Liquid Distribution and Hold-up Measurement in Counter Current Flow Packed Column by Electrical Capacitance Tomography

: In order to meet the requirements and well suit for in-situ process measurement of industrial scale gas-liquid mass transfer applications, such as natural gas processing and post-combustion carbon capture, tomography (ECT) is used to analyse the distribution of a liquid phase across the packing of a counter current gas-liquid packed column and to quantify the liquid hold-up. The new method eliminates the requirement of a fully flooded reference calibration and only requires vacant and dry calibration steps. The calculation procedure is simplified by using a normal sensitivity matrix which does not include the packing information. The validity of the proposed method was confirmed through finite element method (FEM) analysis studies to certificate neither packing geometry nor orientation relative to the tomography probe nor had a significant impact on phase identification. An experiment is conducted on a counter current gas-liquid packed bed column with 190mm diameter and polypropylene Sulzer Mellapak 250 Y as the packing. According to the experiment with various liquid load, the inclination angle of structured packing corrugation sheets has an impact on the radial distribution of liquid hold-up in the upper portions of packed beds and liquid hold-up fluctuations of ~0.5% are observable below the flooding limit and even at no gas flow conditions which can meet the empirical correlations from literature. The experiment results show that the proposed method provides the confidence to use ECT in the industrial field service in gas-liquid packed column to provide the real-time liquid distribution and local liquid hold-up measurement.


Introduction
Structured packings are tower internals that are used in separation processes such as absorption, distillation, and liquid-liquid extraction. The combination of large surface areas, low gas pressure drops and high separation efficiencies make structured packing ideal for large scale atmospheric gas absorption processes, such as amine based post-combustion CO 2 capture. The effective design and process optimization of these industrial scale absorption towers is strongly linked with the liquid dispersion and gas/liquid interactions within the packed bed.
Structured packing liquid hold-up quantification has traditionally been measured on a packing volume averaged basis through the drain and collect method [1][2][3]. The advent of radiation based densitometry allowed for the in-situ quantification of liquid hold-up in structured packing, which enabled liquid hold-up to be calculated at cross sections along the height of the column [4] and provided further information about the distribution of liquid along the height of the packing. This knowledge led to observations that liquid hold-up profiles were unevenly distributed near the interfaces of packing elements and resulted in an evolution in packing element design which featured geometries that smoothed flow between packing elements (e.g. Koch-Glitsch Flexipac-HC, Montz type M, Sulzer MellapakPlus) [5].
Radiation based tomography imaging techniques provided another step change in liquid distribution quantification in packed columns. These techniques are able to characterize and quantify liquid distribution patterns not only along the height of the column but also in the cross section providing critical knowledge on not only liquid hold-up [6] but also 2-D and 3-D hydrodynamic liquid spreading patterns of distillation columns [7; 8], trickle bed reactors [9] and counter-current gas-liquid columns with structured packing [10]. Recently Jenzen [11; 12] used ultra-fast x-ray tomography to demonstrate a step change in tomographic techniques for packed bed hydrodynamics that enabled observation of dynamic liquid load and liquid distribution on timescales that were relevant to the hydrodynamics of the system (temporal resolution of 2000 frames per second and spatial resolution of 1 mm).
Dual-plane x-ray tomography has also been used to determine phase fractions and local velocity distributions in a fluidized bed application [13].
Experimental hydrodynamic data extracted from these tomography systems can be used to validate the complex mathematical modelling efforts of liquid distribution over tower internals with complex geometries and can supplement traditional experimental campaigns leading to a richer understanding of modelling mass transfer systems. Mechanistic liquid distribution models [14], two phase immiscible flow models [15], and computation fluid dynamics (CFD) simulations [16] used in modern mass transfer modelling could all benefit from enhanced hydrodynamic knowledge of real systems.
While ultra-fast x-ray tomography is able to provide critical information on industrially relevant metallic structured packings at the lab scale, the inherent nature of high energy radiation measurements means the costs of instrument systems and practicalities of safely handling the radiation are impractical for industrial based field measurements. In contrast, electrical measurements have been used as an alternative to radiation based densitometry for in-situ quantification of liquid hold-up in structured packed beds. Both electrical capacitance [17] and electrical resistance measurements [18] have been demonstrated to produce liquid hold-up measurement accuracies similar to radiation based techniques while also having the benefit of drastically reduced costs, orders of magnitude higher acquisition rates, and safer installation and use. It has been suggested that electrical measurements may be scalable and appropriate for industrial field service [17].
Tomography systems based on electrical measurements has been deployed in various industrial field service applications to characterize and quantify two-phase fluid flows both with and without fixed structural internals. Electrical Resistance Tomography (ERT) systems have been used to investigate the mixing characteristics in a packed-bed external loop airlift bioreactor [19], the effect of particles and liquid load on the phase distribution in trickle bed reactor [20], and gas distribution and void fraction in a packed bubble column with different packing materials [21]. Son et al. used ERT to measure the liquid distribution in pilot-scale packed column, in order to study the effects of the liquid load, gas factor, and liquid properties on the liquid distribution under various offshore conditions [22]. Similarly, Electrical Capacitance Tomography (ECT) systems have been used to investigate pulse flow and pulse velocity in co-current trickle bed reactors [23] and solid phase distributions in a gas-solid fluidized bed [24]. Hamidipour used a twin-plane ECT to study the hydrodynamics of gas-liquid co-current down-flow and up-flow packed beds by cross-correlating each plane's tomogram to axial dispersion residence time distribution and modelled liquid hold-ups and pseudo-interstitial velocities for pulsed flow in the system [25].
Operators of industrial scale mass transfer operations that are highly dynamic in nature, such as post combustion CO 2 capture systems with varying gas inlet flows and varying product recovery constraints, would benefit from real time in situ hydrodynamic data of the column internals. This information could be used to reduce settling time between plant states, increase process agility, troubleshoot reactors that are operating outside of design specifications, and allow for more efficient operation at off-design conditions.
When considering the development of this type of measurement system, several practical considerations make electrical capacitance tomography (ECT) a strong choice for the measurement technology. Absorption mass transfer operations (e.g. aqueous amine based post combustion CO 2 capture) are gas phase dominant, therefore electrical capacitance measurements preferred over conductivity measurements which would prefer a continuous liquid film path between each sensor array contact. The in-situ process probes would be low cost to manufacture, safe to operate, free of moving parts, and could be coated to increase corrosion resistance as they would not be required to directly contact the fluid or packing. Obvious drawbacks remain: in-situ tomography is unable to extract data that is critical for the effective modelling of mass transfer reactions such as local velocity distributions, fluid composition measurements, and film and rivulet liquid parameters necessary to quantify the true liquid surface area. Further electrical capacitance tomography will struggle to image systems that utilize a grounded metallic packing phase, which is the current industry standard for many mass transfer applications. The coating of metallic packing by the nonconductive material will improve the performance of the ECT measurement.
Nevertheless, the potential merits of an ECT instrument system that is fit for industrial scale applications warrant further investigation. This work develops a measurement technique appropriate for industrial applications, evaluates the technique's robustness and measurement accuracy through a FEM approach, and compares the measurements of a prototype ECT instrument system against traditional lab based quantification techniques in a counter current gas-liquid column fitted with polypropylene Mellapak 250.Y structured packing.
In developing an ECT measurement system that is fit for industrial field service, the practicalities of field calibration and operation must be considered. In typical electrical tomography systems, it is difficult to relate the electrical measurement tomogram to physical liquid loadings because the local electrical field is affected by many ancillary factors such as 3-D geometry of the liquid film and the inherent electrical conductivity of the liquid as well as the volume of liquid present. Some compensation method should be used according to the research [22]. In industrial scale operations however, these compensation mechanisms may not be practical. The alternative demonstrated in this work constructs a tomogram image and determines liquid hold-up from a calculation model with single reference, and uses a normal sensitivity matrix which just includes the pipe wall information (to simplify the calculation procedure) for the liquid hold-up calculation. This methodology has several benefits, namely: 1) Eliminating the need to take a background tomogram with a fully submerged column.
2) Simplifying the calculation to neglect electrical field complexities not related to liquid hold-up, eliminating the need to regress signals against volumetric hold-up measurements.
3) Simplifying the calculation by using a normal sensitivity matrix calculated by FEM without including the packing information, which can be used for different packing structures, column diameters and liquid conductivities. 4) Allowing FEM to be a useful tool to analyse and quantify the effective measurement error in the application that cannot be validated by the experiment conveniently.
These benefits would enable the measurement system to be practically deployed on existing plant facilities with reasonable installation and commissioning times.
Further the designed calculation model for the ECT could realize the online liquid hold-up calculation and liquid distribution reconstruction in the practical packing column application.

Liquid Hold-up Calculation Model by ECT
In this work, a liquid calculation model for ECT is designed that does not have to submerge the column to make the calibration. This model can be used to deal with different packing structure and is easy to be used in the field application. In the packed column with the gas, liquid and packing, when the permittivity of liquid is much larger than that of the other two substances, the ECT is able to differentiate liquid to calculate the liquid hold-up and reconstruct the liquid distribution.

Principle of ECT
ECT measures capacitance between the electrodes, then reconstructs the relative permittivity distribution in the sensitive field. Both forward problem and inverse problem are involved in ECT. For the forward problem, a linearized relationship between the normalized permittivity distribution g and the normalized capacitance data C norm is: where S is the sensitivity matrix. For the typical inverse problem, the target of ECT reconstruction is to estimate the permittivity distribution based on measured capacitance. The conventional image reconstruction algorithm was reviewed in [26] with spatial resolution of 5% of the column diameter [27].
The measurement principle and structure of ECT system is shown in Fig. 1.

Liquid Hold-up Calculation Models
In the previous research, the parallel model was used for the stratified two-phase dynamic flow with packing [17]. In terms of different two-phase flow mixture, either parallel model in equation (2) or series model in equation (3) can normalize the measured capacitance [30]: where j is the location of the measurement projection, P is the maximum number of measurements. C mea(j) is the measured capacitance at the j th location. C l(j) and C h(j) are the reference capacitance at the j th location when the sensitive field is full of low permittivity media and high permittivity media separately.
In industrial field applications, the full calibration with high permittivity media C h(j) is inconvenient to acquire as it would require the column cross section to be flooded with liquid. Therefore, a normalization method with single reference media only is developed in this work in order to expand the ECT's application. The normalization model is expressed in equation (4): is the reference capacitance when the packed column is full of low permittivity media, i.e. gas or gas with packing.
Within the ECT sensing field, the permittivity distribution and measured capacitance have an approximately linear relationship: where k is the pixel number of the sensitive field and w is the maximum number of pixels. ε mea(k) and ε ref(k) are the measured permittivity and reference permittivity at the k th pixel respectively. Sensitivity matrix S is calculated using the FEM. The element of normalized S is s j,k , which describes the mapping relationship between the j th measurement projection and the k th pixel on the image. The ratio of ε mea(k) and ε ref(k) is derived from equation (5) and shown in equation (6).
The Ramu-Rao's model [31] is used to calculate the relationship between phase fraction and the phase permittivity. For two-fluid immiscible two-phase flow, the low permittivity phase is continuous phase, the permittivity of the two-phase mixture depends on the high permittivity phase in mixture ratio (HMR) when the mixture can be assumed as homogeneous flow: where ε mixture is the permittivity of the immiscible two-phase mixture, and ε low is the permittivity of low permittivity phase.
According to the assumption of Ramu-Rao's model, the permittivity of the two phase should have huge difference. In the packed column with gas, liquid and packing three different media, the relative permittivity of liquid (i.e. water is ~80) is much larger than that of packing (i.e. polypropylene is ~2.2) and gas (~1). When these three media in the sensitive field is assumed as homogeneous flow, the liquid in mixture ratio (LMR) can be obtained from the Ramu-Rao's model based on Maxwell equations:

Liquid Hold-up Calculation Procedure
ECT has been used in many applications for two-phase flow measurement. In the packed column, as three different media with different relative permittivity (gas /packing/liquid) are existed in the sensitive field, it will cause the difficulties for the ECT measurement and data analysis. The sensitivity matrix S, which is calculated by the FEM simulation, is a key parameter in the liquid hold-up calculation and distribution reconstruction. The common sensitivity matrix S just includes the information of pipe wall, and does not contain the packing information. If it is used directly in the packed column, it will cause a large error of quantitative measurement for liquid hold-up and liquid distribution analysis.
In order to realize the accurate measurement, the sensitivity matrix containing both the gas phase and the fixed packing is required. However, modelling the complex packing geometry in the FEM software is complex. Even after the FEM model computed the accurate sensitivity matrix including the packing information, the orientation of ECT sensor electrodes relative to packing should match the FEM model for the S matrix to be valid. This method is complex and almost impractical to be used in the field application.
For the purpose of solving this problem, the alternative proposed here is to use the common sensitive matrix S (only includes the pipe wall information) for the calculation. After the calibration with gas, the real time gas/liquid/packing ECT results are used to subtract the gas/packing results to acquire the liquid hold-up present in the system.
The ECT can be used to compute the packing column with any packing geometry based on this alternative. It is a fundamental methodology for designing electrical tomography systems from electricity principles rather than calibrating and correlating with liquid hold-up measurements.

Fig.2. Calculation procedure for ECT measurement in packed column
The detailed procedure is shown in Fig. 2: Step 1: The column is full of gas at first to take reference, in order to get C ref in equation (4). The common sensitivity matrix S is calculated by the simulation with an empty field (empty column full of gas with relative permittivity of 1).
Step 2: The packing material is added into the packed column. The capacitance of gas/packing mixture is measured by ECT again, to get the C mea with packing. The measured capacitance can be used to calculate the packing fraction.
Step 3: The liquid is sprayed from the top of the column and gas is added from the base of the column, the ECT measures the capacitance of the gas/liquid/packing mixture. The model will be used to calculate the total fraction of packing and liquid.
Step 4: The result in step 3 subtracts the result in step 2 to get the liquid hold-up in packed column.

Calculation Method Validation Through Finite Element Model
In order to validate the calculation method, two FEM modelling investigations were employed. The first investigates the influence of packing geometry on the

Parametric Study of Packing Geometry
Packing can have a variety of geometric structures (e.g. corrugation and inclination angles, perforated sheets and gauze materials) that are customized for different applications. The geometric structure of the packing may have an influence on the capacitance calculation, which could impact the accuracy of the calculation method. FEM simulation is used to calculate the sensitivity matrix, therefore accurately describing the geometric structure in the FEM simulation could be important. However, accurately describing the geometric structure in the FEM simulation is impractical for two reasons. First, the actual geometry of real packing materials is really complex due to manufacturing variations such as sheet and gauze surfaces inconsistencies, perforation locations, and the existence fasteners and wall wiper bands. Second, the orientation of the ECT sensor electrodes relative to structured packing out in the field is unlikely to match what is represented in FEM simulation.
In order to assess the effect of packing geometry on the calculation method with normal sensitivity matrix a parametric study was performed where packings of As seen in table 1, the calculation method underestimates the true value of the packing fraction, but the underestimation is similar in magnitude for each packing geometry implying that packing geometry does not have an effect on the packing fraction calculation, this is very important in the liquid hold-up calculation step. (The fraction is considered as a relative quantity, the "absolute error" will be used as the calculation error to evaluate the performance).
As packing geometry does not have an effect on the packing fraction and liquid hold-up calculation, the combination of common sensitivity matrix and calculation method can be used on any type of structured or random packing type where the packing fraction is known. Additionally, this finding would imply that the ECT sensor electrodes could be installed anywhere along the column without considering its orientation relative to the packing, which would be a very convenient feature for industrial field applications.

Evaluation of Measurement Accuracy
Having established that the packing structure does not have a significant influence on the calculation method, FEM analysis is used to assess the robustness and accuracy of the calculation model when measuring fluids of both high and low permittivity. Fig. 4 shows the 3D model of the viewing field as built in the FEM software with dimensions that match the experimental test rig and a structured packing as shown in Fig. 3(b).  As stated previously, the calculation model is designed to operate without taking a reference measurement of high permittivity media for convenience of industrial applications. In order to compensate the media fraction measurement results different relative permittivity, a coefficient α is be applied to correct the liquid hold-up F L , as expressed in equation (9).
The correction coefficient α in equation (9)    and is able to provide confidence that the method and sensor system have potential in an industrial field application.

Experimental Description
A packed column test rig was constructed to simulate a small scale gas-liquid absorption application as shown in   The ECT sensor electrodes, described previously in Fig. 4 increasing the excitation frequency of the system can minimize the effect [39].
Additionally it was demonstrated that an imaged object which is electrically grounded becomes invisible to ECT [40], implying that a highly conductive liquid may need to be electrically floating to be able to be imaged by ECT. This effect likely occurs because when the liquid is connected to the ground, an electrical charge exchange happens between liquid phases that are inside and outside of the viewing field. The liquid can be seen as an equipotential body connected to the ground, and the calculated capacitance will be constant regardless of the amount of liquid present in the viewing field. In order to understand the effect of liquid phase electrical conductivity on the ECT measurement performance, two aqueous NaCl solutions with conductivities of 0.1mS/cm and 30mS/cm were used in this experiment.
The measurement procedure begins with an empty air-filled pipe ECT reference calibration measurement to determine C ref . Next, the dry packing material is added into the column and a second ECT measurement is made to determine the fraction of the packing. Finally, the NaCl solution is sprayed at the top of the column to conduct the experiment. Liquid load was varied from 13-39 m 3 /m 2 h and ECT measurements were used to compute the liquid hold-up at the cross section and to reconstruct the liquid distribution using the calculation method with common sensitivity matrix determined in section 3.2.
Global liquid hold-up was computed from liquid tank level difference using the level indicator and compared with the local hold-up measurements take from the ECT sensor.

Tomographic cross section images: low conductivity
A NaCl solution with 0.1mS/cm electrical conductivity was used to represent a low conductivity liquid. 2D reconstructed tomogram images for a range of liquid loads are shown in Fig. 11, with the colored scale bar representing the normalized liquid distribution. The image is reconstructed from an average of 7140 frame taken over 10 seconds. A cutout 3D time series tomogram is also displayed in Fig. 11 to show the variation of the image over the 10 second measurement time.
(a) 13 The tomograms in Fig. 11 show not only the intuitive result that liquid hold-up on the packing increases with liquid load but also a banding like liquid distribution, with liquid forming predominantly in two channels at low liquid loads and starting to form in a third at higher liquid loads (Fig. 11

Tomographic cross section images: high conductivity
An NaCl solution with a 30 mS/cm electrical conductivity was used to represent a high conductivity liquid. 2D reconstructed tomogram images and cutout 3D time series tomograms are displayed in Fig. 12 in the same manner as described in section 5.1.1. The tomograms in Fig. 12 show a liquid distribution behavior similar to that of the low conductivity test shown in Fig. 11, with liquid hold-up increasing with liquid load and liquid distribution predominately flowing in two distinct bands at low liquid loads before increasing to three bands at higher liquid loads.
Inspection of the packing section after testing (by dyed liquid) confirmed the banding flow pattern as mineral scaling visually observed in the small circular pattern of a diameter similar to the liquid distributor was observed at the top of the packing ( Fig. 13 (d)) spreading into a banding pattern along the length (Fig. 13 (a) -(c) and at the bottom of the packing section ( Fig. 13 (e)).  In contrast, Mellapak 250.Y PP has a much more gradual inclination angle of 49° from vertical and as such has a much broader radial liquid hold-up distribution profile.
Liquid is able to spread from the center packing channels more rapidly achieving a broader liquid distribution across the first packing section more rapidly than Mellapak 250.X. This data can meet the knowledge that a steeper inclination angle allows for a higher liquid load to be used and has lower pressure drop but requires a little bit higher packing height to get everything distributed.

Real-Time Measurement of Liquid Hold-up
Previously, a major drawback of radiation based (x-ray and gamma-ray) tomography techniques is that images are acquired at rates that are too slow to observe liquid hydrodynamics on packing structures. Recent advances have introduced an ultra-fast electron beam x-ray tomography technology that is capable of drastically improving the image acquisition rate on relatively narrow columns of 80mm diameter [43] at acquisition rates of 2000 frames per second with a measurement resolution of ~1mm (~1.25% of column diameter). Janzen [11] used the ultra-fast tomography system to provide new insights into temporal evolution of   The high and low conductivity datasets appear to both follow the same linear pattern but with the high conductivity dataset providing a larger degree of variance in the readings. A possible explanation for this variance is that high conductivity media, particularly liquid droplets located near the pipe wall, may be causing imaging artifacts that disturb the electrical permittivity measurements in the viewing field.
This effect might be mitigated in applications where gas flow and packing internals such as wipers minimize the formation of droplets on the column wall. Another possible explanation for this variance would be the effect of electromagnetic interference from other equipment such as the liquid pump and flow sensors.
Complete electromagnetic shielding of the viewing field might mitigate this effect.
Finally, another explanation of the variance could be the ability of the liquid phase in the viewing field to find electrical ground or some other form of leakage current, which could also cause imaging artifacts. This affect is unlikely considering the non-continuous nature of the liquid phase on the packing with other grounded liquid phases, for example in tanks and pipe runs, but may be mitigated through empirical correction factors. Data from low and high conductivity liquids suggest the proposed method is capable of analyzing aqueous absorption solvents, but higher measurement noise and variance was observed in the high conductivity test. Potential reasons for the variance include high conductivity droplets on the column wall causing measurement artifacts, electromagnetic interference from other equipment, and charge transfer or electrical earthing of the liquid in the viewing field. Overall the experimental campaign was able to provide confidence that proposed calculation method could be suitable for industrial field service in gas-liquid packed columns and demonstrate that an ECT system is able to provide in-situ liquid distribution measurements which could be used for accurate real-time liquid distribution and local liquid hold-up measurements.