## September 2021

## Catalysts

# Avoid common pitfalls in upscaling catalytic fixed-bed reactors

Driving innovation is an inescapable strategic reality, not only for accelerating new products development and technological solutions but also for creating new markets.

Driving innovation is an inescapable strategic reality, not only for accelerating new products development and technological solutions but also for creating new markets. Multidisciplinary collaborations—such as research and development, business and marketing, and engineering—are indispensable to define potential business and market share targets. The development speed of new products is very demanding because the needs of customers have been influenced by rapid disruptive changes.

In the early stages of so-called product conceptualization, the purpose of a new product or technology must match the company’s direction to compete in the world market. Effective synergistic collaboration between multidisciplinary functions is a key success factor in this stage of development. Development must be based on numerous information exchanges between specialists, researchers and engineers to conceptualize the commercial process, including optimal operating conditions for large-scale production.

## Challenges in dissimilarity of mass throughput

A commercial reactor is usually designed to deliver high throughputs to maximize profits while minimizing total investment cost. Conversely, laboratory and pilot reactors are commonly used for experimentally investigating new phenomena and producing the necessary information that is applicable or adaptable to the upscale design of new—or the improvement of existing—commercial processes and facilities. The utilization of laboratory and pilot units with low mass throughput is inevitable due to:

- Minimizing total investment and economic risk
- Maintaining flexibility for frequent reconfiguration
- Widening operating range
- Easing handling and waste disposal
- Decreased concern and smaller risk of safety and environmental impacts
- Increasing project speed, including smooth startup and shutdown.

It is logical that the flow regimes inside laboratory, pilot plant and commercial reactors are significantly different. Generally, the flow regime of fluid can be classified into three types: laminar, transition and turbulent flows. As expected, this flow regime dissimilarity can significantly impact the observed catalyst performance in a heterogeneous (solid-fluid) catalytic reactor. The following section will focus on the fixed-bed reactor, as it is the most commonly used.

## Rate-controlling mechanisms and flow behavior

By focusing on a typical porous catalyst pellet packed in a fixed bed, several sequential and parallel mass transfer and reaction steps can be seen, as illustrated in **FIG. 1**.^{1}

- Step 1: Reactants transfer from the bulk fluid stream through a stationary film to the external surface of the pellet
- Step 2: Reactants next diffuse into the pores to catalytic sites on the internal walls
- Step 3: Reactants adsorb on the active sites
- Step 4: Reactants are converted to products via surface reaction
- Step 5: Products desorb from the active sites
- Step 6: Products next diffuse inside the pores to the pellet external surface
- Step 7: Products transfer from the pellet surface through the film to the bulk fluid stream.

For most heterogeneous catalytic reactions, it is reasonable to assume that the first-order surface reaction, as well as very fast adsorption and desorption steps, control the overall reaction rate. Making use of pseudo-steady-state approximation, the following relation between the observed global, film-diffusion, pore-diffusion and true-kinetic rate coefficients can be derived (Eq. 1)^{1,2}:

(1)

The effect of internal diffusion on the observed reaction rate can be considered by the so-called effectiveness factor (η), which is defined as “the ratio of the real reaction rate of the catalyst particle to the imaginary reaction rate when the whole particle is assumed to bathe in the surface reactant concentration.” Meanwhile, the effects of fluid velocity and flow regime can be represented as a function of the pellet-based Reynolds (Re) number. Eq. 1 can therefore be transformed to Eq. 2:

(2)

As shown in **FIG. 2**, laboratory and pilot reactors, which are generally small in size and designed for low mass throughput, frequently exhibit a laminar-flow regime. As a result, the mass transfer resistance of the stationary film around the pellet is dominant, and this becomes the rate-limiting step. The film resistance dramatically decreases when the flow regime becomes highly turbulent, as is typical in a commercial reactor. In other words, this shift from film diffusion-rate controlling to pore diffusion-rate or surface-reaction controlling generally occurs when upscaling to a high-capacity commercial reactor. Pore diffusion rate will dominate when the pellet size is relatively large or the internal catalytic sites have very high reactivity.

## Rate-controlling mechanisms and temperature

Another major difference between laboratory/pilot and commercial reactors is the effect of heat loss on the surrounding area during operation. Due to a high surface area per volume of tubing and small piping, as well as a small quantity of reaction heat generation (or absorption) corresponding to low mass throughput, most laboratory and pilot reactors are run isothermally, in practice. Their superficial fluid velocity is relatively low and the flow regime is mostly laminar or (at most) transitional.

Conversely, the corresponding effect of significant heat loss in a large-column commercial reactor with huge mass throughput is essentially negligible. Therefore, these reactors are generally designed and operated in adiabatic mode. Their superficial fluid velocity is quite high and the flow regime is mostly turbulent. The implication is that the rate-limiting step for the former reactors is typically film diffusion (particularly true at high reaction temperature), whereas for the latter it is pore-diffusion and/or surface reaction. Since this discussion is focused on individual catalyst pellets, the influence between isothermal and adiabatic operations is not considered here.

Generally, the effect of temperature on the observed (or apparent) activation energy is investigated by carrying out experiments in a laboratory reactor at sufficiently high fluid velocity to ensure a reasonably fast film diffusion rate. Nevertheless, in the significantly high temperature range using catalyst powder, the film diffusion step would become rate-limiting and the observed global reaction resistance becomes more or less proportional to the external mass transfer film resistance. From Eq. 2, we obtain Eq. 3:

(3)

Since the gas density and viscosity depend only slightly on temperature, so does the corresponding Reynolds number. In other words, according to Eq. 3, the experimentally determined apparent activation energy should be quite small. Conversely, in the low temperature range, the rate of reaction becomes very slow and therefore the rate-limiting step. The determined activation energy becomes essentially equal to the true activation energy defined by the Arrhenius law.

In the intermediate temperature range using a typical commercial catalyst pellet, the pore-diffusion step becomes rate-limiting. From Eq. 2, we obtain Eq. 4:

(4)

The effectiveness factor in the case of an irreversible *n*-th order reaction is given by Eq. 5:

(5)

Substituting the effectiveness factor from Eq. 5 into Eq. 4 yields Eq. 6:

(6)

Applying the Arrhenius equation to *k _{obs}* and

*k*in Eq. 6, Eq. 7 is obtained after simplification:

_{Intr}(7)

Since the second term on the left hand side corresponds to that on the left hand side, Eq. 7 indicates that the apparent activation energy in the case of pore-diffusion control is approximately half of the true activation energy (Eq. 8):

(8)

**FIG. 3 **displays the effect of temperature on the observed global rate constant, as well as the region of each rate-limiting step and its observed apparent activation energy.

The unintentional shift of the rate-controlling step over temperature variation represents another common pitfall in the design scale-up of fixed-bed reactors for highly exothermic and endothermic reactions. Due to the unavoidable difference in flow regimes between laboratory/pilot reactors operated isothermally and commercial reactors operated adiabatically, experimental data obtained in the lab reactor are useful for determining the true reaction kinetics and reaction scheme; those obtained in a small-scale pilot reactor are useful for investigating the conditions closer to the commercial unit.

However, both types of data are often insufficient for upscaling to a commercial adiabatic reactor. In practice, the commercial reactor is frequently designed at a highly turbulent flow through a packed bed of catalyst pellets to attain high throughput with acceptable pressure drop. Therefore, pore diffusion generally becomes the rate-limiting step. When adiabatic operation is adopted, an unintentional shift from pore diffusion control to film diffusion—or, more frequently, intrinsic rate control—is likely to occur, especially when a large temperature difference exists between the inlet and outlet of a catalyst bed. As a result, the designed reactant conversion and/or product selectivity may not be achieved if the facilities and reactor are designed without considering the above-mentioned shift.

Another common pitfall is the substantial reduction of catalyst size in case of exothermic reaction to increase production rate by minimizing pore diffusion limitation. This may lead to a runaway reaction and can be handled by reducing the catalyst pellet to an optimal size. However, if the reaction is highly exothermic, the adiabatic reactor may have to be replaced by a multi-tubular reactor with internal cooling.

## A handy scaling correlation applicable for non-isothermal reactors

To enhance the upscaling success rate, the effect of the three common rate-controlling steps on the observed global rate as a function of flow behavior and temperature must be clarified. From Eq. 5, if the reaction order can be approximated as pseudo-first-order (*n* = 1), the effectiveness factor becomes (Eq. 9):

(9)

The substitution of Eq. 9 into Eq. 2 yields (Eq. 10):

(10)

The Arrhenius form of the intrinsic rate constant is (Eq. 11):

(11)

Substituting Eq. 11 into Eq. 10 yields (Eq. 12):

(12)

By defining a new parameter as (Eq. 13):

(13)

Eq. 12, which expresses the global kinetic rate as a function of flow behavior and temperature, becomes Eq. 14:

(14)

Based on Eq. 14,** TABLE 1** summarizes the effect of flow behavior and temperature on the individual rate controlling step. Note that, as revealed in **FIG. 3**, the exponential effect of pore diffusion rate control is typically represented by an apparent activation energy, which is half of the true intrinsic value.

## Estimating catalyst performance in a commercial fixed-bed reactor

To successfully scale up from a laboratory and pilot reactor to a commercial scale, the global kinetic correlation (Eq. 14) must be experimentally determined. First, Eq. 14 is transformed to a linear form by taking the natural logarithm of both sides. If the experimental conditions (mainly reaction temperature) are chosen, such that the film diffusion is the rate-limiting step, then Eq. 3 is valid. By varying the *Re _{p}^{n} *(proportional to fluid velocity), the value of ψ can be obtained from the slope of

**FIG. 2**.

Next, experimental conditions (mainly using sufficiently small catalyst pellet size at relatively low temperature and high fluid velocity) are chosen, such that the surface reaction rate is the rate-limiting step, the true intrinsic activation energy E_{A,true} can be estimated from a plot similar to **FIG. 3**. Finally, experiments are carried out at sufficiently high fluid velocity so that the last term of Eq. 14 may be ignored. By varying reaction temperature T, a plot similar to **FIG. 3** can be used to obtain the value of κ from the slope and the earlier obtained value of E_{A,true}. In this way, the handy correlation (Eq. 14) for the non-isothermal reactor can be determined. An example is given in Eq. 15.

## Case study

Consider the case of a gas-phase, fixed-bed reactor involving the production of olefins from an isomerization reaction using a typically porous catalyst. The reaction is mildly exothermic and the proprietary catalyst was tested extensively in three different scales (laboratory, pilot and demonstration units) using the above-mentioned variety of experimental conditions. The obtained correlation is shown in Eq. 15:

(15)

**TABLE 2** compares the experimental and predicted % conversion for the four scales of the fixed-bed reactor. Obviously, the correlation was reasonably accurate for the laboratory, pilot and demonstration reactors. Though the actual conversion data for the commercial unit is unavailable, the predicted conversion is expected to be quite satisfactory.

## Takeaway

The unsuspected shift of the rate-controlling step is a common pitfall during comprehensive new process/product development, beginning from catalyst development and testing at laboratory and pilot scales to the up-scaled design and adiabatic operation of the commercial unit. The most effective approach is to “begin with the end in mind.” More specifically, a viable commercial unit should be conceptually designed as soon as basic catalyst performance data in laboratory scale has been obtained.

To make the commercial unit viable (technically and economically feasible), the necessary and essential targets of catalyst performance and improvement can be reasonably determined. These scientific targets are valuable preliminary requirements for the catalyst developer to satisfy before more extensive catalyst testing is carried out in the laboratory and subsequent pilot scales. To enhance the successful design and operation of the commercial reactor with mass throughput by operating in adiabatic (non-isothermal) mode and turbulent flow regime, the most scientifically sound approach is to develop a handy practical correlation similar to Eq. 14, which can handle exothermic/endothermic reactions taking place using catalyst of optimal pellet size and shape. Of course, the crucial issue of catalyst stability and deactivation must also be addressed adequately and the requirements incorporated into the above catalyst performance targets. Note: Although the present contents are based on the assumption of irreversible first-order reaction, the same or at least a similar methodology is applicable to more complex reaction types and pathways. **HP**

**LITERATURE CITED**

- Levenspiel, O.,
*Chemical reaction engineering,*3rd Ed., John Wiley & Sons, New York, New York, 1998. - Worstell, J.,
*Adiabatic fixed-bed reactors practical guides in chemical engineering,*1st Ed., Elsevier, 2014. - Fogler, H. S.,
*Element of chemical reaction engineering,*5th Ed., Prentice Hall, Upper Saddle River, New Jersey, 2016.

**NOMENCLATURE**

*a _{p}* Cross-sectional area of the pore, m

^{2}

*A*Observed or apparent pre-exponential factor, s

_{obs}^{-1}

*A*True pre-exponential factor, s

_{true}^{-1}

*E*Observed or apparent activation energy, J/mol·K

_{A,obs}*E*True activation energy, J/mol·K

_{A,true}*C*Concentration of A at the surface of catalyst, mol/m

_{As}^{3}

*d*Catalyst particle diameter, m

_{p}*D*Effective diffusivity, m

_{e}^{3}/sec

*k*Observed overall rate constant, s

_{obs}^{-1}

*k*Mass transfer rate constant within the catalyst pore, m/sec

_{PD}*k*Intrinsic reaction rate constant, s

_{Intr}^{-1}

*k*Mass transfer rate constant within at fluid-solid film, m/sec

_{FD}Κ Characteristic constant

*n*Characteristic constant/reaction order

*η*Effectiveness factor, dimensionless

*R*Gas constant

*Re*Packed-bed Reynolds number, dimensionless

_{p}*S*Exterior surface area of the catalyst particle, m

_{c }^{2}

*T*Temperature, K

*v*Average pore volume, m

_{p }^{3}

*V*Catalyst pellet volume, m

_{c }^{3}ψ Characteristic constant.

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