CHEMICAL ENGINEERING TRANSACTIONS VOL. 51, 2016 A publication of The Italian Association of Chemical Engineering Online at www.aidic.it/cet Guest Editors: Tichun Wang, Hongyang Zhang, Lei Tian Copyright © 2016, AIDIC Servizi S.r.l., ISBN 978-88-95608-43-3; ISSN 2283-9216 Research on the Rate Prediction Model of Diesel Oxidation in Storage Yun Xiong*, Peng Su, Jian Zhou, Sheng Qi Dept. of Oil Application & Management Engineering, LEU, Chongqing 401311, China xy0001@vip.sina.com The existent gum of five diesel samples under five different partial pressure of oxygen (PPO) (21%, 15%, 10%, 5%, 1%) was investigated by means of storage test method. The formation rate of existent gum (K) was established by the least square method. The influence of diesel composition and partial pressure of oxygen on K is examined. Multiple linear regression method and least square method were carried out to establish two models to predict the existent gum formation rate. Results indicate that existent gum increases linearly with the storage time during oxidation reaction. The reaction of olefin and oxygen is the main one of forming existent gum. The relationship between K and PPO is power function, mass fraction of olefin has a linear effect on K. F test results proved the correctness of the diesel oxidation model, which can be used to predict the diesel oxidation. 1. Introduction How to precisely predict the storage stability of liquid fuel is one of the problems haunted the fuel workers for a long time. Both fuel composition and external conditions exerts great influences on the fuel stability (Xu et al., 2010). The good prediction model should be grounded on the fundamental knowledge of all factors that contribute to the degradation of fuel, which includes the intrinsic factors such as unsaturated hydrocarbons (Lin et al., 2012; Ren et al., 2012), nitrogen-containing compound, oxygen-containing compound and sulfur - containing compound (Joanna et al., 1987; Isabelle et al., 1999; Mushrush et al., 1991) as well as external conditions such as light, temperature and the presence of metals (Batta et al., 1991; Wu et al., 2008). Little work has been done to consider the influence of external oxygen especially the lower oxygen partial pressure. Furthermore, present researches mainly focus on qualitative descriptions rather than quantitative model establishment. Existent gum amounts were chosen as indicators of the degree of oxidation of different diesel fuels, which were aged under different oxygen partial pressures, the mathematical relationship between diesel composition, oxygen partial pressure and diesel oxidation rate was established, which provides a theoretical basis for predicting the oxidative deterioration rate of diesel. 2. Materials and Methods 2.1 Fuel samples Two kinds of 0# automobile diesel samples (numbered SH1 and SH2) were obtained from Sinopec Chongqing Branch Corporation, two kinds of 0# ordinary diesel samples (numbered SY1 and SY2 ) from PetroChina Chongqing Branch Corporation, and one kind of military diesel sample (numbered PB1) from PingBa depot. The Physical and chemical properties of diesel samples were summarized in Table 1. 2.2 Qualitation and quantification of diesel by GC/MS The components of diesel samples were determined using a gas chromatograph mass spectrometer (GC7890A/MS5975C, Agilent). The column was capillary column (HP-1MS; 30m × 250 μm ×0.25 μm). Operating conditions were as following: ultra-high purity helium was used as the carrier gas at a flow rate of 1.0 mL min-1 and analyses were performed in constant flow mode while the injector temperature was set at 340°C for split injection at a split ratio of 10:1. The inject volume was 1 μL. The initial oven temperature was maintained at 100 °C for 1 min before it was increased by 5 °C min−1 to 300 °C and kept isothermal for 5 min. DOI: 10.3303/CET1651020 Please cite this article as: Xiong Y., Su P., Zhou J., Qi S., 2016, Research on the rate prediction model of diesel oxidation in storage, Chemical Engineering Transactions, 51, 115-120 DOI:10.3303/CET1651020 115 mailto:xy0001@vip.sina.com The ionization potential of the mass-selective detector was 70 eV and the scan range was 30–650 u. Identification of compounds were achieved by a mass spectra database search (NIST05 Library) and co- eluted with corresponding standards. Peak area normalization method was used in order to obtain the mass fraction of each component. The results were shown in Table 2. Table 1: Physical and chemical properties of diesel samples Item Distillation temperature/℃ Existent gum Acidity Colority 50% 90% 95% mg/100ml level SH1 260 332 340 19.2 1.59 7 Item Distillation temperature/℃ Existent gum Acidity Colority 50% 90% 95% mg/100ml level SH2 280 340 355 42.0 2.99 3 SY1 266 334 350 79.0 3.24 11.5 SY2 275 345 360 31.3 2.64 6 PB1 233 295 310 13.2 1.36 6 Table 2: Component of diesel samples Component w% SH1 SH2 SY1 SY2 PB1 Paraffin 62.27 56.22 61.34 55.87 50.75 Cycloparaffin 5.77 6.82 8.04 6.77 11.91 Benzene 6.70 5.71 2.98 6.67 1.31 Naphthalane 10.44 10.01 10.06 9.79 18.39 Tricyclic aromatics 0.83 0.49 2.46 1.48 1.12 Non-Conjugated diene 4.98 8.20 7.86 9.28 4.69 Conjugated diene 0 2.54 0.58 2.14 0.04 Oxygen-containing compounds 8.16 7.02 6.03 6.06 8.53 Nitrogen-containing compounds 0.62 1.59 0 1.72 0.94 Sulfur-containing compounds 0.23 1.40 0.65 1.25 2.32 2.3 Storage test 5L of diesel was taken and poured into five 1L beakers, which were later placed within five apparatuses, and the temperature of all the apparatus was set at 95℃. Then, the apparatus was filled with one atmosphere air first and then slowly purged with nitrogen to decrease the oxygen content in the air to obtain five different oxygen partial pressures, 21%, 15%, 10%, 5%, 1%. Regular supply of oxygen into the apparatus was needed later to maintain the oxygen partial pressure at the set value. 100ml sample was taken periodically with 4mm valve inserted into the device. Test apparatus is shown in Figure 1.For diesel samples taken periodically during the storage test process, their existent gum was measured according to GB / T509 "Determination of engine fuel existent gum". Figure 1: Schematic diagram of experimental unit 1 - Heating cover 2 - Cover plate 3 - Intake valve 4 - Oxygen sensor 5 - Temperature sensor 6 - Exhaust valve 7 - Seal ring 8 - Tool housing 9 - Controller 1 2 3 4 5 6 7 8 9 116 http://s.g.wanfangdata.com.cn.hccck.com/Paper.aspx?f=detail&q=%e5%85%b3%e9%94%ae%e8%af%8d%3a%22peak+area+normalization+method%22+DBID%3aWF_QK 3. Results and discussions 3.1 Existent gum results The existent gum results of diesel samples were summarized in figure2~figure6. 0 10 20 30 40 50 15 20 25 30 35 40 45 50 55 60 E xi st en t g um ( m g/ 10 0m l) Storage time (d) SH1-1 SH1-2 SH1-3 SH1-4 SH1-5 0 10 20 30 40 50 0 40 80 120 160 200 240 280 E xi st e n t g u m ( m g /1 0 0 m l) Storage time (d) SH2-1 SH2-1 SH2-1 SH2-1 SH2-1 Figure 2: Dotted lines of SH1 samples Figure 3: Dotted lines of SH2 samples 0 10 20 30 40 50 60 80 100 120 140 160 180 200 220 240 E xi st en t g um (m g/ 10 0m l) Storage time (d) SY1-1 SY1-2 SY1-3 SY1-4 SY1-5 0 10 20 30 40 50 0 40 80 120 160 200 240 E xi st en t g um (m g/ 10 0m l) Storage time（ d） SY2-1 SY2-2 SY2-3 SY2-4 SY2-5 Figure 4: Dotted lines of SY1 samples Figure 5: Dotted lines of SY2 samples 0 20 40 60 80 100 10 15 20 25 30 35 40 45 50 55 E xi te nt g um ( m g/ 10 0m l) Storage time（ d） PB1-1 PB1-2 PB1-3 PB1-4 PB1-5 Figure 6: Dotted lines of PB1samples 3.2 Relationship between existent gum and storage time The existent gum was usually preferred as an indicator for diesel storage stability, which increased linearly with storage time as can be seen from figure 2 to 6. It is assumed that the existent gum S (mg / 100ml) and the storage time t (d) exists a linear relationship during the oxidation reaction process as follows: S=Kt+c0 (1) S is the existent gum (mg/100ml), K is a diesel gum growth rate (mg • (100ml • d)-1), t is the storage time (d), c0 is the intercept. The least squares method is used to carry linear fit between existent gum and storage time for 5 groups of diesel fuels. The slope of the fitted line K, intercept c0, F value are listed in Table 3. F0.95 (1,9) is 5.12, it is can be seen F value of all diesel samples is greater than the F0.95 (1,9), so at the 95% confidence level F test is significant, oxidation reaction process established linear relationship between existent gum and storage time. 117 Table 3: K,c0,F of regression equation Item K c0 F Item K c0 F SH1-1 0.7140 25.20 44.15 SY1-1 3.0927 82.95 469.21 SH1-2 0.6567 22.16 70.01 SY1-2 2.5320 80.99 772.53 SH1-3 0.4731 23.82 59.24 SY1-3 1.5691 84.86 223.79 SH1-4 0.3228 22.64 23.33 SY1-4 1.3996 71.99 111.91 SH1-5 0.2473 18.86 39.08 SY1-5 0.8218 73.00 74.81 SH2-1 5.2127 36.68 458.88 SY2-1 5.0800 19.51 394.25 SH2-2 4.3272 28.81 899.11 SY2-2 4.2564 20.22 387.27 SH2-3 3.6545 27.09 316.45 SY2-3 3.8655 22.09 637.16 SH2-4 2.0436 34.27 129.97 SY2-4 2.6254 19.63 169.85 SH2-5 1.0363 35.54 199.73 SY2-5 1.1836 25.51 169.82 PB1-1 0.5536 12.96 558.72 PB1-2 0.4691 13.33 483.09 PB1-3 0.3518 13.04 644.62 PB1-4 0.2700 14.22 223.56 PB1-5 0.1891 11.91 232.32 3.3 Relationship between existent gum and diesel component In order to determine which component in diesel has great influence on K, the linear correlation analysis was carried between regression equation K and chemical composition based on Table 2 and Table 3. Correlation coefficient obtained was summarized in Table 4. Table 4: Correlation coefficient of K with component of diesel samples PPO(0.1MP) Component 0.21 0.15 0.10 0.05 0.01 Alkane -0.49948 -0.50749 -0.62016 -0.37546 -0.43860 Aromatic -0.42318 -0.41416 -0.28326 -0.35154 -0.42109 Olefin 0.98756 0.98846 0.98005 0.99690 0.99267 Oxygen-containing compounds -0.79560 -0.79051 -0.71448 -0.78563 -0.88599 Nitrogen-containing compounds 0.58011 0.59129 0.70968 0.54322 0.48506 Sulfur-containing compounds -0.00514 -0.0083 0.04555 -0.58248 -0.05032 As can be seen, under different PPO, K and olefin content is positively correlated, and there is a higher correlation coefficient (0.98) between olefin content and K. So it is assumed that a linear relationship may exist between them. 3.4 Relationship between K and PPO SPSS (18.0, IBM) software was used to perform curve estimation of K and oxygen partial pressure listed in Table 3, the power function model (2) was found as a fitting function which converges and was more consistent with the actual situation. K=a1xb (2) a1 is a coefficient (mg (100ml)-1 d-1 (0.1MPa) -b), b is oxygen pressure reaction order, x is the PPO (0.1MPa). Table 5: The fitting equation of relationship between PPO and K Item Fitting equation R2 SH1 K= 1.4031x0.4359 0.9223 SH2 K=12.8504x0.5729 0.9845 SY1 K= 6.8983x0.5435 0.8978 SY2 K=10.4060x0.4565 0.9891 PB1 K= 1.0393x0.4380 0.8683 118 Fitting equation and R2 are listed in Table 5. The model above can reflect the relationship between K and PPO more accurately.as R2 is larger. The value of coefficient b was around 0.5 and quite similar for different fitting equations. So suppose PPO on the different components of the diesel oxidation reactions share the same reaction order, the power function model was corrected to model (3). K=a2x0.5 (3) The results in Table 6 were fitted according to model (3). The corrected power function model (4) has a better correlation between K and x. It was proved that the hypothesis is true, the reaction order of oxygen on different diesel is 0.5. Table 6: Corrected fitting equation Item Fitting equation R2 SH1 K= 1.5958x0.5 0.9312 SH2 K=11.1114x0.5 0.9795 SY1 K= 6.3254x0.5 0.9203 SY2 K=11.3543x0.5 0.9870 PB1 K= 1.1771x0.5 0.8922 3.5 Establishment of oxidation model As has been discussed in section 3.4, there is only one coefficient a2 in corrected model (3), and a2 is quite different in different types of diesel. Olefin is the main reason for promoting existent gum, and when the PPO is constant, there exists a linear relationship between k and mass fraction of olefin in diesel. It is assumed that in the model (3), a2 was determined by olefin content in diesel. So the oxidation model (4) was proposed. In the model, a2= f(x), x is the mass fraction of olefin. K= f(x)P0.5 (4) Among these unsaturated hydrocarbons, conjugated diene is the most active one. If diesel contains a small amount of conjugated diene, diesel will be oxide to form existent gum easily (Mo et al 2002). Therefore, olefin in diesel is divided into conjugated diene and non-conjugated diene, a2 is determined by two olefins content. Four types of diesel, SH1, SH2, SY1, PB1 were chosen to set up oxidation model. Non-conjugated dienes (x1) and conjugated dienes (x2) were independent variables while coefficient of a2 is dependent variable. a2=a3x1+ a4x2+c2 (5) By using multiple linear regression analysis, equation (5) was worked out, and binary linear regression equation (6) was got. a2= -4.556+1.222x1+2.223 x2 (6) The R2 of the fitting equation (6) is 0.999, the model (7) is got by plugging the equation (6) into equation (4). K=( -4.556+1.222x1+2.223 x2)P0.5 (7) Equation (7) is the diesel oxidation rate model, which is in terms of non-conjugated dienes and conjugated dienes in diesel. The model shows that the conjugated diene is indeed more active, its oxidation rate is approximately 1.8 times of the non-conjugated diene reaction rate. 3.6 Model verification Diesel sample SY2, which was not included in oxidation model was used for establishing model verification. Model (7) was applied to predict the oxidation rate of SY2. Experimental values (Exp) and predicted values (Pre) and their relative error (R) are listed in Table7. The relative error of model (8) is below 6%, in which GB / T509 requires the relative error below 15%. The correlation coefficient (r), and F test were calculated based on experimental and predicted values. r, F value and F test of F0 .95 (r-1, n-r) are listed in Table 8. F value is greater than the F0.95 (1, n-2), so at the 95% confidence level F test is significant. The model can predict the oxidation accurately. 119 Table 7: Comparison of experimented and calculated result for K Sample PPO(0.1MPa) Exp Pre R SY2 0.21 5.0800 5.2958 4.25% 0.15 4.2564 4.4752 5.14% 0.10 3.8655 3.6546 5.45% 0.05 2.6254 2.5843 1.56% 0.01 1.1836 1.1558 2.34% Table 8: r,F of the regression model Item r F F0 .95 (1, 3) Model 0.995 297.74 10.13 4. Conclusions Existent gum increases linearly with storage time. 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