytic, stripping, and separation reactions. Also, the diverse application of PBRs determines the physical appearance of the equipment. However, the general physical structure of PBRs looks almost similar, regardless of the varied applications. All PBRs should consist of chambers [5]. The sections should be of different sizes and shapes. The chambers could be extended or shorter. Also, the compartments could be circular, rectangular, or tubular. The chambers are where catalysts remain and allow chemical reaction [13]. The reactants require sufficient fluid flow for them to produce the targeted products.
The liquid is necessary because it enables the movement of the catalyst. Also, fluid allows reactants to interact with chemical agents. The interaction among catalysts, reactants, and fluid determines the chemical make-up of the process [4]. For better results, chemical engineers must use the right amount of each component. The substances should balance for a uniform chemical reaction to occur. Fluid should not be too much because it can distribute particles wider in the reactor. As a result, the elements fail to interact properly, leading to inefficient chemical reactions. Such an outcome can be detrimental to the stakeholders because it does not produce the wanted products [14]. At the same time, chemical industries can record significant losses because they had already spent many resources to set up PBRs. The chemical sector should rely on experts to make effective chemical reactors [4]. The professionals account for the chemical capacity of the reactors.
The multi-tube reactor is a more effective outlay for the PBR. Thousands and thousands of pipes with interior diameter varying from 15 to 25 mm make up the reactor [11]. For practical purposes, the reactor is conducted with several tubes and is usually operated near to overrun temperatures. Such reactors are intended to have the highest yield. Nevertheless, the time required to load such reactors, and the varied pressure falls that result in various residency durations across tubes, raises concerns about this reactor type. Due to its efficiency for heterogeneous procedures, the multi-tube reactor has become the most used treatment reactor for PBR.
Thermal conduction between fluids, catalysts, and heat regulation media regulates heterogeneous reactions. The PBR gains a lot of benefits in process engineering as a result. Small and modest variations in temperatures inflow settings have little effect on the PBR reactor. Since this system would maintain a steady state, there would be no impact on the temperature gradient other than a curvature shift to change the scales. Menzinger et al.’s analysis visually depicts this slow temperature rise to illustrate that it is purely a transition along the curve without slope deviations. The graph can be seen below.
Figure 2. Effects of a Gradual Temperature Increase in a PBR
If the process contains an activator-prevention system working at variable rates, the PBR permits considerable fluctuations in temperature and some other aspects of reactivity to be seen. This activator-prevention system is a dynamic state wherein the reactor has both positive feedback and self-acceleration. Because of the heat released during exothermic reactions, this mechanism is in existence. The stimulator is the heat production, whereas the inhibitor is the reactant utilization. This system can equalize out and trigger reactor disturbances, like a hot spot area, which can force the reactor to shut down [10]. Whenever the temperature of the inlet is substantially and rapidly changed, a different type of disturbance arises. Owing to a surge in the inlet circumstances, a rise in temperature will generate potentially hazardous thermal conditions for the reactor. Nevertheless, if the reactor’s temperature drops, a hotspot zone can form. This is the case because of the slower reaction rates linked to cooler temperatures. The high reactant content flow will move faster to the reactor’s combustion section, wherein a rapid reaction will take place. If the process is exothermic, it will produce an instantaneous hot zone, which is extremely dangerous to operate and may make the catalyst ineffective for further reactions.
A good virtual experiment set-up helped study the effect of the particle size parameter on the PBR performance. The particles under focus had the sizes of 180-2000 µm using BaTiO3 and Al2O3 regarding the carbon dioxide conversion in the system [12]. The results indicated that particles with smaller diameter increased the conversion rate with over 70% provided enough voltage was supplied.
Other factors that can be studied using the CFD simulation are the bed height, porosity, and inlet concentrations [13]. A study carried out to simulate these properties indicated that a mass transfer resistance had a critical role in the PBR efficiency. The resistance could be decreased by up surging the flow rate that helps minimize the boundary later thickness [13]. Another aspect worth noting that an inlet with a high concentration increases the efficiency of the system. This is the same case with the increased height of the bed, which increases the residence time to ensure complete interaction of the chemicals. Increased porosity reduces the conversion rates, which reduces the PBR efficiency [13]. An increased fluid density increases the conversion rates. The figure below indicates the effect of these parameters, as studied in the experiment by Sasmal’s team.
Figure 3. Effect of (a) Flow rate, (b) Bad height, (c) Inlet concentration of 4-CP,
(d) Porosity of bed on 4-CP degradation in packed bed reactor
Source: https://www.eeer.org/journal/Figure.php?id=eer-2019-184f2&number=1113&p_name=0456_1113
When contrasted to a batch reactor, a PBR has numerous advantages, including the simplicity with which the biocatalyst and substrates can be separated, the ability to run for extended periods of time (without losing enzyme activity), and more influence over reactivity settings. It also has a large surface area and a small footprint. The liquid within the PBR must be characterized in order to learn more about the reaction’s impact from the catalysts. The residence time distribution (RTD), typically indicates the conductivity that transports liquid within the reactor, is the most extensively used method. This residence time is affected by the fluid flow and has a direct impact on the pace of chemical conversions.
2.3 PBR Design Limitations
An efficient PBR facilitates the production of desired chemical products. It earns shareholders significant revenue. However, the design of the PBRs is never easy as many stakeholders would anticipate. Owners must set aside enough capital for various materials and processes. A reliable PBR must entail the mass transportation of reactants [15]. Also, the PBRs should consist of the transportation of chemical reactions. The other factor is heat which must spread within the reactors. Operators must have a detailed understanding of all the requirements and resources to establish productive equipment. For instance, fathoming the necessity of heat transfer mitigates the cost of operations of PBRs [16]. The other consideration should be the packed catalyst. It enables chemical engineers to model the device as accurately as possible [15]. The engineers could decide to model the packed bed as porous or non-porous.
A porous structure is necessary for the transportation of particles based on diverse magnitude. However, allowing particles to flow in different scales introduces many challenges in PBRs. The first problem is the difficulty in assessing the mass within the reactor [17]. The other challenge is analyzing the energy used in the chemical reactions. The chemical industry players were advised to mitigate the setback if they want to realize objectives [18]. Operators could do so by shunning the porous structure. The strategy permits the accurate analysis of the mass and energy within the PBRs. The evaluations indicate to operators where they need to improve for the chemical reactions to be successful. The improvement could be the adjustment of the energy used. It could also be the adjustment of the mass of the particles [17]. All required components in the chemical reactions should be in line with the capacity of the PBRs.
Pressure drop is another challenge related to the design and efficiency of PBRs. Pressure is crucial for the flow of fluid with the area of the tubular, circular, or rectangular reactor. Pressure should not drop for the reactants to produce intended results. The chemical industry stakeholders can mitigate the pressure drop by relying on larger catalysts pellets [19]. However, the application of the larger catalysts elements has adverse effects on the chemical reactions. It prevents intra-particle diffusion when chemical reactions occur [20]. The ramification is chemical reactions occur slower than usual. As such, the reactions require more resources directed to the production of energy. Operators cannot afford to augment the cost of artificial power. The reason is it would undermine the generated revenues needed by the shareholders. The design problem requires workable solutions [19]. Also, the solution should be cheap for investors to continue investing.
A cheaper solution ought to be identifying chemical particles which are moderately large enough. The elements should prevent pressure drop. Also, the particles should facilitate the reaction at a significant rate until the climax [7]. It should guarantee a faster rate of chemical conversation at constant pressure. Operators should consider using particles with an estimate of a radius of one millimeter [8]. The solution introduces macroporous or the spaces between reacting particles. Likewise, the bed allows pores within catalysts to exchange substances with the external surroundings. The pores on the surfaces of the catalyst are called microstructures. Chemical engineers should consider the solutions because they are cheaper. It only requires exchanging larger catalyst pellets with those with the capacity to prevent pressure drop. The catalysts should allow interaction of the elements in and without [7]. Reactions occur productively and leave stakeholders satisfied. Consequently, the chemical industry receives more investment capital.
2.4 PBR Simulations: CFD, MATLAB, and Cold Flow
The CFD modeling works based on fluid mechanic principles. It relies on numerical information to solve problems related to chemical reactors. Also, the simulation method entails the use of algorithms in mitigating problems related to fluid flows within PBRs. The CFD simulations allow the integration of chemical reactions [18]. Other incorporated elements are combustion procedures and fluid movement. The three offers a three-dimensional lesson of the PBR performance. Chemical engineers can utilize CFD simulations to model the interaction of reactants, fluids, and packed catalysts pellets. Therefore, CFD is necessary for determining how independent elements interact within PBR boundaries [16]. At the same time, the modeling facilitates the identification of solids and tracks them within a system. Navier-stoke equations provide the principles used in CFD models [18]. Chemical engineers must solve the equations in their transient condition or steady state.
CFD modeling is one of the dominant simulation approaches. The other prominent modeling process is cold flow. The stakeholders in chemical industries like the two models because of their particular applications. The simulations indicate the rate of fuel blending and conversion rate. Likewise, the models allow observing the chemical reactions of the blended fuels [11]. The stated capabilities should prompt PBR proprietors to utilize the CFD modeling. The application of the simulations means better management of the reactants. Also, owners succeed in mitigating the adverse effects of pressure drop. The simulations should consist of ideas like the type of tubular structure to use [5]. The modeling should indicate whether to apply larger or smaller catalyst pellets. Another factor is the fluid characteristic. The fluid flow augments or lowers the rate of chemical reactions based on the level of friction.
As indicated in the previous paragraphs, CFD modeling contributes to solving basic mathematical equations in assisting the formulation of efficient PBRs. The simulation approach demonstrates the flow movement of liquid. At the same time, the modeling demonstrates how pressure drop affects the chemical reactions within packed beds. PBR engineers should understand the equations related to CFD models may lack assessment solutions [6]. As a result, users must rely on numerical analysis to obtain desired results. The reason for missing evaluation solutions is CFD only allows simulation of the liquid flow [18]. At the same time, the model offers equations for the volumetric flow rate and other features related to it. The productivity of CFD has made it a leading modeling tool in almost every industry. The tool assists medical researchers in accomplishing their objectives. Other areas include chemical engineering and hydrodynamics [19].
The application of CFD in hydrodynamic requires consideration of several essential factors. Engineers must identify the resistant force and the propulsion of the moving fluids. The consideration of the maneuverability of the liquid is necessary because it determines the amount of energy needed by the system [5]. The other essential element is seakeeping. CFD indicates the areas needing more security and those which are already secure. Additional factors are the design of the propeller of the hydrodynamic systems. It has to be appropriate to allow faster movement. PBRs require some considerations like hydrodynamic systems. PBR engineers should consider the size of the tubular structure and packed bed. The concern permits PBRs makers to create a tube with sufficient size [11]. It prevents the pressure drop and increasing volumetric flow rate. Simulating a suitable PBR system ensures energy saving by overreliance on gravity.
Figure 4. CFD PBR simulation [5]
CFD models have both advantages and disadvantages. However, the pros are more than the cons. Therefore, PBR engineers should rely on CFD to create the best and efficient systems. The following are the pros and cons of the simulation tool [5]:
Pros
The engineers require limited time and resources to establish the PBR systems when using CFD models. The reason is the simulations indicate whatever the engineers need [10]. The items include tubular structure, packed bed, and catalysts.
CFD enables PBR makers to assess challenging issues related to the system. Therefore, CFD eliminates the need to conduct dangerous real-time experiments [5]. Engineers only need to recognize the issues through models.
CFD offers an opportunity for PBR developers to analyze the system beyond its ordinary limits. It means engineers can assess the structure of PBR further than how it should be [10]. Hence, the opportunity allows the creative advancement of PBRs.
CFD models saturate the users with endless details. The simulation highlights even a minor aspect of the system [5]. As a result, PBRs makers do not leave anything unaccounted for in the procedure.
CFD modeling adds value to the final products. The reason is the simulation allows the addition of more graphs. The graphs contribute to understanding the outcomes of the simulations [10]. Subsequently, engineers can decide to improve the current PBR system or establish another one.
CFD provides an opportunity for simulators to doubt the outcomes. All must understand it is challenging to obtain needed results in uncertain situations [11]. Therefore, users must be open-minded to create alternative models.
CFD permit users to simplify any mathematical equations. The simplification process is for enabling correct calculus [10]. Thus, the more simplification is successful, the more accurate the mathematical outcomes.
CFD users can capitalize on incomplete simulations. The advantage of the unfinished models is to expedite the description of challenging problems [11]. Examples are multiphase phenomena and turbulence.
CFD simulations can be successful even if the user has no prior training. A user tends to understand the output is factual effortlessly [10]. Subsequently, the user can apply the results in bettering the system.
Cons
CFD models have a higher likelihood of causing an unintended error. The reason is the process entails simplified flow simulations [11]. Also, simple boundaries can cause mistakes.
CFD requires limited computing values. Therefore, each cell has fewer computing values, leading to interpolation mistakes [5]. PBR engineers should endeavor to mitigate the unwanted effects of computing values.
Occasionally, computation time can be more than usual. It means users might take a significant duration before obtaining the needed models [11]. However, the situation occurs when using vast simulations.
CFD simulations might need many resources. The augmented costs tend to result from misguided consultation services [5]. Thus, PBR engineers must use experiments when CFD proves to be expensive.
MATLAB modeling is necessary for identifying and monitoring the chemical reactions within a PBR. Users rely on simulation software to assess the state of the latest design. Also, the modeling software enables the diagnosis of the issues affecting a new design and how to eradicate them. The efficiency of MATLAB is an outcome of examining a system using difficult scenarios [17]. For example, the scenario could be a satellite located in outer space. Another captivating factor concerning MATLAB is its matrix-based language. The language permits any natural expression related to computational mathematics [12]. Therefore, MATLAB processes and produces the best images of a simulation. A user needs to write script files. Likewise, users should jot down the function files. The outcome is MATLAB software performs all the operations automatically [17]. Users can test the results and continue to simulate them whenever necessary.
MATLAB has several uses and produces desired results in many applications. The tool incorporates programming, computation, and visualization techniques. As such, MATLAB allows the identification of problems and solutions expressed using simple mathematics. MATLAB uses include mathematics and computation processes [21]. Also, the tool is necessary for establishing system algorithms and simulation models. Users can rely on the programmed language to conduct data analysis. MATLAB permits system exploration and visualization whenever necessary. Therefore, the scientific community relies on the tool for simplified and complex computation procedures [17]. The use of GUI enables MATLAB developers to install applications within the tool. PBR engineers should use MATLAB because it provides an opportunity to capture the reality of a system. MATLAB is illustrated as a reliable tool because it processes the best image of reality [21]. Hence, users can recognize every area the system requires improvement or new design.
Figure 5. MATLAB simulations [21]
MATLAB is the acronym for the Matrix Laboratory, and it has advantages and disadvantages. PBR engineers should understand the pros and cons before using the tool to simulate PBRs. The understanding ensures better results because PBR makers know what to do [17]. The following are the pros and cons of MATLAB.
Advantages
MATLAB provides users with a file-oriented structure. Also, the tool consists of a command-line interface [17]. The features contribute to the productivity of MATLAB.
Users can install MATLAB in any of their Operating Systems. The users can install the tool in Macintosh, Windows, Vista, and Linux [21]. Therefore, PBR simulators should capitalize on the independence of the tool when implementing simulations.
MATLAB consists of a vast built-in library. The feature entails numerous predefined operations. Hence, the elements contribute to the easiness of working with MATLAB and saving time [17]. The predefined operations include neural networks, image processing, and control systems. Additional elements are signal processing and communication capacities [21]. PBR engineers require determining whatever toolkit they want and use it.
MATLAB does not rely on devices to provide plotting and imaging. Users can apply any gadgets they have to undertake the two stated operations [21]. Thus, the capabilities save time and resources needed to obtain specific devices during a simulation process.
MATLAB users can create GUI-related applications. Users should license GUI applications using the MAC address [21]. For the licensing to be successful, clients should be using a limited number of code scripts [21]. In this way, users can compile the applications free of p-code.
MATLAB allows language interpretations. As a result, users can recognize errors with ease [17]. At the same time, customers can fix the problems effortlessly.
MATLAB users should know they can perform matrix operations efficiently. The reason is that tool handles and manipulates mega data [21]. Subsequently, users can advance and code various algorithms over a short period.
PBR engineers should use MATLAB because of its efficiency in simulating the chemical system. Also, the PBR makers should apply the tool because it is cheap compared to others like CFD [17]. Clients should always purchase simulation tools that are productive but cheaper.
Cons
One of the setbacks when applying MATLAB is the interpreted language. A user must wait for the tool to communicate the meaning of applications. As such, users have to use much time understanding the interpretations instead of executing operations [21]. PBRs should consider using C, C++ tools if MATLAB proves to be too slow in interpreting the language.
MATLAB may be cheap, but it is expensive than other options. For example, customers can afford regular C compared to MATLAB. Also, Fortran Compiler is cheaper than MATLAB [17]. PBR engineers should make comparisons and purchase a simulation model which is affordable.
MATLAB functions better with an efficient computer. The PC must have enough memory space for MATLAB to produce better simulations [21]. Many clients might bypass MATLAB because of the costs of the needed computer system.
The windows position MATLAB on the top position. The implication is users cannot plan and implement real-time applications [17]. Therefore, PBR engineers ought to consider a tool enabling the simulation of real-time tasks.
MATLAB is never free, meaning users must obtain a license. MathWorks Inc. is the organization that provides the license to use the tool [21]. PBR engineers should contact the company and acquire the appropriate license.
Cold flow is another essential tool for the simulation of PBRs. Cold flow expedites making appropriate choices regarding the efficiency of PBRs. The typical use of cold flow is the simulation of SNCR and SCR systems [22]. The reason for the preference is cold flow allows the injection and optimization of chemicals like ammonia. Cold flow is a better modeling tool compared to the CFD simulations. One of the primary advantages of cold flow is better resource management. The tool expedites planning advanced system designs. It mitigates the need to implement post-construction alterations in chemical systems. PBR engineers should apply cold flow because it projects both internal and external elements of the chemical system [11]. Cold flow offers details on how the internal part of a packed bed should look like [22]. Also, the tool facilitates the creation of the best external features to sustain pressure and volumetric flow rate.
The use of cold flow guarantees the development of scaled models depicting intended chemical systems. The tool leaves nothing to chance because the purpose is to benefit the users to the maximum. Therefore, the models entail all the needed elements of the simulated systems. Cold flow simulations emphasize the internal structure because it plays a crucial role in completing chemical reactions [15]. For example, the models simulate properly packed bed space. It should be enough to permit the recommended volumetric flow rate with the tubular structure hosting the catalyst pellets [22]. Sufficient space means the liquid movement will be effective. Also, the flow does not interfere with the reactants and the catalysts. To be specific, adequate tubular areas prevent pressure drops. The pressure drop undermines the chemical reactions [15]. As a result, the system has to use increased amounts of energy than usual.
Flow cold modeling is specific and detailed to ensure users create productive chemical systems. The simulations include explanations of the velocity measurements. The illustration facilitates the establishment of structures allowing an appropriate speed of the elements reacting within a system. Another measurement was indicated as relating to the gases the chemical system should produce [22]. The modeling assessments provide an opportunity to design suitable structural devices. For example, PBR engineers should create appropriate turning vanes and battle plates. Other creations are curved entrances, packed beds, and reaction tubes [15]. When the PBR engineers do everything right, the system prevents an increased volumetric flow rate within the chemical system. The pressure requires sufficient levels of fluid movement for the chemical reactions to occur successfully [22]. The reacting chemicals and catalysts should be distributed in a way that limited friction occurs. Subsequently, the pressure remains constant until the chemical reactions are over.
Figure 6. Cold Flow simulations [22]
Table 1. A comparison data outcome of cold flow and CFD simulations [22]
2.5 PBR Optimization
Chemical engineers should optimize PBRs based on an understanding of how the system works. One of the lessons is PBRs are inefficient if the pressure drops. Also, the systems fail to produce desired results whenever the volumetric flow rate increases. An increase in fluid flow within a PBR lowers the rate of reactions because of friction [19]. Notably, augment liquid movement prevents efficient chemical reactions. Increased liquid flow undermines intimate interaction between the reactants and the catalysts [24]. Chemical engineers should identify methods of mitigating the increase of volumetric flow rate. Simultaneously, chemical engineering experts should eradicate pressure drops. The best approach is to determine the sizes of the catalysts. The size of the pellets should be large enough to allow liquid movement and chemical reactions [19]. The other optimization is creating sufficient tubular, circular, or rectangular packed beds.
The optimization of PBRs requires paying attention to catalysts layers. The PBRs should consist of catalyst beds with varied activities. The reactor with several catalysts’ layers should remain undivided [23]. The reason is that the shell tends to entail a single cooling circuit. Another way to optimize PBRs is by creating them with a single catalyst layer. The creators must define the roles of the catalyst beds. In such a scenario, the creators should divide the reactor shell into several zones. Each of the divisions should consist of various temperatures. PBR engineers could optimize the chemical systems using the integrated illustrated optimization measures [23]. The integration of the two means one shell zone requires doubled catalyst layer. The shell zone should have catalyst beds with specific activities. The length of the packed layers should equal the size of the shell zones.
An example of PBR optimization is the oxidation of hydrochloric acid. The chemical reaction involves the conversion of the acid into chlorine. The procedure occurs within a fixed-bed tubular reactor. The conversation processes required varied design approaches [23]. The design techniques consisted of numerous cooling sections. Also, the strategies involved graded catalyst beds and coupling of cooling and graded catalyst zones. The zone numbers differed from 1, 320, 360, 360, 380, 400, 420, 440, and 460 [23]. On the other hand, the temperature zones varied from 0, 1, 2, 3, and 4. The reactor shell split had numbers from -100, -50, 0, 50, 100, and 150 [23]. The other axis had numbers from 1, 2, 3, and 4 [23]. The table below indicates the meaning of the stated figures. It is the table depicting the elements required for the conversion of HCl into Cl2. The layers and temperature must be right to obtain the intended results.
Figure 7. The depiction of Conversion of HCl into Cl2 [23]
The outcome relied on obtaining the first objective function purposed to augment the rate of the HCl conversion. Noteworthy, optimization facilitates reaching equilibrium for the conversion to be a success. Nonetheless, the limitation of the procedure is it fails to address the change in temperature during the chemical reactions in the PBR [11]. As a result, the PBR needed the implementation of additional three objective functions. In this way, the experimenters could assess the temperature outcomes through the axial temperature gradient. Using the axial temperature gradient within the PBR indicates the temperature with minimal errors [23]. The advantage of the approach is experimenters can decrease temperature deviation. The enablers of the reduction objective are the four catalyst beds with stipulated specific activities. In the arrangement, the experimenters don’t have to split the PBR shell.
The reason for avoiding splitting the PBR shell is experimenters can accomplish a flexible system. The achievement of the stated system requires the alteration of the shell side temperature. The modification allows progressive application of the PBR [23]. The illustrations on the optimization of the PBRs lay a foundation for future research to recognize the unpredictable behavior of PBRs. As an illustration, it is difficult to predict the outcomes related to the depletion of catalyst activity. Thus, chemical stakeholders may not understand how to handle the chemical changes occurring in each zone. PBR engineers should determine temperature profile as another challenging element in chemical reactions [11]. However, engineers can mitigate the issue through control strategies. One of the mitigation measures ought to consider the size of the tubular packed bed [23]. It should be large enough to prevent increased volumetric flow rate and pressure drop.
2.6 Methane combustion reaction
Natural gas (which primarily consists of methane) is a desirable form of energy due to its availability and intense burning temperatures per molecule of carbon dioxide produced. Nevertheless, the emissions produced by traditional flame combustion (mostly NOx) have negative consequences for the environment and human and animal health. Catalytic natural gas burning seems to be among the greatest potential solution to flammable combustion in terms of pragmatic and safe utilization of fossil energy. The inclusion of catalysts allows for enhanced methane combustion at considerably low temperatures minimizing the generation of contaminants.
2.7 Mechanisms and kinetic study of catalytic methane combustion (CMC)
With an enhanced electron threshold, reduced charge tolerance, and a high Carbon-Hydrogen bond power, methane is perhaps the most resilient alkane chemical relative to other higher alkanes, making it significantly challenging to activate with weak conditions. Traditional methane flame combustion frequently necessitates a relatively high temperature (>1400oC). As a result, mechanical and kinetic investigations are critical for influencing catalytic process design refinement to have effective combustion under reduced temperatures. In oxygen, the process is said to be zero-order, but in methane, it is first-order. The table below summarizes the important kinetics parameters.
Table 2. Kinetics parameters of the catalytic methane combustion (CMC)
The Langmuir-Hinshelwood, the Eley-Rideal, and the Mars-van Krevelen mechanisms are three different types of mechanisms and kinetics frameworks for CMC presented in the literature. The underlying reaction is the rate-determination phase for the first two processes—the electromagnetic characteristics of transitional particles on the catalytic surface influence the reaction rate. On the other hand, the latter mechanism considers the CMC to be an interface reaction, with the rate of the reaction primarily associated with the crystalline oxygen vacancies.
The gas-stage reaction mixture particles are deposited onto the catalytic platform, and the reaction occurs through mass transfer in the Langmuir-Hinshelwood mechanism. To reach equilibrium, the generated compounds are removed from the surface of the catalyst. The Langmuir-Hinshelwood mechanism was well-fitted by the kinetic parameters of CMC Trimm and Lam over Pt/Al2O3 catalysts, suggesting that both deposited methane and oxygen were a part of the process. The research indicated that the increased temperatures were primarily due to a shift in the reaction pathway from oxygen to methanol adsorption. Through DRIFT (diffuse reflectance infrared spectroscopy), Jodowski et al. discovered that methanol’s adsorption on Co-Pd/-Al2O3 catalysts only occurred with preabsorbed oxygen on the surfaces (in oxygen-robust circumstances), implying that the Langmuir-Hinshelwood process ought to be avoided.
According to the Eley-Rideal mechanism, just one gaseous phase reactant must be deposited onto the catalytic surface. The deposited chemical then combines with the remaining reactant in the gaseous state. The generated byproducts are then removed from the surface of the catalyst. According to Seimanides and Stoukides, this method may accurately estimate the CMC through Pd/ZrO2 catalysts in the band of 450oC to 600oC. It’s very plausible that it’s the only deposited molecular oxygen in the methane gas that reacts.
A great number of experimental studies on CMC validate the Mars-van Krevelen mechanism. Unlike the previous two methods, it implies that the adsorptive layer is a key player. First, one of the reactant molecules in the gaseous phase produces a thin layer of a covalent bond with the surface of catalysts. The residual gaseous stage can further combine with the covalently linked reactant, creating a void after decomposing the byproducts. Since crystalline and adsorbed oxygen radicals are present on the catalytic surface, distinguishing between Mars-van Krevelen and Eley-Rideal processes is difficult. Applying the in-situ technique of the isotopically marked process, Pfeffer et al. demonstrated that one 16O particle (lattice stage) in PdO was confined to two Pd particles. It was discovered that perhaps the 16O atom in PdO, instead of the deposited 18O atom in the gaseous state, was involved in oxidizing methane. This finding is consistent with Au-Yeung et al.’s findings.
Furthermore, change in Pd’s oxidation potential plays a key part during the process, implying that the Mars-van Krevelen mechanism is better suited for catalytic methane combustion. As a result, given the complexity of the mechanisms and their reliance on experimental parameters and catalysis, there has yet to be a consensus mechanism to detail the CMC adequately. The Langmuir-Hinshelwood and Eley-Rideal mechanisms appear to be less universally acknowledged than the Mars-van Krevelen mechanism.
2.8 Effect of operational conditions on CMC
Temperature effects- As per the Arrhenius equation, the fundamental rate of CMC reaction is associated with temperatures and activation energy. The reaction rate increases dramatically as the reaction temperature rises. The figure below illustrates the various rates of reactions and their corresponding temperature levels.
Figure 8. Correlation between the temperature and reaction rate
The impact of the velocity of space and the duration of residence- Methane combustion, in theory, is inversely proportional to the space velocity, as seen below. It was discovered that as the space velocity of the reactant molecules decreases, the methane conversion rises. An identical pattern has been observed with other catalysts.
Figure 9. Inverse proportionality between space velocity/residence time and conversion
Effect of operating pressure- As pressure rises, the methane conversion diminishes. Furthermore, the effect of operating pressure has been said to vary with temperatures. At lower temperatures, a rise in pressure causes a reduction in methane conversions and a reduction in combustion efficiency.
2.9 COMSOL software
The COMSOL software is used in the development of mathematical modelling which helps drive the new breakthroughs in engineering and physics. Therefore, the software is used across all the engineering fields, scientific research, manufacturing and modelling of systems of Multiphysics [34]. Therefore, aspects such as understanding, prediction, innovation and optimization of processes and designs are provided by the software. Simulation applications can also be made based on the existing models, which may be shared outside or within the simulation world [34]. Modelling is an important aspect in relation to experiments for the optimization of processes. It is a quick, efficient and accurate method of determining specific parameters compared to experimental methods and prototype testing. A scientists can gain better understanding of any process and design through the development of the models that have been validated experimentally. It is possible for one to study the process or set-up in a convenient manner compared to the laboratory. Therefore, Multiphysics is essential as far as the accurate modelling of processes and designs is concerned.
Any COMSOL Multiphysics user is not prone to any restriction of the software because he has the full control of the model’s features. There interface provides room for creativity as different physic and chemistry phenomena can be coupled together [35]. Therefore, the accurate models of the software put into consideration the different operating conditions of as system and any physical and chemical effects that may he experienced. This is why it is possible to understand, design and operate the different systems under any realistic conditions [35]. The setting up of this simulation is objective such that is shall be used by the chemical engineering students as an online confirmation with the laboratory experiments. It also contains the model manager that plays a pivotal role in simplifying and streamlining simulation and modeling work through the provision of data management for simulation [36]. The users of the software have the option of collaborating and organizing their models centrally with the version control that has the ability of updating models and tracking changes. It also contains options for the efficient storage of applications and models together with their revisions and data. The adoption of the software to carry out the simulation is informed by its features described above.
2.9 Problems in designing PBRs
During the design of the reactors, it is important for the design engineers to include mass transfer that stands in for the transport of the given species is in the reactor [37]. It is also important for them to consider essential aspects, including the chemical reactions that take place and heat transfer, together with their coefficients. An understanding of the optimization process as far as heat transfer is concerned is critical for the purpose of reducing the operation cost of the PBR [38]. The transfer coefficients should be studied and should encompass both the PBR materials and the species under transfer. The catalysts that are used in the reactor need to be considered to achieve success in the modeling process of the reactors. There is a possibility of the catalysts getting modeled as a porous one or a non-porous one. The porous structure modeling presents particle transport having different magnitude orders. This aspect presents a challenge when analyzing the energy and mass transport aspects in the system.
It is worth noting that there is heavy reliance on the pressure drop that takes place across the length of the reactor when designing the reactors. It has been scientifically proven that the pressure drop may be caused by the use of catalysts particles that are large, which presents a reduced intraparticle diffusion [39]. The end result of the process is reducing the rate of progression of the reactions. There arises a challenge regarding the identification of a particle size that has the capability of limiting any drops in pressures. The particle size needs to also be small enough to ensure that there is an increased rate of reaction progression. The typical diameter of such a particle is approximately 1mm. A microporous bed structure is used to define the space that exists between the particles in the system. However, a microstructure is used to describe the pores that exist inside the individual catalysts.
The design problems discussed above give rise to various design options as far as the reactors are concerned. Different factors may undergo variations to study how the designed reactor is going to work by incorporating the process kinetics into perspective [40]. For example, an engineer would want to design a PBR that is working efficiently and effectively and giving out the desired output. The desired product can only be achieved through the consideration of the specific kinematics that has taken place, the volume measurements, pressure drops, among other parameters. Other variations may include the changes in temperatures, the concentration of the reactants that are being introduced into the system, the aspects that affect the reaction rate of the system, and the specific products that are yielded from some conversions [41]. An add-on on the design problems and the variations involved is that different packaging shapes which are available in the market may also be considered. The fact that the designing and packaging shapes have on the reaction also needs to be put under consideration. There are factors that may present a significant change based on the application of the PBR. An example is the diameter of the catalysts, which represents the ratio between the surface area that is in contact with the material’s unit volume. Other factors include the structural strength of the system, the transport properties, the macroporous volume in cases of porous COSMOL material, costs of manufacturing, among others [41].
3.0 Kinetics expressions in PBR
Under the reactors, there are different reactions and conversions that take place based on the different conditions induced either from the outside or inside the reactor. For example, there are some reactions that take place once a certain temperature level is reached or exceeded. Any temperature levels below that mean that the reactions cannot occur. Other reactions take place under different conditions of pressure. They are also dependent on the kind of chemicals that are reacting. Science through different experiments and software has made it simple for researchers to model the different kinetic reactions under different circumstances. For example, in the chemical reactions engineering field, there is a high relevance attached to the simulations for the investigation and optimization of any reaction system of process. Modeling of the reactions is useful to the engineers so that they can get a virtual understanding of the chemistry going on in the PBR to get the optimum size of the reactor. It is also important to understand the kind of interactions that take place. During the design and construction of the PBR, it is important to understand the elements in the reactor, their products, and the possible processes that take place. A good example is when the PBR reactor has an intended function of reducing the noxious chemicals that are always released into the environment by other systems. The perfect example of such a gas is nitrogen oxide. There can be the introduction of a chemical to ensure that the less toxic form of the gas is released. It is important for the design engineer to know that ammonia may be needed in reducing the levels of nitrogen oxide. However, the amount should be proportional in the sense that a lot of ammonia is not wasted in the atmosphere, thereby using unpleasant smells and affecting human health. Chemistry suggests that ammonia can also get consumed through oxidation. This is a reaction that is incomplete parallelism with the no reduction reaction [42]. The following reactions depict the case highlighted above:
4NH3+4NO+O2 4N2+6H20
This is a case of the no reduction equation that is carried out by ammonia. The following equation shows the parallel oxidation using the same chemical.
4NH3+3O2 2N2+6H20
Temperature is the main determinant of the reaction rates of the equations presented above. In this case, the amount of ammonia to be included in the system, the system’s shape, and other parameters are yet to be known. To get a clear amount of ammonia to be used, it is important for scientists to carry out a study on the reaction kinetics and rates, which are in close association with ammonia. The laws that relate to reaction rates are hypothetically based, meaning that they are justified by specific assumptions regarding the mechanisms of reactions that get support from a number of experiments carried out in controlled conditions. They are known as control experiments. In the event that a designer comes to a conclusion that the reaction ratio between NH3 and NO is 1:1, he needs to note that there is the consumption of ammonia in the subsequent reaction implying that the reaction may increase [42]. This is the point where the COSMOL Multiphysics software comes in to help analyze the ratios and give the exact amount of ammonia that needs to be used in the reaction. It gives room for carrying out several studies so that the optimal ratio can be determined and used in the PBR. However, it is good to keep in mind that temperature influences the rates of the conversions above, and it changes across the different sections of the reactor. The case study above is not only tied to ammonia and nitrogen oxide but to other materials and catalysts that may be applied in the PBR reactors.
3.1 How COMSOL design works on different media
There is a difference between the way COMSOL design works for porous catalysts and the way it works for heterogeneous and non-porous catalysts. In order to understand how it works in the porous media, the diagram below can be considered for the illustration process:
From the diagram above, it can be seen that species B gets injected into the channel and flows along the shown channel. At some point, specimen A gets introduced. The brown patch shows a porous catalyst that forces the introduced species is to go through an irreversible reaction that is not reversible. The resulting species is represented by C. The equation shown in the figure has several parameters where CB and CA represent the concentration of the species B and A, respectively. The reaction rate is represented by k, which presents the Arrhenius equation. Temperature is represented by T. The heterogeneous catalysis is represented in his case, where the two species get injected into the tube. They undergo partial mixing before going through the catalyst. Navier-Stokes equations may be used to explain the different flow properties in the system, which call for specific inputs, including dynamic viscosity density, absolute temperature, and flow velocity for every species [43]. Mass transport in such media occurs through convection and diffusion. Another applicable equation is the Brinkman equation which accounts for the permeability and porosity in porous media. COMSOL Multiphysics produces 3D results for species concentration, pressure drop, and velocity. Therefore, different steps may be used in modeling such kinds of reactions. The steps may be based on the intended outputs, the inputs, and the expected chemical reactions that may take place in the system. COMSOL is, therefore, a good software that helps model different scenarios in the PBR to understand some of the effects that the parameters present and the expected outputs when their values are either increased or reduced. Therefore, the combination of the PBR testing with COSMOL Multiphysics is a great step in the establishment of the relationship amongst the stated factors.
3.2 Summation
The literature review indicates chemical industries are crucial in solving global issues. The businesses contribute to the production of pharmaceutical products for the health and other sectors. Also, the chemical industries facilitate waste management and water purification. In several decades in the future, the global population will have augmented significantly [1]. An increase in human beings is good news, but it has inherent economic and social issues. For instance, a ballooning population could overwhelm health care facilities. At the same time, human beings could demand pharmaceutical products in large numbers. The other need relates to the collection and elimination of waste in industries and residential. Apart from that, human beings want clean water for drinking and other home and industry activities. PBR engineers can accomplish their objectives through better design of chemical facilities [8]. The design should involve optimization of the PBRs to meet the global product demands.
Optimization of PBR design means chemical engineers must consider the effects of pressure drop. It lowers the rate of chemical reactions and the speed of reactant conversion [18]. Also, the stakeholders must identify the issues related to fluid movement within PBRs. It is imperative to mitigate liquid flow because an increased volumetric flow rate undermines the speed of chemical reactions [4]. Too much liquid leads to friction between reactants, catalysts elements, and the wall of the packed reactors. The implication is a slow rate of chemical reactions, leading to significant consumption of energy. An increased rate of consumption of electricity is no in line with sustainable development [1]. The design should be right to contribute to the preservation of natural resources as energy. Also, proper designs allow chemical reactions to occur without hindrances. However, it is challenging to design better models without relevant simulations and optimization methods.
Chemical engineers should use CFD to determine the rate of fluid movement. Also, the CFD model should assist in determining the effects the liquid flow has on the operations of PBRS [18]. CFD is an essential tool because it enables the depiction of PBRs using mathematical equations and images. MATLAB is another modeling approach chemical engineers should use. It consists of interpreted languages, enabling the easier simulation of PBRs. Also, the tool has mathematical and imaging capabilities [21]. Users rely on the capacities to simulate the situation of chemical systems. Subsequently, PBR engineers can eliminate technical issues related to the functions of the systems. Cold Flow is more of the simulation methods. It relies on mathematics and imaging to indicate the status of a chemical system [22]. Cold flow demonstrates the areas that engineers should improve. Also, the simulation indicates where PBR creators should do replacements.
CHAPTER THREE
RESEARCH OBJECTIVE
The primary goal of the research is to highlight the essentiality of the chemical industries. All should understand, without the chemical sector, human beings would be struggling with diseases. Also, the struggle would include the lack of clean water. Also, the masses would not drive their cars and cook in their homes. The reason is that chemical industries produce pharmaceutical products, clean water, gas, and burning fuel [1]. The vitality of the industry should influence stakeholders to improve on it. Chemical engineers should focus on improving PBRs. The facilities allow the efficient production of chemicals used in various spheres of life. However, PBRs fail to produce desired results because of some limitations. The facilities could have issues with the design. To be specific, PBRs could have limited space, leading to the increase of volumetric flow rate. Simultaneously, PBRs could allow the prevalent pressure to drop, causing the system to use more energy than usual [2]. Stakeholders should mitigate the stated problems via design, simulation, and optimization.
The research objective for this project is to determine how the pressure drop and fluid flow characteristics affect the PBRs’ working efficiency. The project focuses on utilizing better modeling methods to formulate the best PBRs. The strategy is reasonable. It leads to the optimization of PBRs. Also, it enables saving energy resources [3]. Subsequently, stakeholders receive favorable returns for their investments and continue to invest more in the sector.
CHAPTER FOUR
MATERIALS AND METHODS
4.1 Introduction of the COMSOL use
Catalytic reactors are widely used in industrial applications, and packed bed reactors are among the most frequent types. As a result, dealing with a differential reaction chamber to oxidize methane is among the experiments performed in the module operations lab course. This paper explains what packed bed reactors are and how they are operated, the reaction in the laboratory, and some context on the COMSOL Multiphysics software program. Packed bed reactors are the most popular reactors used in the manufacturing of large industrial chemicals. They are mostly employed in polymerization, combustion, and sewage treatment for gas-phase processes. A packed bed reactor consists of a vessel with one or more tubes with packed catalytic particles in a static, non-movable bed. In principle, the gas reactant stream goes through these compact pipes, reacts with the catalysts, and then exits on the opposite end as the process stream. In large-scale production, packed bed reactors are a cost-effective option [27]. This fact owes that, due to long catalytic lifespan, they may function almost continuously, resulting in lower yearly and closure expenses.
COMSOL Multiphysics is a software suite created in 1997 by Germund Dahlquist’s postgraduates in Stockholm, Sweden. The application was originally known as FEMLAB since it analyzes and solves complicated problems using the numerical simulation approach. The software includes a collection of modules for various applications. For the applications outlined, every package includes modeling techniques and equations. Several modules’ modeling techniques can be combined to describe complex structures and procedures accurately. Fluid, heat, mass flow modelling, and chemical processes are all available in the Chemical Engineering Module [28]. Both transient and steady-state assessments can be performed with these techniques. Batch reactors, isolators and catalytic converters, purification, heat exchangers, and packed bed reactors are among the systems that the module may model. Models can be made in one, two, or three dimensions; they use partial differential equations to link the physics to every component. Several models are frequently required to simulate all features of a system. Modeling reactors, for example, may necessitate coupling fluid flow structure.
The first step in generating a COMSOL simulation is to generate the geometries that will be analyzed. It can be one-dimensional, two-dimensional, or three-dimensional geometries [29]. The numerous modeling tools offered in COMSOL can also be used to create irregular geometry. The meshing of the model is the next phase. Meshing entails dividing the geometries into subcategories that are analyzed separately before being put together to provide a holistic overview of the processes at hand. At and around boundaries, it’s usually best to select a small mesh size because that’s where the most abnormalities will arise. After mesh generation, the model’s mechanics can be described within the subdomains and at every one of the model’s borders [30]. After that, the model can be constructed, and post-processing can take place. Manipulation of the algorithm to generate charts for relevant information and fluxes is known as post-processing. Numerical simulations can then be conducted to improve the model.
4.2 Equipment
The figure below depicts the packed bed catalytic reactor and gaseous chromatograph conceptually. The mechanism can accommodate the movement of air, nitrogen, and methane. The gases might either proceed through a diversion line or via reactors by altering valves after passing through the dehumidifier. To evaluate the gas chromatograph, the gas goes through the circumvent line without reacting. Pressure gauges are used to configure the inflow species flow velocity manually. Both the reactors and the circumvent gases pass through the chromatographic column, which displays the quantities of methanol, oxygen, carbon dioxide, and nitrogen.
Figure 10. Mechanism of the packed bed reactor and gas chromatograph [27]
The reactor is a 0.340-inch-diameter cylinder with a 3-inch segment of 0.5 percent Pd/alumina catalytic weighing 5.26 grams. The catalytic granules are 3.2mm wide and tubular. A piece of glass packing particles precedes the catalyst section, which equally distributes the intake flow across the catalyst’s cross-section. The figure below shows a cross-sectional layout of the cylindrical reactor.
Figure 11. Cross-sectional layout of the cylindrical reactor [28]
The catalytic reactor is used to identify the sequence of methane reactions and the frequency of methanol reactions in the air. The reaction order in methanol is found by adjusting the rate of flow of methane while keeping the overall rate of flow of gases into the reactor fixed and observing the transformation of methane to CO2. At temperatures of 227°C, the flow rate is maintained at 300 mL/min (STP). The oxygen-to-methane ratio is modified.
4.3 Experiment
The reaction sequence concerning methane is calculated using results from five testing sessions. To successfully model the reaction, all test runs’ units of measurement have to be consistent with COMSOL. As a result, all quantities are translated from ml to m³, and all flow rates are translated from minutes to seconds. The pressure is estimated to be 101,325 Pa, and the temperatures are reported in Kelvin values. Since there are no pressure indicators in the batch reactor, this hypothesis is not hundred percent true, but it is strong enough to provide reliable estimations. With air and methane, the input volume flow speeds are initially set by moving the hydrometer to the stream corresponding to the intended flow rate. The total concentration is determined by rearranging the ideal gas law. COMSOL Multiphysics is used to generate models of the reactors employing data collected from the actual reactor.
Several aspects of the process must first be determined to simulate the reactor properly in COMSOL. Experiments are conducted to determine species’ order, activation energy, pre-exponential component, and inlet/outlet levels. The speed of the input gas is calculated using the volume flow rate and the reactor’s cross-sectional area. Nitrogen serves as a gaseous conductor in this investigation, with a consistent, predominant concentration compared to the other reactant molecules. Furthermore, each mole of gas reacted result in the production of a mole of gas. The speed is expected to be fixed because of these two requirements.
Several stages of the simulation analysis are simplified with the COMSOL Multiphysics simulation platform, including defining your geometries, setting physics, meshing, solving, and data preprocessing the findings. Alternatively, you can transform your simulation into a program that everyone can use, independent of modeling background, by integrating a customized graphical user interface. These apps can be distributed over the internet via COMSOL Servers or compiled to run independently using COMSOL Compiler. Using a specified simulation interface for various applications spanning flow and heat transfer to engineering mechanics and electromagnetism analysis speeds up system setup.
The dependent parameters’ basic qualities, source conditions, and model parameters can be random functions. Several typical problem categories are solved using preset Multiphysics frameworks. You can use the Multiphysics menu to select multiple physics and define the interconnections yourself. You can also create your partial differential equations (PDEs) and combine them with other models and concepts to create your model.
4.4 Safety
Equipment must have adequate protection because it facilitates the gathering, analysis, and presentation of research findings. Secure locations should be the storage for all used equipment. For example, computers, flash disks, and memory cards should be in a securely locked room [31]. At the same time, it is rational to copy the information in more other devices like a smartphone to guarantee safety and availability. The distribution of similar data to different devices ensures using available data if the other gets lost. Adversaries can access and manipulate information stored in devices [31]. At the same time, the equipment can malfunction, leading to the loss of data. The best way to prevent search instances is to secure information on various devices. Modern researchers should capitalize on cloud resources [32]. Cloud computing expedites the storage and distribution of data from a secure server. The setup does not allow much data storage within the hardware.
Materials must be secure to provide reliable and secure research data. However, the security of the materials is rather complex. A researcher must identify credible and reliable sources of information. Researchers must determine whether the sites for needed data are secure. For instance, scholars should investigate the background of the sites and authors [32]. Such assessments confirm the validity and safety of the gathered data. In the era of augmented adversaries’ activities, researchers need to be careful when accessing online resources. Some online sources of information are not as secure as researchers may assume [31]. Therefore, investigators should ascertain whether a potential source of data is safe or not. Scholars can do so by installing security software in devices used in conducting the research [32]. The software notifies an investigator whenever an online site or material has corrupted applications.
All the supplies must have sufficient protection for the research to end successfully and timely. For example, it is wise to use electronic money systems to transact whenever necessary. The strategy secures cash and allows the accomplishment of objectives. The equipment must be functional and in secure locations away from any form of threat [32]. At the same time, resources should be in safer locations as well. It is the responsibility of researchers to ensure all the needed items and resources expedite achieving the goals. Therefore, investigators need to study how to access and secure their supplies at all the time. Research can be expensive and time-consuming [31]. As such, the security of all supplies should be a priority. Investigators should collaborate with third parties like IT gurus. The collaboration is for gathering details on how to secure information [32]. Also, the cooperation enlightens on how to distribute data safely among the audience.
Computer ergonomics will also be considered in any computational project for safety issue. Computer ergonomics addresses ways to optimize your computer workstation to reduce the specific risks of computer vision syndrome, neck and back pain, carpal tunnel syndrome and other disorders affecting the muscles, spine, and joints [33]. The physical injury and eye strain from prolonged computer use may happen for students. Thus, some tips should be given here for safety consideration. First, the student should have a chair that supports for his/her lower back. Second, he/she needs to adjust the position of the computer screen to prevent outside lighting. Third, the computer screen should be positioned right directly to the student’s face. Lastly, the wrist and hand should form a 90-degree angle with the arm.
CHAPTER 5
RESULTS AND DISCUSSION
The expected results from the virtual experiment above is that there shall be a reduction in pressure as the length of the reactor increases. This shall force the volumetric flow to increase. The concentration of the reactant shall reduce in combination with the reduction because of conversion. This in the end shall lower the reaction rate. These results should be in resonance with the Ergun equation that describes the PBR pressure drops, as described in the introductory section of this paper. The results are shown in the diagram below.
From the diagram above, it can be seen that the pressure drops with an increased reactor length. The results above are simulated with catalytic granules that are 3.2mm in diameter. The large diameter of the particles is informed by the large diameter of the PBR. The large particles increase the breakdown voltage which causes a partial system discharge, which reduce the overall PBR performance.
It is worth noting that for the reactions that are in the liquid phase, any small changes in the parameters of pressure have minimal or no impact on the concentration of the species in the PBR. Therefore, there is no effect on rates of reaction. However, for the reactions that have gas-phase conversions, pressure affects the concentration of the species. Reduced pressure levels mean that there is reduced concentration. The end result is a reduction in the rates of reaction. In this case, the reduction in pressure with length can be explained in different dimensions. The first one is that there is a reduced concentration of the species in the reactor. After the species passes through the porous catalytic bed, there are reactions that take place, which give out another product. Reduced pressure means that the product will take a long to be formed because of reduced reaction rates. Products get formed at a faster rate when the reaction rate is high. However, reduced rates mean that it shall take time for the reactions to be completed. The Ergun equation is the perfect one in explaining the scenario above. At the 0-meter reactor length, where the length of the reactor is 4m, the pressure is 12 bars. At around 5 m, the pressure drops to approximately 11 bars. At 4 m, the pressure has had a maximum drop of up to 9 bars. Looking at the reactor with the 21m length, the pressure at 0m is 12 bars. At around 0m, the pressure drops to approximately 11 bars. When the reactant reaches 20m in the reactor, the pressure drops up to 9 bars. The graphical representation above is a clear indication of the expected results from the virtual experiment. Therefore, during the virtual experiment, there is an expectation that pressure drop shall be experienced.
CHAPTER 6
CONCLUSION
This research is essential in presenting the relationship between the length of the PBR and pressure. The aspects of catalytic granules’ diameter and other factors that affect the reaction rates are also analyzed. It is a virtual experiment that aims at helping the chemical engineering students when they perform their experiments in the laboratory. Recommendations are going to be made regarding the results obtained so that specific improvements can be made at the industrial level. The simulation of the virtual experiment can be actualized in the laboratory before getting actualized at the industrial level. Therefore, the research intends to add more knowledge to the existing knowledge body. Most researchers have come up with theories that explain the phenomenon regarding PBRs. The pressure drop aspect has been explained by different scientists, which necessitated the development of some situations. An example is the Ergun equation, which is used to explain the relationship amongst the various parameters in the equation. Other equations have also been developed to supplement the equation. This study shall incorporate the equations and apply them in the virtual experiment to explain the scenarios that take place, especially the expected results highlighted in the section above. Other factors that come into play apart from the pressure drops in the PBR are important because they have an influence on the reaction rates, which affect the performance of the reactor. Therefore, the virtual experiment aims to have extensive coverage as far as pressure drops and other factors in the PBR are concerned.
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