- Email: [email protected]
Prediction of Cracking Gas Compressor Performance and Its Application in Process Optimization
PROCESS SYSTEMS ENGINEERING Chinese Journal of Chemical Engineering, 20(6) 1089—1093 (2012)
Prediction of Cracking Gas Compressor Performance and Its Application in Process Optimization* LI Shaojun (李绍军)** and LI Feng (李凤)
Key Laboratory of Advanced Control and Optimization for Chemical Processes (East China University of Science and Technology), Ministry of Education, Shanghai 200237, China Abstract Cracking gas compressor is usually a centrifugal compressor. The information on the performance of a centrifugal compressor under all conditions is not available, which restricts the operation optimization for compressor. To solve this problem, two back propagation (BP) neural networks were introduced to model the performance of a compressor by using the data provided by manufacturer. The input data of the model under other conditions should be corrected according to the similarity theory. The method was used to optimize the system of a cracking gas compressor by embedding the compressor performance model into the ASPEN PLUS model of compressor. The result shows that it is an effective method to optimize the compressor system. Keywords compressor, characteristic curve, neural-network, modeling
1
INTRODUCTION
Cracking gas compressor is usually a centrifugal compressor. It is the key equipment in ethylene plants, the role of which is to raise the static enthalpy and pressure of cracking gas [1]. Usually, the performance information of compressor is provided by manufacturer based on experimental data. However, compressors are often operated under off-design conditions. Operators are faced with enormous problems without the performance information of compressor. Therefore, in order to describe the performance of compressor under various conditions, appropriate analysis and prediction of characteristic curves for a compressor is necessary. Intensive experimental studies under various operating and environmental conditions are performed to better understand the pumping characteristics of a compressor and determine its performance curves. Consequently, designers have to deal with a large amount of experimental data, which is time consuming and expensive. Moreover, the data from the compressor rig tests are usually scattered and not uniformly distributed over the operation range, so the performance map of a compressor is usually illustrated as discrete points. In order to predict the compressor characteristic curve, semi-empirical and empirical models were used in the literature. Some of them used approximation methods based on experimental data. Sieros et al. [2] applied analytical functions to nonlinear models for performance maps of different design types. An overview of curve fitting methods for characteristics of centrifugal compressors and turbines was presented by Moraal and Kolmanovsky [3]. Ghorbanian and Gholamrezaei [4] used artificial neural network to predict the performance map of compressor. Kong et al. [5, 6] used genetic algorithm to determine the unknown coefficients of third-order equations relating the mass flow rate,
compression ratio, and isentropic efficiency. Yu et al. [7] used neural-network to analyze and predict the compression ratio of a compressor. Tirnovan et al. [8] combined the theoretical relations with measured data by using least square methods. Most of above researches focused on the modeling of performance map, especially in the design and experimental phases. However, in an ethylene plants, experimental analysis could not be carried out in the production process, there is no other method of comparison in the literature, and one only has an analysis figure provided by manufacture. In this study, the characteristic curves are predicted from the input and output variables of a compressor with a model based on the artificial neural network. The results are embedded in Aspen Plus software to optimize the system of cracking gas compressor and the performance curves under off-design conditions are predicted. 2
COMPRESSOR PERFORMANCE ANALYSIS
Characteristics of a compressor are normally described as the relationships of compression ratio ε, efficiency η, volume flow rate v (or mass flow rate m) and rotational speed of shaft n [9], expressed by curves, which is named compressor characteristic performance map. A state is specified when two of the four parameters are given. If only some running-state data are given, most of the information needs to be predicted. In the conventional approach, the compression ratio ε and efficiency η are expressed as functions of volume flow rate v at constant rotational speed n, ε = f (v, n ) (1)
η = g ( v, n )
(2)
Following issues may arise when these data are
Received 2012-04-17, accepted 2012-07-25. * Supported by the National Natural Science Foundation of China (20976048, 21176072), and the Fundamental Research Funds for the Central Universities. ** To whom correspondence should be addressed. E-mail: [email protected]
1090
Chin. J. Chem. Eng., Vol. 20, No. 6, December 2012
used for a simulation of centrifugal compressor. The first issue is interpolations and extrapolations of data near certain stable state when the speed is given. The second problem is lacking of the characteristics for startup and shutdown of compressor. The general relation among the compression ratio, speed, flow rate and efficiency should be found for these two issues. The key is how to utilize the experimental data provided by manufacturer. The general method employed is the two-dimensional linear interpolation [10]. Although it is simple and easy to compute, its precision is low. Because of the highly non-linear performance and small working range of a compressor, the interpolation method is of limited use. Moreover, for the use of a compressor, when the performance map under the design condition provided by manufacturer is inapplicable because its operation condition is changed, the parameters should be corrected by using the similarity theory of centrifugal compressors [11]. Compressor characteristics under all conditions can be expressed by the relationships of corrected pressure, corrected ratio ε′, efficiency η′, corrected volume flow rate v′ and corrected speed n′. Ma et al. [12] corrected the mass flow ration and rotational speed by inlet temperature and pressure as follows, with the density change between the inlet and outlet of the stage neglected. Gc =
G Tin Pin N
Nc =
Tin
(3) (4)
where Tin and Pin are the inlet temperature and pressure of compressor. In this paper, we use the corrected method in another form that the engineers are familiar with. (1) Correction for volume flow rate
v′ = v m′ = m
Tin′ Tin
Pin Pin′
(5)
Tin′ Tin
(6)
(2) Correction for speed
n′ = n
Tin′ Tin
(7)
where ε, η, v and n are the parameters under the condition of compressor at inlet temperature of Tin, the inlet pressure Pin is under the standard state, ε′, η′, v′ and n′ are corrected parameters that meet the requirement of standard state (T is absolute temperature). Two models are used in this paper: ε ′ = f (v′, n′) (8)
η ′ = g (v′, n′)
(9)
3 PREDICTION BASED ON NEURAL NETWORKS AND DISCUSSIONS An artificial neural network (ANN) [13] is a computational structure inspired by biological neural system. A multi-layer ANN consists of a system of simple interconnected neurons, or nodes. The neurons are connected to each other by adjustable weights, which may be propagated to several other neurons. By selecting a suitable set of interconnected neurons, weight and transfer function, artificial neural network can approximate any smooth and measurable function between the input and output vectors. The neural networks are widely applied in many areas such as prediction, system modeling and control. Neural network training is traditionally carried out using the BP gradient descent algorithm. This technique is effective for training feed-forward neural networks that use summation unit functions and continuously differentiable transfer functions. The values of weights and bias are set during network training process. Initially, the weights and bias are set randomly. The training of network adjusts the values of weights and bias so that the mean square error (MSE) between target values and the predicted values is minimized. The mean square error is calculated by MSE =
1 N [ y (k ) − y (k )]2 ∑ N k =1
(10)
where y(k) is the actual value, and y (k ) is the network output value. Because of the relations of input and output parameters of compressor are highly non-linear, the log-sigmoid function is used by the two three-layer BP neural networks to generate their outputs. Training accuracy of neural network depends on the sample selection. The selection and disposal of samples is necessary before training. Here the samples are selected from the performance curve of the compressor provided by manufacturer, as shown in Fig. 1. The prediction of compressor characteristic curve is performed with the two tri-layer BP networks. The experimental data of compressor are samples of training for neural-networks. In order to ensure the accuracy of the model, following procedures are implemented (here the modeling of the 4th compression ratio and poly-tropic of a compressor is taken as an example). (1) Collect the experimental data. 273 and 266 sets of data are selected in the two models. (2) Improve the learning efficiency. The input data of training samples are normalized in the range [−1, 1] and their output data are normalized in the range [0.1, 0.9], by 2 x − xmin） 0.8( y − ymin ) （ x= − 1, y = + 0.1 (11) xmax − xmin ymax − ymin
(3) Train the two BP neural networks. The models of the compressor ratio and poly-tropic efficiency are built, each of which has two inputs, one output and three hidden layers. The training MSE values between
1091
Chin. J. Chem. Eng., Vol. 20, No. 6, December 2012
Figure 1 Characteristic map of compressor
predicted values and actual values for the compression ratio and poly-tropic efficiency of the 4th stage compressor are 2.5×10−4 and 1.5×10−5, respectively. By using these two models, parameters at constant normalized corrected speed ratios n = 0.7, 0.75, 0.8, 0.85, 0.9, 0.95, 1.0, 1.05 are represented in Figs. 2 and 3.
Figure 2 Compression ratio of the fourth-stage of compressor
Figure 3 Poly-tropic efficiency of the fourth-stage of compressor
(4) Predict the compressor performance under other operating conditions. For other compressor speed ratios, the compression ratio and efficiency maps can be calculated by BP model. For example, the performance
curves at constant normalized corrected speed ratio n = 1.012, not provided by manufacturer, is shown in Figs. 2 and 3. Such results can be used to optimize the operation of equipment. 4
APPLICATION IN ASPEN PLUS MODEL
A cracking gas compression system of an olefins plant is used to illustrate the application of the performance curve prediction. This system is composed of a four-stage centrifugal compressor, 8 heat exchangers, 7 flash separators and a caustic scrubbing tower, as shown in Fig. 4. The cracking gas compressor consists of 4 stages (1ST, 2ND, 3RD, and 4TH), with caustic scrubbing between the 3RD and 4TH. The cracking gas comes from quench tower as feedstock enters the separator. FW1, FW2, FW3 and FW4 are water streams, which are added to stage inlets of compressor to reduce the outlet temperature. The PR-BM (Peng Robinson Boston-Mathias) cubic equation of state is selected as the global thermodynamic property method. STEAMNBS is selected for water and steam where appropriate. In the production process of ethylene, the fourthstage outlet temperature of the compressor is higher than 100 °C, at which one of the main components in cracking gas, 1, 3-butadiene, may polymerize [14]. It will coke at compressor blades, impacting the normal working condition and resulting in the loss of dienes [15]. The poly-tropic efficiency of the fourth-stage is only about 65%, lower than that of the other stages (75%-80%). There are several methods to reduce the outlet temperature, e.g., increasing the stage of compressor and reducing the compression ratio of the 4th stage, or adjusting the operating conditions to make the system more balance. By the analysis of thermodynamics, the outlet temperature of a compressor can be calculated as follows Tout = Tin ε
m −1 m
= Tin ε
k −1 kη
(12)
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Chin. J. Chem. Eng., Vol. 20, No. 6, December 2012
Figure 4
Crack gas compressor system of the olefins plant
Table 1 Relative speed n/n0
R2 flow rate/kg·h−1
Power /kW
Comparison of the two conditions 1st stage
2nd stage
Outlet pressure/Pa
Efficiency /%
Outlet temperature/°C
Outlet pressure/Pa
Efficiency /%
Outlet temperature/°C
case 1
0.955
0
5361
494466
79.72
78.1
1313172
78.98
85.1
case 2
0.959
350
5533
500545.5
79.60
78.7
1341543
78.74
86.0
Relative speed n/n0
R2 flow rate/kg·h−1
Power /kW
3rd stage
4th stage
Outlet pressure/Pa
Efficiency /%
Outlet temperature/°C
Outlet pressure/Pa
Efficiency /%
Outlet temperature/°C
case 1
0.955
0
5361
3372096
75.72
93.5
7518315
64.82
102.1
case 2
0.959
350
5533
3489633
75.28
94.9
7522368
67.43
97.4
where m is the poly-tropic index and k is the adiabatic index. According to Eq. (12), the outlet temperature is influenced by compressor efficiency, inlet temperature, compression ratio, and adiabatic index. Adiabatic index is a constant when the gas components through the compressor are not changed. The inlet temperature of compressor has a direct affect on the outlet temperature. Decreasing the inlet temperature can significantly reduce the outlet temperature. When the inlet temperature is adjusted by cool water, the inlet temperature is usually set at 25 °C. According to Eq. (12), decreasing the compressor compression ratio and increasing the efficiency can also reduce the outlet temperature. Because the cracking gas should reach the required pressure, reducing the fourth-stage compression ratio means increasing the compression ratios of other three stages, by increasing the rotation speed. According to the flow-sheet, there is a feedback stream used to prevent the compressor surge. Increasing its flow rate will decrease the compression ratio and increase the poly-tropic efficiency. It usefully decreases the fourth-stage outlet temperature. In order to solve the problem, a process simulation software, Aspen plus [16], is used to model the process, with which each process in petroleum chemical industry can be described accurately. As mentioned above, the compression ratio and
efficiency are the two main factors to model a compressor. The preset methods in Aspen Plus are interpolation and extrapolation or polynomials method, the precision of which is lower. In this study, we use a tri-layer neural network to model the performance map for the four-stage compressor. In order to optimize this compressor, the compression ratio and poly-tropic efficiency of these four sections are modeled separately. Eight BP neural network models are built and embedded into the Aspen Plus model. The change in outlet temperature is examined by adjusting the operation conditions. We can obtain all the compressor parameters under any condition conveniently by the method based on analysis and prediction of its characteristic performance map. Table 1 lists the comparison of two cases. Case 1 is optimized through multiple trials of Aspen Plus with the outlet temperature as the constraint condition and the energy consumption as the objective. Case 2 is the optimization results of the fourth stage compressor. In Case 1, the outlet temperature of the fourth stage deceases from 102.1 °C to 97.4 °C and the relative rotation speed increases from 0.955 to 0.959. By increasing the flow rate of the feedback stream, the poly-tropic efficiency of the fourth stage is increased from 64.82% to 67.43%. Although the energy consumption increases, the increment percentage
Chin. J. Chem. Eng., Vol. 20, No. 6, December 2012
is very small in an ethylene industry. This adjustment is feasible to prevent coking from the change of the normal working condition of compressor.
5
6
5
CONCLUSIONS 7
In this paper, an analysis and prediction approach for characteristic curves of centrifugal compressor is presented. BP neural networks are used to reproduce the relationship between input and output variables of compressors. Experimental data provided by manufacturer are used for neural network training and the models of compression ratio and poly-tropic efficiency are set up. Predictions from the model of characteristic maps are used for the simulation and optimization of a cracking gas compressor system, and satisfactory results are obtained. REFERENCES 1
2
3 4
Li, J.H., “Technical measures to inhibit coking of cracking gas compressor”, Journal of Chemical Industry &Engineering, 31 (4), 46-48 (2010). Sieros, G., Stamatis, A., Mathioudakis, K, “Jet engine component maps for performance modeling and diagnosis”, Propulsion & Power, 13 (5), 665-674 (1997). Moraal, P., Kolmanovsky, I., “Turbo charger modeling for automotive control application”, SAE Trans, 108, 1324-1338 (1999). Ghorbanian, K., Gholamrezaei, M., “An artificial neural network approach to compressor performance prediction”, Applied Energy,
8
9
10
11 12
13 14
15
16
1093
86, 1210-1221 (2009). Kong, C.D., Kho, S.H., Ki, J.Y., “Component map generation of a gas turbine using genetic algorithms”, Trans ASME J Eng Gas Turbines Power, 128 (1), 92-96 (2006). Kong, C.D., Ki, J.Y., “Components map generation of gas turbine engine using genetic algorithms and engine performance deck data”, Trans ASME J Eng Gas Turbines Power, 129 (2), 312-317 (2007). Yu, Y.H., Chen, L.G., Sun, F.R., Wu, C.H., “Neural-network based analysis and prediction of compressor’s characteristic performance map”, Applied Energy, 84, 48-55 (2007). Tirnovan, R., Giurgea, S., Miraoui, A., Cirrincione, M., “Modeling the characteristics of turbo compressors for fuel cell systems using hybrid method based on moving least squares”, Applied Energy, 86, 1283-1289 (2009). Teemu, T.S., Pekka, R., Juha, H., Jari, B., “Predicting off-design range and performance of refrigeration cycle with two-stage centrifugal compressor and flash intercooler”, International Journal of Refrigeration, 33 (6), 1152-1160 (2010). Lazzaretto, A., Toffolo, A., “Analytical and neural-network models for gas-turbine design and off-design simulation”, Int. J. Applied Thermodynamics, 4 (4), 173-182 (2001). Xu, Z., The Principle of Centrifugal Compressor, Machine Press, Beijing (1990). (in Chinese) Ma, W.T., Liu, Y.W., Su, M., Yu, N.H., “Multi-stage axial flow compressors characteristics estimation based on system identification”, Energy Conversion and Management, 49 (2), 143-150 (2008). Simon, H., Neural Networks: A Comprehensive Foundation, 2nd edition, Prentice-Hall Inc., Canada (2001). Ma, P.F., Wu, C.B., LI, F.Y., “Cause analysis of coking of pyrolysis gas compressor and retrofits”, Chemical Engineering & Machinery, 36 (2), 150-153 (2009). (in Chinese) Zhao, J.Y., Liang, L.W., Cao, T.T., Yu, B.W., “The application of process simulation technology in the ethylene plant”, Petrochemical Technology, 39, 908-909 (2010). (in Chinese) MIT, Aspen-tech, User’s Guide of ASPEN PLUS 10, USA (2001).
Prediction of Cracking Gas Compressor Performance and Its Application in Process Optimization* LI Shaojun (李绍军)** and LI Feng (李凤)
Key Laboratory of Advanced Control and Optimization for Chemical Processes (East China University of Science and Technology), Ministry of Education, Shanghai 200237, China Abstract Cracking gas compressor is usually a centrifugal compressor. The information on the performance of a centrifugal compressor under all conditions is not available, which restricts the operation optimization for compressor. To solve this problem, two back propagation (BP) neural networks were introduced to model the performance of a compressor by using the data provided by manufacturer. The input data of the model under other conditions should be corrected according to the similarity theory. The method was used to optimize the system of a cracking gas compressor by embedding the compressor performance model into the ASPEN PLUS model of compressor. The result shows that it is an effective method to optimize the compressor system. Keywords compressor, characteristic curve, neural-network, modeling
1
INTRODUCTION
Cracking gas compressor is usually a centrifugal compressor. It is the key equipment in ethylene plants, the role of which is to raise the static enthalpy and pressure of cracking gas [1]. Usually, the performance information of compressor is provided by manufacturer based on experimental data. However, compressors are often operated under off-design conditions. Operators are faced with enormous problems without the performance information of compressor. Therefore, in order to describe the performance of compressor under various conditions, appropriate analysis and prediction of characteristic curves for a compressor is necessary. Intensive experimental studies under various operating and environmental conditions are performed to better understand the pumping characteristics of a compressor and determine its performance curves. Consequently, designers have to deal with a large amount of experimental data, which is time consuming and expensive. Moreover, the data from the compressor rig tests are usually scattered and not uniformly distributed over the operation range, so the performance map of a compressor is usually illustrated as discrete points. In order to predict the compressor characteristic curve, semi-empirical and empirical models were used in the literature. Some of them used approximation methods based on experimental data. Sieros et al. [2] applied analytical functions to nonlinear models for performance maps of different design types. An overview of curve fitting methods for characteristics of centrifugal compressors and turbines was presented by Moraal and Kolmanovsky [3]. Ghorbanian and Gholamrezaei [4] used artificial neural network to predict the performance map of compressor. Kong et al. [5, 6] used genetic algorithm to determine the unknown coefficients of third-order equations relating the mass flow rate,
compression ratio, and isentropic efficiency. Yu et al. [7] used neural-network to analyze and predict the compression ratio of a compressor. Tirnovan et al. [8] combined the theoretical relations with measured data by using least square methods. Most of above researches focused on the modeling of performance map, especially in the design and experimental phases. However, in an ethylene plants, experimental analysis could not be carried out in the production process, there is no other method of comparison in the literature, and one only has an analysis figure provided by manufacture. In this study, the characteristic curves are predicted from the input and output variables of a compressor with a model based on the artificial neural network. The results are embedded in Aspen Plus software to optimize the system of cracking gas compressor and the performance curves under off-design conditions are predicted. 2
COMPRESSOR PERFORMANCE ANALYSIS
Characteristics of a compressor are normally described as the relationships of compression ratio ε, efficiency η, volume flow rate v (or mass flow rate m) and rotational speed of shaft n [9], expressed by curves, which is named compressor characteristic performance map. A state is specified when two of the four parameters are given. If only some running-state data are given, most of the information needs to be predicted. In the conventional approach, the compression ratio ε and efficiency η are expressed as functions of volume flow rate v at constant rotational speed n, ε = f (v, n ) (1)
η = g ( v, n )
(2)
Following issues may arise when these data are
Received 2012-04-17, accepted 2012-07-25. * Supported by the National Natural Science Foundation of China (20976048, 21176072), and the Fundamental Research Funds for the Central Universities. ** To whom correspondence should be addressed. E-mail: [email protected]
1090
Chin. J. Chem. Eng., Vol. 20, No. 6, December 2012
used for a simulation of centrifugal compressor. The first issue is interpolations and extrapolations of data near certain stable state when the speed is given. The second problem is lacking of the characteristics for startup and shutdown of compressor. The general relation among the compression ratio, speed, flow rate and efficiency should be found for these two issues. The key is how to utilize the experimental data provided by manufacturer. The general method employed is the two-dimensional linear interpolation [10]. Although it is simple and easy to compute, its precision is low. Because of the highly non-linear performance and small working range of a compressor, the interpolation method is of limited use. Moreover, for the use of a compressor, when the performance map under the design condition provided by manufacturer is inapplicable because its operation condition is changed, the parameters should be corrected by using the similarity theory of centrifugal compressors [11]. Compressor characteristics under all conditions can be expressed by the relationships of corrected pressure, corrected ratio ε′, efficiency η′, corrected volume flow rate v′ and corrected speed n′. Ma et al. [12] corrected the mass flow ration and rotational speed by inlet temperature and pressure as follows, with the density change between the inlet and outlet of the stage neglected. Gc =
G Tin Pin N
Nc =
Tin
(3) (4)
where Tin and Pin are the inlet temperature and pressure of compressor. In this paper, we use the corrected method in another form that the engineers are familiar with. (1) Correction for volume flow rate
v′ = v m′ = m
Tin′ Tin
Pin Pin′
(5)
Tin′ Tin
(6)
(2) Correction for speed
n′ = n
Tin′ Tin
(7)
where ε, η, v and n are the parameters under the condition of compressor at inlet temperature of Tin, the inlet pressure Pin is under the standard state, ε′, η′, v′ and n′ are corrected parameters that meet the requirement of standard state (T is absolute temperature). Two models are used in this paper: ε ′ = f (v′, n′) (8)
η ′ = g (v′, n′)
(9)
3 PREDICTION BASED ON NEURAL NETWORKS AND DISCUSSIONS An artificial neural network (ANN) [13] is a computational structure inspired by biological neural system. A multi-layer ANN consists of a system of simple interconnected neurons, or nodes. The neurons are connected to each other by adjustable weights, which may be propagated to several other neurons. By selecting a suitable set of interconnected neurons, weight and transfer function, artificial neural network can approximate any smooth and measurable function between the input and output vectors. The neural networks are widely applied in many areas such as prediction, system modeling and control. Neural network training is traditionally carried out using the BP gradient descent algorithm. This technique is effective for training feed-forward neural networks that use summation unit functions and continuously differentiable transfer functions. The values of weights and bias are set during network training process. Initially, the weights and bias are set randomly. The training of network adjusts the values of weights and bias so that the mean square error (MSE) between target values and the predicted values is minimized. The mean square error is calculated by MSE =
1 N [ y (k ) − y (k )]2 ∑ N k =1
(10)
where y(k) is the actual value, and y (k ) is the network output value. Because of the relations of input and output parameters of compressor are highly non-linear, the log-sigmoid function is used by the two three-layer BP neural networks to generate their outputs. Training accuracy of neural network depends on the sample selection. The selection and disposal of samples is necessary before training. Here the samples are selected from the performance curve of the compressor provided by manufacturer, as shown in Fig. 1. The prediction of compressor characteristic curve is performed with the two tri-layer BP networks. The experimental data of compressor are samples of training for neural-networks. In order to ensure the accuracy of the model, following procedures are implemented (here the modeling of the 4th compression ratio and poly-tropic of a compressor is taken as an example). (1) Collect the experimental data. 273 and 266 sets of data are selected in the two models. (2) Improve the learning efficiency. The input data of training samples are normalized in the range [−1, 1] and their output data are normalized in the range [0.1, 0.9], by 2 x − xmin） 0.8( y − ymin ) （ x= − 1, y = + 0.1 (11) xmax − xmin ymax − ymin
(3) Train the two BP neural networks. The models of the compressor ratio and poly-tropic efficiency are built, each of which has two inputs, one output and three hidden layers. The training MSE values between
1091
Chin. J. Chem. Eng., Vol. 20, No. 6, December 2012
Figure 1 Characteristic map of compressor
predicted values and actual values for the compression ratio and poly-tropic efficiency of the 4th stage compressor are 2.5×10−4 and 1.5×10−5, respectively. By using these two models, parameters at constant normalized corrected speed ratios n = 0.7, 0.75, 0.8, 0.85, 0.9, 0.95, 1.0, 1.05 are represented in Figs. 2 and 3.
Figure 2 Compression ratio of the fourth-stage of compressor
Figure 3 Poly-tropic efficiency of the fourth-stage of compressor
(4) Predict the compressor performance under other operating conditions. For other compressor speed ratios, the compression ratio and efficiency maps can be calculated by BP model. For example, the performance
curves at constant normalized corrected speed ratio n = 1.012, not provided by manufacturer, is shown in Figs. 2 and 3. Such results can be used to optimize the operation of equipment. 4
APPLICATION IN ASPEN PLUS MODEL
A cracking gas compression system of an olefins plant is used to illustrate the application of the performance curve prediction. This system is composed of a four-stage centrifugal compressor, 8 heat exchangers, 7 flash separators and a caustic scrubbing tower, as shown in Fig. 4. The cracking gas compressor consists of 4 stages (1ST, 2ND, 3RD, and 4TH), with caustic scrubbing between the 3RD and 4TH. The cracking gas comes from quench tower as feedstock enters the separator. FW1, FW2, FW3 and FW4 are water streams, which are added to stage inlets of compressor to reduce the outlet temperature. The PR-BM (Peng Robinson Boston-Mathias) cubic equation of state is selected as the global thermodynamic property method. STEAMNBS is selected for water and steam where appropriate. In the production process of ethylene, the fourthstage outlet temperature of the compressor is higher than 100 °C, at which one of the main components in cracking gas, 1, 3-butadiene, may polymerize [14]. It will coke at compressor blades, impacting the normal working condition and resulting in the loss of dienes [15]. The poly-tropic efficiency of the fourth-stage is only about 65%, lower than that of the other stages (75%-80%). There are several methods to reduce the outlet temperature, e.g., increasing the stage of compressor and reducing the compression ratio of the 4th stage, or adjusting the operating conditions to make the system more balance. By the analysis of thermodynamics, the outlet temperature of a compressor can be calculated as follows Tout = Tin ε
m −1 m
= Tin ε
k −1 kη
(12)
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Chin. J. Chem. Eng., Vol. 20, No. 6, December 2012
Figure 4
Crack gas compressor system of the olefins plant
Table 1 Relative speed n/n0
R2 flow rate/kg·h−1
Power /kW
Comparison of the two conditions 1st stage
2nd stage
Outlet pressure/Pa
Efficiency /%
Outlet temperature/°C
Outlet pressure/Pa
Efficiency /%
Outlet temperature/°C
case 1
0.955
0
5361
494466
79.72
78.1
1313172
78.98
85.1
case 2
0.959
350
5533
500545.5
79.60
78.7
1341543
78.74
86.0
Relative speed n/n0
R2 flow rate/kg·h−1
Power /kW
3rd stage
4th stage
Outlet pressure/Pa
Efficiency /%
Outlet temperature/°C
Outlet pressure/Pa
Efficiency /%
Outlet temperature/°C
case 1
0.955
0
5361
3372096
75.72
93.5
7518315
64.82
102.1
case 2
0.959
350
5533
3489633
75.28
94.9
7522368
67.43
97.4
where m is the poly-tropic index and k is the adiabatic index. According to Eq. (12), the outlet temperature is influenced by compressor efficiency, inlet temperature, compression ratio, and adiabatic index. Adiabatic index is a constant when the gas components through the compressor are not changed. The inlet temperature of compressor has a direct affect on the outlet temperature. Decreasing the inlet temperature can significantly reduce the outlet temperature. When the inlet temperature is adjusted by cool water, the inlet temperature is usually set at 25 °C. According to Eq. (12), decreasing the compressor compression ratio and increasing the efficiency can also reduce the outlet temperature. Because the cracking gas should reach the required pressure, reducing the fourth-stage compression ratio means increasing the compression ratios of other three stages, by increasing the rotation speed. According to the flow-sheet, there is a feedback stream used to prevent the compressor surge. Increasing its flow rate will decrease the compression ratio and increase the poly-tropic efficiency. It usefully decreases the fourth-stage outlet temperature. In order to solve the problem, a process simulation software, Aspen plus [16], is used to model the process, with which each process in petroleum chemical industry can be described accurately. As mentioned above, the compression ratio and
efficiency are the two main factors to model a compressor. The preset methods in Aspen Plus are interpolation and extrapolation or polynomials method, the precision of which is lower. In this study, we use a tri-layer neural network to model the performance map for the four-stage compressor. In order to optimize this compressor, the compression ratio and poly-tropic efficiency of these four sections are modeled separately. Eight BP neural network models are built and embedded into the Aspen Plus model. The change in outlet temperature is examined by adjusting the operation conditions. We can obtain all the compressor parameters under any condition conveniently by the method based on analysis and prediction of its characteristic performance map. Table 1 lists the comparison of two cases. Case 1 is optimized through multiple trials of Aspen Plus with the outlet temperature as the constraint condition and the energy consumption as the objective. Case 2 is the optimization results of the fourth stage compressor. In Case 1, the outlet temperature of the fourth stage deceases from 102.1 °C to 97.4 °C and the relative rotation speed increases from 0.955 to 0.959. By increasing the flow rate of the feedback stream, the poly-tropic efficiency of the fourth stage is increased from 64.82% to 67.43%. Although the energy consumption increases, the increment percentage
Chin. J. Chem. Eng., Vol. 20, No. 6, December 2012
is very small in an ethylene industry. This adjustment is feasible to prevent coking from the change of the normal working condition of compressor.
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CONCLUSIONS 7
In this paper, an analysis and prediction approach for characteristic curves of centrifugal compressor is presented. BP neural networks are used to reproduce the relationship between input and output variables of compressors. Experimental data provided by manufacturer are used for neural network training and the models of compression ratio and poly-tropic efficiency are set up. Predictions from the model of characteristic maps are used for the simulation and optimization of a cracking gas compressor system, and satisfactory results are obtained. REFERENCES 1
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