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Evaluation of ANN modeling for prediction of crude oil fouling behavior
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Applied Thermal Engineering 28 (2008) 668–674 www.elsevier.com/locate/apthermeng
Evaluation of ANN modeling for prediction of crude oil fouling behavior Javad Aminian, Shahrokh Shahhosseini
*
Department of Chemical Engineering, Iran University of Science and Technology, PO Box 16765-163, Narmak, Tehran, Iran Received 20 March 2007; accepted 14 June 2007 Available online 3 July 2007
Abstract In this research, artificial neural network (ANN) modeling for prediction of crude oil fouling behavior in preheat exchangers of crude distillation units has been evaluated. Outputs of the ANN model have been compared with appropriate sets of experimental data in order to compute overall mean relative error (OMRE). The value of OMRE was also computed for three different threshold fouling models. The OMRE of ANN model was 26.23% whereas the lowest OMRE obtained using threshold fouling models was 47.9%. In order to identify relative significance of the governing variables, a sensitivity analysis, named sequential zeroing of weights (SZWs), has also been performed. This analysis showed that the influence of crude velocity and tube diameter on the fouling rate is higher than tube surface temperature. 2007 Elsevier Ltd. All rights reserved. Keywords: Crude oil; Fouling; Modeling; Neural networks; Sensitivity analysis
1. Introduction Fouling in preheat exchangers of crude distillation units (CDU) is a serious operating problem for oil refineries. Two main effects of fouling on preheat network operation are reduced heat recovery and increased pressure drop. About half of the financial penalties due to the fouling in an oil refinery are attributed to crude distillation unit. Depending on the refinery age and subsequent design modifications, the number of heat exchangers used in the preheat train varies from 16 to 60 [1]. Recovery of thermal energy in the preheat train is critical for the overall energy efficiency of the CDU. The worldwide costs, associated specifically with crude oil fouling in preheat trains were equated to around 20% of all heat exchanger fouling which is estimated to be of the order of $4.5 million/year [2]. It arises from additional fuel required for the furnace due to the reduced heat recovery in the preheat train, produc-
*
Corresponding author. Tel.: +98 21 73912701. E-mail address: [email protected] (S. Shahhosseini).
1359-4311/$ - see front matter 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2007.06.022
tion loss during undesirable shutdowns, on-line cleaning devices and treatment plants and also environmental penalties associated with disposal of cleaning chemicals. Crude oils have different compositions depending on the place where they have been produced. A crucial factor governing fouling is the amount of asphaltenes in the crude and their solubility and reactivity at high temperatures. Asphaltene is a highly condensed aromatic material that is responsible for the black color of many oils. Heavy crude oils tend to have higher asphaltene contents and are more likely to causes fouling. Fouling can occur throughout the preheat network, although different mechanisms are likely to occur in different exchangers. Crude oil passes through a desalter unit before it reaches to the high temperature heat exchangers. Upstream of the desalter, deposition of salts, waxes and corrosion products is common. However, downstream of the desalter, the dominant mechanism is chemical reaction fouling that is due to elevated temperatures of this area. The translation of fundamental understanding of fouling and its effects to refinery applications is hampered by the complex nature and variability of crude feed stocks.
J. Aminian, S. Shahhosseini / Applied Thermal Engineering 28 (2008) 668–674
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Nomenclature ANN CDU E FFN OMRE Pr R Rf Re Rmdiffi RMSE
artificial neural network crude distillation units activation energy (kJ mol1) feed forward network overall mean relative error Prandtl number universal gas constant fouling resistance (m2 K kW1) Reynolds number difference between RMSE and RMSEi root mean square error of the complete network predictions RMSEi root mean square error of the network predictions when the weights of the ith input variable are set to zero
Since crude oils often feature synergetic combinations of the mechanisms, fouling mechanisms that have been identified via controlled studies of some particular fluids cannot be applied directly to the refinery situations [3]. The applicability of the models developed from laboratory data to the field situations is an important issue. Crude petroleum and many organic fluids have complex composition that causes difficulties to isolate the key factors of fouling. Even when they have been identified, their exact role in the fouling is not determined. If fouling mechanisms in the field and laboratory are not identical, the data from the two situations could not be comparable [4]. Therefore, a number of semi-empirical models have been reported for fouling phenomena and no mechanistic model has been proposed. These semi-empirical models have some coefficients whose values are to be determined using a set of experimental data. It is a commonly accepted practice to use another set of data from the same laboratory or field or from other sources to evaluate the model. Unfortunately, none of the researchers who have developed such a models for crude oil fouling have reported to conduct so. Therefore, it is not possible to judge about the applicability of the models to other set of data. However, in this work a set of data is used to develop ANN model and another set of data is employed to evaluate the model. Neural networks have recently become the focus of much attention, largely because of their capability to handle complicated and non-linear systems. Nowadays, there is a vast amount of literature on ANN applied to practi-
SZW Tb Ts Tfilm
sequential zeroing of weights bulk temperature (C) surface temperature (C) film temperature (C)
Greek symbols a constant parameter in Eqs. (1)–(4) b constant parameter in Eqs. (1)–(4) c constant parameter in Eqs. (1)–(4) q density (kg m3) sw wall shear stress (N m2)
cal problems of thermal engineering with special concern to fouling phenomenon in chemical plants. Malayeri and Mu¨ller-Steinhagen presented the use of neural network analysis for the prediction of fouling behavior under sub-cooled flow boiling [5]. They reported the advantages and disadvantages of the neural network architecture when the technique is applied to fouling data. It has been shown that the predictability of ANN is promising when dominant variables are known and also adequate data are presented to the network. Romeo and Gareta and Teruel et al. presented the use of neural network to study fouling behavior of boilers [6,7]. Lalot and coworkers demonstrated ANN application for online fouling detection in an electrical circulating heater [8–10]. Radhakrishnan et al. recently developed a successful neural network based fouling model for preheat exchangers of CDU and presented a preventive maintenance scheduling tool using historical plant operating data [11]. The present study seeks to address crude oil fouling by evaluating recently developed threshold fouling models and comparing them with a neural network model which is developed in this work. 2. Threshold fouling models The threshold fouling concept for crude oil was introduced by Ebert and Panchal in 1995 [12]. They developed the following correlation for predicting the linear rate of fouling as a function of film temperature and fluid velocity.
Table 1 Constant parameters for some of threshold fouling models E (kJ mol1) Panchal model Polley model Nasr model
48 48 22.618
a (m2 K kW1 h1) +04
5.03 · 10 1 · 10+6 10.98
b
c
0.66 0.8 1.5472
1.45 · 1004 (m2 K kW1 h1 Pa1) 1.5 · 1009 (m2 K kW1 h1) 0.96 · 1010 (m2 K kW1 h1)
J. Aminian, S. Shahhosseini / Applied Thermal Engineering 28 (2008) 668–674
39.02 61.36 61.47 113.22 177.34 59.02
3.4232 7.9001 10.22 37.498 5.4049 23.04 3.359 4.259 2.393 2.931 1.312 1.703 3.222 4.027 2.317 2.801 1.297 1.658 8.8 21.1 7.6 18.4 1.5 17.1 14.4 31.6 12.8 27.8 4.5 26.2
Percent of mean relative error
Nasr model fouling rate · 103 E = 50 (m2 K kW1 h1) Nasr model fouling rate · 103 E = 48 (m2 K kW1 h1) Polley model fouling rate · 103 E = 50 (m2 K kW1 h1) Polley model fouling rate · 103 E = 48 (m2 K kW1 h1) Panchal model fouling rate · 103 E = 48 (m2 K kW1 h1)
4 6.6 3.1 5.4 0 3.4 2.6 7.9 3.5 37.5 5.4 25.7 288 288 284 283 275 275 344 393 349 396 331 419
Polley has computed the parameters of Eq. (3), applying Knudsen’s experimental data, and reported them as shown in the second row of Table 1. Knudsen’s experiment is related to identify threshold fouling for Alaskan crude. It featured an annular test cell with a heated inner rod, where bulk flow velocities varied in the range of 0.91–3 m/s, at two bulk temperatures of 149 and 204 C. During the
1.77 1.77 2.13 2.13 3.17 3.17
ð3Þ
5.5 5.5 5.5 5.5 5.5 5.5
dRf ¼ aReb Pr0:33 expðE=RT w Þ cRe0:8 dt
Experimental fouling rate · 103 (m2 K kW1 h1)
When applying Eq. (1) Prandtl number was determined employing a set of experimental data to be a constant value of about 2.5. However, Panchal and coworkers used another set of data in which Prandtl number varied in the range of 2.5–8.2. Therefore, it was necessary to include Prandtl number in Eq. (2). They assumed that the power of Prandtl number to be 0.33 according to the common heat transfer correlations. Panchal and coworkers obtained their laboratory experimental data using a high-pressure autoclave fouling unit under various conditions [14]. They have calculated constant parameters of Eq. (2) employing the experimental data and reported them as presented in the first row of Table 1. Panchal threshold model was improved by Polley et al. in 2002 as show by Eq. (3) [15]. The model was validated employing Knudsen’s experimental results [16]. The model differs primarily in the use of wall temperature, Tw, in the deposition term and Reynolds number rather than wall shear stress in inhibition term.
Tb (C)
ð2Þ
Ts (C)
dRf ¼ aReb Pr0:33 expðE=RT film Þ csw dt
Velocity (m s1)
where a, b, c and E are constants to be determined from experimental data. This approach provides a semi-empirical basis for quantitative interpretation of fouling data in terms of deposition and inhibition mechanisms. This concept suggests that a combination of low temperature and high shear stress will produce a threshold condition such that the fouling rate will be essentially zero. Therefore, a threshold condition is in fact the boundary between no fouling and fouling zones. The approach appears to be very useful for heat exchanger designers, since threshold conditions for each crude oil can be used to mitigate fouling without reducing heat recovery by selection of robust designs and network structures that do not foul. Ebert and Panchal model assumes all the chemical reactions to be included by the Arrhenius term in Eq. (1). In addition, it ignores the effects of crud oil thermal conductivity and specific heat and only considers the impacts of crud oil density and viscosity as presented by Reynolds number. To modify this correlation, Prandtl number was also incorporated into the model by Panchal and coworkers in 1997 [13]
Developed ANN Model fouling rate · 103 (m2 K kW1 h1)
ð1Þ
Tube diameter (mm)
dRf ¼ aReb expðE=RT film Þ csw dt
Table 2 Comparison between the ANN model and threshold fouling models for Shell West hollow refinery data [13,15,17]
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J. Aminian, S. Shahhosseini / Applied Thermal Engineering 28 (2008) 668–674
experiment, heater surface temperature varied in the range of 232–371 [16]. The latest threshold fouling model (Eq. (4)) has been developed by Nasr and Givi in 2006 which, is independent of Prandtl number [17]. dRf ¼ aReb expðE=RT film Þ cRe0:4 dt
ð4Þ
Nasr has estimated the constant parameters of Eq. (4) using the experimental data, measured by Saleh et al. for an Australian light crude oil as shown in the third row of Table 1. The experiment focuses on thermal fouling caused by the heating of Gippsland crude oil at moderate temperatures. The oil was maintained under nitrogen at a pressure of 379 kPa, and re-circulated at bulk temperatures of 80– 120 C through an electrically heated annular probe at
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velocities in the range of 0.25–0.65 m/s, where heater surface temperatures was between 80 and 260 C [18]. 3. Evaluation of the developed ANN model In this study, experimental data of fouling rate reported by Panchal [13], Polly [15] and Nasr [17] are used to develop an ANN model. They were obtained for four different tube diameters as mentioned in Tables 2–5. These tables also show, in these experiments, crude velocity varies from 0.91 to 3.17 m/s and tube surface temperature varies from 232–467 C. As a rule of thumb, a combination of high surface temperature, large tube diameter and low fluid velocity causes fouling formation to increase. Therefore, these variables were measured by the researchers to investigate their impacts on the fouling rate. Tube diameter,
Table 3 Comparison between the ANN model and threshold fouling models for Scarborough et al. data [13,15,17] Tube diameter (mm)
Velocity (m s1)
Ts (C)
Tb (C)
Experimental fouling rate · 103 (m2 K kW1 h1)
Panchal model fouling rate · 103 (m2 K kW1 h1)
Polley model fouling rate · 103 (m2 K kW1 h1)
15.2 15.2 15.2 15.2 15.2 15.2 15.2 15.2
2.48 1.25 2.48 1.25 1.25 1.29 2.53 2.53
414 467 379 432 401 374 404 376
363 371 351 360 353 344 353 345
3.2 20.1 2.8 11.4 7.9 5.6 4 1.2
3.1 11.6 2.2 8.5 6.4 4.7 2.2 1.2
4 37.3 1.6 23.9 14.8 8.4 2.2 0
21.54
68.18
Percent of mean relative error
Nasr model fouling rate · 103 (m2 K kW1 h1) 1.293 2.242 1.26 1.938 1.731 1.523 1.271 1.231 63.52
Developed ANN Model fouling rate · 103 (m2 K kW1 h1) 32.199 20.098 3.8952 11.412 7.8908 4.7388 3.9824 1.2036 7.01
Table 4 Comparison between the ANN model and threshold fouling models for Knudsen et al. data [13,15,17] Tube diameter (mm)
Velocity (m s1)
Ts (C)
Tb (C)
Experimental fouling rate · 103 (m2 K kW1 h1)
9.5 9.5 9.5 9.5 9.5 9.5 9.5 9.5 9.5 9.5 9.5 9.5 9.5 9.5 9.5 9.5 9.5 9.5 9.5 9.5
0.91 0.91 0.91 0.91 0.91 0.91 0.91 0.91 1.68 1.68 1.68 1.68 1.68 1.68 2.44 2.44 2.44 2.44 3.05 3.05
232 246 260 261 288 316 343 371 260 288 302 316 343 371 315 316 343 371 316 329
204 204 204 204 204 204 204 204 204 204 204 204 204 204 204 204 204 204 204 204
7 25 5 2 2 6 9 37 0 21 3 1.1 7 26 1.5 2.7 5 72.5 0.5 1
Percent of mean relative error
Panchal model fouling rate · 103 (m2 K kW1 h1) 2.3
Polley model fouling rate · 103 (m2 K kW1 h1)
3.5 3.6 5.1 7.1 9.7 13 0.0019 2.4 3 3.8 5.5 7.7 1.4 1.4 2.8 4.5 – 0.2
0.9 2 3.4 3.5 7.4 13.5 21.9 34 0 2.3 4 6 11.2 18.6 2.2 2.3 6.2 11.7 0.23 1.6
65.97
91.32
–
Nasr model fouling rate · 103 (m2 K kW1 h1) 1.853 1.927 2.011 2.017 2.208 2.448 2.724 3.064 0.985 1.047 1.081 1.116 1.191 1.278 0.981 0.983 1.026 1.073 0.991 1.008 60.46
Developed ANN Model fouling rate · 103 (m2 K kW1 h1) 6.9986 24.995 2.8702 2.0048 1.9982 6.8184 9.0005 27.19 5.31E03 20.999 3.0149 1.098 1.9937 25.997 1.8012 2.948 5.5489 72.499 0.28444 1.2212 13.73
45.18 57.37 57.59 99.13 45.09
28.71
0.927 0.946 0.915 0.924 0.939 0.961 1 0.934 0.955 0.922 0.934 0.945 0.966 1.005 0 0 0 0 0 0 0.35 2.4 2.7 0.8 1 0.8 1.2 1.8
0.03 0 0.3 1.2 1.2 3.8 7.1
120
Percent of mean relative error
0 0 0.5 1.1 0.8 5.6 8.1 230 230 220 220 227 223 223 21.1 21.1 21.1 21.1 21.1 21.1 21.1
1.15 0.95 1.16 0.98 1.16 1.16 0.98
260 255 260 255 270 288 295
Experimental fouling rate · 103 (m2 K kW1 h1)
Percent of Mean Relative Error
Nasr model fouling rate · 103 E = 48 (m2 K kW1 h1) Nasr model fouling rate · 103 E = 44 (m2 K kW1 h1) Polley model fouling rate · 103 E = 48 (m2 K kW1 h1) Polley model fouling rate · 103 E = 44 (m2 K kW1 h1) Panchal model fouling rate · 103 (m2 K kW1 h1)
crude velocity and tube surface temperature are used as inputs of the network and its output is fouling rate. All of the conventional threshold fouling models, which were explained in Section 2 have also been developed using a combination of these parameters. It is a common practice in ANN modeling to divide all of the related experimental data into two parts. The first part is used to train the model and the second part is applied to test the model. For this reason, the experimental data presented in Tables 2–5, were also used in the same manner. In the training phase, 27 randomly data points were introduced to the network. The remaining 14 data points were used for the test phase. A feed forward network (FFN) combined with back propagation algorithm was used to train the ANN model. FFNs often have one or more hidden layers of sigmoid neurons followed by an output layer of linear neurons. If the last layer of a FFN has sigmoid neurons, then the outputs of the network are limited to a small range, while a linear transfer function enables outputs to take any value. A trial-and-error approach was used to minimize the error in order to determine the optimal combination of number of hidden layers and number of neurons. The best performance was obtained when a network consists of four layers, with 3, 5 and 6 neurons in the input layer, the first and the second hidden layers, respectively, and just one neuron in the output layer. The activation function (transfer function) used in the hidden layers is tangent sigmoid function and also linear transfer function is assumed for the output layer. In order to evaluate ANN model, its outputs have been compared with crude oil fouling experimental data, reported by Panchal [13], Polley [15] and Nasr [17], as shown in the last column of Tables 2–5. ANN model predictions were also compared with the outputs of the threshold fouling models, which were mentioned in Section 2. Tables 2–5 show that the ANN model predictions for crude oil fouling rate is significantly better than those of threshold fouling models. The ANN model results in an overall
Panchal Model
Tb (C) Ts (C) Velocity (m s1) Tube diameter (mm)
Table 5 Comparison between the ANN model and threshold fouling models for Shell Wood River refinery data [13,15,17]
0.25222 0.0687 0.25122 0.00439 0.79472 9.8055 8.1009
J. Aminian, S. Shahhosseini / Applied Thermal Engineering 28 (2008) 668–674
Developed ANN Model fouling rate · 103 (m2 K kW1 h1)
672
100
Polley Model Nasr Model
80
Developed ANN Model (a)
60
40 (a)
20
0 Scarborough (b) Experimental
(c)
Knudsen Experimental
Shell Wood River (d) refinery
Shell West hollow (d) refinery
Fig. 1. Comparison of the ANN model and threshold fouling models for various experimental data: (a) minimum reported fouling rate, (b) cited in Ref. [19], (c) cited in Ref. [15] and (d) cited in Ref. [13].
J. Aminian, S. Shahhosseini / Applied Thermal Engineering 28 (2008) 668–674
mean relative error (OMRE) of 26.23%. By comparison, OMRE of the models proposed by Panchal, Nasr and Polley were 47.9%, 60.68% and 75.36%, respectively. A summary of this comparison can be seen in Fig. 1. 4. Sensitivity analysis The scope of this section is to implement a recently developed sensitivity analysis approach, which is used to rank the general importance of the input variables for the output variable of the neural model. This approach is called sequential zeroing of weights (SZWs). SZW method proposed by Nord and Jacobsson [20] estimates the degradation in output variables of a trained neural network when the weights connecting the ith input variable to the nodes of the hidden layer are all set to zero. In this way, the contribution of that variable to the network response is excluded. According to this method, the measure that is calculated in order to reveal the importance of the ith input variable is the difference between the root mean square error (RMSE) of the complete network’s predictions and RMSE obtained when the ith variable is excluded from the trained network (RMSEi), both being calculated on the same data set Rmdiff i ¼ RMSEi RMSE
ð5Þ
Generally, the values of Rmdiffi are greater than zero. The variable with the greater importance is the one that leads to a greater value of Rmdiffi. The numeric values of Rmdiffi are shown in Fig. 2. It can be seen that the influence of tube diameter and velocity of the crude on the fouling rate is higher than tube surface temperature. SZWs method can only be implemented after a neural network is trained. Therefore SZWs results can be validated based on the assumption that the ANN model is a sufficiently accurate model. This assumption can be satisfied since the results of the ANN model that are presented in Section 3 are more reasonable than previous threshold fouling models.
Root Mean Square Error Difference (Rmdiffi) 2.00E-03 1.80E-03 1.60E-03 1.40E-03 1.20E-03 1.00E-03 8.00E-04 6.00E-04 4.00E-04 2.00E-04 0.00E+00 Tube Diameter
Crude velocity
Surface temperature
Fig. 2. Result of sensitivity analysis.
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5. Conclusion In this paper, an ANN model has been established in order to predict total fouling rate of crude oil employing an experimental data set that has been reported in the literature. Results of the ANN model were compared with those of three different threshold fouling models. The ANN model predicts crude oil fouling rate with an OMRE of 26.23%. Whereas, OMRE of the models proposed by Panchal, Nasr and Polley were 47.9%, 60.68% and 75.36%, respectively. A sensitivity analysis, named sequential zeroing of weights (SZWs), has also been performed on the ANN model. The results of this analysis revealed that the influence of tube diameter and velocity of the crude on the fouling rate is higher than tube surface temperature. Whilst the results given in this paper are obtained for the specific experimental data that are reported by Panchal, Polley and Nasr the principles of the ANN modeling and sensitivity analysis are readily applicable to other situations. Acknowledgement The authors are thankful for the comments and advice given by the anonymous reviewers. They have substantially improved the content of this work and pointed out some research directions of particular interest. References [1] C.B. Panchal, E.-Ping Huangfu, Effect of mitigating fouling on the energy efficiency of crude oil distillation, Heat Transfer Engineering 21 (2000) 3–9. [2] H. Mu¨ller-Steinhagen, Heat exchanger fouling: mitigation and cleaning technologies, Transactions of IChemE (Rugby UK), 2000. [3] B.L. Yeap, D.I. Wilson, G.T. Polley, S.J. Pugh, Mitigation of crude oil refinery heat exchanger fouling through retrofits based on thermohydraulic fouling models, Chemical Engineering Research and Design 84 (2004) 53–71. [4] S. Asomaning, C.B. Panchal, C.F. Liao, Correlating field and laboratory data for crude oil fouling, Heat Transfer Engineering 21 (2000) 17–23. [5] M.R. Malayeri, H. Mu¨ller-Steinhagen, Neural network analysis of heat transfer fouling data, in: The 4th United Engineering Foundation Conference on Heat Exchanger Fouling: Fundamental Approaches & Technical Solutions, Davos, Switzerland, 2001, pp. 145–150. [6] L.M. Romeo, R. Gareta, Neural network for evaluating boiler behavior, Applied Thermal Engineering 26 (2006) 1530–1536. [7] E. Teruel, C. Cortes, L.I. Diez, I. Arauzo, Monitoring and prediction of fouling in coal-fired utility boilers using neural networks, Chemical Engineering Science 60 (2005) 5035–5048. [8] S. Lalot, S. Lecoeuche, Online fouling detection in electrical circulating heaters using neural networks, International Journal of Heat and Mass Transfer 46 (2003) 2445–2457. [9] S. Lalot, On-line detection of fouling in a water circulating temperature controller (WCTC) used in injection moulding: part 1: principles, Applied Thermal Engineering 26 (2006) 1087–1094. [10] S. Lalot, On-line detection of fouling in a water circulating temperature controller (WCTC) used in injection moulding: part 2: application, Applied Thermal Engineering 26 (2006) 1095–1105. [11] V.R. Radhakrishnan, M. Ramasamy, H. Zabiri, V. Do Thanh, N.M. Tahir, H. Mukhtar, M.R. Hamid, N. Ramli, Heat exchanger fouling
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J. Aminian, S. Shahhosseini / Applied Thermal Engineering 28 (2008) 668–674 model and preventive maintenance scheduling tool, Applied Thermal Engineering (2007), doi:10.1016/j.applthermaleng.2007.02.009. W.A. Ebert, C.B. Panchal, Analysis of exxon crude-oil-slip stream coking, in: Proceedings of Mitigation of Industrial Heat Exchangers, California, June 18–23, 1995, p. 451. C.B. Panchal, W.C. Kuru, C.F. Liao, W.A. Ebert, J.W. Palen, Threshold condition for crude oil fouling, in: Proceedings of Understanding Heat Exchanger Fouling and Its Mitigation, Barga, Italy, May 11–16, 1997. W.C. Kuru, C.B. Panchal, C.F. Liao, J.W. Palen W.A. Ebert, Development of high temperature, high pressure fouling unit, in: Proceedings of Understanding Heat Exchanger Fouling and Its Mitigation, Engineering Foundation Conference, Lucca, Italy, 1997. G.T. Polley, D.I. Wilson, B.L. Yeap, S.J. Pugh, Evaluation of laboratory crude oil threshold fouling data for application to refinery preheat trains, Applied Thermal Engineering 22 (2002) 777–788.
[16] J.G. Knudsen, L. Dahcheng, W.A. Ebert, The determination of the threshold fouling curve for a crude oil, in: T.R. Bott et al. (Eds.), Understanding Heat Exchanger Fouling and Its Mitigation, Begell House, New York, 1999, pp. 265–272. [17] M.R. Jafari Nasr, M. Majidi, Modeling of crude oil fouling in preheat exchangers of refinery distillation units, Applied Thermal Engineering 26 (2006) 1572–1577. [18] Z. Saleh, R. Sheikholeslami, A.P. Watkinson, Heat exchanger fouling by a light Australian crude oil, in: Heat Exchanger Fouling and Cleaning Fundamentals and Applications, Santa Fe, 2003. [19] C.E. Scarborough, D.C. Cherrington, R. Diener, L.P. Golan, Coking of crude oil at high heat flux levels, Chemical Engineering Progress 75 (1979) 41–46. [20] L.I. Nord, S.P. Jacobsson, A novel method for examination of the variable contribution to computational neural network models, Chemometrics and Inteligent Laboratory Systems 44 (1998) 153–160.
Applied Thermal Engineering 28 (2008) 668–674 www.elsevier.com/locate/apthermeng
Evaluation of ANN modeling for prediction of crude oil fouling behavior Javad Aminian, Shahrokh Shahhosseini
*
Department of Chemical Engineering, Iran University of Science and Technology, PO Box 16765-163, Narmak, Tehran, Iran Received 20 March 2007; accepted 14 June 2007 Available online 3 July 2007
Abstract In this research, artificial neural network (ANN) modeling for prediction of crude oil fouling behavior in preheat exchangers of crude distillation units has been evaluated. Outputs of the ANN model have been compared with appropriate sets of experimental data in order to compute overall mean relative error (OMRE). The value of OMRE was also computed for three different threshold fouling models. The OMRE of ANN model was 26.23% whereas the lowest OMRE obtained using threshold fouling models was 47.9%. In order to identify relative significance of the governing variables, a sensitivity analysis, named sequential zeroing of weights (SZWs), has also been performed. This analysis showed that the influence of crude velocity and tube diameter on the fouling rate is higher than tube surface temperature. 2007 Elsevier Ltd. All rights reserved. Keywords: Crude oil; Fouling; Modeling; Neural networks; Sensitivity analysis
1. Introduction Fouling in preheat exchangers of crude distillation units (CDU) is a serious operating problem for oil refineries. Two main effects of fouling on preheat network operation are reduced heat recovery and increased pressure drop. About half of the financial penalties due to the fouling in an oil refinery are attributed to crude distillation unit. Depending on the refinery age and subsequent design modifications, the number of heat exchangers used in the preheat train varies from 16 to 60 [1]. Recovery of thermal energy in the preheat train is critical for the overall energy efficiency of the CDU. The worldwide costs, associated specifically with crude oil fouling in preheat trains were equated to around 20% of all heat exchanger fouling which is estimated to be of the order of $4.5 million/year [2]. It arises from additional fuel required for the furnace due to the reduced heat recovery in the preheat train, produc-
*
Corresponding author. Tel.: +98 21 73912701. E-mail address: [email protected] (S. Shahhosseini).
1359-4311/$ - see front matter 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2007.06.022
tion loss during undesirable shutdowns, on-line cleaning devices and treatment plants and also environmental penalties associated with disposal of cleaning chemicals. Crude oils have different compositions depending on the place where they have been produced. A crucial factor governing fouling is the amount of asphaltenes in the crude and their solubility and reactivity at high temperatures. Asphaltene is a highly condensed aromatic material that is responsible for the black color of many oils. Heavy crude oils tend to have higher asphaltene contents and are more likely to causes fouling. Fouling can occur throughout the preheat network, although different mechanisms are likely to occur in different exchangers. Crude oil passes through a desalter unit before it reaches to the high temperature heat exchangers. Upstream of the desalter, deposition of salts, waxes and corrosion products is common. However, downstream of the desalter, the dominant mechanism is chemical reaction fouling that is due to elevated temperatures of this area. The translation of fundamental understanding of fouling and its effects to refinery applications is hampered by the complex nature and variability of crude feed stocks.
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Nomenclature ANN CDU E FFN OMRE Pr R Rf Re Rmdiffi RMSE
artificial neural network crude distillation units activation energy (kJ mol1) feed forward network overall mean relative error Prandtl number universal gas constant fouling resistance (m2 K kW1) Reynolds number difference between RMSE and RMSEi root mean square error of the complete network predictions RMSEi root mean square error of the network predictions when the weights of the ith input variable are set to zero
Since crude oils often feature synergetic combinations of the mechanisms, fouling mechanisms that have been identified via controlled studies of some particular fluids cannot be applied directly to the refinery situations [3]. The applicability of the models developed from laboratory data to the field situations is an important issue. Crude petroleum and many organic fluids have complex composition that causes difficulties to isolate the key factors of fouling. Even when they have been identified, their exact role in the fouling is not determined. If fouling mechanisms in the field and laboratory are not identical, the data from the two situations could not be comparable [4]. Therefore, a number of semi-empirical models have been reported for fouling phenomena and no mechanistic model has been proposed. These semi-empirical models have some coefficients whose values are to be determined using a set of experimental data. It is a commonly accepted practice to use another set of data from the same laboratory or field or from other sources to evaluate the model. Unfortunately, none of the researchers who have developed such a models for crude oil fouling have reported to conduct so. Therefore, it is not possible to judge about the applicability of the models to other set of data. However, in this work a set of data is used to develop ANN model and another set of data is employed to evaluate the model. Neural networks have recently become the focus of much attention, largely because of their capability to handle complicated and non-linear systems. Nowadays, there is a vast amount of literature on ANN applied to practi-
SZW Tb Ts Tfilm
sequential zeroing of weights bulk temperature (C) surface temperature (C) film temperature (C)
Greek symbols a constant parameter in Eqs. (1)–(4) b constant parameter in Eqs. (1)–(4) c constant parameter in Eqs. (1)–(4) q density (kg m3) sw wall shear stress (N m2)
cal problems of thermal engineering with special concern to fouling phenomenon in chemical plants. Malayeri and Mu¨ller-Steinhagen presented the use of neural network analysis for the prediction of fouling behavior under sub-cooled flow boiling [5]. They reported the advantages and disadvantages of the neural network architecture when the technique is applied to fouling data. It has been shown that the predictability of ANN is promising when dominant variables are known and also adequate data are presented to the network. Romeo and Gareta and Teruel et al. presented the use of neural network to study fouling behavior of boilers [6,7]. Lalot and coworkers demonstrated ANN application for online fouling detection in an electrical circulating heater [8–10]. Radhakrishnan et al. recently developed a successful neural network based fouling model for preheat exchangers of CDU and presented a preventive maintenance scheduling tool using historical plant operating data [11]. The present study seeks to address crude oil fouling by evaluating recently developed threshold fouling models and comparing them with a neural network model which is developed in this work. 2. Threshold fouling models The threshold fouling concept for crude oil was introduced by Ebert and Panchal in 1995 [12]. They developed the following correlation for predicting the linear rate of fouling as a function of film temperature and fluid velocity.
Table 1 Constant parameters for some of threshold fouling models E (kJ mol1) Panchal model Polley model Nasr model
48 48 22.618
a (m2 K kW1 h1) +04
5.03 · 10 1 · 10+6 10.98
b
c
0.66 0.8 1.5472
1.45 · 1004 (m2 K kW1 h1 Pa1) 1.5 · 1009 (m2 K kW1 h1) 0.96 · 1010 (m2 K kW1 h1)
J. Aminian, S. Shahhosseini / Applied Thermal Engineering 28 (2008) 668–674
39.02 61.36 61.47 113.22 177.34 59.02
3.4232 7.9001 10.22 37.498 5.4049 23.04 3.359 4.259 2.393 2.931 1.312 1.703 3.222 4.027 2.317 2.801 1.297 1.658 8.8 21.1 7.6 18.4 1.5 17.1 14.4 31.6 12.8 27.8 4.5 26.2
Percent of mean relative error
Nasr model fouling rate · 103 E = 50 (m2 K kW1 h1) Nasr model fouling rate · 103 E = 48 (m2 K kW1 h1) Polley model fouling rate · 103 E = 50 (m2 K kW1 h1) Polley model fouling rate · 103 E = 48 (m2 K kW1 h1) Panchal model fouling rate · 103 E = 48 (m2 K kW1 h1)
4 6.6 3.1 5.4 0 3.4 2.6 7.9 3.5 37.5 5.4 25.7 288 288 284 283 275 275 344 393 349 396 331 419
Polley has computed the parameters of Eq. (3), applying Knudsen’s experimental data, and reported them as shown in the second row of Table 1. Knudsen’s experiment is related to identify threshold fouling for Alaskan crude. It featured an annular test cell with a heated inner rod, where bulk flow velocities varied in the range of 0.91–3 m/s, at two bulk temperatures of 149 and 204 C. During the
1.77 1.77 2.13 2.13 3.17 3.17
ð3Þ
5.5 5.5 5.5 5.5 5.5 5.5
dRf ¼ aReb Pr0:33 expðE=RT w Þ cRe0:8 dt
Experimental fouling rate · 103 (m2 K kW1 h1)
When applying Eq. (1) Prandtl number was determined employing a set of experimental data to be a constant value of about 2.5. However, Panchal and coworkers used another set of data in which Prandtl number varied in the range of 2.5–8.2. Therefore, it was necessary to include Prandtl number in Eq. (2). They assumed that the power of Prandtl number to be 0.33 according to the common heat transfer correlations. Panchal and coworkers obtained their laboratory experimental data using a high-pressure autoclave fouling unit under various conditions [14]. They have calculated constant parameters of Eq. (2) employing the experimental data and reported them as presented in the first row of Table 1. Panchal threshold model was improved by Polley et al. in 2002 as show by Eq. (3) [15]. The model was validated employing Knudsen’s experimental results [16]. The model differs primarily in the use of wall temperature, Tw, in the deposition term and Reynolds number rather than wall shear stress in inhibition term.
Tb (C)
ð2Þ
Ts (C)
dRf ¼ aReb Pr0:33 expðE=RT film Þ csw dt
Velocity (m s1)
where a, b, c and E are constants to be determined from experimental data. This approach provides a semi-empirical basis for quantitative interpretation of fouling data in terms of deposition and inhibition mechanisms. This concept suggests that a combination of low temperature and high shear stress will produce a threshold condition such that the fouling rate will be essentially zero. Therefore, a threshold condition is in fact the boundary between no fouling and fouling zones. The approach appears to be very useful for heat exchanger designers, since threshold conditions for each crude oil can be used to mitigate fouling without reducing heat recovery by selection of robust designs and network structures that do not foul. Ebert and Panchal model assumes all the chemical reactions to be included by the Arrhenius term in Eq. (1). In addition, it ignores the effects of crud oil thermal conductivity and specific heat and only considers the impacts of crud oil density and viscosity as presented by Reynolds number. To modify this correlation, Prandtl number was also incorporated into the model by Panchal and coworkers in 1997 [13]
Developed ANN Model fouling rate · 103 (m2 K kW1 h1)
ð1Þ
Tube diameter (mm)
dRf ¼ aReb expðE=RT film Þ csw dt
Table 2 Comparison between the ANN model and threshold fouling models for Shell West hollow refinery data [13,15,17]
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experiment, heater surface temperature varied in the range of 232–371 [16]. The latest threshold fouling model (Eq. (4)) has been developed by Nasr and Givi in 2006 which, is independent of Prandtl number [17]. dRf ¼ aReb expðE=RT film Þ cRe0:4 dt
ð4Þ
Nasr has estimated the constant parameters of Eq. (4) using the experimental data, measured by Saleh et al. for an Australian light crude oil as shown in the third row of Table 1. The experiment focuses on thermal fouling caused by the heating of Gippsland crude oil at moderate temperatures. The oil was maintained under nitrogen at a pressure of 379 kPa, and re-circulated at bulk temperatures of 80– 120 C through an electrically heated annular probe at
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velocities in the range of 0.25–0.65 m/s, where heater surface temperatures was between 80 and 260 C [18]. 3. Evaluation of the developed ANN model In this study, experimental data of fouling rate reported by Panchal [13], Polly [15] and Nasr [17] are used to develop an ANN model. They were obtained for four different tube diameters as mentioned in Tables 2–5. These tables also show, in these experiments, crude velocity varies from 0.91 to 3.17 m/s and tube surface temperature varies from 232–467 C. As a rule of thumb, a combination of high surface temperature, large tube diameter and low fluid velocity causes fouling formation to increase. Therefore, these variables were measured by the researchers to investigate their impacts on the fouling rate. Tube diameter,
Table 3 Comparison between the ANN model and threshold fouling models for Scarborough et al. data [13,15,17] Tube diameter (mm)
Velocity (m s1)
Ts (C)
Tb (C)
Experimental fouling rate · 103 (m2 K kW1 h1)
Panchal model fouling rate · 103 (m2 K kW1 h1)
Polley model fouling rate · 103 (m2 K kW1 h1)
15.2 15.2 15.2 15.2 15.2 15.2 15.2 15.2
2.48 1.25 2.48 1.25 1.25 1.29 2.53 2.53
414 467 379 432 401 374 404 376
363 371 351 360 353 344 353 345
3.2 20.1 2.8 11.4 7.9 5.6 4 1.2
3.1 11.6 2.2 8.5 6.4 4.7 2.2 1.2
4 37.3 1.6 23.9 14.8 8.4 2.2 0
21.54
68.18
Percent of mean relative error
Nasr model fouling rate · 103 (m2 K kW1 h1) 1.293 2.242 1.26 1.938 1.731 1.523 1.271 1.231 63.52
Developed ANN Model fouling rate · 103 (m2 K kW1 h1) 32.199 20.098 3.8952 11.412 7.8908 4.7388 3.9824 1.2036 7.01
Table 4 Comparison between the ANN model and threshold fouling models for Knudsen et al. data [13,15,17] Tube diameter (mm)
Velocity (m s1)
Ts (C)
Tb (C)
Experimental fouling rate · 103 (m2 K kW1 h1)
9.5 9.5 9.5 9.5 9.5 9.5 9.5 9.5 9.5 9.5 9.5 9.5 9.5 9.5 9.5 9.5 9.5 9.5 9.5 9.5
0.91 0.91 0.91 0.91 0.91 0.91 0.91 0.91 1.68 1.68 1.68 1.68 1.68 1.68 2.44 2.44 2.44 2.44 3.05 3.05
232 246 260 261 288 316 343 371 260 288 302 316 343 371 315 316 343 371 316 329
204 204 204 204 204 204 204 204 204 204 204 204 204 204 204 204 204 204 204 204
7 25 5 2 2 6 9 37 0 21 3 1.1 7 26 1.5 2.7 5 72.5 0.5 1
Percent of mean relative error
Panchal model fouling rate · 103 (m2 K kW1 h1) 2.3
Polley model fouling rate · 103 (m2 K kW1 h1)
3.5 3.6 5.1 7.1 9.7 13 0.0019 2.4 3 3.8 5.5 7.7 1.4 1.4 2.8 4.5 – 0.2
0.9 2 3.4 3.5 7.4 13.5 21.9 34 0 2.3 4 6 11.2 18.6 2.2 2.3 6.2 11.7 0.23 1.6
65.97
91.32
–
Nasr model fouling rate · 103 (m2 K kW1 h1) 1.853 1.927 2.011 2.017 2.208 2.448 2.724 3.064 0.985 1.047 1.081 1.116 1.191 1.278 0.981 0.983 1.026 1.073 0.991 1.008 60.46
Developed ANN Model fouling rate · 103 (m2 K kW1 h1) 6.9986 24.995 2.8702 2.0048 1.9982 6.8184 9.0005 27.19 5.31E03 20.999 3.0149 1.098 1.9937 25.997 1.8012 2.948 5.5489 72.499 0.28444 1.2212 13.73
45.18 57.37 57.59 99.13 45.09
28.71
0.927 0.946 0.915 0.924 0.939 0.961 1 0.934 0.955 0.922 0.934 0.945 0.966 1.005 0 0 0 0 0 0 0.35 2.4 2.7 0.8 1 0.8 1.2 1.8
0.03 0 0.3 1.2 1.2 3.8 7.1
120
Percent of mean relative error
0 0 0.5 1.1 0.8 5.6 8.1 230 230 220 220 227 223 223 21.1 21.1 21.1 21.1 21.1 21.1 21.1
1.15 0.95 1.16 0.98 1.16 1.16 0.98
260 255 260 255 270 288 295
Experimental fouling rate · 103 (m2 K kW1 h1)
Percent of Mean Relative Error
Nasr model fouling rate · 103 E = 48 (m2 K kW1 h1) Nasr model fouling rate · 103 E = 44 (m2 K kW1 h1) Polley model fouling rate · 103 E = 48 (m2 K kW1 h1) Polley model fouling rate · 103 E = 44 (m2 K kW1 h1) Panchal model fouling rate · 103 (m2 K kW1 h1)
crude velocity and tube surface temperature are used as inputs of the network and its output is fouling rate. All of the conventional threshold fouling models, which were explained in Section 2 have also been developed using a combination of these parameters. It is a common practice in ANN modeling to divide all of the related experimental data into two parts. The first part is used to train the model and the second part is applied to test the model. For this reason, the experimental data presented in Tables 2–5, were also used in the same manner. In the training phase, 27 randomly data points were introduced to the network. The remaining 14 data points were used for the test phase. A feed forward network (FFN) combined with back propagation algorithm was used to train the ANN model. FFNs often have one or more hidden layers of sigmoid neurons followed by an output layer of linear neurons. If the last layer of a FFN has sigmoid neurons, then the outputs of the network are limited to a small range, while a linear transfer function enables outputs to take any value. A trial-and-error approach was used to minimize the error in order to determine the optimal combination of number of hidden layers and number of neurons. The best performance was obtained when a network consists of four layers, with 3, 5 and 6 neurons in the input layer, the first and the second hidden layers, respectively, and just one neuron in the output layer. The activation function (transfer function) used in the hidden layers is tangent sigmoid function and also linear transfer function is assumed for the output layer. In order to evaluate ANN model, its outputs have been compared with crude oil fouling experimental data, reported by Panchal [13], Polley [15] and Nasr [17], as shown in the last column of Tables 2–5. ANN model predictions were also compared with the outputs of the threshold fouling models, which were mentioned in Section 2. Tables 2–5 show that the ANN model predictions for crude oil fouling rate is significantly better than those of threshold fouling models. The ANN model results in an overall
Panchal Model
Tb (C) Ts (C) Velocity (m s1) Tube diameter (mm)
Table 5 Comparison between the ANN model and threshold fouling models for Shell Wood River refinery data [13,15,17]
0.25222 0.0687 0.25122 0.00439 0.79472 9.8055 8.1009
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Developed ANN Model fouling rate · 103 (m2 K kW1 h1)
672
100
Polley Model Nasr Model
80
Developed ANN Model (a)
60
40 (a)
20
0 Scarborough (b) Experimental
(c)
Knudsen Experimental
Shell Wood River (d) refinery
Shell West hollow (d) refinery
Fig. 1. Comparison of the ANN model and threshold fouling models for various experimental data: (a) minimum reported fouling rate, (b) cited in Ref. [19], (c) cited in Ref. [15] and (d) cited in Ref. [13].
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mean relative error (OMRE) of 26.23%. By comparison, OMRE of the models proposed by Panchal, Nasr and Polley were 47.9%, 60.68% and 75.36%, respectively. A summary of this comparison can be seen in Fig. 1. 4. Sensitivity analysis The scope of this section is to implement a recently developed sensitivity analysis approach, which is used to rank the general importance of the input variables for the output variable of the neural model. This approach is called sequential zeroing of weights (SZWs). SZW method proposed by Nord and Jacobsson [20] estimates the degradation in output variables of a trained neural network when the weights connecting the ith input variable to the nodes of the hidden layer are all set to zero. In this way, the contribution of that variable to the network response is excluded. According to this method, the measure that is calculated in order to reveal the importance of the ith input variable is the difference between the root mean square error (RMSE) of the complete network’s predictions and RMSE obtained when the ith variable is excluded from the trained network (RMSEi), both being calculated on the same data set Rmdiff i ¼ RMSEi RMSE
ð5Þ
Generally, the values of Rmdiffi are greater than zero. The variable with the greater importance is the one that leads to a greater value of Rmdiffi. The numeric values of Rmdiffi are shown in Fig. 2. It can be seen that the influence of tube diameter and velocity of the crude on the fouling rate is higher than tube surface temperature. SZWs method can only be implemented after a neural network is trained. Therefore SZWs results can be validated based on the assumption that the ANN model is a sufficiently accurate model. This assumption can be satisfied since the results of the ANN model that are presented in Section 3 are more reasonable than previous threshold fouling models.
Root Mean Square Error Difference (Rmdiffi) 2.00E-03 1.80E-03 1.60E-03 1.40E-03 1.20E-03 1.00E-03 8.00E-04 6.00E-04 4.00E-04 2.00E-04 0.00E+00 Tube Diameter
Crude velocity
Surface temperature
Fig. 2. Result of sensitivity analysis.
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5. Conclusion In this paper, an ANN model has been established in order to predict total fouling rate of crude oil employing an experimental data set that has been reported in the literature. Results of the ANN model were compared with those of three different threshold fouling models. The ANN model predicts crude oil fouling rate with an OMRE of 26.23%. Whereas, OMRE of the models proposed by Panchal, Nasr and Polley were 47.9%, 60.68% and 75.36%, respectively. A sensitivity analysis, named sequential zeroing of weights (SZWs), has also been performed on the ANN model. The results of this analysis revealed that the influence of tube diameter and velocity of the crude on the fouling rate is higher than tube surface temperature. Whilst the results given in this paper are obtained for the specific experimental data that are reported by Panchal, Polley and Nasr the principles of the ANN modeling and sensitivity analysis are readily applicable to other situations. Acknowledgement The authors are thankful for the comments and advice given by the anonymous reviewers. They have substantially improved the content of this work and pointed out some research directions of particular interest. References [1] C.B. Panchal, E.-Ping Huangfu, Effect of mitigating fouling on the energy efficiency of crude oil distillation, Heat Transfer Engineering 21 (2000) 3–9. [2] H. Mu¨ller-Steinhagen, Heat exchanger fouling: mitigation and cleaning technologies, Transactions of IChemE (Rugby UK), 2000. [3] B.L. Yeap, D.I. Wilson, G.T. Polley, S.J. Pugh, Mitigation of crude oil refinery heat exchanger fouling through retrofits based on thermohydraulic fouling models, Chemical Engineering Research and Design 84 (2004) 53–71. [4] S. Asomaning, C.B. Panchal, C.F. Liao, Correlating field and laboratory data for crude oil fouling, Heat Transfer Engineering 21 (2000) 17–23. [5] M.R. Malayeri, H. Mu¨ller-Steinhagen, Neural network analysis of heat transfer fouling data, in: The 4th United Engineering Foundation Conference on Heat Exchanger Fouling: Fundamental Approaches & Technical Solutions, Davos, Switzerland, 2001, pp. 145–150. [6] L.M. Romeo, R. Gareta, Neural network for evaluating boiler behavior, Applied Thermal Engineering 26 (2006) 1530–1536. [7] E. Teruel, C. Cortes, L.I. Diez, I. Arauzo, Monitoring and prediction of fouling in coal-fired utility boilers using neural networks, Chemical Engineering Science 60 (2005) 5035–5048. [8] S. Lalot, S. Lecoeuche, Online fouling detection in electrical circulating heaters using neural networks, International Journal of Heat and Mass Transfer 46 (2003) 2445–2457. [9] S. Lalot, On-line detection of fouling in a water circulating temperature controller (WCTC) used in injection moulding: part 1: principles, Applied Thermal Engineering 26 (2006) 1087–1094. [10] S. Lalot, On-line detection of fouling in a water circulating temperature controller (WCTC) used in injection moulding: part 2: application, Applied Thermal Engineering 26 (2006) 1095–1105. [11] V.R. Radhakrishnan, M. Ramasamy, H. Zabiri, V. Do Thanh, N.M. Tahir, H. Mukhtar, M.R. Hamid, N. Ramli, Heat exchanger fouling
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