# Ultrasonic-Assisted Extraction and Swarm Intelligence for Calculating Optimum Values of Obtaining Boric Acid from Tincal Mineral

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}O

_{3}), amking Turkey the world’s major supplier [2,3].

_{2}B

_{4}O

_{7}·10H

_{2}O), colemanite (Ca

_{2}B

_{6}O

_{11}·5H

_{2}O), and ulexite (NaCaB

_{5}O

_{9}·8H

_{2}O). In the western part of Turkey, the most of the boron ore reserves are found, and the main boron mineral is found as tincal ores, which naturally exist in Eskisehir City. Others are mainly located in Bigadic-Balıkesir, Emet-Kütahya, and Kestelek-Bursa as colemanite, and Bigadic-Balıkesir and Kestelek-Bursa as ulexite [4,5,6].

^{3}. Its aggregates have white and colorless crystalline states [7]. In the literature, the extraction of boric acid from tincals has been accomplished using mostly different organic acid solutions. Researchers have used hydrochloric acid [8], sulfur dioxide saturated water [9], and chlorine saturated water [10], ammonium chloride [11], phosphoric acid [12], oxalic acid [13], and sulfuric acid [14] to obtain boric acid from minerals. The boric acid extraction methods from tincal include electrolysis condcuted at 80 °C with aqueous solution of sulfuric acid [15,16], and boric acid separation using sodium sulphate solution in cold crystallization [17]. When it is being processed by the thermal method it ends up with a 20–29% of boric acid content, whereas when it is subjected to enrichment processes boric acid content could be icnreased to 32% [18]. However, in Turkey, sulfuric acid is the solvent that is generally used to produce boric acid from tincal [19]. Unfortunately, these methods involve long and tedious steps requiring large quantities of toxic solvents, which have costly disposing procedures after extraction, longer extraction times, and complex manipulation, etc.

## 2. Materials and Methods

#### 2.1. Materials and Chemical Analysis

_{2}gas at a heating rate of 5 °C/min. At the end of the heating step, a weight loss of nearly 50% was measured. In addition, attenuated total reflectance of FTIR (Fourier-Transform Infrared) spectroscopy (Shimadzu Corp., Kyoto, Japan) was also used to identify the chemical bonds in the tincal samples.

#### 2.2. Experimental Design for Ultrasound-Assisted Extraction (UAE)

_{1}), pH (X

_{2}), extraction time (X

_{3}), and temperature (X

_{4}) were utilized where X represents for an independent variable (Table 1). The CCD contained a total of 30 experiments. To detect the effect of these four variables responsible for the yield of boric acid extraction, each variable was considered at five different levels in the CCD lowest, low, center, high and highest coded as −2, −1, 0, +1, and +2, respectively (Table 1). The full experimental design was shown in Table 2. The yield of UAE was considered to be the experimental response.

_{0}is the amount of boric acid in the tincal ore. The yield results were shown in Table 2.

#### 2.3. Data Analysis

_{0}+ β

_{1}X

_{1}+ β

_{2}X

_{2}+ β

_{3}X

_{3}+ β

_{4}X

_{4}+ β

_{11}X

_{12}+ β

_{22}X

_{22}+ β

_{33}X

_{32}+ β

_{44}X

_{42}+ β

_{12}X

_{1}X

_{2}+ β

_{13}X

_{1}X

_{3}+ β

_{14}X

_{1}X

_{4}+ β

_{23}X

_{2}X

_{3}+ β

_{24}X

_{2}X

_{4}+ β

_{34}X

_{3}X

_{4}

_{1}, X

_{2}, …, X

_{k}are the independent variables indicate the response Y. β

_{0}, β

_{j}(i = 1, 2, …, k), β

_{ii}(i = 1,2, …, k) and β

_{ij}(i = 1, 2, …, k; j = 1, 2, …, k) are the offset term, linear coefficient, quadratic coefficient, and interaction coefficient, respectively, and k is the quantity of each variable. Here, Equation (3) is the obtained result from Equation (2). These equations have been taken through some regression process to obtain further equations. p = 0.05 was taken into consideration in the variance analysis (ANOVA). The quality of the model was presented by the coefficient of determination (R

^{2}).

#### 2.4. Artificial Intelligence-Based Swarm Intelligence Techniques for Optimization

**Particle Swarm Optimization:**As introduced by Kennedy and his friends [34,35], the particle swarm optimization (PSO) algorithm is a simple and easy-to-design optimization algorithm, which inspires from social behaviors, shown by bird flock or fish school. In the PSO process, a swarm of particles (candidate solutions) are located in the solution space and then the optimum value(s) are tried to be found by the swarm by following a mechanism, like searching for food source in the nature. PSO is an important intelligent optimization since it employs simple, but effective, mathematical calculations to simulate swarm behaviors for solving optimization problems. In detail, the following points are essential for the default PSO algorithmic flow [34,35]:- ○
- All particles have position (variable value) and velocity parameters, which are changed iteratively during the solution process.
- ○
- Velocity is a parameter determining the next movement-direction of a particle.
- ○
- For each particle, movements are affected by its own best known position as well as the best known position (global optimum) within the swarm.
- ○
- As general, particle movements affect the solution flow of the whole swarm and the searching mechanism is run until a stopping criterion (like objective optimum value(s) or total iteration number, total particle numbers, etc.) is met.

**Cuckoo Search:**Cuckoo search (CS) is a popular and simple structured intelligent optimization algorithm as developed by Yang and Deb [36]. Briefly, CS tries to simulate the obligate brood parasitism of some cuckoo species as such species lay the eggs in the nests of other host birds and, in this sense, some of the host birds can engage in conflicts with the intruding cuckoos [37]. As a natural reaction, sometimes a host bird throws such cuckoo eggs out of nests or forms a new nest in a different place after leaving the nest including foreign eggs [36]. In order to simulate an optimization approach in this algorithm, the following mechanisms are employed in an algorithmic manner [36,37]:- ○
- Eggs in the nests are for potential solutions and a cuckoo egg is associated with a new solution.
- ○
- In the algorithm, each nest has one egg free space or multiple eggs free space according to the considered problem details.
- ○
- The main objective here is to use new solutions (if they are better) to replace worse solutions taking place in the nests.
- ○
- Along the solution process, a cuckoo lays one egg at a time and locates an egg in a nest randomly determined.
- ○
- The nests with good eggs (good solutions) are kept for next generations through the algorithmic process.
- ○
- In terms of random solution chances, a cuckoo egg can be detected by a host bird according to a calculated probability.
- ○
- Algorithmic solution steps are run according to some stopping criteria, like objective optimum value(s) or total iteration number, total particle numbers, etc.

**Genetic Algorithms:**As a long-used, popular intelligent algorithm, genetic algorithms (GA) is widely used in optimization problems. As inspired from well-known mechanisms of evolution theory, GA tries to use the objective of naturally selected, good populations for reaching to desired optimum results in the considered problems. At this point, particles in a typical GA are coded (i.e., with binary codes) as in the form of chromosome and during the algorithmic solution process, genes of each particle’s chromosome are taken into some evolution-based updates, like cross-over and mutation [38,39]. In the roots of the algorithm, it is aimed to consider well-produced generations according to their parents to deal with the objective problem better and, in this way, run a natural selection process to obtain the desired results quickly. Some essential points for a default GA can be expressed as follows [38,39,40]:- ○
- Particles (individuals) having better solutions are taken into the cross-over process according to some pre-determined rules, in order to produce new generations.
- ○
- Some members of each new generation are taken into also mutation process to run a chance approach for getting potentially better particles.
- ○
- There are different types of mechanisms to determine which particles will receive cross-over and mutation operations with which parameter/probability values.
- ○
- Algorithmic solution steps are run according to some stopping criteria like objective optimum value(s) or total iteration number, total particle numbers, etc.

**Differential Evolution:**The differential evolution (DE) algorithm is another intelligent optimization technique, which inspires from mechanisms of the evolution theory, like GA. As developed by Storn and Price, DE employs particles in the form of parameter vectors and run mutation and cross-over processes over them to obtain new generations for better optimum values [41]. In the context of mutation, new parameter vectors are created by summing a weighted difference calculated between two vectors (particles) with a third vector. On the other hand, the cross-over is conducted by mixing mutated vectors’ parameters with some other determined vectors, which are called trial vectors. After that process, if a trial vector (particle) has a better fitness value-result, then it is replaced with the associated vector [41,42]. As it can be understood, default DE uses real numbers rather than specific codes used generally in a typical GA.

**Vortex Optimization Algorithm:**The vortex optimization algorithm (VOA) is a recent intelligent optimization algorithm, which was developed by Kose and Arslan [43,44], inspired from vortices in the nature. In the algorithm, particles go through two roles of being a vortex or a normal particle. In detail, a selection process has also been employed to benefit from an evolutionary mechanism for keeping particles with better solutions alive in the solution process. That mechanism can be explained briefly as follows: After fitness calculation, a certain number of ‘non-vortex’ particles (defined with e: elimination rate) whose fitness are worse than average fitness value are removed from the search space and new particles with the same number of eliminated particles are randomly placed in the search space, just before the next iteration. The algorithm also uses an in-system optimization approach to improve the quality of optimization in especially larger problems. The in-system optimization has been done when the total number of particles located out of a certain ‘flow-circle’ (fc: defined with a radius) are above 60% of all particles. The process has been done by normalizing—adjusting variables of ‘vortex’ particles (having better fitness value than the average) to the variables of the current global optimum particle (vortex). Details regarding the algorithm were shaped in time with the performed alternative works [43].

## 3. Results and Discussion

#### 3.1. Characterization of Tincal

^{−1}and 880 cm

^{−1}indicated the characteristic peaks of tincal. When the FTIR spectrum is examined in detail, the decreasing peaks shown with red lines correspond to B

_{2}O

_{3}content due to Tinkal removal. On the other hand, B

_{2}O

_{3}content is high in the peaks shown with blue lines, which also supports the presence of OH peaks. Vibration bands belonging to the 728–880 cm

^{−1}titanium range Na–O are supported with peaks.

#### 3.2. Optimization Analysis of the Central Composite Design

_{1}, X

_{2}, X

_{3}, and X

_{4}, respectively. For the optimization, boric acid extraction yield was considered as dependent variable (or response) of the study. The design table and the yield results are given in Table 2.

^{2}indicates how the dependent variable is explained well by the independent variables while adjusted R

^{2}is for a similar explanation rate as adjusted for the number of independent variables that time. Finally, predicted R

^{2}indicates predictive quality level of the model against new observations and prediction error sum of squares (PRESS) shows the model competency by considering the sum of the squared differences between the experimental response and the predicted response by the regression model. Joglekar and May were proposed that for a significant model, R

^{2}values should be at least 0.80 [45]. In our study, the R

^{2}values of the response were greater than 0.80. For instance, in our study, R

^{2}was 0.9001 indicating that our statistical model is able to explain 90.01% of the variability in the response. In addition, ‘adjusted R

^{2}’ and the ‘predicted R

^{2}’ values were found as 0.8101 and 0.8079, respectively. However, high R

^{2}and predicted R

^{2}values confirm the high significance of our model. Additionally, it can be seen that the predicted and adjusted R

^{2}values are slightly smaller than the R

^{2}value. In relation to this, it was declared that this is an acceptable situation if there are many terms in a design, which is the case of our study [25].

_{4}, X

_{1}X

_{3}, X

_{1}X

_{4}, X

_{2}X

_{4}, X

_{12}, X

_{22}, and X

_{42}were found as the significant terms for the response.

_{4}) was the most important for the boric acid extraction, and the least effective term was solid/solvent ratio (X

_{1}). In Table 2, it can be seen that the highest yields were observed when the extraction temperature is equal to or higher than 90 °C (such as in the experiments 8, 10, and 27). The next term that showed less individual effect was found to be extraction time (X

_{3}). However, by analyzing the mutual effects in the RSM, solid/solvent ratio and extraction time together (X

_{1}X

_{3}) showed a great effect on the yield, as well as solid/solvent ratio and extraction temperature together (X

_{1}X

_{4}). In case of pH, only X

_{2}X

_{4}and X

_{22}were found to be significant (Table 4). In addition, in order to confirm that CCD and its outcomes are acceptable and reproducible, ‘adequate precision’ of the response was determined by ANOVA. In the literature, a ratio greater than 4 is found to be too attractive, and a ratio greater than 4 is generally expected, and a higher value is accepted as the better [46]. Our ratio was 11.610 and indicated that this model is suitable to be used to navigate the design space for this study.

_{1}− 23.22722 X

_{2}− 6.49975 X

_{3}− 3.69762 X

_{4}+ 0.51572 X

_{1}X

_{2}+ 0.13322 X

_{1}X

_{3}+ 0.069186 X

_{1}X

_{4}− 0.038608 X

_{2}X

_{3}− 0.17424 X

_{2}X

_{4}+ 0.007476 X

_{3}X

_{4}+ 0.21589 X

_{12}+ 3.20892 X

_{22}+ 0.029597 X

_{32}+ 0.019882 X

_{42}

_{1}, X

_{2}, X

_{3}, and X

_{4}are the solvent/solid ratio, pH, extraction time, and extraction temperature, respectively. As it was mentioned earlier, highly significant and significant factors for the model (p < 0.05) were X

_{4}, X

_{1}X

_{3}, X

_{1}X

_{4}, X

_{12}, X

_{22}, X

_{42}, and X

_{2}X

_{4}. The rest of the factors were found to be insignificant and. thus, these insignificant regression coefficients were removed from Equation (4) to get a better model equation and it was described as Equation (5) below:

_{4}+ 0.13322 X

_{1}X

_{3}+ 0.069186 X

_{1}X

_{4}− 0.17424 X

_{2}X

_{4}+ 0.21589 X

_{12}+ 3.20892 X

_{22}+ 0.019882 X

_{42}

#### 3.3. Traditional and Intelligent Optimization

## 4. Conclusions and Future Work

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**General scheme of the solution approach in this study. UAE: ultrasonic-assisted extraction; CCD: central composite design; RMS: Response surface methodology.

**Figure 6.**Default solution flow idea under the early vortex optimization algorithm [44].

**Figure 7.**The XRD pattern analysis of solid phase tincal that was obtained from the separation process (the 0.075 mm (200-mesh) fraction) (the highest peak indicates tincal).

**Figure 8.**FTIR (Fourier Transform Infrared) spectra (made to illuminate the chemical structure of tincals) of solid phase tincal exhibited the infrared absorption bands (the bands at 728 cm

^{−1}and 880 cm

^{−1}show the characteristic peaks of tincal).

**Figure 9.**Thermal dehydration of tincal with thermal analysis with TG (green) and DTA (blue) curves regarding standard tincal.

**Figure 10.**Parity plot of CCD (actual and predicted values for the designed response) pointing to a powerful linear relationship.

**Figure 11.**Response surface plot shows the individual and synergistic effects of (

**A**) pH and solvent/solid ratio (mL/g); (

**B**) extraction time (min) and solvent/solid ratio (mL/g); (

**C**) extraction temperature (°C) and solvent/solid ratio (mL/g); (

**D**) extraction time (min) and pH; (

**E**) extraction temperature (°C) and pH; and (

**F**) extraction temperature (°C) and extraction time (min) on the boric acid extraction yield (%).

**Table 1.**Coded levels (at five levels of lowest, low, center, high and highest coded as −2, −1, 0, +1, and +2, respectively) of independent variables used in the central composite design (CCD).

Indep. Variables | Symbol | Levels | ||||
---|---|---|---|---|---|---|

Lowest | Low | Center | High | Highest | ||

−2 | −1 | 0 | +1 | +2 | ||

Solvent/solid ratio (mL/g) | X_{1} | 15 | 20 | 25 | 30 | 35 |

pH | X_{2} | 1 | 2 | 3 | 5 | 7 |

Extraction time (min) | X_{3} | 30 | 40 | 50 | 60 | 70 |

Extraction temperature (°C) | X_{4} | 30 | 50 | 70 | 90 | 100 |

**Table 2.**Central composite design (CCD) used in this study and yield results by considering different solvent/solid ratio, pH, extraction time, and extraction temperature.

Run | Solvent/Solid Ratio (mL/g) | pH | Extraction Time (min) | Extraction Temperature (°C) | Yield (%) |
---|---|---|---|---|---|

1 | 30 | 5 | 40 | 50 | 40 |

2 | 20 | 5 | 40 | 90 | 54.5 |

3 | 20 | 2 | 40 | 90 | 66.45 |

4 | 25 | 3 | 50 | 70 | 30 |

5 | 30 | 5 | 60 | 50 | 51.25 |

6 | 25 | 3 | 50 | 70 | 30.5 |

7 | 25 | 3 | 50 | 30 | 26.25 |

8 | 25 | 3 | 50 | 100 | 79.25 |

9 | 25 | 3 | 50 | 70 | 29.5 |

10 | 30 | 5 | 60 | 90 | 82.75 |

11 | 25 | 3 | 50 | 70 | 29.75 |

12 | 30 | 5 | 40 | 90 | 49.75 |

13 | 20 | 5 | 50 | 50 | 39.375 |

14 | 20 | 5 | 60 | 90 | 36.375 |

15 | 25 | 3 | 70 | 70 | 43.125 |

16 | 30 | 2 | 40 | 50 | 28.25 |

17 | 15 | 3 | 50 | 70 | 55 |

18 | 25 | 3 | 50 | 70 | 30.75 |

19 | 20 | 2 | 40 | 50 | 53.125 |

20 | 25 | 3 | 50 | 70 | 30 |

21 | 20 | 5 | 40 | 50 | 50 |

22 | 25 | 7 | 50 | 70 | 62.75 |

23 | 20 | 2 | 60 | 50 | 50.25 |

24 | 25 | 3 | 30 | 70 | 34.875 |

25 | 30 | 2 | 40 | 90 | 63.75 |

26 | 30 | 2 | 60 | 50 | 32.5 |

27 | 30 | 2 | 60 | 90 | 82.5 |

28 | 25 | 7 | 50 | 70 | 50.35 |

29 | 35 | 3 | 50 | 70 | 42.5 |

30 | 20 | 2 | 60 | 90 | 58.75 |

Source | Std. Dev. | R^{2} | Adjusted R^{2} | Predicted R^{2} | PRESS | |
---|---|---|---|---|---|---|

Linear | 14.04 | 0.3667 | 0.2611 | 0.0332 | 7217.32 | |

2FI | 12.35 | 0.6324 | 0.4281 | −0.0465 | 7812.20 | |

Quad. | 7.30 | 0.9001 | 0.8101 | 0.8079 | 5316.28 | Suggest. |

Cubic | 3.47 | 0.9887 | 0.9549 | - | + | Alias. |

Variable | Sum of Square | df | Mean Square | F-Value | p-Value | |
---|---|---|---|---|---|---|

Model | 6714.29 | 14 | 479.95 | 9.01 | <0.0001 | Very significant |

X_{1} | 0.47 | 1 | 0.47 | 8.802 × 10^{−3} | 0.9266 | |

X_{2} | 232.16 | 1 | 232.16 | 4.36 | 0.0556 | |

X_{3} | 24.28 | 1 | 24.28 | 0.46 | 0.5107 | |

X_{4} | 545.01 | 1 | 545.01 | 10.23 | 0.0064 | |

X_{1}X_{2} | 211.76 | 1 | 211.76 | 3.97 | 0.0661 | |

X_{1}X_{3} | 709.89 | 1 | 709.89 | 13.32 | 0.0026 | |

X_{1}X_{4} | 684.06 | 1 | 684.06 | 12.84 | 0.0030 | |

X_{2}X_{3} | 4.21 | 1 | 4.21 | 0.079 | 0.7826 | |

X_{2}X_{4} | 403.36 | 1 | 403.36 | 7.57 | 0.0156 | |

X_{3}X_{4} | 35.78 | 1 | 35.78 | 0.67 | 0.4263 | |

X_{1}^{2} | 678.86 | 1 | 678.86 | 12.74 | 0.0031 | |

X_{2}^{2} | 635.82 | 1 | 635.82 | 11.93 | 0.0039 | |

X_{3}^{2} | 204.15 | 1 | 204.15 | 3.83 | 0.0705 | |

X_{4}^{2} | 1194.79 | 1 | 1194.79 | 22.42 | 0.0003 | |

Residual | 745.97 | 14 | 53.28 | |||

Lack of Fit | 668.01 | 8 | 83.50 | 6.43 | 0.0179 | Highly significant |

Pure error | 77.96 | 6 | 12.09 | |||

Cor. Total | 7949.77 | 29 | ||||

Adeq. Precision | 11.610 |

_{1}= solvent/solid ratio, X

_{2}= pH, X

_{3}= extraction time, X

_{4}= extraction temperature, df = degrees of freedom. p < 0.0100 is significant, 0.0100 ≤ p < 0.0500 is highly significant, p ≥ 0.0500 is not significant. Cor. Total of all information corrected for the mean.

**Table 5.**The optimum conditions for the boric acid extraction from tincal (by considering different intelligent optimization algorithms and also Design Expert).

Technique/Method | Solvent/Solid Ratio (mL/g) | pH | Extract. Time (min) | Extract. Temperature (°C) | Yield (%) |
---|---|---|---|---|---|

PSO | 31.64 | 4.58 | 47.78 | 95.79 | 84.42 |

CS | 34.15 | 4.70 | 48.93 | 99.67 | 91.56 |

GA | 31.72 | 4.64 | 46.82 | 96.13 | 85.08 |

DE | 33.67 | 4.66 | 48.86 | 98.81 | 89.52 |

VOA | 32.76 | 4.60 | 47.68 | 98.58 | 87.84 |

Design Expert | 32.72 | 4.66 | 48.61 | 98.55 | 88.13 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Gezer, B.; Kose, U.
Ultrasonic-Assisted Extraction and Swarm Intelligence for Calculating Optimum Values of Obtaining Boric Acid from Tincal Mineral. *Processes* **2019**, *7*, 30.
https://doi.org/10.3390/pr7010030

**AMA Style**

Gezer B, Kose U.
Ultrasonic-Assisted Extraction and Swarm Intelligence for Calculating Optimum Values of Obtaining Boric Acid from Tincal Mineral. *Processes*. 2019; 7(1):30.
https://doi.org/10.3390/pr7010030

**Chicago/Turabian Style**

Gezer, Bahdisen, and Utku Kose.
2019. "Ultrasonic-Assisted Extraction and Swarm Intelligence for Calculating Optimum Values of Obtaining Boric Acid from Tincal Mineral" *Processes* 7, no. 1: 30.
https://doi.org/10.3390/pr7010030