Octane number prediction for gasoline blends

Fuel Processing Technology 87 (2006) 505 – 509 www.elsevier.com/locate/fuproc

Octane number prediction for gasoline blends Nikos Pasadakis a,⁎, Vassilis Gaganis a , Charalambos Foteinopoulos b a

Mineral Resources Engineering Department, Technical University of Crete, 73100 Chania, Greece b MotorOil Hellas, Corinth Refineries S.A., 20100 Corinth, Greece

Received 5 September 2005; received in revised form 29 November 2005; accepted 29 November 2005

Abstract Artificial Neural Network (ANN) models have been developed to determine the Research Octane Number (RON) of gasoline blends produced in a Greek refinery. The developed ANN models use as input variables the volumetric content of seven most commonly used fractions in the gasoline production and their respective RON numbers. The model parameters (ANN weights) are presented such that the model can be easily implemented by the reader. The predicting ability of the models, in the multi-dimensional space determined by the input variables, was thoroughly examined in order to assess their robustness. Based on the developed ANN models, the effect of each gasoline constituent on the formation of the blend RON value, was revealed. © 2006 Elsevier B.V. All rights reserved. Keywords: RON; Gasoline; Neural networks

1. Introduction Gasoline is the key profit generator for the petroleum refining industry. The revenue of the gasoline production dominates in the overall refinery economics, since in a modern refining scheme up to 70% of the crude oil is converted into gasoline. Gasoline is produced by blending different fuel streams coming from various production processes. Atmospheric straight run cuts together with products from catalytic reforming and cracking, isomerisation etc. units are the most commonly used feeds for the production of the final gasoline. These fractions are referred to as gasoline components. The blend recipes are determined such that the properties' specifications of the final gasoline are met, while maximizing the profitability of the product under the constraint of the gasoline components' availability. Therefore, optimum control on gasoline blending operations is a key question in the refineries. Research and Motor Octane numbers (RON, MON) constitute the main quality characteristics of the gasoline, as they

⁎ Corresponding author. Tel.: +30 28210 37669; fax: +30 28210 69554. E-mail address: [email protected] (N. Pasadakis). 0378-3820/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.fuproc.2005.11.006

provide a sensitive indication of the anti-knocking behavior of the fuel. The higher the octane number the better the gasoline resists detonation and the smoother the engine runs. Other important technological properties of the commercial gasolines are the Reid Vapor Pressure (RVP), ASTM distillation points, flash point, aromatic and sulfur content etc. These properties are monitored during production to ensure the required technological and environmental quality level of the final gasoline. Although the final gasoline has to meet all the product specifications, RON and MON are considered to be the most important ones. This is especially true during the last decade, when the increase in the compression ratio of motor vehicle engines led to higher requirements in octane rating of the fuels. Additionally, restrictions in using octane number improvers increased the demand in high octane value components. It is estimated that the elimination of the lead additives in gasoline itself caused a gap in the octane rating of the produced gasoline of 2 to 6 numbers depending on their specifications. RON and MON values, as well as most of the gasoline properties, blend in a non-ideal fashion, i.e. they depend nonlinearly on the mixture composition. Therefore, algorithms more complex than linear are necessary for their reliable prediction. There is a marked interest in the refineries to utilize algorithms for the prediction of the octane rating of gasoline blends. Such

N. Pasadakis et al. / Fuel Processing Technology 87 (2006) 505–509

algorithms have to be accurate and robust and they have to remain accurate after the usual changes of the feedstock composition in the refinery. They also serve as the basic tool for the determination of an optimum composition ensuring the desired octane quality, while taking at the same time into account the cost and the availability of the gasoline components. Blending models are appropriate in off-line and in on-line blend operations. In the later case they are incorporated into linear programming schemes, the success of which depends heavily on the prediction quality of the blending model. Till now the calculations of the blends recipes are mostly empirical and they heavily depend on the production experience. Several blending models have been presented in the literature for the calculation of the blend octane rating [1–7]. In general, all these models recognize the non-linear dependence of the blend octane number by modeling it with functions containing a linear part and a non-linear correction term. The well known in the industry Ethyl RT-70 method [1] models the non-linearity of the blending through the fuel sensitivity (RONMON) and the olefin and aromatic content of the components. An approach quite similar to the Ethyl method was presented by Stewart [2]. In this model, the non-linearity was expressed through the olefin content of the gasoline components. Gary and Handwerl [3] presented the Blending Octane Number method, where the gasoline components blend in a linear mode according to their volumetric contribution. However, the Blend Octane Numbers (BONs) were employed instead of the normal RON and MON ratings, thus accounting for the model nonlinearity. The BONs are determined by regression analysis, still based on user experience. A similar method that transforms the non-linear blending octane numbers to linearly blending quantities was presented by Rusin et al. [4]. Non-linear models utilizing second order terms have also been presented [5] where the blend effect (non-linearity) in the mixture octane rating is expressed by a set of interaction coefficients between the components. In a similar approach Zahed et al. [6] presented a polynomial model predicting the blend RON in five components' mixtures. Finally, in a recent study [7] a neural network model was presented for the prediction of the RON of gasoline blends. The algorithm employs the volumetric concentrations of five gasoline components and certain specific properties of the blend, such as the density, RVP, distillation points and sulfur content. However, the blend properties used as input variables in the model were calculated as linear functions of

Table 2 Accuracy indicators of the ANN model Sample set

Min error

Max error

R2

RMSEP

Training Test

− 0.5 − 0.2

0.5 0.4

0.985 0.989

0.17 0.18

the components' concentrations, thus providing no additional information. Different predicting accuracies have been reported for the aforementioned models within and outside the employed training data span. The standard deviation of the prediction error was generally less than 0.8 RON/MON numbers. It should be noted that all the proposed prediction models have been built within a relatively narrow interval of the gasoline components content and RON/MON values, thus rendering their extrapolation capabilities as questionable. In this work a new ANN based prediction model for the calculation of the RON value of gasoline blends is presented. The model utilizes as input variables the volumetric concentrations of seven most commonly employed refinery streams in the gasoline production. The employed fractions were gasoline streams from fluidized catalytic cracking (FCC), reforming (REF), isomerization (ISO), alkylation (ALK) and dimersol (DIM), together with the butanes' fraction (C4) and oxygenate additives (MTBE). Additionally, the RON values of the first five fractions weighted by their concentrations in the blends were included as input variables, such that the developed models would remain accurate in their predictions, even when the quality of the feed stream changes over time. The RON values of the C4 and MTBE were omitted since they are constant thus resulting to an input vector for the ANNs consisting of 12 variables. The algorithm was trained on a large data set from the routine refinery production and found to provide accurate results with the Root Mean Squared Error of Prediction (RMSEP) less than 0.2 RON. The model parameters (ANN weights) are presented such that the model can be easily implemented by the reader. Number of samples

506

50 40 30 20 10 0

Table 1 Gasoline components employed for the blends preparation

FCC REF ISO ALK DIM MTBE C4 Blend

92.5 98.2 77.5 93.3 93.8

94.0 103.6 86.2 94.7 97.6

93.4 101.4 84.5 94.0 95.0 115.0 92.0

93.5

99.0

Number of samples

Typical RON

38 28 16 7 2 3 5

0.2

0.3

0.4

0.5

0.6

0.7

4

Max RON

100.0 54.4 32.0 20.7 14.8 13.3 7.4

0.1

Absolute error of training set

Fraction Min vol. Max vol. Typical vol. Min % % % RON 6.6 0.0 0.0 0.0 0.0 0.0 0.0

0

3 2 1 0

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Absolute error of test set

Fig. 1. Distribution of the absolute errors of prediction for the training and test sets.

N. Pasadakis et al. / Fuel Processing Technology 87 (2006) 505–509

2. Experimental samples and measurements The samples of the gasoline components and of their respective blends were collected from the storage tanks in the MOH Corinth (Greece) refinery, before the addition of any improvers. 173 sample sets were collected in this way during a period of 1 year, such that any variations in the fractions' composition due to different crude oil feedstock or disturbances of the operating parameters could be accounted. Special care was taken for performing sampling during time periods, when the operational routine of the production units changed. RON values were determined in the refinery laboratory according to the ASTM D-2699 procedure under well established schemes for the quality control of the measurements, validated in interlaboratory exercises. The gasoline components employed as well as the ranges of their volumetric content in the blends and of their RON values are presented in Table 1. Typical values of the volumetric content of the gasoline components in the commercial gasoline and their typical RON values according to the refinery experience are also presented. 3. Development of the ANN models Artificial neural networks have found wide application in modeling and optimizing problems in chemical industry. The theory and the use of ANNs have been extensively presented in the literature [8]. Briefly speaking, an ANN is a complex function that enables the modeling of linear or non-linear dependencies between variables, without any a priori knowledge or assumption of the specific model form. The ANN developed during this study consists of an input layer, two hidden layers and an output layer, which include 12, 5, 3 and 1 nodes, respectively. The selection of this topology was based on a large set of trials using different architectures by monitoring the performance of each candidate ANN against the validation error, the normality of the distribution of the residuals and the size of the determined weights. The independent variables vector forms the input layer of the ANN which is multiplied by a weights matrix W1 between the input and the first hidden layer. Hidden layer nodes receive the weighted inputs and transform them using a non-linear activation function

507

S(.). A second weights matrix W2 is then applied and the vector result is fed to the second hidden layer, where it is further transformed using the same non-linear function. Finally the output of the second hidden layer, weighted with the respective layer weight matrix W3 enters the output layer, where the nonlinear function S(.) is once more applied for obtaining the final model output. In a mathematical manner, the ANN model can be expressed by:

ð

W 1d x Þ ð W 2 d 5x1S ð 5x12 3x1 3x5 12x1

y ¼ S W 3d S 1x3





while, the activation function is defined by: 8 9   < Sðz1 Þ = 1 SðZnx1 Þ ¼ Sðz2 Þ ¼ : ; 1 þ e−zi nx1 Sðzn Þ nx1 where, x denotes the input data vector, W1, W2, W3 denote the weights of the successive layers and y denotes the dependent variable (RON) of the data set. The model is described by the set of the adjustable parameters (weights matrices), which are determined during an iterative procedure called training or learning. This procedure is an optimization problem which aims at finding the minimum of the error function in the multidimensional space defined by the adjustable parameters, i.e. to minimize the differences between the ANN output and the experimentally determined dependent variable of the training data set. The training problem is therefore expressed by:

min

W1 ;W2 ;W3

E¼

i¼N X

2 ð yANN −yexp i Þ i

i¼1

¼

N h X i¼1

ð

ð

ð

S W3 d S W2 d S W1 dxi





Þ

; −yexp i

i

where, N denotes the cardinality of the training samples set. The input and the output variables were scaled within the [0.1 ÷ 0.9]

Table 3 ANN model's weights 1st layer 0.2087 1.1257 2.6420 1.7237 4.7096

0.4459 0.1266 1.6635 1.8355 4.8410

2.8362 0.2666 4.0455 0.3566 0.7076

2.1097 0.4585 4.4081 2.4034 2.4094

0.8870 1.8505 4.1850 0.3377 4.2803

2nd layer 0.8793 1.9060 0.7502

4.5494 1.4435 2.2726

2.6979 1.3434 4.2463

1.7050 4.8181 0.4229

2.1606 4.1556 5.0000

3rd layer 4.9924

5.0000

4.8129

0.9645 1.5529 1.9259 0.5088 2.6084

0.9285 0.0476 0.3407 0.6100 1.2407

0.2556 0.4403 1.1853 0.0413 1.2962

0.1968 0.1336 2.1670 0.6413 0.3586

0.7356 0.2347 1.8113 0.6480 0.5321

0.1448 0.8412 4.2393 0.8242 5.0000

1.4056 0.2343 0.2121 0.0509 1.0356

508

N. Pasadakis et al. / Fuel Processing Technology 87 (2006) 505–509 96.5

4. Evaluation of the developed ANN model

96

The way an ANN model describes a multivariate space is especially critical in cases like the current one, where the available training data are not uniformly distributed within the variables space. The performance of the developed ANNs was thoroughly studied by applying the models to a series of “synthetic” blends, which spanned the input variables' space in a predetermined systematic way. The purpose of this test was twofold. Firstly to verify that the model describes successfully the general dependencies between the input and output variables, instead of “passing” through separate points and secondly to reveal the influence of each gasoline component on the blend RON (blend effect). The composition of the “synthetic” blends was estimated as follows: for each one of the seven gasoline components involved in this study, twenty “synthetic blends” were calculated containing the component of interest at concentrations uniformly distributed within its allowed margins (Table 1). The rest of the mixture comprised of all the remaining fractions in concentrations proportional to their typical contribution in the commercial gasoline (Table 1). Typical RON values presented in Table 1 were accepted as the RON values of the gasoline components. In fact, the blends derived in this manner represent mixtures of a “typical” gasoline and the component of interest at increasing concentration levels. These “synthetic” blends are successive adjacent points in the seven-dimensional space of fractions concentrations and hence they can be used to observe in a systematic way how well did the ANN model “learn” the input data structure. The RON values of the “synthetic” blends were calculated by a series (more than 10) of separately trained ANN models developed with identical structure, input and output populations but with different initial weights. The obtained RON values

RON value

95.5

95

94.5

94

93.5

0

10

20

30

40

50

60

70

80

90

100

FCC content (% vol.) in the "synthetic" blend

Fig. 2. RON calculated profiles of blends with varying FCC fraction content.

RON value

range. The available sample population was split randomly into two subsets, a training one including 160 of the available samples and a test one including 13 samples. The latter was used for evaluating the performance of the trained ANN. The back propagation training algorithm with a momentum term was used. Specific care was taken to avoid over-fitting by means of checking the validation error and the normality of the distribution of the residual errors. A great number of ANN models were trained in order to ensure that individual models describe equally well the dependence between the RON value and the employed input variables. The statistical indicators of the selected “best-performing” ANN model for the training and the test sample sets are presented in Table 2. Additionally, the prediction errors for both the training and the test sets are demonstrated as histograms in Fig. 1. The weights of the selected ANN model are presented in Table 3. 98

98

98

97

97

97

96

96

96

95

95

95

94

94

94

93

93

93

92

0

50

100

92

0

20

RON value

% FCC 98

97

97

96

96

95

95

94

94

93

93 0

10

% ALK

60

% REF

98

92

40

20

92

0

5

10

92

0

20

40

% ISO

15

% DIM

Fig. 3. RON values of the “synthetic” mixtures (dotted line—ANN calculated, continuous line—linear blending rule).

N. Pasadakis et al. / Fuel Processing Technology 87 (2006) 505–509

were found to exhibit a pronounced stability in their patterns, indicating that all the trained ANN models could converge to close points on the multidimensional error surface. In other words, the similarity in these solutions indicates that the ANNs have been “trained” to describe the overall performance of the sample set instead of passing through separate points. To demonstrate this, the calculated RONs of blends with varying amounts of FCC gasoline fraction using three independently trained ANN are presented in Fig. 2. Subsequently, the average values of the RON profiles from 10 independently trained ANNs were calculated (Fig. 3, dotted lines) for the five main refinery fractions involved in the gasoline blending. For comparison purposes, the RON values of the same ‘synthetic’ blends were calculated assuming a linear blend law (Fig. 3, continuous lines). A significant deviation from the linear blend rule can be observed, exhibiting a specific pattern for each gasoline component. From the FCC profile it can be noticed that according to the developed models the addition of FCC into a blend generally leads to lower RON values with a non-linear behavior especially in the 20–70 vol.% content. The addition of reformate increases the RON value of the blend in a smoother fashion than the linear mixing rule. The opposite is true for the isomerate, the addition of which leads to the decrease of the blend RON. It should be mentioned that the above results have been derived by applying the ANN models to blends containing the specific gasoline component mixed with a “typical” gasoline consisting of the remaining components at certain invariable proportions. Therefore it is not known whether the same blend effect could be observed in mixtures containing the gasoline components in significantly different concentrations, lying out of the variables ranges employed during the current study. 5. Conclusions Reliable RON prediction of gasoline blends can be obtained using Artificial Neural Network models with accuracy compa-

509

rable to the respective of the standard ASTM method. The analysis of the ANNs predictions within the range of the training set values can provide information on the mutual influence between the gasoline components in the blends, revealing the nature of the blend effect. Further development of the proposed algorithm should include prediction of other significant and non-ideally blended properties of gasolines such as RVP and distillation profiles. Once developed, the ANN prediction models can be involved in optimization algorithms to determine the composition of blends with desired RON value, satisfying at the same time other refinery constrains like cost and availability. References [1] W.C. Healy, C.W. Maasen, J. Peterson, A new approach to blending octanes, 24th Midyear Meeting of the American Petroleum Institute's Division of Refining, New York, 1959, p. 39. [2] W.E. Stewart, Predict octanes for gasoline blends, Petroleum Refiner 38 (1959) 135–139. [3] J.H. Gary, G.E. Handwerl, Petroleum Refining Technology and Economics, 3rd ed., Marcel Dekker, New York, 1994. [4] M.H. Rusin, H.S. Chung, J.F. Marshall, A ‘transformation’ method for calculating the research and motor octane numbers of gasoline blends, Industrial and Engineering Chemistry Fundamentals 20 (1981) 195–204. [5] D.C. Modgomery, Design and Analysis of Experiments, John Wiley and Sons, New York, 1991. [6] A.H. Zahed, S.A. Mullah, M.D. Bashir, Predict octane number for gasoline blends, Hydrocarbon Processing 5 (1993) 85–87. [7] B.S.N. Murty, R.N. Rao, Global optimization for prediction of blend composition of gasolines of desired octane number and properties, Fuel Processing Technology 85 (2004) 1595–1602. [8] J.R.M. Smits, W.J. Melssen, L.M.C. Buydens, G. Kateman, Using artificial neural networks for solving chemical problems. Part I. Multi-layer feedforward networks, Chemometrics and Intelligent Laboratory Systems 22 (1994) 165–189.