Fixed Bed Column Modeling of Cd(II) Adsorption on Bone Char Using Backward Bayesian Multiple Linear Regression

Document Type: Original Research Paper


1 Department of Water Engineering, College of Agriculture, Fasa University, P.O.Box 74616-86131, Fasa, Iran

2 Department of Statistics, Faculty of Science, Fasa University, P.O. Box 74616-86131, Fasa, Iran

3 Department of Water Engineering, College of Agriculture, Shiraz University, P.O. Box 71365, Shiraz, Iran


In this work, the backward Bayesian multiple linear regression (BBMLR) as a new approach is presented to predict the adsorption efficiency (AE) of Cd(II) ions by ostrich bone char (OBC) in the fixed bed adsorption with four operational variables consisting of pH (2-9), inlet Cd(II) concentration (Co= 25-100 mg/L), bed depth (h= 3-9 cm) and feed flow rate (Q= 0.5-30 mL/min). The performance of the BBMLR was evaluated using the coefficient of determination (R2), normalized root means square error (NRMSE) and mean residual error (MRE). The AE of Cd(II) ions by OBC increased from 42.3% to 99.9% when pH was increased from 2 to 9 with h of 6 cm and Q of 1.5 mL min-1. It was found that the AE dramatically increased from 70.5% to 99.9% with decreasing Q from 30 to 0.5 mL min-1 at pH of 7 and h of 6 cm. At pH= 7 and Q= 1.5 mL min-1, the AE increased from 71.9% to 100% when h increased from 3 to 9 cm. The BBMLR model presented excellent performance (NRMSE=6.69%) for predicting Cd(II) removal in a continuous adsorption system, although it gave a slight underestimation (approximately 3.52%). The BBMLR is more sensitive to the pH, followed by h and Q, while the Co has no significant effect on it. This research displays that OBC has great potential as an eco-friendly low-cost adsorbent in removing Cd(II) ions from the contaminated waters.


Alkurdi, S.S.A., Al-Juboori, R.A., Bundschuh, J. and Hamawand, I. (2019). Bone char as a green sorbent for removing health threatening fluoride from drinking water. Environ Int., 127, 704-719.
Amiri, M.J., Abedi-Koupai, J. and Eslamian, S. (2017a). Adsorption of Hg(II) and Pb(II) ions by nanoscale zero-valent iron supported on ostrich bone ash in a fixed-bed column system. Water Sci. Technol., 76(3), 671-682.
Amiri, M.J., Abedi-Koupai, J., Eslamian, S.S. and Arshadi, M. (2016). Adsorption of Pb(II) and Hg(II) ions from aqueous single metal solutions by using surfactant-modified ostrich bone waste. Desalin. Water Treat., 57(35), 16522-16539.
Amiri, M.J., Abedi-Koupai, J., Jafar Jalali, S.M. and Mousavi, S.F. (2017b). Modeling of fixed-bed column system of Hg (II) ions on ostrich bone ash/nZVI composite by artificial neural network. J. Environ. Eng.-ASCE., 143(9), 04017061.
Amiri, M.J., Arshadi, M., Giannakopoulos, E. and Kalavrouziotis, I.K. (2018). Removal of mercury (II) and lead (II) from aqueous media by using a green adsorbent: kinetics, thermodynamic, and mechanism studies. J. Hazard. Toxic Radioact. Waste., 22(2), 04017026.
Awual, M.R. (2015). A novel facial composite adsorbent for enhanced copper(II) detection and removal from wastewater. Chem Eng J., 266, 368-375.
Awual, M.R. (2017). New type mesoporous conjugate material for selective optical copper(II) ions monitoring & removal from polluted waters. Chem Eng J., 307, 85-94.
Bahrami, M., Amiri, M.J., Mahmoudi, M.R. and Koochaki, S. (2017). Modeling caffeine adsorption by multi-walled carbon nanotubes using multiple polynomial regression with interaction effects. J. Water Health., 15(4), 526-535.
Box, G.E.P. and Tiao, G.C. (1973). Bayesian Inference in Statistical Analysis, Addison Wesley Publishing.
Carlin, B.P. and Louis, T.A. (2008). Bayesian Methods for Data Analysis, Chapman and Hall/CRC. London.
Chowdhury, S. and Saha, P. (2013). Artificial neural network (ANN) modeling of adsorption of methylene blue by NaOH-modified rice husk in a fixed-bed column system. Environ. Sci. Pollut. Res., 20(2), 1050-1058.
Cruz, M.A.P., Guimaraes, L.C.M., Costa Junior, E.F., Rocha., S.D.F. and Mesquita, P.D.L. (2020). Adsorption of crystal violet from aqueous solution in continuous flow system using bone char. Chem Eng Comm., 270(3), 372-381.
Gelman, A., Carlin, J.B., Stern, H.S. and Rubin, D.B. (2003). Bayesian Data Analysis, Chapman and Hall/CRC. London.
Ghosh, A., Joshi, P.K. (2014). Hyperspectral imagery for disaggregation of land surface temperature with selected regression algorithms over different land use land cover scenes. ISPRS J Photogramm Remot Sens., 96, 76–93.
Hu, A., Ren, G., Che, J., Guo, Y., Ye, J. and Zhou, S. (2020). Phosphate recovery with granular acid-activated neutralized red mud: Fixed-bed column performance and breakthrough curve modelling. J Environ Sci., 90, 78-86.
Khoshravesh, M., Gholami Sefidkouhi, M.A. and Valipour, M. (2017), Estimation of reference evapotranspiration using multivariate fractional polynomial, Bayesian regression, and robust regression models in three arid environments. Appl. Water Sci., 7, 1911–1922.
Khurram, A.M., Farooq, U., Athar, M.M. and Salman, M. (2019). Biosorption of Cd(II) ions from its aqueous solutions using powdered branches of Trifolium resupinatum: equilibrium and kinetics. Green Chem Lett Rev., 12(3), 217-224.
Lü, L., Lu, D., Chen, L., Luo, F. (2010). Removal of Cd(II) by modified lawny grass cellulose adsorbent. Desalination., 259, 120–130.
Maeda, C.H., Araki, C.A., Moretti, A.L., Barros, M.A.S.D. and Arroyo, P.A. (2019). Adsorption and desorption cycles of reactive blue BF-5G dye in a bone char fixed-bed column. Environ. Sci. Pollut. Res., 26, 28500–28509.
Masomi, M., Ghoreyshi, A.A., Najafpour, G.D. and Mohamed, A.R.B. (2015). Dynamic adsorption of phenolic compounds on activated carbon produced from pulp and paper mill sludge: experimental study and modeling by artificial neural network (ANN). Desalin. Water Treat., 55(6), 1453–1466.
Mousavi, S.F., Esteki, M., Mostafazadeh-Fard, B., Dehghani, S. and Khorvash, M. (2012). Linear and nonlinear modeling for predicting nickel removal from aqueous solutions by dried sunflower stalks. Environ Eng Sci., 29, 765–775.
Pollution, 6(2): 451-461, Spring 2020
Pollution is licensed under a "Creative Commons Attribution 4.0 International (CC-BY 4.0)"
Oguz, E. (2017). Fixed-bed column studies on the removal of Fe3 and neural network modelling. Arab J Chem., 10 (3), 313–320.
Press, S.J. (1989). Bayesian Statistic: Principles, Models and Application, John Wiley and Sons, New York.
Rojas-Mayorga, C.K., Mendoza-Castillo, D.I., Bonilla-Petriciolet, A. and Silvestre-Albero, J. (2016). Tailoring the adsorptionbehavior of bone charfor heavy metal removalfrom aqueous solution. Adsorpt Sci Technol 34(6), 368-387.
The Council of the European Communities, Directive on pollution caused by certain dangerous substances discharged into the aquatic environment of the community [76/464/EEC], Off. J. Eur. Commun. L 129/23 (May) (1976).
Ticlavilca, A.M., McKee, M. and Walker, W.R. (2013). Real-time forecasting of short-term irrigation canal demands using a robust multivariate Bayesian learning model. Irrig Sci., 31, 151–167
Wang, M., Liu, Y., Yao, Y., Han, L. and Liu, X. (2020). Comparative evaluation of bone chars derived from bovine parts: Physicochemical properties and copper sorption behavior. Sci Total Environ., 700, 134470.
Zellner, A. (1971). An introduction to Bayesian inference in econometrics, John Wiley & Sons, New York.
Zhu, G., Su, Y., Li, X., Zhang, K. and Li, C. (2013). Estimating actual evapotranspiration from an alpine grassland on Qinghai-Tibetan plateau using a two-source model and parameter uncertainty analysis by Bayesian approach. J Hydrol., 476, 42–51.