# Problem set #6

```CHE 441
__________________
LAST NAME, FIRST
Problem set #6
1) A 1000 lb-mole per hour mixture of 5% methane, 20% ethane, 25% propane, 30% n-butane,
and 20% n-pentane at 14.7 psia and 90F is to be compressed first to 50 psia, then to 200 psia
using a two-stage compressor system. For the second stage, 938.3 lb-mole per hour mixture of
5.32% methane, 21.19% ethane, 26.11% propane, 29.90% n-butane, and 17.48% n-pentane at 44
psia and 86.86F is to be compressed to 200 psia. Determine the power required for each stage
assuming an adiabatic efficiency of 80% for the compressor and compare the results with Hysys
(or another process simulation software). Determine the temperatures of the compressed gas and
compare the results with Hysys.
 is
The adiabatic power, Pad, required for a single stage compression of a gas mass flow rate m
given by
k 1


RT1k  P2  k
 w = m Z
   1

M (k  1)  P1 


Where Z is the compressibility factor
R is the gas constant = 1.98 Btu / (lb-moles- deg R)
M is the molecular weight of the gas
T1 is the inlet temperature in degree R
Degree R = Degree F + 459.7
k = Cp/Cv
m is the mass flow rate of the gas in lbm/sec
The actual power for compression Pactual = Pad/a where a is the efficiency of the compressor
The temperature of the compressed gas T2 is calculated by
k 1
(T2) ideal = T1 (P2/P1) B, B =
, (T2) Actual – T1 = ((T2) ideal – T1)/ a
k
You might use the Prop program to determine Cp of the gas mixture and Cv = Cp  R.
2) Consider an air cooler where the flow rate of liquid is large compared to the air, and the
effectiveness, , of the cooler is known to depend on the flow rate of air according to the relation,
-0.3
 ~ mair . The air inlet temperature is 25oC and the liquid inlet temperature is 120oC.
a. If the airflow rate increases 80%, the percentage increase in the heat removal is __________
At a given airflow rate the outlet air temperature is 55oC
b. When the airflow rate increases 50%, the heat transfer increases 20%, the new air outlet
temperature is
__________
c. When the airflow rate increases 100%, the heat transfer increases 40%, the new air outlet
temperature is
__________
3) The elementary gas-phase reaction (CH3)3COOC(CH3)3  C2H6 + 2CH3COCH3 is carried
out isothermally in a batch reactor at 12 atm and 400 K starting with pure di-tert-butyl
peroxide[(CH3)3COOC(CH3)3]. The down time for the batch reactor is 4 hours. The specific
reaction rate constant at 400 K is 0.05/min. Gas constant Rg = 0.08205 Latm/molK.
a) Determine the batch reaction time for 90% conversion.
b) If the batch reaction time is 2 hours what reactor size would be required to process 3000
moles of di-tert-butyl peroxide per day?
.
4) Triphenyl methyl ether is produced from the reaction of triphenyl methyl chloride with
methanol, both dissolved in benzene, according to the following reaction:
CH3OH + (C6H5)3CCl → (C6H5)3COCH3 + HCl
The reaction is second-order for methanol and first-order for triphenyl methyl chloride with a
rate constant of 4.4810-3 (m3/kmol)2/s at 298oK, 101 kPa. Feed concentrations are 0.11 kmol/m3
for the triphenyl methyl chloride and one-half that concentration for the methanol.
a) For 50 percent conversion of methanol utilizing a singl CSTR, calculate the required reactor
space time.
b) What reactor type, CSTR, PFR, or batch, would you recommend for this reaction?
5) Instead of expanding T cells in a batch reactor, you decide to expand them in a CSTR.
Assume that you are growing cells in a 1 L CSTR, with a volumetric flow rate of feed and exit at
0.0294L/h. If, at some point in time, a bacterial contaminant gets introduced in the feed stream
at a concentration of 10 cells/L, and the bacteria grows at a rate rB= kCB where k= 0.46 h-1, how
long will it be before the concentration of bacteria in the reactor (and in the outlet stream with
the T cells) is 105 cells/L.
6) The ester ethyl acetate is produced by the reversible reaction
CH3COOH + C2H5OH  CH3COOC2H5 + H2O
(1)
The heat of formation at 25oC are given: HAo =  486.18 kJ/mol, HEo =  277.61 kJ/mol, HEAo =
 463.25 kJ/mol, HWo =  285.77 kJ/mol. The subscripts EA, A, E, and W denote ethyl acetate,
acetic acid, ethanol, and water respectively. Determine the heat of reaction (1) at 500oC if Cp =
 13.39 J/moloK.
7) An aqueous glucose stream is to be catalytically hydrogenated to sorbitol in a slurry tank
reactor. Feeds to the reactor are an aqueous stream with a concentration of 2.6 kmol/m3 at a flow
rate of 10-3 m3/s and a 120 percent of stoichiometric hydrogen gas stream. The reaction is to be
operated isothermally at 423oK, where the reaction is observed to follow the kinetics shown here:
− rglucose = k(Chydrogen)0.6Cglucose, where k = 3.7610-4 (kmol/m3)-0.6s-1
The reaction is conducted at 10,000 kPa, the solubility of hydrogen may be assumed to be 5
kmol/m3 at this pressure.
The actual kinetics of the reaction require adjustment to account for catalyst mass transfer effect.
Neglecting these effects, calculate the conversion for a 2-m3 CSTR.
8) Dilute propylene oxide is to be catalytically hydrolyzed to propylene glycol in an adiabatic
PFR according to the kinetics
63,010  -1
− rpropylene oxide = kCpropylene oxide, where k = 4.71109 exp 
s
 RT 
R = 8.314 kJ/kmol∙K
The reaction is conducted isothermally at 300oK. The feed consists of a 10 weight percent
aqueous stream of propylene oxide at 300oK with a flow rate of 0.01 m3/s. Water stream
containing 0.1 weight percent aqueous sulfuric acid (the catalyst) at 300oK is added at a flow rate
of 0.01 m3/s. Size the reactor to achieve 90 percent conversion.
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