CHEG 4142 - Chemical Engineering Unit Operations and Process Simulation

Homework 5 Problem 1: CO₂ is absorbed into propylene carbonate in a packed column (“Colulmns→RadFrac→ABSRBR1” in Aspen). The inlet gas stream is 20 mol% CO₂ and 80 mol% methane. The gas stream flows at a rate of 17,500 kmol/hr and the column operates at 60°C and 60.1 atm. The inlet solvent flow is 2,000 kmol/hr. Use Aspen Plus to determine the concentration (mol%) of CO₂ in the exit gas stream. Use Peng Robinson-SRK as your property method. Assume no reboiler or condenser. Use a 10-stage column with a random packing of ceramic Raschig rings (25 mm) and a section packed height of 0.3 m.

• Outlet composition of CO2 is 19.6 mol % in stream 3 which is this RadFrac's distillate stream

Problem 26.4-2: A saturated liquid feed of 200 mol/h at the boiling point containing 42 mol % heptane and 58% ethyl benzene is to be fractionated at 101.32 kPa abs to give a distillate containing 97 mol % heptane and a bottoms containing 1.1 mol % heptane. The reflux ratio used is 2.5:1. Calculate the mol/h distillate, mol/h bottoms, theoretical number of trays, and the feed tray number. Equilibrium data are given below at 101.32 kPa abs pressure for the mole fraction n-heptane H and yH

• Distillate and bottoms flows are easily calculated using the mole balance F = D + W and FxF = DxD + WxW

• From there, we know that the q line is vertical, since the feed is a liquid at boiling point

• Next, we obtain the enriching operating line with the equation Y,n+1 = (R/R+1)*Xn + Xd/(R+1)

• Plugging in the 2.5 reflux ratio for R, we get the line equation Y,n+1 = 0.714Xn + 0.277

• Stepping off of the operating lines, we get N = 10.5 steps, which means we need 9.5 theoretical trays + a reboiler

Homework 8 Problem 1: Methylcyclohexane (MCH) and toluene are difficult to separate from one another via distillation. Therefore, phenol is used to extract toluene and produce MCH in high concentrations. The extraction process is done in a distillation column with two feed streams as shown in the diagram below. For this problem, you will be simulating this process in Aspen Plus and investigating how the two inlet flow rates impact the outlet MCH concentration and energy usage by the column’s condenser.

c) Keeping the phenol flow rate at only 100 lbmol/hr, use an Optimization to determine what flow rate of MCH/toluene will minimize condenser heat duty while ensuring that there is at least 80% MCH in the distillate.

• Using these conditions for the column, we run an optimization (O-1) in Aspen

• Vary our MCH/toluene flow rate from 50 to 500 kmol/hr

• Objective function (what we're minimizing) will be condenser duty

• Inequality constraint will be that the mole fraction of MCH in the distillate stream will be >= 0.8

• O-1 converges at an inlet MCH/toluene flow rate of 153 kmol/hr, which gives a minimum duty of -24257791.8 BTU/hr

Problem 24.2-6: An experimental filter press having an area of 0.0414 m2 (R1) is used to filter an aqueous BaCO3 slurry at a constant pressure of 267 kPa. The filtration equation obtained was where t is in s and V in m3.

a) If the same slurry and conditions are used in a leaf press having an area of 6.97 m2 , how long will it take to obtain 1.00 m3 of filtrate?

b) After filtration, the cake is to be washed with 0.100 m3 of water. Calculate the time of washing.

• Using the given t/V equation and constant pressure of 267 kPa, we can calculate time for both instances using the equation in the integrated form of KAV^2/2 + BV

• We solve for KA and B, which come out to be 723 and 20.2, respectively

• We then plug that back into the integrated equation to solve for time

Some general knowledge about PFD's and P&ID's that would be useful in industry

• Here is an example PFD of a process

• The first number corresponds to the unit that operation is a part of, the last number indicates which of that specific operation it is (multiple towers in a unit), and the letter corresponds to what it is

  • Ex: P = pump, T = tower, R = reactor, etc.

  • A/B/... indicates the presence of a spare unit operation, in case the previous one(s) fail (usually multiple with pumps)

• For P&ID's(process and instrumentation diagram), it takes the PFD into more detail

  • Symbols and circles used to represent each instrument

  • The first letter represents the measured variable for the instrument (Pressure, level, flow, temperature)

  • The next letters represent the function of the instrument (Indicator, recorder, controller, transmitter)

  • Number below represents what value the variable is at

Problem 5.2-2: Methane gas is being pumped through a 305-m length of 52.5-mm-ID steel pipe at the rate of 41.0 kg/m2 · s. The inlet pressure is p1 = 345 kPa abs. Assume isothermal flow at 288.8 K.

a. Calculate the pressure p2 at the end of the pipe.

• The viscosity is 1.04 × 10 –5 Pa · s.

• Considering the material and its size, we can obtain friction factor f from the relative roughness

• We can then use this in the pressure drop equation, assuming methane is behaving as an ideal gas, and obtain a p2 = 298 kPa

Problem 7.1-1: Using Fig. 7.1-2 and a flow rate of 60 gal/min, do as follows:

a. Calculate the brake hp of the pump using water with a density of 62.4 lbm/ft 3 .

b. Do the same for a nonviscous liquid having a density of 0.85 g/cm3 .

• Obtaining a mass flow rate from the volumetric flow rate and density yields 8.341 lbm/s

• Now that we have a mass flow rate, we can use that to get brake power which is equal to 0.60 kW.

• Getting the brake power for a nonviscous fluid results in a lower power of 0.51kW

• These results make sense since the nonviscous liquid is less resistant to flow, which is what the pump is inducing

Problem 22.1-4: A gas mixture at 2.026 × 10 5 Pa total pressure containing air and SO2 is brought into contact in a single-stage equilibrium mixer with pure water at 293 K.

The partial pressure of SO2 in the original gas is 1.52 × 10 4 Pa. The inlet gas contains 5.70 total kg mol and the inlet water 2.20 total kg mol. The exit gas and liquid leaving are in equilibrium.

Calculate the amounts and compositions of the outlet phases. Use equilibrium data from Fig. 22.2-1.

• From equilibrium data, we obtain a Henry's Law relationship of yA1 = 14.8xA1

• We can then solve for mole fractions xA1 and yA1

• Finally, using these mole fractions, we can find the outlet liquid and gas streams, L1 and V1

Problem 26.2-1: A mixture of 100 mol containing 60 mol % n-pentane and 40 mol % n-heptane is vaporized at 101.32 kPa abs pressure until 40 mol of vapor and 60 mol of liquid in equilibrium with each other are produced. This occurs in a single-stage system and the vapor and liquid are kept in contact with each other until vaporization is complete. The equilibrium data are given in Example 26.3-2. Calculate the composition of the vapor and the liquid.

• I rewrote the eq. data shown in the table on the right

• Using this data, I produced the plot shown on the right to obtain the relationship between x1 and y1

• Taking the trend line curve equation, we can then produce a quadratic to solve for mole fractions of pentane and heptane in the vapor and liquid phases

Problem 24.2-1: Data for the filtration of CaCO3 slurry in water at 298.2 K (25°C) are reported as follows (R1, R2, M1) at a constant pressure (–Δp) of 46.2 kN/m2 (6.70 psia). The area of the plate-and-frame press was 0.0439 m2 (0.473 ft 2 ) and the slurry concentration was 23.47 kg solid/m3 filtrate. Calculate the constants α and Rm. Data are given as t = time in s and V = volume of filtrate collected in m3 .

• First, I plotted V vs t/V fromthe data in the table

• Using the line of best fit to solve for y-intercept results in a y-intercept of 28232

• A more accurate slope can be obtained using m = kp/2

• Now, with these values we can obtain alpha (specific cake resistance) and Rm (resistance due to medium)

Homework 3 Problem 2: To enhance the effective surface, and hence the chemical reaction rate, catalytic surfaces often take the form of porous solids. One such solid may be visualized as consisting of a larger number of cylindrical pores, each of diameter D and length L.

Consider conditions involving a gaseous mixture of A and B for which species A is chemically consumed at the catalytic surface. The reaction is known to be first order k₁C_A. Under steady state, flow over the porous solid is known to maintain a fixed value of the molar concentration C_A0 at the pore mouth.

Beginning from fundamentals, obtain the differential equation that governs the variation of C_A with distance x along the pore. Applying appropriate boundary conditions, solve the equation to obtain an expression for C_A(x).

Quiz 2 Question 2

At the inlet to a constant diameter section of the Alaskan pipeline, pressure is 8.5*10^6 Pa and elevation is at 45m inlet, 115m outlet. Calculate the outlet pressure using the Bernoulli equation. Why might this be different from results obtained in Aspen?

Homework 3 Problem 3: Butane (C4H10) is to be isomerized to isobutane in a plug-flow reactor. This liquid-phase elementary reaction is done adiabatically at a high pressure (25 atm). A feed stream of 0.9 mole fraction regular n-butane and 0.1 mole fraction i-pentane (an inert molecule also known as 2-methyl-butane) is introduced to the reactor at 330 K, 25 atm and at a rate of 160 kmol/hr. The kinetic data for the forward and reverse reactions are as follows:

o Forward: k=0.008639; E=6.57e+07 J/kmol; To=360 K

o Reverse: k=0.003442; E=7.26e+07 J/kmol; To=360 K

a) Find the PFR volume necessary to process this feed stream with a 70% conversion of butane. Remember to explain the Property Method you chose for this simulation and why you chose it.

b) Plot product-stream molar composition and reactor temperature as a function of reactor length.

c) Use a Sensitivity Analysis to determine volume of a CSTR required to achieve the same conversion under the same conditions. Discuss why you think this is the case.

Homework 2 Problem 1: Shantal, an intern you supervise at the chemical company you work for, notices a flow rate problem with one of the water pipes on your production floor. The poor flow rate is due to three reasons: The city water pressure at the water meter is poor (P=200 kPa); the piping has a small diameter (D=1.27 cm) and has been crudded up, increasing its roughness (e/D=0.05); and the inlet to the reactor using the water is 15 m higher than the water meter.

Shantal proposes two possible solutions to the problem. Option 1 is replacing all the piping after the water meter with new smooth piping (e/D=0.00) with a diameter of 1.9 cm. Option 2 is installing a booster pump while keeping the original pipes; the booster pump has an outlet pressure of 300 kPa, which would be installed at ground-level on your production floor. She has taken it upon herself to do the math and comes to the conclusion that Option 2 would increase the pressure (P₂) at the pipe outlet more than Option 1 would.