CHEE 323 J.S. Parent 1

Mass Transfer Effects Resulting from Immobilization

Immobilization of an enzyme transforms a homogeneous (soluble) catalyst into a heterogeneous (insoluble) system. While this technique often improves enzyme stability and allows for its retention within a continuous reactor, it also introduces mass transfer effects that require careful design consideration.

Carrier binding techniquesintroduce external masstransfer effects betweenthe liquid phase and thesolid surface.

Entrapment methods fixthe enzyme in a polymericmatrix, creating internal masstransfer effects that arediffusion processes.

CHEE 323 J.S. Parent 2

External Mass Transfer Effects

An enzyme immobilized through binding to a carrier bead and placed in a simple flow may be represented by the following illustration.

The change in concentration of a reagent A from [A]bulk to [A]surface takes place in a narrow fluid layer next to the surface of the sphere.

In all but the simplest cases, we express the mass transfer rate as:

whereNA = transfer rate: mole/skc = convective mass transfer coefficient: m/sAP = surface area of the particle: m2

[A]= concentration of solute at the surface and in the bulk, respectively: mole/m3

])A[]A([AkN spcA

CHEE 323 J.S. Parent 3

Convective Mass Transfer Coefficient, kc

Having defined kc by the rate equation for convective mass transfer,

it remains for engineers to determine its value for different situations. This is a difficult task, as kc is influenced by

properties of the fluid (density, viscosity) dynamic characteristics of the fluid (velocity field) properties of the solute (diffusivity)

In complex situations we apply mass transfer correlations of the form:

where, Sh = Sherwood number = kcd/DAB

Re = Reynolds number = vd/Sc = Schmidt number = DAB

Estimating kc therefore requires a characteristic dimension (d), solute diffusivity (DAB), fluid velocity (v) as well as fluid density ( and viscosity().

])A[]A([AkN spcA

)Sc(Re,fSh

CHEE 323 J.S. Parent 4

External Mass Transfer: Single Sphere

Extensive data have been compiled for the transfer of mass between moving fluid and certain shapes, such as flat plates, spheres and cylinders.

For a single sphere the Froessling equation can be used:

provided that Re is within 2-800 and Sc is within 0.6-2.7.

Catalytic reactors seldom use such simple geometry, and designers must search the literature for correlations that apply to their particular configuration, flow patterns as well as fluid and solute properties.

3/12/1AB ScRe522.00.2Sh

CHEE 323 J.S. Parent 5

You are required to process 1 litre per minute of an aqueous solution containing 0.3 M of substrate.

The desired conversion is 80%.

Rate data for the immobilized enzyme have been acquired. The system follows Michaelis-Menten kinetics, and given 95 particles per litre of solution, the reaction rate is given by:

Antibiotic Synthesis in an Immobilized Enzyme PFR

To illustrate the type of analysis required for heterogeneous catalytic reactor design, consider the large scale production of a modified antibiotic using a PFR configuration.

Q = 1 LPM[A]o = 0.3 M

T = 20C

[A] = 0.024 M

]A[M05.0

]A[]E[sM6.9dt

]A[dr

1T

11

A

CHEE 323 J.S. Parent 6

Assumptions Made in the PFR Analysis

To simplify the preliminary design process a series of assumptions regarding both the catalyst and the fluid flow characteristics:

Catalytic Reaction Simplifications: enzyme is stable over the time course of the reaction no product or reactant inhibition takes place the reaction is irreversible

Plug Flow Reactor Simplifications No axial mixing (backmixing) to disrupt plug flow Isothermal process No change in fluid properties upon reaction

These simplifications are often unjustified. “Real” PFR design would use much more detailed reaction rate and residence time distribution information.

CHEE 323 J.S. Parent 7

PFR Design Equation

Given that Michaelis-Menten kinetics applies to this immobilized enzyme case, the governing rate expression is:

Vmax = 3.84E-5 M-1s-1 Km = 0.05 M-1

Rearranging yields,

and integration generates the PFR design equation:

We can express this design equation in terms of reactant conversion, X = ([A]0 -[A])/([A]0:

]A[K]A[V

dt]A[d

rm

maxp

tV])A[]A([]A[]A[

lnK maxoo

m

t

omax

]A[

]A[

M dtV]A[d1]A[

K

o

tVX]A[X1

1lnK maxom

CHEE 323 J.S. Parent 8

PFR Design Equation

Up to this point the design equation is explicit in time, as required for a batch process.

Given that the residence time for the reactor is tres = V/Q,

where V = reactor liquid holdup: m3 Q = liquid volumetric flow rate: m3/s

Given our process requirements: [A]o = 0.3 M Q = 1 LPM X = 0.80

the liquid phase volume of our PFR isV = 139 liters

and the total PFR volume including immobilized enzyme is:Vtot = V /

= 139/0.6 = 232 liters

QV

VX]A[X1

1lnK maxom

CHEE 323 J.S. Parent 9

PFR Sizing

Reaction kinetics for an ideal PFR dictate that the total reactor volume needed to achieve 80% conversion is 232 liters.

To minimize backmixing, we need the reactor length to be much greater than the diameter.

For convenience, a single straight-run PFR is desirable, so we will (arbitrarily) choose L/D = 15.

D Given a total volume of 232 liters andan aspect ratio of 15:

column diameter = 0.27 m column length = 4.05 m

LThese are physically realizable dimensions.

CHEE 323 J.S. Parent 10

PFR Reaction Profile - Substrate Consumption Rate

To this point we have ignored mass transfer by treating the process as kinetic controlled. This is true only when the rate of mass transfer is sufficient to supplysubstrate to the immobilizedenzyme site.

Is the rate of reactionlimited by mass transfer?

Given that mass transfer is governed by the following:

are kc (Re, Sc) and Ap great enough to avoiddepletion of substrate at theliquid-solid interface?

PFR Conversion Profile

0.00

0.20

0.40

0.60

0.80

1.00

0.0 1.0 2.0 3.0 4.0

Length (m)

Con

vers

ion

0.0E+00

5.0E-06

1.0E-05

1.5E-05

2.0E-05

2.5E-05

3.0E-05

3.5E-05

Rea

ctio

n R

ate

(mol

e/ l

sec)

Conversion

Rate])A[]A([AkN spcA

CHEE 323 J.S. Parent 11

Mass Transfer Correlation for a Packed Bed

Mass transfer between liquids and beds of spheres has been studied experimentally and the data correlated to:

for the range (0.0016<Re<55, 165<Sc<70600, 0.35<<0.075)where = void fraction of the packed bed

kc = convective mass transfer coefficient: m/sv = bulk fluid velocity: m/s

Sc = Schmidt number: /DAB (dimensionless) = kinematic viscosity (): m2/sDAB= Diffusivity of solute in water: m2/s

Re= Reynolds number: dp*G/dp = particle diameter: mG = mass per unit time per unit of empty column

cross-sectional area: kg/m2 s fluid viscosity: kg/ms

Re09.1

Scvk

orRe09.1

j 3/2cD

CHEE 323 J.S. Parent 12

kc for Our Packed Bed Reactor

Rearranging our correlation for mass transfer in a packed columngives us kc as a function of easily(!) estimated properties.

Bulk Velocity, v= 4.85E-04 m/sVoid Fraction, = 0.6

Particle diameter = 2.00E-02 mFluid viscosity = 9.94E-4 Pa.sMass flux = 0.29 kg/m2s (liq flow*density/empty column area)

Re = 5.85 (in range of correlation)

Diffusivity, DAB = 2.0*10-9 m2/sKinematic viscosity, = 9.95*10-7 m2/s

Sc = 497 (in range of correlation)

Therefore, kc = 2.41*10-6 m/s

3/2cScRe

v09.1k

CHEE 323 J.S. Parent 13

Extent of Mass Transfer Limitation

The maximum demand for substrate takes place at the entrance of the reactor where [A] is greatest. From our PFR conversion calculations (see slide 10),

rA, max = 3.29*10-5 mole/l s

The mass transfer rate per particle is given by:

For which the maximum transfer rate ([A]s=0) is:

Given that we have 95 particles for each litre,

Therefore, the reaction rate at the top of our PFR is completely mass transfer limited to a maximum rate of 2.2*10-5 mole/ls and we would not achieve our desired conversion with the current design.

])A[]A([AkN spcA

particles/mole10*27.2

]A[AkN

7

pcmax,A

sl/mole10*16.2N 5max,A