Article Cite This: Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Novel Naphtha Molecular Reconstruction Process Using a SelfAdaptive Cloud Model and Hybrid Genetic Algorithm−Particle Swarm Optimization Algorithm Kexin Bi†,‡ and Tong Qiu*,†,‡ †
State Key Laboratory of Chemical Engineering, Department of Chemical Engineering, and ‡Beijing Key Laboratory of Industrial Big Data System and Application, Tsinghua University, Beijing 100084, China
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ABSTRACT: Naphtha is an important product of crude oil and has widespread industrial applications. Additionally, the composition of naphtha is influenced by the procurement and operations of crude oil, which has different characteristics in each region. In this paper, a novel molecular reconstruction process is proposed to provide an accurate composition for local refineries. An effective probability density function composed of the gamma distribution trend, regional features, weight features, and uncertainty is constructed using a selfadaptive cloud model and used in this process. A hybrid genetic algorithm−particle swarm optimization method is applied in this process after comparing with other optimization methods. The results of the proposed molecular reconstruction process are much closer to the actual composition than that of other methods, which verifies that this process has high performance and is feasible for industrial application.
1. INTRODUCTION An accurate characterization of crude oil components is essential for enabling refineries to enhance product quality and increase profitability. Naphtha is a type of light component from the fractional distillation of crude oil, and it can be used, for example, as feedstock for ethylene pyrolysis, reforming, and gasoline production.1 A detailed composition of naphtha can be provided by instrumental analysis techniques,2 such as gas chromatography (GC), GC × GC, and GC−mass spectrometry (GC−MS). However, it is not feasible to apply these timeconsuming and highly expensive methods widely in industry, especially in refineries in western part of China. Therefore, a process called “molecular reconstruction” is introduced to avoid the insufficiency of molecular information that results from instrumental analysis. The molecular reconstruction process generates simplified mixtures of molecules in crude oil from rough characterization analysis.3 In this work, the properties4 of naphtha, including nparaffins, isoparaffins, olefins, naphthenes, and aromatics (PIONA), such as ASTM D86 data, average molecular weight (MW), and hydrogen−carbon molar ratio (H/C) are considered to fall within the molecular reconstruction process. The predefined set of key compounds in naphtha can be represented by the molecular type homologous series (MTHS5) matrix. Then, the component fractions of key compounds in the MTHS matrix need to be calculated from the known properties of naphtha. Probability density functions (PDFs) have been suggested to model the carbon number distribution in each homologous series,6 and the gamma © XXXX American Chemical Society
distribution has been proved to be suitable in theory and application for general prediction models.7 However, for practical application in the refineries of various regions in China, the actual carbon number distribution may deviate from the gamma distribution as a result of feedstock mixing or other pretreatments before refining.8 The instability of operating conditions during the refining process may also add uncertainty into the distribution. To obtain an accurate molecular reconstruction result for local refineries, an intelligent optimization process with an effective PDF should be applied. The complex carbon number distribution of actual homologues can be simplified based on the thoughts of Seasonal−Trend decomposition.9 The basic trend of the distribution obeys the gamma distribution, and regional features can be reflected by a fluctuating trend as a function of the homologue carbon number. The uncertainty of the distribution is introduced using a cloud model.10 Then, the PDF can be calculated by superimposing the three functions. A proper optimization algorithm is also required for the high-performance molecular reconstruction process, and stochastic reconstruction processes based on an intelligent optimization algorithm have been adopted extensively in studies. de Oliveira11 attempted to use the genetic algorithm (GA) in the stochastic reconstruction process of petroleum Received: Revised: Accepted: Published: A
May 11, 2019 August 4, 2019 August 8, 2019 August 8, 2019 DOI: 10.1021/acs.iecr.9b02605 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
Article
Industrial & Engineering Chemistry Research fractions and obtained a final set of molecules that had properties very close to the experimental data. Chen12 applied the simulated annealing algorithm (SA) for molecular reconstruction with a three-step structure-oriented lumping (SOL) structural increments and Monte Carlo sampling, and the process was successfully applied in vacuum gas oil (VGO). Zhang and Chen13 used the least-squares method in the prediction of the naphtha pyrolysis product composition content and provided accurate results. Classic optimization methods might have inherent defects when used alone; hence, hybrid or improved algorithms have been proposed, such as hybrid GA−particle swarm optimization (PSO) described recently by our group.14 The algorithm selection is the core to determining the optimization efficiency when solving a problem, and comparisons are required to obtain a highperformance model for industrial application. In this work, we propose a novel naphtha molecular reconstruction process that first uses a self-adaptive cloud model and the hybrid GA−PSO algorithm. A novel PDF construction method inspired by Seasonal−Trend decomposition is adopted, and a cloud model that includes information about the regional gamma distribution parameters and naphtha pretreatment features is plugged into the optimization process for local refineries. Different types of intelligent optimization algorithms have been evaluated in the naphtha molecular reconstruction problem, including the GA,15 PSO,16 SA,17 and hybrid GA−PSO.14 The molecular reconstruction process with an acceptable overall performance is then compiled and applied in relevant software, such as Ethylene cracker Simulation and Optimization System (EcSOS18).
to determining a reasonable solution. Thus, suitable parameters need to be selected in the optimization process instead of directly using compound fractions. Klein19 recommended considering the parameters of the PDF as optimization variables. For the gamma distribution, the correlation between the PDF and parameters is6 f (x ;k , θ ) =
(2)
where k is the shape parameter and θ is the scale parameter of the gamma distribution, and x is the carbon number of the homologue series. Then, k and θ of different types of homologues are considered to be parameters that need to be optimized in the molecular reconstruction process. After a series of numerical adjustments of the MTHS matrix, an objective function needs to be set for convergence checking. In this process, the weighted squared relative error of naphtha properties is used as the objective function N ij X exp − X cal yz 1 min F(PDF) = ∑ μi jjjj i exp i zzzz N i=1 k Xi {
2
(3)
where Xexp denotes the experimental value of the measured i properties, Xcal i denotes the calculated value of the predicted composition properties, μi denotes the weight coefficient of each property, and N is the total number of properties used in the molecular reconstruction process. The minimum value of the objective function F can be determined by an optimization process, as shown in Figure 1, by the adjustment of the PDF.
2. METHODS 2.1. Intelligent Molecular Reconstruction Process Designed for Industry Software. Molecular reconstruction is a simulation process that converts common properties into molecular composition information. For naphtha, PIONA, true boiling point (TBP) distillation curve (converted from ASTM D86 data), average molecular weight, and hydrogen−carbon molar ratio are considered to be important properties for characterization,19 which can be set as input data in the molecular reconstruction model. Additionally, the output should be the information about the component fractions of key compounds in the MTHS matrix. Historical data collected by local refineries are used to add prior knowledge and uncertainty into the model by analyzing the previous PDFs of naphtha homologues. During the simulation process, the component fractions in the MTHS matrix are calculated after obtaining the detailed PDF of a specific sample. For example, the fraction of npentane is described as
Figure 1. Intelligent molecular reconstruction process of naphtha for local refineries.
P(series = P, Cnum = 5) = P(series = P) × P(Cnum = 5|series = P)
x k − 1 e −x / θ Γ(k)θ k
2.2. Optimization Parameter Selection and Initialization. To reduce the time consumption of optimization and eliminate some local optimal areas, parameter initialization should be executed before optimization using the input information.20 As discussed in Section 2.1, k and θ of different types of homologues are set as optimization parameters, but the initial value and searching area of the optimization process need to be determined before optimization. As was demonstrated in our previous study,14 an industrial Internet plug-in based on a support vector machine (SVM) using a radial basis function kernel can be applied to determine the
(1)
where series = P indicates that the compound belongs to the nparaffin homologue and P represents the probability of the compound appearing in the PDF function. For naphtha, approximately 30 variables need to be optimized in the MTHS matrix and several properties are applied to constrain these variables. Using these variables directly in the optimization process has many drawbacks, such as high computational complexity and unfeasibility with regard B
DOI: 10.1021/acs.iecr.9b02605 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
Article
Industrial & Engineering Chemistry Research correlations between the input properties of naphtha and the distribution parameters. The historical data are collated to provide a training dataset for the SVM model. The correlations of the SVM can be obtained using the Lagrange multiplier method and Karush−Kuhn−Tucker conditions21 y ̅ (x ) =
∑
(αi − αi*)exp( −γ xi − xj 2 ) + b
l o o 1 o o b= m ∑ o0
