Optimization of drying ammonium tetramolybdate by microwave heating using response surface methodology

2.1 Materials

The ammonium tetramolybdate is obtained from Zhang Jia Kou, He Bei province of China. It is white powder, and the particle size is about 74 μm. Before the experiment, three samples were dried at 60°C for 24 h, then, their exact moisture content was determined. The results show that the moisture content of ammonium tetramolybdate is 17.23%. Also there is 48.53% of molybdenum content in the raw material.

2.2 Drying equipment and procedure

Microwave drying experiment is operated in the microwave reactor furnace which is researched and designed by Key Laboratory of Unconventional Metallurgy, Ministry of Education. The microwave drying experiments are carried out in a lab-made microwave muffle furnace, and the microwave equipment consists of four sections: two magnetrons (at the frequency of 2450 MHz and 3.0 kW power), which worked as microwave sources and it is cooled by water circulation; a waveguide for transporting microwaves; a resonance cavity to manipulate microwaves for a specific purpose; and a control system to regulate the temperature and microwave power. The inner dimensions of the microwave cavity are 260 mm in height, 420 mm in length and 260 mm in width. In addition, the accuracy of weight is 0.0001 g, the accuracy of measure is 0.001 m. The schematic diagram of the microwave drying system is shown in Figure 1.

Figure 1:

Schematic diagram of the microwave drying system.

An intelligent control system is used in the equipment. The setting temperature for sample, voltage and electric current can be revealed by the display and control unit. The voltage and electric current can be adjusted via the control unit.

The sample with certain thickness is put into a Teflon container. The microwave temperature is set before switching on microwave. Microwave would be turned off automatically when the actual temperature achieves or exceeds the setting temperature. However, the microwave is turned on when actual temperature is less than the setting temperature, and the sample is heated again. The process is performed over and over until the worker stops the equipment. In the process, the PC is set to automatically record the data anytime.

2.3 Computing method of dehydration ratio

The samples are placed in the microwave reactor furnace with different material thickness (6.59–23.41 mm) and ammonium tetramolybdate is heated for varying heating time (3.95–14.05 min) at different drying temperature (49.86–80.14°C). The experiments are carried out as follows: the initial weight (W₁) of ammonium tetramolybdate is obtained by weighting the sample in the Teflon container with the electronic balance, meanwhile setting and marking down the microwave heating temperature. Then, starting the drying experiments and the weight of ammonium tetramolybdate (W₂) is noted every t min after the temperature reaches set value. The dehydration ratio is calculated by the following equations:

where γ is the dehydration ratio, %. W₁ is the total mass of raw material and the Teflon container, g. W₂ is the total mass of material and the Teflon container after t min, g. W is the mass of the Teflon container, g. In the process, W was not changed. The σ is the moisture content of raw material, %. In this work, the σ is 17.23%.

2.4 Experiment’s design

Response surface methodology (RSM) is employed as a kind of design for experiments. RSM not only can be used for designing experiments, building models, estimating factorial effects and funding the best operant conditioning of the factors but also for statistics and dealing with the data [13–15]. Continuous variables of the model are funded, and the effects among factors are estimated by using response surface methodology; therefore, the best scopes of factors are determined.

Central composite design (CCD) is applied to investigate the effects of three independent variables, i.e. drying time, drying temperature and material thickness. Experimental data obtained from the CCD model experiments can be described in (2):

where γ is the predicated response; β₀ is a constant; β_i is the ith linear coefficient; β_ii is the ith quadratic coefficient; β_ij is the ijth interaction coefficient; and χ_ij is the independent variable.

3.1 Design of RSM

Based on the initial experiment, the scope of factors is determined. The three variables and two levels central composite design are employed to optimize the drying condition in order to obtain a high dehydration ratio. This method helps to optimize the effective parameters with a minimum number of experiments and also to analyze the interactions between the parameters and results [16]. The three independent variables set were χ₁ (drying time), χ₂ (material thickness), χ₃ (drying temperature), respectively, and each variable has set two levels. Optimization of microwave drying conditions for ammonium tetramolybdate is based on the numerical and graphical software. A total of 20 experiments are designed and shown in Table 1.

A total of 20 experiments are designed by the Design Expert Software (Version 7.15) from Stat-Ease Inc. (USA) and given in Table 2.

In these 20 experiments, eight factorial points, six axial points and six replicates at the central points are performed. The dehydration ratio is obtained under these experiments at the same external environment condition to avoid interference with others.

3.2 Model fitting

Model fitting is employed to choose the model based on the 20 experiments. This process is important for data analysis. If the worse model is chosen, then errors could be obtained [17]. The results of different model fittings are shown in Table 3.

Table 3 shows that the adjusted R-squared and the predicted R-squared of quadratic are better than others. The quadratic model is suggested.

The data from the experiments (Table 2) are analyzed by linear multiple regression software. The corresponding second-order response model for (3) is founded after analysis for the regression.

3.3 ANOVA of regression equation

The significance of the coefficients can be shown in (3) by ANOVA. In addition, the effectiveness of the model can be further judged. The ANOVA of regression equation is shown in Table 4.

Values of “Prob> F” less than 0.0500 indicate that the model terms are significant. In addition, the corresponding variables are more significant if the F value is greater and p value is smaller [18, 19]. It can be seen that χ_a , χ_b and χ_c and the interaction terms χ_aχ_b , χ_aχ_c and χa2 have significant effects on the response. However, other variables, such as χ_bχ_c , χb2,χc2, have nonsignificant effects to the response. Values of “Prob> F” greater than 0.1000 indicate that the model terms are not significant on dehydration ratio. The analysis of credibility of the model is shown in Table 5.

In Table 5, the correlation coefficient R² (R-squared) is 0.9792, close to 1, which indicates that the regression model is adequate, and the value of 97.92% is due to the change of independent variable; only an error of 2.08% could not be explained by this model [20]. The correction coefficient R_adj² (adj R-squared) is 0.9605, which indicates the independent variables are a linear correlation. The smaller the coefficient of variation (CV) and the better stability of the experiment, therefore, in this case 8.24% of the CV, indicates the credibility of this experiment research. The adequate precision denotes the signal-to-noise ratio (SNR). For a fixed model, adequate precision measurement of the SNR is necessary and desirable if the value of SNR is more than 4 [21]. The adequate precision is 27.544 (>4), which indicates that the quadratic model is applicable and commendable. As we can see, this regression equation could provide a good model for optimization of drying ammonium tetramolybdate by microwave heating.

Figure 2 shows the relationship between predicated dehydration ratio and the experimental values. It could detect a value, or group of values, that are not easily predicted by the model. The data points are split evenly by the 45° line, indicating the model could represent the relation between independent variable and dependent variable.

Figure 2:

Predicted vs. experimental relative dehydration ratio.

3.4 Analysis of RSM

The results of the experiments are analyzed by a three-dimensional mathematical model. The effects of different variables’ interaction are obtained and result in three three-dimensional figures, i.e. Figure 3, Figure 4 and Figure 5.

Figure 3:

Interactive effect of material thickness and drying time on dehydration ratio.

Figure 4:

Interactive effect of drying temperature and time on dehydration ratio.

Figure 5:

Interactive effects of drying temperature and material thickness on dehydration ratio.

Figure 3 shows the interactive effect of material thickness and drying time on the dehydration ratio. As can be seen, the dehydration ratio increases with the drying time increasing and material thickness declining. However, the tendency of growing is slowly weakened. The effect of drying time is more and more obvious, with the increase of material thickness. It may be explain that the interior moisture is migrated hard to the surface, and migration rate is less than surface vaporizing rate. With the increase of material thickness, the evaporation of water is more and more difficult [22].

The interactive effects between drying temperature and time on the dehydration ratio are shown in Figure 4. As can be seen, the interactive effect of drying temperature and time on the dehydration ratio is significant. The effects of drying temperature and time are approximate. The dehydration ratio is no more than 20% with temperature of 56°C and drying time of 6 min. However, when the drying time is doubled, the dehydration ratio achieves 80%. Thus, extending drying time is beneficial to improving the dehydration ratio. The drying temperature changes from 56°C to 74°C, and the dehydration ratio is improved from 19% to 73% at drying time of 6 min. But when the drying time is 12 min, the dehydration ratio is only improved from 80% to 98%. Consequently, moisture could be removed quickly by enhancing lower temperatures, but if desiring a greater level of dehydration, the drying time must be extended.

Figure 5 shows the interactive effect of drying temperature and material thickness on dehydration ratio. As the figure shows, the dehydration ratio increases with decreasing material thickness and raising drying temperature. The dehydration ratio is reached 100% with drying temperature 74°C and material thickness 10 mm. The evaporation of moisture needs to absorb energy, so the higher temperature fixed indicates the energy could be improved quickly. Meanwhile, the microwave cannot penetrate the material if material is too thick; conversely, if material is too thin, the ammonium tetramolybdate may stimulate the “spark phenomenon”, and it is a disadvantage for the drying process. Therefore, the faster evaporation rate, the faster removal of moisture could be.

3.5 Parameter optimization and validation

The molybdenum content of ammonium tetramolybdate must be not <56% (wb). Thus, the dehydration ratio must be <77.42%. The result of parameter optimization by RSM is given in Table 6.

In order to examine the reliability of parameter optimization by RSM, an experiment is completed under the optimized parameter. The accuracy of the parameter could not become true; therefore, the drying time is approximate at 9.5 min, the material thickness is approximately 15 mm and the drying temperature is approximately 67°C. Thus, the experimental dehydration ratio with three repetitions are 79.14%, 79.23% and 79.17%, with an average of 79.18%, compared to the predicted value. The deviation is only -0.64%. The last molybdenum content, not <56.3% (wb), reached the demand.

3.6 Comparison of microwave and conventional heating

The effect of drying time on dehydration ratio between microwave and conventional heating is shown in Figure 6. The microwave drying process is completed with drying temperature of 67°C, material thickness of 15 mm and different drying time under microwave a power of 2.0 kW. Meanwhile, the material is carried out in an oven at a power of 2.05 kW under the same condition. As can be seen that the conventional heating consumes 100 min when the dehydration ratio is 80.4%, whereas the dehydration ratio is 79.18% with 9.5 min under microwave heating, indicating that microwave heating has greater ability to shorten time than the conventional heating for drying ammonium tetramolybdate. In addition, considering energy consumption, the energy consumption is 0.32 kW·h when the dehydration ratio is 79.18% using microwave heating, however, it is 3.42 kW·h using oven heating. Therefore, microwave heating has advantages of rapidity and energy conservation than conventional heating. It has great significance in clean and efficient production for drying ammonium tetramolybdate and provides the theoretical basis.

Figure 6:

Effect of drying time on dehydration ratio using oven and microwave heating.