http://www.press.ierek.com ISSN (Print: 2537-0154, online: 2537-0162) International Journal on: The Academic Research Community Publication DOI: 10.21625/archive.v2i4.395 Approach to Accurate Octane Number Calculation for Gasoline Blending Manal Mahmoud Metwally1 1Chemical Engineering Department, Cairo University, Egypt Abstract The octane number of gasoline is one of the most important measures of gasoline quality to predict accurately the octane ratings of blending gasolines. This measured on a scale that ranges from that equivalent to isooctane (octane number of 100) to that of n-heptane (octane number of zero) octane no is effected by the saturates, aromatics, and olefins contents of gasoline. We take it as a standard and measure octane number by comparison with this standard. The accurate octane blending method will optimize the blending of gasoline components, when gasoline components are blended together, we will calculate the octane number of the blend with different octane number of the component or if the four components are of equal octane number. The blend octane number may be greater than, equal to or less than that calculated from the volumetric average of the octane numbers of the blend components, which indicates nonlinear blending. Blending would be linear if octane number of a blend was equal to that predicted by summing the octane numbers of the components in proportion to their concentrations. In practices, the discrepancies between the octane numbers of blends and the linearly predicted values have been correlated by specific empirical equations and these have been used to correct the linear predictions. © 2019 The Authors. Published by IEREK press. This is an open access article under the CC BY license (https://creativecommons.org/licenses/by/4.0/). 1. Introduction In (1955) Schoen and Mrstik developed a graphical correlation for predicting octane numbers of blends as a series of binary systems based on the octane rating and volumetric olefin contents of the two components being blended. Stewart (1959) refined this method to be applicable to multicomponent blends yielding more self-consistent results. Stewart’s correlation also required the octane rating and volume percent olefins of the components being blended. Auckland and Charnock (1969) developed a blending index to blend octane number linearly. The blending is obtaining blend values by blending indices linearly which obtain the molar property of a real solution by a linear combination of the partial molar properties of its components. This method can only be used to find the blending value of a component at a particular composition and cannot be used to predict its blending values in other mixtures. In (1981) Rusin et al. presented a method consists of three steps: (a) transformation of component properties (b) linear blending of these transformed properties, and (c) inverse transformation of the results. This method is similar to the blending index method. Due to the back and forth transformation, this method may also cause inconsistency in data transformation between these three steps. In (1959) Healy et al. correlated gasoline component blending with differences in octane level and hydrocarbon type among components. Sometimes this method gives unreasonable blending values especially if the hydrocarbon pg. 457 https://creativecommons.org/licenses/by/4.0/ Metwally / The Academic Research Community Publication type or octane number of the new component is outside the range of the component previously tested (Morris, 1975). An interesting equation was proposed by Morris et al. (1975) for describing nonlinear gasoline blending behavior as follows: oc tan e number = x1a1 + x2a2 + b12 x1 x2 (1) Where ai and xi are the octane number and the volume fraction of component i, respectively and b12 is the interac- tion coefficient for components 1 and 2. This Equation (1), is effective in correlating the octane numbers of gasoline blends. Therefore, an additional blending study with the new component and other components must be carried out to determine the additional interaction terms. With n components, n(n-1)/2 interaction parameters are required. If two components are blended so K = 2(2-1)/2 = 1 ∴The equation will be octane no. ON)2 = a1x1+a2x2+b12x1x2 ((b12) one binary interaction parameter). If three components are blended together so K = 3(3-1)/2 = 3 ∴ The equation ON)3 = a1x1 + a2x2 + a3x3 + b12x1x2 + b13x1x3 + b23x2x3 ((b12), (b13), (b23) are the binary interaction parameters) if four new components are added to an eight-component gasoline pool, K = 4(4-1)/2 = 6 ∴ The equation ON)4 = a1x1 + a2x2 + a3x3 + a4x4 + b12x1x2 + b13x1x3 + b14x1x4 + b23x2x3 + b24x2x4 + b34x3x4 ((b12), (b13), (b14), (b23), (b24), (b34) are the binary interaction parameters) the number of interaction parameters increases drastically from 28 to 66. This means that the thirty-eight blending studies with the new components and the other components must be carried out to determine these additional 38 interaction parameters. In (1993) Zahed et al. proposed a model with five independent variables for predicting the octane number of gasoline blends. The octane numbers predicted from this equation are no longer even close to the original octane numbers of the gasoline components. The octane number of n-heptane predicted from this model is 108.77 versus the defined value of zero. Similarly, the octane number of iso-octane predicted from this model is -108.95 versus the defined value of 100. The usefulness of this kind of approach is very limited. Using this model to predict the octane number of blend at other conditions will be very unreliable. 2. Materials: Table 1 represents a typical industrial blending process employed to produce a quality gasoline from various product streams. Four blending data (Table 1) for gasoline produced from four different blend cuts: Straight Run Gasoline (SRG), Straight Run Naphtha (SRN), Reformate (REF) and Fluidized Catalytically Cracked Gasoline (FCCG). The raw gasoline cut qualities (RON, RVP and SG) were determined by the Quality Control department prior to blending using standard ASTM analytical methods. We used four kinds of additives from methanol and originate, such as XXX, XXY and XXYY. We noticed the effect of each one of them on at least four blends to determine the results for each of them to reach Maximum Octane Number. And we determined the objective function Table 1. shows gasoline (RON 95) specification: EUROGRADE GASOLINE (RON 95) PRODUCT SPECIFICATIONS Test Unit Method Limits Min Max Density 15oC kg/m3 ASTM D 4052 775 Appearance Visual Clear&Bright Colour Undyed Continued on next page pg. 458 Metwally / The Academic Research Community Publication Table 1 continued Research Octane Number, RON ASTM D2699 95 Motor Octane Number, MON ASTM D2700 85 Distillation ASTM D86 Initial boiling point oC To be reported 10% oC 70 50% oC 120 90% oC 180 Final boiling point oC 210◦C Evaporated at 150 oC %vol 75 Vapor Pressure Summer (1st May till 30th September) bar ASTM D5191 0.4 0.6 Winter (1st October till 30th April) bar ASTM D5191 0.4 0.7 Copper Corrosion (3hrs at 50 oC) ASTM D130 1a Induction Period min. ASTM D525 360 Existent Gum mg/100ml ASTM D381 5 Total Sulphur mg/kg ASTM D 5453 10 Benzene Content %vol UOP 744 1 Olefins %vol ASTM D 1319/ ASTM D 5134 18 Aromatics %vol UOP 744 42 Oxygenates %wt ASTM D4815 NIL Doctor Test ASTM D4952 Negative Lead mg pb/ L I P 224 5 Table 2. Blend data Sample Reformate Isomerate MTBE Blend A Blend B Blend C Blend DTest Method Units RON ASTM D2699 101.2 87.3 115 95.1 95.2 95.2 95.2 MON ASTM D2700 90 77 99 84.2 84.2 84 84 Aromatic UOP 870 %VOL 75.6 0 0 41.7 38.9 34.4 31.5 Density 15ºC ASTM D4052 kg/m3 826.1 663.2 740.5 754.3 744.9 742.0 734.9 Vapor pressure ASTM D5191 Bar 0.2 0.89 0.25 0.50 0.522 0.57 0.559 Exhaust Emission UOP 539 CO %mol 2.6 2.65 2.7 2.7 CO2 %mol 12.3 12.36 11.9 11.8 H2 %mol 1.2 1.22 1.2 1.2 N2 %mol 83.9 83.8 84.3 84.2 pg. 459 Metwally / The Academic Research Community Publication 3. Results and Discussion 3.1. Statistical model for prediction of octane number (ON) In a previous work by the author, a third order statistical model was elaborated to predict the value of ON upon adding naphta to gasoline (manal, 2012). It was found that a third degree model was adequate for describing the required correlation. In the present work, a more ambitious aim was set to predict the effect of four additions in different percentages on the ON of gasoline. The masses of different additives are represented by the following symbols: X1 = Mass of . . . (g) X2 = Mass of . . . (g) X3 = Mass of . . . (g) X4 = Mass of . . . (g) As a first trial, a factorial 24 first order model was suggested. 3.2. First order (linear) model The center of design and the normaliXed values of the four variables as well as the minimum and maximum value of each are shown in Table 3. 1. Table 3. Levels of design in 24 factorial experiment Variable Coded value X = – 1 Center X = 0 Coded value X = + 1 ∆X X1 71 76.5 82 5.5 X2 7 9.5 12 2.5 X3 1 2.5 4 1.5 X4 5 10 15 5 20 mixes were prepared including 16 with different combinations of X values and 4 at the center of design. Per- centages in Table 1 were normaliXed to add up to 100% each time. The coded first order design equation for 4 variables takes the form: ON = a0 + a1X1 + a2X2 + a3X 3 + a4X4 + a12X1X2 +a13X1X3 + a14X1X4 + a23X2X3 + a24X2X4 +a34X3X4 + a123X1X2X3 + a124X1X2X4 + a134X1X3X4 +a234X2X3X4 + a1234X1X2X3X4 (4.1) Where Xi is the coded value of Xi defined as: X i = Xi −Xo 4X (4.2) Where: X0 is the central value of Xi. A first regression using Design Expert® software was obtained neglecting three order and four order interaction terms because of the negligible interaction between light and heavy naphta and methanol. The following coded equation was obtained: ON = 97.70 − 0.62 X 1 + 0.39 X 2 + 2.75 X 3 + 1.37 X 4 + 0.068 X 1X 2 − 0.075 X 1X 3 − 0.069 X 1X 4 − 0.12 X 2X 3 + 0.4 X 2X 4 − 1.4 X 3X 4 (4.3) pg. 460 Metwally / The Academic Research Community Publication This equation can be transformed in terms of actual variables using equation (4.2) to get ON = 77.857 + 0.1129 X 1 − 0.4586 X 2 + 4.713 X 3 + 2.351 X 4 + 0.0049 X 1X 2 − 0.0091 X 1X 3 − 0.025 X 1X 4 − 0.033 X 2X 3 + 0.032 X 2X 4 − 0.1866 X 3X 4 (4.4) This equation yielded a determination coefficient R2 = 0.951. On performing the ANOVA and calculating the F – values the software was able to eliminate all interaction terms to obtain a simpler equation in the form: ON = 99.4−0.156 X 1 + 0.315 X 2 + 1.834 X 3 + 0.2656 X 4 (4.5) However, the value of R2 in that case decreased to 0.847 which suggests that the original equation (3.1) was more suitable in interpreting experimental data. To further emphasiXe that result, a plot of predicted values against actual values of ON is shown in Figure (3.2) showing a reasonable match between the two values. Also Figure (3.3) illustrates a three dimensional plot of ON against X3 and X4 indicating an increase in ON with increasing values of the two variables, which is in accordance with their positive coefficients in equation (3.4). Also, Fig (3.6) shows contour lines corresponding to that figure. The point (5) shown in figure corresponds to the calculated value of ON corresponding to values of X3 and X4 = 2.5 and 9.8 respectively. 3.2.1. Second order (quadratic) model Whereas first order models require performing experiments at the upper and lower ends of the design (X = ±1) with replicate runs at the center of design (X = 0), quadratic models also require performing more experiments at selected coded levels (X = ± α ). The value of α depends on the number of independent variables.in case of 4 variables, α = 1.68. Consequently, besides the 16 runs, 8 more runs were performed at levels ±1.68 besides 2 replicates at center of design, a total of 26 runs. Generally, a coded second order model shows as: ON = a0 + a1X 1 + a2X 2 + a3X 3 + a4X 4 + a12X 1X 2 + a13X 1X 3 + a14X 1X 4 + a23X 2X 3 + a24X 2X 4 + a34X 3X 4 + a1121 + a22 2 2 + a33Z23 + a44Z 2 4 (4.6) The following coded regression equation was obtained using Design Expert® software: ON = 98.55−0.62 Z1 + 0.39 Z2 + 2.75 Z3 +1.37 Z4 + 0.068 Z1Z2 −0.075 Z1Z3 −0.69 Z1Z4−0.12 Z2Z3 + 0.4 Z2Z4 −1.4 Z3Z4 −0.15 21 −0.29 2 2 −0.68 2 3 −0.2 2 4 (4.7) This equation transforms to the following form on using actual variables through equation (4.3): ON = 42.935 + 0.868 X1 + 0.4218 X2 + 6.223 X3 + 2.5128 X4 +0.0049 X1X2 −0.0091 X1X3 −0.025X1X4 −0.033 X2X3 +0.032 X2X4 −0.1866 X3X4 −0.0.00493 21 −0.0465 2 2 −0.302 23 −0.0081 2 4 (4.8) All coefficients were significant on applying the F – test except the coefficients of X 1X2, X1X3 and X2 X3. The value of R2 was exceptionally high = 0.9987 proving that the regression equation models perfectly the experi- mental data. pg. 461 Metwally / The Academic Research Community Publication To confirm these findings, Figure (3.1) was drawn to compare experimental and calculated ON values showing a perfect alignment of points along the 45o line. Also, Figure (3.2) shows a three-dimensional plot of ON against X3 and X4 indicating an increase in ON with increasing values of the two variables, which is in accordance with their positive coefficients in equation (3.3). Contour lines were drawn in Fig (3.4) displaying calculated values of ON as function of X3 and X4 revealing an increase in ON as both variables increase. Point (5) indicates a predicted value of ON = 98.4 for X3 = 2.5 and X4 = 9.8. To conclude, the quadratic model obtained for factorial 24experiments has been successfully used to predict exactly the Octane Number values as function of the 4 addition levels. Figure 1. Comparisonbetween actual and calculated values of ON from linear model Figure 2. ONvariation as function of variables X3 and X4 for linear model Figure 3. Contourlines for dependence of ON on variables X3 and X4 for linear model pg. 462 Metwally / The Academic Research Community Publication Figure 4. Comparison between actual andcalculated values of ON from quadratic model Figure 5. ONvariation as function of variables X3 and X4 for quadratic model Figure 6. Contourlines for dependence of ON on variables X3 and X4 for quadratic model pg. 463 Metwally / The Academic Research Community Publication 4. References 1. Schoen, W.F. and Mrstik, A.V (1955). “Calculating Gasoline Blend Octane Ratings”, Ind. and Engr. Chem., 47(9), 1740-1742 (1955). 2. Auckland .M.H.T and Charnock. D.J, The Development of Linear Blending Indices for Petroleum Proper- ties, J. Inst. Of Petroleum, 55(545), 322- 329, 1969. 3. Rusin .M.H, Chung .H.S, and Marshall. J.F., A transformation method for calculating the research and motor octane numbers of gasoline blends, Ind. Eng. Chem. Fundam., 20(3), pp. 195-204, 1981. 4. Morris, W.E (1975). “Interaction Approach to Gasoline Blending”, NPRA Paper AM- 75-30, National Petroleum Refiners Association annual meeting 5. Healy .Jr. W.C, Maassen. C.W, and Peterson. R.T. (1959). A new approach to blending octanes, API Division of Refining, 24th midyear meeting, New York. 6. Zahed .A. H, Mullah .S. A, and Bashir .M. D. (n.d.) Predict Octane Number for Gasoline Blends. Hydroc Proc, 72(5), 1993, 85-87. 7. Manal .M. M,Environmental modeling and experimentation of gasoline blending in refineries, M.Sc Thesis, University of Cairo, 2011. pg. 464 Introduction Materials: Results and Discussion Statistical model for prediction of octane number (ON) First order (linear) model Second order (quadratic) model References