Novel combinatorial extensions to breakthrough curve modeling of an adsorption column — Depth filtration hybrid process

Highlights

• Novel breakthrough models for fixed bed column/depth filtration hybrid process were proposed.

• Theoretical breakthrough curve models were combined for modeling of hybrid system.

• Mathematical modeling of depth filter was coupled with breakthrough models of fixed bed column.

• Combinatorial approaches were successful in predicting breakthrough profiles of hybrid system.

Abstract

This work introduces novel scenarios for the breakthrough curve modeling of an adsorption column/depth filtration hybrid system. Four well-known theoretical breakthrough models including Thomas, Adams–Bohart, Yoon–Nelson, and BDST were employed to describe the normalized concentration profiles. In the first approach, the theoretical models were combined for better estimation of the breakthrough curves and the Thomas/Yoon–Nelson and Thomas/BDST combinations were obtained as the best extensions. In the second approach, an adsorption-transport model was developed for the depth filter to obtain the transient concentration gradient across the filter medium thickness. The model was then combined with the theoretical breakthrough models to predict the adsorption column breakthrough curves. Results revealed that a decrease in the feed flowrate and filter pore size could intensify the concentration polarization on the filter surface. Both model extensions could successfully approximate the breakthrough curves of the hybrid system with more than 99% agreement with the experimental data, while the prediction accuracy of the original breakthrough models seldom exceeds 93%.

Introduction

Hybrid and integrated separation systems are considered to be the next generation of novel processes for water and wastewater treatment applications. Hybrid processes consist of several standalone separation systems arranged in series, whereas in integrated scenario, separation systems are combined to form a united separation unit. In light of the synergistic effects of combining the individual unit operations, hybrid and integrated processes take the advantages of higher removal efficiency, faster removal kinetics, shorter footprints, fewer shortcomings in the performance and, more applicability for a wide range of contaminants compared with the individual separation operations [1], [2].

Adsorption–filtration hybrid processes are of great interest to researchers due to their superior efficiency and faster kinetics in the removal of various contaminants from water. Moreover, these systems are easily handled and offer less energy consumption and operational cost [3], [4]. Many examples of successful applications of adsorption–filtration hybrid processes have been addressed in the literature. Hilbrandt et al. used a submerged ultrafiltration (UF)/adsorption hybrid system for the removal of phosphate from water. Their results indicated the maximum removal of 87% with rather no fouling for the submerged ultrafiltration membrane [5]. Hao et al. used the same configuration of the adsorption/UF hybrid process equipped with an aeration system for the removal of arsenic from the river water in pilot-scale [6]. Shemer et al. employed a hybrid process consisting of a stirred tank for the semi-batch adsorption of silica from brackish water followed by a hollow fiber UF membrane to remove the adsorbents from the treated water [7]. Lin et al. could remove almost 80% of phenol contaminant from water using a hybrid process consisting of clay adsorption and UF membrane [8]. Besides, successful application of the adsorption–filtration hybrid systems for the removal of boron [9], rubidium [10], chromate [11], and antibiotics [12], from water has been addressed in the literature.

Mathematical modeling of separation processes is a useful approach to obtain fundamental information about the macro-behavior of the systems as well as the phenomena involved in the micro-scale. Investigation of the fixed-bed adsorption columns (FBACs) via mathematical modeling is an area of research interest. Dynamic characteristics of FBACs are described by the normalized concentration vs time profile, known as the breakthrough curves [13]. Investigation and modeling of the breakthrough curves can provide important information about the dynamic adsorption process, necessary for the design, operation, optimization and, the scale-up of the process, such as the break time (t_b at which the outlet to inlet concentration ratio reaches to 5%), maximum bed capacity, bed saturation (exhaustion) rate and the effects of the operating parameters on the adsorption column performance [14], [15], [16]. For this purpose, several mathematical models have been prevalently employed for the estimation of the breakthrough curves by researchers such as, Thomas [17], Adams–Bohart [18], Yoon–Nelson [19], Clark [20] and Bed depth service time (BDST) [21] models. These models are simple and easy-to-use that allow for the characterization of the dynamic behavior of a continuous adsorption process (e.g., FBAC) with a low computation time and a reliable fitting performance [22]. Rahman et al. used the mathematical models to describe the nitrate adsorption in a FBAC. Their results showed that Thomas model could satisfactorily predict the experimental data [23]. Jafari et al. employed the theoretical models for breakthrough curve modeling of a FBAC for adsorption of azure-II and auramine-O by activated carbon (AC) [24]. Nazari et al. investigated the fixed-bed adsorption of cephalexin by walnut shell-based AC in terms of the theoretical breakthrough curve models [25]. Zhang et al. reported the successful modeling of methylene blue (MB) adsorption by a straw-based adsorbent using the mathematical breakthrough curve models [26]. Furthermore, there have been some other research works in the literature that studied the breakthrough curve modeling and investigated the impacts of important operating variables such as feed flowrate, initial concentration and adsorption bed length on dynamic adsorption of MB by peanut husk [27], Fox nutshell [28], acid-modified local clay beads [29], and phoenix tree leaf powder [30], in FBAC.

Filtration of a solution using a porous filter medium is usually considered as a complex process in nature. Well understanding of the physical phenomena and the fundamental mechanisms of the filtration process, especially in micro-scale, has been remained as a challenge for the researchers up to now [31], [32], [33]. As a result, numerous studies are being carried out for describing the transport behavior of filtration processes via mathematical modeling. Werzner et al. proposed a mathematical model to describe the short-term depth filtration of liquid metals using ceramic foam filters. For this purpose, they solved a two-dimensional transient flow field through the filter, numerically [31]. Wende Li et al. investigated the concentration polarization and the surface fouling in pressure-driven membrane filtration processes by simultaneous solving the Navier–Stokes and the convection-diffusion equations [34]. Vinther et al. worked on the mathematical modeling of dextran solution filtration by hollow fiber ultrafiltration membranes. Navier–Stokes and continuity equations were solved for both solute and solvent to predict their corresponding mass fluxes [35]. Tien et al. mathematically modeled the flux decline in a cross-flow filtration process considering the cake formation mechanism at the surface of the membrane [36]. Salehi et al. successfully predicted the concentration profile in the transport of copper ions through the nanocomposite chitosan/polyvinyl alcohol thin adsorptive membranes by solving the adsorption–diffusion mathematical model [37]. Madaeni and Salehi also developed an adsorption–transport mathematical model to describe the passage of the saturated brine cations (Fe²⁺, Ca²⁺, and Mg²⁺) through a nanofiltration membrane [38].

Despite many efforts on the mathematical modeling of individual FBAC and membrane filtration systems, there is no study considering the mathematical modeling of hybrid adsorption-filtration systems in the literature. In our previous study [39], we introduced a novel hybrid separation process consisting of a FBAC followed by a dead-end filtration (DEF) cell to remove MB as a model contaminant from water. Granular activated carbon (GAC) was used as the adsorbent in FBAC and cellulose acetate depth filter sheets were employed as the filter medium in DEF cell. The current work deals with the establishment of general and straightforward strategies for an accurate approximation of the concentration profiles of the hybrid process, for the first time. Mathematical modeling of the FBAC-DEF hybrid process was started with a simplifying assumption that allowed for generalization of well-known dynamic adsorption models for breakthrough curve modeling of the hybrid process. The idea was then developed via some extensions to enhance the modeling accuracy. Following approaches were employed for mathematical modeling of the breakthrough curves of the FBAC-DEF hybrid process:

• The whole process (fixed bed + filter) was considered as a single dynamic adsorption system. Accordingly, four well-known theoretical models including Thomas, Adams–Bohart, Yoon–Nelson and, BDST were used for breakthrough curve modeling of the whole process.

• As the first model extension strategy, individual breakthrough models were combined to describe the breakthrough behavior of the whole hybrid system.

• In the second model extension strategy, FBAC and DEF systems were analyzed, separately. An adsorption-transport mathematical model was developed for the depth filtration process. This model was then combined with the four aforementioned theoretical adsorption models to approximate the breakthrough curves of the FBAC.