Flow Regime Transition in Open-Cell Solid Foam Packed Reactors

Article pubs.acs.org/IECR

Flow Regime Transition in Open-Cell Solid Foam Packed Reactors: Adaption of the Relative Permeability Concept and Experimental Validation Johannes Zalucky,† Felix Möller,† Markus Schubert,*,† and Uwe Hampel†,‡ †

Institute of Fluid Dynamics, Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstraße 400, 01328 Dresden, Germany AREVA Endowed Chair of Imaging Techniques in Energy and Process Engineering, Technische Universität Dresden, 01062 Dresden, Germany

‡

S Supporting Information *

ABSTRACT: The trickle-to-pulse flow regime transition in silicon-infiltrated silicon carbide (SiSiC) foam packed fixed bed reactors has been investigated. Based on the film stability concepts of Grosser et al. [AIChE J. 1988, 34, 1850. DOI: 10.1002/ aic.690341111] as well as Attou and Ferschneider [Chem. Eng. Sci. 2000, 55, 491. DOI: 10.1016/S0009-2509(99)00344-9], two predictive models have been adapted to foams’ specific geometric parameters. To account for the different nature of solid foams and their interactions with various fluids, the fixed bed characteristics (specific surface area and bed porosity) and fluid specific parameters (gas and liquid density, liquid viscosity, surface tension) have been incorporated in the model. Ergun parameters and static liquid holdup which are required for the modeling of the prevailing tractive forces were determined experimentally. The modeling results were compared to regime transition measurements performed for SiSiC solid foams with different linear pore densities (20, 30, and 45 PPI), for different reactor diameters (50 and 100 mm) and initial liquid distributors (spray cone nozzle and multipoint distributor) as well as liquids with various physicochemical properties (water, Tergitol, 50% glycerin) under ambient operating conditions. Compared to conventional random fixed bed reactors, the onset of pulsing in solid foam packed fixed beds is significantly shifted toward larger liquid and gas fluxes allowing high throughputs in the trickle regime. Moreover, the homogeneity of initial liquid distribution strongly affects the trickle-to-pulse flow transition.

1. INTRODUCTION In recent decades, trickle-bed reactors (TBRs) obtained high significance especially in the chemical processing and petrochemical industries.1−4 Reactions such as oxidation and hydrogenation, hydrocracking, hydrodesulfurization, etc. have been carried out in these multiphase reactor types.5 TBRs are three-phase reactors with cocurrent downflow of gas and liquid at moderate velocities. Reaction takes place at the active sites of the catalyst particles that form a fixed bed. In this operation mode, the gas continuous or trickling flow regime occurs. It is characterized by a dispersed liquid phase flowing in rivulets and films accompanied by a continuous gas phase.6 Due to low velocities, inertia forces are low and the flow of the liquid is therefore mainly controlled by capillary, gravity, and gas drag forces. However, different flow regimes can occur in the fixed bed depending on operating conditions as well as fluid and packing properties. At high liquid and gas velocities, respectively, the pulse flow regime evolves due to partial and temporary blocking of the intercatalyst pores by the liquid phase. Blocked by the liquid barriers in the macropores, the gas accumulates and forms alternating gas and liquid rich zones, which travel fast through the reactor bed. The pulse regime provides a rather high wetting efficiency and periodic rewetting of the catalytic surface as well as intensive interactions between fluid and solid phases, which results in better heat and mass transfer.7 For the design and scale-up of trickle-bed reactors, the knowledge of the transition between the flow regimes is very © 2015 American Chemical Society

crucial since all hydrodynamic parameters such as pressure drop per unit length of packing and liquid holdup, as well as heat and mass transfer coefficients, change significantly with the flow regime.7 In current industrial applications, the catalyst particles of various shapes (spheres, cylinders, trilobes, etc.) are randomly packed to form fixed beds and are limited in minimal particle size to reach reasonable relations between specific surface area and pressure drop.8 In order to improve the concepts of tricklebed reactors with respect to better products and higher energy efficiency, process intensification methods are of great interest for the chemical industry. One approach is the replacement of conventional random catalyst packings by solid ceramic foams. Their open-cell three-dimensional (3D) network is characterized by a high specific surface area for the immobilization of the catalyst as well as a high porosity, which result in comparably low pressure drop.9,10 Basically, the same flow regimes evolve in solid foam packed reactors with cocurrent gas−liquid downflow. However, there are yet only few published data for the transition between the regimes. Stemmet et al. reported regime transitions in aluminum foams in both cocurrent upflow10,11 and downflow.11 For the Received: Revised: Accepted: Published: 9708

June 19, 2015 September 15, 2015 September 15, 2015 September 29, 2015 DOI: 10.1021/acs.iecr.5b02233 Ind. Eng. Chem. Res. 2015, 54, 9708−9721

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Industrial & Engineering Chemistry Research

Furthermore, two research groups18−20 proposed solutions predicting various regime transitions based on microscale phenomena (microscale models). Holub et al.19 developed the slit model describing that gas and liquid follow a path in an inclined slit through the catalyst bed. They derived Ergun-like equations for dimensionless pressure drops as well as drag forces and developed an empirical expression for the onset of pulsing. Depending on the Kapitza number, liquid Reynolds number, and Galilei number as well as on liquid dimensionless pressure drop and the viscosity term of Ergun’s equation (E1), the regime transition can be predicted. The single-slit model from Holub et al. was revised by Iliuata et al.,21 who developed the double-slit approximation, which describes that liquid and gas flow in separate, connected, and inclined slits through the catalyst bed. However, the purpose of the enhanced double-slit model was to describe holdup and pressure drop in trickle flow and had no intention of predicting regime transitions. Its universal geometry notion and abandonment of empirical twophase flow parameters in the slit models constitutes its biggest advantage, while the missing option to allow more complex geometries and flow structures to be implemented is its biggest disadvantage. Thus, the slit model severely lacks prediction accuracy, even when compared to the limited set of measurement data.18 Ng20 used Bernoulli’s law to describe the liquid and gas flow within the catalyst bed. The author developed equations describing the transition between trickling and pulsing flow as well as transitions to the other flow regimes. However, the author used semiempirical saturation expressions developed for spherical particle packings which disqualifies the model for application on solid foams. Moreover, the model was shown to be not reliable20 when compared to measurement data of Chou et al.22 Other flow regime transition models are of rather phenomenological or semiempirical nature. The first semiempirical approach to describe the force balance between the solid surface and the fluid phases was proposed by Grosser et al.1 The model is based on the concept of Sáez and Carbonell,23 who developed the relative permeability concept to predict the two-phase pressure drop as well as the liquid holdup in tricklebed reactors. The governing momentum equation for each fluid phase i (either gas or liquid) is given by

latter case, three pairs of velocities were identified in which pulse flow occurred when using 30 vol % glycerol solution. Focusing on the gas−liquid mass transfer coefficients, Stemmet et al. did not provide a detailed investigation of the regime transition. Mohammed et al.12 studied the flow hysteresis in polyurethane solid foam reactors, which is attributed to different liquid prewetting modes. Focusing on pressure drop and holdup hysteresis, only a few annotations and one rudimentary flow regime map for 25 PPI foams were provided. More recently, Tourvieille et al. investigated the induced pulse flow in a foam packed milli-reactor by optical observation.13,14 By feeding the reactor with ethanol/nitrogen and methanol/nitrogen in slug-annular or Taylor flow, stable pulse flow has been reached at very low superficial velocities. Their studies in the nickel chromium foams included flow pattern analysis, residence time distributions, and characteristic pulse parameters13 as well as mass transfer and biphasic pressure drop.14 However, using a rectangular milli-channel as well as an artificially induced flow pattern, the data are hardly transferable to tubular reactors of larger diameter. As the solid materials of those three research groups differ significantly from the present study, a strong influence of the contact angles is expected. Additionally, the few available regime transition data do not allow deriving any reliable correlation for the flow regime transitions. Thus, the present work aims on the experimental investigation of the trickle-to-pulse flow regime transition in packed bed reactors with ceramic open-cell solid foams made of silicon infiltrated silicon carbide (SiSiC). In particular, the influence of the foam linear pore density ranging from 20 to 45 PPI (see Figure 1), reactor diameter, initial liquid distribution,

⎛ ∂u ⎞ ρi εi⎜ i + ui ·∇ui⎟ = −εi∇pi + εiρi g + Fi + ∇(εi τ̲ i + εi R̲ i) ⎝ ∂t ⎠

Figure 1. Micro computed tomography images of representative SiSiC foams of varying pore density (cube side length 10 mm).

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and liquid properties are studied. In addition, a predictive regime transition model is developed. Here, the film stability models of Grosser et al.1 and Attou and Ferschneider2 are implemented and accordingly adapted to feature the foams’ specific geometric and hydraulic parameters based on experimentally determined expressions for dry pressure drop and gravimetric static liquid holdup.

and the closure equations ε = εl + εg

(2)

and 0=

2. FLOW REGIME TRANSITION MODELING 2.1. Literature Model Approaches. In order to predict the transition between trickling and pulsing flow, different approaches were proposed. The easiest approaches consider empirical correlations derived from flow regime maps.3,6,15−17 The maps cover a wide range of liquid and gas fluxes as well as fluid properties and are valid as a first approximation within the specified boundary conditions. For modeling purposes, however, empirical equations are entirely inappropriate.

∂εi + ∇·(εiui) ∂t

(3)

By neglecting the macroscopic viscous and inertial contribution,23 eq 1 simplifies to ∇Pi =

Fi εi

(4)

The term on the right-hand side of eq 4 may be expressed by the modified Ergun relation introducing the permeability parameter ki. 9709

DOI: 10.1021/acs.iecr.5b02233 Ind. Eng. Chem. Res. 2015, 54, 9708−9721

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Industrial & Engineering Chemistry Research ⎛ E Re Fi E Re 2 ⎞ = ⎜ 1 i + 2 i ⎟ ρigui εi ki Gai ⎠ ⎝ ki Gai

and the gas side force equation Fint,g =

(5)

The permeability for each phase has been given as a function of the reduced liquid saturation δl and the gas saturation S: kl = δ l

ni

⎛ εl − εl,s ⎞n1 ⎟⎟ = ⎜⎜ ⎝ ε − εl,s ⎠

kg = S n2 =

⎛ εg ⎞n2 ⎜ ⎟ ⎝ε⎠

−

⎡ ⎞⎤ ⎛⎛ c 2 ⎞2 βg 1 ⎢ (1 − ε) ρg Sv 1 − c ⎜⎜ 2⎟⎥ ⎟ (1 − εβg ) ⎜⎜ug − ul + ug ⎟⎥ − 2 ⎢E2 ⎟ ⎜⎝ 1 − βg ⎟⎠ βg ⎢ ε3 ⎠⎥⎦ ⎝ ⎣

(6)

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In the original formulation c is given by 1/3 derived from geometric considerations. Besides liquid and gas drag forces, Attou and Ferschneider2 determined also a drag force

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The equations contain the liquid and gas holdups εl and εg, the static liquid holdup εl,s, and the packing porosity ε, as well as empirical relative permeability coefficients for gas and liquid n1 and n2, respectively. It was suggested by Sáez and Carbonell to empirically correlate the static liquid holdup with the dimensionless Eötvös number

εl,s = (a + b Eo)̈ −1

Fw,l = −0.6328D−1.25ε−0.75ρl 0.75 μ l 0.25μ l1.75 εl −2

ε σJ(εl) g

(8)

⎛ ⎞c ⎛ ⎞ ⎛ρ ⎞ − ε 1 ⎟ ⎜ 1 + 1 ⎟ F ⎜⎜ g ⎟⎟ pc = pg − pl = 2σ ⎜⎜ ⎟ dmin ⎠ ⎝ ρl ⎠ ⎝ 1 − βg ε ⎠ ⎝ de

(9)

Fint,l = 2c 2 ⎡ ⎞⎤ ⎛ βg 1 ⎢ (1 − ε) μg Sv (1 − εβg )2 − 2c ⎜⎜ug − E ul⎟⎟⎥ 2⎢ 1 3 1 − βg ⎠⎥⎦ βg ⎣ ε ⎝

⎡ c ⎞2 ⎤ ⎛ βg 1 ⎢ (1 − ε) ρg Sv 1−c ⎜ ⎟⎥ (1 ) E u u εβ − − 2 g ⎜ g 1 − β l⎟ ⎥ βg 2 ⎢⎢ ε3 ⎠ ⎥⎦ ⎝ g ⎣

2 2 ⎞3 ⎛ ⎛ (1 − ε)ρ Sv 2⎞⎤ 1 ⎟ ⎡⎢ (1 − ε) μ1Sv l ⎜ E1 ul + E 2 ⎜ ul ⎟⎥ +⎜ 3 ⎟ ε ε3 ⎝ ⎠⎥⎦ ⎝ 1 − βg ⎠ ⎢⎣

(13)

which is used for coupling of the gas and liquid force balances, has a different origin in the model of Attou and Ferschneider.2 The detailed mathematical derivation of eqs 10, 11, and 12 can be found in the Supporting Information. In contrast to the Leverett J-function24 in eq 9, which depends on the dynamic holdup, Attou and Ferschneider2 developed an expression for the capillary pressure accounting for the surface tension of the liquid, the equivalent diameter, and the minimum diameter, which describes the diameter for three spheres in contact. Furthermore, both transition models1,2 share several steadystate assumptions for a developed trickling flow, such as • uniform distribution of gas and liquid at the column top • no maldistribution of the flow pattern • no condition (flow, saturation, etc.) changes in the radial direction • only condition changes in the axial direction Further details of the original concepts and models can be taken directly from the original publications. As discussed above, neither purely empiric correlations nor detailed microscale models are applicable to solid foams. While the former are not applicable due to the inverse void geometry of solid foams, the latter use replacement geometries which are not even representative of the less complex particle networks. However, the adaption of semiempirical macroscale models seems reasonable because of not underlying any specific geometry. 2.2. Model Adaption for Solid Foams. In order to make use of the macroscale models of Grosser et al.1 and Attou and Ferschneider,2 the equations developed for trickle-bed reactors need to be accordingly adapted for ceramic foams and related to the morphological parameters embedded in eqs 1−13. Due to the complex geometry of solid foams, several simplified geometries and corresponding hydraulic parameters were proposed in the past for different types of solid foam as summarized by Huu et al.25 Beyond the mere implementation of the solid foam geometry parameters, several aspects have to be considered:

which can be expressed by the Leverett J-function. The original relative permeability model by Sáez and Carbonell23 with the constitutive equations for the drag forces Fi between the phases showed a reasonably good correlation for a wide range of pressure gradients and liquid holdup data. Therefore, their model was adopted by Grosser et al.1 to predict the onset of pulsing by adding perturbations in holdup, interstitial phase velocities, and pressure terms around the steady state. The onset of pulsing is determined numerically by searching maximal velocities not containing imaginary solutions of state. Physically translated, the Grosser model predicts the onset of pulsing by the loss of the laminar film stability, which occurs at the transition point to the pulsing flow. Using a similar permeability theory, Attou and Ferschneider2 used a geometric approach to describe the correlation of forces in the fixed bed. Accounting for the growing liquid films over the solid surface of spherical particles, the model includes the geometric correction factor c for the relative permeability in the liquid side force equation

+

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exerted on the liquid from the column wall, which also includes the column diameter D. Furthermore, the capillary pressure expression

In conventional random catalyst packings, the parameters a and b were determined as 20 and 0.9, respectively,23 with a mean relative deviation of 25% of the Eötvös correlation (eq 8) for 17 experimental data points using various liquids and packings. The relative permeability coefficients have been determined from gas and liquid phase pressure drop and are correlated to the fluid saturations. With the known permeabilites, the phase-wise forces are then coupled via the capillary pressure pc = pl − pg =

2c 2 ⎡ ⎞⎤ ⎛ βg 1 ⎢ (1 − ε) μg Sv 2 − 2c ⎜ ⎟⎥ E (1 ) 2 u u εβ − − 1 g ⎜ g 1 − β l⎟⎥ βg 2 ⎢⎣ ε3 ⎝ g ⎠⎦

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Industrial & Engineering Chemistry Research (i) Attou and Ferschneider2 used the geometrical correction factor c in their force balances (eqs 10, 11) describing the additional volume of a sphere when covered with a liquid film. This needs to be adapted for solid foams since the surface, which can be covered with liquid, is now a complex strut network. Therefore, a new correction factor c has to be developed. (ii) The minimum or bottleneck diameter (dmin) between spherical particles, which was used to describe the capillary pressure in the Attou and Ferschneider2 model in eq 13, is replaced by the window diameter (dW) of the solid foam, which is the narrowest part to be passed by the fluids. (iii) Both film stability models require a set of Ergun parameters E1 and E2 in eqs 5, 10, and 11, which have to be determined via dry pressure drop measurements. (iv) The models include a characteristic hydrodynamic length, which is an argued aspect within solid foam research.8,9,25−28 However, since the drag forces already base on the Ergun approach,29 it seems reasonable to use the reciprocal specific surface area as proposed in the original Ergun equation (de = 1/Sv). Therefore, no new equivalent diameter for the foams’ geometry is required here. (v) The relative permeability coefficients n1 and n2 in eqs 6 and 7 used by Grosser et al.1 have to be adjusted. (vi) The static liquid holdup values for solid foams are required for the relative permeability terms in eq 6. Though both film stability models have been set up on a physical basis, the complexity of the bed and the flow morphology require a certain degree of pragmatic empiricism to reflect the multiphase physics. Primarily, this expressed by the Ergun parameters, the static liquid holdup values, and the permeability coefficients. Due to their importance in regime transition prediction, all three aspects will be subsequently discussed in detail. 2.2.1. Pressure Drop. In terms of pressure drop across packings, the semiempirical Ergun approach is the most widely used concept, which originally traces back to Ergun and Orning30 and Ergun.29 They determined the single-phase pressure drop Δp (1 − ε)2 μSv 2 (1 − ε)ρSv 2 = E1 u + E2 u ΔL ε3 ε3

currently have to be determined for every packing by singlephase pressure drop experiments to describe their packing specific relation. 2.2.2. Static Liquid Holdup. The static liquid holdup

εl,s =

Vl Vb

(15)

is usually defined as the ratio of liquid volume trapped in the void volume of the packing after draining to the bed volume. Under flow conditions, the static liquid holdup reduces the void volume of the bed and decreases the open hydraulic cross section for fluid flows. Thus, higher static liquid holdups shift the trickle-to-pulse flow regime transition to lower fluid fluxes. Few data for static liquid holdup in solid foams have been reported in the literature.8,12,26,36 Comparing the different foam types, the values scatter widely and depend on material, foam segment height, pore density, and specific surface area.36 As the correlation proposed by Sáez and Carbonell notably underestimates the static liquid holdup in solid foams, Stemmet et al.8 and Edouard et al.26 published new static liquid holdup correlations. However, both differ significantly from each other, probably because they were developed for different solid foam materials, i.e., silicon carbide and aluminum, which differ in morphology and contact angle. Hence, the available static liquid holdup correlations are not applicable to the SiSiC foams presented here. Therefore, the static liquid holdup is measured. 2.2.3. Permeability Coefficients. In the original permeability model,23 four permeability terms ki, function of the fluid saturation to the power of ni, were introduced as empirical prefactors to the viscosity term and inertial term in the gas and liquid side force eqs 10 and 11. The original coefficients were obtained by a parameter fit to experimental permeability values.23 As the original four parameter approach gave only slightly better results than a two parameter approach, the model was simplified to two fitting terms kl and kg containing two permeability coefficients n1 and n2.23 Due to the different void network geometry in solid foams, the holdups and corresponding permeabilites are expected to differ largely from those in particle beds. The sensitivity of the permeabilities has also been described by Nemec and Levec.37 To the authors’ knowledge, no relative permeabilities for foams have been reported in literature so far. As the straightforward measurement of these empirical factors is difficult, the permeability coefficients will be treated as fitting parameters for regime transition modeling.

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of gas flow through porous media in packed columns. The parameters E1 and E2 are 150 and 1.75 for spherical particles, respectively. For the description of the particles, Ergun used the specific surface area Sv. Macdonald et al.31 applied Ergun’s equation to different packing shapes and types and recommended 180 and 1.8 for E1 and E2, respectively. With changing particle size and shape of the packing, these parameters for Ergun’s equation can vary widely.19 For solid foams, various pressure drop correlations depending on Ergun’s equation with different hydraulic lengths have been proposed in recent years.25,27,28,32−34 A summary of the pressure drop correlations and hydraulic model notions for solid foams can be found in the articles of Huu et al.25 and Dietrich.32 As indicated by Incera Garrido et al.,35 the pressure drop in ceramic solid foams widely scatters due to fluctuations in product quality and the morphological and material variety of solid foams. Moreover, most of the foam parameters provided by the supplier are coarse classifications rather than accurate values (e.g., pore density). Thus, the values for the parameters

3. EXPERIMENTAL SECTION The experimental setup is shown in Figure 2. All experiments were performed in acrylic columns of 50 and 100 mm diameter (E-7). The columns were packed on top of a metal sieve support with SiSiC solid foam segments each of 0.1 m height up to a total packing length of 0.8 m. The ceramic foams’ properties provided by the supplier (Fraunhofer IKTS, Dresden, Germany) can be found in Table 1. The given (hydraulic) porosity ε was determined by displacement experiments and denotes the void fraction which is accessible to fluids. As the diameters of the custom-made foam elements were well-alligned with the column diameter, no additional sealing to the column wall was required to prevent major bypass flows. To determine the dry pressure drop, a differential pressure transducer (I-1, I-2, type Omega PD 23 V0.2 and PD 23 V0.5) 9711


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performed with column packings consisting of eight, five, three, and one foam segment. For the transition experiments, the column was connected to the gas and liquid flux supply branch depicted in Figure 2. The gas side consists of two mass flow controllers (E-2 and E-3, type Omega FMA-2611 and FMA-2613) adjusting the gas flux from the oil-free compressed air supply. The latter branch consists of the rotary piston pump (E-4, type Waukesha Cherry-Burrell Universal 1 Series 060-UI) and two Coriolis mass flow controllers (E-5 and E-6, type Rheonik Coriflow RHM 0.6 G0.5″ and RHM 20 GMT G1″) through which liquid was recirculated. All experiments were carried out under atmospheric conditions. For the influence of the initial distribution, a full cone spray nozzle (SN) and a multipoint distributor (MPD), which is identical to the one used by Mohammed et al.,12 were employed. To properly adjust the cone of the spray nozzle to the column cross section, an additional head space of 20 cm was necessary. For the determination of the regime transition between trickling and pulsing flow, the gas and liquid superficial velocities were varied in ranges of ug = 0.1−1 m s−1 in 0.1 m s−1 steps and u1 = 0.005−0.04 m s−1 in 0.005 m s−1 steps. Prior to the experiments, the packing was prewetted using the Kan liquid method.38 The column-sided excess pressure transducers were connected to an analog-to-digital converter transferring the signals to a computer. The pressure fluctuation data were used as indication for the onset of flow instabilities, i.e., the transition to pulse flow. After a short startup time, the data were collected for 3 min with a sampling rate of 200 Hz for each measurement point. Fluid properties summarized in Table 2 were determined with the ring method for the surface tension and with a Hoeppler falling sphere viscometer for the liquid viscosity.

Figure 2. Experimental setup used for regime transition measurements.

Table 1. Morphological Properties of the SiSiC Solid Foams Used in This Study PPI

D [mm]

ε

S̅v [m2 m−3R]

d̅s [μm]

20 30 45

50, 100 50, 100 50, 100

0.87 0.89 0.85

983 1594 2031

458 357 194

was connected 2.5 cm below the upper and above the lower end of the 0.8 m long foam packing, respectively. For accurate determination of Ergun parameters E1 and E2, pressure drop was measured for superficial gas velocities up to 3 m s−1 and up to 1.7 m s−1 for solid foams of 50 mm and 100 mm diameter, respectively, with increments of 0.1 m s−1. The static liquid holdup was studied by gravimetric determination of the column mass using a scale (Sartorius isi 10). The method is expected to yield more representative results than gravimetric measurements outside the column8 and is less complicated than tracer techniques12,26 which were previously used to determine the static liquid holdup in solid foams. At first, the packing was flooded from the bottom at very low liquid velocities and subsequently drained three times to ensure complete wetting of solid foams. In a third cycle, the foam was drained for 30 min before taking the column weight. To determine the static liquid holdup from the mass values, the mass of the empty column with dry foams was subtracted and calculated: εl,s =

ms,d − ms − ∑ mf 1 Vl = Vb ρl Vb

Table 2. Fluid Properties for the Transition, Static Liquid Holdup, and Pressure Drop Measurements fluid (abbrev) air deionized water (H2O) Tergitol, 0.8 μL L−1 (Ter) glycerin, 51 wt % (Gly)

σ [mN m−1]

ρi [kg m−3]

μi [mPa s]

72.4 51.5 68.6

1.2 1000 1000 1130

0.0223 1 1 6.5

4. RESULTS AND DISCUSSION 4.1. Pressure Drop Measurements. Figure 3 shows the single-phase pressure drop per unit length for three SiSiC solid foams (diamonds for 50 mm diameter, triangles for 100 mm diameter). As the pressure drop is mainly affected by the foam morphology and therefore mainly attributed to the solid material and porosity, only limited data obtained for morphological similar foam types with comparable pore density are included for comparison. With an increase of the superficial gas velocity, the pressure drop per unit length increases, which was already described by Ergun and Orning.30 With increasing pore density the pressure drop increases significantly and reaches values up to 2500, 3600, and 8200 Pa m−1 at 2 m s−1 for 20, 30, and 45 PPI pore densities,

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After free outflow, the wet packing was exposed to forced downward gas flow of 40 L min−1 for at least 10 s and the column weight was determined again. The flooding, free, and forced drainage cycle was repeated again twice for assessment of reproducibility. Static liquid holdup for deionized water was determined for pore sizes of 20, 30, and 45 PPI in both column diameters. For experiments with Tergitol (Ter) and glycerin solutions (Gly) only foams of 100 mm were studied. The whole procedure was 9712


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Figure 3. Pressure drop per unit length for gas phase pressure drop and various pore densities. The solid and dashed lines show the model depending on Ergun’s equation; the empty markers represent literature data.9,27,34,35,39

others the tortuosity,30 was found to be significantly higher. Most likely, the deviation is attributed to less morphological homogeneity and an increased probability of blocked pores due to the more difficult manufacturing process of the bigger foam segments with high pore density. Additionally, a comparison of the data presented in Figure 3 and pressure drop correlations in the literature25,27,32,40 was carried out (not shown). Though being developed for ceramic solid foams of comparable nominal pore density, none of the correlations was able to predict pressure drop with acceptable accuracy for all three foam specifications. Considering the significant deviations in pressure drop data in Figure 3, the discrepancy between the empiric correlations is hardly surprising. 4.2. Static Liquid Holdup. 4.2.1. Forced and Free Drainage. Figure 4 depicts the static liquid holdup for 20, 30, and 45 PPI foams with diameters of 50 mm and 100 mm as

respectively. This can be attributed to the increasing specific surface area as well as to the decreasing pore and window sizes. Additionally to the change in the idealized geometry, one should keep in mind that, due to the small pore sizes in 45 PPI foams, blocked pores are more likely to occur during the manufacturing process. Therefore, pressure drops can be disproportionately higher than in coarser foams as in the present case. The foams in this study belong to the group with the highest porosity among the ceramic foams in the literature and, hence, should yield the lowest pressure drop per unit length. Yet, comparing literature and present pressure drop data, other morphological characteristics, such as surface smoothness and strut sharpness, appear to significantly affect the pressure losses as well. For instance, the foams used by Inayat et al.27 (SiSiC, 30 PPI) and Incera Garrido et al.35 (Al2O3, 45 PPI) yielded lower pressure drops even though the corresponding foam porosities were slightly lower compared to our foams. Nevertheless, the data given by Dietrich et al.9 (ObSiC, 20 PPI), Inayat et al.27 (SiSiC, 20 and 30 PPI), and Incera Garrido et al.35 (Al2O3, 45 PPI) seem to be very comparable with the investigated foams. By fitting eq 14 against the experimental data, the Ergun parameters have been evaluated by the global particle swarm optimization method. Compared to the original Ergun parameters (E1 = 150, E2 = 1.75), the parameters in Table 3 are significantly higher for solid foams. Interestingly, the optimization resulted in one parameter set for five of the six investigated foam packings. For foams with 100 mm and 45 PPI pore density, the value of E2 does not agree with the global value obtained for the other five foam specifications. Thus, the value for E2, which reflects among Table 3. Calculated Ergun Parameters from Measurements for 20, 30, and 45 PPI SiSiC Foams specification

E1

E2

100 mm, 45 ppi all other foams

524 524

3.27 2.37

Figure 4. Free and forced static liquid holdup for deionized water as a function of the packing length for 50 mm and 100 mm column diameter with various pore densities. 9713


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In principle, the glycerin holdup is affected by three facts. One is the slightly lower surface tension (68.6 mN m−1) compared to pure deionized water (72.4 mN m−1) as shown in Table 3 which will slightly increase the surface wettability and therefore also the wetted area. The second one is the higher viscosity leading to thicker liquid films, i.e., higher liquid loading per wetted surface area. The third one is the increased liquid density, which will on the contrary slightly decrease the liquid content due to gravitational forces. 4.2.3. Modeling of the Static Liquid Holdup. A common approach to predict the static liquid holdup is the correlation with the Eötvös number. For solid foams, a crucial point is the definition of an appropriate characteristic length, which is required for Eötvös correlations. Thus, different approaches were tested and are exemplarily plotted for deionized water in Figure 6.

a function of the packing length, calculated according to eq 16. In particular, the effect of the packing length was studied to account for the additional volume of liquid Vl,seg,1, which is trapped in the lowest foam segment at the junction to the metal sieve support. Such liquid accumulations were also reported by Grosse and Kind.36 By subtracting the total liquid volume in the lowest foam segment, the static liquid holdup in an infinite packing εl,s, n =

Vl,seg, n − Vl,seg,1 Vb(n − 1)

(n ≥ 2)

(17)

was calculated. The solid and dashed lines denote the free and forced drainage, respectively. In general, the free static liquid holdup is higher than the forced drainage value, as a part of the dynamic liquid holdup is trapped in the foam segments by capillary forces. This dynamic amount is pushed out by short exposure of the packing to gas flow induced shear stress. Furthermore, the values in Figure 4 reveal that the static liquid holdup constantly rises with increasing pore density because of (a) increasing specific surface area and therefore offered liquid adhesion area and (b) increasing capillary forces due to decreasing pore and cell sizes. With decreasing packing diameter, the liquid holdup increases. This is attributed to liquid volume trapped between column wall and segment circumference which has a greater influence in smaller diameters. This finding is also in agreement with the results of Gunjal et al.41 and Rao et al.42 Concerning the representation of the static liquid holdup, we recommend using the infinite, forced static liquid holdup values since they most likely represent flow conditions in the core of the packing. 4.2.2. Effects of the Surface Tension and the Viscosity. With the addition of the surfactant Tergitol, the liquid surface tension was decreased from 72.4 to 50.2 mN m−1. Since the SiSiC foam is covered with a passivated silicon oxide layer, it is commonly considered to be only moderately hydrophilic. As expected, the addition of Tergitol led to an increase in the liquid’s affinity to perfectly wet the foam surface and, therefore, an increase in static liquid holdup in Figure 5 was observed.

Figure 6. Static liquid holdup prediction for deionized water by different Eötvös correlations using various characteristic lengths.

The model representation originally proposed by Sáez and Carbonell23 is not suitable since it was developed for spherical particle packings. The models adjusted by Edouard et al.43 and Stemmet et al.10 tend to overestimate the static liquid holdup. As the latter used aluminum foams with different morphology than SiSiC foams, the disagreement between measured and predicted static liquid holdups is not surprising. In order to find an appropriate model for the static liquid holdup, the equivalent diameters proposed by Huu et al.,25 Lacroix et al.,28 and Dietrich et al.9 as well as the strut diameter ds were applied and the parameters a and b in eq 8 determined. The models for the equivalent or hydraulic diameter, respectively, by Huu et al.25 and Dietrich et al.9 overestimate the static liquid holdup and do not match the measured data properly. Excellent agreement was found with the model of Lacroix et al.28 (R2 = 0.9998). The same applies if the strut diameter ds is used as the equivalent diameter (R2 = 0.9998). Therefore, it was decided to use the equivalent diameter proposed by Lacroix et al.,28 which is based on the cubic cell model.

Figure 5. Infinite static liquid holdup for deionized water (H2O), Tergitol (Ter), and 51 wt % glycerin solution (Gly).

Though the holdup unambiguously increases for all pore densities, the quantitative effect of lowered surface tension turns out to be quite variable, which can be attributed to the complex interaction of adhesion and capillary forces. Using 51 wt % glycerin solutions, the static liquid holdup increases clearly compared to deionized water and yields the highest static liquid holdup values as shown in Figure 5. 9714


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outlet. In contrast, the flow regime transition is characterized acoustically by nonperiodic, irregularly occurring pulse noises at the reactor outlet. Visually, the transition is identified by the formation and migration of local liquid accumulations near the reactor wall, which occurred irregularly and did not cover the whole cross section. In Figure 8, the flow regime maps originating from both methods, i.e., variation coefficient of the pressure transducer

Since the presented Eötvös correlations only describe the case of deionized water for static liquid holdup, values for the change of surface tension as well as the change of viscosity need to be determined. A more exact approach would be to fit the Eötvös correlation against all static liquid holdup values from all various liquid properties. Since a sufficiently good fitting is not possible, the different predictions for varying liquid properties are required instead. For Tergitol and glycerin measurements, the same method as for deionized water was applied. However, it was found that, in this case, the equivalent diameter definition proposed by Dietrich et al.9 is the most appropriate representative length in the Eötvös number for SiSiC foams in combination with liquids other than deonized water. Hence, the equivalent diameter definition de = 4ε/Sv should be used. The final correlation for the static liquid holdup prediction for foams with 50 mm diameter and deionized water is given by εl,s = (7.556 + 4.162 Eo)̈ −1

(R2 = 0.9998)

(18)

For foams of 100 mm diameter with deionized water εl,s = (5.107 + 8.045 Eo)̈ −1

(R2 = 0.9974)

(19)

is recommended, whereas εl,s = (5.273 + 0.03665 Eo)̈ −1

(R2 = 0.9600)

(20)

Figure 8. Comparison between visual observations (symbols) and pressure signal variation coefficients (contour) with good agreement (left) and bad agreement (right).

is proposed for foams of 100 mm diameter in combination with Tergitol and glycerin solutions. 4.3. Transition between Trickling and Pulsing Flow. Fast excess pressure transducers were used as one approach for the identification of the prevailing flow regime and the transition between them. In Figure 7 the measurement signals for the different flow regimes are shown. In trickle flow (Figure 7a), the pressure

signal and the corresponding acoustically supported visual observations, are compared. The resulting flow regime maps are shown in Figure 9. The gas continuous flow (GCF) or trickle flow on the lower left and the pulse flow (PF) in the upper right corner are separated by the regime transition region shown as the shaded area. At first glance, foams of 20 PPI and 30 PPI show similar behavior concerning the onset of liquid pulsing regardless of the operation parameters. Yet, the finer 30 PPI foam requires higher fluid fluxes to reach the transition regime and the fully developed pulse flow. In contrast, the finest 45 PPI foam packing shows considerable larger transition regions. The fluxes required to enter the transition region lie between 20 PPI and 30 PPI at comparable operation conditions. The fluxes needed to reach stable pulse flow are the highest compared to all other structures. Thus, it can be concluded that the hydrodynamics of 45 PPI foam are up to a certain extent stronger dominated by local effects, i.e., local flow instabilities, than by global effect due to limited cross-talk between the flow paths. 4.3.1. Concept of Available Flow Paths. To understand the influence of different effects on the regime transition, the following model representation of available flow paths is considered: In dry state, the 3D solid foam network consists of parallel axial flow paths or channels interconnected by radial passages. The total number of available channels as well as the number passage is a square function of linear pore density and of reactor diameter. Thus, with higher pore density, the number of channels and windows increases strongly while, vice versa, the size of each channel and window decreases. In trickle flow, the channel and window network is more or less homogeneously covered with a stationary thin liquid film which reduces the cross section open to the gas and liquid flow. Additionally, each channel can be either predominantly used by liquid or gas flows or equally traversed by both of them. With rising liquid fluxes, the thin liquid films grow until reaching a critical film

Figure 7. Excess pressure signal for trickle flow, regime transition, and pulse flow.

signal remains nearly constant with only minor perturbations for the whole measurement duration, whereas for the transition area (Figure 7b) clear fluctuations become visible. The pressure signal for pulsing flow (Figure 7c) shows strong fluctuations. The variation coefficient of the pressure signal was used as one regime-characteristic parameter. While fully developed pulse flow can be clearly identified, the trickling regime and transition between trickling and pulsing flow, cannot be distinguished adequately. Furthermore, it was observed that the accuracy for the identification of the pulse flow region decreases with the large column diameter. For the optical and acoustic identification, the following criteria were used: Optically, pulse flow was characterized by the periodic occurrence of moving liquid barriers which covered the whole cross section. Congruently, the pulse flow was acoustically indicated by periodically clearly audible release of shock waves at the reactor 9715


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the number of possible bypass flow channels is smaller than in 30 PPI foams. Congruently to the model representation of available flow paths, the global pulsing is stabilizing at the lowest superficial velocities in 20 PPI foams which have the lowest amount of possible bypasses. Similarly, stable pulse flow evolves also at lower superficial velocities in 30 PPI foams than in 45 PPI foams. With decreasing column diameter, the regime transition is shifted to slightly lower fluid velocities in 20 and 30 PPI foams as the number of possible bypasses is significantly reduced. In 45 PPI foams, local pulsing was found to start at significantly higher velocities, which has several reasons: Compared to the foam segments with 100 mm diameter, the 50 mm segments showed a diameter undersize (approximately one cell size) compared to the housing column, which possibly allows more flow bypassing in the smaller reactor diameter. Additionally, it is known that the 100 mm diameter foams suffer from structural inhomogeneity due to the challenging production process, which results for example in closed pores. This may provoke local pulsing already at lower velocities. The deviations between the two diameters also appeared in the dry pressure drop measurements (see also Figure 3). The onset of stable pulse flow, however, again can be attributed to the “earlier” blockage of available bypass flow routes in the core of the packing. 4.3.3. Effect of the Initial Distribution. Figure 9b shows the transition regions for different initial distribution conditions of the deionized water for the 100 mm solid foams. Changing the liquid distribution system from spray cone nozzle (SN) to multipoint distributor (MPD) leads to a shift of the regime transition to higher fluxes for the two coarser structures. As the MPD with eight outer and four inner evenly concentrically distributed liquid inlets introduces significantly lower initial distribution homogeneity than the SN, the prechanneling of the liquid on top of the packing creates rather independent flow paths for gas and liquid. Thus, the blockage of the gas starts at higher liquid flow rates in all three foam types. In 45 PPI foams, however, the less homogeneous initial distribution of liquid also seems to provoke the onset of stable pulse flow at lower superficial velocities. Possibly, this traces back to slightly higher liquid holdups which also affect the flow stabilization. This is also supported by the findings of Mohammed et al., who reported slightly higher pressure drop when using the MPD instead of the SN.12 4.3.4. Effect of Surface Tension and Viscosity. Figure 9c summarizes the effects of altered liquid phase surface tension and viscosity using aqueous mixtures of Tergitol (Ter) and glycerin (Gly) distributed by a spray cone nozzle. With the addition of the surfactant Tergitol, the surface tension decreases (σL = 50.2 mN m−1) and the transition regime shifts toward lower superficial velocities compared to the deionized water (σL = 72.4 mN m−1) for all employed foams. Here, the lower surface tension results in an improved wettability of the solid foam and, thus, in an improved liquid distribution. The effect is comparable to changing from multipoint distributor to the spray nozzle (see section 4.3.3). In addition, the static liquid holdup for the Tergitol mixture is generally higher than with deionized water. This leads to cavity blockage at lower velocities. Comparing the shape and size of the regime transition area in the three different foams, one could also conclude that the dominance of the capillary effect in the 45 PPI foams is significantly decreased since both surface tension

Figure 9. Regime transition regions between trickling and pulsing flow for variation of (a) column diameter, (b) initial liquid distribution, and (c) liquid properties.

thickness at which two neighboring films bridge the channel or window in-between and make it impassable to the bulk flow. The rigidity of those liquid barriers is mostly dominated by capillary forces, which is a function of the diameter of the blocked network path. With rising liquid velocity, the number of blocked network paths increases until a critical amount of blockage is reached, which then locally hinders parts of the gas flow. When the expansion forces of the trapped gas exceed the capillary forces of the liquid barrier, the barrier is suddenly broken and pushed downstream. This local accumulation and removal of liquid is then experienced as local pulsing which is entitled the “regime transition”. Besides some part of the gas flow being trapped, the majority of gas is able to bypass the liquid barriers in a trickle-flow manner. When liquid throughput and gas throughput are increased further, the open flow paths vanish and global pulsing (“pulse flow”) occurs. As long as open flow channels are available, however, the pulsing will stay unsteady. 4.3.2. Effect of Pore Density and Column Diameter. Figure 9a shows the transition regions for different column diameters for foams of 20, 30, and 45 PPI obtained for deionized water distributed via a spray cone nozzle. In the reference system with 100 mm column diameter, the regime transition, i.e., the onset of local pulsing, is reached at lowest throughputs in 45 PPI foams, which have the network with the narrowest pores, i.e., highest local blocking probability. Due to their wider pore network and therefore decreased capillary forces, the regime transition in 30 PPI foams was encountered at significantly higher fluid fluxes. Though having the widest pore network, the local pulsing in 20 PPI foams was encountered somewhere inbetween the other two foams, which seems reasonable, since 9716


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model) yields satisfying predictions for the regime transition compared to the experiments. Instead, both predict the regime transition at velocities far higher than studied. As both approaches were developed for spherical particle beds, the deviations in the results are rather big as could have been expected. Beside using empirical Ergun constants, the geometrical correction factor provides the only degree of freedom to adjust the model of Attou and Ferschneider2 for solid foams. The factor expresses the geometric constriction of flow channels by liquid films due to the surface covering liquid film. Considering ongoing discussions on suitable regular shapes representing solid foam morphologies,25 it is obvious that a single geometric correction factor is not sufficient. The parametric study indicated by the red lines in Figure 10 reveals that the model from Attou and Ferschneider2 is almost insensitive in terms of the correction factor c and therefore is not capable of recreating the measured transitions at all. Hence, the model has not been considered further in this study. On the contrary, Grosser et al.’s model is strongly sensitive to the permeability coefficients n1 and n2, which are usually determined experimentally by measuring pressure drop along packings of known liquid holdup. Owing to the complexity of multiphase flows in porous media, the semiempirical coefficients are recommended auxiliary tools simplifying the description of multiphase flows.37 Studying the influence of gas velocity, packing shape, diameter, and pressure on the relative permeability parameters under trickling flow conditions, Nemec and Levec 37 found that constant relative permeability parameters as proposed by Sáez and Carbonell23 are not entirely appropriate. These parameters are rather a function of the operation conditions and setup parameters, and depend in particular on the type of packing. Though several groups44−47 already reported permeability parameters for the Forchheimer equation to describe biphasic pressure drop in solid foams, no relative permeability parameters have been reported so far in the literature. Moreover, the required accurate determination of dynamic liquid holdups was not in the scope of the present work. Therefore, the parameters for the investigated foams were varied in a range between 3 and 12 for both variables to improve the agreement between measurements, i.e., the onset of flow instabilities, and the model. To reduce computational time, the parameter sets were optimized by minimizing the absolute average residual error (AARE) in a grid search method. It is important to mention that the Grosser model assumes uniform initial phase distributions. Hence, the influence of the initial distribution on the regime transition will not be discussed and only experimental data obtained with a spray cone nozzle will be subsequently considered for comparison between model and experiment. 4.4.1. Effect of the Column Diameter. A comprehensive analysis of suitable parameters n1 and n2 for different foam types and reactor diameters revealed that different sets were required although the sets are in similar ranges (see Table 4). Considering the well-known scattering in the foam template properties (e.g., pore distribution) as well as in the final ceramic foam geometries after several manufacturing steps (slurry infiltration, kneading, drying, burning, silicon infiltration, and oxidation), the nominal morphological properties in Table 1 should only be considered as an educated guess. Furthermore, effects such as initial distribution, wettability issues, or other

and liquid contact angle are lowered with the addition of Tergitol. With the addition of glycerin the viscosity increases significantly (μL = 6.5 mPa s), whereas surface tension and density remain in the range of deionized water. It was found that the regime transition is shifted to very low superficial velocities in all three solid foam packings. The high viscosity results in strong liquid−solid interactions due to the high drag force. When operating the reactor without any gas flux, the viscous forces were found to be high enough to restrain the liquid on top of the first segment in all packings even at low liquid fluxes. Even with minimal gas flux, however, the gas pressure buildup was strong enough to prevent the liquid backlog. Though the surface tension (σL = 68.6 mN m−1) is also slightly lower than compared to deionized water, the earlier onset of local pulsing most likely traces back to the thicker and more rigid liquid films. As also indicated by the high static liquid holdup values (see Figure 5), this increases the general liquid content of the packing. Further, it is worth mentioning that the dispersed bubbly flow regime was encountered using the viscous system in the 45 PPI foam packed reactor (dashed area in Figure 9c). Beyond that, neither spray flow nor dispersed bubbly flow has been found in any other configuration studied here. 4.4. Model Comparison. Based on the extracted Ergun constants and static liquid holdup correlations developed above, the existing models of Grosser et al.1 and Attou and Ferschneider2 were adapted to foam packed fixed bed reactors. A first analysis of whether the models predict the regime transition with simple adjustment of the permeability coefficients n1 and n2 and of the geometric correction factor c, respectively, is shown in Figure 10 as lines marked with crosses. In the presented example for foams with 50 mm diameter and 20 PPI, neither the original permeability parameters n1 = 2.9 and n2 = 4.8 (Grosser model) nor the geometric correction factor c = 1/3 (Attou and Ferschneider

Figure 10. Comparison of the models of Grosser et al.1 and Attou and Ferschneider2 with different parameter sets for 50 mm diameter and 20 PPI pore density. 9717


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measurement branch at higher gas velocities. Moreover, the dashed lines in Figure 11a show that a universal permeability parameter set for each diameter (last row in Table 4), as proposed by Sáez and Carbonell,23 does not yield satisfying differentiation between the three pore densities. The influence of characteristic parameters, e.g., specific surface area, porosity, strut diameter, or static liquid holdup, seem to be underestimated by the model. 4.4.2. Influence of Surface Tension and Viscosity. Ashrafi et al.48 studied the permeabilites for various liquids in sediments and found that relative permeability parameters depend on phase holdups and fluid properties. Additionally, their results indicate that the interaction between a liquid film and a gas flow is affected by film viscosity and thickness, for example in terms of the waviness of the film surface. In the present study, the prediction of the regime transition was tested for both Tergitol and glycerin solutions with the permeability coefficient of deionized water (Table 4). As shown by the red and black lines in Figure 11b, the model predicts qualitatively correctly the shift of the regime transition toward lower velocities when using liquid properties differing from deionized water. In order to improve the prediction accuracy and to account for findings of Ashrafi et al.48 in terms of liquid property dependent permeabilities, the relative permeability parameters were newly determined in the same manner for the various liquids in this study (not shown). However, the prediction accuracy in terms of AARE was only slightly improved.

Table 4. Relative Permeability Parameters for Foam Density and Column Diameter Variations 50 mm

100 mm

PPI

n1

n2

PPI

n1

n2

20 30 45 all

10.0 7.6 7.6 8.6

4.2 3.2 3.0 3.0

20 30 45 all

8.4 7.0 10.6 9.2

4.4 3.4 3.0 3.0

violated model assumptions cannot be accounted for in the model. Quite conveniently, the parameter sets are in similar ranges independent of the reactor diameter, especially concerning the gas permeability coefficient n2. In contrast, the liquid permeability parameter n1 scatters more widely, which is more likely to trace back to the flatness of the AARE optimization criteria, making it sensitive to the data range, data balancing, and other aspects. Therefore, the variations of n1 in Table 4 should not be overinterpreted. Moreover, the model transition curves in Figure 11, which correspond to the parameter sets, show why AARE minimization yields widely scattered values of the permeability parameter n1.

5. SUMMARY The flow regime transition in SiSiC solid foams with cocurrent downward flow of gas and liquid was investigated. The onset of pulsing was studied experimentally for various pore densities, reactor diameters, initial distributors, and different liquid properties. All variations were found to significantly alter the gas and liquid velocities at which the transition occurs. Hereby, 20 and 30 PPI foams showed a comparable behavior, while the behavior of the 45 PPI foam packing differed significantly. However, all observed behavior can be explained with the concept of available flow paths. By increasing the diameter or using less homogeneous initial liquid distribution, the onset of pulsing is shifted toward higher fluid fluxes. Increased viscosity or lowered surface tension results in much earlier pulsing. To predict the regime transition between trickle and pulse flow, the film stability models of Grosser et al.1 and Attou and Ferschneider2 were adapted to foam specific parameters based on experimentally determined dry pressure drop and static liquid holdup. With the exception of 45 PPI foams with 100 mm diameter, the dry pressure drop was correlated to a single set of Ergun type parameters. The static liquid holdup increased with increasing pore density and specific surface area, respectively, as well as with decreasing surface tension and increasing liquid viscosity. While the model of Attou and Ferschneider2 strongly overpredicts fluxes needed to reach pulse flow, the model of Grosser et al.1 can be adapted to solid foams and predict the regime transition properly. When using deionized water and air as fluids, the rather simple model predicts the transition with adequate accuracy. However, one should keep in mind that the relative permeability coefficients depend on the fluid properties, foam density, and column diameter. For future applications of the model to related reactor concepts, i.e., other types of solid foams, different liquids, or different operation conditions (temperature, pressure), the determination of relative perme-

Figure 11. Comparison of measurements and model predictions with the modified model of Grosser et al.1

In general, all the predicted transition lines tend to be too steep at lower gas velocities, i.e., underestimate the stabilizing effect of low to moderate and possibly laminar gas flows. The manifold effect of gas fluxes to the trickle flow had already been reported by Nemec and Levec,37 which is why they suggested using different permeability parameter sets for different gas flow rates. As to be seen for all curves in Figure 11, the predicted transition lines run more or less parallel to each other, independent of the parameter set. Therefore, the optimized parameter set tends to fit the curve more closely to the steeper 9718



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ability coefficients based on pressure drop at known liquid holdups is therefore highly recommended. Although the overall prediction accuracy of the adopted Grosser model needs still further improvement, it allows a rough estimation of effects for different foam geometries and different liquids. Moreover, it predicts correctly that the trickleto-pulse flow transition occurs at much higher fluxes compared to typical industrial catalyst carriers (see Figure 12).

Article

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge the Helmholtz Association for support of the research within the frame of the Helmholtz Energy Alliance “Energy Efficient Chemical Multiphase Processes” (HEA-E0004).

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NOMENCLATURE

Abbreviations

AARE = absolute average residual error Al2O3 = alumina GCF = gas continuous flow Gly = glycerin solution H2O = deionized water MPD = multipoint distributor ObSiC = oxide bound silicon carbide PF = pulse flow PPI = pores per (linear) inch SiC−Al2O3 = silicon carbide alumina SiSiC = silicon infiltrated silicon carbide SN = spray nozzle TBR = trickle-bed reactor Ter = Tergitol solution Notation Latin Symbols

a, b = Eötvös fitting parameters c = geometric correction factor D = column diameter d1 = sphere diameter including thin liquid film de = equivalent diameter dmin = minimum diameter from three spheres in contact ds = strut diameter E1 = Ergun parameter describing viscosity forces E2 = Ergun parameter describing inertia forces Fg = gas drag force Fint,g = gas/liquid drag force Fint,l = liquid/solid drag force Fl = liquid drag force Fw,l = liquid/wall drag force g = Earth acceleration J = Leverett J-function ki = permeability of phase i mf = mass of dry solid foam ms = mass of dry setup ms,d = mass of drained setup n = number of segments n1 = liquid relative permeability coefficient n2 = gas relative permeability coefficient pc = capillary pressure pi = pressure of phase i (i = l, g) Δp/ΔL = pressure drop per unit length R̲ i = pseudoturbulence stress tensor (i = l, g) Sv = specific surface area S = gas phase saturation t = time ui = superficial velocity of phase i (i = l, g)

Figure 12. Comparison of trickle-to-pulse flow regime boundaries for different packings with water/air flow.15,22,49,50

The transition shift underpins that solid foams are promising catalyst carriers for multiphase applications. The comparison of trickle-to-pulse flow transition with typical industrially used catalyst carriers reveals that solid foam packed reactors can be operated under significantly higher fluid fluxes in trickle regime before entering pulse flow. From the reaction engineering point of view, the study presented here indicates that catalytic active foams might open up new operation windows in trickle flow. Though the pulse regime is known to enhance both heat and mass transfer, it also significantly decreases liquid residence times as liquid-rich pulses travel fast through the bed. Assuming a moderately fast reaction, the reduced residence time of pulse flow in conventional catalytic packed beds leads to lower conversions. The operation in fast trickle flow, i.e., trickle flow with elevated throughput(s), might be a promising operation window as the mass and heat transfer rates increase with rising fluid fluxes.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.5b02233. Mathematical derivation of eqs 10, 11, and 12 (PDF) 9719


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Mass Transfer Performance and Pressure Drop. Chem. Eng. J. 2015, 267, 332. (15) Blok, J. R.; Varkevisser, J.; Drinkenburg, A. A. H. Transition to Pulsing Flow, Holdup and Pressure Drop in Packed Columns with Cocurrent Gas−Liquid Downflow. Chem. Eng. Sci. 1983, 38, 687. (16) Sato, Y.; Hirose, T.; Takahashi, F.; Toda, M.; Hashiguchi, Y. Flow Pattern and Pulsation Properties of Cocurrent Gas−Liquid Downflow in Packed Beds. J. Chem. Eng. Jpn. 1973, 6, 315. (17) Talmor, E. Two-phase Downflow through Catalyst Beds: Part I. Flow Maps. AIChE J. 1977, 23, 868. (18) Holub, R. A.; Duduković, M. P.; Ramachandran, P. A. Pressure Drop, Liquid Holdup, and Flow Regime Transition in Trickle Flow. AIChE J. 1993, 39, 302. (19) Holub, R. A.; Duduković, M. P.; Ramachandran, P. A. A Phenomenological Model for Pressure Drop, Liquid Holdup, and Flow Regime Transition in Gas−Liquid Trickle Flow. Chem. Eng. Sci. 1992, 47, 2343. (20) Ng, K. M. A Model for Flow Regime Transitions in Cocurrent Down-flow Trickle-Bed Reactors. AIChE J. 1986, 32, 115. (21) Iliuta, I.; Larachi, F.; Al-Dahhan, M. H. Double-slit Model for Partially Wetted Trickle Flow Hydrodynamics. AIChE J. 2000, 46, 597. (22) Chou, T. S.; Worley, F. L.; Luss, D. Transition to Pulsed Flow in Mixed-Phase Cocurrent Downflow through a Fixed Bed. Ind. Eng. Chem. Process Des. Dev. 1977, 16, 424. (23) Sáez, A. E.; Carbonell, R. G. Hydrodynamic Parameters for Gas−Liquid Cocurrent Flow in Packed Beds. AIChE J. 1985, 31, 52. (24) Leverett, M. C. Capillary Behavior in Porous Solids. Trans. Soc. Pet. Eng. 1941, 142, 152. (25) Huu, T. T.; Lacroix, M.; Pham-Huu, C.; Schweich, D.; Edouard, D. Towards a more Realistic Modeling of Solid Foam: Use of the Pentagonal Dodecahedron Geometry. Chem. Eng. Sci. 2009, 64, 5131. (26) Edouard, D.; Lacroix, M.; Pham, C.; Mbodji, M.; Pham-Huu, C. Experimental Measurements and Multiphase Flow Models in Solid SiC Foam Beds. AIChE J. 2008, 54, 2823. (27) Inayat, A.; Freund, H.; Zeiser, T.; Schwieger, W. Determining the specific surface area of ceramic foams: The tetrakaidecahedra model revisited. Chem. Eng. Sci. 2011, 66, 1179. (28) Lacroix, M.; Nguyen, P.; Schweich, D.; Pham-Huu, C.; SavinPoncet, S.; Edouard, D. Pressure drop measurements and modeling on SiC foams. Chem. Eng. Sci. 2007, 62, 3259. (29) Ergun, S. Fluid Flow through Packed Columns. Chem. Eng. Prog. 1952, 48, 89. (30) Ergun, S.; Orning, A. A. Fluid Flow through Randomly Packed Columns and Fluidized Beds. Ind. Eng. Chem. 1949, 41, 1179. (31) Macdonald, I. F.; El-Sayed, M. S.; Mow, K.; Dullien, F. A. L. Flow through Porous Media-the Ergun Equation Revisited. Ind. Eng. Chem. Fundam. 1979, 18, 199. (32) Dietrich, B. Pressure Drop Correlation for Ceramic and Metal Sponges. Chem. Eng. Sci. 2012, 74, 192. (33) Fourie, J. G.; Du Plessis, J. P. Pressure Drop Modelling in Cellular Metallic Foams. Chem. Eng. Sci. 2002, 57, 2781. (34) Moreira, E. A.; Innocentini, M. D. M.; Coury, J. R. Permeability of Ceramic Foams to Compressible and Incompressible Flow. J. Eur. Ceram. Soc. 2004, 24, 3209. (35) Incera Garrido, G.; Patcas, F. C.; Lang, S.; Kraushaar-Czarnetzki, B. Mass Transfer and Pressure Drop in Ceramic Foams: A Description for different Pore Sizes and Porosities. Chem. Eng. Sci. 2008, 63, 5202. (36) Grosse, J.; Kind, M. Hydrodynamics of Ceramic Sponges in Countercurrent Flow. Ind. Eng. Chem. Res. 2011, 50, 4631. (37) Nemec, D.; Levec, J. Flow through Packed Bed Reactors: 2. Two-phase Concurrent Downflow. Chem. Eng. Sci. 2005, 60, 6958. (38) Kan, K.-M.; Greenfield, P. F. Pressure Drop and Holdup in Two-Phase Cocurrent Trickle Flows through Beds of Small Packings. Ind. Eng. Chem. Process Des. Dev. 1979, 18, 740. (39) Richardson, J. T.; Peng, Y.; Remue, D. Properties of Ceramic Foam Catalyst Supports: Pressure Drop. Appl. Catal., A 2000, 204, 19. (40) Inayat, A.; Schwerdtfeger, J.; Freund, H.; Körner, C.; Singer, R. F.; Schwieger, W. Periodic Open-cell Foams: Pressure Drop

Vb = volume of packed bed Vl = fluid volume in packed bed Vl,seg,n = liquid volume of the nth segment Vl,seg,1 = liquid volume of the first segment W = W-terms for onset of pulsing condition Eö = Eötvös number (ρlgde2ε2/σ(1 − ε)) Gai = Galileo number of phase i (i = l, g) Rei = Reynolds number of phase i (i = l, g) Greek Symbols

βg = gas saturation βl = liquid saturation δ = reduced liquid saturation ε = (open) porosity εg = dynamic gas holdup εl = dynamic liquid holdup εl,acc = accumulated liquid fraction εl,s = static liquid holdup εl,seg,n = segmental static liquid holdup μi = viscosity of phase i (i = l, g) ρi = density of phase i (i = l, g) σ = liquid surface tension τ̲ i = volume averaged viscous stress tensor

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REFERENCES

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Flow Regime Transition in Open-Cell Solid Foam Packed Reactors

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