CHE 441 ______
LAST NAME, FIRST
Problem set #10
1. Run the program Basis and turn in the last display of the program.
2. A low density thin-film polyethylene membrane with a thickness of 0.1 mm is proposed to separate 40,000 m3/h of air into an enriched oxygen stream and an enriched nitrogen stream. The air is compressed, cooled, and purified before entering the membrane at 25oC and 10 atm. The pressure on the permeate side of the membrane is 1 atm. Assume perfect mixing on both sides of the membrane so that compositions are uniform and equal to the exit composition. Neglect pressure drop and mass transfer resistances on both sides of the membrane. Composition of the feed air stream may be assumed to be 21 mol percent oxygen and 79 mol percent nitrogen. Determine the membrane surface area required for a stage cut (fraction of feed permeated) of 0.3. The following data are available at 25oC.
O2 / N2Diffusivity Di, cm2/s
Henry’s law constant Hi, cm3(STP)/(cm3×Pa) / 4.62´10-7
4.72´10-7 / 3.2´10-7
2.28´10-7
Ans: 35,900 m2
3. The endothermic liquid-phase elementary reaction A + B ® 2C proceeds to 80% completion (based on A) in a single steam-jacketed, continuous-stirred reactor (Table 9-3). From the following data, the steady-state temperature is calculated to be 231.8oF
Reactor volume: 40 ft3 Steam jacked area: 50 ft2
Jacket steam: (400oF saturation temperature)
Overall heat-transfer coefficient of jacket, U: 150 Btu/hr×ft2×oF
Volumetric flow rate is 12.0 ft3/hr
Heat of reaction, D= 15,000 Btu/lbmol of A at 68oF.
Table 9-3
ComponentA / B / C
Feed (lbmol/hr)
Feed temperature (oF)
Specific heat (Btu/lbmol×oF) / 40.0
80.0
51.0 / 40.0
80.0
44.0 / 20
80
55.0
From the steady state energy balance for a flow reactor
- - FA0- DHRx(T)FA0X = 0, determine
a. (Btu/hr) = 1.26´106 Btu/hr
b FA0(Btu/hr) = 7.438´105 Btu/hr
c. DHRx(T)FA0X (Btu/hr) = 5.595 Btu/hr
d. The reaction rate constant k = 1.8 ft3/lbmol×hr
4. An absorption refrigeration system using an NH3-H2O system is shown in Figure 1. The purpose of the cycle is to absorb 8×106 Btu/hr of energy as heat into the refrigerator at a temperature of about 0oC. For the conditions shown, calculate
a) The amount of 97.5 wt% NH3 going to the refrigerator.
b) The concentration and quantity of strong liquor fed to the column.
: Chemical Process Analysis: Mass and Energy balances by Luyben and Wenzel.
Figure 1. An absorption refrigeration system using NH3-H2O.
Solution
a) The amount of 97.5 wt% NH3 going to the refrigerator. = 16,461 lb/hr
b) The concentration and quantity of strong liquor fed to the column.
xs = 0.3111
5. A valve tray tower has been designed to separate a mixture of 60 mol percent benzene and 40 mol percent toluene into an overhead product containing 96 mol percent benzene and a bottom product containing 25 mol percent benzene. Calculations have shown that 6.1 theoretical stages will be required to obtain the desired separation conducted essentially at atmospheric pressure. The temperature at the top of the column is 82.8oC while at the bottom of the column it is 100.5oC. Assuming the reboiler acts as one theoretical stage, estimate the number of actual trays required. To simplify the calculation, assume that mixtures of benzene and toluene may be considered as ideal. At an average temperature of 91.6oC, the vapor pressure of pure benzene is 1070 mmHg, and the vapor pressure of pure toluene is 429 mmHg. Use propw program to determine the viscosity of 60 mol percent benzene and 40 mol percent toluene mixture at 91.6oC.
Ans: 9 actual trays.
6. [3]A feed mixture enters a distillation column at a rate of 200 moles/hr. The feed has the following composition:
FRL / Benzene / Toluene / Xylene / CumeneMole fraction / 0.20 / 0.30 / 0.10 / 0.40
Relative volatility / 2.25 / 1.00 / 0.33 / 0.21
The feed enters as a two-phase mixture that is 30% vapor. The column has a partial reboiler and a total condenser. Feed is returned to the column from the condenser as a saturated liquid. The specifications require that 99.8% of the cumene be recovered in the bottoms and 99.5% of the toluene be recovered in the distillate. The equilibrium data can be represented by constant relative volatilities. We have decided to operate at total reflux. What is the recovery of xylenes in the distillate using the following equation:
Nmin =
Ans: = 0.05313
7.[4] For a process, the following process streams must be cooled or heated:
StreamNumber / Cp
(Btu/hroF) / Tin
(oF) / Tout
(oF)
1
2
3
4 / 2000
4000
3000
2000 / 400
300
90
170 / 320
100
310
310
Use the MUMNE algorithm for heat-exchanger networks and a minimum approach temperature of 10oF.
a. Determine the temperature interval diagram.
b. Determine the cascade diagram, the pinch temperature, and the minimum hot and cold utilities.
c. Determine the minimum number of heat exchangers above and below the pinch.
d. Determine the heat-exchange network above the pinch.
e. Determine the heat-exchange network below the pinch.
Solution
a. Determine the temperature interval diagram.
b. Determine the cascade diagram, the pinch temperature, and the minimum hot and cold utilities.
c. Determine the minimum number of heat exchangers above and below the pinch.
d. Determine the heat-exchange network above the pinch.
Above the pinch, Cph < Cpc
e. Determine the heat-exchange network below the pinch.
Below the pinch, Cph > Cpc
8. The reaction A + B ® Product is first order in A and one-half order in B, and has an activation energy of 90 kJ/mol. Gas constant Rg = 8.314 J/mol×K. Determine ratio of the rate of disappearance of A at condition 2 to the rate of disappearance of A at condition 1.
Condition 1 / T = 573 K / CA = 1.5 mol/L / CB = 2.0 mol/LCondition 2 / T = 623 K / CA = 1.0 mol/L / CB = 2.5 mol/L
Ans: 3.395
[3] J. D. Seader and E. J. Henley, Separation Process Principles, Wiley, 1998
[4] Turton et al, Analysis, Synthesis, and Design of Chemical Processes, Prentice Hall, 2012, pg 543.