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A Two-parameter Model for the Determination of Optimum Liquefied Petroleum Gasses (LPG) Storage Volume

A Two-parameter Model for the Determination of Optimum Liquefied Petroleum Gasses (LPG) Storage Volume
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  This article was downloaded by: [UNIVERSITY OF KWAZULU-NATAL]On: 10 February 2015, At: 00:53Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registeredoffice: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Click for updates Petroleum Science and Technology Publication details, including instructions for authors andsubscription information: A Two-parameter Model for theDetermination of Optimum LiquefiedPetroleum Gasses (LPG) Storage Volume A. Kamari a , A. Bahadori b  & A. H. Mohammadi aca  Thermodynamics Research Unit, School of Engineering, Universityof KwaZulu-Natal, Howard College Campus, Durban, South Africa b  School of Environment, Science & Engineering, Southern CrossUniversity, Lismore, Australia c  Institut de Recherche en Génie Chimique et Pétrolier (IRGCP),Paris, FrancePublished online: 05 Feb 2015. To cite this article:  A. Kamari, A. Bahadori & A. H. Mohammadi (2015) A Two-parameter Model for theDetermination of Optimum Liquefied Petroleum Gasses (LPG) Storage Volume, Petroleum Science andTechnology, 33:4, 494-501, DOI: 10.1080/10916466.2014.986280 To link to this article: PLEASE SCROLL DOWN FOR ARTICLETaylor & Francis makes every effort to ensure the accuracy of all the information (the“Content”) contained in the publications on our platform. However, Taylor & Francis,our agents, and our licensors make no representations or warranties whatsoever as tothe accuracy, completeness, or suitability for any purpose of the Content. Any opinionsand views expressed in this publication are the opinions and views of the authors,and are not the views of or endorsed by Taylor & Francis. The accuracy of the Contentshould not be relied upon and should be independently verified with primary sourcesof information. Taylor and Francis shall not be liable for any losses, actions, claims,proceedings, demands, costs, expenses, damages, and other liabilities whatsoever orhowsoever caused arising directly or indirectly in connection with, in relation to or arisingout of the use of the Content.This article may be used for research, teaching, and private study purposes. Anysubstantial or systematic reproduction, redistribution, reselling, loan, sub-licensing,systematic supply, or distribution in any form to anyone is expressly forbidden. Terms &  Conditions of access and use can be found at    D  o  w  n   l  o  a   d  e   d   b  y   [   U   N   I   V   E   R   S   I   T   Y   O   F   K   W   A   Z   U   L   U  -   N   A   T   A   L   ]  a   t   0   0  :   5   3   1   0   F  e   b  r  u  a  r  y   2   0   1   5  Petroleum Science and Technology , 33:494–501, 2015Copyright  C   Taylor & Francis Group, LLCISSN: 1091-6466 print / 1532-2459 onlineDOI: 10.1080/10916466.2014.986280 A Two-parameter Model for the Determination of OptimumLiquefied Petroleum Gasses (LPG) Storage Volume A. Kamari, 1 A. Bahadori, 2 and A. H. Mohammadi 1,3 1 Thermodynamics Research Unit, School of Engineering, University of KwaZulu-Natal, Howard College Campus, Durban, South Africa 2 School of Environment, Science & Engineering, Southern Cross University, Lismore, Australia 3  Institut de Recherche en G´ enie Chimique et P´ etrolier (IRGCP), Paris, France In this work, a mathematical-based methodology is employed to develop a reliable model for theprediction of safe volume for liquefied petroleum gases (LPG) storage vessels. To this end, a novelsoft computing approach namely least square support vector machine (LSSVM) modeling optimizedwith coupled simulated annealing (CSA) optimization technique is utilized. To evaluate the performanceand accuracy of the LSSVM model, graphical (cross plot and error distribution curve) and statistical(error parameters) analyses have been utilized. Additionally, comparative studies are conducted betweenthe LSSVM model and a multilayer perceptron artificial neural network (MLP-ANN) model. Obtainedresults prove that the proposed CSA-LSSVM model is more robust, reliable and efficient than thedeveloped MLP-ANN model for the prediction of liquid volume correction factor. Consequently, thedevelopedLSSVMmodelresultsindicateanaverageabsoluterelativedeviationequalsto0.02782%fromthe corresponding liquid volume correction factor literature values, and a squared correlation coefficientof 0.9999. Keywords : storage tank, liquefied petroleum gases, error analysis, least square support vector machine,modeling 1. INTRODUCTION Nowadays, liquefied petroleum gases (LPG) are very applicable in various industries as LPG canstore and also transport in special tanks (Shebeko et al., 2000). Here it should be noted that thesetechnological materials are of high fire hazard. There are many accidents associated with explosionsand fires have included LPG vessels (Davenport, 1988; Shebeko et al., 1996), which happen oftenin fire script when explosion of the vessels is very plausible, and consequently it can be sometimeshazardous and disastrous (Shebeko et al., 2000). As a result, there are various approaches reported inliterature for prevention of such hazardous accidents including isolating the vessels walls as thermal,implementation of safety relief valves, tanks with double walls and safety relief valves together withsome passive fire protection tools, locating the vessels in underground, and finally use of dispersedwater for cooling of the vessels (Kletz, 1977; Birk, 1989; Roberts, 1995; Shebeko et al., 1996;Shebeko et al., 2000). Address correspondence to A. Bahadori, School of Environment, Science & Engineering, Southern Cross University,Lismore, NSW, Australia. E-mail: versions of one or more of the figures in the article can be found online at 494    D  o  w  n   l  o  a   d  e   d   b  y   [   U   N   I   V   E   R   S   I   T   Y   O   F   K   W   A   Z   U   L   U  -   N   A   T   A   L   ]  a   t   0   0  :   5   3   1   0   F  e   b  r  u  a  r  y   2   0   1   5  DETERMINATION OF OPTIMUM LPG STORAGE VOLUME  495 TABLE 1Maximum Permitted Filling Density (%)  Aboveground Vessels (1993)Specific Gravity at 15.6  ◦ C Up to 5000 L Over 5000 L 0.496–0.503 41 440.504–0.510 42 450.511–0.519 43 460.520–0.527 44 470.528–0.536 45 480.537–0.544 46 490.545–0.552 47 500.553–0.560 48 510.561–0.568 49 520.569–0.576 50 530.577–0.584 51 540.585–0.592 52 550.593–0.560 53 56 Asamatteroffact,experimentaldeterminationoftheliquidvolumetemperaturecorrectionfactordataforLPGstoragevesselsiscostlyandtimeconsuming.Therefore,searchingforsomeotherquick and accurate methods for determination of the liquid volume temperature correction factor data forLPG storage vessels is important. As a consequence, most available methods for determination of liquid volume temperature correction factor data for LPG storage vessels are unsuitable due to thefact that most of these methods have been developed based on limited data set and specific ranges.Noneofpreviouslypublishedcorrelationsaregenerallyapplicableinawidevarietyofconditionsandconsequently simpler and more robust model is required to estimate the liquid volume temperaturecorrection factor data for LPG storage vessels. Moreover, there is no simplified method existsin the literature for rapid estimation of safe storage volume of LPG according to the authors’knowledge. Hence, our efforts have been focused at developing and reliable and robust modelthat can aid petroleum and chemical engineers for rapid forecasting safe volume for LPG storagevessels in a temperature range between –55 ◦ C and 60 ◦ C as a function of temperature, maximumfilling density, water capacity of storage vessel, specific gravity of liquid gas at 15.6 ◦ C, and a noveldeveloped liquid volume temperature correction factor. The proposed strategy in this study utilizesleastsquaresupportvectormachine(LSSVM)toconstructnonlinearmodeling.Moreover,fortuningthe optimal parameters of LSSVM algorithm a novel feature selection mechanism based on coupledsimulated annealing (CSA) optimization has been employed. Additionally, statistical and graphicalerror analyses were conducted to establish the adequacy and accuracy of the model, and finally theobtained results by the CSA-LSSVM model were compared with a multi-layer perceptron neuralnetwork model. 2. SAFE VOLUME There are several existing methods to determine the safe volume for LPG storage vessels in a tem-perature range from –55 to 60 ◦ C, which require many adjustable parameters and more complicated.These methods implement storage temperature, specific gravity of liquid gas, maximum filling den-sity, water capacity of storage vessel for determining liquid volume temperature correction factor.As a result, the volume of liquid stored in a vessel must be limited to permit adequate room forthermal expansion. The maximum volume (V) of liquid gas at a certain temperature that may be    D  o  w  n   l  o  a   d  e   d   b  y   [   U   N   I   V   E   R   S   I   T   Y   O   F   K   W   A   Z   U   L   U  -   N   A   T   A   L   ]  a   t   0   0  :   5   3   1   0   F  e   b  r  u  a  r  y   2   0   1   5  496  A. KAMARI ET AL. FIGURE 1  Structure of the optimal network with two input parameters, on hidden layer and six hidden layer neurons. charged into a vessel is calculated as follows: V   = DW  100 SGF  (1)where  V   stands for maximum volume of liquid gas at a certain temperature,  D  denotes maximumfilling density (see Table 1),  W   expresses water capacity of storage vessel at 15.6 ◦ C or 60 ◦ F,  SG represent specific gravity of liquid gas at 15.6 ◦ C, and finally  F   is liquid volume correction factorfrom temperature T ◦ through 15.6 ◦ C. In a view of above issues, itcan be concluded that a volumetric TABLE 2Ranges and Averages of the Input/Output Data (Temperature, Specific Gravity and Liquid Volume CorrectionFactor) Used for Developing the ANN and LSSVM Models Performance E  aa  ,% E  r b  ,% SD c  RMSE  d   R 2 e LSSVM, Total 0.027824453 –0.000562672 0.000363448 0.000357704 0.9999LSSVM, Training 0.026583569 –1.23202E-05 0.000303773 0.000333219 0.9999LSSVM, Testing 0.032773039 –0.002757449 0.000199541 0.000442061 0.9999ANN 0.071121503 –0.001003869 0.001036845 0.001053415 0.9998    D  o  w  n   l  o  a   d  e   d   b  y   [   U   N   I   V   E   R   S   I   T   Y   O   F   K   W   A   Z   U   L   U  -   N   A   T   A   L   ]  a   t   0   0  :   5   3   1   0   F  e   b  r  u  a  r  y   2   0   1   5
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