Clays and Clay Minerals

, Volume 58, Issue 3, pp 431–448 | Cite as

Application of Box—Behnken Design to Modeling the Effect of Smectite Content on Swelling to Hydrocyclone Processing of Bentonites with Various Geologic Properties

  • Selçuk ÖzgenEmail author
  • Ahmet Yildiz


As advances in technology have led to increased use of bentonites, more high-quality bentonite has been sought. The volume of high-quality bentonites available is shrinking and use of bentonite reserves containing impurities is inevitable. The aim of this study was to apply Box–Behnken experimental design and response surface methodology to model and optimize some operational parameters of a hydrocyclone to produce three groups of bentonite concentrates. The four significant operational parameters of hydrocyclones are feed solid ratio, inlet pressure, vortex diameter, and apex diameter, and these parameters were varied and the results evaluated using the Box–Behnken factorial design. In order to produce bentonite concentrates using a hydrocyclone, mathematical model equations were derived by computer simulation programming applying a least-squares method, using Minitab 15. Second-order response functions were produced for the swelling and to establish the quantity of smectite in the bentonite concentrates. Predicted values were found to be in good agreement with the experimental values (R2 values of between 0.829 and 0.999 for smectite and three different swelling groups for the bentonites). Although in natural states these bentonites are not suitable for industrial use, enhancements were obtained giving up to 81.45% smectite and by increasing swelling by 194% for the three bentonite groups. The swelling properties of the bentonites are improved by increasing the proportion of smectite content. The graphics were designed to relate swelling and smectite content according to the two-dimensional hydrocyclone factors, and each factor was evaluated in itself. The present study revealed that the Box–Behnken and response surface methodology can be applied efficiently to model the hydrocyclone for bentonite; the method is economical and provides the maximum amount of information in a short period of time and with the smallest numberof experiments.

Key Words

Bentonite Box—Behnken Design Clay Minerals Hydrocyclone Modeling Process Optimization Response Surface Methodology Optimization Smectite Swelling 


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© The Clay Minerals Society 2010

Authors and Affiliations

  1. 1.Department of Mining EngineeringAfyon Kocatepe UniversityAfyonkarahisarTurkey

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