Ind. Eng. Chem. Res. 1990,29,968-977
968
Generalized Description of Fluid Flow, Void Fraction, and Pressure Drop in Fixed Beds with Embedded Tubes Felix A. Schneidert and David W. T. Rippin* Technisch-Chemisches Laboratorium, Eidgenossische Technische Hochschule, CH-8092 Zurich, Switzerland
Esmond N e w s o d Swiss Aluminium R & D, CH-8212 Neuhausen am Rheinfall, Switzerland
Generalized definitions of voidage, superficial mass flow, and hydraulic diameter were combined to compare axial and radial flow fixed beds with respect to their mean void fraction and pressure drop. Experimental measurements were made with two separate radial flow configurations in which substantial changes in the configurations could be made. For relatively open beds (volume occupied by cooling tubes is 25%), the pressure drop could be represented by a general correlation for beds with particles of widely dispersed sizes. For more closely packed tubes, the pressure drop correlation had to be modified to incorporate factors for extension of the length of the flow path and for the variance of the mass flux due to flow restrictions between the tubes. The use of values of these factors derived directly from the geometry of the radial flow configuration gave satisfactory predictions of the pressure drop for all configurations studied. The increasing pressure drop limitation of fixed-bed axial flow reactors with decreasing catalyst particle size has been successfully circumvented by using radial flow reactors (RFRs). More active catalysts can therefore be fully exploited with higher effectiveness factors and increased production rates per unit volume of reactor, as in ammonia synthesis (Dybkjaer and Gam, 1984),methanol synthesis (Linde, 1983), catalytic reforming, and auto exhaust converters. Design criteria for RFRs have been proposed (Chang et al., 1983), the highest conversion being achieved when the flow is uniformly distributed in the axial direction, the direction of the radial flow, inward or outward, being of secondary importance. A conventional packed-bed reactor consists of a bundle of tubes filled with catalyst through which the reactant flows in an axial direction. The auxiliary cooling fluid flows around the tubes and heat is transferred to it through the heat-exchange surface of the tube walls (Figure 1A). An adiabatic radial flow reactor (Figure 1B) was developed for ammonia synthesis (Hansen, 1964). In recent years, alternative flow configurationshave been developed, among them being the radial flow reactor in which the bed of catalyst particles surrounds the bundle of tubes through which the cooling fluid flows (Figure IC),as described by Ohsaki et al. (1980, 1984) and Dobson (1982). The direction of flow of reactants through the catalyst bed is then orthogonal to the axes of the cooling tubes. Many previous axial and radial flow designs have operated adiabatically, with heating or cooling usually separated from the reaction. In nonadiabatic axial flow reactors, such as those used for selective oxidation, the performance is limited by the pressure drop and heat transfer. The nonadiabatic radial flow configuration in which the particle bed surrounds the cooling tubes allows for a more flexible reactor design. The severity of temperature and pressure gradients in the bed can be further reduced by adjustment of the cooling/ heating capacity as the reaction progresses, and the optimal reaction path can be followed more closely than in quench systems (Ohsaki
* To whom enquires may be addressed. 'Present address: Swiss Aluminium R & D, CH-8212 Neu-
hausen am Rheinfall, Switzerland. 1Present address: Paul Scherrer Institute,Department 4FB, CH-5303 Wurenlingen, Switzerland.
0888-5885/90/2629-0968$02.50/0
et al., 1985). The nonadiabatic radial flow reactor thus has considerableadvantages, not only over adiabatic fiied-bed reactors but also over nonadiabatic axial flow reactors. However, the RFR configuration with the particles surrounding the heating/cooling tubes complicates the description of fluid flow. The overall characteristics of the bed of particles within a reactor depend upon the local characteristics of the particles, the arrangement of the cooling surface within the reactor, and the influence exercised by the cooling surface on the structural arrangement of the particles in the neighborhood of the surface. Three types of bed characterization are of interest. (a) Mean Void Fraction. This depends only on the bed structure with no directional consideration. (b) Pressure Drop. This depends upon the bed structure and the direction of flow or the path followed by the fluid through the bed. (c) Heat Transferred from the Fluid Flowing through the Bed to the Cooling Surface. This depends upon the flow path and the structure between that path and the cooling surface through which the heat is transferred. The present paper is concerned with the comparison of the mean void fraction and the pressure drop in axial and radial flow reactors. The comparison of heat-transfer performance will be taken up in a later paper. First the characterizing the parameters will be defined, which are common to the particle bed independently of whether it is located in an axial or a radial configuration. The predictions of the correlations obtained by other workers for the void fraction and the pressure drop in axial flow configurations (i.e., for beds of particles inside circular tubes) will be compared with the experimental results obtained in the present work for a range of radial flow configurations. Proposals are made for modifying the correlations for the axial flow configuration that retain the same general form but incorporate additional factors to account for special features of the radial flow configuration. With these modifications, satisfactory performance predictions are obtained, and a common basis is arrived at for characterizing both the axial and the radial configurations or, equivalently, beds of particles both within and surrounding tubes. Generalized Description of Fixed-Bed Reactors. Since there is a variety of usage in the characterization of Q 1990 American Chemical Society
Ind. Eng. Chen1. Res., Vol. 29, No. 6, 1990 969 'b
VC
(3 8
V
vb
0V e
Cooling system: tubes and liquid.
u
Fixed bed with packing
v
..::I::.
8 m)
Effective free reactor volume Packing (solid phase)
Figure 3. Definition of void fractions. Figure 1. Qpes of fixed-bed reactors. (A) Axial flow reactor (AFR). (B) Adiabatic radial flow reactor. (C) Nonadiabatic radial flow reactor (RFR).
Embedded tubes Radial Flow Reactor RFR
v vb
+
Filled tubes Axial Flow Reactor AFR
Cooling system: tubes and liquid.
nectors, etc., are not incorporated into the reactor volume. (2) Void Fractions. Two void fractions are required to describe the relations between these three volumes. They can be the conventional void fraction, q,, of the bed, together with either E,, the fraction of volume remaining after installation of the cooling system in the reactor shell, or the fraction of free volume in the whole reactor shell, where er =
(3) Surfaces and Hydraulic Diameters. Three types of surface are defined Fr,the area of contact between the particle bed and the reactor shell; F,, the heat-exchanger surface between the particle bed and the cooling fluid; and F,, the total external surface area of the particles making up the bed. Hydraulic diameters are defined with reference to surface-to-volumeratios within cylindrical tubes and have no directional orientation. The classical definition for an infinite fixed bed of spheres (Dp= particle diameter), as used in pressure drop correlations (VDI W h e a t l a s , 1984), is
Fixed bed with packing General flow direction of reactants
Figure 2. Fixed-bed and cooling system volumes in radial and axial flow reactors.
fixed beds, a set of consistent definitions has to be made that are sufficientlygeneral to cover axial, radial, or other flow configurations. (1) Volumes and Heat-Transfer Surfaces. Within the total reactor volume, V,, the cooling system occupies a volume Vc and provides a cooling surface of area Fc for exchange between the fluid flowing through the bed and the auxiliary cooling fluid. The remainder of the reactor is occupied by the fixed bed of particles of volume v b (Figure 2). The particle bed can be further divided into V,, the volume of the solid particles themselves, and the interstitial volume, Ve, which is available for fluid flow ( v b = vp+ ve = vr- V,). In the simplified description used in the subsequent analysis, auxiliary installations such as distributors, con-
If additional surfaces are in contact with the fixed bed, such as,in our case, the outer shell r and the cooling system c, the free volume and the wall area must be correspondingly modified: vb Dh*P
- v~
+ + Fp
(3)
= 4Fr Fc
For structured fixed-bed reactors, three definitions of the hydraulic diameter may be considered D, for the empty reactor shell, Dh,b for the fiied-bed geometry, and Dbp for the interparticular free volume: whole reactor volume Vr = 4Dhs = 4fixed-bed-shell contact area F, Dh*b
(4)
fixed-bed volume = -4 vb (5) + cooling area F, Fr
= 4fixed-bed-shell
+
970 Ind. Eng. Chem. Res., Vol. 29, No. 6, 1990
free interstitial volume = 4packing + cooling + shell
-
ve
4Fp+ F, + F r (6) The interconnections between these values are
Dh*p
Description of Representative Configurations A complete industrial-scale reactor may have cooling or other geometrical arrangements that vary with the location in the reactor. For purposes of characterization, the reactor should, if necessary, be divided into a number of homogeneous regions. (1) StandardAxial Flow Reactor. The standard axial flow reactor used for solid-catalyzed gas reactions with large heat loads contains within the reactor shell a bundle of tubes filled internally with catalytic packing. Reactants flow through the tubes in parallel and are distributed and collected at the bottom and top of the shell. The heatexchange surface is defined by the internal tube diameter, D t p = Dt,i* he arrangement of the bank of tubes is characterized (as in the radial flow reactor) by two parameters: S,, the distance between the centers of tubes in a row; and S,,.the distance between the center lines of successive rows. (Smce the coordinate z is used for the direction of flow of reactants, the inter-row distance for the radial flow reactor is designated as Sz.) The characterizing parameters for the pressure drop and heat transfer of the reactant fluid in the axial flow reactor are Fr,AFR = 0, Dhj,AFR = (9) For this configuration, there is essentially no direct contact area between the particle bed and the reactor shell: Fc,AFR = v b / ( v b / F c ) = Vb/(Dt/4) %,AFR
= (7/4)D?/(s,s2) Dh,b,AFFt
l/Dt
C
D
Figure 4. Characterization of bed and tube arrangements. (A) Radial flow over cooling tube D,. (B) Tube spacing S,, S., (C) Flow constrictions B,, Bd. (D) Inscribed circle Dbj.
When local conditions are considered in the interior of the bed, there is in this region no direct contact area between the particle bed and the reactor shell:
F~,RFR = Vc/(Vc/Fc) = Vc/(Dt/4) C~,RFR=
1- (7/4)Dt2/(S,S2)
(12)
(10)
+ (1- q,)(1.5/Dp)
(11)
(2) Radial Flow Reactor Hydraulic Diameters. In the flow arrangement used in radial flow reactors recently described in the literature (Figure IC), the reactor comprises a cylindrical shell containing the particle bed within which the cooling tubes are arranged in concentric rings. The reactants enter at the center of the shell, flow over cooling tubes orthogonal to their axes, and are collected at the outer surface of the reactor shell. The external cooling tube diameter is representative for heat transfer: = Dt,a (Figure 4A). e local geometry of the tube configuration is described by the inter-tube distance (S,) and the inter-row distance (SJ as before. At this stage, the mean flow velocity of the reactants across the tube bank in the radial direction is assumed to be constant. Changes in velocity and possible changes in tube arrangement between the center and the circumference of the reactor shell are not considered. Thus, with reference to a complete industrial radial flow reactor, local behavior is being characterized. For the particle bed and the cooling surface of the radial flow reactor, Fr,RFR = 0, D h j W = O3
DtK
B
= Dt cb
D4p,AFR =
A
Constructional Flexibility. In contrast to the axial reactor, the structure of the particle bed in the radial flow reactor depends on the tube arrangement. This can be characterized by two additional dimensionless parameters: xz = S,/(2S2) relative distance between tubes in a row relative tube diameter DZ = Dt/(2Sz) Any possible triangular arrangement of the RFR tubes must lie within the region of the DZ-XZ space bounded by the constraints DZ < 1 separation on the z axis DZ < XZ DZ
