Mass Transfer Effects Resulting from Immobilization

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 techniques
• introduce external mass
• transfer effects between
• the liquid phase and the
• solid surface.
• Entrapment methods fix
• the enzyme in a polymeric
• matrix, creating internal mass
• transfer effects that are
• diffusion processes.

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
  Abulk to Asurface 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
• where NA transfer rate mole/s
• kc convective mass transfer coefficient m/s
• AP surface area of the particle m2
• A concentration of solute at the surface
  and in the bulk,
• respectively mole/m3

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 rvd/m
• Sc Schmidt number m/rDAB
• Estimating kc therefore requires a characteristic
  dimension (d), solute diffusivity (DAB), fluid
  velocity (v) as well as fluid density (r ) and
  viscosity(m).

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.

5
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
• Ao 0.3 M
• T 20?C
• A 0.024 M

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
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.

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 (A0 -A)/(A0

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
• Ao 0.3 M Q 1 LPM X 0.80
• the liquid phase volume of our PFR is
• V 139 liters
• and the total PFR volume including immobilized
  enzyme is
• Vtot V / e
• 139/0.6 232 liters

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 and
• an aspect ratio of 15
• column diameter 0.27 m
• column length 4.05 m
• L
• These are physically realizable dimensions.

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 supply
• substrate to the immobilized
• enzyme site.
• Is the rate of reaction
• limited by mass transfer?
• Given that mass transfer
• is governed by the following
• are kc (Re, Sc) and Ap
• great enough to avoid
• depletion of substrate at the
• liquid-solid interface?

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 (0.0016ltRelt55, 165ltSclt70600,
  0.35ltelt0.075)
• where e void fraction of the packed bed
• kc convective mass transfer coefficient m/s
• v? bulk fluid velocity m/s
• Sc Schmidt number n/DAB (dimensionless)
• n kinematic viscosity (m/r) m2/s
• DAB Diffusivity of solute in water m2/s
• Re Reynolds number dpG/m
• dp particle diameter m
• G mass per unit time per unit of empty
  column
• cross-sectional area kg/m2 s
• m fluid viscosity kg/ms

12
kc for Our Packed Bed Reactor

• Rearranging our correlation for mass transfer in
  a packed column
• gives us kc as a function of
• easily(!) estimated properties.
• Bulk Velocity, v? 4.85E-04 m/s
• Void Fraction, e 0.6
• Particle diameter 2.00E-02 m
• Fluid viscosity 9.94E-4 Pa.s
• Mass flux 0.29 kg/m2s (liq flowdensity/empty
  column area)
• Re 5.85 (in range of correlation)
• Diffusivity, DAB 2.010-9 m2/s
• Kinematic viscosity, n 9.9510-7 m2/s
• Sc 497 (in range of correlation)
• Therefore,
• kc 2.4110-6 m/s

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 3.2910-5 mole/l s
• The mass transfer rate per particle is given by
• For which the maximum transfer rate (As0) 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 2.210-5 mole/ls and we would not
  achieve our desired conversion with the current
  design.