4 Material Balances 8~.2.90 gmol biomass lgmolethanol ] 126.78gbiomass Yxs,max -- gmol ethanol 46 gethanol " 1 gmolbiomass Yxs,max = 1.69 g biomass g ethanol Therefore, on a mass basis, the maximum possible amount of biomass produced per gram ethanol consumed is roughly twice that per gram glucose consumed. This result is consistent with the data listed in Table 4.4. Example 4.8 illustrates two important points. First, the chem- the membrane into the buffer. Cells in the broth are too large ical reaction equation for conversion of substrate without to pass through the membrane and pass out of the tubes as a growth is a poor approximation of overall stoichiometry when concentrate. cell growth occurs. When estimating yields and oxygen requirements for any process involving cell growth, the full Figure 4P 1.1 Hollow-fibre membrane for concentration of stoichiometric equation including biomass should be used. cells. Second, the chemical nature or oxidation state of the substrate has a major influence on product and biomass yield through the number of available electrons. Fermenlalion brolh 4.7 Summary of Chapter 4 Buffer At the end of Chapter 4 you should: solution ~ ll~w-fihre lllClllbrallC (i) understand the terms: system, surroundings, boundary and process in thermodynamics; (ii) be able to identify openand closedsystems, and batch, semi- batch, fed-batch and continuous processes;, The aim of the membrane system is to produce a cell suspen- (iii) understand the difference between steady state and equi- sion containing 6% biomass. librium; (iv) be able to write appropriate equations for conservation of (a) What is the flow rate from the annular space? mass for processes with and without reaction; (b) What is the flow rate of cell suspension from the mem- (v) be able to solve simple mass-balance problems with and brane tubes? without reaction; and (vi) be able to apply stoichiometric principles for macroscop- Assume that the cells are not active, i.e. they do not grow. ic analysis of cell growth and product formation. Assume further that the membrane does not allow any mol- ecules other than water to pass from annulus to inner cylinder, or vice versa. Problems 4.1 Cell concentration using membranes 4.2 Membrane reactor A battery of cylindrical hollow-fibre membranes is operated at A battery of cylindrical membranes similar to that shown in steady state to concentrate a bacterial suspension from a fer- Figure 4Pl.1 is used for an extractive bioconversion. menter. 350 kg min-1 fermenter broth is pumped through a Extractive bioconversion means that fermentation and extrac- stack of hollow-fibre membranes as shown in Figure 4P1.1. tion of product occur at the same time. The broth contains 1% bacteria; the rest may be considered Yeast cells are immobilised within the membrane walls. A water. Buffer solution enters the annular space around the 10% glucose in water solution is passed through the annular membrane tubes at a flow rate of 80 kg min-1; because broth space at a rate of 40 kg h - 1. An organic solvent, such as 2-ethyl- in the membrane tubes is under pressure, water is forced across 1,3-hexanediol, enters the inner tube at a rate of 40 kg h-1. 4 Material. Balances 83 Because the membrane is constructed of a polymer which dehydrated egg product leaving the enzyme reactor is 0.2%. repels organic solvents, the hexanediol cannot penetrate the Determine: membrane and the yeast is relatively unaffected by its toxicity. (a) which is the limiting substrate; On the other hand, because glucose and water are virtually (b) the percentage excess substrate; insoluble in 2-ethyl-1,3-hexanediol, these compounds do not (c) the composition of the reactor off-gas; and enter the inner tube to an appreciable extent. Once immobil- (d) the composition of the final egg product. ised in the membrane, the yeast cannot reproduce but convert glucose to ethanol according to the equation: 4.5 Azeotropic distillation C6H1206 -~ 2 C 2 H 6 0 4- 2 C O 2. Absolute or 100% ethanol is produced from a mixture of 95% ethanol and 5% water using the Keyes distillation process. A Ethanol is soluble in 2-ethyl-l,3-hexanediol; it diffuses into third component, benzene, is added to lower the volatility of the inner tube and is carried out of the system. CO 2 gas exits the alcohol. Under these conditions, the overhead product is a from the membrane unit through an escape valve. In the aque- constant-boiling mixture of 18.5% ethanol, 7.4% H 2 0 and ous stream leaving the annular space, the concentration of 74.1% benzene. The process is outlined in Figure 4P5.1. unconverted glucose is 0.2% and the concentration of ethanol is 0.5%. If the system operates at steady state: Figure 4P5.1 Flowsheet for Keyes distillation process. (a) What is the concentration of ethanol in the hexanediol stream leaving the reactor? (b) What is the mass flow rate of CO2? 74. 1% benzene . ~ 18.5%ethanol 7.4% water 4.3 Ethanol distillation Liquid from a brewery fermenter can be considered to contain 10% ethanol and 90% water. 50 000 kg h-1 of this fermenta- 95% ethanol ~ 1 1 m , , - tion product are pumped to a distillation column on the 5% water Distillation factory site. Under current operating conditions a distillate of Benzene ~ B I ~ - tower 45% ethanol and 55% water is produced from the top of the column at a rate one-tenth that of the feed. (a) What is the composition of the waste 'bottoms' from the still? (b) What is the rate of alcohol loss in the bottoms? L ~ 100% ethanol 4.4 Removal of glucose from dried egg The enzyme, glucose oxidase, is used commercially to remove Use the following data to calculate the volume of benzene glucose from dehydrated egg to improve colour, flavour and which should be fed to the still in order to produce 250 litres shelf-life. The reaction is: absolute ethanol: p (100% alcohol) = 0.785 g cm-3; p (ben- zene) = 0.872 g cm -3. C6H120 6 + 0 2 + H 2 0 --9 C6H120 7 + H 2 0 2. (glucose) (gluconic acid) 4.6 Culture of plant roots A continuous-flow reactor is set up using immobilised-enzyme beads which are retained inside the vessel. Dehydrated egg Plant roots produce valuable chemicals in vitro. "A batch cul- slurry containing 2% glucose, 20% water and the remainder ture of Atropa belladonna roots at 25~ is established in an unreactive egg solids, is available at a rate of 3 000 kg h - 1. Air air-driven reactor as shown in Figure 4P6.1. Because roots is pumped through the reactor contents so that 18 kg oxygen cannot be removed during operation of the reactor, it is are delivered per hour. The desired glucose level in the proposed to monitor growth using mass balances. 4 Material Balances 84 Figure 4P6.1 Reactor for culture ofplant roots. 4.8 P r o d u c t y i e l d in a n a e r o b i c d i g e s t i o n Anaerobic digestion of volatile acids by methane bacteria is Off-gas represented by the equation: Nulrien! medium ,T CH3COOH + NH 3 --9 biomass + CO 2 + H20 + CH 4. (acetic acid) (methane) The composition of methane bacteria is approximated by the empirical formula CH1.4Oo.40N0.20. For each kg acetic acid consumed, 0.67 kg CO 2 is evolved. How does the yield of methane under these conditions compare with the maximum Air-driven possible yield? Roots reaclor 4.9 Stoichiometry of single-cell protein synthesis kir (a) Cellulomonas bacteria used as single-cell protein for human or animal food are produced from glucose under anaerobic conditions. All carbon in the substrate is Drained liquid converted into biomass; ammonia is used as nitrogen source. The molecular formula for the biomass is CHI.5600.s4No.16; the cells also contain 5% ash. How does the yield ofbiomass from substrate in mass and molar terms compare with the maximum possible biomass yield? 1425 g nutrient medium containing 3% glucose and (b) Another system for manufacture of single-cell protein is 1.75% NH 3 is fed into the reactor; the remainder of the medi- Methylophilus methylotrophus. This organism is produced um can be considered water. Air at 25~ and 1 atm pressure is aerobically from methanol with ammonia as nitrogen sparged into the fermenter at a rate of 22 cm 3 min- I. During a source. The molecular formula for the biomass is 10-day culture period, 47 litres 0 2 and 15 litres CO) are col- CH 1.6800.36N0.22; these cells contain 6% ash. lected in the off-gas. After 10 days, 1110 g liquid containing (i) How does the maximum yield of biomass compare 0.063% glucose and 1.7% dissolved NH 3 is drained from the with (a) above? What is the main reason for the differ- vessel. The ratio of fresh weight to dry weight for roots is ence? known to be 14:1. (ii) If the actual yield of biomass from methanol is 42% (a) What dry mass of roots is produced in 10 days? the thermodynamic maximum, what is the oxygen (b) Write the reaction equation for growth, indicating the demand? approximate chemical formula for the roots, CHaOflN6. (c) What is the limiting substrate? 4.10 Ethanol production by yeast and bacteria (d) What is the yield of roots from glucose? Both Saccharomyces cerevisiae yeast and Zymomonas mobilis bacteria produce ethanol from glucose under anaerobic condi- 4 . 7 O x y g e n r e q u i r e m e n t for g r o w t h o n tions without external electron acceptors. The biomass yield glycerol from glucose is 0.11 g g-1 for yeast and 0.05 g g-I for Z. mobilis. In both cases the nitrogen source is NH 3. Both cell Klebsiella aerogenesis produced from glycerol in aerobic cul- compositions are represented by the formula CH 1.800.5N0.2. ture with ammonia as nitrogen source. The biomass contains 8% ash, 0.40 g biomass is produced for each g glycerol con- (a) What is the yield of ethanol from glucose in both cases? sumed, and no major metabolic products are formed. What is (b) How do the yields calculated in (a) compare with the the oxygen requirement for this culture in mass terms? thermodynamic maximum? 4 Material Balances 85 4.11 D e t e c t i n g u n k n o w n products References Yeast growing in continuous culture produce 0.37 g biomass 1. Felder, R.M. and R.W. Rousseau (1978) Elementary per g glucose consumed; about 0.88 g 0 2 is consumed per g Principles of Chemical Processes, Chapter 5, John Wiley, cells formed. The nitrogen source is ammonia, and the bio- New York. mass composition is CH1.7900.56N0.17. Are other products 2. Himmelblau, D.M. (1974) Basic Principles and also synthesised? Calculations in ChemicalEngineering, 3rd edn, Chapter 2, Prentice-Hall, New Jersey. 4.12 Medium formulation 3. Whitwell, J.C. and R.K. Toner (1969) Conservation of Mass and Energ7, Chapter 4, Blaisdell, Waltham, Pseudomonas 5401 is to be used for production of single-cell Massachusetts. protein for animal feed. The substrate is fuel oil. The composi- 4. Cordier, J.-L., B.M. Butsch, B. Birou and U. yon Stockar tion of Pseudomonas 5401 is CH 1.8300.55N0.25. If the final cell (1987) The relationship between elemental composition concentration is 25 g 1-1, what minimum concentration of and heat of combustion of microbial biomass. Appl. (NH4)2SO 4 must be provided in the medium if(NH4)2SO 4 is Microbiol. Biotechnol. 25,305-312. the sole nitrogen source? 5. Roels,J.A. (1983) EnergeticsandKinetics in Biotechnolog7, Chapter 3, Elsevier Biomedical Press, Amsterdam. 4.13 O x y g e n d e m a n d for p r o d u c t i o n o f 6. Atkinson, B. and F. Mavituna (1991) Biochemical recombinant protein Engineering and Biotechnolog7 Handbook, 2nd edn, Chapter 4, Macmillan, Basingstoke. Production of recombinant protein by a genetically- engineered strain of Escherichia coli is proportional to cell growth. Ammonia is used as nitrogen source for aerobic respi- Suggestions for Further Reading ration of glucose. The recombinant protein has an overall formula CHI.5500.31N0.25. The yield ofbiomass from glucose is measured at 0.48 g g-1; the yield of recombinant protein Process Mass Balances (see also refs 1-3) from glucose is about 20% that for cells. Hougen, O.A., K.M. Watson and R.A. Ragatz (1954) (a) How much ammonia is required? Chemical Process Principles: Material and Energ7 Balances, (b) What is the oxygen demand? 2nd edn, Chapter 7, John Wiley, New York. (c) If the biomass yield remains at 0.48 g g- l, how much dif- Shaheen, E.I. (1975) Basic Practice of Chemical Engineering, ferent are the ammonia and oxygen requirements for Chapter 4, Houghton Mifflin, Boston. wild-type E. coliunable to synthesise recombinant protein? 4 . 1 4 Effect o f g r o w t h on o x y g e n d e m a n d Metabolic S t o i c h i o m e t r y (see also ref5) Erickson, L.E., I.G. Minkevich and V.K. Eroshin (1978) The chemical reaction equation for conversion of ethanol Application of mass and energy balance regularities in fer- (C2H60) to acetic acid (C2H402) is: mentation. Biotechnol. Bioeng. 20, 1595-1621. C2H60 + 02 --~ C2H402 + H20. Heijnen, J.J. and J.A. Roels (1981) A macroscopic model describing yield and maintenance relationships in aerobic Acetic acid is produced from ethanol during growth of fermentation processes. Biotechnol. Bioeng. 23,739-763. Acetobacter aceti, which has the composition CH 1.800.5N0.2. Nagai, S. (1979) Mass and energy balances for microbial Biomass yield from substrate is 0.14 g g- 1; product yield from growth kinetics. Adv. Biochem. Eng. 11, 49-83. substrate is 0.92 g g-1. Ammonia is used as nitrogen source. Roels, J.A. (1980) Application of macroscopic principles to How does growth in this culture affect oxygen demand for microbial metabolism. Biotechnol. Bioeng. 22, acetic acid production? 2457-2514.