Article pubs.acs.org/IECR
Hybrid Compressor Model for Optimal Operation of Compressed Dry Air System in LCD Production Industry Kiwook Song, Changhyun Jeong, Jiyeon Nam, and Chonghun Han* School of Chemical and Biological Engineering, Institute of Chemical Processes, Seoul National University, San 56-1, Shillim-dong, Kwanak-gu, Seoul 151-742, Korea ABSTRACT: Compressed dry air (CDA) is a widely used utility in liquid crystal display (LCD) production industry usually utilized as an air knife and an air curtain for room and glass cleaning to prohibit particles from entering the chamber. CDA is consumed in various sites of the production line and demand for CDA fluctuates largely from moment to moment. Therefore, it is common to supply compressed air with a number of small-capacity compressors rather than few large-capacity ones. To find an optimal operating strategy of such a compressor network, a first hybrid modeling technique of an ideal model and an empirical model is used to predict the efficiency and power consumption of each compressor. Ideal compression work is calculated using thermodynamic equation with slight modification. An artificial neural network is configured to predict the efficiency. Then, actual power consumption of each compressor is given by the ratio of ideal work to efficiency. Then, optimization procedure is applied to search optimal operating configuration. The proposed method is applied to LCD production industry to show good prediction accuracy. Energy saving of total compression work is achieved by optimization scenario of segregating full-load and part-load compressor group.
1. INTRODUCTION Compressed air is widely used in various chemical processes. Especially, compressed dry air (CDA) is an essential utility needed in a variety of processes in LCD (Liquid Crystal Display) production industry, such as in air knife or air curtain to be used in glass cleaning. A CDA system is composed of compressors, filters (coalescent, adsorbent, oil removing, etc.), and driers. Among them, compressors far and away take the majority of energy consumption. Hence, reducing the energy consumption of compression through modeling and optimization is crucial. Compressors can be categorized into centrifugal compressors, reciprocating compressors, and rotary compressors, which are chosen for use subject to given process conditions.1 When a large amount of constant-pressure air is needed such as in the case of CDA production processes, it is common to use multistage centrifugal compressors of various capacities. It is preferred to supply compressed air with a number of smallcapacity compressors rather than few large-capacity ones. These small-capacity compressors are interconnected to each other and form a network. Constant pressure supply of compressed air is very important and, due to the fluctuating demand of CDA, compressors in the network need to be operated with redundant capacity. In industry, efficiencies and power requirements of compressors are calculated based on the design characteristic curves or other shortcut methods.2 Many works on optimization of utility systems have been performed to reduce energy consumption through modeling and optimization.3−5 Most of these works have assumed the performance of utility to be constant or have expressed simple correlation equations such as a second-order polynomial function of a single variable.6 Application of artificial neural network to compressor performance map prediction was investigated by various authors.7,8 However, actual © 2012 American Chemical Society
compressor performance varies with operating conditions and accurate nonlinear modeling of the process variables determining the power consumption rate is needed. This article first presents modeling accurately the multistage compressors using hybrid technique of ideal thermodynamic models and artificial neural network (ANN) as nonlinear empirical modeling method. The model is developed to predict efficiency and power consumption of each compressor in the network. Then, optimization procedure is applied to search optimal operating conditions of a compressor network in LCD production industry. Finally, the results of field application are presented and discussed. The proposed methodology can also be utilized in other industries, such as air utilities in oil refinery and petrochemical production plant.
2. MODELING OF COMPRESSORS Multistage compressors consist of N compression stages in series with interstage cooling systems. Figure 1 shows a schematic diagram of a 3-stage compressor. After suction of air into the first stage of the compressor, air is compressed to the desired level through the stages. Compressed air is cooled with cooling water in interstage coolers between each compression stage. Components such as speed-reducing gears, couplings, and bearings that are needed for transferring power among the compressor and its drivers are typical causes of power losses. The efficiency of the compressor varies due to changing operation and ambient conditions. Major factors include the ambient temperature, relative humidity, interstage cooling temperatures, aging of the auxiliary components, and so forth. Received: Revised: Accepted: Published: 4998
August 8, 2011 March 6, 2012 March 8, 2012 March 8, 2012 dx.doi.org/10.1021/ie2017543 | Ind. Eng. Chem. Res. 2012, 51, 4998−5002
Industrial & Engineering Chemistry Research
Article
Figure 1. Schematic diagram of a 3-stage compressor.
Manipulated variables of compressors are mainly the flow rate and ratio of discharge pressure to the suction pressure at each compression stage. Ambient condition variables consist of ambient temperature and relative humidity. Under the operation range of a typical centrifugal compressor, we might assume that the compressibility factor of air is constant to be 1. Then, minimum compression power required for all of the N compression stages under an adiabatic and reversible compression process is given by the following equation, where the flow rate of air is in the unit of volume per time. The subscript (i) refers to the stage number of the N-stage compressor, the superscript s refers to the suction and d refers to the discharge of each stage. ⎡ ⎤ k − 1/ k i = 1 kF(i)ρ RT s ⎢⎛ P d ⎞ ⎥ a (i) ⎜ (i) ⎟ − 1⎥ Wideal = ∑ ⎢⎜ s ⎟ (k − 1)Mwa ⎢ P(i) ⎥ ⎝ ⎠ N ⎣
⎦
Figure 2. Schematic diagram of the artificial neural network.
variables and ambient condition variables, and the relation between them is highly nonlinear. An empirical modeling tool such as artificial neural network (ANN) can be used here as a nonlinear modeler. ANNs are widely used for modeling nonlinear behaviors because they allow flexibility in determining model structures and typically give good modeling performances when sufficient amount of data are provided.9,10 In this study, a feed-forward back-propagation network with one hidden layer is employed to model the relation between the input variables (flow rate, discharge pressure, ambient temperature, and relative humidity) and the target variable (efficiency). The network consists of three layers; input layer, hidden layer, and output layer. The input layer has four nodes, each corresponding to the input variables. The number of nodes in the hidden layer is a manipulated variable and might be different for each compressor model. For simplicity, hidden layer with 15 nodes is used for each compressor. Full-connectivity of layers is assumed with sigmoid function as the activation function. Schematic diagram of the neural network is shown in Figure 2. Nodes in the hidden layer and output layer are calculated by eq 4.
(1)
In most industrial cases however, temperature, pressure, and flow rate at each compression stage are not measured. In addition, the eq 1 is valid for dry air and hence modification of the molecular weight and density is needed for humid air. In this case, a simplified and modified ideal thermodynamic equation is needed. It is assumed that (1) the temperature of compressed air entering each compression stage is equal to the ambient temperature by perfect cooling. (2) The compression ratios of all of the compression stages of a multistage compressor are equal to each other. (3) The suction pressure and temperature of first stage is equal to the ambient conditions. Then, ideal power consumption is calculated by eq 2. ⎡⎛ d ⎞k − 1/Nk ⎤ ⎥ Nk Fρ̃aRTe ⎢⎜ P(N) ⎟ − 1⎥ Wideal = ⎢⎜ ⎟ (k − 1)M̃ wa ⎢ Pe ⎥ ⎠ ⎣⎝ ⎦
h = activation(U1a + b1) y = activation(U2h + b2)
Here, a, h, and y are vectors of input nodes, hidden nodes and output nodes, respectively. U1 is a vector of weights between the input and hidden layer, whereas U2 is a vector of weights between the hidden layer and output layer. b1 and b2 correspond to bias. The activation function is given in eq 5.
(2)
Here, only the suction condition at the first stage and discharge condition at the last stage of the compressor measurement is required. The ambient pressure is assumed to be constant as 1 atm. The mean molecular weight and mean density are used for humid air. The ideal thermodynamic model cannot accurately predict the actual consumption power of compressors. The actual power consumption is given in the eq 3, which is the ideal power divided by compressor efficiency. Wactual =
Wideal η
(4)
y=
2 −1 (1 + exp(− 2x))
(5)
Because the ideal work and the efficiency are known, actual power consumption can be calculated by eq 3. The total structure for hybrid compressor modeling technique is shown in Figure 3.
(3)
3. CASE STUDY The proposed modeling method is applied to compressed dry air (CDA) system in liquid crystal display (LCD) industry consisting of a network of 32 centrifugal compressors. CDA system consists of compressors followed by driers and filters and the compressed dry air is widely used in the LCD industry, mainly
The efficiency of compressor varies due to operating conditions. To predict the efficiency and power consumption of compressors, hybrid technique of ideal thermodynamic models and empirical modeling methods is applied. Figure 2 shows the overall modeling process. Ideal compression work is calculated by eq 2. Efficiency of compressor is function of manipulated 4999
dx.doi.org/10.1021/ie2017543 | Ind. Eng. Chem. Res. 2012, 51, 4998−5002
Industrial & Engineering Chemistry Research
Article
The objective of the optimization is to minimize the total electric power consumption of the compressor network. The formulation of the optimization is as follows: j=1
min
∑ Wj (6)
n
Subject to Total air demand:
Figure 3. Modeling structure for compressor efficiency and actual power consumption prediction.
j
∑ Fj = F0
as air knife and air curtain for glass cleaning and drying. The compressors in the network are all 3-stage compressors. Thirtytwo compressors in parallel generate compressed air at a maximum flow rate of 260 kCMH (1000 Cubic Meters per Hour). Models are constructed for each compressor for the prediction of efficiency on the basis of the operating data of past eight months, and are combined with thermodynamic eq 2 to form a hybrid model for predicting the actual power consumption. The variables used are the discharge pressure at the last stage, air flow rate, ambient temperature, and relative humidity of the air. Data sets are collected every minute during normal operation of the process. Statistical outliers, which may be caused by measurement errors or abnormal operations, were removed. Ten percent (about 30 000 data sets) of the data set were used for the training set and the rest were used as numerous crosschecking test sets. Performance of the model of compressor #1 is demonstrated in Figure 4 for about 400 observations. The modeling results
(7)
n
Surge control: P(dN )j ≤ Fj αj + βj , for j = 1, 2, ···, n
(8)
Power load of electrical motor: Wj , L ≤ Wj ≤ Wj , U , forj = 1, 2, ···, n
(9)
The constraints for each compressor are the safety limit for operation below a surge line15 and lower and upper bound of power load of electrical motor. The parameters of surge line are obtained from the performance curves provided by the vendors. Conventional operation of compressor network sets all compressors linked in the network to operate part-loaded and therefore every compressor responds to dynamic changes of total air demand, which is not energy-efficient. Small-capacity centrifugal compressors should be operated full-loaded for optimal operation. However, because of fluctuating demand of CDA, operation of the compressor network requires redundancy to supply compressed air at constant pressure. Therefore, few compressors must remain running part-loaded to stably follow up the varying demand for safe operation. This is a typical optimization problem occurring in the compressor network of CDA processes. For the CDA system in the case study, among the 32 compressors 25 compressors are used to supply compressed air ranging from 160 kCMH (1000 cubic meters per hour) to 190 kCMH. The total demand of CDA changes from moment to moment in this range. The operating conditions of every compressor change as the total demand fluctuates and hence the efficiencies of the compressors are kept low. In this study, we categorize the compressors into two groups: (1) full-load operating group and (2) part-load operating group. The full-load operating group is fixed to operate fullloaded so that they are not affected by the varying demand. The part-load operating group will be operated in lower efficiency but can follow the demand fluctuation and keep the overall discharge pressure of the compressors constant. 4.1. Optimization Case I. Optimization procedure requires constant full load operation of compressors to keep the maximum efficiency level of each compressor. On the other hand, enough safety margins are needed. There should always be capacity redundancy to flexibly follow up situations when the demand increases rapidly. Therefore, the number of compressors to be used is fixed to 25 for safety. Among the 32 compressors in the network, 25 compressors are operated. These compressors are further divided into partload operating group and full-load operating group, 5 and 20 compressors respectively. Setting 20 compressors as full-loaded operation is recommended because the total demand of compressed air is always above 160 kCMH, which is the sum of full
Figure 4. Comparison of the measured value and predicted values of compressor power consumption.
show excellent agreement between the measured and predicted values of the electric power consumption with average error of less than 1.2%. Root mean squared error (rmse) of the actual power consumption is 6.99 kW, which corresponds to about 0.7% of the average value. Similar performances were obtained for other 31 compressors with average error ranging between 0.5−2%, rmse ranging between 5−20 kW.
4. OPTIMIZATION OF COMPRESSOR NETWORK A variety of compressed-air system energy saving studies were performed including minimization of compressed air leaks, minimization of pressure drop, recovering waste heat, and using high-efficient motors.11−14 In this work, energy saving of a compressed-air system is achieved by optimal configuration of the compressor network. 5000
dx.doi.org/10.1021/ie2017543 | Ind. Eng. Chem. Res. 2012, 51, 4998−5002
Industrial & Engineering Chemistry Research
Article
capacities of about 20 compressors. In optimization case I, let us operate the most efficient 20 compressors (efficiency rank 1 to 20) as the full-load operating group and 5 next ones (efficiency rank 21 to 25) as the part-load operating group. The efficiency rank is calculated by the model at given operating conditions (discharge pressure, ambient temperature, and relative humidity). 4.2. Optimization Case II. In optimization case II, let us operate the most efficient 5 compressors (efficiency rank 1 to 5) as the part-load operating group and 20 next ones (efficiency rank 6 to 25) as the full-load operating group. 4.3. Optimization Results. The optimization results are shown in Table 1.
Now, the mean molecular weight and density is calculated by the following equations. ρ̃ =
optimization Case I
optimization case II
25 866 0.45543
24 812 0.4726 4.07
24 650 0.4781 4.70
total work (kW) average efficiency percentage saved (%)
P P M̃ wa = d Mwa + v Mww Pe Pe
■
*Tel: +82-2-880-1887, E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS The authors gratefully acknowledge the project for energysaving of utility systems of LGDisplay Co., Human Resources Development of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Ministry of Knowledge Economy (20094010100040), the Brain Korea 21 Project initiated by the Ministry of Education of Korea(ME), the Energy Resources Technology Development Project provided through the Korea Energy Management Corporation/Ministry of Knowledge Economy of Korea(MKE), the Industrial strategic Technology Development Program “Design of topside LNG regasification plant of LNG FSRU(10031883)” by the MKE, and the LNG Plant R&D Center funded by the Ministry of Land, Transportation and Maritime Affairs(MLTM) of the Korean government.
■
■
APPENDIX Calculations of mean molecular weights and mean density are as follows. Relative humidity is the ratio of vapor pressure of water to the saturation vapor. (10)
Saturation vapor pressure can be calculated using the Antoine’s equation.16 B t /°C + C
(11)
For water, A = 16.3872, B = 3885.70, C = 230.170 and these parameters are valid for temperature range 0−200 °C.17 When we know the atmospheric pressure, usually assumed constant to be 1 atm, and the vapor pressure of water, partial pressure of dry air is just the difference of the two.
Pd = Pe − Pv
AUTHOR INFORMATION
Corresponding Author
5. CONCLUSIONS This article presented hybrid modeling technique of ideal thermodynamic models and empirical modeling method to predict the efficiency and actual power consumption of multistage centrifugal compressors. The modeling methodology was applied to CDA system of LCD industry and proved its excellence in prediction. Using the models developed, strategic optimization of the compressor network was done. Minimizing the total power consumption of compressors while meeting the safety margin constraint can be achieved by decomposing the compressors in the network into part-load group and full-load group. The optimization technique was applied to CDA compressor network in LCD industry and 4.7% of power consumption was saved.
ln P sat/kPa = A −
(14)
Mwa and Mww refers to the molecular weight of dry air and water vapor respectively.
As can be seen from the result table, the optimization case II is the more optimal solution. The result shows about 5% energy saving. Hence, the optimization strategy of a multistage compressor network is to operate the most efficient 5 compressors part-loaded to flexibly meet the fluctuating demand and the next efficient 20 compressors full-loaded.
Pv = Φ × P sat
(13)
Rd is the specific gas constant for dry air which is equal to 287.05 J/kg K. Rv is the specific gas constant for water vapor, which is equal to 461.495 J/kg K.
Table 1. Optimization Results of Optimization Case I and II before optimization
Pd P + v R dT R vT
(12) 5001
NOMENCLATURE a = vector of nodes in the input layer F(i) = flow rate of air at the compression stage i [m3/s] F = flow rate of air at the discharge of a multistage compressor [m3/s] h = vector of nodes in the hidden layer j = jth compressor in the compressor network k = adiabatic exponent of air, constant as 1.398 Mwa = molecular weight of dry air [28.96 kg/kg mol] M̃ wa = mean molecular weight of air [kg/kg mol] Mww = molecular weight of water [18.02 kg/kg mol] N = total number of compression stages of a multistage compressor n = total number of compressors in the compressor network d P(i) = discharge pressure of the air at the compression stage i [kPa] s P(i) = suction pressure of the air at the compression stage i [kPa] Pe = atmospheric pressure [kPa] Psat = saturation vapor pressure [kPa] R = universal gas constant [8.314 kJ/kg mol K] Rd = specific gas constant for dry air [287.05 J/kg K] Rv = specific gas constant for water vapor [461.495 J/kg K] Te = ambient temperature [K] U1 = vector of weights between the input layer and hidden layer dx.doi.org/10.1021/ie2017543 | Ind. Eng. Chem. Res. 2012, 51, 4998−5002
Industrial & Engineering Chemistry Research
Article
U2 = vector of weights between the hidden layer and output layer Wideal = ideal power required for multistage compression [kW] Wactual = actual power required for multistage compression [kW] W = electric power delivered to an electric motor [kW] y = vector of nodes in the output layer Greek Symbols
αj = slope of the surge control line of a compressor [kPa s/ m3] βj = intercept of the surge control line of a compressor [kPa] η = efficiency of a compressor [0−1] ρa = density of air Φ = relative humidity of ambient air
■
REFERENCES
(1) O’Neill, P. Industrial Compressors, Theory and Equipment. Butterworth-Heinemann: Oxford: 1993. (2) Bloch, H. A Practical Guide to Compressor Technology; WileyInterscience: 2006. (3) Hui, C.; Natori, Y. An industrial application using mixed-integer programming technique: A multi-period utility system model. Comput. Chem. Eng. 1996, 20, S1577−S1582. (4) Iyer, R.; Grossmann, I. Optimal multiperiod operational planning for utility systems. Comput. Chem. Eng. 1997, 21 (8), 787−800. (5) Kirishnaswami, P.; Chapman, K.; Abbaspour, M. Gas Machinery Research Council Technical Papers 2004. (6) Saxena, M. Optimize gas turbine-driven centrifugal compressors. Hydrocarbon Processing 2000, 79 (11). (7) Ghorbanian, K.; Gholamrezaei, M. An artificial neural network approach to compressor performance prediction. Applied Energy 2009, 86 (7−8), 1210−1221. (8) Yu, Y.; Chen, L.; Sun, F.; Wu, C. Neural-network based analysis and prediction of a compressor’s characteristic performance map. Applied Energy 2007, 84 (1), 48−55. (9) Bulsari, A. Neural Networks for Chemical Engineers; Elsevier Science Inc.: New York, NY, USA; 1995. (10) Himmelblau, D. Applications of artificial neural networks in chemical engineering. Korean J. Chem. Eng. 2000, 17 (4), 373−392. (11) D’Antonio, M.; Epstein, G.; Moray, S.; Schmidt, C. Compressed Air Load Reduction Approaches and Innovations 2005. (12) Galitsky, C. Energy Efficiency Improvement and Cost Saving Opportunities for the Vehicle Assembly Industry: An ENERGY STAR Guide for Energy and Plant Managers 2008. (13) Kaya, D.; Phelan, P.; Chau, D.; Sarac, H. Energy conservation in compressed-air systems. Int. J. Energy Res. 2002, 26 (9), 837−849. (14) Shanghai, H.; McKane, A. Improving Energy Efficiency of Compressed Air System Based on System Audit 2008. (15) ZAFAR, R. Understand multistage compressor antisurge control. Hydrocarbon Processing 1985, 64 (3), 69−74. (16) Smith, J.; Van Ness, H.; Abbott, M. Introduction to Chemical Engineering Thermodynamics, 6th ed.; McGraw-Hill International ed.: United States of America; 2001. (17) Poling, B.; Prausnitz, J.; John, P. The Properties of Gases and Liquids; McGraw-Hill: New York; 2001.
5002
dx.doi.org/10.1021/ie2017543 | Ind. Eng. Chem. Res. 2012, 51, 4998−5002
