Multi objective optimization
In most of previous studies, only adsorption step has been carried out to investigate the effect of different parameters on the adsorbent performance. Optimization of the TSA unit in terms of energy requirements and performance of the process appears as a good deal for VOC removal technologies. Accordingly, a model is required to describe the effect of process variables on recovery of VOCs and operating costs. After preliminary tests and in the fixed feed condition, duration of heating step (A), duration of cooling step (B), regeneration flow rate (C) and humidity of air (D) are considered as effective variables and their practical range are identified in Table 3. In this study, the Design-expert® software is utilized via the central composite design (CCD) method through performing 30 tests with five levels for each variable. Table 3 shows corresponding results for VOCs recoveries and operating costs per each cycle. The RSM proposed a 2FI correlation to relate diethyl ether recovery, ethanol recovery and operating costs to the independent variables. The results of analysis of variance showed that the P values for all three objectives are lower than 0.05 indicating that the model terms are significant and have significant effects because of the large F value. The large F-value showed that the model is significant while only 0.01 % chance that a ”Model F-Value” with this large F value could occur due to noise. Values of ”Prob>F” less than 0.05 indicate that the model terms are significant. The results of the diethyl ether and ethanol recoveries showed thatincrease in the variable B leads to increase in diethyl ether recovery while increase in the variables A, C and D results in decrease in diethyl ether and ethanol recoveries. Increase in parameters C, A and B directly increase operating costs and increase in parameter D leads to lower operating cost.The model accuracy for all objectives has been higher that 99.98 % (R2) indicating a good fitting of the correlation with the data. ”Adeq Precision” measures the signal to noise ratio. A ratio greater than 4 is desirable. In this study, the “Adeq Precision” ratio higher than 103 is obtainedwhich indicates an adequate ratio. Also the “Adj R-Squared” is highe than 99.69 % which is close to “R-Squared” indicating a good accuracy of model. This model can be used to navigate the design space. Equations 26-28 show the empirical correlation for each objectives obtained by the RSM.
Diethyl ether cyclic recovery (%) =+84.88123+0.076377×A+0.24750×B+0.012657×C-685.03606×D-3.09525E-003×A×B-6.63543E-004×A×C+7.02308×A×D+1.54004E-004×B×C+7.04970×B×D+0.68891×C×D Eq. (26)
Ethanol cyclic recovery (%)= +63.86180+0.059023× A +0.16952×B +0.011428×C-299.78004×D-2.82108E-003×A×B-6.03091E-004×A×C+3.07032×A×D+4.22973E-004×B×C+3.09206×B×D+0.30129×C×D Eq. (27)
Operating costs ($)= -7.23003E-004+0.000000×A+4.81994E-005×B+0.029585×C+0.24099×D+0.000000×A×B+3.90000E-003×A×C+1.74583E-012×A×D+2.95818E-003×B×C-0.016066×B×D-8.92557E-004×C×D Eq. (28)
The predicted versus actual data for all three objectives confirmed that the predicted values of the model were in a good agreement with the given data.Figure 8 shows three- dimensional plot for interaction of variables on the objectives. The plot given in Figure 8 is easy-reading and straightforward in which a linear surface is seen between the independent parameters on the responses.