Homework #1 1.18 Nitrogen gas can be injected into oil wells to increase the recovery of crude oil (enhanced oil recovery). Usually, natural gas is produced with the oil and it is desirable to recover the nitrogen from the gas for reinjection into the well. Furthermore, the natural gas must not contain more than 3 mol% nitrogen if the natural gas is to be put into a pípeline. A total of 170,000 SCFH (based on 60°F and 14.7 psia) of natural gas containing 18% N2, 75% CH4, and 7% C2Hs at 100°F and 800 psia is to be processed for N2 removal. A two-step separation process has been proposed consisting of (1) membrane, separation with a nonporous glassy poly imide membrane, followed by (2) pressure-swing adsorption using molecular sieves to which the permeate gas is fed. The membrane separator is highly selective for N2 (SPn,,cH 16) and completely impermeable to ethane. The pressure- swing adsorption step selectively adsorbs methane, giving 97% pure methane product in the adsorbate, with an 85% recovery of CH4 fed to the adsorber. The nonpermeate (re tentate) gas from the membrane step and adsorbate from the pressure-swing adsorption step are combined to give a methane stream that contains 3.0% N2. The pressure drop across the membrane is 760 psia. The permeate at 20°F is compressed in two stages to 275 psia and cooled to 100°F before entering the adsorption step. The adsorbate gas, which exits the adsorber during regeneration at 100°F and 15 psia, is compressed in three stages to 800 psia and cooled to 100°F before being combined with nonpermeate gas to give the final pipeline natural gas (a) Draw a process flow diagram of the separation process using appropriate symbols from Tables 1.2 and 1.3. Include the gas compressors and heat exchangers. Label the diagram with all of the data given above, and number all process streams. (b) Compute by material balances, using' the data above, the component flow rates of N2, CH4, and C2Hs in Ibmol/h for all process streams entering and exiting the two separa tion operations. Place the results in a material balance table similar to Table 1.5 21 시 4

21. A large containment is filled with steam, air, and nitrogen. The containment also has a pool of water, which is sprayed in the containment atmosphere. Heat is added to the con- tainment at a specified rate. Use the given data to find a) the initial containment pressure and b) the time it takes for the containment pressure to reach the pressure limit of 145 psia (1 MPa). Total mass of water (water in the pool and steam) m,, = 3.42E6 lbm (1.55E6 kg) Water-steam quality x = 0.03 Air mass m, = 0.132E6 lbm (6E4 kg) Nitrogen mass m, = 2200 lbm (998 kg) Containment initial temperature T; = 688 R (109 C) Initial relative humidity ø = 100% Rate of heat addition to containment atmosphere Q = 1.02E8 Btu/h (30 MW) [Ans.: 7.66 h].

Boiling Point Elevation/Freezing Point DepressionT = m KWhere: T = T(solution) - T(pure solvent) * m = (# moles solute / Kg solvent) Kb = boiling point elevation constant. Kf = freezing point depression constant. Kb and Kf depend only on the SOLVENT. Below are some common values. Use these values for the calculations that follow. Solvent Formula Kb (°C / m) Kf (°C / m) Water H2O 0.512 -1.86 Ethanol CH3CH2OH 1.22 -1.99 Chloroform CHCl3 3.67   Benzene C6H6 2.53 -5.12 Diethyl ether CH3CH2OCH2CH3 2.02   *Please note that ΔT as defined above will be a negative number for freezing point depression. Therefore, Kf must also be given as a negative number.

2. Fruit is impeded from ripening when it reaches high temperatures (>32°C). Farmer Joe is roo worried that Princeton's summer heat wave will affect the ripening of his ground cherries. The spherical fruit (1 cm in diameter) is surrounded by a spherical papery husk (husk = 0.3 W/m K) with an inner diameter of 2 cm and an outer diameter of 2.1 cm. The air in between the fruit and the husk is stagnant (air = 0.03 W/m K). On a calm day in July, the Princeton air (outside of the husk) is very warm, with a temperature of ~38°C and a heat transfer coefficient of hPrinceton,calm = 10 W/m².K. (a) Sketch the system, labeling all temperatures, dimensions, and proportionality constants.