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 90F 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 86.86F 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 Pad = m 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 Latm/molK. 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 4.4810-3 (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/moloK. 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 = 3.7610-4 (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 = 4.71109 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.