DOI: 10.3303/CET2292087 Paper Received: 22 December 2021; Revised: 9 March 2022; Accepted: 15 May 2022 Please cite this article as: Gonzalez-Delgado A., Tejada-Tovar C., Villabona-Ortiz A., 2022, Computer-aided Modeling and Evaluation of a Packed Bed for Chromium (vi) Removal Using Residual Biomass of Theobroma Cacao L., Chemical Engineering Transactions, 92, 517-522 DOI:10.3303/CET2292087 CHEMICAL ENGINEERING TRANSACTIONS VOL. 92, 2022 A publication of The Italian Association of Chemical Engineering Online at www.cetjournal.it Guest Editors: Rubens Maciel Filho, Eliseo Ranzi, Leonardo Tognotti Copyright © 2022, AIDIC Servizi S.r.l. ISBN 978-88-95608-90-7; ISSN 2283-9216 Computer-aided Modeling and Evaluation of a Packed Bed for Chromium (vi) Removal using Residual Biomass of Theobroma Cacao L. Ángel Darío González-Delgadoa, Candelaria Tejada-Tovarb,*, Angel Villabona- Ortízb aChemical Engineering Department, Nanomaterials and Computer-Aided Process Engineering Research Group (NIPAC), Universidad de Cartagena, Avenida del Consulado St. 30, Cartagena de Indias 130015, Colombia bChemical Engineering Department, Process Design and Biomass Utilization Research Group (IDAB), Universidad de Cartagena, Avenida del Consulado St. 30, Cartagena de Indias 130015, Colombia ctejadat@unicartagena.edu.co The use of residual biomass in environmental applications continues gaining attention of the scientific community, the presence of heavy metals in the environment represents a problem of interest due to their toxicity, accumulation, and persistence. Bio-adsorption allows the use of agricultural or industrial waste, it is an efficient and non-destructive method for the removal of heavy metals, making it a viable method due to its low cost and easy implementation, however, the behaviour at large scale of these biomass-based emerging technologies is unknown; in this work, the modeling and computer-aided scaling up of an industrial scale column for the adsorption of Cr (VI) present in aqueous solution on an adsorbent based on Theobroma cacao L. was performed using Aspen Adsorption V10 software. The parameters for the modeling were obtained from experiments performed by the authors and scientific literature. Results show parameters as flowrate of feedstock, bed diameter and bed length showed sensitivity in the performance of the breakthrough column. 1. Introduction Heavy metals in water bodies could be concentrated in the living tissues of organisms due of bioaccumulation and magnification; thus, caused by the increase in polluted effluents product of industrial activities such as battery manufacturing, mining, smelting, refining, tanneries and soldering (Jencarova and Luptakova, 2012). Usually, Cr (VI) is found in water environments as chromate ions (CrO42-) o dichromate (Cr2O72-), which easily crosses biological barriers, being carcinogenic, moreover, Cr (VI) is 500 times more toxic than Cr (III). Due to its toxicity, chromium causes respiratory problems, lung cancer and affects the male reproductive system (Hedberg et al., 2019). In addition, the concentration of chromium in industrial wastewater usually exceeds the threshold limit set by governing institutions, thus those effluents need to be treated in order to reduce the concentration before being discharged. Several processes are being implemented for this issue, such as membrane filtration, chemical precipitation, ion-exchange, oxidative techniques, filtration and ultrafiltration (Jencarova and Luptakova, 2012). Adsorption is an economic process widely used to separate heavy metal at low concentrations from aqueous solution, considering it is a simple and highly efficient operation without toxic sludge generation. The use of adsorbents of agricultural and agro-industrial origin are extensively used due to their high availability and high selectivity for heavy metals (Khalil et al., 2021). Adsorption studies using agricultural and agro-industrial materials as adsorbents for removing heavy metals in a batch system, have allowed to have comprehensive isotherm data, in order to understand the interactions mechanisms between the pollutant and the adsorbent (Al- Ghouti and Da’ana, 2020). Yet, experimental approaches are costly and time-consuming and restricts the evaluation of operating variables desirable to design a packed bed column. From the isotherm equilibrium data, a viability study can be explored to prove their scalability onto a bigger proportion (Chatterjee et al., 2018). 517 Packed bed columns are devices stuffed with adsorbent, in which the polluted solution flows through the bed containing the contaminant to be removed into the adsorbent surface. Then, continuous packed bed systems are preferred for industrial wastewater treatment due of their capacity for handling large volumes of polluted solution (Jafari and Jamali, 2016). It also provides information on breakthrough and exhaustion times, which are important to evaluate the feasibility of adsorbents, considering the packed beds operate until the saturation of adsorbents (Elabbas et al., 2016). The breakthrough curves information can be used for design adsorption columns, because provide information about the change of the concentration as a function of the time (Shahid et al., 2019). Nevertheless, the experimental work at big scale in continuous systems is expensive and require large intervals of time. In this sense, few studies have reported the challenge to scale, model and simulate the system for future transition from laboratory to industrial application (Igberase and Osifo, 2019; Upadhyay et al., 2021). Hence, in this present work, simulation of packed bed adsorption of Cr (VI) ion onto cocoa husk was carried out using Aspen Adsorption simulator tool to solve sets of equations of the model. Factors affecting the dynamic column performance were investigated, including the effect of as flowrate of feedstock, bed diameter, porosity and, bed length. 2. Methodology The system of chromium (VI) ion–contaminated stream flowing through the cacao husk packed fixed bed adsorption column was simulated on the software Aspen Adsorption® V10.0. Physical properties that are crucial for execution of these simulation-based experiments were taken from data base of the investigation line, as well as bulk density, particle density, and particle size of cocoa husk. For the application of response surface methodology, software Statgraphics V19 was used. 2.1 Data collection The data required for the simulation of the properties of the adsorbent and the adsorption isotherm were obtained from research group data collection. The Bulk density and particle size of the cocoa husk, were determined by experimentation, and are equal to 518 kg/m3 500 µm, respectively. Freundlich parameters are shown in Table 1: Table 1. Freundlich isotherm parameters Model Parameter Value Freundlich KF [(mg g-1)(mg L-1)-1/n] 8.69 1/n 1.53 R2 0.9974 SS 0.5782 2.2 Aspen adsorption assumptions and mathematical background Using Aspen Adsorption® V10, liquid adsorption system was used to developed the simulations, taking intoaccount the below assumptions: The behaviour of fluid across the column was assumed to be without axial dispersion; ideal mixing in the liquid phase, so molar concentrations are calculated from molar volumes; Isotherm model used was Freundlich; with an isothermal energy Balance; lumped mass-transfer rate, with a solid-film linear resistance; the film model wasfluid; there is no pressure drop through the column; constant superficial velocity; and mass transfer coefficient was assumed constant. Figure 1a shows the adsorption process as designed in Aspen Adsorption for simulation. The discretization method used in all the simulations was based on the first-order Taylor series expansion, by assuming a volume of control (Vc), considering that the column has a cylindrical configuration with an area A and height Δz. Then, the partial differential mass balance equation which was used to express the chromium ion concentration in a small control volume inside the adsorbent bed is presented in Eq(1): Δ𝑍 𝛿𝐶𝑖 𝛿𝑡 = (𝜇 0 𝐶𝑖) 𝑧 − (𝜇 0 𝐶𝑖) 𝑧+Δ𝑧 − ( 𝐷𝐿𝑖 𝛿𝐶𝑖 𝛿𝑧 ) 𝑧 + ( 𝐷𝐿𝑖 𝛿𝐶𝑖 𝛿𝑧 ) 𝑧+Δ𝑧 − 𝜌 𝑠 Δ𝑍 𝛿𝑄 𝑖 𝛿𝑡 (1) In Eq(1), DLi is the axial dispersion coefficient (m2/s), ρs is the bed column density (kg/m3), µ0 is the interstitial velocity (m/s),z is the axial position (m), t is the process time (s), Ci is the concentration of pollutant in liquid- phase (kg/m3), and Qi is the solid-phase concentration of pulutan (g/kg) (Biswas et al., 2020). For simulation, linear lumped resistance kinetic model was assumed, which indicates that the initial concentration is a driving force for mass transfer during adsorption process. In addition, the adsorption of chromium ions onto cocoa husk process is represented by Freundlich model as it gives a much higher R2 value (equal to 0.99), as well as the adjustment of experimental points was closer. 518 2.3 Experimental design The experiments were designed by using a Response Surface Central composite design: 23 + star, made in Statgraphics V.19. The independent variables and their ranges are presented in Table 2. Simulation experiments were developed for the 17 experiments in Aspen Adsorption, and the response variables, namely saturation time and exhaustion C/Co, were obtained. Table 2. Parameters used for simulation Parameter -1 0 1 Inlet flowrate, m3/s 7.5×10-7 2.88×10-6 5×10-6 Bed height, m 0.30 0.45 0.60 Bed diameter, m 0.06 0.072 0.084 3. Results and discussion 3.1 Establishment of the base simulation breakthrough A base simulation for the adsorption of Cr (VII) onto cocoa husk was established as a reference point, prior to the studies on the affecting parameters. The initial values specifications are presented in Table 3, and these values will remain the same throughout the study except for the manipulated variable. Table 3. Parameters used for base case simulation Parameter Value Inlet flowrate, m3/s 7.5×10-7 Inlet concentration, mg/L 30 mg/L Bed height, m 0.3 Bed diameter, m 0.06 Bed porosity, m3 void/m3 bed 0.25 Bulk density, kg/m3 518 Constant mass transfer coefficient, 1/s 3.2×10-10 Freundlich isotherm KF, (mg g-1 (mg L-1)1/n 8.69 1/n 1.53 The plot of the base-case simulation breakthrough curve is shown in Figure 1b. The plot indicates that the column achieves breakthrough time at about 118.65 s, under the conditions stated in Table 2. It is observed a common “S” shape on the simulated breakthrough. 0 200 400 600 800 0.0 0.2 0.4 0.6 0.8 1.0 C f/C i Time (s) Figure 1. (a) Adsorption process flowsheet in Aspen Adsorption®, (b) Concentration ratio profile of the stream exiting from the cacao husk for the base simulation case 3.2 Analysis of variance and factors and response interactions The regression analysis of experimental data obtained in Table 4 led to the conclusion that breakthrough time of the bed for this system can be expressed as a function of inlet flowrate, bed height and breakthrough time, via Eq(2). The same, for the case of saturation time of the bed, can be modeled by Eq.(3). In addition, the description of exhaustion C/Co ratio, can be described by Eq(4). The predicted R2, values were found to be very close to 1 in case of all models which indicates that the suggested models can be good predictors of the experiment results. F EE D P R O D B ED 1 F EE D P R O D U CT (a) (b) 519 Table 4. Parameters used for simulation and responses Factors Responses Run Inlet flowrate, m3/s Bed height, m Bed diameter, m Breakthrough time, s Saturation time, s Exhaustion C/Co 1 2.88×10-6 0.60 0.075 97.21 372.87 0.9590 2 2.88×10-6 0.45 0.075 76.01 273.92 0.9503 3 5×10-6 0.3 0.084 37.25 149.66 0.9791 4 7.5×10-7 0.3 0.06 118.65 442.64 0.9475 5 5×10-6 0.3 0.06 15.82 68.26 0.9533 6 5×10-6 0.45 0.075 42.96 165.17 0.9648 7 5×10-6 0.60 0.084 79.89 273.92 0.9649 8 7.5×10-7 0.60 0.084 521.66 1703.49 0.9503 9 7.5×10-7 0.60 0.06 252.74 883.15 0.9560 10 2.88×10-6 0.3 0.075 76.02 277.79 0.9533 11 2.88×10-6 0.45 0.075 73.96 279.62 0.9560 12 2.88×10-6 0.45 0.084 92.34 343. 0.9503 13 2.88×10-6 0.45 0.075 76.01 279.62 0.9560 14 7.5×10-7 0.3 0.084 248.79 853.10 0.9503 15 5×10-6 0.60 0.06 35.20 138.03 0.9503 16 7.5×10-7 0.45 0.075 301.19 1023.94 0.9533 17 2.88×10-6 0.45 0.06 48.88 180.67 0.9560 Table 5 show the analysis for the three evaluated responses for the breakthrough time, saturation time, exhaustion C/Co ratio. While it was observed that, for breakthrough time and saturation time, as well as all three evaluated factors, i.e., inlet flowrate (A), bed height (B), and bed diameter (C), as well as their interaction such as AA, AB and AC, with significant factors (with P-value <0.005); for Exhaustion C/Co ration time, there was not any significant variable. Thus, might be because, the increase of the bed height enhance the adsorption due to the growth of the amount of active sites that allow the union of the ions with the functional groups, this effect is evident in the adsorption of Cr(VI) with bed heights as shown in Figure 2. Table 5. ANOVA for evaluated factors over response Response Source Sum of square F-Ratio P-Value Breakthrough time, s A: Inlet flowrate, m3/s 146241.0 123.22 0.0000 B: Bed height, m 23118.1 19.48 0.0031 C: Bed diameter, m 25891.3 21.82 0.0023 AA 21979.5 18.52 0.0036 AB 14890.0 12.55 0.0094 AC 13941.3 11.75 0.0110 BB 78.8 0.07 0.8041 BC 2519.97 2.12 0.1884 CC 11.78 0.01 0.9234 Total error 8307.71 Saturation time, s A: Inlet flowrate 1.63×106 163,99 0,0000 B: Bed height 241180.0 24,21 0,0017 C: Bed diameter 259537.0 26,05 0,0014 AA 227331.0 22,82 0,0020 AB 150546.0 15,11 0,0060 AC 129208.0 12,97 0,0087 BB 1428.5 0,14 0,7162 BC 20679.1 2,08 0,1928 CC 0.11 0,00 0,9975 Total error 69733.5 Exhaustion C/Co A: Inlet flowrate, m 3/s 0,000105177 1,87 0,2142 B: Bed height, m 0,0000133722 0,24 0,6411 C: Bed diameter, m 0,000124238 2,20 0,1812 AA 0,0000352913 0,63 0,4548 AB 0,0000365513 0,65 0,4472 AC 0,0000365513 0,65 0,4472 BB 0,00000710613 0,13 0,7330 BC 0,000105851 1,88 0,2129 CC 0,0000594573 1,05 0,3386 Total error 0,000394616 520 Figure 2. Three-dimensional contour plots to examine the relationship between the factors and (a) breakthrough time, (b) saturation time and (c) exhaustion C/Co In addition, the diminution in exhaustion C/Co caused by increasing in inlet flowrate and bed height, which leads to minimal change in exhaustion capacity. With respect to flow rate, it was found that increasing the inletflow rate results in the decrease in both saturation and breakthrough time, as the result of reduction in residence time of the chromium ions inside the bed which ceases the opportunity for the exchange between the ions and active adsorption centers into the micro- and mesopores of the adsorbent particles, as reported by cadmium and copper adsorption onto water hyacinth (Soriano et al., 2016). Meanwhile, the diminution of the breakthrough time with the augmentation in flowrate is related with the early exhaustion of adsorption sites, since a greater number of ions are entering into the system per unit time in addition to higher number of ions being adsorbed due to lower mass transfer resistance (Upadhyay et al., 2021). 3D contours of Figure 2, visually illustrates the behavior of response variables while varying factors. 6 13 2 8 9 2 2 118.37 5.71 10 212.29 2252.48 2.01 10 1.35 10 1.63 10 241.03 97.99.01 15664.4 BT F H D F F B F D H H D D = − +  − + +  −   −   + +  + (2) 7 13 2 8 9 2 2 572.41 1.11 10 670.47 15250 6.45 10 4.30 10 4.95 10 1026.24 28070.5 1506.95 ST F H D H F B F D H H D D = − −  − + +  −   −   + +  − (3) 2 0 2 2 / 0.89 5494.02 0.088 1.88 3.92 6705.88 83823 0.035 2.02 15.95 C C F H D F F H F D H H D D = + − + + −  −  − +  − (4) 4. Conclusions The analysis of breakthrough curves by simulation in Aspen Adsorption® V10, was found that chromium removal onto cocoa a packed bed of cocoa husk shows higher performance both influent flow rate and bed height. Through the application of response surface methodology, the effect of variation in column bed height, inlet flowrate and bed diameter over the breakthrough time, saturation time time and exhaustion C/C0 ratio of the cocoa husk packed bed was evaluated, finding great influence by all the evaluated variables and their interactions over the system. Nomenclature A– cross-sectional area of the packed bed, m2 BT – the breakthrough time, s C/C0 – exhaustion C/C0 D – bed diameter, m F – inlet flowrate, m3/s F-ratio–relates the variances of independent samples H – bed height, m (a) (b) (c) 521 T – temperature, °C P – pressure, bar P-value–probability of obtaining the observed results Qi – cocoa husk adsorption capacity, mg/g ST – the saturation time, s w – fin width, m z – bed axial position, m Acknowledgments The authors thank to the Universidad de Cartagena for the time of the researchers and the laboratory equipment for developing this research. References Al-Ghouti M. A., Da’ana D. A. 2020. Guidelines for the use and interpretation of adsorption isotherm models: A review. J. Hazard. Mater. 393: 122383. https://doi.org/https://doi.org/10.1016/j.jhazmat.2020.122383 Biswas S., Sharma S., Mukherjee S., Meikap B. C., Sen T. K. 2020. 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Res. 0–27. https://doi.org/10.1007/s11356-021-17216-9 522 190tejadatovar.pdf Computer-aided Modeling and Evaluation of a Packed Bed for Chromium (vi) Removal using Residual Biomass of Theobroma Cacao L.