2.1. Polymer membrane activated carbon desulfurization and denitrification sorbents

Two main methods for diesel desulfurization are non-hydrodesulfurization (non-HDS) and hydrodesulfurization (HDS). As a non-HDS method, adsorptive desulfurization has the advantages of being low cost, easy to operate and environmentally friendly as well as not reducing the cetane number of diesel fuel, among others.

Also, there are two main methods for diesel denitrification: non-hydrodenitrogenation (non-HDN) and hydrodenitrogenation (HDN). As a non-HDN method, adsorptive denitrogenation has the advantages of being low cost and the simplicity of equipment and operation; however, the capacity of the adsorbent is limited.

In non-HDS and non-HDN, spherical activated carbons are often used as adsorbents. In this study, we mainly improve the selectivity of sulfur compounds and nitrogen compounds under the premise of no changing the activated carbon adsorption sulfur capacity and nitrogen capacity. For this purpose, the surface of activated carbon is coated with a layer of highly selective polymer membrane materials. The diffusion behavior, dynamic selective adsorption and adsorption capacity of DBT and QL are researched in three different polymer membrane systems (PVA, PVC, and PMA). In order to obtain the optimizing desulfurization and denitrification properties, coated active carbon are evaluated by NN-PR model. Meanwhile, the MD method and the adsorption experimental method are discussed and compared.

2.2. Preparation of simulated diesel

Petroleum fractions mainly contain DBT and substituted derivatives under a temperature higher than 300 °C. In this study, DBT was selected as a model diesel sulfur compound component. QL is a toxic, biodegradable organic nitrogen compound and it was selected as nitrogen compound in diesel components. N-octane was selected as the main solvent of the model diesel. In order to make a comparison and take verification tests, two types of model diesel (single-component and two-component) were prepared.

2.3. Single-component and double-component adsorption experimental data

The equilibrium adsorption experiment data including two important parameters of adsorption rate constant and adsorption capacity are shown in Table 1.

3.1. Pattern recognition

In this study, screening technology for desulfurization agent and denitrification agent are based on the intelligent pattern recognition theory. Pattern recognition establishes the perception formed from experience and analyzes the data accumulated by a measurement system. It is a useful method to extract information from data (^{Nianyi, Wencong, Ruiliang, Chonghe, & Pei, 1999}).

Feature selection and extraction are two keys for pattern recognition. In general, the more different types of candidate features we obtain, the better the recognition results should be. Nevertheless, it is difficult to distinguish high dimension features because of the dimension disasters. In this study, the neural network feature extraction method is used for feature selection and extraction, which is a nonlinear filtering characteristic algorithm by calculating contribution ratio of different independent variables forecasting ability.

The framework of the neural network for the pattern recognition model is shown in Fig. 1.

Fig. 1 The framework of neural network for pattern recognition model. 

3.2. Artificial neural networks

The first artificial neural network was developed by McCulloch and coworkers in the early 1940s (^{McCulloch & Pitt, 1943}). ANN is classified as a non-symbolic artificial intelligence technique, which simulates the human brain and its underlying process is based on graphs and algorithms (^{Papadopoulos, Beligiannis, & Hela, 2011}). In the last few decades, some important researches have been reported in the field of ANNs and their efficiency has been proven in various applications in the fields of engineering. The learning modes of neural networks from the input samples make them very suitable for solving pattern recognition problems, which are one of the successful application areas of neural networks (^{Christopher, 1995}).

The most widely used training algorithm of NNs is the back-propagation (BP) algorithm, which is a gradient-based method. The basic structure of BPNN is shown in Fig. 2.

Fig. 2 Basic structure of BPNN. 

Usually, BPNN is represented by the following model:

(1)

where pot (l ) (l = 1, 2, ..., L ) is the node number of each layer. Ê_j is the estimated value of the design objective. The hidden layer error is determined by the back propagating algorithm. The BP algorithm is repeated several times until obtaining the reasonable residual error. The steps of the optimization procedure and the learning algorithm are detailed in ^{Perlovsky (2001)}.

3.3. Neural network for pattern recognition

In the neural network for pattern recognition, firstly, known samples are used to train the neural network, which can give different outputs corresponding to different kinds of inputs. Then, the unknown samples can be distinguished by the trained NN-PR model. The flow chart of the neural network for pattern recognition is shown in Fig. 3.

Fig. 3 Flow chart of neural network for pattern recognition. 

The roles of the main parts of NN-PR are as follows:

4.1. Optimizing the neural network for pattern recognition

Any continuous function can be approximated with a single hidden layer BP network. In generally, any mapping mode (from M -dimensional to N -dimensional) can be recognized by a three-layer BP neural network based on Kolmogorov theory (^{Hanafizadeh, Zavasan, & Khaki, 2010}; ^{Kolmogorov, 1963}). In this network, the input layer includes two adsorption factors: adsorption rate constant and adsorption capacity, and the output layer is the adsorption comprehensive performance mode. NN is highly sensitive to the number of hidden layer neurons. There are no theoretical formulas used to compute the number of hidden cells, and it is often selected by experiential Eq. (2):

(2)

where n is the number of hidden nodes. m and k are the numbers of input nodes and output nodes, respectively; a is a constant between 1 and 10. According to experience, the more hidden nodes in the NN, the better prediction result will be obtained. However, the NN configuration will be more complictated. The number of hidden nodes should be no less than the total number of input and output nodes. According to Eq. (2), the number of hidden nodes is designated as 4.

The optimizing NN-PR model is implemented by using Matlab programming software. The basic parameters are shown in Table 2. The parameters are debugged to improve the accuracy and speed of convergence.

Fig. 4 is the network training error curve. The network has reached accuracy after 170 times which is set as the number of epochs.

Fig. 4 Network training error curve. 

4.2. Denoting two grades

To distinguish different modes based on pattern recognition, a set of input sample data can be mapped to an output vector. By using the adsorption rate constant and adsorption capacity as two criterions (superior class and inferior class) and the comparison standards, we can get the following classifications: For DBT, the data range DBT q > 575 μmol/g and K > 0.0636 h (μmol/g)⁻¹ are superior class points (the output values are set as 1) and denoted as grade I; others are inferior class points (the output values are set as 0) and denoted as grade II. For QL, the data range q > 320 μmol/g and K > 0.0462 h (μmol/g)⁻¹ are superior class points, and denoted as grade I; others are inferior class points and denoted as grade II. There are eight types of AC_Styrene (the adsorption performance) date are distinguished for different modes, and each AC_Styrene data set include 10 for training and 5 for testing. There are 80 training data and 40 testing data are used for the implementation of the NN (shown as Table 3). For any unknown samples, the grade can be recognized correctly according to what kind of point is close to.

4.3. Recognized results

The recognized results of activated carbon coating materials adsorption comprehensive performance are shown in Table 3.

From Table 3, DBT adsorbability of activated carbon coated with PVC is higher than the original activated carbon. For example, sample No. 1, DBT adsorbability increased from grade II (q is 560 μmol/g and K is 0.0527 h (μmol/g)⁻¹) to grade I (q is 582 μmol/g and K is 0.0639 h (μmol/g)⁻¹), while the adsorption rate of QL decreased from graded I to grade II (q is 555 μmol/g and K is 0.0438 h (μmol/g)⁻¹). The main reason for their changes is that PVC coated on the surface of the spherical activated carbon is good for the diffusion of DBT, while bad for the diffusion of QL, which may be related to the interaction of functional groups, which indicates that PVC film has a better permeability to DBT.

Also, it can be seen from Table 3 that the activated carbon coated with polyvinyl alcohol could increase the adsorption rate of QL and decrease the adsorption rate of DBT, which shows that PVA film has a better permeability to QL.

5.1. Molecular dynamic simulations

Molecular dynamics simulations (^{Frenkel & Smit, 2001}) are widely used for computer simulations of large and complex calculating systems. The basic principle of MD simulation is to set up an appropriate system based on Newton's motion laws, statistical thermodynamics and statistical physics principle, and to calculate the macroscopic physical properties through the trajectory of the system.

In the past 20 years, with the rapid development of the molecular simulation technique, the technique has become an important tool to study the molecular structure of the polymer membrane material and the mechanism of adsorption and diffusion in the polymer membrane. The development of molecular dynamics simulations provided huge impetus for researching the microscopic mechanisms for permeation of molecules dissolved in the polymer film. MD would explain the way in which a variety of factors affected the separation performance on the molecular scale; whilst the molecular simulation technique can provide a feasibility study, process optimization and material properties screening prediction before the experiment (^{Tamai, Tanaka, & Nakanishi, 1995}).

In this study, molecular dynamics simulation was used to investigate the diffusion behavior of the model diesel components in three different membranes. In accordance with the real diesel environment, DBT and QL were selected as representatives of sulfur and nitrogen compounds. The diffusion coefficients of DBT and QL in three different membranes were calculated by Einstein equation. Then, in order to get and verify the most favorable diesel desulfurization and denitrification membrane systems, a comparison of the diffusion selectivity of the three different molecular membranes was performed.

5.2. Results of the molecular dynamics simulations

In the MD method, diffusion coefficients are used to study diffusional adsorption performance of DBT and QL in different PVA, PVC and PMA membrane systems. Mean square displacement (MSD) curves obtained by the MD method are used to analyze and calculate the diffusion coefficients.

Diffusion of molecules in the polymer film system can be calculated by MSD as shown in Eq. (3)

(3)

where r _i (t ) is the position coordinate of the molecule i at t point, and r _i (0) is the initial position coordinate of the molecule i .

The relationship between the diffusion coefficient (D ) and MSD can be expressed as Eq. (4) which is the exponential form of Einstein equation (^{Konduri & Nair, 2007}):

(4)

where D is the diffusion coefficient; d is set as 3 and is the dimension of molecules' random motion; α is the exponent; and t is time.

The results for the diffusion coefficients are shown in Table 4. To provide scientifical theoretical support, the single-component system, which DBT and QL exist alone, and the double-component system, which DBT and QL exist together, are studied together.

According to Table 4, when the DBT and QL exist alone, the DBT diffusion coefficients are lower than the QL diffusion coefficients in the PVA and PMA membrane systems; which means that the relative concentration of the DBT is higher than that of QL. They are the same as in the double-component PVA and PMA membrane systems. While in the PVC membrane system, the DBT diffusion coefficients are higher than the QL's both in the PVC single-component or in the PVC double-component. Therefore, it can be concluded that the PVC is advantageous for removing sulfur compounds in diesel fuel, which is the same as the result of the NN-PR method.

Also, according to the diffusion coefficient of the molecules in Table 4, it can be seen that the QL diffusion coefficients are lower than the DBT diffusion coefficients in the PVC membrane systems when the DBT, or QL, exists alone; which are the same as in the double-component PVC membrane systems, while in the PVA and PMA membrane systems, the QL diffusion coefficients are higher than those of the DBTs, whether they are in single-component or in double-component solutions; thus, it can be concluded that the PVA and PMA membranes are advantageous for removing nitrogenous compounds in diesel fuel. But, which one is better than that of the PVA or PMA membrane?; further comparisons of the diffusion selectivity of the different membranes are needed.

In order to get the optimal denitrification membrane, a comparative study of the diffusion selectivity in the double-component solute systems of different molecular diffusion membranes is done by the MD method. The results of two types of diffusion selectivity are shown in Fig. 5, one is the QL-DBT selectivity D _DBT /D _QL , and the other one is the DBT-QL selectivity D _QL /D _DBT .

Fig. 5 The diffusion selectivity of polymer membranes in the double-component solute systems. 

From Fig. 5, it can be seen that D _DBT /D _QL is greater than 1 in the PVC; while in PVA and PMA, D _DBT /D _QL is less than 1. Also, it can be seen that D _QL /D _DBT is greater than 1 in PVA and PMA membrane systems, especially for the PVA membrane, while for the PVC membrane, D _QL /D _DBT is less than 1. The results suggest that PVA is advantageous for diesel denitrifying, and hence it was selected as the optimal denitrification membrane. Again, it was verified that the PVC film was advantageous for diesel desulfurizing, which fully agrees with the result of the NN-PR method.

6.1. Breakthrough curves coated with PVC

Dynamic adsorption breakthrough curves of DBT and QL of styrene-based activated carbon spheres coated with PVC are shown in Fig. 6. It can be seen that the adsorption volumes of DBT and QL decreased at the penetrating point after being coated with PVC. DBT is decreased from 77.0 g-MDF/gA to 58.0 g-MDF/gA, and QL is decreased from 38.0 g-MDF/gA to 7.0 g-MDF/gA. Nevertheless, the penetrating time (from the penetrating point to the saturation point) of QL is longer than that of DBT, which indicates that the adsorption rate of DBT will increase, while the adsorption rate of QL will decrease; hence, the PVC membrane can enhance the proliferation of DBT, which also shows that PVC is fit for removing sulfur compounds in diesel fuel.

Fig. 6 Dynamic adsorption breakthrough curves of DBT and QL of styrene-based activated carbon spheres coated with PVC. 

6.2. Dynamic adsorption breakthrough curves coated with PVA

Dynamic adsorption breakthrough curves of DBT and QL of styrene-based activated carbon spheres coated with PVA are shown in Fig. 7. It can be seen that adsorption volumes of DBT and QL have been decreased drastically at the penetrating point after being coated with PVA. Also, the penetrating time of DBT is longer than that of QL, which indicates that the QL adsorption rate is slightly increased, while the DBT adsorption rate is significantly decreased. It was verified that PVA is fit for removing nitrification compounds in diesel fuel.

Fig. 7 Dynamic adsorption breakthrough curves of DBT and QL of styrene-based activated carbon spheres coated with PVA.