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Q1: Problem 1. For each of the following signals (represented via Laplace transforms X(s)),what can you say about their time-domain representation x(t) without solving for all the parameters of an explicit analytical solution? (note: please show the general structure of the partial fraction expansion for each system, but DO NOT estimate coefficients or fully invert the transforms to obtain an analytical solution). Specifically, \bullet \text { What are } x(0) \text { and } x(\infty) ? \text { - Does } x(t) \text { as } t \rightarrow \infty \text { converge to a steady-state or diverge to infinity? } • Is x(t) smooth or oscillatory? For each case, draw a qualitative yet informative sketch of the time-domain response. In addition, apply the Initial Value Theorem to determine the slope of the response at t = 0,and make this information part of your sketch. a)X(s)=\frac{6(s+2)}{\left(s^{2}+9 s+20\right)(s+4)} b)X(s)=\frac{10 s^{2}-3}{\left(s^{2}-6 s+10\right)(s+2)} c)X(s)=\frac{16 s+5}{\left(s^{2}+9\right)(s+3)} d)\frac{d^{3} x}{d t^{3}}+2\frac{d^{2} x}{d t^{2}}+2\frac{d x}{d t}+x=3S(t) S(t) is the unit step change; all initial conditions at zeroSee Answer
Q2: Problem 2. Consider the spherical reboiler problem examined in EPAs 2 and 3. Using the linearized model from EPA No. 3, Problem 2, obtain the transfer functions that re-late changes in the inlet and outlet flow rates to changes in level. Draw a block diagram representation for the linearized model that incorporates these transfer functions.See Answer
Q3: 1-5. Safety metrics: Classify the following as either leading or lagging safety metrics Explain why. a. Number of reports of unsafe activities in a plant b. Number of near-miss incidents C.Money spent on insurance claims d. Number of visits to the plant first aid facility e. Number of process alarms that were managed without incident f. Time duration to complete maintenanceSee Answer
Q4: 1-9. Codes, standards, and regulations: Go to the www.osha.gov web site and look up the OSHA regulation CFR 1910.119: Process Safety Management of Highly Hazardous Chemicals. Use Appendix A to determine the threshold quantities for the following chemicals. If your plant site exceeds this threshold quantity, then this standard applies. a. Ammonia, anhydrous b. Chlorine c. Hydrogen fluoride d. Propylene oxideSee Answer
Q5: A process description for a reagent mixing and delivery system is provided below. NaHS (a dry powder) is delivered by truck to the mine site in 25 kg bags. The dry NaHS powder is mixed with water in a mixing tank to 5% strength. The resultant NaHS solution is then sent to a storage tank, which is large enough to store one week's supply of 5% strength reagent solution.The fumes from the solutions are hazardous, and need to be sent to a scrubber before release to the atmosphere. Therefore, there is a connection for vapour discharge from both the mixing tank and the storage tank to the scrubber to treat vapour from the tanks before release to the atmosphere. Another reagent, SMBS, is similarly mixed with water and stored in another parallel reagent mixing and delivery system. Similarly, the vapour from SMBS solution is hazardous, and is sent to a scrubber for treatment before release to the atmosphere. There are therefore two parallel reagent mixing and storage systems. The two reagent mixing and storage systems are similar, so in order to allow for plant flexibility, it is proposed to connect each mixing tank with both storage tanks in the parallel trains. This would allow for storage of excess reagent from one train in the second train if required during the operation. Draw a PFD for the two interconnected reagent and mixing systems. Below is a copy of icons that may be useful to use in your PFD: marks)The vapours from SMBS solutions and NaHS solutions are not compatible and can aggressively react producing heat and corrosive liquids when they come into contact. Conduct a HAZOP for the vapour feed lines from the mixing tank and storage tank to one of the scrubbers. Conduct the HAZOP for the process variable "Flow" only. A risk matrix is provided below for use when conducting the HAZOP. Are there any design changes that you would propose to this system as a result of conducting the HAZOP? Discuss.See Answer
Q6: Question 3. A pumping station is used to pump water from a nearby river to a covered storage tank for use on a farm. The tank should be kept full so that water is available for the irrigation system on the farm. Another pump is then required to pressurise the irrigation system using water from the tank when required. (a) (10 marks) On the next page, sketch a P&ID for a feedback controller that willmaintain a high level in the tank and allow for water to be used for irrigation ondemand. The following icons may be useful to use when drawing the P&ID: (b) (8 marks) There are two situations on the farm that could cause damage to the pumps.If the pressure on the suction side of either pump is too low, cavitation in the pump can occur. In addition, if the irrigation system is blocked, the pressure can build in the pipework and cause damage and leakage in the irrigation pipework. On the next page,draw a P&ID showing a system to protect the pumps and irrigation system from damage due to these two events. (c) (5 marks) A PID controller is used for the level controller on the tank. Discuss what can happen to the integral action of the controller if override control in implemented.What can be done to avoid problems with integral control in an override control situation?See Answer
Q7: For the general first-order differential equation: \tau \frac{d y^{p}(t)}{d t}+y^{p}(t)=K x^{p}(t) Where t 5 minutes, is the time constant, and K=0.5 is the gain. Obtain the dynamic responses, yP (t), for the following inputs: A step change of value 1.5, i.e. x (t) = 1.5u(t). An impulse, x" (t) = 1.58(t). A pulse of magnitude 1.5 and duration 1 minutes. A ramp, x(t) = 0.25 t, for a duration of 1 minutes, after which the input stays constant. Develop the Simulink model for the first-order system and simulate the responses indicated in parts (a) to (d). Report the response plots in your assignment report.See Answer
Q8: A thermometer with a time constant of 0.25 min is placed in a temperature bath. After the thermometer comes to equilibrium with the bath, the temperature of the bath is increased linearly with time at a rate of 2°/min. What is the difference between the indicated temperature and the bath temperature? 0.1 min after the change in temperature begins? 1.0 min after the change in temperature begins? O What is the maximum deviation between indicated temperature and bath temperature, and when does it occur? Plot the forcing function & response on the same graph. After a long enough time, by how many minutes does the response lag the input?See Answer
Q9: A step change of magnitude 2 is introduced into a system, (i.e. X(s) = -) having the transfer function: \frac{Y(s)}{X(s)}=\frac{5}{s^{2}+1.6 s+4} Determine the flowing response parameters: Percent overshoot Rise time ii. Maximum value of y (1) Ultimate value of y'(t) Period of oscillation Simulate and plot y"(t). Simulate and plot y"(t).P,See Answer
Q10: The response of the liquid level in a tank is given by the first-order differential equation: A \frac{d h(t)}{d t}=q_{0}(t) where h(t) is the level in the tank in m, gdt) is the flow of the liquid into the tank in m/s, and A =0.5 m is the constant area of the tank in m2. \text { Obtain the transfer function for the tank, } G(s)=\frac{H(s)}{Q_{0}(s)} Assume that initially the valve of the inlet stream was completely closed and the level in thetank was h(0) = 0.25 m. At t = 0, the valve was opened, and the flowrate was maintained atgo(0) = 0.25 m/min. Knowing that the height of the tank is 3.5 m, after which the tank willoverflow. Determine the time needed to fill up the tank. O Simulate and plot the responses obtained in parts (b) and (c). \text { Obtain the response of the level to a unit step in flow, } q_{o}(t)=u(t) .See Answer
Q11:P4.36 100 gmol/min of a solution of 70 mol % ethanol/30 mol % water is fed to a reactor operating at steady state, along with 80 gmol/min of air (79 mol % N₂, 21 mol % O₂). Ethanol (C₂H5OH) reacts with oxygen to make acetaldehyde (CH,CHO). Acetaldehyde is further oxidized to acetic acid (CH₂COOH). Write the two stoichiometrically balanced chemical equations. What is the byproduct of the reactions? What is the limiting reactant? If there is 100% conversion of the limiting reactant and the production rate of acetaldehyde is 25 gmol/min, calculate the fractional conversion of the excess reactant, the yield of acetaldehyde from ethanol, and the composition and flow rate of the reactor effluent stream. See Answer
Q12:P4.41 Hydrogen reacts with iron oxide (Fe₂O3) to produce metallic iron (Fe), with water vapor as a byproduct. 100% conversion of Fe₂O3 is achieved, and the metallic iron is easily separated from the hydrogen-water vapor mixture. The water is condensed, and the hydrogen is recycled. The hydrogen source is contaminated with 1 mol % CO. The recycle:fresh feed ratio is 4:1, and the maximum allowable CO in the gas fed to the reactor is 2.5 mol %. Draw a flow diagram, and complete a DOF analysis. Then calculate the single-pass and overall conversion of H₂ as well as all process flows, for a production rate of 1 ton/day metallic iron. (Hint: Consider changing basis to the gas feed.)See Answer
Q13:Problem 4-1-Butanol reactor variations The dehydration of 1-butanol to isobutene is run as an equilibrium-limited reaction with Keq = 2.4 atm at T = 323 K. The gas-phase reactor is operated at 1atm total pressure, and the feed is to contain 10 mole/min 1-butanol. (CH3)3COH -- (CH3)2C=CH2 + H₂O a) Calculate the equilibrium conversion expected when the feed is pure 1-butanol vapor. Also report the outlet composition and total molar flow rate. b) Calculate the equilibrium conversion expected if this reactor is operated at a total pressure of 0.2 atm. Also report the outlet composition and total molar flow rate. c) It is common to add nitrogen or another inert gas to the feed stream to increase the butanol conversion. Calculate the fractional conversion of butanol expected when the feed is 20 mole% 1-butanol and 80 mole% nitrogen, at the same total pressure and butanol flow rate as before. Also report the outlet composition and total molar flow rate. d) Comment briefly on the difference between the conversions expected for these conditions. Give advantages and disadvantages of each plan.See Answer
Q14:Question 1 [20 points] Propane (C3H8) is stored in a tank at a temperature of 400°C and a pressure of 2 atm. a) Show if the ideal gas law can be used for this calculation. [10 pts] b) Calculate the specific volume of the tank. [10 pts]See Answer
Q15:Question 2 [20 points] Consider a mixture of methanol (55%), formaldehyde (23%) and a variety of other solvents. If the other solvents have an average density of 0.831 g/cm3, estimate the density of the mixture a) Assuming volume additivity [10 pts] b) Assuming average of the pure-component density [10 pts] The density of methanol and formaldehyde are 798 kg/m3 and 815 kg/m3, respectively.See Answer
Q16:Question 3 [40 points] Heptane (C6H₁4) at 250 °C and 12 MPa absolute flows into a reactor at a rate of 200 kg/h. a) Calculate the volumetric flow rate of this stream using conversion from standard conditions. [20 pts] b) Calculate the volumetric flow rate of this stream using ideal gas EOS. [10 pts] c) Which method is accurate? Explain. [10 pts]See Answer
Q17:Question 4 [20 points] A gas occupies a volume of 10 liters at standard temperature and pressure (STP). If the gas is suddenly compressed to half its initial volume while maintaining the same temperature, what will be the new pressure of the gas. Show all calculation steps.See Answer
Q18:Name: Rawon Sanad Problem 1: [20% ] Show complete steps of your solution بیگی 1) [10% ] Determine the enthalpy change and the entropy change of CO2 per unit mass as it undergoes a change of state from 365 K and 14.78 MPa to 380 K and 22.17 MPa, by accounting for the deviation from ideal-gas behavior. Using Zn Name: Te/nit undergoes deviation Rawan Sanad Name: 2) [10% ] A mixture of gases consists of 30 kg of oxygen, 60 kg of carbon dioxide, and 10 kg of This mixture is maintained at 120 kPa and 37°C. Determine the following a) The mole fraction of oxygen b) The mole fraction of carbon dioxide c) The partial pressure of helium d) The apparent molecular weight of this mixture e) The volume of the mixtureSee Answer
Q19:Psych ormal dic Pr ric ir Name: Pawan Sanad Problem 2: (20% ] Show complete steps of your solution 1) [10% ] A room is filled with 120 kg of air at 75 kPa, 30°C dry-bulb temperature and 28.92% relativ humidity. Determine the following: a) The partial pressure of water vapor b) The partial pressure of dry air c) The humidity ratio d) The enthalpy of the mixture per unit mass of dry air e) The dew-point temperature f) The volume of the room anal //////nRawam Sanad Name: 2) [10%] Butane (C4H10) is burned with 180 percent theoretical air. Write the balanced combustion equation and determine the air-fuel mass ratio. F C4H10 + (02 +3.76N₂) → CO₂ + _H₂O + OLD MA _0₂+ N₂See Answer
Q20:# V=320 P=latin Air flowing at 320 m/min is to be conditioned in a constant pressure process at 1 atm from 43°C& and 40 percent relative humidity to 25°C dry bulb and 18.5°C wet bulb. The air is first passed ove T= 43°C coils to remove all the moisture necessary to achieve the final moisture content and then is heating coils to achieve the final state. Fill in the properties table [8%) and determine the following: =40% passed T₁=25°C Twbs=18.5°C 1 2 3 Name: Problem 3: [30%] Tab (°C) 43 -Y = Pv 8.71 25 Pu 117057 P- sat _=W3 Pu = Pesat Heating coils teleeeeeeeeeeeee W₂ =W₂ from then ermine $ (%) 40 too 2 chart (0 2 state 2 $/2=100%. 0.0714 1.635 1.635 a) [3%] Sketch the process on the provided psychrometric chart. b) [2%] The mass flow rate of air in "kg/s" →Pv₁ = 3.484 kpa Cooling coils P=1₁7057 15°C h (kJ/kga) llllllle 1 atm Condensate Condensate removal (m³/kga) T=43 Pat= 8.71 kpap W 0.622 Pu P-PU = 0.622 (3.484) 8.71 (3,484) = 0.0714 T₁=43°C ₁-40% State Twb (°C) اسپنسه 18.5 |Tz=15°C1 Sot = 1.7057 Ⓒ 0,622(1.7057) 1.50 1176037-(1.1257) التي 1/2 = 1.639 8=. 12 2 1.55 T=25°C =316= 0.60 065 03/nName: c) [5%] The rate of condensation in cooling section in "kg/s" d) [7%] The rate of heat removal in the cooling section in "kW" e) [5%] The rate of heat input in the heating section in "kW"See Answer

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