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Ind. Eng. Chem. Res. 2010, 49, 2070–2077
Measurement of Dynamic Liquid Distributions in a Fixed Bed Using Electrical Capacitance Tomography and Capacitance Wire-Mesh Sensor Bartosz Matusiak,*,‡ Marco Jose da Silva,† Uwe Hampel,† and Andrzej Romanowski‡ Institute of Safety Research, Forschungszentrum Dresden-Rossendorf, Bautzner Landstrasse 400, 01328 Dresden, Germany, and Computer Engineering Department, Technical UniVersity of Lodz, Stefanowskiego 18/22, 90924 Lodz, Poland
An intricate problem associated with fixed bed operation is liquid maldistribution, which denotes the fact that the liquid does not homogeneously flow through the bed. In a comparative study we evaluated two capacitance imaging methodsscapacitance wire-mesh sensor and electrical capacitance tomography (ECT)swith respect to their capability of measuring static and dynamic liquid holdup in a fixed bed. The capacitance wire-mesh sensor as an invasive instrument is able to disclose flow structures at higher spatial resolution and was therefore considered the reference instrument for liquid holdup measurement. We found that both methods predict dynamic liquid holdup in the column in a similar way with only small systematic deviation. The results therefore prove that noninvasive electrical capacitance tomography can reliably measure cross-sectional dynamic liquid holdup in a fixed bed, even with a simple and fast linear back projection reconstruction algorithm. 1. Introduction Trickle bed reactors are multiphase reaction devices, where fluids are brought into reaction in a randomly packed bed of catalyst particles. Such reactors are operated, for instance, in the manufacturing of petroleum-based products and in the production of chemicals and pharmaceuticals.1,2 The common operation mode in trickle bed reactors is a concurrent downward flow of liquid and gas through the bed, while upward flow operation remains an exception.3 Several flow regimes can exist in a trickle bed reactor, and the flow regime decisively determines the efficiency of heat and mass transfer.4 An intricate problem associated with fixed bed operation is liquid maldistribution, which denotes the fact that the liquid does not homogeneously flow through the bed. Liquid maldistribution is an economic issue since some amount of the expensive catalyst does not contribute to the reaction. Moreover, liquid maldistribution may impact the safety of reactor operation for some exothermic reactions. To achieve improved utilization of the catalyst bed and better reactor performances, as well as to meet with rising environmental and safety constraints, hydrodynamics in trickle bed reactors and their coupling to chemical reaction still need examination. Hydrodynamic target parameters of such examinations are axial and cross-sectional liquid distribution, saturation, and pressure drop.5,6 In the past, considerable effort was spent to visualize and characterize multiphase flows in fixed bed reactors. Such investigations are very difficult to conduct due to the opaque nature of fixed beds. For many years investigators have utilized local probes, such as annular liquid collectors installed at the bottom of the bed, differential pressure transducers, tracer methods, thermal or phase indicator probes, and colorimetric techniques.7-11 While optical techniques are hardly applicable, tomographic imaging modalities seem to be rather attractive. Thus, Gladden et al.,12,13 Koptyug et al.,14 and Nguyen et al.15 applied magnetic resonance imaging (MRI), which can disclose the phase fraction distribution with good spatial and temporal resolution. However, MRI is limited to small vessels made of * To whom correspondence should be addressed. E-mail:
[email protected]. † Forschungszentrum Dresden-Rossendorf. ‡ Technical University of Lodz.
nonmagnetic materials. X-ray transmission tomography, which was used by Marchot et al.16 and Van der Merwe et al.,17 as well as γ-ray transmission tomography, utilized by Boyer et al.18 and Schubert et al.,19 are another choices, but suffer from low temporal resolution. Moreover, they are cost-intensive and require radiation shielding and complex mechanics. In terms of complexity and temporal resolution, electrical tomography techniques are to be favored. Depending on the electrical property that is to be imaged, there is a choice between electrical resistance tomography (ERT)20 and electrical capacitance tomography (ECT).21 For imaging of gas-liquid flow in a fixed bed, ECT, which reconstructs electrical permittivity, is better suited. The permittivity of a material is given by ε ) ε0εr, where ε0 ≈ 8.85 × 10-12 A s V-1 m-1 denotes the vacuum permittivity and εr is the relative permittivity ranging from 1 for gas and vacuum to roughly 80 for water. Organic liquids have intermediate values, for instance εr ) 2 for oil and εr ) 20 for 2-propanol. Measuring permittivity instead of electrical conductivity has some advantages. First, numerous organic liquids, such as oil, are not electrically conducting and cannot be discriminated, e.g., from gas. Second, electrical conductivity of the same liquid, e.g., water, largely depends on the ion concentration, which may vary over many decades, making it difficult to calibrate the sensor. In general, an ECT system comprises a sensor of 8-32 electrodes which are uniformly arranged on the boundary of a vessel. An associated electronic circuit consecutively measures electrical capacitance between all pairs of electrodes at high speed. The capacitance between two electrodes of indices i and j in turn is related to the relative permittivity distribution ε(x,y) in the cross section by Ci,j ) -
1 ε ε (x, y) ∇φ(x, y) dΓ φj - φi IΓ 0 r
(1)
where φ is the electrical potential and Γ is the area of integration on the detecting electrode. Having obtained a full set of capacitance readings from the ECT sensor, a cross-sectional permittivity image can be computed by applying a so-called image reconstruction algorithm, which numerically seeks a solution εr(x,y) by solving the inverse problem associated with eq 1. There is a choice of solution strategies to this inverse
10.1021/ie900988f 2010 American Chemical Society Published on Web 01/26/2010
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Figure 1. Experimental setup with fixed bed column, media supply, ECT, and wire-mesh sensors.
problem,22 whereby the most popular algorithm is fast linear back projection (LBP). LBP algorithms give a straightforward approximate solution with some compromise in spatial resolution. On the other hand, more sophisticated nonlinear iterative image reconstruction algorithms may be applied, which require higher computational effort but give better results in terms of spatial resolution. In general however, spatial resolution is limited by the soft-field effect, that is, the spread of the electrical field inside the object to maybe 10% of the object diameter. This is a drawback compared to hard-field modalities, such as X-ray or γ-ray computed tomography. The usability of ECT for the investigation of trickle bed reactors was already considered in the past. Some attempts were made by Reinecke and Mewes.23-25 They employed the iterative algebraic reconstruction technique (ART) for image reconstruction, which requires offline data processing and does not allow online observations. Tibirna et al.26 compared reconstruction algorithms for ECT applied to trickle bed reactors, but the tests were performed only for software phantoms. Hamidipour et al.27 recently used ECT to monitor the deposition of fine particles in trickle bed reactors. Furthermore, Warsito and Fan28 proposed a three-phase capacitance model to attain the gas holdup and the solids fraction from the permittivity distribution. However, there is no work so far where ECT measurements have been evaluated or even compared to another imaging modality. Due to the known inherent problems of ECT (low spatial resolution, dependence of quantitative image information on the utilized capacitance model and reconstruction algorithm), this is a missing issue which, we felt, deserves proper attention. In this paper we compared ECT measurements with data from a capacitance wire-mesh sensor, where the latter as an intrusive instrument provided cross-sectional liquid distribution images at superior speed and high spatial resolution. Nonintrusive techniques may be the first choice in the investigation of fixed bed reactors due the fact that they do not affect the flow in the column. However, all currently available nonintrusive techniques suffer from some limitation such as low spatial or temporal resolution. Thus, the use of intrusive techniques is still the only suitable choice.
The wire-mesh sensor is a powerful intrusive imaging instrument which was introduced by Prasser et al.29 It consists of two planes of wire electrodes stretched across the cross section of a pipe at an angle of 90° for wires of different planes. An associated electronics measures the local conductivity in the gaps of the wire crossings. In contrast to electrical tomography, image reconstruction is no longer needed since the sensing volume is confined to the vicinity of each crossing point. As a consequence, a spatial resolution up to 0.5 mm and online visualization are feasible.30 The applicability of the conductivity wire-mesh sensor for fixed beds was recently demonstrated by Llamas et al.31,32 However, with acquisition times in the range of 10-15 s per cross-sectional scan, their system is rather slow and not suited for dynamic holdup measurements. Recently, Da Silva et al.33 introduced a new type of wire-mesh sensor, based on capacitance instead of conductivity measurements. The capacitance wire-mesh sensor is much better suited for fixed bed studies and was therefore employed in this study. 2. Experimental Setup and Data Processing 2.1. Fixed Bed Test Facility Setup. All experiments were performed on a fixed bed test facility which is schematically shown in Figure 1. A PVC column of 100 mm internal diameter and a height of 440 mm was randomly packed with commercial porous R-Al2O3 catalyst spheres (Duranit D99). Relative permittivity for the pure Al2O3 is 9.33.34 For the porous particles the bulk relative permittivity value is accordingly lower and was measured between 2.1 and 2.6. Table 1 shows essential Table 1. Specification of the Bed Particles catalyst support packing shape average diameter total surface area (BET) internal porosity packing porosity bulk density relative electrical permittivity of pure Al2O3 estimated relative electrical permittivity of used porous particle
R-Al2O3 spherical pellets (sphericity < 1.25) 3.2-4.0 mm
