A package for thermal parametric pumping adsorptive processes
Introduction
The parametric pumping process was first described by Wilhelm et al. [30], [31] as a dynamic separation process based on the differences in the adsorption equilibrium caused by a cyclic change of a thermodynamic variable (temperature, pressure, pH) simultaneously with flow reversal. In thermal parametric pumping, the temperature change can be imposed through the bed jacket in direct mode or through temperature change of the fluid stream in recuperative mode [29].
The process to be addressed here is thermal parametric pumping in the recuperative mode operating in a semi-continuous way, with feed at the top of the column. Each operation includes a series of cycles, starting with the hot cycle in upward flow and then the cold cycle in downward flow. A typical cycle starts with the bed equilibrated with the feed solution at the cold temperature and the top reservoir containing the feed solution.
Fig. 1 shows the experimental setup existing at the LSRE (Laboratory of Separation and Reaction Engineering) and described in detail elsewhere [9].
Fig. 2 illustrates the semi-continuous mode of the parametric pumping operation, when the objective is to concentrate the top product. Since the feed solution should not be added to the same reservoir where the top product is collected, the top product is collected during the hot half-cycle. In the cold half-cycle, the feed flows downwards and the bottom product is withdrawn. The end of each half-cycle is set by the time at which all the solution contained in one reservoir is completely transferred to the other reservoir. Temperatures are 60°C at the bottom of the column and 18°C at the top of the bed for the phenol/adsorbent resin Duolite ES861 system; for the phenylalanine/adsorbent resin SP206 system, hot and cold temperatures are 40 and 15°C, respectively.
The separation potential of thermal parametric pumping can be assessed by using the parameter b, introduced by Pigford et al. [21] and defined as , where is the average of the capacity factors at the cold and hot temperatures, T1 and T2, respectively, a=(m(T1)−m(T2))/2 and is the capacity parameter for a linear adsorption equilibrium isotherm with slope K(T). Table 1 reports values of the separation parameter b for some systems studied by parametric pumping.
Various examples of parametric pumping operations at laboratory scale have been published [5], [23], [24], [25]. Batch, semi-continuous and continuous modes of operation have also been addressed [2], [3], [4].
The modeling of parametric pumping processes has been dealt with by various researchers. Pigford et al. [21] first used the equilibrium model to analyze parametric pumping adsorptive processes with linear equilibrium isotherms; Gregory and Sweed [11] applied that model to various process configurations. Equilibrium staged models were used by Grevillot and Tondeur [12], [13], [14]. Mass-transfer rate was included in the works of Sweed and Wilhelm [27] and Gupta and Sweed [15].
Recently, Ferreira and Rodrigues [8] developed a more complete model accounting for axial dispersion in the fluid phase, film mass transfer, intraparticle mass transfer and heat transfer through the wall. The model also assumed perfectly mixed reservoirs. The model successfully predicts the behavior of thermal parametric processes, such as phenol purification with polymeric adsorbent Duolite ES861 [9] and phenylalanine adsorption in polymeric adsorbent SP206 [8].
However, in cyclic processes with long cycle times, i.e., (Dpetc/Rp2)>0.1, the model can be simplified since intraparticle mass transfer can be described by the linear driving force (LDF) approximation. This is not the case in fast cyclic adsorption/desorption processes [1].
The objectives of this work are:
- 1.
the analysis of thermal parametric pumping processes by two simplified models: model I based on equilibrium and axial dispersion, and model II based on linear driving force (LDF) approximation for intraparticle mass transfer and axial dispersion;
- 2.
the test of model validity by comparison with experiments in a pilot plant for the system phenylalanine/water/polymeric adsorbent SP206 and with experimental results from Ferreira and Rodrigues [9] for the system phenol/water/adsorbent resin Duolite ES861; and
- 3.
the development of a user-friendly package of thermal parametric pumping for educational and training purposes.
Section snippets
Modeling of thermal parametric pumping processes
The two simplified models to be developed here are: Model I, which considers equilibrium between fluid and adsorbent particles and axial dispersion in the fluid phase; and Model II, which uses the linear driving force (LDF) approximation to describe intraparticle mass transfer and also includes axial dispersion in the fluid phase. The energy balance for the system is considered in both models.
Dimensionless equations for Model I (equilibrium plus axial dispersion) shown in Table 2 are:
- 1.
mass
Numerical solution
The system of PDEs presented is solved by the method of the lines [22], using orthogonal collocation in finite elements ocfe for the spatial coordinate. The spatial coordinate is discretized based on the evaluation of the set of differential equations written in its residual form and evaluating them in the characteristics roots of a family of orthogonal Gauss–Legendre polynomials. This method is implemented in a numerical package called pdecol by Sincovec and Madsen [26] and Madsen and Sincovec
Simulation results
In this section, the effect of the dispersive parameters, mass Peclet number, Pe, and number of intraparticle mass transfer units, Np, on the separation performance will be studied. The simulations were based on parameter values given in Table 5 for the system phenol/water/adsorbent resin Duolite ES 861 [8].
Package description
The graphic user interface (GUI) was developed in Visual Basic language, version 4.0 which is a fast and reliable developing platform in Windows environment [28]. The user-friendly GUI supported by the Visual Basic facilities allows a fast learning curve of the new package, making easy the understanding of the parametric pumping process, and therefore it is a powerful training and teaching tool.
Experimental example and test of the models
The experimental set-up for the study of thermal adsorptive parametric pumping in recuperative mode is shown in Fig. 1. It contains four main sections: column and ancillary equipment, reservoirs, sample collection and analysis and automation section. The column is an Amicon G90 × 1000 column of 9-cm diameter. The packing was the adsorbent resin SP-206 with average diameter of 400 mm (Mitsubishi, Japan). Peristaltic pumps (Watson–Marlow) were used to circulate the solution downward at 15°C and
Conclusions
A user-friendly package written in Visual Basic was developed for the simulation of parametric pumping adsorptive processes as a tool for educational and training purposes.
Two models were implemented in the package: Model I is the equilibrium + axial dispersion model; Model II is a linear driving force (LDF) model with axial dispersion, which is a convenient tool for the analysis of cyclic processes with long cycle times, such as parametric pumping.
Simulated results from this simplified Model II
Nomenclature
aw specific area of wall (4/d) (m−1) A column section area (m2) C solute concentration in the fluid phase (Kg/m3) CE feed solute concentration (Kg/m3) average solute concentration in the pores (Kg solute/m3 fluid in the pores) CP solute concentration in the pores (Kg solute/m3 fluid in the pores) Cpf heat capacity of the fluid (kJ/Kg K) CPS solute concentration in the pores at particle surface (Kg solute/m3 fluid in the pores) Cs heat capacity of the adsorbent (kJ/Kg K) d column diameter (m) Dax axial dispersion
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2010, Reactive and Functional PolymersComparative study of the adsorption of phenol and salicylic acid from aqueous solution onto nonionic polymeric resins
2005, Separation and Purification TechnologyAdsorptive purification of phenol wastewaters: Experimental basis and operation of a parametric pumping unit
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2004, Reactive and Functional Polymers
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Present address: Chemical Engineering Department, Faculty of Sciences and Technology, University of Coimbra, 3000 Coimbra Codex, Portugal.