Application of analytical solution of advection-dispersion-reaction model to predict the breakthrough curve and mass transfer zone for the biosorption of heavy metal ion in a fixed bed column
Graphical abstract
Introduction
Nowadays, heavy industries have expanded rapidly and the majority of effluents from these industries (e.g., electroplating and battery factories and mining industries) contain toxic heavy metals, which lead to a serious concern for public health. Thus, the treatment of wastewater containing heavy metals from these industries is crucial. Nevertheless, the treatment of this type of wastewater involves expensive techniques. Biosorption with a low-cost sorbent has lately been introduced as an alternative treatment technique for this type of wastewater (Volesky, 2004).
Green macroalga Caulerpa lentillifera is an alga that can be used in shrimp farming as a form of nitrogen controller. However, due to its quick growth, farmers usually have to remove it as waste. Turning such agricultural waste into biosorbent would be an alternative to utilize the waste to remove the dissolved heavy metal ions in wastewater. Previous works have investigated the biosorption of heavy metal ion (Cu2+, Cd2+ and Pb2+) in synthetic wastewater by this alga in batch and column experiments (Apiratikul and Pavasant, 2006, 2008; Apiratikul et al., 2011). The results demonstrated that this biomass has high efficiency to remove heavy metals from the wastewater.
Nevertheless, the practical application of the biosorption process for the treatment of industrial wastewater on a large scale should be operated in a biosorption column with the continuous-flow technique which is the most convenient and effective method (Valdman and Leite, 2000). The results from such a method are generally represented by the breakthrough curve (BTC) and the length of the mass transfer zone (MTZ). Therefore, studies of factors that affect BTC and MTZ are extremely important for the process design, scale-up, optimization, as well as evaluation of the overall performance of the biosorption in the column. One of the essential tools for such studies is a computer simulation using mathematical model. The benefit of the simulation is to reduce the number of experiments in a laboratory scale, the latter of which is more difficult, expensive and time-consuming.
The author’s previous work (Apiratikul and Pavasant, 2008) applied the Bohart-Adams model (Bohart and Adams, 1920), which is an empirical model to explain the BTC from the biosorption column in the laboratory scale. However, the empirical models such as the Bohart-Adams model, which was misunderstood as the Thomas model (Chu, 2020), can only well predict with the specific set of the experiments but cannot be generalized to another set with different process conditions such as column lengths and flow rates. Naja and Volesky (2006) applied the conceptual model of Tan and Spinner (1994), modified by Kratochvil (1997), which is a system of partial differential, ordinary differential, and algebraic equations to describe the effects of flow rates and column lengths on the behavior of the MTZ length of Cu2+ in a biosorption column. Their study utilized FEMLAB software to solve the set of model equations. The finite element analysis together with adaptive meshing and error control using a variety of numerical solvers were used by the software to find the numerical solution. However, solving such a system of equations is very complicated and the software is quite expensive and can be difficult to use without training because it is a specialized software. Thus, simplification of those equations by assuming some conditions and find an analytical solution is very useful. It can later be calculated readily via available software e.g. Microsoft Excel.
The Ogata-Bank model (Ogata and Bank, 1961) is an analytical solution of a system of algebraic and partial differential equations which is a mathematical model for pollutant's transport (Advection-Dispersion-Reaction model). This model is generally used to describe the movement of the contaminant from a continuous source through a porous media in a groundwater system (Knox et al., 1993). The purpose of the present work is to extend the study of the author’s previous work (Apiratikul and Pavasant, 2008) by applying the Ogata-Bank model for the first time to simulate the breakthrough curve and mass transfer zone of the biosorption of single component heavy metal ion (i.e., Cu2+, Cd2+, and Pb2+) by using dried green macroalga Caulerpa lentillifera in a fixed-bed column.
Section snippets
Ogata-Bank model
The governed partial differential equation of pollutant's transport was developed on the basis of the processes for advection, hydrodynamic dispersion, and sorption without degradation of pollutants. The equation can be written as follows:
where C denotes the aqueous phase concentration of the pollutant (mM), t is the operating time (min), x is the vertical distance from the top of column (cm), Dh is the longitudinal or axial hydrodynamic dispersion coefficient (cm2
Determination of the model’s coefficients from the sorption experiment in column
Algal biomass was collected from a shrimp farm and washed by deionized water. The sorption experiment was performed in cylindrical fixed-bed columns with 1.5 cm internal diameter. The packing density of sorbent was controlled at about 0.140 g/mL. In other words, one gram of biomass was packed at the bed depth of 4 cm. The porosity was calculated from dividing void volume by the total volume which was estimated to be 0.42. Synthetic wastewater containing heavy metal ion (Cu2+ or Cd2+ or Pb2+) at an
Calibration of the model and the model’s coefficients
The results from the reference experiments along with the calibrated model are illustrated in Fig. 1 and the best fit of the model’s coefficients are summarized in Table 1.
(x =4 cm, Q =6 mL/min, Co =0.1 mM, pH = 5, T =294 K, =0.140 g/mL,
bed volume =7.07 mL).
Fig. 1 shows that the model fits well with the experimental data, which is also confirmed by high R2 value in Table 1 that are very close to unity. It can be seen from the figure that the breakthrough time (tb) at the same conditions can be
Conclusions
This work adopts the analytical solution of contaminant transport model developed by Ogata and Bank (1961) to predict the breakthrough curve of the single-component metal ion sorption in a fixed bed column. The predicted results from the model were consistent with experimental data for Pb2+ and Cd2+ sorption at different bed depths. However, the model predicts slower breakthrough time than it would be in the experimental results when the flow rate was changed. This might be due to other
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
The author wishes to acknowledge Dr. Pailin Chatanantavet for proofreading and improving the use of English in this article.
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