Artificial neural network-based surrogate modeling of multi-component dynamic adsorption of heavy metals with a biochar

https://doi.org/10.1016/j.jece.2018.08.038Get rights and content

Highlights

  • Performance of ANNs for multi-metallic adsorption breakthrough curve modeling was analyzed.

  • Activation function used in ANNs played a relevant role to reduce model overfitting.

  • Cascade and Feed forward neural network with distributed time delay were the best models.

  • New findings on ANNs modeling of dynamic adsorption processes are reported.

Abstract

This paper reports the application of four neural network surrogate models for the correlation and prediction of asymmetric breakthrough curves obtained from the multi-component adsorption of cadmium, nickel, zinc and copper ions on a biochar. Artificial neural networks namely: Feed forward back propagation neural network, Feed forward back propagation neural network with distributed time delay, Cascade forward neural network and Elman neural network have been assessed and compared where their limitations and capabilities have been discussed. The impact of the architecture of these surrogated models, including the activation functions and training algorithms, has been analyzed using error and residuals analyses in different zones of the adsorption breakthrough curves obtained from single, ternary and quaternary solutions of tested heavy metals. Overall, the bed adsorption capacities for these metals ranged from 2.01 to 5.40, 0.16 to 4.46 and 0.03 to 2.15 mmol/g in single, ternary and quaternary feeds, respectively, at tested operation conditions. Highest adsorption capacities were obtained for copper in single and multi-metallic solutions and they ranged from 2.15 to 5.4 mmol/g. Results of this paper showed that Cascade forward neural network was the best model for multi-metallic adsorption breakthrough curve modeling. This neural network showed the lowest modeling errors for the multi-component adsorption breakthrough curves. This paper introduces new results on the application of ANNs surrogate models for the simulation of multi-component adsorption process involved in water treatment and purification.

Introduction

Packed-bed column is the common process configuration used for the adsorption of pollutants from industrial streams, groundwater and wastewaters in large-scale applications [1,2]. The determination of several operating parameters of adsorption columns implies the analysis of breakthrough curves [[1], [2], [3], [4], [5]]. In particular, the modeling of packed-bed adsorption of water pollutants is challenging due to the nonlinear behavior of the adsorption process that depends on the number of adsorbates, pH, temperature, feed flow and column characteristics [1,3,4]. For example, the axial dispersion and mass transfer phenomena influence the shape of concentration profile of adsorption columns causing asymmetric breakthrough curves. The presence of several pollutants in the column feed also increases the complexity of breakthrough modeling [6]. The correlation and prediction of multi-component breakthrough curves are difficult due to non-interaction, antagonistic and synergistic adsorption effects caused by the pollutants present in the fluid to be treated.

The study of the adsorption process in packed-bed columns generally involves the application of mechanistic and phenomenological models such as mass transfer equations [1,3,7]. These models are developed considering certain assumptions and may show some limitations for the simulation of adsorption breakthrough curves in multi-component solutions. Mass transfer equations also require different parameters that are usually obtained from empirical correlations. As an alternative, these adjustable parameters can be generated from the data fitting of experimental data but the inaccuracies involved in this task could significantly affect the modeling results [3].

The application of surrogate models is an option for the breakthrough analysis especially in multi-component adsorption. These models are designed to approximate the principal features of complex systems allowing a better accuracy for data correlation and prediction [[8], [9], [10]]. Artificial neural networks (ANNs) are reliable and flexible surrogate models that can be used to simulate challenging processes [9,10]. This type of surrogate models is able to model multivariable systems and can be used to identify non-linear relationships between independent and dependent variables [11]. For instance, recent studies have reported the application of ANNs for the modeling of the evolution and fluctuation of NOx emissions from a fluidized bed combustion process [12], the optimization of a tri-bed twin-evaporator adsorption chiller [13], the prediction of NOx emissions from circulating fluidized bed combustors at different operating conditions [14], the modeling of CO2 equilibrium absorption in alternative solvents [15] and the analysis of analytical chemical data [16]. These and other studies have shown the advantages of ANNs to model difficult, multivariable and non-linear processes. Note that the simulation and prediction of adsorption process performance have been also successful with ANNs [17,18]. Specifically, they have been applied to model kinetics, isotherms and breakthrough curves for the adsorption of a variety of pollutants including the analysis of multi-component systems [17,[19], [20], [21], [22], [23], [24]].

There is a variety of ANNs with different parameters and configurations [17,23,24,25]. Overall, the numerical performance of ANNs models is diverse and is related to the specific problem to be solved [[26], [27], [28]]. Some of the available surrogate models could show limitations for multi-component breakthrough analysis depending on the characteristics of the adsorption process [26]. Therefore, it is clear that there is no a general ANNs model that can be used to all adsorption systems and, consequently, different models should be tested for identifying the best option for the application at hand. To the best of author’s knowledge, the detailed evaluation and comparison of the performance of different ANNs in the modeling of multi-component breakthrough adsorption curves have not been reported specially for systems with three or more adsorbates.

The main objectives of this manuscript were to assess and compare a set of ANNs-based surrogate models for the analysis of multi-metallic adsorption breakthrough curves. Four ANNs have been applied and tested for the modeling of the heavy metal adsorption in packed-bed columns with a biochar using single, ternary and quaternary solutions of cadmium (Cd2+), nickel (Ni2+), zinc (Zn2+) and copper (Cu2+) ions. The impact of ANNs architecture, activation function and training algorithm in model performance has been analyzed. This study is necessary to understand the capabilities and limitations of ANNs-based surrogate models for the simulation of multi-component breakthrough curves involved in the process design of water treatment technologies. Note that the multi-metallic adsorption in packed beds is complex due to the antagonistic adsorption between the cations that compete for the active sites of the adsorbent causing even the desorption of heavy metal ions [23,29]. Therefore, this case of study included asymmetrical breakthrough curves from the antagonistic adsorption in ternary and quaternary metallic solutions that imply challenging characteristics to obtain an accurate modeling. Results of this paper showed the advantages and limitations of tested ANNs in the multi-component adsorption breakthrough modeling where some remarks for the selection of the best surrogate model were discussed.

Section snippets

Experimental determination of breakthrough curves for the multi-component adsorption of heavy metals

Multi-metallic adsorption of Cd2+, Ni2+, Zn2+ and Cu2+ on a commercial biochar, commonly known as bone char, was selected as case of study for testing and analyzing the performance of ANNs-based surrogate breakthrough models. This commercial adsorbent was obtained from the pyrolysis of cow bones and its composition included hydroxyapatite (70–76 wt. %), calcite (7–9 wt. %) and an amorphous carbon phase (9–11 wt. %). It had a surface area of 113.3 m2/g and a micropore volume of 0.001 cm3/g with

Multi-metallic adsorption on biochar packed-bed columns

Experimental breakthrough curves for tested feed compositions are reported in Fig. 2, Fig. 3. Concentration profiles suggested that the presence of axial dispersion and mass transfer resistances affected the metal adsorption with the bone char micro-columns causing asymmetric breakthrough curves. Overall, these curves showed different asymmetry degrees depending on the composition and metals present in the column feed and, consequently, they were challenging to be modeled with traditional

Conclusions

Numerical performance of four ANNs-surrogate models has been analyzed for the simulation of breakthrough curves obtained from the multi-component adsorption of heavy metals on bone char. Results showed that Cascade, FFBP-DTD and Elman ANNs may be better than FFBP if a proper architecture is applied. FFBP is a popular ANNs model applied in adsorption and other related applications but its performance could be inferior with respect to other surrogate models. Activation function used in the hidden

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