Recycle packed column reactor: - allow the reactor to operate at high fluid velocities. - a substrate that cannot be completely processed on a single pass Immobilized Enzyme Reactors

Fluidized Bed Reactor: - a high viscosity substrate solution - a gaseous substrate or product in a continuous reaction system - care must be taken to avoid the destruction and decomposition of immobilized enzymes

- An immobilized enzyme tends to decompose upon physical stirring. - The batch system is generally suitable for the production of rather small amounts of chemicals.

Diffusional Limitation in Immobilized Enzyme System Immobilized enzyme system normally includes - insoluble immobilized enzyme - soluble substrate, or product They are heterogeneous systems

CONCENTRATION DIFFERENCE FILM TRANSFER DRIVING FORCE DIFFUSION HIGH Immobilized Enzyme SbSb ELECTRIC ATTRACTION Low S concentration Substrate

CONCENTRATION DIFFERENCE FILM TRANSFER DRIVING FORCE DIFFUSION HIGH Immobilized Enzyme SbSb ELECTRIC ATTRACTION REACTION PRODUCT

FILM TRANSFER DRIVING FORCE DIFFUSION HIGH Immobilized Enzyme SbSb INTRA-PARTICLE TRANSFER

FILM TRANSFER PRODUCT HIGH Immobilized Enzyme SbSb INTRA-PARTICLE TRANSFER REACTION

Diffusional Limitation in Immobilized Enzyme System In immobilized enzyme system, the overall production rate is determined by - liquid film mass transfer (external diffusion) substrate, product - intraparticle mass transfer (internal diffusion) substrate, product in porous supports - enzyme catalysis reaction

Diffusional Limitation in Immobilized Enzyme System Diffusion effects in surface-bound enzymes on nonporous support materials. Ss: substrate concentration at surface; Sb: substrate concentration in bulk solution. Enzyme Ss Sb Liquid Film Thickness, L E+S

Diffusion effects in surface-bound enzymes on nonporous support materials. Enzyme Ss Sb Liquid Film Thickness, L No intraparticle diffusion Assume: -Enzyme are evenly distributed on the surface of a nonporous support material. -All enzyme molecules are equally active. -Substrate diffuses through a thin liquid film surrounding the support surface to reach the reactive surface. -The process of immobilization has not altered the enzyme structure and the intrinsic parameters (Vm, Km) are unaltered.

Diffusion effects in surface-bound enzymes on nonporous support materials. is the maximum reaction rate per unit of external surface area (e.g. g/cm 2 -s) To determine the significant effect of external diffusion resistance on the rate of enzyme catalytic reaction rate: Damköhler numbers (Da) is the liquid mass transfer coefficient (cm/s) Is the substrate concentration in bulk solution (g/cm 3 )

Diffusion effects in surface-bound enzymes on nonporous support materials. When Da >> 1, the external diffusion rate is limiting; Da << 1, the reaction rate is limiting; Da ≈ 1, the external diffusion and reaction resistances are comparable.

Diffusion effects in surface-bound enzymes on nonporous support materials. The reaction rate is : The external diffusion rate (g/cm 2 -s): the maximum reaction rate per unit surface area. (g/cm 2 -s) is the liquid mass transfer coefficient (cm/s).

Diffusion effects in surface-bound enzymes on nonporous support materials. Accumulation of substrate Ss = substrate gain - substrate consumption According to the mass balance of substrate at the surface : E+S

Diffusion effects in surface-bound enzymes on nonporous support materials. At steady state, the reaction rate is equal to the external diffusion rate: According to the mass balance of substrate at the surface :

Diffusion effects in surface-bound enzymes on nonporous support materials. At steady state, the reaction rate is equal to the external diffusion rate: With the equation and known S b, K L, V m ’ or K m, to determine numerically or graphically: - The substrate concentration at the surface. - The reaction rate.

Graphical solution for reaction rate per unit of surface area for enzyme immobilized on a non-porous support

Diffusion effects in surface-bound enzymes on nonporous support materials. When the system is strongly external diffusion (liquid film mass-transfer) limited, [Ss]≈0, the overall reaction rate is equal to the rate: The system behaves as pseudo first order. The rate is a linear function of bulk substrate concentration. Da>>1

Diffusion effects in surface-bound enzymes on nonporous support materials. To increase the overall reaction rate with external diffusion limitation -Increase the bulk concentration of substrate. -Increase the liquid film mass transfer coefficient k L.

The liquid film mass transfer coefficient k L: (H. Fogler, Elements of Chemical Reaction Engineering 1999, p705) D AB is mass diffusivity of the substrate in the liquid phase, a function of temperature and pressure (m 2 /s) ν is the kinematic viscosity (m 2 /s), a function of temperature. U is the free-system liquid velocity (velocity of the fluid flowing past the particle) (m/s). dp is the size of immobilized enzyme particle (m). At specific T and P, increasing U and decreasing d p increase the liquid film mass transfer coefficient and the external diffusion rate.

Diffusion effects in surface-bound enzymes on nonporous support materials. When the system is strongly reaction limited, [Sb] ≈ [Ss] the overall reaction rate is equal to the rate: Da << 1 can be determined experimentally.

Diffusion Effects in Enzymes Immobilized in a Porous Matrix - Substrate diffuses through the tortuous pathway within the porous support to reach the enzyme. - Substrate reacts with enzyme on the pore surface.

Diffusion Effects in Enzymes Immobilized in a Porous Matrix Assume: -Enzyme is uniformly distributed in a sphere support particle. -There is not partitioning of the substrate between the exterior and interior of the support.

Diffusion Effects in Enzymes Immobilized in a Porous Matrix At steady state, the intraparticle diffusion rate of substrate equals to the reaction rate in a spherical shell: is the reaction rate per unit volume of support (mg/cm 3 -s). De is the effective diffusivity (cm 2 /s). R r r+ Δr

Diffusion Effects in Enzymes Immobilized in a Porous Matrix When→ 0 Re-arrange this equation yields Dividing the two sides of the equation by

Diffusion Effects in Enzymes Immobilized in a Porous Matrix Then is the maximum reaction rate per unit volume of support (mg/cm 3 -s). De is the effective diffusivity (cm 2 /s). Dividing the two sides of the equation by r 2, yields,

The above equation can be written in dimensionless form by defining the following dimensionless variables: =Thiele modules

With boundary conditions of This differential equation can be solved numerically. Refer to H. Fogler, Elements of Chemical Reaction Engineering 1999, p746 for analytical solution for first order reaction.

At steady state, the rate of substrate consumption is equal to the rate of substrate transfer through the external surface of the support particle into the sphere. Under diffusion limitations, the rate per unit volume is usually expressed in terms of the effectiveness factor as follows:

is the effectiveness factor. the rate is diffusion limited. the rate is reaction limited. The relationship can be obtained empirically. Analytical expression is available for some special cases

Relationship of effectiveness factor with the size of immobilized enzyme particle and enzyme loading

At specific conditions (T, P) for a fixed system, To increase the intra-particle mass transfer rate: - Decrease the size of immobilized enzyme particle - Increase the substrate concentration - Increase the porosity or specific surface area of the particle

Electrostatic and Steric Effects in Immobilized Enzyme Systems The optimum pH for immobilized enzyme system will shift from that of soluble free enzyme The charged matrix may repel or attract substrate, product, cofactors or H + Electrostatic effect The activity of enzyme toward a high-molecule- weight substrate may be reduced. Steric hindrance

Summary of Diffusion Effects - Determine the support to be non-porous or porous. - Identify the substrate determining the reaction rate. - Conduct mass balance of the substrate of interest. Accumulation of substrate of interest = rate of substrate gain - substrate consumption rate (production formation rate, or reaction rate) At steady state, Rate of substrate gain = substrate consumption rate

Summary of Diffusion Effects At steady state, the reaction rate per unit surface area is equal to the rate of net substrate gain in regard to the external diffusion. With the equation and known S b, K L, V m ’ or Km, to determine graphically or numerically: - The substrate concentration at the surface. - The reaction rate. In surface-bound enzymes on nonporous support materials. Consider external diffusion rate (liquid film mass transfer rate)

Summary of Diffusion Effects At steady state, the reaction rate per unit volume is equal to the rate of net substrate gain in regard to the intraparticle diffusion. In surface-bound enzymes on porous support materials. Consider intraparticle diffusion rate.

is the effectiveness factor. the rate is diffusion limited. the rate is reaction limited.

At specific conditions (T, P) for a fixed system, To increase the intra-particle mass transfer rate: - Decrease the size of immobilized enzyme particle - Increase the substrate concentration - Increase the porosity or specific surface area of the particle

Electrostatic and Steric Effects in Immobilized Enzyme Systems - The optimum pH for immobilized enzyme system will shift from that of soluble free enzyme Electrostatic effect - The activity of enzyme toward a high-molecule- weight substrate may be reduced. Steric hindrance