Mass transfer immobilized enzyme particles

Another type of mass transfer equipment, shown in Figure 6.2d, is normally referred to as the packed- (fixed-) bed. Unlike the packed column for gas-liquid mass transfer, the packed-bed column is used for mass transfer between the surface of packed solid particles (e.g., catalyst particles or immobilized enzyme particles) and a single-phase liquid or gas. This type of equipment, which is widely used as reactors, adsorption columns, chromatography columns, and so on, is discussed in greater detail in Chapters 7 and 11. 

Apparent reaction rates with immobilized enzyme particles also decrease due to the mass transfer resistance of reactants (substrates). The Thiele modulus of spherical particles of radius R for the Michaelis-Menten type reactions is given as... 

Consider an idealized simple case of a Michaelis-Menten type bioreaction taking place in a vertical cylindrical packed-bed bioreactor containing immobilized enzyme particles. The effects of mass transfer within and outside the enzyme particles are assumed to be negligible. The reaction rate per dilfcrential packed height (m) and per unit horizontal cross-sectional area of the bed (m ) is given as (cf. Equation 3.28) ... 

The catalytic behavior of enzymes in immobilized form may dramatically differ from that of soluble homogeneous enzymes. In particular, mass transport effects (the transport of a substrate to the catalyst and diffusion of reaction products away from the catalyst matrix) may result in the reduction of the overall activity. Mass transport effects are usually divided into two categories - external and internal. External effects stem from the fact that substrates must be transported from the bulk solution to the surface of an immobilized enzyme. Internal diffusional limitations occur when a substrate penetrates inside the immobilized enzyme particle, such as porous carriers, polymeric microspheres, membranes, etc. The classical treatment of mass transfer in heterogeneous catalysis has been successfully applied to immobilized enzymes I27l There are several simple experimental criteria or tests that allow one to determine whether a reaction is limited by external diffusion. For example, if a reaction is completely limited by external diffusion, the rate of the process should not depend on pH or enzyme concentration. At the same time the rate of reaction will depend on the stirring in the batch reactor or on the flow rate of a substrate in the column reactor. 

The mass transfer of a cell to an Immobilized enzyme particle brings a relatively modest number of hydrolyzable bonds per cell particle to the catalyst. The above lysozyme data Indicate that the reaction rate Is essentially mass transfer controlled,... 

Quantitative analytical treatments of the effects of mass transfer and reaction within a porous structure were apparently first carried out by Thiele (20) in the United States, Dam-kohler (21) in Germany, and Zeldovitch (22) in Russia, all working independently and reporting their results between 1937 and 1939. Since these early publications, a number of different research groups have extended and further developed the analysis. Of particular note are the efforts of Wheeler (23-24), Weisz (25-28), Wicke (29-32), and Aris (33-36). In recent years, several individuals have also extended the treatment to include enzymes immobilized in porous media or within permselective membranes. The important consequence of these analyses is the development of a technique that can be used to analyze quantitatively the factors that determine the effectiveness with which the surface area of a porous catalyst is used. For this purpose we define an effectiveness factor rj for a catalyst particle as... 

As most biochemical reactions occur in the liquid phase, bioreactors usually handle liquids. Processes in bioreactors often also involve a gas phase, as in cases of aerobic fermentors. Some bioreactors must handle particles, such as immobilized enzymes or cells, either suspended or fixed in a liquid phase. With regard to mass transfer, microbial or biological cells may be regarded as minute particles. 

In the design and operation of various bioreactors, a practical knowledge of physical transfer processes - that is, mass and heat transfer, as described in the relevant previous chapters - are often also required in addition to knowledge of the kinetics of biochemical reactions and of cell kinetics. Some basic concepts on the effects of diffusion inside the particles of catalysts, or of immobilized enzymes or cells, is provided in the following section. 

The immobilization of enzymes may introduce a new problem which is absent in free soluble enzymes. It is the mass-transfer resistance due to the large particle size of immobilized enzyme or due to the inclusion of enzymes in polymeric matrix. If we follow the hypothetical path of a substrate from the liquid to the reaction site in an immobilized enzyme, it can be divided into several steps (Figure 3.2) (1) transfer from the bulk liquid to a relatively unmixed liquid layer surrounding the immobilized enzyme (2) diffusion through the relatively unmixed liquid layer and (3) diffusion from the surface of the particle to the active site of the enzyme in an inert support. Steps... 

If an enzyme is immobilized on the surface of an insoluble particle, the path is only composed of the first and second steps, external mass-transfer resistance. The rate of mass transfer is proportional to the driving force, the concentration difference, as... 

An enzyme is immobilized by copolymerization technique. The diameter of the spherical particle is 2 mm and the number density of the particles in a substrate solution is 10,000/L. Initial concentration of substrate is 0.1 mole/L. A substrate catalyzed by the enzyme can be adequately represented by the first-order reaction with k0 = 0.002 mol/Ls. It has been found that both external and internal mass-transfer resistance are significant for this immobilized enzyme. The mass-transfer coefficient at the stagnant film around the particle is about 0.02 cm/s and the diffusivity of the substrate in the particle is 5 x 10-6 cm2/s. 

The efficiency of the operation is conditioned by three main factors (1) active enzyme concentration, (2) mass transfer rate, and (3) operational parameters, such as plugging. Mass transfer rate depends in large part upon the linear velocity of the fluid through the bed. Hence, in order to maximize the efficiency, high L/D ratios are required, which may also reduce back mixing. However, the length of the bed is limited by the pressure that immobilized particles may withstand [116]. Flow rate, L/D ratio, pH, and temperature are some of the operational parameters that should be optimized for an efficient operation. In Shukla et al., a fixed bed reactor is used for phenol oxidation by HRP [87]. At least three cycles were needed for 80% phenol removal under the optimal L/D ratio, HRT, temperature, and substrate concentration. 

Myristic acid was purchased from Sigma (St Louis, MO) and ethanol (99.85 %) from Prolabo (France). Ultra pure carbon dioxide (99.995 %) was purchased from Airgaz (France). The lipase (E C. 3.1.1.3.) was a commercial enzyme from Mucor miehei kindly supplied by Novo Nordisk (Denmark). This lipase (Lipozyme TM) is immobilized on Duolite A568 (Rohm and Hass). The resin particles have a size comprised between 300 to 600 pm. In order to see if a phenomenon of internal mass transfer occurs during the enzymatic esterification, we sieved the support into different size series. The average granulometry was determined by Coulzer Sizer method (Table 1). 

Enzymes can be immobilized in sheets. One design had discs of enzymes fastened to a rotating shaft to improve mass transfer, and an alternate design had the feed stream flowing back and forth through sandwiches of sheets with enzyme. However, volumetric efficiency of such reactors is low because sheets with finite spacing offer less area than that of packed particles. 

In many cases the influence of particle mass transfer on the reaction rate can be neglected (value of Thiele modulus approaches zero or the enzyme is immobilized exclusively on the particle surface). Then, value of the effectiveness factor is unity and the solution of Eqs. (1) - (3) is substantially simpler. 

Accumulated protons generated within the pores of a catalyst cause the formation of a proton gradient. The extent of such a gradient is predominantly a matter of the proton formation rate, which is dependent on the immobilized enzyme s activity and the mass transfer driven transport of protons to the outside of the catalyst particles. At steady state a mass balance occurs. 

The two-stage biocatalytic reaction can be performed in a single reactor [14], but the separation of the two reactions is preferred because of different reaction parameters (e.g., pH value, temperature, oxygen) and stability of the enzymes used. With water as the solvent and enzymes fixed on a carrier, the process runs in a repeated batch mode at room temperature (20-30°C). Higher temperatures lead to increased reaction rates, but also to higher byproduct formation and reduced stability of the biocatalysts. A pH value between 7.0 and 8.5 is recommended with respect to thermodynamics, enzyme activities and stability and formation of byproducts. The use of cells is not recommended with respect to operational stability and possible product contamination. Therefore purified enzymes covalently immobilized on a polymeric carrier are chosen for the industrial process for both steps. The particle diameter of the spherical biocatalyst is about 100-300 pm, to allow for acceptable mass transfer and filtration times. 

The other important phenomenon that, in addition to the mass transfer, occurs when enzymes become heterogeneous catalysts, is the partitioning of substrates, products, inhibitors, metal and hydrogen ions between a bulk solution and a carrier. An elegant and simple theory describing the effect of microenvironment inside the particles of immobilized enzymes on their kinetics, has been developed by the group... 

If the internal mass transfer resistance is negligible, what is the concentration of the substrate at the surface of the particle What is the effectiveness factor for this immobilized enzyme ... 

The first step in characterizing the heparinase binding rate to the catalyst particles is to establish experimental conditions where neither enzyme denaturation or external mass transfer are important. This can be accomplished by controlling the duration of immobilization, the mixing rate, and the catalyst particle size. In the absence of diffusional limitations and enzyme denaturation effects, the disappearance of enzymatic activity from the bulk phase equals the rate at which the enzyme binds to the catalyst particle. The molar conservation equation for heparinase in the bulk phase is given by... 

Dlffuslonal or mass-transfer effects such effects would arise from dlffuslonal resistances to the translocation of substrate, product, or effector to or from the site of the enzymic reaction and would be particularly pronounced in the case of fast enzymic reactions and configurations, where the particle size or membrane thickness are relatively large. An immobilized enzyme functioning under conditions of dlffuslonal restrictions would hence be exposed, even in the steady state, to local concentrations of substrate product or effector different from those in the bulk solution." ... 

In some biochemical systems the limiting mass transfer step shifts from a gas-liquid or solid-liquid interface (as discussed earlier) to the interior of solid particles. The most important cases are solid substrates and cell aggregates (such as microbial floes, cellular tissues, etc.) and immobilized enzymes (gel-entrapped or supported in solid matrices). In the former, diffusion of oxygen (or other nutrients) through the particle limits metabolic rates, while in the latter, substrate reactant or product diffusion into or out of the enzyme carrier often limits the overall global bioreaction rates. 

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