Real-Time Optimization Model for Continuous Reforming Regenerator

Jiang Shubao; Jiang Hongbo; Li Zhenming; Tian Jianhui

(1.Research Institute of Petroleum Processing, East China University of Science and Technology, Shanghai 200237;2.International Joint Research Center of Green Energy Chemical Engineering,East China University of Science and Technology, Shanghai 200237;3.Petro-Cyber Works Information Technology Co., Ltd., Beijing 100007)

Abstract: An approach for the simulation and optimization of continuous catalyst‐regenerative process of reforming is proposed in this paper.Compared to traditional method such as finite difference method, the orthogonal collocation method is less time‐consuming and more accurate, which can meet the requirement of real‐time optimization (RTO).In this paper,the equation‐oriented method combined with the orthogonal collocation method and the finite difference method is adopted to build the RTO model for catalytic reforming regenerator.The orthogonal collocation method was adopted to discretize the differential equations and sequential quadratic programming (SQP) algorithm was used to solve the algebraic equations.The rate constants, active energy and reaction order were estimated, with the sum of relative errors between actual value and simulated value serving as optimization objective function.The model can quickly predict the fields of component concentration, temperature and pressure inside the regenerator under different conditions, as well as the real‐time optimized conditions for industrial reforming regenerator.

Key words: catalytic reforming regenerator; kinetics; model; orthogonal collocation method; real‐time optimization

1 Introduction

Catalytic reforming is one of the main processes in refinery, which transforms naphtha into aromatics‐rich reformate oil and produces hydrogen as a by‐product[1].According to the modes of reforming catalyst regeneration, the catalytic reforming can be divided into three types: the semi‐regenerative reforming (SR), the cyclic regenerative reforming (CR), and the continuous catalyst regenerative reforming (CCR)[2].In contrast to the semi‐regenerative and cyclic regenerative reforming,CCR could recover the activity of reforming catalyst continuously, which has been extensively developed in the last few decades.In the reforming reactors using this technology, the catalyst is prone to deactivation,which would reduce the activity of catalyst and affect the selectivity of products.There are many factors causing the deactivation of catalyst, which can be divided into six types[3].Unlike other inactivation factors, coke inactivation on the catalyst is reversible and the catalyst could be reactivated by burning the coke deposited, which is necessary for the continuous operation of catalytic reforming.The whole regeneration process is carried out in an environment with less oxygen.The coke combustion is an exothermic reaction, and its reaction heat causes the rapid rising of catalyst temperature[4].

There are two stages in the regenerator of counter‐current catalytic reforming process which was developed by the Sinopec Corp.in China[5‐6].The main combustion reactions take place in the first stage of regenerator,leading to formation of H2O and CO2as the main products in the gas phase, while a small amount of residual coke is burned off in the second stage of regenerator.The main reactions occurring in the regenerator are as follows[3].

The catalyst regeneration requires appropriate reaction conditions, so as to prevent the deterioration of catalystsdue to too high temperature and to extend the life of catalysts.In the last few decades, a lot of experiments were carried out to study the deactivation and the regeneration of catalysts with respect to the properties of coke deposited on catalyst by temperature programmed oxidation or other methods[7‐11], and there are some reports about the models for catalyst regeneration process.Zhang, et al.[12]simulated the regeneration of catalysts used in propane dehydrogenation technology.With their model, the oxygen concentration and coke content along the reactor can be precisely obtained, and the heat release from the coke combustion could be reflected via a temperature field.Santamaria, et al.[13]showed that the temperature rise of regenerator could be controlled through limiting the oxygen content instead of the inlet temperature of regeneration gas.In addition,some operating parameters were studied, including the regeneration time, the regeneration gas flow rate, the oxygen concentration, and the inlet temperature of the regeneration gas[12,14‐17].

Through studying kinetic equation of coke combustion about platinum‐tin catalysts such as R‐32 and 3861, Liu,et al.[18]found that the coke is a kind of hydrocarbons with a high carbon to hydrogen ratio, and hydrogen combustion rate is much faster than carbon combustion rate during the combustion of coke.They made an assumption that the combustion rate of carbon in coke has a first‐order relationship with carbon content and an-order relationship with the partial pressure of oxygen.

in which,CCis the mass fraction of carbon in coke;kis the rate constant of carbon combustion reaction;PO2is the oxygen partial pressure, bar;nis the reaction order of oxygen partial pressure.

By studying the factors that influencing the catalyst of regeneration such as the oxygen content, the inlet temperature of the regeneration gas, and the initial coke content in catalyst, Pan, et al.[19]established a simple kinetic equation to describe the combustion of coke as follows:

Xiong, et al.[20]established a mathematical simulation package for continuous reforming coke combustion.Their kinetic equations are as follow:

where,rCis the rate of carbon combustion, kg/(kg∙min);rHis the rate of hydrogen combustion, kg/(kg∙min);k1is the rate constant of carbon combustion reaction;k2is the rate constant of hydrogen combustion reaction;HHis the mass fraction of hydrogen in coke.

At present, the refining and chemical enterprises are developing rapidly in China, in which real‐time optimization has become a new trend.Since catalytic reforming is one of the main processes in petroleum processing, it is necessary to develop real‐time optimization model of continuous reforming reactor and regenerator.The traditional sequential modular approach requires iterative solution and takes a long time, which cannot meet the requirements of real‐time optimization.Compared with sequential modular approach, the equation‐oriented method requires less time and the equations can be solved simultaneously[21‐22].In this paper, the equation‐oriented method combined with the orthogonal collocation method and the finite difference method is adopted to build the RTO model for catalytic reforming regenerator.

A regenerator of counter‐current continuous catalytic reforming unit from the Sinopec Corp.in China is selected for simulation in this paper.The catalyst for catalytic reforming is the PS‐Ⅵ platinum‐tin catalyst,which has many advantages such as low coke deposition,low hydrogen to hydrocarbon ratio, high selectivity,good activity stability, etc.[23]Referring to the established kinetic models for coke burning by some researchers, the combustion kinetic model for PS‐Ⅵ platinum‐tin catalyst regeneration was proposed and the kinetic parameters were estimated with the sum of relative errors between the actual value and the simulated value regarded as optimization objective function.Based on the obtained kinetic parameters, the fields of component concentration,pressure and temperature inside the regenerator can be predicted.

2 Simulation Details

2.1 Model expression

The specific process of two‐stage catalyst regeneration incounter‐current continuous catalytic reforming process is as follows: Regeneration area of the catalyst is the annular space between the outer screen and the central tube.Through the catalyst conveying tube the catalyst enters the first stage regenerator, in which the combustion reaction in the first stage happens, then the catalyst enters the second stage regenerator through the catalyst conveying tube to complete the combustion reaction in the second stage.High temperature regeneration gas containing a certain amount of oxygen passes the catalyst bed to burn off the coke, and then leaves the regenerator through the central tube.

The CCR regenerator is a radial direction reactor, in which the coke and regeneration gas are in contact by means of cross flow.In order to simplify the model, the reasonable assumptions were proposed as follows:

(a) The regeneration gas crosses the regenerator in radial direction without back‐mixing, and the catalyst drops by gravity in axial direction without back‐mixing[24‐25].

(b) Because the inlet temperature of catalyst is lower than that of regeneration gas, using the orthogonal collocation method to solve the whole process of regeneration will result in a certain error, the first stage of regenerator is divided into two parts, in which fifteen percent of the first stage regenerator is solved by difference method and the rest of the regenerator is solved by orthogonal collocation method.

(c) During the combustion of coke, carbon dioxide,carbon monoxide and water are formed.Because the platinum on catalyst has catalytic activity, and the carbon monoxide reacts with oxygen to form carbon dioxide quickly[24], only the final combustion products including water and carbon dioxide are considered in the model.

(d) The hydrogen combustion is supposed to be a first order reaction.

(e) According to the analysis data about the coke deposited on reforming catalyst, the atomic ratio of carbon to hydrogen in coke is 1:0.66, and the corresponding mass ratio of carbon to hydrogen is 1:0.055.

Based on the model assumptions mentioned above, the coke combustion kinetic equations are established as following:

in which,n1is the reaction order of oxygen partial pressure;m1is the reaction order of carbon content in coke;kiis the reaction rate constant, bar-n∙min-1;ki0is the pre‐exponential factor,bar-n∙min-1;Eaiis the activation energy, kJ/mol;Ris the gas constant, J/(mol∙K); andTis the reaction temperature, K.

2.2 Model equations

2.2.1 Difference equations

The top 15% of the first stage regenerator was cut into two‐stages in axial direction and four‐layers in radial direction, and each layer corresponds to the location of collection points in sequence.The eight annular beds are regarded as CSTR reactors in connection, and the constraint equations are as follows.

Material balance in axial direction:

Material balance in radial direction:

Heat balance:

Momentum balance:

where,Ci,j-1is the mass fraction of carbon at the entrance ofithannular bed in (j-1)th layer;Ci,jis the mass fraction of carbon at the outlet ofithannular bed injth layer;ρbis the bulk density of the catalyst, kg/m3;Sis the crosssectional area of the regenerator, m2;lis the height of annular bed, m;Fsis the circulation rate of catalyst, kg/min;Hi,j-1is the mass fraction of hydrogen at the entrance ofithannular bed in (j-1)th layer;Hi,jis the mass fraction of hydrogen at the outlet ofithannular bed injth layer;ri-1is the radius difference of (i-1)thannular bed, m;riis the radius difference ofithannular bed, m; Δriis the radius difference ofithannular bed, m;FO2i-1,jis the molar flow rate of oxygen at the entrance of (i-1)thannular bed injth layer, kmol/min;FO2i,jis the molar flow rate of oxygen at the outlet ofithannular bed injth layer, kmol/min;rO2is the reaction rate of oxygen, kmol/(kg∙min);FCO2i,jis the molar flow rate of carbon dioxide at the outlet ofithannular bed injth layer, kmol/min;FCO2i-1,jis the molar flow rate of carbon dioxide at the entrance of (i-1)thannular bed injth layer, kmol/min;rCO2is the reaction rate of carbon dioxide, kmol/(kg∙min);FH2Oi,jis the molar flow rate of steam at the outlet ofithannular bed injth layer, kmol/min;FH2Oi-1,jis the molar flow rate of steam at the entrance of (i-1)thannular bed injth layer, kmol/min;rH2Ois the reaction rate of steam, kmol/(kg∙min);Gsis the mass flow rate of catalyst per unit cross‐sectional area, kg/(min∙m2);Cpsis the specific heat capacity of catalyst, kJ/kg;Ti,jis the temperature at the outlet ofithannular bed injth layer, K;Tsi,j-1is the temperature of catalyst at the entrance ofithannular bed in (j-1)th layer, K;Ggis the molar flow rate of regeneration gas per unit cross‐sectional area, kmol/(min∙m2);Cpgis the specific heat capacity of regeneration gas, J/(mol∙K);Tgi-1,jis the temperature of regeneration gas at the entrance of (i-1)thannular bed injth layer, K; ΔHCis the reaction heat of carbon combustion, kJ/mol; ΔHHis the reaction heat of hydrogen combustion, kJ/mol;Pi-1,jis the pressure of regeneration gas at the entrance of (i-1)thannular bed injth layer, bar;Pi,jis the pressure of regeneration gas at the outlet ofithannular bed injth layer, bar;εis the void fraction of the bed;µis the viscosity of the regeneration gas, Pa∙s;ubis the velocity of gas across the bed, m/s;dpis the equivalent diameter of catalyst, m;ρfis the density of regeneration gas, kg/m3; andgis the constant of gravity, N/kg.

2.2.2 Differential equations

Differential equations are adopted to describe the left 85% of the first stage and the whole second stage of regenerator.Inside the catalyst bed, an infinitesimal annular body with the height ofdland the width ofdris selected to get the differential equations according to the balance of material, heat and momentum.Then the dimensionless method is used to deal with these differential equations.

Material balance:

Heat balance:

The pressure is calculated according to the Ergun formula:

where,zis the position of collocation point in axial direction;lis the height of annular bed, m;Lis the height of regenerator, m;xis the position of collocation point in radial direction;r0is the radius of outer screen, m;r4is the radius of inner screen, m;ris the radius of annular bed, m;R1is the radius difference between outer screen and inner screen, m;FO2is the molar flow rate of oxygen, kmol/min;FCO2is the molar flow rate of carbon dioxide, kmol/min;andFH2Ois the molar flow rate of steam, kmol/min.

2.3 Boundary conditions

The regenerator is a radial moving bed reactor, and the corresponding boundary conditions are as follows:

where,Gg0is the initial molar flow rate of regeneration gas per unit cross‐sectional area, kmol/(min∙m2);FO20is the initial molar flow rate of oxygen, kmol/min;Tg0is the initial temperature of regeneration gas at the entrance, K;CC0is the initial mass fraction of carbon in coke;HH0is the initial mass fraction of hydrogen in coke; andTs0is the initial temperature of catalyst, K.

2.4 The method of solution

For the top 15% of first stage in the regenerator, every annular bed is connected and internal condition of the annular bed is the same as that of the outlet according to CSTR reactors supposed, which can be described by algebraic equations based on the balance of material, heat and momentum.

For the left part of regenerator, differential equations for describing the catalyst bed were discretized into algebraic equations by orthogonal collocation method.All these algebraic equations are required as constraint conditions by the SQP method for solving the equation‐oriented models[26‐29].

The orthogonal collocation method is called the weighted residual method, and this method is founded by Lanczos[30].In the process of solving the boundary value problem, Villadsen and Stewart[31]made an important improvement in orthogonal collocation method.The orthogonal polynomials that can satisfy the boundary conditions are chosen as the trial function, and the roots of orthogonal polynomials are used as collocation points to make the lower collocation results reliable.

In this paper, to solve the regenerator model with initial value problem, we take the roots of the Legendre orthogonal polynomial as the collocation point[32], while combining the two-dimension orthogonal collocation method[33‐35].The trial solution and partial derivatives of each collocation point are as follows:

where,y(zl,xk) is the trial solution of collocation point;yx(zl,xk) is the partial derivatives along thexdirection at the collocation point;yz(zl,xk) is the partial derivatives along thezdirection at the collocation point.

The parameter matrix ofDliis shown in Table 1 andBjkis the transposed matrix ofDli, thus, the first‐order partial derivatives of certain collocation point can be calculated using the function values of corresponding collocation points in the field.

Table 1 The parameter matrix of Dli

2.5 Parameters estimation

Model parametersEc,EH,KC0,KH0,nc, andmcwere simultaneously estimated by the SQP algorithm[36]and the initial value of parameters is cited from other literature[20].The optimization objective function is the sum of the square of relative error between the actual value and the calculation value, and four sets of commercial data under different conditions were adopted to ensure the reliability of estimated parameters.

where,x(i,j),calis theith set of model calculation value ofjcomponent; andx(i,j),realis theith set of measured industrial value ofjcomponent.

The temperature of regeneration gas and catalyst,the pressure of regeneration gas, the flow rate, and concentrations of the regenerator for parameter estimation are shown in Table 2 and Table 3.The structural parameters of regenerator and parameters of catalyst areshown Table 4 and Table 5, respectively.

Table 2 Operating conditions of the first stage regeneration process

Table 3 Operating conditions of the second stage regeneration process

Table 4 Structural parameters of regenerator

Table 5 Parameters of catalyst

3 Results and Discussion

3.1 Parameters analysis

In the model, the inlet temperature of the catalyst is much lower than that of the regeneration gas, which can be seen from the actual calculation results and the data of the industrial installation.After the contact between the catalyst and the regeneration gas, the reaction system reaches the combustion temperature through heat exchange, and then the combustion reaction takes place.The objective function is minimized with the SQP method and the corresponding kinetic parameters obtained are listed in Table 6.

Table 6 Reaction kinetic parameters of coke combustion

According to the estimated kinetic parameters, the pre‐exponential factor of hydrogen combustion reaction is greater than that of carbon combustion reaction, so the reaction rate of hydrogen is faster than that of carbon.There was no significant difference of activation energy between the two reactions, but the effect of reaction temperature on coke combustion was obvious.

3.2 Model validation

As shown in Table 2 and Table 3, another seven sets of data are adopted to validate the reliability of model prediction with the estimated kinetic parameters.The validation results show that the average relative error of outlet temperature of regeneration gas is 0.8%, the average relative error of oxygen content at the first stage is 3.5%, the average relative error of oxygen content at the second stage is 5.9%, and the average relative error of residual coke is 35.2%.The average relative error of residual coke is high, because the number of significant digits of its analysis data is only one.

3.3 Model prediction

3.3.1 Fields of temperature, pressure and concentrations

By adopting the model, the fields of composition, pressure and temperature inside the regenerator can be calculated for specific conditions.

As shown in Figure 4(a), since the temperature of the catalyst is relatively low in the part of the bed near the catalyst entrance, the combustion temperature cannot be reached but the heat exchange between the catalyst and the regeneration gas takes place, so the temperature of regeneration gas decreases along the radial direction and the temperature of catalyst increases along theaxial direction.When the temperature of the catalyst rises after heat exchange, the coke reacts with oxygen,releasing a large amount of heat, and the temperature of the whole bed rises.Along the axial direction of catalyst bed, the temperature of the bed rises first because the coke deposition on the catalyst is higher at the beginning and combustion reaction rate is fast with sufficient oxygen supply.Along the bed radial direction, the temperature of regeneration gas rises because of the heat accumulation,and the highest temperature appears close to the inner screen.The regeneration of catalyst needs to strictly control the temperature field to prevent the excessively high temperature of hot spots, otherwise the structure of catalyst would be destroyed and the regenerator could be damaged.In the later period of the reaction, the reaction rate gradually slows down as the majority of coke has been burned away, and the bed temperature tends to be constant.Since the regeneration process of the catalyst mainly takes place in the first stage of the regenerator, the temperature of the second stage only rises at the beginning and then tends to be constant, which is consistent with the temperature trend of actual regenerator.

Figure 1 Diagram of the catalytic reforming regenerator

Figure 2 Diagram of eight annular beds

Figure 3 Diagram of an infinitesimal annular body

Figure 4 The temperature trend of the first and the second stage regenerator

Figure 5 The carbon trend of the first and the second stage regenerator

As shown in Figure 5(a), in the catalyst bed near the entrance, the carbon contained in the coke is almost unchanged, and the combustion of carbon in coke only takes place near the outer screen, while almost no reaction occurs near the inner screen, which is related to the temperature of the catalyst.After the rising of catalyst temperature, the carbon content decreases along the axial direction.The catalyst is exposed to a relatively low temperature of the regeneration gas near the outer screen,so a longer bed height is needed for a complete burning process.The temperature of the regeneration gas peaks near the inner screen, where oxygen is still sufficient and the reaction rate is faster, so the shorter bed height is enough for a complete burning process.As shown in Figure 5(b), the residual carbon content in coke is burned away in the second stage of regenerator.As shown in Figure 6(a), the combustion process of hydrogen in coke is similar to that of carbon, but its reaction rate is faster than that of carbon.As the mass fraction of hydrogen decreases, the reaction rate also decreases.As shown in Figure 6(b), the mass fraction of hydrogen is very low in the second stage, reflecting that hydrogen in the coke has almost been burned completely.

Figure 6 The hydrogen trend of the first and the second stage regenerator

Figure 7 The pressure trend of the first and the second stage regenerator

As shown in Figure 7(a), as the regeneration gas passes through the bed along the radial direction, the pressure of regeneration gas decreases continuously.For the whole bed, the pressure drop loss is small because of the advantage of radial reactor.As shown in Figure 7(b), the trend of pressure drop in the second stage is consistent with that in the first stage.

Figure 8 The oxygen trend of the first and the second stage regenerator

As shown in Figure 8(a), near the catalyst bed inlet, the oxygen content is almost unchanged, corresponding to the temperature and the amount of coke deposited in the catalyst.When the temperature of the catalyst rises along the radial direction of the bed, the oxygen content in the regeneration gas decreases gradually.This is because the oxygen is continuously consumed in the combustion reaction with coke, which reduces quickly in the middle of the bed.As shown in Figure 8(b), in the second stage of the regenerator, oxygen consumption mainly happens near the entrance of the second stage regenerator.With the reaction progresses, coke tends to be burned completely at the radial direction, and the oxygen content is almost constant in the lower part of the second stage.

As shown in Figure 9, in the process of regeneration,carbon and oxygen can react to produce carbon dioxide.Along the radial direction of the bed, the content of carbon dioxide increases continuously.The content of carbon dioxide at the outlet of the first stage is higher than that at the outlet of the second stage.

As shown in Figure 10, the hydrogen in coke reacts with oxygen to generate steam.Along the radial direction ofthe bed, the content of steam increases continuously.Since coke is mainly composed of carbon, the content of generated steam is much less than that of carbon dioxide.At the bottom of the regenerator in the second stage, the steam content is very low and is almost unchanged since the combustion of hydrogen happens mainly in the first stage of regenerator.

Figure 9 The carbon dioxide trend of the first and the second stage regenerator

Figure 10 The steam content trend of the first and the second stage regenerator

The coke combustion is related to the regeneration gas temperature, the pressure and the coke content in the catalyst.The effect of influencing factors on the catalyst regeneration can be predicted by the established model as shown below.

3.3.2 Influence of regeneration gas temperature

The initial conditions for regeneration are shown in the fourth set of data in Table 2 and Table 3, only the inlet temperature of regeneration gas varies (453.68‒459.68 ℃), respectively.

As shown in Figure 11, as the inlet temperature of the regeneration gas rises, the reaction rate speeds up according to the combustion kinetics, and the average outlet temperature of the regeneration gas rises in the first stage, while the oxygen content drops at the outlet of the first stage, and the content of residual coke deposited on the regenerated catalyst decreases.

3.3.3 Influence of coke mass fraction

The effect of different coke mass fraction on catalyst can be predicted at the same temperature, pressure and oxygen content, only the inlet mass fraction of coke varies (2.5%‒3.7%), respectively.

As shown in Figure 12, as the inlet mass fraction of coke rises, the reaction rate speeds up according to the combustion kinetics, and the average outlet temperature of the regeneration gas rises in the first stage, while the oxygen content drops at the outlet of the first stage, andthe content of residual coke deposited on the regenerated catalyst increases.

Figure 11 The impact of changing input temperature of the regeneration gas on outlet gas temperature,oxygen content, and mass fraction of residual coke

3.3.4 Influence of regeneration gas pressure

The effect of different regeneration gas pressure can be predicted at the same temperature, coke mass fraction and oxygen content, only the inlet of regeneration gas pressure varies (0.287‒0.347 MPa), respectively.

As shown in Figure 13, as the inlet pressure of regeneration gas increases, the reaction rate speeds up according to the combustion kinetics, and the average outlet temperature of the regeneration gas in the first stage rises, while the oxygen content drops at the outlet of the first stage, and the content of residual coke deposited on the regenerated catalyst decreases.

Figure 12 The impact of changing mass fraction of the coke on outlet gas temperature, oxygen content, and mass fraction of residual coke

Figure 13 The impact of changing pressure of the regeneration gas on outlet gas temperature, oxygen content, and mass fraction of residual coke

3.3.5 Optimization of regeneration conditions

It is very important to adopt appropriate regeneration conditions for different coke deposition on catalyst.Based on the regenerator model of continuous catalytic reforming, the inlet temperature and the oxygen content of the regeneration gas can be optimized by SQP method for different inlet coke mass fraction of catalyst.The requirement for residual coke content is less than 0.05%and a lower inlet oxygen content and temperature of regeneration gas are favored for avoiding an excessively high temperature of hot spots.The calculation time of each case is only 14 seconds, which can meet the requirement of real‐time optimization.The results are listed in Table 7.

Table 7 Optimization of oxygen content and inlet temperature of regeneration gas

Since the regeneration model is developed with the equation‐oriented method, it can be easily connected with other EO models for reactors and unit operations in the process of catalytic reforming.Combined with a 44‐lumped catalytic reforming kinetic model for real‐time optimization, which is developed by our research team, the optimization calculation for the integration of reforming reactors and regenerator could be implemented within minutes.

4 Conclusions

The continuous reforming regeneration model is established based on the process flow pattern of regenerator and reaction mechanism of combustion, and the differential equations are discretized by orthogonal collocation method and solved by the SQP method.The validation result have showed the reliability of the model prediction and it is suitable for the real‐time optimization of industrial regenerator.

Acknowledgements:This work was supported by the Science and Technology Development Project of SINOPEC, China (No.319026).