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  • Q1:3. Flue gas stream of 4xy m3/s (x and y are the last two digits of your Sheridan ID number; for example, if the last two digits of your ID number are 78, your gas flow rate is 478 m3/s) is to be treated by an electrostatic precipitator to remove fly ash. a. What plate area is required to remove 1.0 um particles with 80% efficiency if the ash drift velocity is w = 2.57x105 dp? (3 marks) b. Calculate also plate area required to achieve 85%, 90%, and 95 % removal efficiencies of the same particles. (3 marks) c. Calculate % of the plate area increase required to increase removal efficiency from 80% to 85%. Also, calculate % of the plate area increase required to increase removal efficiency from 85% to 90% and from 90% to 95%. Discuss your results. (3 marks) d. Draw a graph of plate area vs removal efficiency. (2 marks)See Answer
  • Q2:7. (Denbigh, ch. 9) Consider a two-component "regular solution:" RT log 71 = b(p)x2, RT log 72 = b(p)x2, (a) Verify that the activity coefficients satisfy the Gibbs-Duhem equation. (b) Show that Asmix is the same as for an ideal solution, and show that Ahmix = b(p)x1x2, unlike an ideal solution which has Ahmix = 0. b/RT=4 ₡1 Apmix 02 0.4 0.6 0.8 O RT b/RT=2 0.5 b/RT=0 -1.0- b/RT =- 2 02 0.4 0.6 0.8 -0.05- locally unstable b/RT=2.5 Aplmix RT globally unstable -0.15 -0.20 b/RT=2 -0.25 -0.30- b/RT=1.5 Figure 2: Molar Gibb's free energy of mixing versus composition for different values of B = b/RT. Wide range of B = b/RT (top graph); narrower range of B = b/RT closer to stability transition (bottom graph). -0.10 T2 500 480 460 440 T 420 400 Tı 380 360 0.0 0.2 0.4 0.6 0.8 1.0 21 Figure 3: Binary phase diagram showing miscible liquid phase and immiscible solid phase. (c) Calculate the molar Gibbs free energy of mixing Aftmix. A graph Aftmix is provided in figure 2. Show that the boundary of the two-phase region for T, P fixed is 2Bx1(1-21)=1, where B = b/RT. Note that a single phase exists for 2Bx1(1 - 21) < 1; two phases coexist for 2Bx1(1 -21) > 1. 8. (Denbigh ch. 9) Consider a binary mixture that has an azeotrope. Show that T is an extremum (minimum or maximum) under constant pressure conditions and P is an extremum under constant temperature conditions at the azeotrope 21 = y1 (equal vapor and liquid phase compositions). 9. (Denbigh ch. 9) Consider two metals that form an ideal solution (i.e. are completely miscible) in the liquid phase but are completely immiscible in the solid phase, as shown in figure 3. The melting points of the pure phases are T1 and T2; the heats of fusion, Ah1 and Ah2, are constant. (a) Prove that this system forms a minimum melting temperature eutectic point as seen in Figure 2. To do this, show that the slope dT/dx of the solid-liquid phase boundary is negative for small x and and the slope of the phase boundary is positive for large x. (b) For the special case Ah1 = Ah2 = Ah and T1 = T2 =To, show that the eutectic composition and temperature are given by x = 1 2' T = Ah + RTo log 2 AhToSee Answer
  • Q3:CHEE 205 In Class Challenge 1 CHEE 205 – In Class Challenge 8: Solving Systems of Equations in MATLAB Introduction Engineers frequently encounter systems of linear equations in their work. For example, in chemical and environmental engineering, these systems can represent mass balances around process units or interactions between pollutants in an environmental system. The ability to solve these systems is therefore crucial. In this challenge, we're going to solve a system of equations related to a process in a chemical plant. We have a system of reactors where the concentrations and the flow rates of the species involved need to be balanced at a steady state. Objective Our goal for this in-class challenge is to: Solve a system of linear equations that represent mass balances around a set of mixing tanks. The Challenge Consider a system where: Reactor 1 receives an inflow with a concentration of A at 4 M, and it sends out an outflow at a rate of x1 L/min. Reactor 2 receives the x1 L/min flow from Reactor 1 and also has an inflow at a rate of 3 L/min with a concentration of A at 2 M. Reactor 2 sends out an outflow at a rate of x2 L/min. Reactor 3 receives the x2 L/min flow from Reactor 2 and drains all of its inflow. Write and solve the mass balance for chemical A in each reactor. For example, for Reactor 1, the mass balance can be written as: 4 - x1*4 = 0 where x1 is the flow rate from Reactor 1 to Reactor 2. Similar equations can be written for Reactor 2 and 3. Write a script in MATLAB to solve this system of equations. Starter Code % Define the system matrix A and the right-hand side vector B % Solve the system % Display the results CHEE 205 – In Class Challenge 8: Solving Systems of Equations in MATLAB [Name] [Date] Submit Your Solution in the Below Mentioned Format Our goal for this in-class challenge is to: Solve a system of linear equations that represent mass balances around a set of mixing tanks. In Class Challenge Solution Format Code Output [Insert your code output here] MatLab Code [Copy and paste your code here] CHEE 205 In Class Challenge Introduction to MatLab and PythonSee Answer
  • Q4:Problem (10 Marks: Given the following partial differential equation below: ou ou = you, 22u dx 0<x<1, and t > 0 1. Write down the Crank-Nicolson finite difference scheme. 2. What order approximation is this in time and in space? 3. Discuss the stability of this finite difference scheme using the von Neumann stability criterion. 4. Use the Crank-Nicolson finite difference scheme with Ax =0.25, At = 0.0625 to solve numerically the given problem for two steps in t-direction, where u(x,0) =sin(xx), 0<x<1 u(0,t)=u(1,t)=0, t>0See Answer
  • Q5: Assignment Outline: Active Cell Balancing Circuits in MATLAB Simulink Objective: To design and simulate various models of active cell balancing circuits using MATLAB Simulink, and to analyze their performance and efficiency. Introduction: 1. Overview of Cell Balancing: О Importance of cell balancing in battery packs. Differences between passive and active balancing. Benefits of active balancing: enhanced efficiency, extended battery life, and improved performance. 2. Types of Active Cell Balancing: О О о ○ Switched capacitor balancing. Inductor-based balancing. Transformer-based balancing. Resonant balancing. Assignment: Modeling Active Cell Balancing Circuits Using MATLAB Simulink Objective: To design, simulate, and analyze various models of active cell balancing circuits using MATLAB Simulink. The goal is to understand the impact of different balancing techniques on battery performance and efficiency. Introduction: Provide a brief overview of cell balancing, emphasizing its importance in battery management systems (BMS). Explain the differences between passive and active cell balancing, highlighting the advantages of active balancing methods. Tasks: 1. Literature Review: ○ Research different active cell balancing techniques. О Summarize the working principles, advantages, and disadvantages of each technique. 2. Modeling in MATLAB Simulink: о Task 1: Switched Capacitor Balancing о Design a switched capacitor cell balancing circuit. Simulate the circuit for a battery pack with 4 cells. Analyze the results and observe how the balancing affects the cell voltages. Task 2: Inductor-Based Balancing Design an inductor-based cell balancing circuit. Simulate the circuit for the same 4-cell battery pack. Compare the performance with the switched capacitor balancing. О О Task 3: Transformer-Based Balancing ◉ Design a transformer-based cell balancing circuit. Simulate and analyze its performance. Task 4: Resonant Balancing Design a resonant balancing circuit. Simulate and analyze its performance. 3. Analysis and Comparison: о Compare the efficiency, balancing speed, and complexity of the different circuits. ○ Discuss the trade-offs involved in each balancing method. о Provide graphical results and observations from the simulations. 4. Conclusion: ○ Summarize your findings. ○ Discuss which balancing method you find most effective and why. О Propose potential improvements for each balancing technique. Deliverables: 1. A detailed report including: ○ Introduction to cell balancing. О Literature review on active balancing techniques. О О O Explanation of the modeling process in MATLAB Simulink. Analysis and comparison of the simulation results. Conclusion and discussion. 2. MATLAB Simulink models for each balancing technique. 3. Simulation results (graphs, data tables, etc.). Submission Guidelines: • Submit the report in PDF format. Include the MATLAB Simulink model files in a zipped folder. • Ensure that the report is well-structured, with clear sections and sub-sections. Assessment Criteria: • Understanding of active cell balancing techniques. Accuracy and functionality of MATLAB Simulink models. Depth of analysis and comparison. Clarity and coherence of the report. Quality of graphical results and observations.See Answer
  • Q6:2. Consider the following reaction scheme reported by Stull et al. (1969): CH₂Cl(g) + H₂O(g) → CH₂OH() + HCl() 2CH₂OH(g) → (CH₂)₂0(g) + H₂O(g) In the first reaction, methyl chloride reacts with water to form methanol and hydrochloric acid. In the second reaction methanol decomposes via a condensation reaction to form dimethyl ether. At 600 K, the equilibrium constants for the reactions are 0.00154 and 10.6 respectively. (a) (b) If the steam ratio is set to 1, X'is the moles of HCl formed, and Yis the moles of dimethyl ether formed; show by mass balance that at equilibrium the mole fraction of methanol will be: (X-2Y) 2 Assuming that the gas phase reactions are ideal, what will be the composition (mol %) of the final gas stream? (c) In an attempt to generate more methanol, the steam ratio is adjusted to 7:1. Is this a sensible thing to do, explain your reasoning?See Answer
  • Q7:1. Pease (1932) studied the gas phase hydrogenation of ethene to form ethane at normal pressure and across the temperature range 202 to 272 °C. (a) C₂H₂ + H₂ → C₂H6 Pressure was not varied as part of this experimental study, but would pressure have any influence on this reaction? Justify your answer. A series of different mixtures of the two reagent components was generated and an initial reaction rate was determined, shown in Table 1.1. Table 1.1: Initial reaction rate for the hydrogenation of ethene at 232 °C. [H₂] [mol m²] [mol m³s¹] [C₂H₂] [mol m 0.0005 0.0005 1.720E-23 1.376E-23 1.032E-23 6.878E-24 3.439E-24 0.0004 0.0003 0.0002 0.0001 0.0005 0.0005 0.0005 0.0005 0.0005 0.0005 0.0005 0.0005 Temp ["C] 202 212 222 232 242 252 262 272 0.0004 0.0003 0.0002 0.0001 (b) From the rate data provided in Table 1, determine the reaction order. The rate constant for the reaction was evaluated over a range of temperatures and is provided in Table 1.2. 1.376E-23 1.032E-23 Table 1.2: Rate constant values determined for the hydrogenation of ethene at atmospheric pressure. k [not stated] 4.587E-18 1.174E-17 2.893E-17 6.878E-17 1.581E-16 6.878E-24 3.439E-24 3.522E-16 7.613E-16 1.600E-15/n(c) (d) (e) Based on the information provided in Table 1.2, if the reaction rate constant follows an Arrhenius type expression, determine the constants within the Arrhenius equation stating units. Comment on your answer to part c, are the values determined sensible? Write out the full rate equation for this reaction.See Answer
  • Q8:Problem 4.2 Background: Reaction rate parameters can be fitted to experimental data for simple reaction systems where only one reaction is occurring at a time (as in problem 4.1). Consider a system where a conversion A → B occurs by two parallel reactions occurring at the same time. Both reactions are first order reactions. n = k₁C r₂ = K₂C mol lem³-s Where r is the rate of reaction and C is the reactant concentration reactions, the ,k is the reaction rate coefficient [s-¹], mol Làm Because both are first order r = (k₁ + k₂)C The reaction rate coefficients, k, are temperature-dependent, following the Arrhenius equation. k₁ = A₁ exp k₂ = A₂ exp . EA₁ RT EA₂ RT Where A is the Arrhenius prefactor [s], EA is activation energy temperature [K], and R is the ideal gas constant mol-K] Tis Problem: Consider the two competing reactions. Suppose that Reaction 1 has a prefactor of 1.106 s- and activation energy of 25,000 J/mol and Reaction 2 has a prefactor of 1.108 s- and activation energy of 50,000 J/mol. Use the Arrhenius rate law to calculate the values for k1 and k2 at the various temperatures listed. Graph the reaction rate constants k1 and k2 against temperature. Include appropriate axis labels and plot formatting. Use a log scale y-axis and show the axis labels in scientific notation. Add columns to the table to calculate these values. Add together k1 and k2 to get a total k representing the total reaction rate constant. Make a column to show when temperatures have a total rate constant greater than 10,000 1/s, as a Boolean output. Make a column that shows "Reaction 1" or "Reaction 2" for which reaction contributes more to the overall reaction rate. Make a column that shows when the overall reaction rate is a mix of the two, with both reactions accounting for at least 20% of the whole. A EA M T 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000 1050 1100 rxn 1 k1 rxn2 k2 k1+k2 k>10000 dominant mixedSee Answer
  • Q9:Problem 4.1 Background: The production of biodiesel involves the following reaction of triglycerides (TG) with methanol to produce fatty acid methyl esters (FAME). TG +3MeOH ⇒ 3H₂O + 3FAME The reaction as written is an overall reaction rate and not an elementary reaction. Which is to say, the reaction orders are not inferrable from the stoichiometry. For the purposes of this problem, we will assume that this reaction rate can be described useing a reaction order exponent, r = kC", but that the reaction order n is unknown. The reactant concentration will follow different reaction concentration trajectories (integrated rate laws) depending on the actual reaction order (with respect to TG), where C is the concentration of TG and Co is the concentration of TG at time zero. Zero Order First Order Second Order C = Co - kt C = C₂e-kt 1 C . = 1 Co Со +kt Problem: Analyze the provided experimental data. The reaction order of the transesterification reaction with respect to TG concentration is unknown. The integrated rate law will linearize differently depending on its reaction order. The concentration trajectory observed in samples collected from a transesterification process are provided in the table here. Use this data to determine the most likely reaction order and find the values for k and Co- Linearize each of the integrated rate laws. In the boxes at the top of the table, write in the variables that can be substituted for y=mx+b. This has been filled in for the zero order case to demonstrate. Use the apostrophe symbol (") at the start of a cell to force the contents to be read as text. Transform the provided t and C into linearized x and y for each case. Fit linear trends to each of them, fitting slopes and intercepts. In the provided textbox, provide your explanation for which reaction order best explains the experimental data. Justify your answer using the quality of the regression fit and use any appropriate metrics. • For the best fit reaction order, calculate the corresponding fitted C_0 and k. Time, t (min) 2 5 10 15 20 25 30 35 40 45 TG conc, C (mmol/L) 24 14 8.2 5.8 4.5 3.7 3.1 2.7 2.4 2.1 Best Fit Rxn Order C_0 k Zero Order X y m b X slope intercept R^2 t с -k C_0 y First Order X y m b X slope intercept R^2 V Second Order X y m b X slope intercept R^2 Which reaction order best explains the experimental data? Justify your answer: y The provided experimental data is best explained by a second order reaction. The linearization yields a higher R^2, indicating a better quality fit.See Answer
  • Q10:Q: A reversible chemical reaction 2A + B = C can be characterized by the equilibrium relationship: K=, where the nomenclature c; represents the concentration of constituent i. Suppose that we define a variable x as representing the number of moles of C that are produced. Conservation of mass can be used to reformulate the equilibrium relationship as: K=. CC,0 + x (Ca,o2x)²(Cb,o - x) where the subscript 0 designates the initial concentration of each constituent. If K = 0.016, Ca,o = 42, Cb,o = 28, and Cc,o = 4, determine the value of x using: a). Bisection method with initial guesses of x = 0 and xu = 20 and within a total error of 2 (determine required number of iterations in advance). b). False-Position method with initial guesses of x₁ = 0 and xu = 20 and within an approximate error of 10%. c). Newton method with xo = 10 and within an approximate error of 1%. d). Secant method with xo = 0 and x₁ = 10 and within an approximate error of 1%.See Answer
  • Q11:Problem 3. A fan is to be selected to ventilate a bathroom whose dimensions are 2 m x 3 mx 3 m. The air velocity is not to exceed 7 m/s to minimize vibration and noise. The combined efficiency of the fan-motor unit to be used can be taken to be 50 percent. If the fan is to replace the entire volume of air in 15 min, determine (a) the wattage of the fan-motor unit to be purchased, (b) the diameter of the fan casing (assume a round duct), and (c) the pressure difference across the fan. Take the air density to be 1.25 kg/m³ and disregard the effect of the kinetic energy correction factors. Air 7 m/s Exhaust fanSee Answer
  • Q12:Problem 1. Water flows at a rate of 0.040 m³/s in a horizontal pipe whose diameter is reduced from 15 cm to 8 cm by a reducer. If the pressure at the centerline is measured to be 480 kPa and 440 kPa before and after the reducer, respectively, determine the irreversible head loss in the reducer. Take the kinetic energy correction factors to be 1.05. 480 kPa 15 cm Water 440 kPa Reduce 8 cmSee Answer
  • Q13: MECH 1215 LABORATORY THREE (WEEK 16) ADIABATIC COMPRESSION LAB OBJECTIVE 1. On completion of the laboratory the students will have familiarised themselves with polytropic processes, in particular adiabatic and isothermal compressions, and how to experimentally determine the polytropic index from Equation 1. PV = C₁ Thermodynamics lab 2 Where P is the pressure, V is the volume, n is a constant (the polytropic index) that defines the behaviour of the compression process and c, is some constant. 2. STRUCTURE Students will work in groups of 3 or 4, depending on laboratory group size on the day, and each group will carry out up to three (3) repeat experiments for both (1) adiabatic and (2) isothermal compression experiments. However, each student will use the data generated individually. [1] Note 1: You are expected to run each experiments multiple times (a minimum of 3 repeats of each of isothermal and adiabatic compression experiments is required. More is better). Isothermal compression Adiabatic compression (or as close to this as possible) In particular the students will be required to find the value of n for air under conditions of MECH1215: Thermofluids 1 You are expected to find these values within the 2 hour lab session, using a combination of experimentation, mathematical manipulation of equations and data-processing with either excel or MatLab. Once you have found values for n, there is a supplemental question to answer. Details in the sections detailing the tasks to be be undertaken in as part of this lab processes. Laboratory 3 Page 1 of 10 MECH 1215 Introducing ReLOAD Protocol ReLOAD Protocol has been been introduced to the lab this year. This will be used in generation and collation of experimental data. There is also an opportunity for you to use the ReLOAD user interface to evaluate the correctness of your data, particularly you estimated values of polytropic index “n”. Details of the implementation of the ReLOAD protocol is provided in the section on Experiment methodology. 3. DELIVERABLES Thermodynamics lab 2 Each student is required to submit one lab report covering the experiment which should be concise and accurate. Maximum length: 10 pages (excluding cover and reference pages) Important note - Each report should have: Introduction: Putting the work into context and describing the background theory. The introduction should start with some background to the experiment, applications in the real world and relevance of the experiments you are about to undertake. Introduce the appropriate equations and explain the assumptions behind them, their limitations and again relate this to real systems. Aim/Objectives: Explain what your hope to achieve from the lab practical. All aims and objectives should be mentioned. Apparatus A list of the apparatus used and a diagram of the experimental system, with proper labels showing each part/component with a brief description of the function of each (Hand drawing diagrams should be avoided). Methodology: Providing enough information to enable someone to repeat the measurements themselves to the same degree of accuracy. It should have the settings used on any equipment and what controls were in place such as room temperature, placement of equipment, data processing, etc. MECH1215: Thermofluids 1 Laboratory 3 Page 2 of 10 MECH 1215 Results: Conclusions: In a concise form for each task, with the important data clearly highlighted, with no room for interpretation, example calculations provided and all questions within that task answered. Any post- processing of data, curve fitting, figures/plots should be presented and fully described. A description of your data analysis procedure (including any mathematical derivations). Must include graphs and fitted expressions to give n and work for the different scenarios. The results must show repeatability with error bars use to demonstrate this. This will mean that a minimum of two (3) repeats of test is carried out with all measurements recorded. Discussion: Containing an analysis and interpretation of the results based on the information collected and explaining its significance. Identify important issues, discuss the accuracy of the results and explain your findings. Compare your results with theoretical values and standard values from literature (i.e. lecture notes, books, scientific papers). Concise list of the conclusions arising from each experiment. No new information should be contained within this section. References Citations to appropriate literature must be included. Thermodynamics lab 2 Please follow Library referencing guidelines for references and citations: https://library.leeds.ac.uk/info/1402/referencing. The School of Mechanical Engineering follows Leeds Harvard or Leeds Numeric. Select one of these styles and be consistent throughout the report. Formatting exactly as per the guidelines. Please note: Experiments can be done as a group to generate data. The laboratory support staff on ground will guide you on the exact format for this. So please follow their lead. Data processing and report writing MUST be done individually. You are advised to bring your own laptop. This is to allow you start processing your data individually once you have generated your data. You can then be able to ask for further guidance from the support staff around. MECH1215: Thermofluids 1 Laboratory 3 Page 3 of 10 MECH 1215 ● When reporting data, please ensure you use the correct number of decimal places, ensure consistent number of decimal places, and add appropriate labels and units in every plot. All graphs, diagrams and images should be labelled as Figure followed by a number and caption. Do not use Picture 1 for example. Tables should be labelled as Table 1 etc. (It is not necessary to include a graph title when an appropriate figure caption is used and placed underneath the graph). Thermodynamics lab 2 Each section listed in the lab handout must have its own section header and be clearly distinguished from the other sections. Please order the report as per the lab handout. Marks will be awarded for presentation of figures, equations and tables. A Laboratory report should be written in 3rd person, mainly in the present tense. Past tense should only be used when describing the work carried out and the results obtained. Format the document appropriately. Do not provide a report where each task is answered one after another throughout the document. The report should be submitted electronically as per the instructions on Minerva. Standard University penalties will be applied to work handed in after the deadline without mitigating circumstances. MECH1215: Thermofluids 1 Laboratory 3 Page 4 of 10 MECH 1215 Experiment Methodology Adiabatic Gas Law Apparatus You will be provided the apparatus showed bellow. It consists of a piston within a cylinder and mechanical parts to allow a rapid compression, together with the following instrumentation: A pressure probe A temperature probe A position gauge The output signals are fed into a data logger connected to a computer. Arduino software is used to run a suitable programme to acquire the data. ReLOAD is used to provide an interactive platform for running the experiments and collation of generated data. ReLOAD Protocol Thermodynamics lab 2 Note that these task are here to help you work through the laboratory session. The tasks should not form the basis of the structure of the laboratory report i.e. DO NOT write a report which is itemised task 1, task 2 etc. with responses to each individual task. Instead incorporate the work appropriately into the methodology, results and discussion section where suitable. Each of the adaibaitic compression apparatus is assigned a unique number (1 – 8) on ReLOAD. Student MUST check that the number on the compression apparatus to identify the same number on ReLOAD. MECH1215: Thermofluids 1 All students should now have a loggin to ReLOAD from using ReLOAD as part of MECH1010. Laboratory 3 Page 5 of 10See Answer
  • Q14:8.1 F. Salvador, J. L. Gonzalez, and M. A. Herraez [Int. J. Chem. Kinet., 14, 875 (1982)] studied the kinetics of the isomeriza- tion of cholest-5-en-3-one in cyclohexane in the presence of trichloroacetic acid as a catalyst. The stoichiometry of this reaction is A → B, where A refers to cholest-5-en-3-one and B to cholest-4-en-one. Species A and B both form association complexes with trichloroacetic acid. In the presence of excess acid, the kinetics of the isomerization reaction are described by a rate expression that is pseudo first-order in A: r = kobserved (A) At 25.4°C the observed rate constant is 1.087 × 10-³ s-¹ for the concentration of trichloroacetic acid employed (7.37 x 10-³M). Consider this reaction as it takes place in a semibatch reactor operating at 25.4°C. Initially, this reactor contains 20 L of a cyclohexane solution that contains the desired amount of trichloroacetic acid, but no A. The reactor is fed with a cyclohexane solution containing species A (2 x 10-3 M) and trichloroacetic acid (7.37 x 10-3 M). The feed stream enters at 25.4°C at a constant rate of 5 L/min for a total time of 30 min. Subsequently, the reactor functions as a batch reactor. The reactor is well stirred during both phases of the reaction. Prepare plots of the concentrations of species A and B as functions of time for a total elapsed time of 100 min. At what time does the concentration of species A pass through a maximum? How much total time is necessary to convert 98% of the A fed to the reactor into B?See Answer
  • Q15:Problem 1: Normal-butane is stored in a steel tank and the temperature of the tank and butane inside is kept at a constant temperature T = 85°F Use these parameters for your calculation. Acentric factor w = 0.193, critical temperature Tc = 305.62°F, critical pressure pc = 550.6 psia, Vc = 4.1 ft³/lbmol. a) Use Lee-Kesler's correlation to calculate the n-butane vapor pressure inside the canister. (5 points) b) Write down the van der Waals EOS and calculate the constants a, b using the critical properties given above. Use n = 1 pound-mole, or Ibmol. (5 points) c) Calculate the critical volumes Vc, ft³/lbmol, from VDW EOS. Compared the calculated Vc and the given value. (5 points) d) Plot pressure p vs. volume V for one Ibmol of butane gas. Use Vmin = b + 0.2, V₁ = 1.02Vmin, V₂ = 1.02V₁, V3 = 1.02V₂, ... until Vmax > 150 ft³. (10 points) a) Using VDW EOS b) Using the Ideal Gas EOS e) Use the calculated vapor pressure, and p vs. V plot to estimate the system volumes at the dew point and bubble point, respectively. (5 points)See Answer
  • Q16: See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/334454536 Modeling and Simulation of a Water Gas Shift Reactor operating at a low pressure Article - July 2019 CITATIONS 3 3 authors: Wail El Bazi ENSA khouribga Maroc 14 PUBLICATIONS 33 CITATIONS SEE PROFILE M.S. KADIRI Ecole Nationale des Sciences Appliquées de Khouribga, Morocco 21 PUBLICATIONS 318 CITATIONS SEE PROFILE All content following this page was uploaded by Wail El Bazi on 12 January 2021. The user has requested enhancement of the downloaded file. READS 4,020 ResearchGate A. El Abidi Cadi Ayyad University - Ecole Nationale des Sciences Appliquées - Safi - Morocco 19 PUBLICATIONS 77 CITATIONS SEE PROFILE JOURNAL INTERNATIONAL LOF ENGINERING BESR International Journal of Innovation Engineering and Science Research AND SO INOVATION SCIENCE R SEARCH Modeling and Simulation of a Water Gas Shift Reactor operating at a low pressure Wail El Bazi¹*, Abderrahim El-Abidi²,³, Moulay Saddik Kadiri¹, Said Yadir²,3 ¹ Laboratory of Process Engineering and Industrial Systems Optimization (LIPOSI) ENSA Khouribga, Sultan Moulay Slimane University, Béni Mellal, Morocco *corresponding author: w.elbazi@usms.ma ² Laboratory of Materials, Processes, Environment and Quality (LMPEQ), ENSA Safi, Cadi Ayyad University, Marrakech, Morocco 3 Laboratory of Electronics, Instrumentation and Energy (LEIE), Faculty of Science, Chouaib Doukkali University, El Jadida, Morocco Open Access ABSTRACT In order to study the WGS on an industrial scale at a low pressure, the modeling and simulation of a WGS reactor operating at a pressure close to Patm and processing an industrial charge in the presence of a high temperature shift catalyst (Fe2O3/Cr2O3) were performed. The Profiles of the carbon monoxide conversion, temperature and pressure along the reactor were obtained. The effect of several operating parameters (inlet temperature, H₂O/CO ratio) on the conversion of carbon monoxide along the reactor has been determined. The estimated catalytic mass to convert 60.5% of the carbon monoxide contained in the inlet is 170.76 t. The pressure drops in the reactor are not negligible and the maximum temperature reached is without any harmful effect on the catalyst. The choice of an optimal inlet temperature and a high H₂O/CO ratio improves the conversion of carbon monoxide. Keywords- Packed bed reactor, catalyst, water gas shift reaction I. INTRODUCTION Hydrogen is an important source of energy and is involved in various industrial processes such as: ammonia synthesis, methanol synthesis, etc. [1]. The production of this molecule can be carried out through several ways: Production from methane [2], biological production [3], water electrolysis [4], chemical production of aluminum and sodium hydroxide [5], or WGS (water gas shift reaction) which is a chemical reaction converting a mixture of carbon monoxide (CO) and water vapor (H₂O) into a mixture of carbon dioxide (CO₂) and hydrogen (H₂): CO+H2O = CO2 + H2 AHR (298K) This slightly exothermic reaction discovered by the Italian physicist Felice Fontana in 1780 [1] can occur in the presence of catalysts based on several metals such as Cu, Fe, Ni, Pd, PT, Rh, Ru [6] or even metal oxide [7]. At high temperatures (350-450°C) catalysts based on iron oxides and chromium oxide III (Cr2O3) can be used [7]. At low temperatures (120-240°C) copper or copper oxide catalysts can be used with promoters of alumina oxide (Al2O3) [7] and zinc oxide (ZnO) [8]. WGS can occur at pressures ranging from 1 to 83.75 bars [ 7-10]. but often industrial reactors operate at high pressures [ 8,11-12]. Numerous models of the water gas shift reactors have been published to date. Elnashaie et al developed a steady-state one-dimensional heterogeneous model to study the behavior of industrial reactors operating at high temperatures [11]. Their work also focused on the effect of temperature on the conversion of carbon monoxide. Adams et al used a dynamic two-dimensional heterogeneous model to study the behavior of reactors operating at both high and low temperatures [13]. Adams was also Volume 2 Issue 6 November - December 2018 == 41.2 KJ/mol 47 | Wail El Bazi et al. "International Journal of Innovation Engineering and Science Research" interested in the effect of important parameters on Xco (H₂O/CO - temperature ratio). Falleiros Barbosa Lima et al investigated an industrial reactor operating at high temperatures, using different one- dimensional pseudo homogeneous models [14]. The effect of catalyst deactivation on reactor performance was also investigated. A steady-state one-dimensional pseudo-homogeneous model was also used by Shokry et al to predict the evolution of molar flow rate along and at the outlet of an industrial WGS reactor operating at low temperatures [12]. These authors also studied the effect of pressure, inlet temperature, H₂O/CO ratio on Xco. The major disadvantage of operating at high pressures is the enormous energy costs that it would be interesting to reduce them by carrying out the WGS at low pressures. In addition, the operating life of the catalyst can reach 15 years if the reactor operates at a low pressure [15]. Indeed, several papers have been carried out to study this reaction and to determine its kinetic expressions in the presence of catalysts allowing its activation at pressures close to the atmospheric pressure [8,16-23]. It would therefore be interesting to use these expressions in the simulation and study of the behaviour of reactors operating at pressures on the order of 1 atm. In fact, the work of Maklavany et al has been interested in this topic. These authors used the kinetic expression of WGS in the presence of a low temperature shift catalyst (CuO/ZnO/Al₂O3) to simulate a laboratory reactor operating at 1.2 bar. Two models were used: a steady state 2D homogeneous isothermal model [24] and a 1D homogeneous isothermal model with axial dispersion [25]. The effect of temperature on the variation of several parameters along the reactor (CO concentration, pressure, reaction rate, superficial velocity) was also studied. In our study, we also carried out the simulation of a reactor operating at a low pressure. But in our case, it is in the presence of a high temperature shift catalyst (Fe2O3 /Cr₂O3) and for a large reactor. This will allow the industrial-scale study of the reaction at a low pressure and clarified the strengths and weaknesses of the realization of WGS under this condition. The model we used to simulate the fixed catalytic bed is the steady state one-dimensional pseudo homogeneous model that is widely used in the study of the behaviour of industrial catalytic convertors, sites of the WGS [12,14,26] or other gas phase reactions [27,28,29]. In the first part of this study, we used the kinetic rate expression corresponding to this catalyst in the modeling and simulation of an industrial WGS reactor. This allowed the prediction of profiles of the carbon monoxide conversion, temperature and pressure along the reactor. Then, the work was continued by studying the effects of the operating parameters (inlet temperatures, H₂O/CO ratios) on the conversion of carbon monoxide in order to define the optimal conditions of the reaction realization. II. DESCRIPTION A. Description of the studied catalyst and the operating conditions for establishing the kinetic rate expression The kinetic rate expression corresponding to the chosen catalyst was carried out by Keiski et al [18]. The characteristics of the catalyst, as well as the operating conditions under which the kinetic rate expression was established, are presented in Table I [7,13,18]. TABLE I. Catalyst CCE C12 Ref: [7,13,18] CATALYST CHARACTERISTICS AND OPERATING CONDITIONS FOR THE ESTABLISHMENT OF THE WGS KINETICS [7,13,18] Equivalent spherical diameter, dp (μm) Composition Fe₂O3/Cr₂O3 (89/9%) Operating conditions for the establishment of WGS kinetics T: [575-675 K], P : 1 atm H₂O/CO (molar) : [2.4-12.1] Gas mixture of different fractions of: CO, CO2, H2O, Hz, Nz 2800 Volume 2 Issue 6 November December 2018 Shape Cylinder Catalyst density, Pc (kg/m³) B. Description of the reactor and the operating conditions considered in the simulation The characteristics of the simulated reactor are presented in Table II. 3730 48 | Wail El Bazi et al. "International Journal of Innovation Engineering and Science Research" Packed bed diameter D (m) 0.09 Packed bed length, L (m) 2.2 TABLE II. REACTOR CHARACTERISTICS Number of packed beds (tubes) 6000 The first simulations were run to predict the profiles of carbon monoxide conversion, temperature and pressure along the reactor operating at a low pressure and for a feed flow of an industrial nature. We ran these Simulations under the operating conditions presented in Table III. TABLE III. OPERATING CONDITIONS USED FOR THE PREDICTION OF X(Z), T(Z) AND P(Z) Molar flow rate of the feed gas mixture, F₁,0 Inlet pressure, Po Inlet temperature, To (mol. s-¹) (atm) (K) CO: 23.28 CO₂: 94.19 H₂ : 364.149 H₂O: 228.93 N₂: 134.354 Keq III. EQUATIONS Thermal property of the packed bed Adiabatic The compositions and the inlet pressure of the gas mixture of table 3 are close to those studied when establishing the kinetic rate expression of the WGS [18]. The temperatures remain within the temperature range of the kinetic study [18]. At the same time, in order to evaluate the WGS at low pressures in a situation close to an industrial case, each partial molar flow rate of WGS reagent (CO, CO2, H₂O, H₂) presented in Table 3 is equal to 30% of the actual partial molar flow rate of the same reagent feeding the high pressure WGS reactor of the Alexandria Fertilizers Company (AlexFert) [12]. The molar flow rate of nitrogen shown in this table is equal to 30% of the real molar flow rate of the inerts feeding the company's reactor. A. kinetic expression The kinetic expression used is a simple power-law model [7,18]: -rco (mol.kg cata¯¹. h¯¹) = 2623447 exp -79759 RT В = ex p To study the effect of temperature on the carbon monoxide conversion along the reactor, other simulations were performed for other inlet temperatures (575 K, 605 K, 620 K) while keeping the other operating conditions (Table 3) and the same reactor characteristics (Table 2). Finally, the study of the effect of the H₂O/CO ratio on the Xco profile along the reactor required further simulations for [H₂O]/[CO] = 3 which corresponds to Fo(H₂O) = 69.84 mol.s-¹ and Fo(CO) = 23.28 mol.s 1 and for [H₂O]/[CO] = 5 which corresponds to Fo(H₂O) = 116.4 mol.s-¹ and Fo(CO)= 23.28 mol.s-1. These last simulations were established by varying only the molar flow rate of the water vapor. While the other operating conditions (Table III) and reactor characteristics (Table II) have not been changed. 1.12 Volume 2 Issue 6 November December 2018 Сco2 CH2 1 Ссо Снчо Ке void fraction in the packed bed The equilibrium constant, Keq, is given by the equation 2 [7,18]: 4577.8 4.33) T Where -rco is the CO conversion rate, Ci is the molar concentration of species i (mol.dm-³) and ß is the reversibility factor: દ 0.4 590 0.74 C047C0218[1 − B] (2) (1) 49 | Wail El Bazi et al. "International Journal of Innovation Engineering and Science Research" B. Process modeling and numerical solution The following assumptions were made to develop the used mathematical model for the packed bed reactor simulation: Adiabatic reactor. ● ● Steady state condition. Axial dispersion is neglected, because the flow rate is sufficiently high to create a turbulent flow G.dp (Re: = > 40) and (L/dp>150) [30]. Where Re is the Reynolds number, G is the superficial mass velocity (kg.m-². s-¹) and µ is the dynamic viscosity of the mixture (Pa.s). μl Radial dispersion is neglected, because the tube diameter is narrow, the reactor is adiabatic and the WGS is a moderately exothermic. Under these conditions, radial gradients of concentrations and temperatures are not important [30,31,32]. The system of differential equations used is as follows [14]: dXco -coFPresPBS Fco,0 dz The heat and mass transfer as well as the diffusion in the catalyst were lumped in the rate constant. ● ● dT ΣFiCpi dz For the reagent: dp dz C₁ is expressed using the perfect gas equation: Pi RT For the product: For the inert: C₁ = -f² = Where Pi is the partial pressure (Pa), expressed as follows: P₁ = -fPgu ²³ dp - AHRTCO FPresPBS With yi is the molar fraction of the species i The expression of the molar flow rate, Fi (mol. s-1), of each component depends on its nature, be it a reagent, a product or an inert: F₁ = F₁,0 — Fco,o * Xco F₁ = F₁,0 + Fco,o * Xco F₁ = F₁,0 (3) Volume 2 Issue 6 November December 2018 (4) (5) (6) F₁. P = y₁.P i=n Σ=0 Fi (7) (8) (9) 50 |See Answer
  • Q17:Lecture 16: Equilibrium of Multiple Condensable Vapors Problem 6: A tank is filled with propane C₂H₂, the first component, and n-hexane CH₁4, the second component. For a constant temperature, there exist both liquid and vapor phases inside the tank, and the liquid and vapor are in equilibrium. The measured vapor composition is y₁ = 0.925008, y₂ = 0.074992, liquid composition x₁ = 0.243423, x₂ = 0.756577. The total mass inside the container is 5 moles, and the 3.851377 moles are in the liquid phase. 1. Calculate the equilibrium constants K₁, K₂ (3 points) 2. Calculate the moles of propane and n-hexane in the vapor phase, 1v1.1v2 (3 points) 3. Calculate the moles of propane and n-hexane in the liquid phase, 1₁, 12 (3 points) 4. Next, the system temperature is raised above the critical temperature of n-hexane, and both compounds exist as vapor only. Calculate the composition inside the container. (3 points) Propane + n-Hexane Vapors Propane + n-Hexane LiquidsSee Answer
  • Q18: CHE 120 Homework Assignment Week 8 Lecture 15: Equilibrium of Condensable Vapor and Noncondensable Gas Problem 1: Textbook 8.3.5. (5 points) *8.3.5. Calculate the vapor pressure of each compound listed below at the designated temperature using the Antoine equation and the coefficients in Appendix H. Compare your results with the corresponding values of the vapor pressures obtained from the Antoine equation found in the physical properties package on the CD accompanying this book. a. Acetone at 0°C b. Benzene at 80°F c. Carbon tetrachloride at 300 K CHE 120-Spring 2024-Chang 1 Chemical Engineering Physical Properties Heat Capacities Enthalpies Density of Liquid Vapor Pressure Steam Tables Compounds Miscellaneous AMMONIA ACETONE A-D E-H 1-EICOSANETHIOL AR BR2 CL2 CS2 F2 H2 H20 I-L 1-IODOPROPANE M-Q 1,2-PENTADIENE R-X 1,1,1-TRIFLUOROETHANE Formula CCL4 CCL3F CCL2F2 CCLF3 Acetone at O C CF4 CO CO2 Fomula Vapor Pressure (mmHg) (Tis in ℃) t Max logop*= 7.2316 OK Min Ⓒby David Himmelblau 2000. All rights reserved. ACETONE C3H60 Temperature 0 -32 CHE 120-Spring 2024-Chang p* (mmHg) 1277.03 [T+ 237.23 } 77 ℃ CCF CK 70.552 2 Chemical Engineering Physical Properties Heat Capacities Enthalpies Density of Liquid Vapor Pressure Steam Tables Compounds Miscellaneous AMMONIA BENZENE A-D E-H 1-EICOSANETHIOL AR BR2 CL2 CS2 F2 H2 H20 I-L 1-IODOPROPANE M-Q 1,2-PENTADIENE R-X 1,1,1-TRIFLUOROETHANE Formula CCL4 CCL3F CCL2F2 CCLF3 Benzene at 80 F CF4 CO CO2 Fomula Vapor Pressure (mmHg) (Tis in ℃) t Max logop*= 6.90565 OK Min Ⓒby David Himmelblau 2000. All rights reserved. BENZENE C6H6 Temperature 80 -16 CHE 120-Spring 2024-Chang p* (mmHg) 1211.033 (T+ 220.79 } 104 ℃ CC OF CK 102.738 3 Chemical Engineering Physical Properties Heat Capacities Enthalpies Density of Liquid Vapor Pressure Steam Tables Compounds Miscellaneous AMMONIA A-D CARBON-TETRACHLORIDE E-H 1-EICOSANETHIOL I-L 1-IODOPROPANE AR BR2 CL2 CS2 F2 H2 H20 M-Q 1,2-PENTADIENE R-X 1,1,1-TRIFLUOROETHANE Formula CCL4 CCL3F CCL2F2 CCLF3 Carbon-Tetrachloride at 300 K CF4 CO CO2 Fomula Vapor Pressure (mmHg) (Tis in ℃) t Max OK CARBON-TETRACHLORIDE Min logop*= 6.8941 Ⓒby David Himmelblau 2000. All rights reserved. CCL4 Temperature 300 -20 CHE 120-Spring 2024-Chang 1219.58 p* (mmHg) 101 (T+227.17 CC CF K 123.875 t ] 4See Answer

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Answer 2:

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Answer 6:

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