Opportunity to Improve Diesel-Fuel Cetane-Number Prediction from

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Opportunity to improve diesel fuel cetane number prediction from easy available physical properties and application of the least squares method and the artificial neural networks Dicho Stoyanov Stratiev, Ivaylo Marinov Marinov, Rosen Dinkov, Ivelina Kostova Shishkova, Ilian Velkov, Ilshat Sharafutdinov, Svetoslav Nenov, Tsvetelin Tsvetkov, Sotir Sotirov, Magdalena Mitkova, and Nikolay Rudnev Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/ef502638c • Publication Date (Web): 05 Feb 2015 Downloaded from http://pubs.acs.org on February 10, 2015

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Opportunity to improve diesel fuel cetane number prediction from easy available physical properties and application of the least squares method and the artificial neural networks Dicho Stratiev*†, Ivaylo Marinov†, Rosen Dinkov†, Ivelina Shishkova†, Ilian Velkov†, Ilshat Sharafutdinov†, Svetoslav Nenov‡, Tsvetelin Tsvetkov‡, Sotir Sotirov§, Magdalena Mitkova§ and Nikolay Rudnevǁ †

LUKOIL Neftohim Burgas, Bulgaria Department of Mathematics, University of Chemical Technology and Metallurgy 1756 Sofia, Bulgaria § Laboratory of Intelligent Systems, University “Prof. Dr. Assen Zlatarov” Burgas, Bulgaria ǁ Ufa State Petroleum Technical University, Russia ‡

Abstract A data base of 140 diesel fuels having cetane number in the range 10 – 70 points and the physical properties: density at 15°C, and distillation characteristics according to ASTM D-86 T10%, T50%, and T90% was used to develop new procedures for prediction of diesel cetane number by application of the least squares method (LSM) using MAPLE software, and the artificial neural network (ANN) using MATLAB. The existing standard methods of cetane index ASTM D-976 and ASTM D-4737, which are correlations of the cetane number, confirmed the earlier conclusions that they predict the cetane number with a large variation. The four variable ASTM D-4737 method proved to better approximate the diesel cetane number than the two variable ASTM D-976 method. The developed four cetane index models (one LSM and three ANN models) proved to better approximate the middle distillate cetane numbers. Between four and five per cent of the selected data base of 140 middle distillates were the samples whose difference between measured cetane number and predicted cetane index by the four new procedures was higher than the specified reproducibility limit in the standard for measuring the cetane number ASTM D-613. In contrast the cetane indices calculated in accordance with the ASTM D-976 and ASTM D-4737 demonstrated that 18 and 16% of the selected data base of 140 middle distillates respectively were the samples whose difference between measured cetane number and predicted cetane index was higher than the specified reproducibility limit in the standard ASTM D-613. The ASTM D-4737, LSM, and the three ANN models were tested against 22 middle distillates not included in the data base of the 140 diesel fuels. The LSM cetane index showed the best predicting cetane number capability among all other four models. Key words: diesel cetane number, cetane index, least squares method, artificial neural network Corresponding author: D. Stratiev, e-mail:[email protected]; fax:359 5511 5555

1. Introduction Cetane number (CN) is a measure of the ignition quality of the diesel fuel and is determined by a standard engine test as specified by ASTM D 613 and EN ISO 5165. The ignition quality is quantified by measuring the ignition delay, which is the period between the time of injection and the start of combustion (ignition) of the fuel [1]. A fuel with a high CN has a short ignition delay period and starts to combust shortly after it is injected into an engine. The ASTM D 613 and EN ISO 5165 test methods define the CN of a diesel fuel as the percentage by volume of normal cetane (C16H34), in a blend with 2,2,4,4,6,8,8-heptamethylnonane (sometimes called HMN or isocetane), which matches the ignition quality of the diesel fuel being rated under the specified test conditions. By definition, normal cetane has been assigned a CN of 100, whereas HMN has a CN of 15. The CN of diesel fuel depends on its molecular composition. Some of the simpler molecular components such as the n-paraffins have higher CN because they ignite in a diesel engine with relative ease, but others like aromatics have more stable ring structures that require higher temperature and pressure to ignite and therefore have lower CN. Cetane Number is usually measured directly using a test engine. The ASTM and EN ISO procedures of measuring CN are: time-consuming; require skilled operators; highly specialized and expensive engine; instrumentation systems and large sample size [2]. This makes the cost of cetane rating tests substantially higher than that of other fuel property tests. The timeconsuming nature of the ASTM D 613 and EN ISO 5165 test procedures and their relatively high cost have led to the development of empirical mathematical equations for predicting the cetane number. The correlations were derived from physical and chemical properties [3] or molecular structure data of the fuel ACS Paragon Plus Environment

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determined by different analytical techniques like: a combination of supercritical fluid chromatography and gas chromatography (GC) - mass spectroscopy (MS) [2,3,4]; near-infrared (NIR) spectroscopy [5,6]; vibrational spectroscopy [7]; 13C and 1H nuclear magnetic resonance spectroscopy [8]. However most of nowadays refineries don’t possess enough analytical equipment for every day monitoring of diesel fractions’ cetane numbers via data for their molecular structure. This lack of facilities can be explained with the fact that usually the schedule for laboratory control of the processing units in a refinery is based on standard methods (ASTM, EN ISO etc.) for determining physical and chemical properties rather than molecular structure of refinery diesel streams. Reference to above it’s more practical, useful and cheaper to correlate CN with ready available data for these streams (density, distillation and viscosity). Two standardized methods, ASTM D 976 and ASTM D 4737, are available for determining cetane index (CI), which is a correlation for estimating cetane number from diesel fuel physical properties density and distillation characteristics. In 1982, an ASTM taskforce was set-up to study and improve on the existing method ASTM D 976 for calculating CI. This led to the development of a modified equation that was adopted as ASTM D 4737. The difference between the two methods is that whereas ASTM D 976 uses two variables, density and distillation mid-boiling point, ASTM D 4737 uses two additional variables, 10% and 90% distillation temperatures. An investigation of the four-variable equation (ASTM D 4737) was carried out by a panel of the Institute of Petroleum using 167 European distillate fuels [9]. The CN range of this study was between 31 and 62 (This is similar to the CN range of 32.5-56.5, which was found in the original study from which ASTM D 4737 was developed). Results show a very large variation in the relationship between CI and CN. In order to improve the prediction of cetane number from easy available diesel fuel physical properties LUKOIL Neftohim Burgas, University of Chemical Technology and Metallurgy-Sofia, Bulgaria, University “Prof. Dr. Assen Zlatarov” – Burgas, Bulgaria, and Ufa State Petroleum Technical University, Russia investigated 140 diesel fuels with CN varied between 10 and 70 and applied two different mathematical approaches - least squares method and artificial neural network (ANN). The two employed mathematical techniques demonstrated significantly better accuracy in prediction of diesel cetane number than the standardized methods ASTM D 4737 and ASTM D 976. The aim of this work is to discuss the results of the performed study. 2. Experimental Section 2.1. Data base of middle distillates After extensive search of data for middle distillates, characterized by their cetane number and physicochemical properties, in the literature and in the LUKOIL Neftohim Burgas files 140 middle distillates whose cetane numbers varied between 10 and 70 were selected as a data base for this study. We could not find a middle distillate with a cetane number lower than 10 and such with a cetane number higher than 70. The lowest cetane number middle distillate was a high aromatic fluid catalytic cracking (FCC) heavy cycle oil (HCO) and the highest cetane number middle distillate was a very low aromatic hydrocracking diesel. Figure 1 shows the frequency distribution of cetane number of the selection of the 140 middle distillates. 50% of the middle distillates of the selection have a cetane number in the range 45-55; 15% - CN= 40-45, and CN=55-60; 11% CN = 30-40; 5% CN = 10-30, and 4% CN = 60-70. The selection of the 140 middle distillates could be considered as an adequate representative of the refinery middle distillate pool throughout the world. The range of variation of the cetane number of this data base is wider than the ASTM D 4737 cetane number range of 32.5-56.5 and the ASTM D 976 cetane number range of 30-60. In this way both ASTM D 976 and ASTM D 4737 can be tested for their accuracy in prediction of the cetane number for a wider range of middle distillate cetane numbers. Table 1 presents the physicochemical properties and the cetane numbers of the 140 samples of both hydotreated and nonhydrotreated middle distillates (MD). 76 of these middle distillates were analyzed in the LUKOIL Neftohim Burgas refinery by employing ASTM standards. The diesel sample cetane number was measured in accordance with ASTM D 613. The distillation characteristics were measured in accordance with ASTM D-86. The properties of the other 64 diesel fuel samples were taken from the literature. In this work we also investigated the influence of number of input variables in the ANN CN model on its prediction capability. For that reason we included in the data base of the 140 diesel fuels the following properties: viscosity, refractive index, molecular weight, aniline point, and hydrogen content. These properties were found to affect diesel cetane number in an earlier study [10]. 2.2. Applied correlations to estimate some physicochemical properties of middle distillates ACS Paragon Plus Environment

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Some of the properties, pointed as double underlined in Table 1 were calculated by using published in the literature correlation because of lack of enough quantity of the sample for executing all of the analyses and/or the analyses were not presented in the schedule for laboratory control. These properties were estimated by the use of the following correlations: log ν 38 = 4.39371 − 1.94733K w + 0.12769K 2w + 3.2629 x10 −4 API 2 − 1.18246 x10 −2 K w API + +

0.171617 K 2w + 10.9943API + 9.50663x10 − 2 API 2 − 0.860218K w API API + 50.3642 − 4.78231K w 2

Eq.1

(Correlation of Abbott [15], the dimension of viscosity is mm /s) It was found in a recent study that the viscosity correlation of Abbott predicts viscosity of middle distillates with the highest accuracy among all other viscosity correlations published in the literature [16]. In order to estimate the middle distillate viscosity after Abbott’s correlation information about the middle distillate parameters Kw and API gravity is required. These parameters were calculated by the use of equations 2 and 3.

Kw =

3

API =

1.8(Tav. + 273.15) SG

Eq. 2

141.5 − 131.5 SG

Eq. 3

where, density @ 150 C , g / cm3 density of water @ 150 C , g / cm3 density of water at 150C = 0.999024 g/cm3 [17] Tav. = T50%, oC SG = specific gravity, SG =

Molecular weights (g/mole) for all studied middle distillates were calculated from the average boiling point (Tav) in degree Kelvin (T50% assumed in this study) and d420 according to a dependence derived by Goossens [18]:

Mw =

  Tav ) 1.52869 + 0.06486 ln( 1078 − Tav   0.01077Tav d 20 4

Eq. 4

The refractive index (RI) at 20 oC of middle distillates is correlated through their parameters Mw, SG and Tav (K) as is required by Dhulesia [19]. ( −0.0557 ) ( −0.0044) RI 20 = 1 + 0.8447SG1.2056 Tav Mw

Eq. 5

In order to build an accurate predictive CN model some additional acknowledgment for molecular composition of middle distillates is necessary [2]. Therefore aniline point (AP) in degree Celsius, which indicates the degree of aromaticity of the fraction, was calculated from Linden method [20]:

AP = −183.3 + 0.27 API3 Tav + 0.317Tav ACS Paragon Plus Environment

Eq. 6

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In reference [20] another method for AP was proposed. It was developed by Albahri et al. but it isn’t applicable for FCC LCO and HCO (heavy cycle oil). Applying the equation for these middle distillates negative values are received. A simple relation was proposed by Goossens to estimate the hydrogen content (wt.%) of a petroleum fraction based on the assumption of molar additivity of structural contributions of carbon types [21]:

%H = 30.346 +

82.952 − 65.341RI 20 d 20 4

−

306 Mw

Eq. 7

where,

density @ 200 C , g / cm3 density of water @ 40 C , g / cm3 density of water at 40C = 1.000 g/cm3

d420 – relative density, d 420 =

The average absolute deviation (AAD) between middle distillate cetane number (CN) and cetane index (CI) was estimated by the use of eq. 8.

AAD =

1 n ∑ CNi − CI i n i =1

Eq. 8

where n= number of observation

3.

Results and Discussion

The data in Table 1 were used to calculate the cetane index by the procedures described in the standards ASTM D-976 and ASTM D-4737 [22, 23]. Figures 2 and 3 show the agreement between measured cetane number and the cetane indices calculated by the ASTM D-976 and ASTM D-4737 for the data of the 140 diesel fuels. It is evident from these data that the four variable ASTM D-4737 (R2 = 0.9147; AAD = 2.4; quadratic error = 0.27) method better predicts diesel fuel cetane number than the two variable ASTM D-976 (R2 = 0.7967; AAD = 2.7; quadratic error = 0.30). The maximum deviation from the cetane number for the 140 diesel fuels was 11.7 for the ASTM D-4737 method and 13.7 for the ASTM D-976 method. The deviation between the CN and the CI calculated by the ASTM D-4737 for 17.1% of the 140 middle distillates was outside of the limit for reproducibility specified in the ASTM D-613 method. The deviation between the CN and the CI calculated by the ASTM D-976 was for 18.6% of the 140 middle distillates outside of the limit for reproducibility specified in the standard method for measuring the cetane number. The data of the 140 diesel fuels used in this study confirmed the earlier conclusion that the four variable ASTM D-4737 method better approximates the cetane number. However, as mentioned in the Introduction section of this paper the investigation carried out by the Institute of Petroleum using 167 European distillate fuels [9] showed a very large variation in the relationship between ASTM D-4737 CI and CN. That was the reason to apply different approaches to develop procedures that better approximate the cetane number from the diesel fuel physical properties.

3.1. Least Square Method The method of least squares is based upon the assumption that the best analytical approximation to a continuous curve or a set of points is that one for which the sum of squares of approximation errors is minimal. In this subsection we used the same idea for fitting the polynomial surface to given data. We used the following form of 4-variable polynomial by employing the mathematical commercial software MAPLE [24]:

ACS Paragon Plus Environment

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f(x,y,z,t) = a1111 x 4+a1122 x 2 y 2+a111 x3+a112 x 2 y+a113 x 2 z+a114 x 2t+a122 xy 2+a11 x 2+a33 z 2+a44t 2+a12 xy+a13 xz +a14 xt+a23 yz+a24 yt+a34 zt+a1 x+a2 y+a3 z+a4t+a, where: variables x, y, z, t correspond to density at 15oC, ASTM D86 distillation at 50%, 10%, and 90%, respectively. The method determines the coefficients of the polynomial such that 140

∑ ( f (x , y , z ,t ) − C )

2

k

k

k

k

k

 → min,

k =1

where Ck is the cetane number, k=1..140. The usual manner: The minimum is obtained by differentiation with respect to each of the coefficients and solving the obtained system we receive the unknown coefficients. As a result and after simplifications, we obtain the following approximation f ( x , y, z, t ) = (−0.0000024398x + 0.0020033)x 3 +

(-0.00031141y + 0.0000016054y 2 - 0.00048742z - 0.00015121t - 0.48996)x 2 + (-0.00067024y 2 + 0.11558y + 0.21399z + 0.071762t + 29.508)x +

Eq. 9

0.067192y 2 + 0.00044493z 2 - 0.0060410t 2 + 0.000083240yz + 0.0099096yt - 0.0044160zt 11.146y - 22.596z - 7.3688t + 1496.0. Usually sensitivity analysis is used to prove the significance of one or all coefficients of the obtained model [25]. We used the least squares method, therefore there exists only one minimum and the minimum obtained is global. It is not hard to show that all parameters are essential, i.e. if we reject one of coefficients in the polynomial model (Eq. 10), then we receive a significant increment of residuals. We made many calculations with polynomials of 2-nd, 3-rd, 4-th, 5-th and 6-th degree. The sum of squared residuals by the use of polynomials of 4-th, 5-th and 6-th degrees is a negligible small number with respect to tests specified by the ASTM D-613 method. Therefore, we used a polynomial of 4-th degree. For the explicit choose of the polynomial f(x,y,z,t), we found that missing terms (e.g. x3y, x2yz, y3x, etc.) did not effect sensitively on residuals (again with respect to accuracy to the standard test specified by ASTM D 613). The agreement between measured by ASTM D-613 diesel cetane number and the calculated by eq. 10 cetane index is depicted in Figure 3. Using this data, the absolute error E1, which is equivalent to AAD is 1 140 ∑ f ( xk , yk , zk , tk ) − Ck ≤ 1.6 140 k =1 and the quadratic error is E1 =

Eq. 10

1 140 Eq. 11 ∑ ( f ( xk , yk , zk , tk ) − Ck )2 ≤ 0.17. 140 k =1 In fact the introduced numbers E1 and E2 measures the "distance" between function f and the given data. The equation 10 defines E1 as sum of absolute errors, but in equation 11 we introduce standard square error (sum of squared residuals). In literature one may find E2 more often than E1. Obviously, if residuals are least than 1, then E2 < E1. We used both numbers only for completeness. In addition, we introduce the moving squares error. Let for every integer k (k=1..140), f k ( xk , yk , zk , tk ) be the function in the form of f ( x, y, z , t ) and obtained by the least squares method using the given data except the data in the k-th row. Then moving square error is 1 140 E3 = ∑ f k ( xk , yk , zk , tk ) − Ck . 140 k =1 It is not hard to see that in general E1 ≤ E3 . In our case E3 ≤ 2.19 . Obviously, moving square error describes not only the accuracy of the method (i.e. the “distance” between given data and obtained function) but it is a measure for adequacy of the chosen initial function for approximation. In our case the errors E1 and E3 also corresponds to standard test method (repetition) for calculated cetane index by four variable function ASTM D4737-09. The data in Figure 4 indicate a much better prediction of the cetane number of the investigated 140 diesel fuels by the use of the four variables least squared method (R2 = 0.9556; AAD = 1.6; quadratic error = 0.17) than the ASTM D-4737 method which uses the same four variables. E2 =

3.2. Moving Least Squares Method ACS Paragon Plus Environment

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There are many articles devoted to moving least squares method, see for example [26], [27], and [28]. Again, as in previous subsection, let wk = ( xk , yk , zk , tk ) be the input data in a domain D ⊂ R 4 and Ck be the cetane number, k=1..140. In contrast of classical least squares method we use non-negative weight functions rather than weight constants. We will use the function f ( w) = f ( x, y, z , t ) = a1 x+a2 y+a3 z+a4t+a Eq. 12 as an approximation model. The moving least squares problem is equivalent to the following minimization problem: 140

∑α

k

( w − wk )( f ( wk ) − Ck ) 2  → min,

Eq. 13

k =1

Here • denotes the Euclidean norm in R 4 and α k : [0, ∞)  →[0, ∞) are weight functions. Let us assume that weight functions are differentiable and non-negative. Therefore, using the results in [26], the optimization Eq. 13 is solvable. Solving minimization problem Eq. 13 for every point w∈ D , with respect to unknowns a1,a2,a3,a4,a, we receive the approximation for cetane number if the weight functions are known. Most frequently the inverse distance weight functions α k ( w) = w − wk we will use weight functions in the following form 2

2

2

2

−p

, p ≥ 1 , are used. In our calculation

2

α k ( w − wk ) = e −γ ( w − w ) = e −γ (( x − x ) + ( y − y ) + ( z − z ) + (t − t ) ) , Eq. 14 where γ ∈ [0, ∞) is a constant. Obviously if γ = 0 , then the problem (3) is equivalent with the classical least square approximation without weights. If the number γ is sufficiently large, then we may approximate the k

k

k

k

k

initial data with arbitrary small precision. But in this case the approximation algorithm will be inadequate, i.e. we will receive sufficiently small absolute errors in all points wk from the initial data and large errors in middle points. Avoiding this problem we will investigate again the moving square error. Let for any k the f k (γ ) = a1 (γ ) xk+a2 (γ ) yk+a3 (γ ) zk+a4 (γ )tk+a(γ ) Eq. 15 be the solution of the problem 140

∑α

k

( wk − wl )( f ( wl ) − Cl ) 2  → min .

Eq. 16

l =1, l ≠ k

Then obviously the moving square error 1 140 Eq. 17 E3 = ∑ f k (γ k ) − Ck . 140 k =1 is a function of γ , i.e. E3 = E3 (γ ) . Minimizing moving square error we receive the extreme value of γ and we have to use it in our calculations. Using the computer algebra system Maple 16 it is not hard to receive the following results: E3 (0) = 2.186 , E3 (0.001) = 1.933 , and E3 (0.01) = 184.967 . Therefore there exists a minimum of moving square error in the interval [0,0.01]. One may obtain the minimum at γ ≈ 0.0001 and E3 (0.0001) = 1.92 . Using the results above, we construct the following approximation algorithm. For every fixed point w0 = ( x0 , y0 , z0 , t0 ) ∈ D we solve the minimization problem 140

∑e

− 0.0001( w0 − wk ) 2

( f ( wk ) − Ck ) 2  → min .

Eq. 18

k =1

Let a10 , a20 , a30 , a40 , a 0 be the solution of (4), then the number

f ( w0 ) = f ( x0 , y0 , z0 , t0 ) = a10 x0+a20 y0+a30 z0+a40t0+a 0 is an approximation of the cetane number. The agreement between measured diesel cetane number and approximated by the moving least squares method is presented in Figure 5. These data indicate that the moving least squares method (R2 = 0.9358; AAD = 1.9; quadratic error = 0.20) worse approximated diesel cetane number than the least squares method. However it is still better than the ASTM D-4737. We have to point out that we did not filter the data in Table 1. For example the row 139 in Table 1 “conflicts” with all closest rows: 3,137, 138, and 136. Indeed ACS Paragon Plus Environment

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the Euclidean distances between the data in row 139 and the data in cited rows are: 52.71, 64.50, 87.34, and 106.25. The cetane numbers in rows 3,137, 138, 136 are 51,51,50, and 48, respectively. However the cetane number in row 139 is 58.

3.3 Artificial Neural Networks (ANN) The artificial neural networks [29, 30] are one of the tools that can be used to recognise and identify the things. In the first step the ANN has to be learned and after that we can use it for the recognitions and predictions of the properties of the materials. Figure 6 shows a classic three-layered neural network in abbreviated notation. In the many-layered networks, the exits of the first layer become entries for the next one. The equation describing this operation is: a3=f3(w3f2(w2f1(w1p+b1)+b2)+b3),

Eq. 19

where: am is the exit of the m-layer of the neural network for m =1, 2, 3; w is the matrix containing the weight coefficients for every entry; b is neurons entry bias; fm is the transfer function of the m-layer. The neuron in the first layer receives outside entries р. The neurons exit from the last layer and determine the neural network exits а. Equation 19 is connected to the structure and the properties of the neural network (Figure 6). Because it belongs to the learning with teacher methods, a couple of numbers are submitted to the algorithm (an entry value and an achieving aim – on the networks exit) {p1, t1}, {p2 , t2}, ..., {pQ , tQ},

Eq. 20

Q ∈ (1...n), n – numbers of learning couple, where рQ is the entry value (on the network’s entry), and tQ is the exit value corresponding to the aim. The couple {pQ , tQ}corresponds to the input value and the aim (target) on the exit of the ANN. Every network’s entry is preliminary established and constant, and the exit has to match with the aim. The difference between the exit values and the aim is the error – e = t-a. The “back propagation” algorithm [29] uses least-quarter error: Fˆ = (t − a ) 2 = e2.

Eq. 21

In learning of the neural network, the algorithm recalculates the network’s parameters (W and b) to achieve least-square error. The “back propagation” algorithm for i-neuron, for k+1 iteration use equations:

∂Fˆ ∂wim ; ∂Fˆ bim ( k + 1 ) = bim ( k ) − α m ∂bi , wim ( k + 1 ) = wim ( k ) − α

Eq. 22 Eq. 23

where: α - learning rate of the neural network; ACS Paragon Plus Environment

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∂Fˆ ∂wim - relation between the changes of the square error and the changes of the weights; ∂Fˆ ∂bim - relation between the changes of the square error and the changes of the biases; The overfitting [31] appears in different situations, which effect the overtrained parameters and give worse output results as it shows at Figure 7. There are different methods that can reduce the overfitting - “Early Stopping” and “Regularization”. Here we will use Early Stopping [29]. When multilayer neural network are trained, usually the available data must be divided into three subsets. The first subset is named “Training set”, is used for computing the gradient and updating the network’s weights and biases. The second subset is named “Validation set”. The error on the validation set is monitored during the training process. The validation error normally decreases during the initial phase of training, as does the training set error. Sometimes, when the network begins to overfit the data, the error on the validation set typically begins to rise. When the validation error increases for a specific number of iterations, the training is stopped, and the weights and biases at the minimum of the validation error are returned [30]. The last subset is named “test set”. The sum of these three sets has to be 100% of the learning couples. When the validation error ev increases the neural network learning stops when: dev > 0 Eq. 24 The classic condition for the learned network is when e2 < Emax, Eq. 25 where Emax is maximum square error. For the preparation we used MATLAB and neural network structure 8:20:1 (8 inputs, 20 neurons in hidden layer and one output (Figure 8). On the input of the neural newtork we put: density at 15 oC g/cm3;T50%; T90%; Viscosity at 40 oC, mm2/s; Molecular weight, g/mole; Refractive index at 20 oC; Aniline point, oC and hydrogen content, % (m/m). For the target (aim) we used Cetane number ASTM D 613. For the learning process we programed the next options: Epoches=100; Performance (MSE)=0.00001; Validation check=25. We divide the input vector randomly in three different parts: training (70%); validation (15%) and testing (15%). These three different parts (70%, 15%, 15%) are used for the learning algorithm of the ANN to reduse overfitting. After the training process all input values were simulated. The R after the learning process wereTraining R=0.973, Validation R=0.967, Test R=0.936 and All R=0.966. (Figure 9). Figure 10 depicts a graph of agreement between measured diesel fuel cetane number and the calculated values by the Artificial Neural Network (ANN) method. The ANN method as evident from Figure 10 approximates much better than the cetane number of the investigated 140 diesel (R2 = 0.9489; AAD = 1.7; quadratic error = 0.18) than the ASTM D-4737 method. The accuracy of the prediction of diesel cetane number by the ANN is slightly lower than that of the least squares method. This ANN model of cetane number uses eight input variables. In order to evaluate the influence of the number of input variables in the ANN model on its prediction capability another ANN model was developed, in which the number of input variables was four and the variables were the same as those in the ASTM D-4737 method and the LSM method (d15, T10, T50, and T90). For the target we used Cetane number ASTM D-613. The structure of this neural network was 4:30:1 (4 inputs, 30 neurons in hidden layer and one output). For the learning process we programed the next options: Epoches=100; Performance (MSE)=0.00001; Validation check=25. We divided the input vector randomly in 3 different parts: training (70%); validation (15%) and testing (15%). For this process 140 vectors were used for learning and other 22 vectors were employed only for testing. The agreement between measured diesel fuel cetane number and the values calculated by the ANN-2 (four variables) method is presented in Figure ACS Paragon Plus Environment

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Energy & Fuels

11. The four variable ANN-2 method as evident from Figure 11 also approximates much better the cetane number of the investigated 140 diesel (R2 = 0.9516; AAD = 1.7; quadratic error = 0.18) than the ASTM D4737 method. It seems that both the eight variables ANN-1 and the four variables ANN-2 are almost identical in their capabilities to approximate the middle distillate cetane number. Therefore it could be concluded that the number of input variables has no effect on the prediction capability of the ANN model based on the investigated middle distillate physicochemical properties. In our aim to search for a better cetane number ANN model we made a correlation matrix of the cetane number and the physicochemical properties of the 140 middle distillates investigated in this work (Table 2). It showed that the strongest correlation is between the cetane number and the aniline point, and the weakest is between the cetane number and the viscosity. Therefore we decided to develop another eight variables ANN-3 cetane number model in which the viscosity is excluded and T10 variable is included in its place in the new ANN-3 model. The input variables of the ANN-3 model were d15, T10, T50, and T90, Refractive index at 20 oC, hydrogen content, % (m/m), Aniline point, oC, and Molecular weight, mole/g. For the tagret we used Cetane number ASTM D-613. The structure of this neural network was 8:45:1 (8 inputs, 45 neurons in hidden layer and one output). For the learning process we programed the next options: Epoches=1000; Performance (MSE)=0.0001; Validation check=25. We divided the input vector randomly in 3 different part: training (70%); validation (15%) and testing (15%). For this process were used 140 vectors for learning and other 22 vectors only for testing. Figure 12 depicts a graph of agreement between measured diesel fuel cetane number and the values calculated by the eight variable ANN-3 method. The ANN-3 method demonstrates the best diesel cetane number approximation (R2 = 0.9568; AAD = 1.5; quadratic error = 0.16) among all cetane index models studied in this work.

3.4. Evaluation of precision of prediction of the cetane number of the cetane index models The predictive capabilities of the studied in this research two standardized and developed LSM, and three ANN models were classified as proposed by Sanchez et al. [32] according to their statistical indicators and the results are shown in Table 3. Standard deviation (SD) values, which is calculated by eq. 26 and AAD (eq. 8) both are considered the main criteria for establishing the ranking. The correlation coefficient (R2), slope and % of CI values exceeding ASTM D-613 reproducibility were also considered. SD =

RSS n−2

Eq. 26 where n is the number of

observations and RSS is the residual sum of squares, defined in eq. 27 140

RSS = ∑ (CN i − CI i )

2

Eq. 27

i =1

where CNi is the cetane number, determined according to ASTM D-613 and CIi is the cetane index, calculated by one of the studied six models. Standard deviation values for all models range from 1.93 to 3.58 which range is wider than those of R2(0.7967-0.9568) and slopes (0.9892-1.0236). Therefore SD is an useful indicator for classification of precision of predictions of the mentioned methods. SD-based ranking in Table 3 sort out the studied models in the following decreasing accuracy order: ANN-3 ˃ LSM ˃ ANN-2 ˃ ANN-1 ˃ ASTM D-976 ACS Paragon Plus Environment

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The second statistical indicator with broad variation, presented in Table 3, is AAD (1.49-2.71). AAD-based ranking confirms the SD order with the exception of ANN-1 and ANN-2 place, as AAD classifies ANN-2 second and ANN-1 – third in the increasing accuracy order. Another indicator “% of CI values exceeding ASTM D-613 reproducibility” also, to some extent, verify the above accuracy increasing order. The 5 % value of the parameter for ANN-1, ANN-2 and LSM determines that their fitting capability is equivalent to ASTM D-613 accuracy. What’s more, only 4 % of CI values, calculated by ANN-3 model for the 140 diesel boiling fractions from our data base exceeds ASTM D-613 reproducibility and thus the method surpasses even the precision of the cetan number determination tests. In order to evaluate the precision of prediction of cetane number of the methods ASTM D-4737, least squares method, and the ANN 22 middle distillates not included in the data base of the 140 investigated diesel fuels were tested. The properties of these 22 middle distillates and the measured and predicted by the the three methods ASTM D-4737, least squares method, and the ANN cetane numbers are given in Table 4. By the use of equations 1-7 the properties: Viscosity at 40 oC, mm2/s; Molecular weight, g/mole; Refractive index at 20 oC; Aniline point, oC; and Hydrogen content of the 22 tested middle distillates were calculated and then they were used as input along with density at 15 oC g/cm3;T50%;and T90%; for the ANN models. The data in Table 4 confirm that the least squares method (AAD=1.5; SD = 2.1) and the ANN-1 and ANN-3 (AAD=1.7; SD = 2.2) better predicts the cetane number of the tested 22 middle distillates than the ASTM D4737 method (AAD=1.8; SD =2.5). The ANN-2 model exhibited the same accuracy of prediction of CN as the ASTM D-4737 method for tested 22 middle distillates not included in the data base of 140 middle distillates. The mathematical techniques: least squares method and artificial neural network employed in this study along with the selected data base of the 140 middle distillates featuring with a very wide range of variation in the cetane number allowed to develop models which better approximates the diesel cetane number than the standardized methods ASTM D-4737 and ASTM D-976 in the cetane number range between 10 and 70.

4. Conclusions The investigation carried out on the precision of prediction of cetane number of 140 diesel fuels by the methods ASTM D-976 and ASTM D-4737 indicated that the ASTM D-4737 method better approximates the cetane number than the ASTM D-976 method. It also confirmed the relative large variation in the relationship between ASTM D-4737 cetane index and cetane number made by other researchers showing a maximum deviation of 11.7 points for the investigated 140 diesel fuels. The application of the least squares method (LSM) by the use of MAPLE software and the artificial neural network (ANN) using MATLAB to the data base of the 140 diesel fuels led to development of new procedures which achieved much better accuracy in the prediction of cetane number from the easily available physical properties: density at 15°C, and distillation characteristics according to ASTM D-86 T10%, T50%, and T90% ( maximum deviation between 5.7 and 6.7) than the ASTM D-4737. The results of this study showed that the increase of number of input variables from four to eight in the ANN models improves slightly the precision of the prediction of the diesel cetane number. The proposed procedures can be used in refining practice for daily monitoring of the diesel fuel cetane number from the routine laboratory analyses available in the refinery.

Reference (1) Australian Fuel Quality Standards. Measuring cetane number: options for diesel and alternative diesel fuels, Australian Government, Dept. of Environment and Heritage, 2004. ACS Paragon Plus Environment

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Energy & Fuels

(2) Ghosh, P.; Jaffe, S. Ind. Eng. Chem. Res. 2006, 45, 346-351. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(3) Yang, H.; Ring, Z.; Briker, Y. Fuel 2002, 8, 65-74. (4) Windom, B.; Huber, M. Energy Fuels 2012, 26, 1787-1797. (5) Li, Y. Anal. Methods 2012, 4, 254. (6) Alves, J. Fuel 2012, 97, 710-717. (7) Bolanca, T.; Marinovic, S. Acta. Chim. Slov. 2012, 59, 249-257. (8) Mueller, Ch.; Cannella, W. Energy Fuels 2012, 26, 3284-3303. (9) Owen, K.; Coley, T. Automotive Fuels Handbook; Society of Automotive Engineers: Warrendale, PA, 1990. (10)

Sharafutdinov, I.; Dinkov, R.; Stratiev, D.; Shishkova, I.; Marinov, I.; Rudnev, N. OGEM

2013, 39, 92-97. (11)

Sok, Y. Oil & Gas J. 2000, 20, 58-66.

(12)

Lois, E.; Stournas, S. Correlations between diesel fuel properties and engine emissions,

Prepr. Am. Chem. Soc., Div. Fuel Chem. 1992, 37, 25-32. (13)

Environmental Protection Agency. Strategies and issues in correlating diesel fuel properties

with emissions, US EPA, 2001. (14)

Laredo, G.C.; Cano J.L.; López, C.R.; Martin, R.S.; Martínez, M.C.; Marroquín J.O. Fuel

Process. Technol. 2007, 88, 897-903. (15)

Abbott, M. M.; Kaufmann, T.G.; Domash, L. Can. J Chem. Eng. 1971; 49, 379-384.

(16)

Marinov, I.; Stratiev, D.; Sharafutdinov, I.; Rudnev, N.; Petkov, P. Evaluation of available in

literature empirical correlations for viscosity prediction of petroleum fractions originating from different crudes, in press in OGEM. (17)

Miquel, J.; Hernandez, J.; Castells, F. SPE Reservoir Eng. 1992, May, 265-270.

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Goossens, A.G. Ind. Eng. Chem. Res. 1996; 35, 985-988.

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Riazi, M. Characterization and properties of petroleum fractions, ASTM: West

Conshohocken, PA, 2005, pp. 111-163. (21)

Goossens, A. Ind. Eng. Chem. Res. 1997, 36, 2500-2504. ACS Paragon Plus Environment

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Page 12 of 29

ASTM D 4737 – 09, Standard Test Method for Calculated Cetane Index by Four Variable

Equation (23)

ASTM D 976 – 91(reapproved 1995), Standard Test Methods for Calculated Cetane Index of

Distillate Fuels. (24)

MAPLE, computer algebra system, Waterloo Maple Inc., www.maplesoft.com

(25)

Alcazar, L. A.; Ancheyta, J. Chem. Eng. J. 2007, 128, 85–93.

(26)

Levin, D. Math. Comp. 1998, 67, 1517-1531.

(27)

Lancaster, P.; Salkauskas, K. An introduction: Curve and surface fitting; Academic Press,

1986. (28)

Farwig, R. J. Comput. Appl. Math. 1986, 16, 1, 79–93

(29)

Hagan, M.; Demuth, H.; Beale, M. Neural Network Design; PWS Publishing: Boston MA,

1996. (30)

Haykin, S. Neural Networks: A Comprehensive Foundation, MacMillan Publishing

Company: New York, 1994. (31)

Bellis, S.; Razeeb, K. M.; Saha, C.; Delaney, K.; O'Mathuna, C.; Pounds-Cornish, A.;. de

Souza, G.; Colley, M.; Hagras, H.; Clarke, G.; Callaghan, V.; Argyropoulos, C.; Karistianos, C.; Nikiforidis, G. FPGA Implementation of Spiking Neural Networks - an Initial Step towards Building Tangible Collaborative Autonomous Agents; FPT’04, International Conference on FieldProgrammable Technology, The University of Queensland, 2004, pp. 449-452. (32)

Sanchez, S.; Ancheyta, J.; McCaffrey W. C. Energy & Fuels 2007, 21, 2955-2963.

(33)

Marroquı́n-Sánchez G.; Ancheyta-Juárez J. App. Cat. A: General. 2001, 207, 407-420.

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Quiroz-Sosa, G.; Leiva-Nuncio, M. Appl. Catal. A: General 1999, 183, 265-272.


Page 13 of 29

Energy & Fuels

SRGO from TBP analyses

LGO MGO HGO VLGO FCC LCO FCC HCO FCC LCO/HCO blend FCC GO

340 340 361 353 357 357 246 363 348 283 362 353 245 348 359 360 359 248 351 367 354 367 200 240 260 280 300 320 360 200 240 260 280 300 320 340 360 200 220 240 260 280 300 320 340 200 220 240 260 280 300 320 340 200 240 260 280 300 320 340 270 247 250 351 308 366 370 389 376 368 291 295 262 353 374

2.32 2.03 3.22 2.19 2.64 4.41 1.32 3.52 3.56 1.66 3.39 3.07 1.32 3.08 5.00 2.39 4.56 1.29 3.06 3.88 3.32 5.13 1.41 2.23 2.58 3.15 3.33 6.50 10.01 1.21 1.99 2.53 3.08 3.53 6.89 8.95 10.79 1.17 1.60 1.95 2.48 3.07 3.52 5.98 7.43 1.12 1.39 1.76 2.27 2.93 4.05 5.54 7.98 1.17 1.89 2.51 2.90 4.16 5.78 7.93 1.37 1.31 1.37 3.48 2.67 4.76 6.06 4.91 8.48 6.80 2.45 2.55 9.32 3.38 5.42

176 175 200 175 188 205 150 206 208 154 203 199 153 196 227 181 219 153 199 205 199 227 141 164 177 191 206 222 259 140 164 178 191 206 222 239 259 141 152 165 178 192 207 223 241 141 153 165 178 190 207 224 238 141 165 178 191 207 224 239 156 154 156 203 194 221 234 229 242 230 159 157 203 169 223

1.4708 1.4574 1.4699 1.4657 1.4667 1.4931 1.4463 1.4708 1.4690 1.4680 1.4707 1.4672 1.4481 1.4692 1.4775 1.4658 1.4775 1.4481 1.4718 1.4811 1.4747 1.4814 1.4466 1.4633 1.4677 1.4733 1.4783 1.4826 1.4870 1.4477 1.4621 1.4666 1.4739 1.4792 1.4831 1.4867 1.4870 1.4443 1.4534 1.4593 1.4641 1.4719 1.4769 1.4805 1.4833 1.4440 1.4510 1.4587 1.4662 1.4759 1.4753 1.4783 1.4892 1.4452 1.4587 1.4656 1.4742 1.4758 1.4790 1.4877 1.4512 1.4476 1.4488 1.4729 1.4682 1.4790 1.4809 1.4797 1.4997 1.4971 1.5195 1.5414 1.5859 1.5568 1.4879

60.7 67.3 71.2 63.0 68.0 61.6 61.6 72.9 74.7 52.2 72.0 71.9 62.1 69.9 77.1 65.5 74.5 61.7 69.6 67.3 68.1 75.3 56.4 59.0 62.8 65.8 69.3 73.0 83.2 55.8 59.8 63.5 65.5 68.7 72.7 77.0 83.2 58.0 58.7 61.6 65.1 66.7 70.1 74.4 79.1 58.2 60.3 62.0 63.8 64.2 71.2 75.8 75.4 57.4 62.0 64.2 65.3 70.9 75.4 76.4 61.7 62.8 63.0 70.9 69.6 74.5 77.9 76.7 71.5 68.8 30.8 21.6 23.9 21.0 70.5

12.91 13.58 13.21 13.15 13.25 12.14 13.83 13.22 13.33 12.75 13.20 13.33 13.78 13.20 13.06 13.22 13.00 13.76 13.10 12.70 12.96 12.87 13.64 13.12 13.07 12.95 12.85 12.78 12.83 13.58 13.19 13.14 12.92 12.81 12.76 12.71 12.83 13.78 13.47 13.35 13.27 13.02 12.93 12.89 12.88 13.80 13.61 13.38 13.15 12.81 13.01 13.00 12.59 13.73 13.38 13.19 12.90 12.98 12.97 12.66 13.65 13.81 13.78 13.09 13.24 12.95 12.95 12.97 12.13 12.17 10.43 9.51 8.39 9.07 12.53

ASTM D86 distillation, °C 10% (v/v)

50% (v/v)

90% (v/v)

200 196 209 193 202 252 179 243 250 185 228 229 182 234 272 196 268 174 231 235 230 275 182 222 242 262 282 302 342 182 222 242 262 282 302 322 342 182 202 222 242 262 282 302 322 182 202 222 242 262 282 302 322 182 222 242 262 282 302 322 172 175 180 245 240 261 289 260 314 297 208 220 300 228 210

245 239 275 242 259 290 200 282 284 214 279 272 205 270 308 250 300 204 274 285 275 310 185.5 225.5 245.5 265.5 285.5 305.5 345.5 185.5 225.5 245.5 265.5 285.5 305.5 325.5 345.5 185.5 205.5 225.5 245.5 265.5 285.5 305.5 325.5 185.5 205.5 225.5 245.5 265.5 285.5 305.5 325.5 185.5 225.5 245.5 265.5 285.5 305.5 325.5 210 206 209 280 267 303 317 311 333 320 240 246 322 268 308

311 315 337 324 332 336 229 335 324 254 333 323 231 316 347 337 341 230 320 338 324 350 198 238 258 278 292 318 358 198 238 258 278 292 318 338 358 198 218 238 258 278 292 318 338 198 218 238 258 278 292 318 338 198 238 258 278 292 318 338 252 232 234 329 291 345 352 370 360 351 265 273 348 328 359

95% (v/v)


Reference

H2 content, % (m/m)

SRGO blend

173 167 173 165 175 205 161 217 210 167 185 187 156 204 208 169 202 135 177 184 183 205 180 220 240 260 280 300 340 180 220 240 260 280 300 320 340 180 200 220 240 260 280 300 320 180 200 220 240 260 280 300 320 180 220 240 260 280 300 320 148 130 139 168 189 169 257 152 288 271 178 197 279 191 174

Aniline point,°C

SRGO

0.8409 0.8209 0.8421 0.8332 0.8361 0.8773 0.8011 0.8441 0.8416 0.8341 0.8437 0.8379 0.8042 0.8408 0.8559 0.8341 0.8554 0.8042 0.8448 0.8594 0.8492 0.8619 0.8003 0.8283 0.8365 0.8464 0.8553 0.8633 0.8728 0.8018 0.8265 0.8348 0.8472 0.8566 0.8640 0.8708 0.8728 0.7968 0.8120 0.8224 0.8312 0.8444 0.8532 0.8601 0.8659 0.7964 0.8086 0.8215 0.8343 0.8502 0.8509 0.8570 0.8745 0.7982 0.8215 0.8333 0.8477 0.8516 0.8579 0.8723 0.8092 0.8036 0.8056 0.8470 0.8390 0.8577 0.8617 0.8594 0.8903 0.8859 0.9113 0.9427 1.0130 0.9667 0.8715

44.1 49.2 51.0 45.8 47.4 44.5 41.5 53.0 53.5 35.5 49.3 51.1 50.0 49.8 49.0 48.0 53.0 47.5 51.0 47.2 47.0 51.0 43.5 49.3 50.4 51.6 54.8 55.3 54.0 43.1 49.3 50.6 51.5 53.1 53.5 54.1 53.1 42.9 45.5 47.6 49.4 51.2 52.7 53.5 54.4 40.4 43.7 45.9 48.1 49.3 52.2 53.3 54.2 41.2 44.1 47.7 48.6 51.6 52.0 52.6 44.8 43.3 46.0 46.7 50.5 50.5 49.5 50.4 47.0 50.0 13.0 12.0 10.0 14.0 42.0

Refractive index at 20°C

HTGO

45.0 51.0 51.0 47.0 50.0 43.0 45.6 54.4 56.0 37.8 52.5 53.7 46.0 52.0 57.0 48.6 55.0 45.0 51.0 47.8 49.3 55.0 39.7 43.8 47.8 50.6 53.1 56.6 64.8 39.0 44.6 48.5 50.3 52.5 56.2 59.5 64.8 41.3 43.0 46.4 50.2 51.5 54.1 58.1 61.8 41.5 44.6 46.8 48.7 48.9 55.2 59.6 57.7 40.7 46.8 49.2 50.1 54.9 59.1 58.8 46.0 46.0 46.0 53.0 52.0 54.0 58.0 54.0 51.0 48.8 20.0 15.0 13.0 19.0 43.3

FBP

Molecular weight, g/mol

HTGO blend

IBP

Viscosity at 40°C, mm2/s

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75

Type of sample

Density at 15°C, g/cm3

№

Cetane index ASTM D4737 Cetane number ASTM D613

Table 1. Physicochemical properties of the diesel samples under study 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

15

Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140

Visbreaker GO Rainbow Zama crude LGO Fluid coker LSO Fluid coker HTLGO1 Fluid coker HTLGO2 Delayed coker LGO Delayed coker HTLGO LC-finer LGO LC-finer HTLGO SRLGO 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 SET 1 2 SET 1 3 SET 1 4 SET 1 5 SET 1 6 SET 2 7 SET 2 8 SET 2 9 SET 2 10 SET 3 11 SET 3 12 SET 3 SRGO HTGO

37.5 49.8 27.6 35.6 39.0 30.4 36.0 34.1 38.3 41.7 31.0 52.5 66.7 51.4 45.6 40.0 34.5 24.4 45.3 55.7 58.9 57.6 57.7 31.9 35.9 40.4 45.6 36.9 41.1 45.9 36.6 41.0 46.0 33.3 37.5 44.2 45.4 55.2 55.6 55.8 58.3 59.6 62.7 57.7 55.3 53.4 48.1 60.2 59.1 57.9 54.4 60.2 58.9 58.8 60.9 58.5 52.6 74.8 52.5 59.0 52.2 54.2 53.1 53.2 57.0

42.0 52.7 28.3 36.9 40.9 33.2 37.5 34.6 38.1 40.4 32.1 50.6 65.1 47.9 47.2 38.0 37.3 28.1 45.0 56.0 57.0 57.0 58.0 30.0 34.0 40.0 44.0 34.3 39.7 44.8 35.0 39.1 44.6 35.1 39.8 44.2 45.5 57.1 54.0 52.7 57.0 59.0 62.3 56.8 57.4 52.6 47.0 61.0 60.1 58.7 56.0 56.4 56.4 56.5 56.4 56.1 50.0 70.0 54.0 59.0 48.0 51.0 50.0 58.0 59.2

0.7902 0.8329 0.9305 0.8811 0.8697 0.8912 0.8650 0.8773 0.8639 0.8540 0.9002 0.8438 0.8170 0.8557 0.8727 0.8917 0.9137 0.9471 0.8722 0.8230 0.8392 0.8570 0.8647 0.8996 0.8884 0.8764 0.8640 0.8486 0.8331 0.8181 0.8683 0.8532 0.8380 0.8931 0.8825 0.8641 0.8522 0.8290 0.8360 0.8060 0.8270 0.8200 0.8110 0.8210 0.8290 0.8270 0.8410 0.8140 0.8170 0.8140 0.8180 0.8260 0.8260 0.8260 0.8260 0.8260 0.8370 0.8070 0.8140 0.8340 0.8440 0.8380 0.8420 0.8390 0.8349

115 164 163.5 123.8 102.8 139.5 143.7 165.0 146.3 104.9 136.2 197.0 220.0 214.0 220.0 220.0 220.0 257.0 231.0 191.0 192.0 211.0 230.0 175.0 180.0 184.0 193.0 83.0 112.0 138.0 71.0 72.0 76.0 107.0 126.0 108.0 172.0

21.0 185

128 196.0 258.1 220.7 206.5 196.7 194.9 207.6 203.4 196.7 221.3 230.0 253.0 245.0 248.0 257.0 266.0 280.0 257.0 219.0 243.5 270.0 288.5 236.0 239.0 241.5 245.0 165.0 166.0 166.0 176.0 178.0 177.0 201.0 211.0 209.0 221.0 200 221 179 217 214 211 212 213 210 210 213 213 208 206 228 228 227 229 228 219 234 213 235 224 220 223 214.0 240.2

164 261.2 307.5 292.9 286.4 276.3 272.3 281.5 275.9 269.3 297.3 279.0 274.0 292.0 297.0 299.0 303.0 310.0 286.0 255.0 295.5 320.5 329.0 273.0 275.0 276.5 279.5 221.0 220.0 220.0 251.0 250.0 250.0 285.0 285.0 291.0 263.0 274 283 242 279 272 268 265 269 256 254 260 261 252 245 278 272 272 281 270 269 296 231 288 280 279 281 279.0 276.3

246 328.0 342.1 338.2 336.4 332.1 329.5 333.0 331.5 329.3 339.1 329.0 308.0 346.0 346.0 345.0 349.0 351.0 330.0 322.0 349.0 366.5 369.0 312.5 315.0 317.0 318.0 304.0 303.0 302.0 328.0 328.0 328.0 340.0 342.0 341.0 312.0 356 365 345 360 359 351 349 351 343 346 328 330 324 319 323 324 325 326 326 326 346 269 345 339 350 344 342.0 324.6

Page 14 of 29 293 350.6 361.7 361.2 362.4 350.8 349.4 354.6 355.2 356.1 357.8 355 322.0 364.0 364.0 368.0 368.0 368.0 351.0 348.0 369.0 393.0 398.0 335.0 337.0 338.0 340.0 350.0 346.0 346.0 359.0 359.0 359.0 358.0 368.0 367.0 340.0 378 391 381 386 382 380 380 380 378 385 349 352 348 347 347 350 351 353 354 368 364 293 380 381 389 389 372.0 363.6

0.95 2.46 5.15 3.80 3.34 2.92 2.80 3.10 2.98 2.74 4.70 3.40 2.87 4.15 4.74 5.23 5.95 7.24 4.12 2.41 4.02 5.92 6.87 3.76 3.77 3.71 3.69 1.84 1.75 1.67 2.67 2.54 2.42 4.35 4.21 4.25 2.93 3.02 3.44 1.98 3.16 2.85 2.62 2.65 2.86 2.47 2.55 2.45 2.50 2.26 2.14 3.12 3.09 3.08 2.9 2.88 2.82 3.90 1.93 3.85 3.11 3.26 3.35 2.57 2.84

HT – hydrotreated; GO – gasoil; L – light; M – middle; H – heavy; SR – straight-run; V – vacuum


128 1.4410 52.8 13.71 191 1.4644 70.2 13.39 208 1.5289 47.1 10.61 206 1.4956 61.1 12.04 204 1.4881 63.5 12.36 190 1.5035 51.2 11.52 193 1.4857 60.4 12.37 198 1.4936 58.6 12.05 196 1.4847 62.1 12.45 193 1.4783 63.9 12.72 206 1.5085 55.1 11.46 203 1.4708 71.9 13.19 206 1.4528 82.2 14.14 212 1.4782 71.4 12.91 212 1.4896 66.0 12.37 209 1.5025 59.0 11.75 208 1.5175 51.8 11.08 206 1.5403 41.9 10.13 203 1.4899 62.3 12.27 188 1.4580 72.4 13.69 219 1.4667 80.0 13.53 238 1.4775 81.2 13.14 245 1.4823 80.9 12.96 186 1.5096 46.8 11.21 190 1.5017 51.8 11.60 194 1.4933 57.2 12.02 199 1.4846 63.4 12.48 156 1.4776 48.6 12.31 159 1.4669 54.8 12.87 162 1.4567 61.5 13.44 175 1.4893 51.3 12.00 177 1.4789 57.3 12.52 180 1.4685 63.8 13.07 197 1.5043 53.5 11.56 199 1.4970 57.7 11.91 209 1.4840 67.5 12.60 188 1.4775 62.4 12.71 203 1.4610 76.7 13.68 209 1.4652 76.8 13.52 181 1.4471 75.4 14.19 207 1.4593 79.4 13.81 203 1.4550 80.1 14.00 202 1.4491 82.8 14.30 197 1.4560 77.0 13.88 198 1.4612 74.8 13.63 188 1.4606 70.9 13.55 183 1.4703 64.0 13.01 194 1.4515 78.4 14.10 194 1.4535 77.4 13.99 187 1.4520 75.4 14.00 181 1.4551 70.9 13.76 207 1.4587 79.5 13.84 202 1.4590 77.3 13.77 202 1.4590 77.3 13.77 210 1.4585 80.6 13.87 200 1.4591 76.6 13.75 196 1.4667 71.2 13.33 229 1.4449 95.2 14.75 171 1.4532 67.5 13.74 214 1.4636 79.6 13.65 204 1.4709 72.2 13.20 205 1.4668 74.5 13.40 205 1.4694 73.4 13.28 204 1.4675 74.0 13.37 203 1.4649 74.9 13.49 Double underlined data are calculated

16

17

18

18

19

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Table 2 Correlation matrix of cetane number and the physicochemical properties of the 140 middle distillates investigated in this work CN d15 T10 T50 T90 VIS MW RI AP H CN 1 d15 -0.63 1 T10 0.22 0.48 1 T50 0.17 0.62 0.80 1 T90 0.18 0.45 0.37 0.82 1 VIS 0.03 0.63 0.85 0.87 0.58 1 MW 0.38 0.42 0.80 0.97 0.80 0.84 1 RI -0.69 1.00 0.43 0.55 0.40 0.58 0.34 1 AP 0.94 -0.50 0.31 0.37 0.37 0.21 0.57 -0.57 1 H 0.83 -0.95 -0.26 -0.34 -0.21 -0.42 -0.11 -0.97 0.75 1


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Table 3 Ranking of standardized models and developed in this study a LSM, and ANN models for their capability for cetane number prediction of the studied 140 diesel fractions

Model LSM ANN-1 ANN-2 ANN-3 ASTM D-4737 ASTM D-976

R

2

0.9556 0.9489 0.9515 0.9568 0.9147 0.7967

Slope

AAD

AAD-based ranking

0.9983 0.9982 1.0005 0.9995 1.0236 0.9892

1.58 1.67 1.72 1.49 2.43 2.71

2 3 4 1 5 6

SD

SD-based ranking

2.00 2.13 2.10 1.93 3.20 3.58

2 4 3 1 5 6


% of CI values exceeding ASTM D-613 reproducibility 5 5 5 4 17 19

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Table 4 Agreement between measured and predicted cetane number of 22 middle distillates not included in the data base of 140 diesel fuels Density T10, T50, T90, CN CI CI CI CI CI AD CI AD CI AD CI AD CI °C °C °C ASTM ASTM LSM ANN-1 ANN-2 ANN-3 ASTM DLSM ANN-1 ANN-2 at D-613 D-4737 4737 15oC, g/cm3 0.834 241 270 313 52 56.1 54.5 52.9 56.2 53.6 4.1 2.5 0.9 4.2 0.852 207 245 298 39 41.2 40.3 36.6 39.5 39.4 2.2 1.3 2.4 0.5 0.842 228 264 323 45 50.6 49.6 46 49.1 45.8 5.6 4.6 1 4.1 0.839 221 255 316 44 49.4 48.8 47.1 46.2 46.5 5.4 4.8 3.1 2.2 0.84 230 280 338 52 48.8 52.9 52.4 52.8 53.6 3.2 0.9 0.4 0.8 0.8574 270 313 346 54.1 56.3 52.6 50.5 53.8 52.9 2.2 1.5 3.6 0.3 0.8235 201 234 263 48 47.7 46.1 46.7 43.1 45.8 0.3 1.9 1.3 4.9 0.7914 169 188 210 42.8 44.8 44.6 44.2 44.7 46.3 2 1.8 1.4 1.9 0.8155 179 218 305 47.5 47 47.6 43.1 48.3 43.2 0.5 0.1 4.4 0.8 0.8255 186 243 326 48.9 49.6 49.4 47.3 49.0 47.8 0.7 0.5 1.6 0.1 0.8312 198 259 327 50.7 51.5 50.8 50 51.0 50.6 0.8 0.1 0.7 0.3 0.8382 202 275 333 50.9 51.8 50.6 50.5 50.9 51.2 0.9 0.3 0.4 0.0 0.8414 224 282 336 51.9 53.6 52.1 50.9 52.9 53.5 1.7 0.2 1 1.0 0.8521 257 290 327 53.2 53.5 51.3 49.9 51.6 49.5 0.3 1.9 3.3 1.6 0.8267 213 241 268 48.5 49.1 47.8 47.5 47.1 48.1 0.6 0.7 1 1.4 0.7942 173 194 219 43.4 46.1 46 45.3 46.7 46.3 2.7 2.6 1.9 3.3 0.8587 260 312 366 54.6 54.6 52.2 49.9 53.4 51.1 0 2.4 4.7 1.2 0.8277 224 250 291 50.4 52.6 52.1 49.5 53.7 51.2 2.2 1.7 0.9 3.3 0.7912 179 191 210 44.6 46.4 47.2 45.9 42.2 47.5 1.8 2.6 1.3 2.4 0.8354 206 266 317 50.8 51.5 49.8 49.9 48.4 51.0 0.7 1 0.9 2.4 0.8382 202 275 333 50.9 51.8 50.6 50.5 50.9 51.2 0.9 0.3 0.4 0.0 0.8387 205 272 349 51.3 51.4 50.9 50.2 54.8 50.3 0.1 0.4 1.1 3.5 Absolute average deviation 1.8 1.5 1.7 1.8 Standard deviation 2.5 2.1 2.2 2.5 1

AD CI ANN-3 1.6 0.4 0.8 2.5 1.6 1.2 2.2 3.5 4.3 1.1 0.1 0.3 1.6 3.7 0.4 2.9 3.5 0.8 2.9 0.2 0.3 1.0 1.7 2.2

Middle distillates with numbers from 1 to 5 were characterized in LUKOIL Neftohim Burgas; Middle distillates with numbers from 6 to 13 were characterized in ref. 33; Middle distillates with numbers from 14 to 22 were characterized in refs. 34 and 35. 2 AD = absolute deviation; AD = CN − CI


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Figure 1 Frequency distribution of cetane number of middle distillates in the selection of the 140 middle distillates under study


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Energy & Fuels

Figure 2 Agreement between measured diesel fuel cetane number and calculated cetane index by the four variable ASTM D-4737 method


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Figure 3 Agreement between measured diesel fuel cetane number and calculated cetane index by the two variable ASTM D-976 method


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Energy & Fuels

Figure 4 Agreement between measured diesel fuel cetane number and calculated by the Least Squares method


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Figure 5 Agreement between measured diesel fuel cetane number and calculated by the Moving Least Squares method


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Energy & Fuels

P 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Rx1

1 R

W1 S1xR

b1 S1x1

1

n

+ S x1 1

а1

F1

1

S x1 1

W2 S2xS1

b2

n

+ S x1

S2x1

2

а2

2

2

F

W3

3 2 S2x1 S xS 1 b3

n3

+ S x1

S3x1

Figure 6 A classic three-layered neural network.


3

3

F

а3 S3x1

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Figure 7. The learning process


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Energy & Fuels

Figure 8. The neural network structure


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Fig. 9. The correlation coefficient R for the training, Validation, Test and All


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Figure 10 Agreement between measured diesel fuel cetane number and calculated by the Artificial Neural Network (eight variable ANN-1) method


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Figure 11 Agreement between measured diesel fuel cetane number and calculated by the four variable ANN2 method


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Energy & Fuels

Figure 12 Agreement between measured diesel fuel cetane number and calculated by the eight variable ANN-3 method


Opportunity to Improve Diesel-Fuel Cetane-Number Prediction from

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