# Development of Molecular Distillation Based Simulation and Optimization of Refined Palm Oil Process Based on Response Surface Methodology

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Molecular Distillation Process: Modeling and Validation

## 3. Refined Palm Oil Deodorization Process Simulation by ASPEN HYSYS

^{−4}and 8 × 10

^{−4}kPa, at a temperature of 175 °C–180 °C and a feed flow rate between 250 and 2000 kg/h [11]. The vapor pressure estimations and the simulation of refined palm oil are discussed below.

#### 3.1. Vapor Pressure Estimation

_{B}), critical temperature (T

_{C}), critical pressure (P

_{C}), acentric factor (ω) and liquid molar volume (V

_{l20}) for each component, and can be seen in Table A1 in the Appendix, as accomplished by Lim et al. [13]. Equation (2) refers to an extension of the Antoine equation from Lim et al.’s work, and its parameters are shown in Table 3. However, the equation available in ASPEN HYSYS is shown in Equation (3). Therefore, the parameters of the Antoine equation used in this study were obtained by minimizing the least square error of Equation (4) through Solver Add-in, in Microsoft Excel and Matlab optimization.

^{calc}= A

_{1}− B

_{1}/T + C

_{1}T + D

_{1}·lnT + E

_{1}T

^{6}

^{exp}= A

_{2}+ B

_{2}/(T + C

_{2}) +D

_{2}·lnT + E

_{2}T

^{6}

^{2}) of each component are summarized in Table 4. The coefficient of determination was calculated by regression data analysis in Microsoft Excel between the correlation of lnP

^{calc}and lnP

^{exp}as Equation (5).

#### 3.2. Refined Palm Oil Deodorization Process Simulation and Validation

## 4. RSM-Based Process Model

^{k}factorial design (level are coded as 1 and −1), 2k axial portion and the number of center point. In this case, the least number of 3 center points is used. Therefore, the design contained a total of 17 simulation runs according to Equation (6) [16]:

^{k}+ 2k + n

_{0}

_{0}is number of center points.

_{1}), distillation temperature (x

_{2}), and pressure (x

_{3}) were independent variables. These three variables are used and assumed to influence the responses of beta-carotene concentration (y

_{1}), tocopherol concentration (y

_{2}) at residue stream and free fatty acid (oleic acid) concentration (y

_{3}) in the distillate stream.

_{i}and x

_{i}are coded and actual values of variable i, respectively; and subscript i are 1 = feed flow rate, 2 = column temperature and 3 = column pressure, and H, L are highest and lowest values.

_{1}), (y

_{2}) and (y

_{3}). The regression coefficient value for linear, quadratic and interaction are shown in Table 9.

#### 4.1. The Effect of Feed Flow Rate on Responses

_{1}), tocopherol (y

_{2}) and FFA (y

_{3}) are investigated at a temperature of 150 °C and pressure of 5.05 × 10

^{−4}kPa (run No. 2 and 3). Decreasing the feed flow rate from 1500 to 1000 kg/h at constant temperature and pressure does not make any changes to the responses. The contour plots and response surface curves in Figure 5, Figure 6 and Figure 7, reveal that the feed flow rate does not show significant deviation on responses.

#### 4.2. The Effect of Temperature on Responses

^{−4}kPa respectively (run no. 4 and 5). In Figure 8, Figure 9 and Figure 10, the temperature shows significant deviation in the responses of beta-carotene (y

_{1}), tocopherol (y

_{2}) and FFA (y

_{3}). It can be clearly seen that, the concentrations of the responses decrease with increasing the distilling temperature. According to the Clauses Clapeyron relation, the vapor pressure of substance increases non-linearly with temperature. Therefore, increasing temperature (Equation (11)) will increase mean free path which will lengthen the average distance of traveling molecule reaching the condensation board. The longer the distance of molecule travels the higher the rate of vaporization of molecule. As a result, low concentration of beta-carotene and tocopherol are found in the residue and low concentration of free fatty acid is found in the distillate.

#### 4.3. The Effect of Pressure on Responses

_{A}is Avogadro’s number and P is the pressure.

_{1}, x

_{1}x

_{2}, and x

_{1}x

_{3}are not considered in this case due to the insignificant effect to the responses.

_{1}= 5.25 × 10

^{−4}− 2.49 × 10

^{−4}x

_{2}+ 1.83 × 10

^{−4}x

_{3}+2.42 × 10

^{−5}x

_{1}

^{2}− 1.88 × 10

^{−4}x

_{2}

^{2}− 2.15 × 10

^{−4}x

_{3}

^{2}+ 2.07 × 10

^{−4}x

_{2}x

_{3}

_{2}= 8.60 × 10

^{−4}− 4.12 × 10

^{−4}x

_{2}+ 2.92 × 10

^{−4}x

_{3}+ 3.54 × 10

^{−5}x

_{1}

^{2}− 3.31 × 10

^{−4}x

_{2}

^{2}− 3.56 × 10

^{−4}x

_{3}

^{2}+ 3.38 × 10

^{−4}x

_{2}x

_{3}

_{3}= 9.15 × 10

^{−1}− 5.34 × 10

^{−1}x

_{2}+ 2.69 × 10

^{−1}x

_{3}− 1.63 × 10

^{−3}x

_{1}

^{2}− 3.74 × 10

^{−1}x

_{2}

^{2}− 3.91 × 10

^{−1}x

_{3}

^{2}+ 2.50 × 10

^{−1}x

_{2}x

_{3}

^{2}value of responses, concentration of beta-carotene, tocopherol and FFA are 0.959, 0.961 and 0.951 respectively, show a very good fit. The nonlinear Equations (12)–(14) now represent the MD process model which will be used for optimizing the process in the next section.

## 5. Optimization of MD for Refined Palm Oil Process

_{1}, y

_{2}and 0.3 for y

_{3}. The optimization variables are feed flow rate, temperature and pressure. Lower and upper bounds for variables are specified between a valid lower and upper bound. The actual (re-scaled) upper bound and lower bound is shown in the Table 10.

_{1}+ y

_{2}) + 0.3y

_{3}

_{1}≤ 2000, 100 ≤ x

_{2}≤ 200, 0.00001 ≤ x

_{3}≤ 0.001, 0≤ y

_{1}≤ 1, 0 ≤ y

_{2}≤ 1, 0 ≤ y

_{3}≤ 1.

_{1}, x

_{2}and x

_{3}were found to be 1291 kg/h, 147 °C and 0.0007 kPa, respectively, and the corresponding responses of y

_{1}, y

_{2}and y

_{3}were 0.000575, 0.000937 and 0.999840, respectively.

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix

**Table A1.**Physical properties of pure components in palm oil, reproduced with permission from [13]. Copyright Springer, 2003.

Component | T_{B} (K) | T_{C} (K) | P_{C} (kPa) | ω | V_{l20} (m^{3}/kmol) |
---|---|---|---|---|---|

Tripalmitin | 864.21 | 947.10 | 396.82 | 1.6500 | 0.8906 |

Triolein | 879.92 | 954.10 | 360.15 | 1.8004 | 0.9717 |

Oleic acid | 646.52 | 813.56 | 1250.2 | 0.8104 | 0.3172 |

Tocopherol | 794.52 | 936.93 | 838.45 | 1.1946 | 0.4533 |

Beta-carotene | 908.58 | 1031.1 | 678.41 | 1.6255 | 0.5348 |

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**Figure 1.**Comparison of distillated mass flow rate in study [10] and this work as a function of flash vessel operating temperature (°C).

**Figure 2.**Comparison of distillate mole fraction in study [10] and this work as a function of flash vessel operating temperature (°C).

**Figure 4.**Carotene recovery of refining of edible oil in study [11] and this work.

**Figure 5.**Response surface curve (

**a**) and contour plot (

**b**) of beta-carotene concentration as a function of temperature and feed flow rate.

**Figure 6.**Response surface curve (

**a**) and contour plot (

**b**) of tocopherol concentration as a function of temperature and feed flow.

**Figure 7.**Response surface curve (

**a**) and contour plot (

**b**) of FFA concentration as a function of temperature and feed flow.

**Figure 8.**Response surface curve (

**a**) and contour plots (

**b**) of beta-carotene concentration as a function of temperature and pressure.

**Figure 9.**Response surface curve (

**a**) and contour plot (

**b**) of tocopherol concentration as a function of temperature and pressure.

**Figure 10.**Response surface curve (

**a**) and contour plot (

**b**) of free fatty acid (FFA) concentration as a function of temperature and pressure.

Parameters | DIMSOL | ASPEN PLUS [10] | ASPEN HYSYS (This Work) |
---|---|---|---|

Operating temperature (K) | 369 | 336 | 336 |

Distillation mass ratio | 0.212 | 0.212 | 0.212 |

Distillation DBP molar fraction | 0.775 | 0.790 | 0.793 |

Residue DBP molar fraction | 0.429 | 0.409 | 0.420 |

Components | Mass Fraction | MW | Formula | CAS No. |
---|---|---|---|---|

Tripalmitin | 0.493682 | 807.320 | C_{51}H_{98}O_{6} | 555-44-2 |

Triolein | 0.470891 | 885.449 | C_{57}H_{104}O_{6} | 122-32-7 |

Oleic acid | 0.033899 | 282.467 | C_{18}H_{34}O_{2} | 112-80-1 |

Tocopherol | 0.000886 | 430.706 | C_{29}H_{50}O_{2} | 59-02-9 |

Beta-carotene | 0.000552 | 536.873 | C_{40}H_{56} | 7235-40-7 |

**Table 3.**Pure component parameters for Equation (2), reproduced with permission from [13]. Copyright Springer, 2003.

Component | Antoine Parameters | ||||
---|---|---|---|---|---|

A_{1} | B_{1} | C_{1} | D_{1} | E_{1} | |

Tripalmitin | 108,841 | −4,098,952 | 19.96 | −17,792 | −3.6 × 10^{−15} |

Triolein | −514,215 | 19,737,838 | −91.13 | 83,685 | 1.4 × 10^{−15} |

Oleic acid | 136.45 | −19,702 | −0.01 | −14.87 | 7.2 × 10^{−}^{19} |

Tocopherol | −15.90 | −5118 | 0.05 | 0 | 0.00 |

β-carotene | −91.32 | −15.90 | 0.239 | 0 | 0.00 |

Component | Antoine Parameters | R^{2} | ||||
---|---|---|---|---|---|---|

A_{2} | B_{2} | C_{2} | D_{2} | E_{2} | ||

Tripalmitin | 1.509 × 10^{5} | 1.196 × 10^{5} | −0.074 × 10^{5} | −0.21 × 10^{5} | 0.00 | 0.99 |

Triolein | −0.013 × 10^{7} | −3.170 × 10^{7} | 0.000 | 0.000 | 0.00 | 0.99 |

Oleic acid | 519.688 | −0.106 | −399.010 | −71.37 | 0.00 | 0.99 |

Tocopherol | −64.849 | 594.994 | −219.253 | 13.052 | 0.00 | 0.99 |

β-carotene | 24.079 | −16,160 | −100.623 | 5.191 | 0.00 | 0.99 |

**Table 5.**Simulations results of refining of edible oil in study [11] and this work.

Condition | Distillation Mass Ratio | Patent Recovery | Simulation Recovery | Prediction Error | ||
---|---|---|---|---|---|---|

kg/h | Percent (%) | kg/h | Percent (%) | (%) | ||

Simulation 1 | 0.036 | 1.0395 | 95.98% | 1.0351 | 98.96% | 3.1% |

Simulation 2 | 0.036 | 0.5449 | 98.73% | 0.5467 | 99.03% | 0.3% |

Simulation 3 | 0.036 | 0.1249 | 98.03% | 0.1266 | 99.29% | 1.218% |

Simulation 4 | 0.036 | 0.2969 | 97.38% | 0.3258 | 99.25% | 1.87% |

**Table 6.**Central composite circumscribed (Min and Max = Star Points) design with three independent variables.

Coded Variables | |||
---|---|---|---|

Run | X_{1} | X_{2} | X_{3} |

1 | 0 | 0 | −1 |

2 | 0 | 0 | 0 |

3 | −1 | 0 | 0 |

4 | 0 | 0 | 0 |

5 | 0 | 1 | 0 |

6 | −0.59 | 0.59 | −0.59 |

7 | 0 | 0 | 0 |

8 | 0.59 | −0.59 | 0.59 |

9 | −0.59 | −0.59 | −0.59 |

10 | 0.59 | 0.59 | 0.59 |

11 | 0 | −1 | 0 |

12 | 0.59 | 0.59 | −0.59 |

13 | -0.59 | 0.59 | 0.59 |

14 | 0.59 | −0.59 | −0.59 |

15 | 0 | 0 | 1 |

16 | 1 | 0 | 0 |

17 | −0.59 | −0.59 | 0.59 |

Variables | Coded Variables and Design Range | ||||
---|---|---|---|---|---|

Feed flow rate (kg/h) | 1000 (−1) | 1203 (−0.59) | 1500 (0) | 1797 (0.59) | 2000 (1) |

Temperature (°C) | 100 (−1) | 120 (−0.59) | 150 (0) | 180 (0.59) | 200 (1) |

Pressure (kPa) | 1.00 × 10^{−5} (−1) | 2.11 × 10^{−4} (−0.59) | 5.05 × 10^{−4} (0) | 7.99 × 10^{−4} (0.59) | 1.00 × 10^{−3} (1) |

Run | Input Variables | Composition Mass Fraction (Responses) | ||||
---|---|---|---|---|---|---|

x_{1} (kg/h) | x_{2} (°C) | x_{3} (10^{−4} kPa) | y_{1} (10^{−4}) | y_{2} (10^{−4}) | y_{3} | |

1 | 1500 | 150 | 0.10 | 0.28 | 0.54 | 0.09 |

2 | 1500 | 150 | 5.05 | 5.27 | 8.62 | 0.91 |

3 | 1000 | 150 | 5.05 | 5.27 | 8.62 | 0.91 |

4 | 1500 | 150 | 5.05 | 5.27 | 8.62 | 0.91 |

5 | 1500 | 200 | 5.05 | 7.27 | 9.63 | 0.08 |

6 | 1203 | 180 | 2.11 | 1.13 | 1.73 | 0.12 |

7 | 1500 | 150 | 5.05 | 5.27 | 8.62 | 0.91 |

8 | 1797 | 120 | 7.99 | 5.64 | 9.07 | 1.00 |

9 | 1203 | 120 | 2.11 | 5.57 | 9.04 | 0.99 |

10 | 1797 | 180 | 7.99 | 4.07 | 6.45 | 0.48 |

11 | 1500 | 100 | 5.05 | 5.57 | 8.95 | 1.00 |

12 | 1797 | 180 | 2.11 | 1.13 | 1.73 | 0.12 |

13 | 1203 | 180 | 7.99 | 4.07 | 6.45 | 0.48 |

14 | 1797 | 120 | 2.11 | 5.57 | 9.04 | 0.99 |

15 | 1500 | 150 | 1.00 | 5.48 | 8.89 | 0.96 |

16 | 2000 | 150 | 5.05 | 5.27 | 8.62 | 0.91 |

17 | 1203 | 120 | 7.99 | 5.64 | 9.07 | 1.00 |

Term | Coefficient | Coefficient | Coefficient |
---|---|---|---|

Constant | 5.25 × 10^{−4} | 8.60 × 10^{−4} | 9.15 × 10^{−1} |

x_{1} | 1.35 × 10^{−20} | 3.49 × 10^{−20} | −1.27x10^{−18} |

x_{2} | −2.49 × 10^{−4} | −4.12 × 10^{−4} | −5.34 × 10^{−1} |

x_{3} | 1.83 × 10^{−4} | 2.92 × 10^{−4} | 2.69 × 10^{−1} |

x_{1}x_{1} | 2.42 × 10^{−5} | 3.54 × 10^{−5} | −1.63 × 10^{−3} |

x_{2}x_{2} | −1.88 × 10^{−4} | −3.31 × 10^{−4} | −3.74 × 10^{−1} |

x_{3}x_{3} | −2.15 × 10^{−4} | −3.56 × 10^{−4} | −3.91 × 10^{−1} |

x_{1}x_{2} | 6.88 × 10^{−21} | −1.38 × 10^{−20} | 2.82 × 10^{−17} |

x_{1}x_{3} | −1.38 × 10^{−20} | 9.01 × 10^{−21} | 2.73 × 10^{−17} |

x_{2}x_{3} | 2.07 × 10^{−4} | 3.38 × 10^{−4} | 2.50 × 10^{−1} |

Variable Description | Low Bound | High Bound |
---|---|---|

Inlet Mass flow rate (kg/h) | 1000 | 2000 |

Temperature (°C) | 100 | 200 |

Pressure (kPa) | 0.001 | 0.00001 |

**Table 11.**Predicted result from the Response Surface Methodology (RSM) model and ASPEN HYSYS Simulation.

Components | Responses Result from RSM Model | Responses Result from ASPEN HYSYS Simulation |
---|---|---|

Beta-carotene | 0.000554 | 0.000545 |

Tocopherol | 0.000896 | 0.000890 |

FFA | 0.999000 | 0.953000 |

Parameters | Regression Statistics |
---|---|

Multiple R | 1 |

R Square | 1 |

Adjusted R Square | 1 |

Standard Error | 3.18 × 10^{−6} |

Observations | 3 |

© 2017 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**

Tehlah, N.; Kaewpradit, P.; Mujtaba, I.M.
Development of Molecular Distillation Based Simulation and Optimization of Refined Palm Oil Process Based on Response Surface Methodology. *Processes* **2017**, *5*, 40.
https://doi.org/10.3390/pr5030040

**AMA Style**

Tehlah N, Kaewpradit P, Mujtaba IM.
Development of Molecular Distillation Based Simulation and Optimization of Refined Palm Oil Process Based on Response Surface Methodology. *Processes*. 2017; 5(3):40.
https://doi.org/10.3390/pr5030040

**Chicago/Turabian Style**

Tehlah, Noree, Pornsiri Kaewpradit, and Iqbal M. Mujtaba.
2017. "Development of Molecular Distillation Based Simulation and Optimization of Refined Palm Oil Process Based on Response Surface Methodology" *Processes* 5, no. 3: 40.
https://doi.org/10.3390/pr5030040