Edward Kugler of Johns Hopkins University for assistance
`in development of the IR cells and wafer pressing and han-
`dling techniques, and Professor G. C. A. Schuit for valuable
`discussions on the mechanism of adsorption. This work was
`supported in part by Grants from the General Motors Cor-
`poration, Mobil Oil, and a National Scieiace Foundation En-
`ergy Related Traineeship.
`
`Literature Cited
`Aipart, N. L., Kaiser, W, E., Szyrnanski, H. A., "lR--Theory and Practice of In-
`frared Spectroscopy", 2nd ed, p 303, Plenum Publishing Co., New York, N~Y.,
`197’3.
`Armistead, C. G., Hambleton, F. H., Hockey, d. A,, Stockton, J. W., J. Sci. In-
`strum., 44, 872 (1967).
`Cotton, F. A., Francis, F. J., J. Am. Chem. Soc,, 82, 2985 (1960).
`Cotton, F. A., Wilkinson, G,, "Advanced Inorganic Chemistry", 3rd ed, p 643,
`Interscience, New York, N.Y., 1973.
`Dautzenberg, F. M., Naber, J. E., van Ginnekan, A. J. J., "Shell’s Flue Gas
`Desulfudzatlon Pro~ess", paper given at A.I,Ch.E. 681h Annual National
`Meeting, Houston, Texas, Feb. 28-Mar 4, 1971, and Chem, Eng. Prog., 67,
`NO, 8, 86 (1971),
`Farrauto, R. J., Wedding, B., J. CataL, 33, 249 (1973).
`Farraro, J. R., Walker, A,, J. Chem, Phys., 42, 1278 (1965),
`
`Fishel, N. A., Lee, R. K., Wilhelm, F. C., Environ. Sci. Technol., 8, 260
`(1974).
`Ghandi, H. S., Shelef, M., J. Catal., 28, 1 (1973).
`Groenendaal, W., Naber, J. E., Pohlanz, J. B., "The Shell Flue Gas Desulfurization
`on Oil and Coal Fired Boilers", paper presented at A.I.Ch.E. National Meeting,
`Tulsa, Okla., Mar 10-13, 1974.
`Gryder, J., personal communication, Department of Chemistry, Johns Hopkins
`University, Baltimore, Md., 1975.
`Kent, S. A., MChE Thesis, University of Delaware, Newark, Del., 1976.
`Keppeler, G., Z. Agnew. Chem., 21,579 (1908).
`Kolta, G. A., Askar, M. H., Thermochim. Acta, 11, 85 (1975).
`Low, J. D., Goodsell, A. J., Takezawa, N., Environ. Sci. Technol., 5, 1191
`(1971).
`Low, J. D., Goodsell, A. J., Takezawa, N., Environ. Sci. Technoi., 6, 268
`(1972).
`Nakamoto, K., McCarthy, P. J., "Spectroscopy an~ Structure of Metal Chelate
`Compounds", pp 287, 268, Wiley, New York, N.Y., 1968.
`Nyquist, R. A., Kagel, R. O., "Infrared Spectra of Inorganic Compounds", p 221,
`Academic Press, New York, N.Y., 1971.
`Wells, A. F., "Structural Inorganic Chemistry", 3rd ed, p 463, Oxford University
`Press, London, England, 1962.
`Yao, Y. Y., J. Catal., 39, 104 (1975).
`Young, D. M., Crowell, A. D., "Physical Adsorption of Gases", p 226, Butter-
`worths, London, 1962.
`
`Received for review January 4, 1977
`Accepted July 27, 1977
`
`Batch Absorption of CO2 by Free and Microencapsulated
`Carbonic Anhydrase
`
`Douglas N. Dean, Michael J. Fuchs, John M. Schaffer, and Ruben G. Carbonell°
`
`Department of Chemical Engineering, University of California, Davis, California 95616
`
`The rates of absorption of CO2 into aqueous buffered solutions containing free carbonic anhydrase and carbonic
`anhydrase microencapsulated in cellulose nitrate microcapsules were measured in a slurry reactor. Using a
`pseudo-steady-state model to describe the absorption process, it was possible to determine gas-liquid mass
`transfer coefficients and the effectiveness factor for the microencapsulated enzyme from the experimental
`data.
`
`Introduction
`Batch absorption techniques are important in the mea-
`surement of reaction rate constants by manometric methods
`(Dixon, 1974). This problem is of general interest in the study
`of transients in multiphase chemically reacting systems and
`in the analysis of slurry adsorbers (Mehta and Calvert, 1967;
`Misic and Smith, 1971; Komiyama and Smith, 1975) and re-
`actors. In this paper, we study the batch absorption of C02
`into aqueous buffered solutions containing the enzyme car-
`bonic anhydrase both free in solution and microencapsulated
`in cellulose nitrate microcapsules.
`The pseudo-steady-state approach of Danckwerts (1970)
`for describing batch absorption systems is used to analyze the
`data. By assuming that the amount of reaction taking place
`in the near vicinity of the gas bubbles is negligible in com-
`parison with the amount of reaction taking place in the bulk
`liquid, one can derive simple expressions for the rate of change
`of the bulk concentration of the reacting species in terms of
`mass transfer coefficients. Previous workers have assumed
`that the flux of dissolved gas through the free liquid surface
`in the absorber is negligible in comparison to the flux of gas
`from the gas bubbles to the liquid. In our experimental system,
`this assumption is found to be quite accurate. Since the ratio
`
`452
`
`Ind, Eng, Chem,, Fundam., Vol. 16, No. 4, 1977
`
`of catalyst particle volume to free liquid volume in the reactor
`used is very small, steady-state effectiveness factors can de-
`scribe the rate of reaction of the microencapsulated enzyme
`in this unsteady-state system.
`We measure the rate of absorption of C02 into an aqueous
`Veronal buffer solution containing the enzyme carbonic an-
`hydrase in homogeneous solution, as well as in cellulose nitrate
`microcapsules by following the change in pH of the solution
`as a function of time. The rate and equilibrium constants for
`all the chemical reactions taking place in this system have
`been studied previously. The nonenzymatic reactions have
`been well summarized by Danckwerts and Sharma (1966) and
`Suchdeo and Schultz (1974) among others. Roughton and
`Booth (1946) and Lindskog et al. (1971) have reported the
`enzymatic rate parameters and several of the enzyme prop-
`erties. Chang {1972) has reported the microencapsulation of
`carbonic anhydrase in cellulose nitrate microcapsules, but
`little quantitative information is available on the effectiveness
`of the microcapsules in enhancing CO2 absorption. Using
`equilibrium and rate constants from the literature, we cal-
`culate the change in pH of the solution as a function of time
`with only one parameter, the liquid phase mass transfer
`coefficient from the bubble to the liquid. Values of this pa-
`
`Akermin, Inc.
`Exhibit 1006
`Page 1
`
`

`

`rameter are estimated by fitting the model to the experimental
`pH vs. time data. The estimated values are in general agree-
`ment with previously reported mass transfer coefficients for
`slurry absorbers by Misic and Smith (1971) and Komiyama
`and Smith (1975}. Using the estimated mass transfer coeffi-
`cients, we then evaluate the effectiveness factor for the mi-
`croencapsulated enzyme. In the next section, we discuss the
`assumptions involved in the model used to study the batch
`absorption of a pure gaseous component i accompanied by
`homogeneous chemical reaction in the liquid phase and het-
`erogeneous reaction within catalyst particles.
`
`Theory
`
`Consider a slurry reaction system where a gas of pure
`component i is continuously dispersed through a solution with
`which it can react. Reactions with absorbed gas can take place
`in the homogeneous phase, as well as in the heterogeneous
`phase (catalyst particles). The macroscopic mass balance
`(Slattery, 1972) for component i, using the liquid volume VL
`as the control volume is given by
`
`d
`
`where c~ is the molar concentration of component i in the
`liquid phase, ri is the intrinsic rate of reaction of i in the liquid,
`v~ is the mass average velocity of component i, and w is the
`velocity of the control volume interfacial area AL relative to
`a stationary coordinate system. The total area of the control
`volume AL consists of the gas-liquid interfacial area At, the
`free surface liquid area Af, and the particle-liquid area Ap.
`The area integral in eq 1 can be written as (Bird et al.,
`1960)
`
`f AL Ci(Vi -- W). ndA = JAL Ci(V* -- W). ndA
`
`+ [~. Ji*- ndA (2)
`
`L
`
`where Ji* is the molar diffusive flux of component i relative
`to the molar average velocity v*. For dilute solutions one can
`assume v* ~ w and eq 2 then becomes
`
`fA Ci(Vi -- W) ndA~- Ag(di* n)g
`
`L
`
`+ Af(J~*. n)f+ Ap(Ji*- n)p (3)
`
`where the brackets denote area averages. If the liquid is well
`stirred, one can assume that the concentration c~ is uniform
`throughout VL. If the liquid volume remains constant with
`time, combination of eq I and 2 results in
`
`dci
`d--~- = -S~(J~* ¯ n)~ - S~(J~* ¯ n)f- S,(J~* . n)" + r~
`(4)
`
`where the surface areas per unit volume of liquid are defined
`as
`
`Sg = A~/VL; St = Af/VL; Sp = Ap/VL
`
`(5)
`
`and the initial condition is ci(O) = Cio. The estimation of the
`fluxes of eq 4 is a problem central to the theory of diffusion
`with chemical reaction. When the system is in steady state,
`one can calculate an enhancement factor to take into account
`the effect of chemical reaction on the rate of absorption of the
`gas. This can be done by means of several models including
`the film theory, penetration theory, and the surface renewal
`theory. This approach, strictly speaking, is not valid for
`transient systems since the bulk concentration of component
`i is continually changing. This in turn will affect the mass
`
`transfer rate of i in the vicinity of the gas bubbles, and thus
`result in time-dependent enhancement factors.
`Danckwerts (1970) assumes that the amount of reaction
`taking place in the film surrounding the gas bubbles is very
`small in comparison to the amount of reaction taking place
`in the bulk fluid. This pseudo-steady-state situation allows
`the fluxes in eq 4 between gas and liquid phases to be ex-
`pressed in terms of mass transfer coefficients and suitable
`driving forces
`
`- <Ji*. n)~ = kL(Ci* - ci)
`
`- <Ji*" n>f = kLf(Cif* - ci)
`
`(6)
`
`(7)
`
`In eq 6 and 7 ]~L and kLf represent mass transfer coefficients
`between gas bubble and bulk liquid and between bulk liquid
`and free surface, respectively. The quantity ¢i* is the liquid
`phase concentration of component i in equilibrium with the
`gas-phase concentration in the gas bubbles while Clf* is the
`same concentration in equilibrium with the gas phase con-
`centration of component i at the free interphase. The con-
`centration ci* can be calculated using the Henry’s law con-
`stant He (Smith and Van Ness, 1975)
`
`ci* = pc!He
`
`(8)
`
`where p is the partial pressure of component i in ~he gas and
`c is the total liquid phase molar concentration.
`For the reaction taking place in the solid catalyst, one can
`show that
`
`- S~{,/~* ¯ n)~ ; ~ V~
`
`where Vp is the volume of particles, ~u is the reaction rate in
`the solid at bulk fluid conditions and ~ is an effectiveness
`factor defined as the actual rate of reaction divided by the rate
`at bulk fluid conditions. Lewis and Paynter (1971) have shown
`that the steady-state n will be valid under unsteady-state
`conditions if the ratio of catalyst to liquid volume is small. I~
`our experiments, this ratio was made 2 X 10-a. Combination
`of eq 4, 6, 7, and 9 results in
`dc~ =
`SgkL(Ci, _ ci) _ SfkLf(Ci _
`
`dt
`
`+
`
`~ xVL ~ib + ri
`
`The pseudo-steady state assumption allows one to use the
`effectiveness factor calculated for steady-state conditions. For
`linear reaction kinetics, ~ is independent of the concentration
`of the reactant. For more complex rate expressions, ~ will be
`a function of ci. The way ~ is defined includes the effect of the
`liquid phase mass transfer resistance at the liquid-particle
`interface (Fink et al., 1973; Wadiak and Carbonell, 1975a,b).
`Recent work on the batch absorption of gases in slurries has
`neglected the se~nd term on the rlgSt-kaad side of eq 10, that
`dealing with the mass transfer of dissolved gas from the liquid
`to the free surface. We will do the same in this work, thus re-
`ducing eq 10 to the form
`
`dC~dt ~ SghL(Ci* - ci) + ~ k~L/ ~ib + ri
`
`(11)
`
`This is the starting point for our analysis of CO~ absorp-
`tion.
`
`Experimental Section
`
`Experiments were first performed by absorbing CO~ into
`aqueous Veronal buffer solutions in the absence of enzyme.
`A diagram of the apparatus is shown in Figure 1. A 400-mL
`glass beaker containing 300 mL of a 0.03 M Veronal buffer
`solution (pH 9.7) was immersed in a constant-temperature
`
`Ind. Eng. Chem., Fundam., Vol. 16, No. 4, 1977
`
`Akermin, Inc.
`Exhibit 1006
`Page 2
`
`

`

`R0tarneter
`
`-- 2,75"--
`
`Constant Temperature
`Baths
`
`Constant Temperature Bath
`Figure I. Experimental apparatus (not drawn to scale).
`
`bath at 5 °C. A glass or stainless steel stirrer and a pH com-
`bination electrode were placed in the beaker as shown in
`Figure 1. A gas sparger was introduced into the solution with
`C02 gas flowing at flow rates of either 41 cm3/min or 61
`cm3/min at 5 °C and 1 atm depending on the experiment. Si-
`multaneously, the time and pH of the solution were recorded
`at every 0.1 pH interval change. The stirrer speed was mea-
`sured at 840 rpm using a stroboscope.
`A second set of experiments was performed with 1 mg of
`carbonic anhydrase (bovine, Sigma Chem. Co.) mixed in the
`same buffer solution, and the corresponding change in pH
`with time was recorded.
`Cellulose nitrate microcapsules containing carbonic an-
`hydrase were made by the procedure described by Paine and
`Carbonell (1975), with a few modifications. The aqueous he-
`moglobin solution was filtered using a Whatman No. 1 filter
`paper, and the separation of the microcapsules was expedited
`by centrifugation on a bench scale centrifuge. The micro-
`capsules were rinsed 5 to 6 times in the same Veronal buffer.
`Approximately 50 mg of enzyme was added in 2.5 mL of the
`hemoglobin solution, resulting in an enzyme concentration
`of 20 mg/mL.
`Approximately 0.6 mL of microcapsules was ~dded to the
`300 mL of 0.03 M Veronal solution and the same procedure
`of measuring the change in pH as a function of time was fol-
`lowed. The experiments using the free and microencapsulated
`enzyme were done with a gas flow rate of 41 cm3/min. The
`volume of microcapsules was measured using a calibrated
`centrifuge tube. A void fraction of 0.33 was assumed.
`The CO2 source was 99.5% pure liquid CO2. Tygon tubing
`of 1/4-in. i.d. was used for gas transferral. The gas fiowed into
`two ice baths in 1/6-in. o.d. stainless steel tubing. The gas
`flowed through a total of 25 coils wound at a 41/2-in. diameter
`and through a Pyrex drying tube containing Drierite filler
`inserted in an ice bath. Two Whatman GF/A filter disks were
`used to prevent dust particles of Drierite from reaching the
`sparger. The gas was then passed through a rotameter that had
`been calibrated by using a standard soap bubble meter at 5
`°C and 1 atm. The sparger was a Kimax #12C sparger. The
`constant temperature bath used is a Neslab Model RTE-8,
`and the pH meter is a Leeds and Northrup Model 74-10 with
`a standard combination electrode.
`
`CO2 Absorption Kinetics
`
`The absorption of CO; into buffered aqueous solutions
`containing carbonic anhydrase is accompanied by several
`chemical reactions (Danckwerts and Sharma, 1966; Suchdeo
`and Schultz, 1974; Sherwood, 1937)
`
`H+ + V- ~-= HV
`
`(12)
`
`454
`
`Ind. Eng. Chem., Fundam., Vol. 16, No. 4, 1977
`
`h2
`H+ + HC03- ~ H2C03
`
`C02 + H20 ~ H2C03
`k-3
`
`k4
`C02 + OH- ~ HC03-
`
`k5
`HC03- ~ H+ + CO32-
`k-5
`
`H+ + OH- ~ H20
`k-6
`
`CO2 + H20 ~ H2C03
`
`(13)
`
`(14)
`
`(15)
`
`(16)
`
`(17)
`
`(18)
`
`The first reaction is the combination of a hydronium and
`Veronal ion to yield Veronal. Reaction 14 is the naturally oc-
`curring reaction in water, while reaction 18 is the same reac-
`tion catalyzed by carbonic anhydrase. Following Suchdeo and
`Schultz (1974), we assume that reactions 12, 13, 16, and 17 are
`so fast that the concentrations of reactants and products are
`related by their equilibrium constants
`
`~1 CHV
`K1 = = --
`k-1 CHCV
`
`k2= CH~CO,~
`K2 = k-2 CHCHCO~
`
`K~ = k~ = c~cco~
`k_5 CHCOa
`
`(19)
`
`(20)
`
`(21)
`
`and
`
`Ks = k~= CH~O
`k-6 CHCOH
`Reactions 14 and 15 are rate-limiting, and these have equi-
`librium constants defined as
`
`(22)
`
`K3 = k.~_3 = CH2CO3
`k-3 CcO2CH20
`
`(23)
`
`and
`
`K4 = k4 = cr~coz
`k-4 CCO2COH
`The forward and reverse enzymatic reactions have been found
`to be of the Michaelis-Menten type (Roughton and Booth,
`1946)
`
`(24)
`
`rf-- keE°cco2
`Km + cCO~
`
`rb = k-~EocH~CO~
`Km~ ÷ CH2CO3
`
`(25)
`
`(26)
`
`here Kin,Kin’ are the Michaells-Menten constants, ke,k-e are
`turnover numbers, and Eo is the enzyme concentration. Since
`at equilibrium the forward and backward rates have to be
`equal and eq 23 must be satisfied, it is easy to show that
`(Roughton and Booth, 1946)
`
`he = k_e
`
`Kin’ = KmK3cH~O
`
`(27)
`
`(28)
`
`First we consider the case where the enzyme is free in so-
`lution and there are no microcapsules present. Applying eq
`11 to each of the components in the chemical reactions 12-18,
`we obtain
`
`dcH
`-- = k_ICHV -- klCHCV + k-2CH2COs -- ~2CHCHCOs
`dt
`
`+ ksCHCOs -- k-5CHCCO~ + k-6CH20 -- ]~6CHCoH (29)
`
`Akermin, Inc.
`Exhibit 1006
`Page 3
`
`

`

`dcH2CO3 _
`dt - k3cco2CH20 - k-3CH2CO3 + ~’f -- rb
`
`Table I. Values of Rate and Equilibrium Constants
`
`Constant
`
`Reference
`
`+ k2CHCHCOs -- k-2CH2CO3 (30)
`
`K~ = 2.021 X l0s L/g-mol
`
`d¢co2
`__ _-- SgkL(CCO2* - CCO2) + h-3CH2CO3 -- k3CCO2CH20
`dt
`
`÷ }-4CHcO8 -- }4Cco2CoH -- rf + rb
`
`(31)
`
`dcHco~
`-- _-- k_2CH2CO3 -- h2CHCHCO3 + ~4CCO2COH -- ~_4CHCO3
`dt
`
`+ k-sCI-ICCOa -- kSCHCO8
`
`(32)
`
`dcco~ = ~5CHCO3 -- k-scHCCO~
`dt
`
`(33)
`
`dcoH
`~ = ~-4CHCO3 -- k4cco2COH + k-6CH20 -- k6CHCOH
`d:
`
`(35)
`
`/(2 = 6.41 × 103 L/g-mol
`Ks = 3.545 X 10-5 L/g-mol
`K~ = 1.648 × 10s L/g-mol
`K5 = 7.63 × 10-2 L/g-mol
`
`K6 = 2.9796 × 10~s L/g-mol
`
`k3 = 4.192 × 10-3 L/g-tool.rain
`k-3 = 118.26 min-I
`k~ = 1.012 × 106 L/g-mol.min
`k-~ = 6.141 × 10-4 min-1
`He = 876 atm
`
`Km = 9 X 10-3 g-mol/L
`(0 °C, 6 < pH < 9.5)
`
`"Biochemist’s Handbook"
`(1961)
`Harned and Owen (1958)
`Harned and Owen (1958)
`Calculated from K6, K2, Ks
`Danckwerts and Sharma
`(1966)
`"Handbook of Chemistry and
`Physics," (1966)
`Pinsent et al. (1956)
`Calculated from K~, ka
`Pinsent et al. (1956)
`Calculated from K~, h,
`"Chemical Engineers’
`Handbook," (1963)
`Lindskog et al. (1971)
`
`!~rn’ = 1.75 X 10-5 g-mol/L
`
`Eq 28, K3Km
`
`dcH~O
`~ = k_3CH2CO~ -- ]~3¢cO2CH20
`dt
`
`+ kaCHCoH -- k-6CH20 -- rf + rb (36)
`
`The forms of the rate terms ri in eq 11 have been taken from
`Danckwerts and Sharma (1966). It is possible to combine eq
`29-36 into the four simpler independent expressions
`
`and
`
`E = K6CH
`K6CH ÷ 1
`
`+
`
`(48)
`
`+ rf-- rb
`
`(49)
`
`dcH = dcr~v dcHz¢O8 I- dcco~ dc~o
`dt dt dt dt dt
`
`dcH2¢O3 = dCHCOs dcoH dcH20
`dt
`dt dt dt
`
`dcco~
`dt
`
`dCoH dcH~o
`
`(37)
`
`(38)
`
`(39)
`
`dcCO,dt = Sd}L(CC°~* - cco~) + ~ "~ ~-~
`dcH20 + dCoH
`-~- = k_3cH2CO~ -- k3CcO2CH20 -- rf + rb
`dt
`
`+ k-4CHCO~ -- k4Cco2COH
`
`co = cHV + cv
`
`(50)
`
`The magnitude of the !~6CH term in E, eq 48, is so much
`greater than 1 for the pH range of these experiments, that in
`a very good approximation, one can write eq 42 and 43 as
`
`dcco2
`dt = S~kL(cCO2* -- CCO2) -- F
`
`dc~_ (B + C) F
`at (AC ---if-D)
`(40) dCH~CO~_ (A + D)
`
`(51)
`
`(52)
`
`dt (AC - BD)
`
`F (53)
`
`One can differentiate eq 19-22 to obtain the time derivatives
`of CHV, cI4CO~, and ci4~o. When these time derivatives and the
`equilibrium expressions (19-22) are substituted into the
`equations above, we find that the entire system of reaction
`equations reduces to three expressions for the concentration
`of C02, H+, and H2CO3
`
`These are the model equations eventually solved numerical-
`ly.
`Estimates of all the rate and equilibrium constants in eq
`41-49 were obtained from the existing literature. These are
`shown in Table I. All values are for a temperature of 5 °C and
`an ionic strength of 0.042 when ionic strength information was
`available. The ionic strength did not vary significantly from
`this value throughout our experiments. The total buffer
`concentration, co is 0.03 M. The value of cco~* from eq 8 was
`(42)
`dCH= I [A?~-BD (E +-~) + E] Fdt A
`6.279 × 10-2 g-mol/L using p = 1 atm. It was not possible to
`correct the Henry’s law constant He to account for the solu-
`bility of CO2 in aqueous solution in the presence of Veronal
`ion. Values of equilibrium constants were not corrected for
`values of activity coefficients of ionic species. As a result, there
`are probably some inaccuracies in the values of the equilib-
`rium and rate constants in Table I.
`The enzyme Michaelis-Menten constants Km and K~’ are
`also listed in Table I. It was found by Roughton and Booth
`(1946), that the turnover number ke depends strongly on the
`pH of the solution. Lindskog et al. (1971) have summarized
`these results. From the data available in Lindskog et al. (1971),
`we derived an empirical equation for ke as a function of pH
`
`dcco~ = SgkL (CCO2" -- CCO2) -- F
`dt
`
`dCH2cOs =
`(E DA--)F
`dt AC ~ BD +
`
`where
`
`(41)
`
`(43)
`
`A=[I+
`
`CoKl + 2KsCH~CO~ + CH~O ]
`(I + KICH)2 K2CH3 (I + K6CH)CHJ
`(44)
`
`K5
`
`K2CH2
`
`(45)
`
`C=l+~+. 1--~
`K2CH K2CH
`
`D = CH~CO~ ÷ 2KSCH~CO~
`K2CH2
`K2CH3
`
`(46)
`
`(47)
`
`ke = he(pH --- 9) [.261(pH) - 1.349]
`
`(54)
`
`where ko (pH = 9) is 6 X 107 min-1. Using these values of the
`kinetic and equilibrium constants, eq 51-53 were solved
`
`Ind. Eng. Chem., Fundam., Vol. 16, No. 4, 1977 4$$
`
`Akermin, Inc.
`Exhibit 1006
`Page 4
`
`

`

`~
`
`~
`
`CH2C0
`
`- CCO~
`
`10
`
`lz
`
`4 6 8
`
`10
`
`12 14 16 18
`
`t (rain)
`
`Figure 2. Experimental and calculated values of pH as a function of
`time. Buffer only, with no enzyme present. Experimental points for
`gas flow rate of 41 cm3/min (e). Theory (--) with SgkL ffi 0.095 min-1.
`Experimental points for gas flow rate of 61 cmS/min (O). Theory
`( .... ) with SgkL ffi 0.195 min-1.
`
`1 I I I
`5
`10
`15
`ZO
`
`25
`
`30
`
`t (min)
`
`Figure 4. Calculated concentrations of intermediates in buffer system
`with no enzyme, SgkL = 0.095 rain-1,
`
`I I I ! I I I
`
`10.0
`
`9.5
`
`90
`
`8,5
`
`8,0
`
`7.5
`
`7.0
`
`0
`
`2
`
`4
`
`6
`
`8 10
`
`12 14 16 18 ZO
`
`t (rnin)
`
`Figure 3. Experimental and calculated values of pH as a function of
`time. Enzyme (1 mg) in solution. Experimental points for gas flow rate
`of 41 cm3/min (e). Theory (--) with SghL = 0.090 min-1.
`
`merically using the Runge-Kutta method of fourth-order
`accuracy (Hildebrand, 1962). The value of SgkL was treated
`as a parameter, chosen to obtain the best possible fit with the
`experimental data of pH vs. time. The enzyme concentration
`E0 in moles per liter was calculated using a molecular weight
`of 30 000 (Lindskog et al., 1971).
`Figure 2 shows the comparison between the calculated and
`experimental values of pH as a function of time for CO2 ab-
`sorption into the buffer with no enzyme present, at two dif-
`ferent gas flow rates: 41 and 61 cm3/min. The values of SgkL
`for these two cases were 0.095 and 0.195 min-1, respectively.
`The good agreement between theory and experiment justifies
`the use of eq 11 to describe the absorption process and proves
`the approximations made in its derivation to be valid, in-
`cluding the pseudo-steady-state approximation, the as-
`sumption of negligible reaction in the stagnant film around
`the gas bubbles, and the neglect of mass transfer at the free
`surface of the liquid. The slight disagreement for large times
`near equilibrium is probably due to the above-mentioned
`inaccuracies in some of the values in Table I as well as exper-
`imental error.
`
`456
`
`Ind. Eng. Chem., Fundam., Vol. 16, No. 4, 1977
`
`In similar slurry absorbers, Misic and Smith (1971) ob-
`tained Sg values of 0.078 to 0.28 cm-1 when the gas flow rates
`were in the range 42-132 cm3/min. Our values of Sg should be
`close to these due to the similarities in slurry geometries. Using
`their figures Sg ffi 0.076 cm-1 when the gas flow rate is 41
`cm3/min and Sg = 0.113 cm-1 when the flow rate is 61 cm3/
`min, assuming the Sg dependence on flow rate is linear. Using
`these estimates, we obtain values of kL = 2 X 10-2 cm/s and
`2.8 X 10-2 cm/s. These are in excellent agreement with esti-
`mates using mass transfer correlations for slurry absorbers.
`The Calderbank and Moo-Young (1961) correlation gives
`estimates of 2.8 × 10-2 cm/s for bubbles greater than 2.5 mm
`in diameter and 6.6 × 10-3 cm/s for bubbles less than 1 mm
`in diameter. Hughmark (1967) obtained a correlation that
`predicts kL to be approximately 5 × 10-2 cm/s. The total
`surface areas around the gas bubbles using these values of Sg
`are Ag ffi 22.8 and 84 cm~ at the two different flow rates.
`In Figure 3 we show the comparison between theory and
`experiment when 1 mg of carbonic anhydrase is added to the
`buffer solution. The value of SgkL used is 0.09 rain-1, since the
`flow rate of gas was approximately 41 cm3/min, the same as
`in one of the previous experiments using buffer only. The
`agreement between theory and experiment is excellent
`throughout the entire range of pH.
`The value of SgkL was changed from 0.095 to 0.090 min-~
`due to the fact that a slightly narrower impeller was used in
`these experiments. The value of 0.090 rain-~ gave better
`agreement with experimental data. Values of SgkL were found
`to be very sensitive to changes in absorber geometry.
`For times less than 1 min, the absorption term in eq 51
`governs the behavior of the system, causing a rapid increase
`in the concentration of C02 in the liquid and a rapid increase
`in the time derivative of the hydrogen ion concentration. This
`is shown in Figure 4 where the concentrations of the inter-
`mediate species are plotted as a function of time for the buffer
`experiment without enzyme. After 1 rain, the first term in F,
`eq 49, dominates with both the k~ and k4 terms being impor-
`tant. This indicates that in the pH range from 9.4 to about 8.5
`reactions 24 and 25 in the buffer are both occurring at ap-
`proximately equal rates. Below pH 8, the buffer loses much
`of its buffering capacity and a sudden drop in pH is experi-
`enced. This portion of the pH-time curve is extremely sensi-
`tive to the choice of Sgka. The pH vs. time curves are concave
`upward for very short times and concave downward in the pH
`range from 8.5 to about ~(.5, where they become concave up-
`
`Akermin, Inc.
`Exhibit 1006
`Page 5
`
`

`

`0
`
`I
`
`CH2C03
`
`-- CC0;
`
`~ ~ dCH
`
`Figure 5. Calculated concentrations of intermediates in system
`consisting of buffer and free enzyme, SgkL = 0.090 rain-1.
`
`0,2
`
`0,4
`
`0.6
`
`1.0
`
`t (rain)
`
`t (min)
`
`ward again. This second inflection point occurs when the
`quantity B, eq 45, goes through zero, at a pH
`
`pH = -log ~22
`
`(55)
`
`independent of SgkL. At this point, dcH/dt goes through a
`maximum, as shown in Figure 5, since the denominator of eq
`52 goes through its lowest point. At pH 7, the absorption term
`is approximately a factor of 10 times bigger than F in eq 51,
`the k8 and k-3 terms dominate in F, and therefore reaction
`25 is no longer important. This is also reflected in Figure 4,
`where we see the HCO3- concentration reaching its equilib-
`rium value after 10 min. Note that the H~C08 concentration
`increases continuously with time while the CO3~- concen-
`tration drops.
`In the enzyme with buffer system, the enzyme rate rf - rb
`is as important as the buffer reaction rate terms throughout
`the entire pH range. This leads to an increased rate of ab-
`sorption when compared to the system with buffer only. This
`is reflected in the higher rate of change of the pH with time
`in Figure 3 when compared to Figure 2 with ~qgkL = 0.090
`min-L Figure 5 shows the concentration of several of the
`components in the liquid as a function of time when the en-
`zyme is present in solution. The rate of change of the hydro-
`nium ion concentration does not go through as sharp a maxi-
`mum as with the buffer system in the absence of enzyme. The
`HC03- concentration reaches its equilibrium value in a
`shorter time, and the rate is then controlled by the conversion
`of CO2 to H2C03.
`In order to study the reaction of the microencapsulated
`enzyme, 0.6 mL of microcapsules was introduced in the buffer.
`The introduction of the microcapsules into the theory replaces
`the rf and rb terms in F, eq 49, by the expression
`
`~ib = --~/ VL \Kin + cco2 Km’ + CH2CO3/
`
`(56)
`
`from eq 11. Here E0 is the enzyme concentration within the
`microcapsule, and the concentrations of CO2 and H2CO3 are
`bulk concentrations. The enzyme concentration Eo is 20
`mg/mL, the enzyme concentration used in making the mi-
`crocapsules. Wadiak and Carbonell (1975a) found that in
`microencapsulation, the enzyme concentration within the
`microcapsules is at least as large as the initial concentration
`of enzyme dissolved in the hemoglobin. The effectiveness
`
`Figure 6. Calculated and experimental values of pH as a function of
`time wkh microencapsulated enzyme. Gas flow rate is 41 cma/min,
`Sgk~ = 0.090 rain-~ and ~ = 0.003.
`
`factor n is going to be a function of the concentration of the
`reactants since the rate expression is nonlinear. However, as
`of yet there are no ways of estimating n for reversible enzy-
`matic reactions theoretically.
`By keeping the same gas flow rate (41 cmS/s) and therefore
`the same SgkL --- 0.090 min-~, we can use ~ as a parameter to
`fit the experimental section rate data for average values of CO2
`and H~CO3 concentrations. Figure 6 shows the result of this
`analysis in the pH range 9.7 to 9.0. The effectiveness factor
`calculated from this theory is n = 0.003. This is an average
`value of the effectiveness factor for the ranges of C02 and
`H2C03 concentration found in the reaction in the time interval
`0 to 1 min. This low value is not unreasonable, considering the
`great speed of the enzymatic reaction.
`Using the theory for effectiveness factors for enzymatic
`reactions developed by Fink et al. (1973) and the value of the
`parameters in Table I, we find that the Thiele modulus for
`microencapsulated carbonic anhydrase is of the order of 500.
`The Sherwood number for mass transfer to the microencap-
`sules, including both the liquid to particle mass transfer
`coefficient (~10-2 cm/s) and the membrane permeability for
`CO~ (,--10-2 cm/s) is of order 100. The effectiveness factor for
`such a system calculated by Fink et al. is of the order of 10-3,
`in agreement with our experimental results. These estimates
`are based on a particle radius of 60 ~, as found by Wadiak and
`Carbonell (1975a) and a diffusivity for C02 in the microcap-
`sule of 10-s cm~/s. The low value of ~ is due not to low mem-
`brane permeabilities but rather to high rates of reaction within
`the capsule.
`
`Conclusions
`The appropriate macroscopic mass balance equations for
`batch absorption of a gas into a liquid with simultaneous
`heterogeneous and homogeneous chemical reactions are
`considered. An order of magnitude analysis shows under what
`conditions the pseudo-steady-state approximation should’give
`accurate results. Equation 11, with one adjustable parameter
`SgkL, gave excellent agreement with experimentally measured
`rates of absorption of CO2 into Veronal buffer solutions
`without enzyme and with free carbonic anhydrase. Estimated
`values of k L are in agreement with the predictions of previous
`correlations. The closeness of the agreement justifies the as-
`
`Ind. Eng. Chem., Fundam., Vol. 16, No. 4, 1977 4~7
`
`Akermin, Inc.
`Exhibit 1006
`Page 6
`
`

`

`sumptions made in the derivation: pseudo-steady-state,
`negligible C02 transfer through the free surface liquid, and
`negligible reaction within the stagnant liquid films sur-
`rounding the gas bubbles. The microencapsulated enzyme
`showed an extremely low effectiveness factor, consistent with
`the very fast rate of the enzymatic reaction.
`
`Nomenclature
`A = variable, eq 44
`Ag = total surface area of gas bubble
`Af -- surface area of free surface liquid
`Ap -- total surface area of catalyst particles
`B = variable, eq 45
`C = variable, eq 46
`ci = concentration of i in bulk liquid
`c~* = equilibrium concentration of i at bubble-liquid in-
`terface
`c~f* = equilibrium concentration of i at liquid-atmosphere
`interface
`C~o -- initial condition on bulk liquid concentration
`c = total molar concentration in liquid
`co = totalbuffer concentration
`E -- variable, eq 48
`Eo = enzyme concentration
`F -- variable, eq 49
`He = Henry’slaw constant
`Ji* = molar flux relative to the molar average velocity
`kl, k2, ks, k4, ks, k6 = rate constants in the forward reac-
`tions
`k-l, k-2, h_3, k-4, k-5, k_5 --- rate constants in the backward
`reactions
`K1, K2, Ks, Ka, Ks, Ks = equilibrium constants
`ke, k-e = turnover numbers for the enzymatic reaction
`Kin, Kin’ = Michaelis-Menten constants for the forward and
`reverse reaction
`hL -- mass transfer coefficient from the bubble to the liei-
`uid
`kaf = mass transfer coefficient from the bulk liquid to the
`free surface
`n = unit normal directed outwardly, away from the control
`volume
`p = partial pressure of the gas
`ri