Case 1:18-cv-00924-CFC Document 399-5 Filed 10/07/19 Page 1 of 50 PageID #: 30654
`Case 1:18—cv-00924-CFC Document 399-5 Filed 10/07/19 Page 1 of 50 PageID #: 30654
`
`EXHIBIT 6
`
`EXHIBIT 6
`
`
`
`

`

`Case 1:18-cv-00924-CFC Document 399-5 Filed 10/07/19 Page 2 of 50 PageID #: 30655
`
`BIOCHEMICAL
`ENGINEERING
`FUNDAMENTALS
`Second Edition
`
`James E. Bailey
`California /rutirute of Technology
`
`David F. Ollis
`Nor1h Carolina State University
`
`,, .
`
`McGraw-Hill Publishing Company
`New York SL Louis San Francisco Auckland Bogoli Caracas
`Hamburg Lisbon London Madrid Mexico Milan
`Montreal New Delhi Oklahoma City
`Paris
`San Juan
`Sfo Paulo Singapore Sydney Tokyo Toronto
`
`APPX 0235
`
`

`

`Case 1:18-cv-00924-CFC Document 399-5 Filed 10/07/19 Page 3 of 50 PageID #: 30656
`
`To Sean
`and
`Andrew, Mark, Stephen, and Matthew
`
`This book was sci in Times Roman.
`The editors were Kiran Verma and Cydney C. Marti n.
`The production supervisor was Diane Renda;
`lhe cover was designed by John Hite:
`project supervision was done by Albert Harrison, Harley Editorial Services.
`Halliday Lithograph Corporation was printer and binder.
`
`BIOCHEMICAL ENGINEERING FUNDAMENTALS
`
`Copyright cC 1986, 1977 by McGraw-Hill, Inc. All rights reserved.
`Printed in the United States or America. Except as permitted under the United St111es
`Copyright Act or 1976, no part of this publication may be reproduced or distributed
`in any form or by any means, or stored in a data base or retrieval system, without
`the prior written permission or the publisher.
`
`67891011 HDHD 99876543210
`
`ISBN (cid:143) -(cid:143) 7-(cid:143)(cid:143)
`
`3212-2
`
`Library or Congress Clltaloging-in-Publicotion Data
`Bailey, James E. (James Edwin), 1944
`Biochemical engineering fundamentals.
`
`(McGraw-Hill chemical engineering series)
`Includes bibliographies and index.
`I. Ollis, David F.
`I. Biochemical engineering.
`II. Title. 111. Series
`TP248.3.B34 1986
`ISBN 0-07-003212-2
`
`85-19744
`
`660'.63
`
`, ..
`
`APPX 0236
`
`

`

`Case 1:18-cv-00924-CFC Document 399-5 Filed 10/07/19 Page 4 of 50 PageID #: 30657
`
`456 BIOCHEMICAL ENGINEERING FUNDAMENTALS
`
`Structured growlh models. Sec Rers. 5· 8 above and
`
`15. A.G. Fredrickson. "Formulation or Structured Growth Models," Bi111ed11111I. Bioeng., 18: 1481,
`1976.
`16. F. M. Williams.·• A Model or Cell Growth Dynamics," J. T/1e11re1. Biol., 15: 190, 1967.
`17. A. Harder and J. A. Rocls, "Application or Simple Structured Models in Bioengineering," p. 55.
`In Aclrcmces i11 Bioclwmirnl Engi11eering, vol. 21, A. Fiechter (ed.), Springer-Verlag, Berlin, 1982.
`18. A. H. E. Bijkerk and R. J. Hall," A Mechanistic Model or the Aerobic Growth or Saccharomyces
`cere1•i.1ie1c," Bimedmol. Bioe11g., 19: 267, 1977.
`19. N. B. Pamment, R. J. Hall, and J. P. Barford, "Mathematical Modeling or Lag Phases in
`Microbial Growth," Bio1ed11wl. Bioeng., 30: 349, 1978.
`20. M. L. Shuler and M. M. Domach, "Mathematical Models or the Growth of Individual Cells,"
`p. IOI in Fm111da1ilms of Biochemical Engineering, H. W. Blanch, E. T. Papoutsakis, and G.
`Stephanopoulos (eds.), American Chemical Society, Washington, D. C, 1983.
`21. D. Ramkrishna, "A Cybernetic Perspective of Microbial Growth," p. 161 in Foundations of Bio(cid:173)
`c/1emical E11gi11eering, H . W. Blanch, E.T. Papoutsakis, and G. Stephanopoulos (eds.), American
`Chemical Society, Washington, D.C., 1983.
`22. D. S. Kompala, D. Ramkrishna, and G . T. Tsao, "Cybernetic Modeling of Microbial Growth on
`Multiple Subslrates," 8i01ed11111I. Biocng, 26: 1272, 1984.
`
`Product rormation kinetics:
`
`23. E. L. Gaden, Chem. Ind. Rev. 1955: 154; J . Biod1cm. Microbiol. Tec/1110/. E11g., I: 413, 1959.
`24. F. H. Dcindoerfer, "Fermentation Kinetics and Model Processes," Adv. Appl. Microbial., 2: 321,
`!960.
`25. D. F. Ollis," A Simple Batch Fermentation Model: Theme and Variations," Ann. N. Y. A cad. Sci.,
`413: 144, 1983.
`26. S. Pafoutova, J. Votruba, and Z. llehacek, "A Mathematical Model of Growth and Alkaloid
`Production in the Submerged Culture of Claviceps purpurea," Biotechnol. Biocng., 23: 2837, 1981.
`27. S. B. Lee and J. E. Bailey, "Analysis of Growth Rate Effects on Productivity of Recombinant
`fad1erid1ia rn/i Populations," Biotedmol. Bioeng., 26: 66, 1984.
`28. S. B. Lee and J. E. Bailey, "Genetically Structured Models for lac Promoter-Operator Function
`in the fadierid,ia wli Chromosome and in Multicopy Plasmids: lac Operator Function,"
`Bio1ed1110(, 8ioe11g., 26: 1372. 1984,
`
`Segregated kinetic models:
`
`29. D. Ramkrishna, "Statistical Models of Cell Populations," Adv. in Bwd,em. Eng., 11 : I, 1979.
`30. Y. Nishimura and J. E. Bailey, "On the Dynamics of Cooper-Helmstetter-Donachie Procaryotc
`Populations," Mmh. Bio.Ki., 51: 505, 1980.
`31. M. A. Hjortso and J. E. Bailey, "Steady-State Growth or Budding Yeast Populations in Well(cid:173)
`Mixed Continuous Flow Microbial Reactors," Math. Biosci., 60: 235, 1982.
`32. r. Shu, "Mathematical Models for the Product Accumulation in Microbial Processes," J. Bio(cid:173)
`chcm. /lliaobiol, Tedmol. Eng., 3 : 95. 1961.
`
`An excellent introduction to the literature on sterilization:
`
`,.
`
`33. N. Blakebrough, "Preservation of Biological Materials Especially by Heat Treatment," in N.
`Blakebrough (ed.), Biochemi<'al u11d Biological Engitweri11g Sric11ce, vol. 2, Academic Press, Inc.,
`New York, I 968.
`
`The factors affecting organisms· suscepllbllity lo steriliiation arc reviewed in Chaps. 20 and 21 or
`Frobisher (Rer. 2 or Chap. I); consideration of phage destruction;
`
`34. Hango ct a l. "Phage Contamination and Control," in Microbial Productio11 of Ami11CJ Acids,
`Kodansha Ltd., Tokyo, and John Wiley & Sons, Inc., New York, 1973.
`
`.; ... -
`
`CHAPTER
`
`EIGHT
`
`TRANSPORT PHENOMENA IN
`BIOPROCESS SYSTEMS
`
`The previous chapters have considered progressively l~r~er s~al_es of dis~a~ce:
`from molecular through cellular to fluid volumes conta1D1Dg m1lhons or b1lhons
`of cells per milliliter. As the sources and sinks of en!ities such as nutrien~s: ce)ls,
`and metabolic products become further separated ID space, the proba?1hty ID·
`creases that some physical-transport phenomena, rather than a chemical rate,
`will influence or even dominate the overall rate of solute processing in the reac(cid:173)
`tion volume under consideration. Indeed, according to the argument of Weisz
`[I], cells and their component catalytic assemblies . operate at :hiclc moduli ~ear
`unity; they are operating at the maximum poss1qle rate without any serious
`diffusional limitation. If, in bioprocess circumstances, a richer supply of carbon
`nutrients is created, evidently the aerobic cell will be able to utilize them fully
`only if oxygen can also be maintained at a higher concentration in the direct
`vicinity of the cell. This situation may call for increased gas-liquid 11_iass transfer
`of oxygen, which has sparingly small solubility in aqueous solutions, to lhe
`culture.
`Evidently, the boundary demarcating aeropic from _ana:robic act!vity de-
`pends upon the local bulk-oxygen concentra~ion, fh~ ~ 2 d1~u~1on coe~c1ent, and
`the local respiration rates in the aerobic region. This hne d1v1des th~ viable fro~
`dying cells in strict aerobes such as mold in mycclial pellets or ussue cells m
`cancer tumors· it determines the depth of aerobic activity near lake surfaces; and
`it divides the ~ohabitating aerobes from anaerobic microbial communities in soil
`
`4S7
`
`APPX 0237
`
`

`

`Case 1:18-cv-00924-CFC Document 399-5 Filed 10/07/19 Page 5 of 50 PageID #: 30658
`
`458
`
`RIOCHEMICAL ENGINEFRING FUNDAMENTALS
`
`TRANSPORT PHENOMENA IN BIOPROCESS SYSTEMS
`
`459
`
`particles. Thus, while the modern roots of biological-process oxygen mass
`transfer began with World War II penicillin production in the 1940s, its implica(cid:173)
`tions arc now established to include many natural processes such as food spoil(cid:173)
`age via undesired oxidation and lake eutrophication due either to inadequate
`system aeration by natural oxygen supplies or to an excessive concentration of
`material such as phosphate or nitrate.
`Other sparingly soluble gases arc also of fermentation interest. Methane and
`other light hydrocarbons have been explored as gaseous substrates for single cell
`protein production; in this demanding conversion, both oxygen and methane
`must be dissolving continuously at rates sufficient to meet the biological demand.
`Methane transfer out of solution is important in anaerobic waste treatment, at
`the metabolic end of which light carboxylic acids (primarily acetic acid) are
`decarboxylated lo give the corresponding alkanes.
`Carbon dioxide is generated in nearly all microbial activity. In spite of its
`large solubility, the interconversion between gaseous and the various forms of
`dissolved carbon dioxide (CO2 , H 2CO3 , HCO3, Co5 - ) couples its mass transfer
`rate to the pH variation; this topic figures importantly in controlling the pH of
`acid-sensitive anaerobic digestors (Chapter 14) where CO2 and q-14 removal
`occur simultaneously.
`Liq11id- liq11id mass transfer is important in SCP production from liquid
`hydrocarbon feedstocks, as well as in fermentation recovery operations; e.g.,
`filtered or whole broth extraction of pharmaceuticals (Chapter 11) employing
`organic solvents.
`Renewable resource bioconversions, such as the use of cellulosic, hemiceltu(cid:173)
`losic, and lignin fractions of agricultural and forest wastes as fermentation feed(cid:173)
`stocks, typically involve rate processes (biomass solubilization, liquefaction,
`hydrolysis} limited by available particµlate substrate surface areas and solute
`dilTusion rates. Other topics also involving liquid-solid mass transfer include
`various sorption and chromatographic methods for product recovery and purifi(cid:173)
`cation, and liquid phase oxygen transfer to mold pellets or beads and biofilms
`containing immobilized cells.
`Operation at high cell densities may often result in mass-transfer limited
`conditions, as observed in reactors as diverse as laboratory shake flasks or large
`scale fermentors for penicillin or extracellular biopolymers (xanthan gum) or
`activated sludge waste plants. The process engineer must, accordingly, know
`when transport phenomena or biological kinetics are rate-limiting in order
`properly to design biorcactors.
`•
`Strong coupling often occurs between solute diffusion and momentum trans(cid:173)
`port or chemical reactions or (even more complex) both. The case of diffusion
`and reaction interaction has been considered in Chap. 4. In such circumstances,
`the Thiele modulus and a saturation parameter KJs0 provide the unifying
`parameters needed lo completely describe cell and enzyme performance; i.e., ef(cid:173)
`fectiveness factor, for such systems. Unfortunately, the variety of circumstances
`under which mass transfer couples with momentum transfer, i.e., fluid mechanics,
`is enormous; indeed, it is the substance of a major fraction of the chemical
`
`engineering literature. For this text, we content ourselves with fundamental c~n(cid:173)
`cepts and tabulated formulas for calculation or estimation of the appropriate
`mass-transfer coefficients for solutes.
`A final brief section of this chapter concerns instances where heat transfer
`may provide an important transport effect which stron~ly influenc<:5 the bio(cid:173)
`process system's behavior through spatial temperature inhomogeneity .. Ex?m(cid:173)
`ples here include relatively exothermic fermentation processes, such as tnckhng(cid:173)
`filter operation for wine-vinegar production or wastewater treatment, a~d that
`gardener's delight, the compost heap (municipal dump, etc.) and other sohd-state
`fermentations.
`
`8.1 GAS-LIQUID MASS TRANSFER IN
`CELLULAR SYSTEMS
`
`The general nature of the mass-transfer problem of primary concern in this
`chapter is shown schematically in Fig. 8. I. A sparingly soluble gas, usually
`oxygen, is transferred from a source, say a rising air bubble, into a _liq~id phase
`containing cells. (Any other sparingly soluble substrate, e.g., the hqu1d ~ydro(cid:173)
`carbons used in hydrocarbon fcrmentatiO!lS, will give the same general picture.)
`The oxygen must pass through a series of transport resistances, the relative mag(cid:173)
`nitudes of which depend on bubble (droplet) hydrodynamics, temperature, cellu(cid:173)
`lar activity and density, solution composition, interfacial phenomena, and other
`factors.
`These arise from different combinations of the following resistances (Fig.
`8.1 ):
`
`I. Diffusion from bulk gas to the gas- liquid interface
`2. Movement through the gas-liquiq interface
`3. Diffusion of the solute through the relatively unmixed liquid region adjacent
`to the bubble into the well-mixed bulk liquid
`4. Transport of the solute through the bulk liquid to a second relatively
`unmixed liquid region surrounding the cells
`5. Transport through the second unmixed liquid region associated with the cells
`6. Diffusive transport into the cellular floe, mycclia, or soil particle
`7. Transport across cell envelope and to intracellular reaction site
`
`All of these resistances appear in Fig. 8. I. When the organisms take the form
`of individual cells, the sixth resistance disappears. Microbial cells themselves have
`some tendency to adsorb at interfaces. Thus, cells may preferentially gather at the
`vicinity of the gas-bubble-liquid interface. Then, the dilfus_ing_ solute oxygen
`passes through only one unmixed liquid region and no bulk l~qu1d before reach(cid:173)
`ing the cell. In this situation, the bulk dissolved 0 2 concentration docs not repre(cid:173)
`sent the oxygen supply for the respiring microbes.
`
`l
`
`APPX 0238
`
`

`

`Case 1:18-cv-00924-CFC Document 399-5 Filed 10/07/19 Page 6 of 50 PageID #: 30659
`
`BIOCHEMICAL ENGINEERING FUNDAMENTALS
`
`TRANSPORT PHENOMENA IN BIOPROCESS SYSTEMS
`
`460
`
`x
`
`Gas
`bubble
`
`/
`
`\
`\
`\
`\
`Q) I
`~ ~
`<D
`I
`@
`I
`I
`I
`I
`I
`I
`
`stag~ant
`region
`
`\
`
`/
`Stagnant
`region~
`I
`I
`I
`I
`I ®
`\~
`I @
`\
`\
`\
`\
`\
`
`\
`
`Cell
`aggregate
`
`Biochemical
`
`~ I I
`®
`
`Cell
`membrane
`
`Bulk
`liquid
`
`0
`
`0
`
`0
`
`461
`
`Gas
`
`~ _J LJ L
`~ Liquid
`
`;
`
`( 11 Rising
`single bubhk
`
`(~) Bubble swarms
`
`(3) Staged
`1.:ounh:r·1.. urrcnt
`fe rmentor
`
`Almosphere
`
`00CO·
`
`_ _______ Acrob1" _______ _
`
`Anaero bk
`
`( 6 ) St ratified, nearly
`horizontal flow
`
`I
`J
`
`Liquid t
`
`Air
`
`( 41 SJ)Jll:ed air hft
`
`Liquid
`
`(51 Tri~kle filter
`counter ~urrent
`
`(7 ) Natu rally turbule nt Jerat1o n
`
`(a l Freely rising. fa lling ra rllLles, flu ids
`
`Figure 8.2 Gas- liquid contacting modes: (a) freely rising, falling particles, lluids.
`
`Liquid- aggregale
`Gas-liquid
`interface
`interface
`Figure 8,1 Schematic diagram of steps involved in transport or oxygen from a gas bubble to inside a
`cell.
`
`Similarly, in the microbial utilization of other sparingly soluble substrates
`such as hydrocarbon droplets, cell adsorption on or near the hydrocarbon-emul(cid:173)
`sion interface has been frequently observed. A reactor model for this situation is
`considered in Chap. 9.
`The variety of macroscopic physical configurations by which gas- liquid con(cid:173)
`tacting can be effected is indicated in Fig. 8.2. In general, we can distinguish fluid
`motions induced by freely rising or falling bubbles or particles from fluid motions
`which occur as the result of applied forces other than the external gravity field
`(forced convection). The distinction is not clear-cut; gas- liquid mixing in a slowly
`stirred semibatch system may have equal contributions from naturally convected
`bubbles and from mechanical stirring. The central importance of hydrodynamics
`requires us to examine the interplay between fluid motions and mass transfer.
`Before beginning this survey, some comments and definitions regarding mass
`transfer arc in order.
`
`8.1.1 Basic Mass-Transfer Concepts
`The solubility of oxygen in aqueous solutions under 1 atm of ajr and near
`ambient temperature is of the order of 10 parts per million (ppm) (Table 8.1 ). An
`actively respiring yeast population may have an oxygen consumption rate of the
`order 0.3 g of oxygen per hour per gram of dry cell mass. The peak oxygen
`consumption for a population density of 109 cells per milliliter is estimated'·by
`assuming the cells to have volumes of 10· 1° ml, of which 80 percent is water.
`The a bsolute oxygen demand becomes
`
`0.3 g 0 1
`g dry mass• h
`
`(io9 cells)(to _ 10 ml)(t g cell mass)(o.2 g dry cell mass)
`cm3
`ml
`g cell mass
`= 6 x 10- 3 g/(ml · h) = 6 g 0 2/(l · h)
`
`APPX 0239
`
`

`

`Case 1:18-cv-00924-CFC Document 399-5 Filed 10/07/19 Page 7 of 50 PageID #: 30660
`
`462
`
`Liquid I
`
`BIOCHEMICAL ENOINEERJNG FUNDAMENTALS
`
`TRANSPORT PHENOMENA IN BIOPROCESS SYSTEMS
`
`Liquid
`
`t t f
`
`Air
`(2) Continuous liquid and air
`
`Barnes
`
`--,
`I
`I I I
`
`. --1
`
`r--. .
`
`I
`I
`I
`L-.
`
`(4) Stirred tank with
`baffles (baffles are
`often used in designs
`(I) and (2) J!so)
`
`t t t
`
`Air
`( I ) Semi·batch I balch
`liquid, continuous
`atr)
`
`t t t
`
`Air
`(3) Multiple propeller
`(semi•batch or
`continuous)
`
`t t t
`(5) Staged cross-current t t t
`
`Air
`
`Air
`
`(b) Mechanically agitated
`
`Figure 8.2 (continued) (b) mechanically agitated.
`
`,, .
`
`Thus, the actively respiring population consumes oxygen at a rate which is of the
`order of 750 times the 0 2 saturation value per hour. Since the inventory of
`dissolved gas is relatively small, it must be continuously added to the liquid in
`order to maintain a viable cell population. This is not a trivial task since the low
`oxygen solubility guarantees that the concentration difference which drives the
`transfer of oxygen from one zone to another is always very small.
`For sparingly soluble species such as oxygen or hydrocarbons in water, the
`two equilibrated interfacial concentrations c91 and c11 on the gas and liquid sides,
`
`Table 8.1 Solubility of 0 2 at l atm 0 2 in water at various
`temperatures and solutions of salt or acid at 2s0ct
`
`Temp,
`·c
`
`0
`10
`15
`20
`
`Water,
`0: mmol/ L
`
`2.18
`1.70
`J.S4
`1.38
`
`Aqueous solutions at 2s·c
`
`Electrolyte
`cone, M
`
`0.0
`0.5
`1.0
`2.0
`
`HCI
`
`1.26
`1.21
`Lt6
`1.12
`
`Temp.
`oc
`
`Water,
`0: mmol/ L
`
`2S
`30
`35
`40
`
`1.26
`1.16
`1.09
`1.03
`
`0:, mmol/ L
`
`H2S04
`
`1.26
`1.21
`1.12
`1.02
`
`NaCl
`
`1.26
`1.07
`0.89
`0.71
`
`t Data from International Critical Tables, vol. 111, p. 271, McGraw(cid:173)
`Hill Book Company, New York, 1928, and F. Todt, Electrochemische
`Sauerstoffmessungen, W. de Guy and Co., Berlin, 1958.
`
`respectively, may typically be related through a linear partition-law relationship
`such as Henry's law
`
`(8.l)
`
`provided that the solute exchange rate across the interface is much larger than
`the net transfer rate, as is typically the case: at 1 atm of air and 25"C, the 0 2
`collision rate at the surface is of the order of 1024 molecules per square centi(cid:173)
`meter per second, a value greatly in excess of the net flux for typical microbial
`consumption requirements cited above.
`At steady state, the oxygen transfer rate to the gas-liquid interface equals its
`transfer rate through the liquid-side film (Fig. 8.1). Taking c, and c1 to be the
`oxygen concentrations in the bulk gas and bulk liquid respectively, we can write
`the two equal transfer rates
`Oxygen flux = mol O J (cm2
`==- ko(c11 - c91)
`= ki(c11 -
`c1)
`
`• s)
`gas side
`liquid side
`
`(8.2)
`
`Since the interfacial concentrations are usually not accessible in mass(cid:173)
`transfer measurements, resort is made to mass-transfer expressions in terms of
`the overall mass-transfer coefficient K, and the overall concentration driving
`
`APPX 0240
`
`

`

`Case 1:18-cv-00924-CFC Document 399-5 Filed 10/07/19 Page 8 of 50 PageID #: 30661
`
`464
`
`BIOCHEMICAL ENGINEERING FUNDAMENTALS
`
`TRANSPORT PHENOMENA IN BIOPROCESS SYSTEMS
`
`force cf - c1, where cf is the liquid-phase concentration which is in equilibrium
`with the bulk gas phase
`
`Mcf-= c8
`In terms of these overall quantities, the solute flux is given by
`
`(8.3)
`
`Flux = K,(cf - c,)
`
`(8.4)
`Utilization of Eqs. (8.1 ), (8.2), (8.3), and (8.4) resulls in the following well(cid:173)
`known relationship between the overall mass-transfer coefficient K
`and the phys(cid:173)
`1
`ical parameters of the two-film transport problem, k", k
`, and M:
`1
`
`I
`1
`I
`- = ~ +-
`K,
`k1 Mk9
`For sparingly soluble species, M is much larger than unity. Further, k
`is typi(cid:173)
`9
`cally considerably larger than k1• Under these circumstances we see from Eq. (8.5)
`that K, is approximately equal to k1• Thus, essentially all the resistance to mass
`transfer lies on the liquid-film side.
`The oxygen-transfer rate per unit of reactor volume Q
`02
`(flux )(interfacial area)
`.
`r
`'d
`Q02 = oxygen absorption rate=
`reactor 1qu1 vo ume
`1
`
`is given by
`
`(8.5)
`
`(8.6)
`
`= k1a'(cf - c1)
`where a'= A/ V is the gas- liquid interfacial area per unit liquid volume and the
`approximation K1 ~ k, just discussed has been invoked. Since our major empha(cid:173)
`sis in this chapter is aeration, we shall concentrate on oxygen transfer and hence(cid:173)
`forth use k, in place of K 1 as the appropriate mass-transfer coefficient. The sym(cid:173)
`bol a, which appears in several correlations, is the gas- liquid interfacial area per
`unit volume of bioreactor (gas + liquid) contents. Head space gas is not included.
`It is important to recognize that Q02 is defined " at a point." It is a local
`volumetric rate of 0 2 consumption; the average volumetric rate of oxygen utili(cid:173)
`zation (moles per time per volume) t,J02 in an entire liquid volume V is given by
`1 f"
`-
`Qo, = V Jo Qo, dV
`
`(8.7)
`
`In general, Q02 is equal to Q0 , only if hydrodynamic conditions, interfacial area/ ·
`volume, and oxygen concentrations are uniform throughout the vessel.
`For example, a complete description of the phenomena underlying the
`observed average transfer rate in a bioreactor depends on power input per unit
`volume, fluid and dispersion rheology, sparger characterization, and gross flow
`patterns in the vessel. Figure 8.3 indicates the relationship between observed
`average transfer rate and the causative phenomena. Since we generally lack
`
`Power per unic volume 1 - - - - - - ,
`.-----t (impeller rpm, etc)
`
`Coalescence and
`breakup or bubbles
`
`Bubble-size
`distribution
`
`Character and incensity
`or now of concinuous
`phase (turbulence)
`
`Relative vclocicies and
`'---~ path lengths of bubbles
`
`Dispersed•phase ~'--__ ___,. _____ '! Instantaneous
`holdup fraction
`transfer nux
`
`Ave rage
`transfer nux
`
`' - -~ Total average transfer race - - . - - (cid:173)
`
`Figure 8.3 Relationships between input agication intensity and resultant gas transfer rate. ( After ":'·
`Resnirk und B. Gui.Or, Ado. Chem. Eng., vol. 7, p. 295 ( /968). Reprimed by permission of Acaden11c
`Press.}
`
`crucial fundamental information on coalescence and redispersion rates, bubble
`size and residence time distribution, we are typically forced to develop cor~ela(cid:173)
`tions based on appropriate averages of bubble size, holdup (gas volume fraction),
`gas bubble and liquid residence times, etc.
`.
`In Table 8.1 we saw that cf is determined by the temperature and composi(cid:173)
`tion of the medium. Composition influences become more complicated when the
`dissolved gas can undergo liquid-phase reaction. This is the case for carbon
`dioxide, which may exist in the liquid phase in any of four forms: CO2, H:2C03,
`HCOj , and COi- . The equilibrium relations
`
`K _
`I -
`
`,.,, rn - 6 .3 M
`[H • J[HC03]
`[C0:2] + [H2C03J
`
`K = [H . J[co~ - J = rn - 10.H M
`[HC03]
`
`2
`
`(8.8)
`
`(8.9)
`
`APPX 0241
`
`

`

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`
`466
`
`IIIOCHEMICAL ENGINEERING FUNDAM!;NTALS
`
`TRANSPORT PHENOMENA IN RIOPROCE.SS SYSTEMS
`
`the important reaction
`
`467
`
`(8.13)
`
`is far slower, with k 1 == 20s-• and k_ 1 == 0.03s- 1 (25°C). Thus, depending on
`circumstances, the slow step in CO 2 removal to the gas phase could be chemical
`[Eq. (8.13)] or physical [CO2 (dissolved) - CO2 (gas)].
`
`8.1.2 Rates of Metabolic Oxygen Utilization
`
`In design of aerobic biological reactors we frequently use correlations of data
`more or less approximating the situation of interest to establish whether the
`slowest process step is the oxygen transfer rate or the rate of cellular utilization
`of oxygen (or other limiting substrate). The maximum possible mass-transfer rate
`is simply that found by setting c1 = O: all oxygen entering the bulk solution is
`assumed to be rapidly consumed. The maximum possible oxygen utilization rate
`is seen from Chap. 7 to be xµm0.fY02 , where x is cell density and Y02 is the ratio
`of moles of cell carbon formed per mole of oxygen consumed.
`Evidently, if k1a'ct is much larger than xµm.JY02, the main resistance to
`increased oxygen consumption is microbial metabolism and the reaction appears
`to be biochemically limited. Conversely, the reverse inequality apparently leads
`to c1 near zero, and the reactor seems to be in the mass-transfer-limited mode.
`The situation is actually slightly more complicated. At steady state, the
`oxygen absorption and consumption rates must balance:
`Q02 = absorption == consumption = xq02
`1a c1 -c1 =r.
`)
`k '( •
`xµ
`02
`Assuming that the dependence of µ on c1 is known, we can use Eq. (8.14) to
`evaluate c1 and hence the rate of oxygen utilization.
`In general, above some critical bulk oxygen concentration, the cell metabolic
`machinery is saturated with oxygen. In this case, sufficient oxygen is available to
`accept immediately all electron pairs which pass through the respiratory chain,
`so that some other biochemical process within the cell is rate-limiting (Chap. 5).
`For example, if the oxygen dependence of the specific growth rate µ follows the
`Monod form, then
`
`(8.14)
`
`(8.15)
`
`A general solution to an equation of this form was given in Sec. 4.4.1., but here
`for the sake of illustration we assume that the value of c1 is considerably less than
`ct. This is not an uncommon situation in biological reactors. Subject to the
`assumption that c, ~ er, C1 is easily seen to be
`_ •[ Y0 2K02 k,a'/xµma1 ]
`c, - c,
`*k '/
`I -
`i 02c1 1a xµm ..
`
`(8.16)
`
`V
`
`- I
`
`- 2
`
`- 3
`
`- 4
`
`...
`"' 0
`e
`c
`.2 e
`
`E
`1:!
`C:
`0
`r.,
`Oil
`..2
`
`- 5
`
`- 6
`
`- 7
`
`- 8
`
`_
`
`5
`
`6
`
`8
`
`9
`
`pH
`I
`·
`d H co
`Figure 8.4 Equilibrium conccnlralions of dissolved CO Hco- co·
`3 • er 1s Iota con-
`J an
`.
`2,
`J•
`2
`centrauo~ of all four forms of CO2, [pro, .. 10- 3 ' aim (ambient concentration); pH adjusted with
`strong acid or strong base.] ( After W. Stumm and J. J. Morgan," Aquatic Cl,emiury" John Wiley and
`'
`S<111s, N. Y. p. 117, /970.)
`
`(values a~ 2?~C~ ind_icate that the total dissolved carbon concentration, c , as
`7
`carbon d1ox1de 1s quite pH sensitive:
`er= [CO2]+ [H2CO3] + [HCO3] + [COi - ]
`_ [i K,
`K 1K 2 ]
`- Co + [H+] + [H +]2
`T.his relation appears in Fig. ~.4, s~owing that below pH 5, nearly all carbon is
`dissolved molecular CO 2, while bicarbonate dominates when 7 < pH < 9 and
`carbonat~ fo_r P_H > 11. Only the dissolved CO2 molecule is transported across,~
`the gas- hqu1d interface, and we may again write Eq. (8.2) for the interfacial _.
`transfer rate.
`
`(8.10)
`
`:~e coupli~g of reaction and mass transfer may occur under neutral to basic
`cond1t1ons. While the reversible reaction (8.11) is rapid,
`H2C03 ~ HCO3 + H+
`[H+][HCOj']
`Kcq(T = 28 C) = .;;;._-=- ~...:: = 2.5 X 10- 4 mol/ L
`[H2C0 3]
`
`o
`
`(8.11)
`
`(8.12)
`
`--------------
`
`H2C0 3
`
`10
`
`II
`
`APPX 0242
`
`

`

`Case 1:18-cv-00924-CFC Document 399-5 Filed 10/07/19 Page 10 of 50 PageID #: 30663
`
`468
`
`BIOCHEMICAL ENGINEERING FUNDAMENTALS
`Table 8.2 Typical values of c01,c, in the pres(cid:173)
`ence of substrate t
`
`TRANSPORT PHENOMENA IN BIO PROCESS SYSTEMS
`
`Organism
`
`Awtohacter vi11elandii
`E. coli
`
`Serratia marcescens
`Pseudomonas denitrijicans
`Yeast
`
`Penicillium chrysoge11um
`
`Aspergi//us oryzae
`
`Temp, •c
`
`Co1.cr,
`mmol/L
`
`30
`37.8
`15
`31
`30
`34.8
`20
`24
`30
`30
`
`0.DIS-0.049
`0.0082
`0.0031
`~0.Dl5
`~0.009
`0.0046
`0.0037
`-0.022
`~0.009
`-0.020
`
`t Summarized by R. K. Finn, p. 81 in N. Blake(cid:173)
`brough (ed.), Biochemical and Biological Engineering
`Scie11ce, vol. I, Academic Press, Inc., New York, 1967.
`
`If the resulting value of c, is greater than the critical oxygen value cc, (about
`3K01), the rate of microbial oxygen utilization is limited by some other factor,
`e.g., low concentration of another substrate, even though the bulk solution has a
`dissolved oxygen level considerably below the saturation value. The critical
`oxygen values for organisms lie in the range of 0.003 to 0.05 mmol/ L (Table 8.2)
`or of the order of O.l to 10 percent of the solubility values in Table 8.1, that is, 0.5
`to SO percent of the air saturation values. For the higher critical oxygen values
`such as obtained for Penicillium molds, oxygen mass transfer is evidently ex(cid:173)
`tremely important.
`, which
`Many factors can influence the total microbial oxygen demand xµ/ Y
`01
`in turn sets the minimum values of k1a' needed for process design through Eq.
`(8.14). The more important of these are cell species, culture growth phase, carbon
`nutrients, pH, and the nature of the desired microbial process, i.e., substrate
`utilization, biomass prodJction, or product yield (Chap. 7).
`fn the batch-system results of Fig. 8.5, a maximum in specific 0
`demand
`2
`occurs in the early exponential phase although x is larger at a later time. A peak
`in the product xµ, and thus the total oxygen demand, occurs near the end of the
`exponential phase and the approach to the stationary phase; this is later than the
`time of achievement of the largest specific growth rate.
`The carbon nutrient affects oxygen demand in a major way. For example,
`glucose is generally metabolized more rapidly than other carbohydrate sub(cid:173)
`stances. Peak oxygen demands of 4.9, 6.7, and 13.4 mol/(L • h) have been
`observed for Pe11icilli111n mold utilizing lactose, sucrose, and glucose, respectively
`(2).
`
`The component parts of oxygen utilization by the cell include cell mainten(cid:173)
`ance, respiratory oxidation for further growth (more biosynthesis), and oxida-
`
`100
`
`80
`
`20
`
`~00
`
`0 q0 ,[J1 U(h-mg dry wt)]
`C Dry wc1i:hl. mi;
`e:,. pit of LUhurc me ilium
`(cid:127) ArithmcllL mean of
`14 rq,tkatc expe riments
`
`-~-t:,_~~-f!---zru'-'L.)- 100 g
`
`~
`
`o o 0 50
`
`0
`
`00
`
`Figure S.5 Oxygen utilization rate in batch culture of MJ>rothccium verrucaria / Reprimed f rom R. T.
`Darby a11d D. R. Goddard, Am. J. B01., vol. 37, p. 379 ( 1950).j
`
`Time. II
`
`lion of substrates into related metabolic end products. I~ _ex~mining metab~l~c
`· Chap s we have seen that oxygen ut1hzat1on for growt 1s
`· h'
`t
`stoic 10me ry m
`·
`,
`b
`t
`sumed
`ically coupled directly to the amount of carbon-source su stra e con
`t
`. •
`/~rthermore more reduced substrates such as paraffins and methane_ require
`reater ox g~n uptake by the cell than substrates such as glucose which h~ve
`g
`· !tely the same carbon oxidation state as the cell. For example, the Y_teld
`~ c giving moles oxygen used per _mole or c~rbon source metabolized
`
`~!~:~:1
`are 1.34, tl!o, and 0.4 for typical microorganisms growing on methane, paraffins,
`F
`.
`and carbohydrates, respectively.
`S med as a reactant in a biotraneformatw11. or
`I
`b
`Oxygen may a so C con u
`.
`.
`r
`example 5-ketogluconic acid production from glucose by ~atch cult1va~1on o
`Acecoba~ter begins with a growth phase in which some medium glucose is c?n-
`'d Here o use for both growth and product formation
`·
`1
`verted to g ucomc ac, ·
`• d ·
`rted to
`2
`•
`occurs. After glucose exhaustion, growth ceases, and glucomc ac1
`is conve
`5-ketogluconic acid with stoichiometry
`C6H 12Q 7 + JO2 _. C6H10O1 + H2O
`
`(S.t 7)
`
`fn the final phase of the process which involves only_ this biotr~ns~o~a~i~~~
`t e s o1c I
`oxygen demand is directly coupled to product formation throug
`ometry of Eq. (8.17).
`
`APPX 0243
`
`

`

`Case 1:18-cv-00924-CFC Document 399-5 Filed 10/07/19 Page 11 of 50 PageID #: 30664
`
`470
`
`BIOCHEMICAL ENGINEERING FUNDAMENTALS
`
`TRANSPORT PHENOMENA IN BIOPROCESS SYSTEMS
`
`471
`
`8.2 DETERMINATION OF OXYGEN TRANSFER RATES
`
`Ideally, oxygen transfer rates should be measured in biological reactors which
`include the nutrient broth and cell population(s) of interest. As this requires all
`the accoutrements for inoculum and medium preparation, prevention of con(cid:173)
`tamination, and environmental control for the cell culture, it is an inconvenient
`and troublesome way to conduct mass-transfer experiments. Consequently, a
`common strategy for study of oxygen transfer rates is to use synthetic systems
`which approximate bioreaction