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.