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Box–Behnken design assisted by theoretical mass and heat transfer using for multi-responses optimization of membrane distillation process

Ali Boubakri, Salah Al Tahar Bouguecha, and Amor Hafiane

Laboratory of Water, Membranes and Environmental Biotechnology, Center for Water Researches and Technologies, Soliman, Tunisia



Received: 13 April 2021  Accepted: 5 July 2021


Desalination of seawater is one of the most promising applications of membrane distillation process (MD). Development of suitable models and optimization of MD performance are the main objectives of this study. Box–Behnken design (BBD) integrated with theoretical mass and heat transfer was used to model and optimize direct contact membrane distillation process (DCMD). Many performance parameters were modeled and optimized at the same time such as permeate flux (Jp), thermal efficiency (η) and specific thermal energy consumption (STEC). For this purpose, three operating parameters were chosen including temperature difference (ΔT), feed velocity (υf) and permeate velocity (υp). The obtained results showed that the developed models were reasonably accurate to predict different performance indicators for MD process. Responses were described by a second-order polynomial regression model using analysis of variance (ANOVA) to fitness models. The optimum conditions applied for MD process were ΔT (40 °C), υf (3.24 10–2 m/s) and υp (6.94 10–2 m/s). Under these optimum conditions, the direct contact membrane distillation performance obtained in terms of Jp, η and STEC was 9.86 kg/(m2 h), 72.93% and 334.73 kWh/m3. Experimental results presented a good agreement with predicted values, for all responses, with a confidence level less than 95%. This study indicates the effectiveness of Box–Behnken design methodology to predict mass and heat transfer models for DCMD process to ensure better performance.

Keywords: Membrane distillation; Box–Behnken design; Multi-responses optimization; Heat and mass transfer; Desalination

Full paper is available at

DOI: 10.1007/s11696-021-01778-6


Chemical Papers 75 (11) 6009–6024 (2021)

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