Functional Link Neural Network for Predicting Crystallization Temperature of Amm

Jin Haozhe; Gu Yong; Ren Jia; Wu Xiangyao; Quan Jianxun; Xu Linfengyi

(1. The Institute of Flow-Induced Corrosion, Zhejiang Sci-Tech Uniνersity, Hangzhou 310018;2. Faculty of Mechanical Engineering & Automation, Zhejiang Sci-Tech Uniνersity, Hangzhou 310018)

Abstract: The air cooler is an important equipment in the petroleum refining industry. Ammonium chloride (NH4Cl)deposition-induced corrosion is one of its main failure forms. In this study, the ammonium salt crystallization temperature is chosen as the key decision variable of NH4Cl deposition-induced corrosion through in-depth mechanism research and experimental analysis. The functional link neural network (FLNN) is adopted as the basic algorithm for modeling because of its advantages in dealing with non-linear problems and its fast-computational ability. A hybrid FLNN attached to a small norm is built to improve the generalization performance of the model. Then, the trained model is used to predict the NH4Cl salt crystallization temperature in the air cooler of a sour water stripper plant. Experimental results show the proposed improved FLNN algorithm can achieve better generalization performance than the PLS, the back propagation neural network, and the conventional FLNN models.

Key words: air cooler; NH4Cl salt crystallization temperature; data-driven; functional link neural network; particle swarm optimization

1 Introduction

The proportion of processed inferior crude oil with high contents of sulfur, nitrogen, and chlorine compounds has been increasing in recent years. The operating conditions are increasingly complex at the oil re fineries, resulting in the intensi fied corrosion of heat exchanger equipment in hydrogenation units, the shortened the service life of the equipment, and even dangerous accidents, such as fires and explosions[1-3]. The corrosion caused by ammonium chloride (NH4Cl) has always been a problem in the petroleum re fining facilities, especially in air coolers[4].

The crystallization temperature of NH4Cl is predicted using a data-driven method because our research group has already successfully built a pH value soft sensing model in the process of complex equipment operation[5].Upon considering the complex nonlinear correlations among in fluencing factors and the difficulty of training the back propagation neural network (BPNN), a functional link neural network (FLNN) model is applied as the core algorithm. The IFLNN-PLS, which was first proposed by He Y L, et al.[6], is an improved FLNN with a small norm of expanded weights and high input-output correlation for enhancing the generalization performance of FLNN. Li M Y, et al.[7]proposed a novel computationally efficient behavior model based on the complex-Chebyshev FLNN(CCFLNN), which is suitable for the dynamic modeling of the wireless power azimuth spectrum. Sahoo DM and Chakaverty S[8]developed a novel FLNN model to identify the structural parameters. However, FLNN is rarely used in the process industry, especially in the petrochemical industry.

In this paper, the method for prediction of the ammonium salt crystallization process is established by analyzing the process flow of the REAC system and the Aspen Plus simulation. Then, the Pearson correlation coefficient(PCC) is used to screen out 10 factors that have a high correlation degree with the crystallization temperature of an ammonium salt. Next, the combination of the improved FLNN and the particle swarm optimization(PSO) algorithm is used to predict the crystallization temperature of ammonium salt in the air cooler of a sour water stripper. The accuracy of the process prediction method and the feasibility of the data-driven method are verified on real data by comparison. The research idea and main content are shown in Figure 1.

Figure 1 Research idea and main content

2 Analysis of in fluencing factors of NH4Cl crystallization

The equipment in the hydrogenation unit is most susceptible to ammonium salt crystal corrosion. The flow diagram of the process is shown in Figure 2. In the unit,crude oil is processed in two hydrogenation reactors.After flowing out from the bottom of the reactor, the hydrogenation reaction effluent passes through three heat exchangers, enters the air cooler for cooling, and finally flows successively into the high-pressure and lowpressure separators to separate oil, gas, and water. The process flow of the acid water stripper device is described in Section 4.

Figure 2 Flow diagram of the process

During the hydrogenation process, the Cl and N contained in crude oil are transformed into HCl and NH3,respectively. During the cooling of the hydrotreating effluent, the partial pressure of HCl and NH3in the gas phase decreases continuously. WhenKp(the ammonium salt dissociation constant) decreases to the deposition value of ammonium salt and the system temperature drops to the crystallization temperature of ammonium salt, NH4Cl salt crystals will appear in the heat exchange equipment and the pipelines[9].Kpis calculated by using Equation (1).

wherePHClis the partial pressure of HCl in the gas phase andPNH3is the partial pressure of NH3in the gas phase. According to the standard curve of the NH4Cl salt crystallization temperature shown in Figure 3, the model of the multiphase flow equilibrium system can be calculated by using Aspen Plus. The intersection of the two curves is the NH4Cl salt crystallization temperature.

Figure 3 Prediction of NH4Cl salt crystallization risk

The chlorine content, the nitrogen content, and the water injection on the crystallization temperature of NH4Cl are analyzed in combination with the characteristic datasets from DCS. The correlation curve between NH4Cl crystallization andKpwithin a pressure range of 4—24 MPa and the NH4Cl standard crystallization curve are obtained as shown in Figure 4.

Figure 4 shows that at the same temperature, the greater the pressure, the larger theKp. The crystallization temperature of NH4Cl salt also increases with the system pressure. The effect of other three factors on the crystallization temperature can be calculated in the same manner. The relationships between the crystallization temperature and the system pressure change, the chlorine content, the nitrogen content, and the amount of water injection are shown in Figure 5. The working conditions of each group of experiments are provided in Table 1.

Figure 4 In fluence of pressure on the NH4Cl crystallization temperature

Figure 5 In fluence of four factors on the NH4Cl salt crystallization temperature

Table 1 Working conditions of each experiment

By taking the in fluence of pressure on the crystallization temperature of ammonium chloride as an example, Figure 5 shows that the crystallization temperature of ammonium chloride increases with the pressure increasing from 4 MPa to 24 MPa.

The results show that the pressure, the nitrogen content,and the chlorine content have considerable influence on the crystallization temperature of NH4Cl salt and are positively correlated with the crystallization temperature of NH4Cl salt. However, the effect of water injection on the crystallization temperature of NH4Cl salt is relatively small.

The main input parameters of the data-driven prediction model are determined based on the above analysis.

3 Realization of the Proposed Improved FLNN Algorithm

FLNN is a kind of feed-forward neural network proposed by Pao Y, et al.[10], and has been verified in the fields of pattern recognition and optimal control. FLNN has several enhancement nodes called functional links. The supplementary inputs are enhanced by the triangular polynomial[11], the Chebyshev[12]orthogonal polynomial,or other nonlinear functions[13]. FLNN has a single layer[14]. Therefore, the error back propagation algorithm can be used to adjust its parameters.

3.1 Architecture of the improved FLNN: FLNN with Chebyshev orthogonal polynomial basis

The structure of the FLNN without any hidden layer is shown in Figure 6.

Figure 6 Architecture of the FLNN

Its implementation can be described as follows. Given original inputX =[x1,x2,x3, …,xn], it will be expanded by the expansion function to enhance the nonlinear ability. The final output of the model can be calculated by the following equation:

whereAiandbiare generated randomly andG(·) is the activation function of the output node, in which the sigmoid function is adopted. The error between the model’s output (ŷ) and the actual output (y) is used for weights updating through a learning algorithm parametrized by the learning ratel.fi(·) is theith nonlinear function, in which, unlike the traditional FLNN,the Chebyshev orthogonal polynomial is introduced as a nonlinear function because of its excellent nonlinear approximation capacity. By combining the FLNN characteristics and the Chebyshev orthogonal polynomial,the proposed CFLNN utilizes the FLNN input pattern and the nonlinear approximation capabilities of the Chebyshev orthogonal polynomial to further improve their nonlinear processing performance. The Chebyshev recurrence relation is described as follows:

3.2 PSO-BP based parameters learning

A method combining PSO and BP-learning is proposed.The PSO algorithm is quite effective in searching for the global optimum but sometimes is inefficient to accelerate the rate of convergence and avoid getting trapped in local optimal. On the contrary, the BP-learning is a powerful algorithm for obtaining the local optimal solution but is relatively weak in searching for the global optimum.Hence, the PSO algorithm is used in the initial stage to accelerate the training rate until the fitness function value remains unchanged or its change is smaller than the prede fined tolerance value[15]. Then, the BP-learning is employed to achieve a better result that is close to the optimum.

In this study, the improved PSO algorithm[16]proposed by Panigrahi B. K. is adopted, in which an adaptive inertia weight is used.

3.3 Implementation process

The CFLNN with the PSO-BP learning algorithm is proposed in this paper. Its implementation process is summarized as follows:

Data are collected and normalized. For the sample setS,Snis derived by normalization using Equation (5). Then,the normal data setSnis divided into three parts, viz.: the training samplesStr, the validation samplesSvr, and the test samplesSte.

Use a uniform distribution to initialize the input vector(EW) in the range of [0, 1] randomly.

The Chebyshev orthogonal polynomial is selected as the expanded function to extend the input variables and the expanded input variables are obtained as follows:

whereXj=[x1,x2,…,xn] is thejth row of the sample set,nis the dimension of the input variables, andkrepresents the number of expansion functions.

The total input variables through theEWcan be calculated as follows:

The PCC betweenIand the outputs can be calculated by Equation (8):

whereĪjis the average value of thejth column inI,ȳis the average value of the output, andrjpresents the correlation between inputsIand the outputs.

Comparing all the |rj|, the larger the PCC, the greater the chance that the corresponding feature column in the relevant matrix will be selected to constitute the final input variablesIs.

Initialize a group of the connection weightWgand connect the inputs and outputs through the sigmoid activation function. The output of the network is calculated according to Equation (9)

The PSO-BP learning algorithm previously mentioned is used to find the optimal weight.

The expected output of the test data set is predicted by the model:

The root mean square error (RMSE) method is used to quantify the prediction accuracy of the test:

whereŷiis theithmodel’s predictive value andyiis theithactual output of the test data.

4 Test and Discussion

4.1 Case study

As a “refuse collection station,” the sour water stripper is one of the important units of the re finery. It is used to purify sour water delivered from other units. The flow chart of the sour water stripper plant is shown in Figure 7.In Figure 7, the inlet sour water coming from the REAC system in Figure 2 obtains heat in the heat exchanger after degassing and degreasing and then enters the top of the stripper. The corrosive gas, such as H2S, NH3, and HCl in the sour water, is stripped after being in contact with the bottom steam. Puri fied water is discharged from the tower bottom.

Figure 7 Flowchart of sour water stripper plant

4.2 Performance and analysis

The crystallization of NH4Cl is one of the main forms of corrosion in the air cooler system. In actual working conditions, the crystallization of NH4Cl is related to the following ten influencing factors as shown in the first ten columns of Table 2. The NH4Cl salt crystallization temperature is chosen as the output variable.

The PLS, BPNN, and FLNN models are used for comparison to validate the performance of our proposed algorithm (IM-CFLNN). All algorithms are executed in MATLAB. The predictive RMSEs of the four models are shown in Table 3.

Table 2 Part of the input and output data used for modeling

The RMSE of the IM-CFLNN model is smaller than that of other models, indicating that after attaching a small range of random weights, the improved FLNN algorithm can achieve more accurate predictive results.

Table 3 RMSE comparison of the performance of the four models

Figure 8 shows the errors updating process of BPNN,FLNN, and IM-CFLNN. The final convergence error of the IM-CFLNN model is much smaller than that of the BPNN and the FLNN. The FLNN and the IM-CFLNN have faster convergence rates than the BPNN. The systematic error of the BPNN model tends to be stationary in step 38, while the convergence rates of FLNN and IMCFLNN are near zero in steps 7 and 8. Therefore, rapid learning ability enables the IM-CFLNN model to predict the crystallization temperature of NH4Cl quickly.

Figure 8 Learning rates of the BPNN model, the FLNN model, and the IM-CFLNN model

The distributions of the datasets collected from the acidic water stripper device using the four models are plotted in Figure 9. The residuals for the test dataset using the four models are also shown in Figure 10.

According to Figure 9, the IM-CFLNN model performs better than other three algorithms and has better prediction ability for the fluctuation points (points 28, 42,and 61), as shown in Figure 10. The IM-CFLNN model is also superior to other models in terms of stability,and its residual value is near the baseline withot large fluctuations. The above results have revealed that the improved FLNN algorithm has a signi ficant advantage in the prediction of the NH4Cl crystallization temperature testing dataset coupled with better generalization performance.

Figure 9 Distributions of NH4Cl crystallization temperature with the PLS model, BPNN model, FLNN model, and IM-CFLNN model ( first 76 points)

Figure 10 Residuals for the crystallization temperature of NH4Cl dataset with the PLS model, BPNN model, FLNN model, and IM-CFLNN model ( first 76 points)

5 Conclusions

In this paper, an improved functional neural network algorithm model for the real-time online prediction of NH4Cl crystallization temperature in the air cooler system is proposed. First, based on the original FLNN,random weights are added to the input variables, and the extended input with a large correlation coefficient is selected to improve the generalization performance of the FLNN. Second, the factors affecting the crystallization temperature of NH4Cl are analyzed. Finally, the proposed algorithm, IM-CFLNN, is validated on real industrial data from DCS and LIMS and the Aspen simulation results. The simulation results have shown that our proposed method can obtain the best generalization performance among the four algorithms. Its maximum predictive RMSE and the mean value of 10 RMSEs are 0.1426 and 0.1245, respectively.Therefore, the IM-CFLNN method can be used as an intelligent prediction model for calculating the crystallization temperature of NH4Cl in the air cooler system.

Acknowledgements:This work is supported by the National Natural Science Foundation of China (Grant No. 51876194,U1909216), the China Petrochemical Corporation Research Project (318023-2), the Zhejiang Public Welfare Technology Research Project (LGG20F030007).