Transient modeling of extraction columns: Parameter estimation, uncertainty analysis, and operation optimization

In this article, a novel tray humidifier column for humidification dehumidification desalination was proposed. The performance of the humidifier column has been investigated with experimental and computational fluid dynamics simulations. The hydrodynamics and heat transfer characteristics of this tray humidifier has been studied. A stainless steel sieve tray with a rectangular cross section with a dimension of 20 × 50 cm was used in the experimental study. In computational fluid dynamics modeling, a transient three-dimensional model has been developed based on the volume of fluid framework by using standard k-epsilon model. The effect of air and seawater flow rate and inlet seawater temperature on the exit air temperature has been investigated. The results show that the humidifier effectiveness of the tray humidifier column varies between 0.67 and 0.87 depending on operating conditions. Then, tray column can be used in humidification dehumidification desalination systems with advantages such as compact equipment, low-pressure drop, and handling solids or other sources of fouling.

Single drop experiments with liquid test systems: A way of comparing two types of mechanically agitated extraction columns

Owing to their complex form, very small size and relatively low density, clays freshly deposited in a bay are vulnerable to resuspension when agitated by waves. The model of resuspension of clays under wave motion is presented from the point of view of (a) entrainment of the bottom clay at rest into the active semi-fluid layer; (b) diffusion of the near-bottom high-concentration mixture into the lower-concentration field in the upper layer. The near-bottom concentration at the initiation of the wave is estimated from the rate of entrainment. The diffusion equation containing the vertical convection term including the terminal fall velocity of clay is derived to obtain the transient concentration profile. The value of the vertical diffusion coefficient is derived from the energy equation of turbulence where energy production is balanced by dissipation. Then the diffusion coefficient is approximated directly from wave parameters. The model is executed by computing the initial near-bottom concentration and the transient concentration profile using experimental wave data form. It was found that the estimated initial concentration in the bottom region is compatible with those obtained from the measured data and then calculated transient concentration profiles show good agreement with the measured profiles.

Using the short-chain-length alkanes from ethane to n-butane as guest molecules, transient concentration profiles during uptake or release (via interference microscopy) and tracer exchange (via IR microimaging) in Zn(tbip), a particularly stable representative of a novel family of nanoporous materials (the metal organic frameworks), were recorded. Analyzing the spatiotemporal dependence of the profiles provides immediate access to the transport diffusivities and self-diffusivities, yielding a data basis of unprecedented reliability for mass transfer in nanoporous materials. As a particular feature of the system, self- and transport diffusivities may be combined to estimate the rate of mutual passages of the guest molecules in the chains of pore segments, thus quantifying departure from a genuine single-file system.

Accurate models for pulsed sieve tray extraction columns (PSEs) depend on the correct prediction of the drop diameter to estimate extractive mass transfer across the phase boundary. Phenomenologically, the drop diameter is determined by a balance of drop breakage and coalescence. While for most industrial solvent systems, coalescence plays a minor role; breakage is mostly the dominant phenomenon determining the drop diameter. However, most modeling approaches for drop breakage in PSEs are characterized by a trade-off between a broad validity range and good prediction accuracy. To overcome this limitation, we developed a hybrid breakage model for drop breakage in PSEs in which a physical-empirical model basis is enhanced by data-driven parameter estimator models (PEMs). The hybrid model is based on a revised form of Garthe’s breakage model, for which we developed a linear PEM for the model parameters and two data-driven PEMs for dstab and d100, respectively. The hybrid breakage model was validated on 743 experimental data sets and evaluated based on the pull metric. In a sensitivity analysis, the model correctly predicted the breakage probability over a wide range of solvent properties, operating conditions, and sieve tray geometries. In future studies, the hybrid breakage model can be incorporated into extraction column models without an initial parametrization.

Magnetic resonance imaging (MRI) was applied as an in situ imaging technique to study transient adsorption/desorption and chromatographic processes in microporous adsorbents. Transient concentration profiles were measured for several different types of systems: the diffusion of water vapor into a bed of 4A zeolite, the movement of pulses of light hydrocarbons through a chromatographic column of 5A or 13X zeolite, and the transient adsorption/desorption of propane or water vapor in a single extrudate of 13X zeolite. The profiles are approximately as predicted from nonlinear diffusion theory and the effect of isotherm nonlinearity on the form of the transient profiles is clearly apparent. The possibility of distinguishing between the concentration profiles in the gaseous and adsorbed phases by MRI methods is also examined.

A possible approach to improving rotating disc contactor design accounting for drop breakage and mass transfer with contamination

Sorption kinetics of methanol in large crystals of ferrierite have been studied in detail by interference microscopy (IFM) and infra-red microscopy (IRM). The IFM measurements yield the transient concentration profiles, thus providing a direct measurement of both the surface resistance to mass transfer and the internal diffusion resistance. It is shown that, for this system, the uptake rate is controlled by the combined effects of surface resistance and diffusion through the 8-ring channels (in the y-direction). Transport through the 10-ring channels (in the z-direction) appears to be blocked by surface resistance. Although the overall uptake curves conform well to the “root t law” the diffusivity values derived from the uptake curves vary widely depending on the assumed direction of diffusion. Even if the correct direction of diffusion is assumed, the diffusivity values derived from the uptake curves are seriously in error as a result of the intrusion of surface resistance. The existence of transport resistances at the crystal surface is clearly apparent from the transient concentration profiles but is not obvious from the uptake curves.

A mathematical model corresponding to homogeneous chemical reactions under transient chronoamperometry conditions at hemispherical microelectrodes has been developed. The analytical solutions for the concentration of species and current were obtained using Duhamel's theorem. This closed-form theoretical expression pertains to the transient concentration profiles and fluxes of chemical species involved in chemical and electrochemical reactions at hemispherical microelectrodes. As t → ∞, the analytical expressions corresponding to the concentration and current approach steady-state values. The solutions obtained are explicit only under limiting current conditions. The approximate expressions for concentrations and current as functions of time corresponding to the EC' and CE mechanisms at hemispherical microelectrodes are also reported.

The use of interference microscopy has enabled the direct observation of transient concentration profiles generated by intracrystalline transport diffusion in nanoporous materials. The thus accessible intracrystalline concentration profiles contain a wealth of information which cannot be deduced by any macroscopic method. In this paper, we illustrate five different ways for determining the concentration-dependent diffusivity in one-dimensional systems and two for the surface permeability. These methods are discussed by application to concentration profiles evolving during the uptake of methanol by the zeolite ferrierite and of methanol by the metal organic framework (MOF) manganese(II) formate. We show that the diffusivity can be calculated most precisely by means of Fick's 1st law. As the circumstances permit, Boltzmann's integration method also yields very precise results. Furthermore, we present a simple procedure that enables the estimation of the influence of the surface barrier on the overall uptake process by plotting the boundary concentration versus the overall uptake.

The interference microscopy technique, which was recently introduced in our laboratory, is applied to study transient intracrystalline concentration profiles in ZSM-5 crystals during adsorption and desorption of isobutane. Two different zeolite samples were used, viz., samples of etched and of nonetched ZSM-5 crystals. Etching has been carried out to remove the outer layer of the crystal surface, which may contain large amounts of defects and impurities. Studying the transient concentration profiles in both samples provides unique information on the influence of surface defects on molecular uptake. It is shown that, depending on their type, the defects of the crystal surface can either increase or decrease the rate of adsorption/desorption. The former effect is associated with adsorption/desorption through cracks in the crystal surface. The latter has its origin in the blockage or structural changes of the external crystal surface, leading to the appearance of surface transport barriers. Owing to the ability of interference microscopy to gain direct insight into the influence of surface defects on molecular uptake, this technique gives more accurate information on the transport diffusivities in zeolite crystals than the classical uptake methods.

The first application of interference microscopy to monitoring mass transfer in nanoporous materials dates back to late 1970s when Caro and colleagues reported results of investigations of water uptake by LTA type zeolites. It was, however, not before the beginning of the new millennium that the developments in both the measuring technique and computational power have enabled the recording of transient guest profiles during molecular uptake and release under well‐defined conditions, leading to the establishment of a novel access to diffusion studies, now referred to as micro‐imaging. In the present contribution, the thus accessible novel type of information is illustrated by an in‐depth analysis of the uptake kinetics of methanol in an all‐silica ferrierite. In particular, two remarkable experimental findings are reported, which may be tracked back to their microstructural and/or microdynamic origin, namely a pronounced asymmetry in the transient concentration profiles and a slowing down of guest uptake with increasing temperature.

The Eulerian model was used for the prediction of air pollutants in some gas flare locations in the Niger Delta region of Nigeria. A continuity equation (mass balance) that incorporates second order reaction schemes for the generation of pollutants at source or in the ensuing atmosphere was used to characterize the n species in the fluid element and the finite difference method (the Crank-Nicholson formulation) was applied for the numerical scheme. Thus, the spatial and transient concentration profiles of key contaminants were obtained for the meteorological conditions under consideration. The first series of simulations were carried out at ground level and at altitudes of 30 and 90 m, for a simulation time of 10 min. The second series of simulations were identical to the first, except that the simulation time was 20 min. The third series of simulations were carried out for 50 min at ground level and at an altitude of 30 m. The concentration profiles were parabolic for at least one of the pollutants at the ground level for 10, 20 and 50 min simulation times, and additionally at an altitude of 30 m for a simulation time of 50 min. Other concentration profiles are exponential in nature. The deterministic Eulerian model provided a satisfactory prediction of the spatial and transient concentration profiles for the pollutants in the gas flares.

The performance of pulsed scale-up column for permeable of selenium and tellurium ions to organic phase, case study: Disc and doughnut structure

Parameter study for separation design in a packed column