4 Bioprocess Engineering questions attached along with Steam tables indexAnswers ideally provided in Excel
Solutions may be hand-written, or typed, or done in Excel. For all questions, be sure to list any assumptions made during the calculations. Ensure that the solution clearly outlines the method and the calculations used in obtaining the solution. Weighting for Marks: question 1 = 25 % question 2 = 25 % question 3 = 25 % question 4 = 25 % Question 1 (i) In a continuous bioreactor system, air sparging through the system evaporates 20 g/h of water. If the bioreactor is to be maintained at 33°C, how much heat must be put into the system to compensate for this evaporative loss? (ii) Steam is used to heat nutrient medium in a continuous-flow process. Saturated steam at 150°C enters a coil on the outside of the heating vessel and is completely condensed. Medium enters the vessel at 15°C and leaves at 44°C. Heat losses from the jacket to the surroundings are estimated as 0.22 kW. If the flow rate of medium is 2350 kg/h and the heat capacity is 3.8 kJ/kg/°C, how much steam is required? (iii) During its exponential phase, the growth rate of a culture is proportional to the concentration of live cells present. If the concentration of cells of a bacteria doubles in 45 minutes, how many cells will be present (relative to the initial level) if this growth rate is maintained for 12 hours? Question 2 To ensure turbulent conditions and minimum mixing time during agitation with a turbine impeller, the Reynolds number should be at least 104. (i) A stirred laboratory-scale vessel with a turbine impeller 5 cm in diameter is operated at 800 rpm. If the density of the broth being stirred is similar to that of water, then what is the upper limit for the viscosity of the suspension if adequate mixing is to be maintained? (ii) The mixing system is scaled up so that the diameter of the tank and its impeller is 15 times larger than the lab-scale system. The stirrer in the large vessel is operated so that the stirrer tip speed (=pND) is the same as in the laboratory system. How does the scale-up under these conditions affect the maximum allowable viscosity? Question 3 A heat exchanger contains 60 tubes, each with a length of 14 m and a diameter of 1 cm. If the exchanger heats 5 kg s-1 of water from 20°C to 70°C as it flows through the tubes, using condensing steam at 120°C, estimate the heat transfer coefficient for the exchanger. Question 4 In a 2,000 litre jacketed vessel, the available heat transfer area in the external jacket is 5 m2. Chilled water at 10°C is available to maintain the reactor contents at 30°C. Estimate the required water flowrate (G kg h-1), if the exit water temperature is not to exceed 20°C. The heat transfer coefficient (U W m-1 °C-1) is given by the expression (Hint: find G by trial & error; i.e. guess value for G, check if guess can be proved correct or incorrect.) cen2932x_ch18-ap01_p907-956.qxd Table A–1 Molar mass, gas constant, and critical-point properties Table A–2 Ideal-gas specific heats of various common gases Table A–3 Properties of common liquids, solids, and foods Table A–4 Saturated water—Temperature table Table A–5 Saturated water—Pressure table Table A–6 Superheated water Table A–7 Compressed liquid water Table A–8 Saturated ice–water vapor Figure A–9 T-s diagram for water Figure A–10 Mollier diagram for water Table A–11 Saturated refrigerant-134a— Temperature table Table A–12 Saturated refrigerant-134a— Pressure table Table A–13 Superheated refrigerant-134a Figure A–14 P-h diagram for refrigerant-134a Figure A–15 Nelson–Obert generalized compressibility chart Table A–16 Properties of the atmosphere at high altitude Table A–17 Ideal-gas properties of air Table A–18 Ideal-gas properties of nitrogen, N2 Table A–19 Ideal-gas properties of oxygen, O2 Table A–20 Ideal-gas properties of carbon dioxide, CO2 Table A–21 Ideal-gas properties of carbon monoxide, CO Table A–22 Ideal-gas properties of hydrogen, H2 Table A–23 Ideal-gas properties of water vapor, H2O Table A–24 Ideal-gas properties of monatomic oxygen, O Table A–25 Ideal-gas properties of hydroxyl, OH Table A–26 Enthalpy of formation, Gibbs function of formation, and absolute entropy at 25°C, 1 atm Table A–27 Properties of some common fuels and hydrocarbons Table A–28 Natural logarithms of the equilibrium constant Kp Figure A–29 Generalized enthalpy departure chart Figure A–30 Generalized entropy departure chart Figure A–31 Psychrometric chart at 1 atm total pressure Table A–32 One-dimensional isentropic compressible-flow functions for an ideal gas with k � 1.4 Table A–33 One-dimensional normal-shock functions for an ideal gas with k � 1.4 Table A–34 Rayleigh flow functions for an ideal gas with k � 1.4 PROPERTY TABLES AND CHARTS (SI UNITS) 907 APPENDIX 1 cen2932x_ch18-ap01_p907-956.qxd 12/18/09 10:05 AM Page 907 TABLE A –1 Molar mass, gas constant, and critical-point properties Gas Critical-point properties Molar mass, constant, Temperature, Pressure, Volume, Substance Formula M kg/kmol R kJ/kg·K* K MPa m3/kmol Air — 28.97 0.2870 132.5 3.77 0.0883 Ammonia NH3 17.03 0.4882 405.5 11.28 0.0724 Argon Ar 39.948 0.2081 151 4.86 0.0749 Benzene C6H6 78.115 0.1064 562 4.92 0.2603 Bromine Br2 159.808 0.0520 584 10.34 0.1355 n-Butane C4H10 58.124 0.1430 425.2 3.80 0.2547 Carbon dioxide CO2 44.01 0.1889 304.2 7.39 0.0943 Carbon monoxide CO 28.011 0.2968 133 3.50 0.0930 Carbon tetrachloride CCl4 153.82 0.05405 556.4 4.56 0.2759 Chlorine Cl2 70.906 0.1173 417 7.71 0.1242 Chloroform CHCl3 119.38 0.06964 536.6 5.47 0.2403 Dichlorodifluoromethane (R-12) CCl2F2 120.91 0.06876 384.7 4.01 0.2179 Dichlorofluoromethane (R-21) CHCl2F 102.92 0.08078 451.7 5.17 0.1973 Ethane C2H6 30.070 0.2765 305.5 4.48 0.1480 Ethyl alcohol C2H5OH 46.07 0.1805 516 6.38 0.1673 Ethylene C2H4 28.054 0.2964 282.4 5.12 0.1242 Helium He 4.003 2.0769 5.3 0.23 0.0578 n-Hexane C6H14 86.179 0.09647 507.9 3.03 0.3677 Hydrogen (normal) H2 2.016 4.1240 33.3 1.30 0.0649 Krypton Kr 83.80 0.09921 209.4 5.50 0.0924 Methane CH4 16.043 0.5182 191.1 4.64 0.0993 Methyl alcohol CH3OH 32.042 0.2595 513.2 7.95 0.1180 Methyl chloride CH3Cl 50.488 0.1647 416.3 6.68 0.1430 Neon Ne 20.183 0.4119 44.5 2.73 0.0417 Nitrogen N2 28.013 0.2968 126.2 3.39 0.0899 Nitrous oxide N2O 44.013 0.1889 309.7 7.27 0.0961 Oxygen O2 31.999 0.2598 154.8 5.08 0.0780 Propane C3H8 44.097 0.1885 370 4.26 0.1998 Propylene C3H6 42.081 0.1976 365 4.62 0.1810 Sulfur dioxide SO2 64.063 0.1298 430.7 7.88 0.1217 Tetrafluoroethane (R-134a) CF3CH2F 102.03 0.08149 374.2 4.059 0.1993 Trichlorofluoromethane (R-11) CCl3F 137.37 0.06052 471.2 4.38 0.2478 Water H2O 18.015 0.4615 647.1 22.06 0.0560 Xenon Xe 131.30 0.06332 289.8 5.88 0.1186 *The unit kJ/kg·K is equivalent to kPa·m3/kg·K. The gas constant is calculated from R � Ru /M, where Ru � 8.31447 kJ/kmol·K and M is the molar mass. Source: K. A. Kobe and R. E. Lynn, Jr., Chemical Review 52 (1953), pp. 117–236; and ASHRAE, Handbook of Fundamentals (Atlanta, GA: American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc., 1993), pp. 16.4 and 36.1. 908 PROPERTY TABLES AND CHARTS cen2932x_ch18-ap01_p907-956.qxd 12/18/09 10:05 AM Page 908 TABLE A–2 Ideal-gas specific heats of various common gases (a) At 300 K Gas constant, R cp cv Gas Formula kJ/kg·K kJ/kg·K kJ/kg·K k Air — 0.2870 1.005 0.718 1.400 Argon Ar 0.2081 0.5203 0.3122 1.667 Butane C4H10 0.1433 1.7164 1.5734 1.091 Carbon dioxide CO2 0.1889 0.846 0.657 1.289 Carbon monoxide CO 0.2968 1.040 0.744 1.400 Ethane C2H6 0.2765 1.7662 1.4897 1.186 Ethylene C2H4 0.2964 1.5482 1.2518 1.237 Helium He 2.0769 5.1926 3.1156 1.667 Hydrogen H2 4.1240 14.307 10.183 1.405 Methane CH4 0.5182 2.2537 1.7354 1.299 Neon Ne 0.4119 1.0299 0.6179 1.667 Nitrogen N2 0.2968 1.039 0.743 1.400 Octane C8H18 0.0729 1.7113 1.6385 1.044 Oxygen O2 0.2598 0.918 0.658 1.395 Propane C3H8 0.1885 1.6794 1.4909 1.126 Steam H2O 0.4615 1.8723 1.4108 1.327 Note: The unit kJ/kg·K is equivalent to kJ/kg·°C. Source: Chemical and Process Thermodynamics 3/E by Kyle, B. G., © 2000. Adapted by permission of Pearson Education, Inc., Upper Saddle River, NJ. 909 APPENDIX 1 cen2932x_ch18-ap01_p907-956.qxd 12/18/09 10:05 AM Page 909 TABLE A–2 Ideal-gas specific heats of various common gases (Continued) (b) At various temperatures cp cv cp cv cp cv Temperature, kJ/kg·K kJ/kg·K k kJ/kg·K kJ/kg·K k kJ/kg·K kJ/kg·K k K Air Carbon dioxide, CO2 Carbon monoxide, CO 250 1.003 0.716 1.401 0.791 0.602 1.314 1.039 0.743 1.400 300 1.005 0.718 1.400 0.846 0.657 1.288 1.040 0.744 1.399 350 1.008 0.721 1.398 0.895 0.706 1.268 1.043 0.746 1.398 400 1.013 0.726 1.395 0.939 0.750 1.252 1.047 0.751 1.395 450 1.020 0.733 1.391 0.978 0.790 1.239 1.054 0.757 1.392 500 1.029 0.742 1.387 1.014 0.825 1.229 1.063 0.767 1.387 550 1.040 0.753 1.381 1.046 0.857 1.220 1.075 0.778 1.382 600 1.051 0.764 1.376 1.075 0.886 1.213 1.087 0.790 1.376 650 1.063 0.776 1.370 1.102 0.913 1.207 1.100 0.803 1.370 700 1.075 0.788 1.364 1.126 0.937 1.202 1.113 0.816 1.364 750 1.087 0.800 1.359 1.148 0.959 1.197 1.126 0.829 1.358 800 1.099 0.812 1.354 1.169 0.980 1.193 1.139 0.842 1.353 900 1.121 0.834 1.344 1.204 1.015 1.186 1.163 0.866 1.343 1000 1.142 0.855 1.336 1.234 1.045 1.181 1.185 0.888 1.335 Hydrogen, H2 Nitrogen, N2 Oxygen, O2 250 14.051 9.927 1.416 1.039 0.742 1.400 0.913 0.653 1.398 300 14.307 10.183 1.405 1.039 0.743 1.400