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Prediction of wax disappearance temperature by intelligent models Xiao-Qiang Bian, Jin Hui Huang, Ying Wang, Yong Bing Liu, Don Thisal Kaushika Kasthuriarachchi, and Lin Jun Huang Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.8b04286 • Publication Date (Web): 28 Feb 2019 Downloaded from http://pubs.acs.org on March 1, 2019
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Prediction of wax disappearance temperature by intelligent models Xiao-Qiang Bian1, Jin-Hui Huang, Ying Wang, Yong-Bing Liu, Don Thisal Kaushika Kasthuriarachchi, Lin-Jun Huang (Petroleum Engineering School, Southwest Petroleum University, Chengdu 610500, China) Abstract It’s well-known reservoir hydrocarbon fluids contanin heavy paraffins that may form solid phases of wax at low temperatures. Problems associated with wax formation and deposition are a major concern in production and transportation of hydrocarbon.Thus, testing of wax disappearance temperature (WDT) is essential in high efficiency development of crude oil. For the sake of reduction of time and improvement of accuracy, the four meta-heuristic models called grey wolf optimizer based support vector machine (GWO-SVM), least squares support vector machine (LSSVM), Genetic algorithm based Adaptive Network-based Fuzzy Inference System (GAANFIS), and Particle Swarm Optimization based Adaptive Network-based Fuzzy Inference System (PSO-ANFIS) was used for the prediction of WDT of respectively binary, ternary and multi-component system at the range of 0.1- 100MPa. The input parameters are molar mass and pressure, and the output is the WDT at every point. The comparison between the four models shows that the GWO-SVM gets the best accordance with experiment data sets with the minimum lowest average absolute relative deviation (AARD= 0.7128%), the maximum determination coefficient (R2= 1
Corresponding author at: Petroleum Engineering School, Southwest Petroleum University, Chengdu 610500,
China (X.-Q. Bian). E-mail addresses:
[email protected] (X.-Q. Bian)
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0.9546), and minimum root mean squared error (RMSE= 2.4208) in all 272 data points. And outliers detection using the Leverage approach to detect the doubt points, where only 6 data points in all all 272 data points. Keywords: Wax disappearance temperature; Intelligent algorithm; Grey wolf optimizer-support vector machine; Least squares support vector machine; GA-ANFIS
1 Introduction
Crude oil and gas condensate are made up of a large number of long n-alkane chains. In the event of the temperature drops to a temperature below wax appearance temperature (WAT), there is wax precipitation in the transport equipment and pipelines, which may lead to plugging of well bores and blockage of pipeline. In order to address the issue of wax deposition, we need to know how it appeared. The temperature reduction severely affects the precopitation of wax, stemmed from gas expansion and heat losses from oil and gas streams to the environments. Besides, wax precipitation is also resulted from segregation of dissolved gases and evaporation of light fraction of the oil mixtures1. The main component of petroleum waxes is normal alkanes2. Therefore, many researchehes preceed from these constituent to get the accurate knowledge of wax precipitation. When wax is first perceived at cooling in a given pressure, the temperature is cloud point temperature, that is, wax appearance temperature (WAT), mostly measured in laboratories. But WAT is not certainly an equilibrium point, which lies on measurements. Experimental studies show that WAT commonly relates to the cooling rate extremely;
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the faster cooling rate, the lower measured WAT. For example, measured WAT applying visual microscopy is higher 10–20 ℃ than applying ‘laser-based solids detection systems’,‘differential scanning calorimetry’, and ‘viscometer experiment3, 4. Differ from WAT, the Wax Disappearance Temperature (WDT) stands for a certain Solid–Liquid Equilibrium (SLE) point. Advisabal experimental techniques and method( i.e. equilibrium step heating) make a great WDT’s value, where measured WDTs are in agreement with the standard values within a reasonable error range in different laboratories. There are four approaches to determine accurate WDT, all of which are experimental measurements, thermodynamic models, empirical models, and intelligent algorithms. Experimental measurement is the most reliable one in four approaches. Some researchers conducted experiments to determine WDT. Metivaud (1999)5 et al. measured WAT of consecutive C14-C21 combining Differential Scanning Calorimetry (DSC), and X-ray, roughly covering from 0 to 50 degrees Celsius only at atmosphere pressure. There’s a great limitation of pressure and temperature. In order to overcome the nonideality of solution to overestimate the precipitation, C.Dauphin et al. (1999)6 measured WAT, waxy solid content and wax composition of a wax system ranging from C18 to C36 at atmosphere pressure, but some paraffins were removed from the series so that it can be provided with various bimodal distributions, covering from 300K315K, which leads to incompleteness of tested syetem and inaccuracy of experiment. But it’s assumed that there’s coexistence of several solid solution in systems. To expand
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pressure range, J. L. Daridon et al. (2002)7 used a high pressure apparatus resting on a polarizing microscope, which is able to determine the visual liquid-solid phase transition in complex systems and measure the WDT at a wider range of pressures below 100 MPa, testing mixture of n-paraffins ranging from C13-C24. However, the experiment setup is so expensive that it cannot not be popularized. M. Milhet (2005)8 measured WDT of two binary systems, C14+ C15 and C14+ C16, under high pressure applying a polar microscope. However, the data received are higher than the data from Metivaud (1999)5 for C14+ C16 system. The reason may be appearance of triclinic phase with increasing pressure, which no longer can be measured. To overcome the drawback, A. Rizzo (2007)9 designed an apparatus based on two sapphire windows, high pressure cell coupled with a detection system of the reflected and refracted light intensities coming from a laser beam. This was designed to observe the phase transformation. Although experimental value of WDT is usually available at increasing pressures, it is expensive, laborious and time-consuming10. There is complex calculation and realization of critical parameters of wax in thermodynamic models, and it’s necessary to understand mathematical principles and analytical solution for establishing equations and computing numerical solution. Won (1986)11 and Won (1989)12 presented two modified regular solution for wax depositon. Hansen Et Al. (1998) presented a improved regular solution employing Flory’s theory (1953)13 of multicomponent solutions for activity coefficient. Besides, W.B. Pedersen et al. (1991)14 raised the Won (1986)11 modified model for WAT calculations. LiraGaleana et al. (1996)15 developed a multi-solid phase for wax precipitation, and
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regarded every solid phase as pure component, considering the ideality only. Therefore, Continho (1998)16 improved a predictive UNIQUAC model for solid and liquid phase equilibriums considering the nonideality based on model proposed by Abrams and Prausnitz (1975)17, which allows solid splits instead of Wilson, although it describes liquid phase inaccurately. To considering the Poynting correction, Zuo et al. (2001)18 raised a solid-solution model to calculate wax precipitation in crude oils and gas condensates, but it overestimates the WAT and amount of precipitated wax. Arcorrding to the study about investigation of the phase behaviors between the wax disappearance temperature (WDT) and the wax appearance temperature (WAT) at atmosphere pressure, Bhat and Mehrotra (2004)19 found the WDT is closer to the saturation temperature of wax precipitation, not WAT. For exploring the effect of pressure (between 0.1 to 50 MPa) on wax phase equilibria, Ji et al. (2004)20 managed to calulate WDT for binary and multi-system by applying the UNIQUAC thermodynamic model. Ghanaei et al. (2007)21 improved a new model for the prediction composition of wax and WDT of binary system of C14-C15 and C14-16 (0.1- 100MPa). Nasrifar and Fani (2011)22 investigatied a new method about estimation of Ponyting correction term to broaden the pressure range, and managed a model for the prediction at low and high pressure of wax precipitation.Ghanaei (2012)23 presented a model applying heat capacity correlations in order to explore the solid- solid phase transition appearring in solidliquid fugacity of pure component as phase change and heat enthalpy, thus describing non-ideality of solid wax phase. Juheng Yang et al. (2016)24 improved Wilson model considering the molecules’ difference and entropy contribution only, developed a new
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solid solution model for liquid phase with regular solution theory and Flory free-volume theory and solid phase with solid solution theory, considering non-ideality of solid phase, enthalpy contribution, the energetic interactions between the components, entropy contribution and differences in size and shape between the molecules. Various empirical studies like the (Pauly et al., 199825; Metivaud et al., 19995; Pauly et al., 20017, 26; Daridon et al., 20027; Pauly et al., 200427; Milhet et al., 20058; Rizzo et al., 20079; Vafaie-Sefti et al., 200728) were accomplished on wax precipitation. Intelligent algorithm has been developed rapidly, and implemented to link WDT and different parameters. ANNs as utilizable methods are benefit for modeling complicated systems in petroleum engineering areas such as prediction of WDT. Gholamreza Moradi (2013)29 et al. proposed ANN, in which a tansig transfer function in three layer feedforward backpropagation, in predicting of WDT at elevated molar mass (87.82293.90) and pressure from 0.1MPa- 100.3MPa with agreeable results. For many years, the modelers either had to manually tune the parameters during a time-consuming trial and error process or for simplicity they used the default settings which are usually far from optimal, metaheuristic optimization algorithms have recently emerged as a remedy to alleviate the difficulty associated with the machine learning methods. Arash Kamari (2013)30 developed a predictive model for calculation of wax precipitation, least-squares support vector machine (LSSVM) modeling majorized with the coupled simulated annealing (CSA) approach, achieving a great agreement between predictions based on the CSA-LSSVM and experiment datas on wax precipitation. With the increasing progress of intelligence algorithms for those years, a Grey Wolf Optimizer
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(GWO) has been reliable for settling numerous optimization issues, like non-convex economic load dispatch31. Nait Amar Menad (201832) proposed RBFNN-GWO for modeling temperature-based oil-water relative permeability. Zhiyu Zhou (201833) proposed DE-SVM to establish the color difference classification model of printing and dyeing, foe which its good global searching ability. Abolfazl Jaafari (201934) developed ANFIS-GWO to estimate landslide susceptibily, for which GWO is able to overcome the shortcoming of ANFIS model and optimize base parameters. However, it’s not very common that researchers utilize intelligent algorithm working out the WDT in literatures. Besides the application of PSO, GA to optimize the control parameters of SVM, in this work, a new framework is provided to optimize these parameters by implementing a new recent metaheuristic algorithms (GWO) that was shown to be more efficient in the optimization process compared with the well-known metaheuristic algorithms. The target in the work is to propose and verify four meta-heuristic models on the basis of reliable experimental WDT datas from existing literatures. In this work, four models were proposed in prediction of the WDT. The input parameters of the proposed models are the pressure and molar mass, and the objective parameter is WDT. The accuracy and reliability of the four proposed models were examined by applying 272 data sets available in the literatures. This work was organized as follows:
Part 2, the brief introduction of GWO-SVM, LSSVM, GA-ANFIS, PSO-ANFIS models.
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Part 3, the used data and factors affecting WDT were given.
Part 4, Comparing the rusult of models with experimental date, the performance of the four meta-heuristic models was validated.
Part 5, The corresponding conclusions were given.
2 Methodology
2.1 GWO-SVM
2.1.1 Support vector machine SVM35 is a statistical learning theory regression method, whose main philosophy is to draw the input data (low dimensional space) into a high dimensional feature space and then to build a kernel function for getting a linear regression function. The input data sets: ( xi ( m) , yi ), i 1, 2,..., N ; m 1, 2,..., n , where xi( m ) denotes the ith element in mth- dimensional space, yi and N are the scalar output and the aggregate of data sets, respectly. The support vector regression (SVR) function as follow (1): f x , x b
（1）
Where λ is the weight vector and b is the threshold value of the regression function, this is, deviation term. According to the minimizing regularized risk function as follow, The regression issue is settled:
R emp f
1 N 1 L yi f , xi N i 1 2
2
（2）
Where: 8
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0, if y f ( , xi ) L [ yi f ( , xi )] y f ( , x) , otherwise E.g. (3) is ε-insensitive loss function developed by Vapnik (1995)
（3） 36
. And the
range of the regression function f(x) is limited by ε-value While the error value between experimental and estimated value is within the range of ε-value, the loss value is regarded as zero. If not, the loss is treated as the absolute difference between the predicted value and the ε-value. The optimization object is expressed by: N 1 2 c * minimize 2 i 1
(4)
yi f xi , b * * subject to f , xi b yi * i , i 0
(5)
where the regularization parameter C is the penalty term. The slack variables ξ and ξ* were served as bias restriction of training data sets beyond range of ε-insensitive. This optimization issue could be transform to a dual issue. The formula is converted to the following function with the optimization theory: maximize
n n 1 n * * * ( )( ) x , x ( ) yi ( i i* ) i i j j i j i i 2 i , j 1 i 1 i 1
n * ( i i ) 0 subject to i 1 0 , * C i i
(6)
(7)
where αi and αi* are respectively Lagrange multiplier and optimal desired weight vector of the regression hyper-plane shown in E.g.(8);. n
f ( x) ( i i* ) xi , x j b
(8)
i 1
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The last regression function as follows: n
f ( x) ( i i* ) K ( xi , x j ) b
(9)
K ( xi , x j ) exp( xi , x j ), 0
(10)
i 1
The value of the penalty parameter (C), the insensitive loss function (ε) and the kernel parameter (γ) will interact on the veracity of training data and predicted data in SVM model. The value changes of one parameter will cause changes of other parameters. The variable C represents the trade-off between model complexity of the training data and the model extension term with the mathematical meaning. The larger C value will result in overfitting of the training data set and minimization of the empirical risk without taking into account the more complex learning. However, the smaller C value will lead to the underfitting of the the training data. The variable ε influences not only the complexity of the approximation function but the number of support vectors.
2.1.2 Grey Wolf Optimizer
Mirjalili (2014)37 developed a novel GWO optimization algorithm, which applied a new swarm intelligence algorithm inspired by grey wolves according to simulating the hierarchical relationship and hunting behavior of grey wolves spontaneously. With the advantage of other metaheuristics algorithms such as Genetic Algorithm (GA)38, Ant Colony Optimization39, and Particle Swarm Optimization40, the evolution process
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of these algorithms population involves random factors while the GWO algorithm represents better results compared with those famous meta-heuristics. The GWO algorithm mainly consists of four parts: social hierarchy, tracking, encircling, and attacking prey process. In portion of social hierarchy, GWO simulates the wolves hierarchy including four types of grey wolves: alpha (α), beta (β), delta (δ) and omega (ω), as shown in Fig. 1. Grey wolves are quite gregarious in the apex predators of the food chain
Fig.1. Grey wolf hierarchy (dominance decrease from top down) The most suitable solution is supposed as the α. Analogously, the β represents the second-class solutions, the δ third-class solutions and the ω is the last remaining best solutions. In the progress of algorithm, α, β, and δ wolves lead the hunting respectively, and the ω wolves follow. At the mention of encircling prey, the behaviors could be mathematically modeled as follows:
D C X p (t ) X (t )
(11)
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X (t 1) X p (t ) A D
(12)
Xp where X represents the present position vector of a grey wolf, is the prensnt prey position, and A , C are respectively the coefficient vectors and emphasize exploitation and exploration obtained by:
A 2a r1 a
(13)
C 2 r2
(14)
r r Where a linearly descends from 2 to 0 with iterations increasing, 1 and 2 are respectively random vectors from 0 to 1. Thus, A is a random value from -a to a. For the sake of simulating the attacking prey, in the case of random values of A lacated in [-1, +1], if
A
