Chapter 15: Diffusion and Reaction in Porous Catalysts

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R12.2 Trickle Bed Reactors


Characteristics and uses of a trickle bed reactor	In a trickle bed reactor the gas and liquid flow (trickle) concurrently downward over a packed bed of catalyst particles. Industrial trickle beds are typically 3 to 6 m deep and up to 3 m in diameter and are filled with catalyst particles ranging fromtoin. in diameter. The pores of the catalyst are filled with liquid. In petroleum refining, pressures of 34 to 100 atm and temperatures of 350° to 425°C are not uncommon. A pilot-plant trickle bed reactor might be about 1 m deep and 4 cm in diameter. Trickle beds are used in such processes as the hydrodesulfurization of heavy oil stocks, the hydrotreating of lubricating oils, and reactions such as the production of butynediol from acetylene and aqueous formaldehyde over a copper acetylide catalyst. It is on this latter type of reaction,

		(R12.2-1)

	that we focus in this section. In a few cases, such as the Fischer-Tropsch synthesis, the liquid is inert and acts as a heat transfer medium.

	CD12.1-A Fundamentals
	The basic reaction and transport steps in trickle bed reactors are similar to slurry reactors. The main differences are the correlations used to determine the mass transfer coefficients. In addition, if there is more than one component in the gas phase (e.g., liquid has a high vapor pressure or one of the entering gases is inert), there is one additional transport step in the gas phase. Figure R12.2-1 shows the various transport steps in trickle bed reactors. Following our analysis for slurry reactors we develop the equations for the rate of transport of each step.

	1. Transport from the bulk gas phase to the gas-liquid interface. The rate of transport per mass of catalyst is


Transport from bulk gas to gas-liquid interface to bulk liquid to solid-liquid interface Diffusion and reaction in catalyst pellet	Figure R12.2-1 (a) Trickle bed reactor; (b) reactant concentration profile.
	2. Equilibrium at gas-liquid interface:

		(R12.2-3)

	C _Ai = concentration of A in liquid at the interface H = Henry's constant

	3. Transport from interface to bulk liquid:
		(R12.2-4)
	where
	k ₁ = liquid-phase mass transfer coefficient, m/s C _Ai = concentration of A in liquid at the interface, kmol/m ³ C _Ab = bulk liquid concentration of A, kmol/m ³

	4. Transport from bulk liquid to external catalyst surface:
		(R12.2-5)

	5. Diffusion and reaction in the pellet. If we assume a first-order reaction in dissolved gas A and in liquid B, we have
		(R12.2-6)

	Combining Equations (R12.2-2) through (R12.2-6) and rearranging in a manner identical to that leading to the development of Equation (12-89) for slurry reactors, we have

The overall rate equation for A		(R12.2-7)

	that is,

		(R12.2-8)

	whereis the overall transfer coefficient for the gas into the pellet (m ³ of gas/g cat.s). A mole balance on species A gives

		(R12.2-9)

	We next consider the transport and reaction of species B, which does not leave the liquid phase.

	6. Transport of B from bulk liquid to solid catalyst interface:

		(R12.2-10)

	where C _B and C _Bs are the concentrations of B in the bulk fluid and at the solid interface, respectively.

	7. Diffusion and reaction of B inside the catalyst pellet:

		(R12.2-11)

	Combining Equations (12-33) and (12-34) and rearranging, we have

The overall rate equation for B		(R12.2-12)

	A mole balance on species B gives

Mole balance on B		(R12.2-13)

	One notes that the surface concentrations of A and B, C_As and C _B s , appear in the denominator of the overall transport coefficientsand.
	Consequently, Equations (R12.2-7), (R12.2-9), (R12.2-12), and (R12.2-13) must be solved simultaneously. In some cases analytical solutions are available, but for complex rate laws, one resorts to numerical solutions. ¹ However, we shall consider some limiting situations.

	R12.2-B Limiting Situations
	Mass Transfer of the Gaseous Reactant Limiting. For this situation we assume that either the first three terms in the denominator of Equation (R12.2-7) are dominant or that the liquid-phase concentration of species B does not vary significantly through the trickle bed. For these conditions
	is constant and we can integrate the mole balance. For negligible volume change= 0, then

Catalyst weight necessary to achieve a conversion X _A of gas-phase reactant		(R12.2-14)

	Mass Transfer and Reaction of Liquid Species Limiting. Here we assume that the liquid phase is entirely saturated with gas throughout the column. As a result, C _As is a constant. Consequently, we can integrate the combined mole balance and rate law to give.
Catalyst weight necessary to achieve a conversion X _B of gas-phase reactant		(R12.2-15)

	R12.2-C Evaluating the Transport Coefficients The mass transfer coefficients, k _g , k _l , and k _c depend on a number of variables, such as type of packing, flow rates, wetting of particle, and geometry of the column, and as a result the correlations vary significantly from system to system. Consequently, we will not give all the correlations here but instead will give correlations for particular systems and refer the reader to four specific references where other correlations for trickle bed reactors may be found. ² Typical correlations are given in Table R12.2-1. Note that the correlation for organic particles tends to under predict the transport coefficient.

Criterion for assuming that plug flow is valid	The representative correlations given in Table R12.2-1 assume complete wetting of the catalyst particles. Corrections for incomplete wetting as flow regimes, pressure-drop equations, and other mass transfer correlations can be found in the reviews by Shah, Smith, and Satterfield. ³ The plug-flow design equation may be applied successfully provided that the ratio of reactor length L to particle diameter d _p satisfies the criterion (Satterfield, 1975)

		(R12.2-16)
	where Pe = Péclet number = d _{p U _l /D _AX D _AX = axial dispersion coefficient n = reaction order}

^aAlso see N. Midoux, B. I. Morsi, M. Purwasasmita, A. Laurent, and J. C. Charpentier, Chem. Eng. Sci., 39, 781 (1984), for a comprehensive list of correlations.
^b In some cases this gives a low estimate of k _l a _i ; see M. Herskowitz and J. M. Smith, AIChE J., 29, 1983); F. Turek and R. Lange, Chem. Eng. Sci., 36 569 (1981)


		The CSTR design equations apply to the trickle bed when ⁴

			(R12.2-17)

		Techniques for determining the single-phase axial dispersion coefficient are given in Chapter 14.

		Example R12.2-1 Trickle Bed Reactor
		The material presented in this example is meant to serve as an introduction to trickle bed reactors. Other worked-out trickle bed example problems can be found in an article by Ramachandran and Chaudhari ⁶. In addition, the hyrodesulfurication of a hydrocarbon in a trickle bed reactor is given in detail by Tarhan⁷.

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Chapter 15: Diffusion and Reaction in Porous Catalysts

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R12.2 Trickle Bed Reactors

CD12.1-A Fundamentals

R12.2-B Limiting Situations

R12.2-C Evaluating the Transport Coefficients