Chonglin Zhong ,Yi Zheng ,Shenghu Xu ,Shaoyuan Li,*

1 Department of Automation,Shanghai Jiao Tong University,Key Laboratory of System Control and Information Processing,Ministry of Education,Shanghai 200240,China

2 Sinopec Jiujiang Branch Corporation,Jiujiang 332004,China

Keywords:Exergy Optimization of operating conditions Fractionator FCCU Exergy Cost

ABSTRACT Exergy indicates the maximal energy that can do work effectively.Different from optimization of product quality or calculation of generic energy conservation in most previous studies,the application of exergy analysis and exergy cost optimization in petrochemical industry is of great economic and environmental significance.Based on the main fractionator in Jiujiang Petrochemical Complex No.2 FCCU,an enhanced exergy cost optimization under different operating conditions by adjusting set points of temperature and valves opening degree for flow control is studied in this paper in order to reduce exergy cost and improve the quality of energy.A steadystate optimization algorithm to enhance exergy availability and an objective function comprehensively considering exergy loss are proposed.On the basis of ensuring the quality of petroleum products,the economic benefits can be improved by optimizing the controllable variables due to the fact that exergy cost is decreased.

1.Introduction

Fluidized catalytic cracking(FCC)is an indispensable process in the oil refinery which is the major supply source of fuels such as gasoline and diesel.A FCC main fractionating tower is an important unit to achieve the separation of different kinds of oil products.A FCC main fractionator is a complex industrial device with strong coupling,nonlinearity and uncertainty.The control level directly affects the distribution and quality of the products.Due to the increasing attention to energy saving and environmental protection,the optimization of the main fractionator should notonly be limited to the improvement of productyield and quality,but also focus on reducing expenditure of energy.Because comprehensive utilization of energy is related to liquid mass flow rates of the valves,the temperature of each fractionator plate as well as the heat transfer of heat exchangers,optimization strategy on operational variables of the main fractionator has large impact on reducing energy loss of the device.Therefore,accurate simulation and reasonable optimization on the main fractionator is one of effective measures to reduce the catalytic cracking unit energy consumption.In order to realize energy saving and consumption reduction of FCCU,many domestic and foreign scholars have done a lot of researches.Nevertheless,most of them focus on technological process optimization,transformation of device or improvement of reaction regeneration technology[1–4].There are relatively few studies on the operational variables optimization and control of the main fractionator.

The concept of exergy derived from the second law of thermodynamics is proposed by Rant in 1956[5].Based on the analysis of exergy,an approach to reduce energy consumption and save exergy maximally can be obtained.The physical exergy of flow under a certain stable operating condition is expressed as:

Symbols H,S and H0,S0are denoted as the enthalpy and entropy of flow in current system state and given environment severally.The research has been widely used in energy saving research on energy intensive chemical process.Exergy analysis is based on the second law of thermodynamics,which is a thermodynamic research method on the rational utilization of energy as well as the improvement of exergy utilization rate.Through calculating exergy consumption of the whole process,the method to reduce the amount of exergy loss caused by irreversible process can be revealed for formulating corresponding energy-saving measures.So far,exergy analysis method has been successfully applied in the heat exchanger networks[6],diabatic distillations[7]and many other fields,but rarely in the dynamic optimization in field of FCC main fractionator.

In view of above considerations,it becomes clear that it is of great economic and environmental significance to calculate as well as to optimize the exergy cost of FCCU main fractionator.Additionally,diverse composition and flow rates of raw materials transported into the main fractionator correspond to different operating conditions.When the operating conditions get changed,the set points of controllable variables should be altered accordingly to achieve the optimal control effect under current operating condition.From the point of view of reducing loss of exergy,the enhanced exergy cost optimization analysis of the main fractionating tower in Jiujiang Petrochemical Complex No.2 catalytic cracking reactor under various operating conditions was carried out in this paper.The rest of the paper is organized as follows.In Section 2,the reaction mechanism and equation derivation of FCC main fractionating tower are introduced,and then a non-linear mathematic model of the fractionator can be achieved.In Section 3,the purpose of exergy optimization,exergy equations and exergy balance analysis method based on the main fractionating tower in Jiujiang Petrochemical Complex No.2 catalytic cracking reactor will be demonstrated.An optimization objective function and an exergy cost optimization algorithm of operating conditions are also proposed for the device.In Section 4,the optimization strategy to reduce the exergy cost is applied in the simulation.The simulation results verify the rationality of the optimization algorithm.Section 5 concludes the whole paper.

2.The Main Fractionator in FCCU

Distillation process has an extremely wide range of applications in the production of petroleum and chemical industry.Distillation makes use of components' different volatility degrees to extract products from mixture with higher purity by separation of several components.The yield of light oil obtained from the main fractionator determines the load of absorption stabilization system downstream.In addition,the main fractionator provides heat source for absorption stabilization system and other devices by heat recovery.Therefore,the reasonable operation of the main fractionator plays an important role in the stable production of FCCU.Under circumstance of the reaction regeneration system feeding's and the reaction depth's being stable,the main fractionator has become a core device for regulating the side-draw light oil production.According to the market information obtained,in the premise of stable operation of the device,the operation parameter optimization of a main fractionator can maximize the market needed light oil production,reduce the energy loss caused by heat reflux and so on.

The distillation process is carried out in a fractionator column with a lot of trays.The oil and gas achieved by catalytic cracking reaction enter the reboiler from the bottom of the fractionating tower.After full heat transfer with the circulating oil slurry at the bottom of the tower,some heavy components are condensed into liquid and then flow to the bottom of the tower.Not condensed gas continues to rise and make full contact with decreasing reflux liquid on the trays.Then the heavier components in the vapor phase are condensed and the lighter components in the liquid phase are vaporized.Therefore,the content of volatile components in the gas phase of the oil will get increased due to the partial vaporization of the liquid.The content of the volatile components in the liquid phase will be improved because the partial condensation of the gas leads to the volatile components in the gas phase diffusing into the liquid phase.In this way,the gas–liquid two-phase that is in contact with each other on the same plate tends to balance.The relation between them can be explained by Raoul's law.Through multiple quality and heat exchanges,the distillation purpose can be achieved.The vapor–liquid exchange on a single tray is shown in Fig.1.

In the field of chemical system engineering,mechanism models for the process simulation tasks should have the following basic characteristics generally:determinate components,basic data unified and reliable,mass balance equations,energy balance equations,strict phase equilibrium equations,chemical reaction kinetics or chemical equilibrium calculation as well as transfer and flow calculation.The model derivation procedure of FCCU main fractionating tower including mass balance,qualitative restrain and phase equilibrium is introduced as follows.Symbol i represents the number of fractionator trays and j represents the type of components in oil.Symbol x is on behalf of mass fraction of products in liquid phase while y is on behalf of mass fraction of products in gas phase.Symbol M denotes the amount of fluid on each tray.

Fig.1.Vapor–liquid exchange on a single tray.

There are 32 trays in the main fractionator of Jiujiang Petrochemical Complex No.2 catalytic cracking reactor.In this paper,due to the fact that the tray efficiency is not 100%,the actual plates are equivalent to 13 layers of theoretical plates,in order to simplify the model and reduce the number of state variables.The fractionating tower is equipped with four cycling reflux for heat removal:the overhead recycle(2nd plate to 3rd plate),one middle cycle 74th plate to 8th plate),two middle cycle(11th plate to 12th plate)and slurry cycle at tower bottom.Due to the complex composition of petroleum and the large number of trays of the main fractionator,the model will contain thousands of differential equations ifthe component is not simplified.It will bring great difficulty to the calculation of the model,and the real-time performance of the optimal solution cannot be guaranteed.In view of this,the petroleum raw materials entering the main fractionator are simplified into four virtual components:recycle oil,slurry,naphtha and diesel oil.Naphtha is extracted from the top of the tower while diesel oil is drawn from the 6th plate.Fig.2 is part of the supervision diagram of main fractionator in Jiujiang Petrochemical Complex No.2 FCCU.The control variables selected in this paper are marked with red box.These control variables have important influence on the material and energy changes of the system.

The control variables are respectively shown below,including inputs about flow and inputs about temperature,both of which can have impact on exergy cost under operating conditions of all sorts(Table 1).

The model will be added to the optimization problem in the form of equality constraints to achieve the steady-state optimization of the FCC primary fractionation system.The main fractionating tower model can be described as follows.For the tower plates of rectifying section,mass balance equations when the main fractionator system achieves a stable state are denoted as follows.

As for the feed plates,the mass balance equations are added with raw material section:

Symbol F means mass flow rate of feed oil.Symbol zjrepresents the mass fraction of the component j in the total feed oil.

Fig.2.Main fractionator in Jiujiang Petrochemical Complex No.2 FCCU.

As for the plates where there are products being drawn,the mass balance equations are added with siding withdrawing section:

Remark 1.In previous studies of establishing mathematical models of the main fractionators,material balance equations are in the same form for all non-feed trays,including plates of rectifying section andstripping section.In this paper,the effect of circulating reflux for heat recovery on the material balance equation as well as siding withdrawing of petroleum products is also considered.For the trays which circulating reflux is drawn from and sent back to,the circulation flow part should be added to the mass balance equations,which is an improvement on mathematical modeling of the main fractionator in comparison with previous modeling methods in terms of mass balance equations.

Table 1 Control variables

When circulating reflux is drawn from the tray,mass balance equations change as shown below,where fimeans mass of circulating reflux from the i th plate.

When circulating reflux is sent back to the tray,mass balance equation is:

For the condenser on the top of the main fractionating tower,

Symbol M1denotes the liquid volume of tower top.

For the reboiler at the bottom of the main fractionating tower,

Symbol MNis the liquid volume of tower bottom.

As the sum of mass fraction of each substance is 1,the mass constraint equations are as follows

Symbol S denotes the number of virtual components in the oil entering the fractionator and N represents the amount of trays.

Calculating the relative volatility is the key to calculating the phase equilibrium.In this paper,the Moπokahob empirical correlation method is applied to petroleum fractions[8].

Parameter αj,z(i)means the relative volatility of the j th lump to the z th one on the i th plate.Symbol P is the whole system pressure(mmHg).Symbol T is the system temperature(K).Symbol Δt denotes atmospheric boiling point difference between the i th lump and the s th lump(K).

The mass fraction of gaseous oil is related to the vapor liquid phase equilibrium constants and the liquid mass fraction.The equation for the mass fraction of gaseous oils can be expressed as follows.

Remark 2.The vapor–liquid equilibrium constant of each oil component varies with the change of temperature.In addition,each column plate,which can be regarded as a small subsystem cascaded with each other and the main fractionator,which can be regarded as a large general system should be in accordance with the first law of thermodynamics,i.e.,conservation of energy.Energy is a function of enthalpy and entropy and varies as the temperature changes.However,most traditional modeling methods of the FCC main fractionator do not take into account the distribution of temperature.Most of them regard temperature as a constant.One of the highlights of this paper is the use of the first law of thermodynamics to acquire the temperature distribution of the whole tower.The equilibrium constants of the enterprise are also considered as functions of temperature,which improves the accuracy of the model.

The equation for temperature distribution using energy conservation is as follows:

Symbol hijindicates the added amount of enthalpy of the component j in the i th tray.Symbol enthajV(i)represents enthalpy of each kilogram of gaseous product j at the i th tray while symbol enthajL(i)represents enthalpy of each kilogram of liquid product j at the i th tray,both of which is determined by the temperature of the plate and physical properties of the product.

Applying aforementioned equation derivation to the main fractionating tower in Jiujiang Petrochemical Complex No.2 catalytic cracking reactor,the mathematical model of the tower can be obtained.

3.Exergy Analysis and Optimization of Operating Conditions

3.1.Purpose of exergy optimization

When people calculate the material balance and energy balance of a process or equipment in chemical production,heat balance calculation based on the first law of thermodynamics can only reflect the utilization of energy quantity,but not energy quality.Thus,it is not a comprehensive evaluation of energy utilization to only rely on the first law of thermodynamics.Compared with energy analysis from a general view,exergy analysis which can measure the effectiveness of energy is of greater significance.The maximal energy that can do work effectively is defined as exergy.Exergy is not only a measure of energy quantity but also energy quality.Exergy has the following characteristics.First,in all processes,the total amount of available and non-effective energy remains unchanged.Second,in the reversible process,exergy is conserved.However,in the irreversible process,exergy will reduce due to the conversion of exergy to non-effective energy.In order to evaluate the utilization of energy in a production process,the common method is to calculate the energy consumption of the process according to the first law of thermodynamics.It is a basic thermodynamic analysis method,but it does not fully reflect the actual use of energy.For example,when cold and hot two parts of material flow exchange heat,although the total energy conservation of the cold and hot material flow remains the same under ideal conditions,because of the heat exchange,the total work capacity of material flow decreases,resulting in the loss of exergy.Therefore,the analysis of exergy is important and necessary in industrial production.

In the past,analysis of the exergy cost of fractionating tower mostly stays at the equipment level.That is,by means of transformation of pipe networks,heat exchanger and fractionating tower device to achieve energy saving.However,the equipment level optimization is complex,long cycle and huge capital expenditure.Especially for the petrochemical refinery which has been put in to operation,it is difficult to realize the equipment level optimization of various operating conditions in real time.Optimizing and controlling the operating variables which can affect the main fractionator income,such as temperature,rate of flow and so on can realize exergy saving and improve economic efficiency with the existing pipeline unchanged.The optimal control results obtained under operating conditions can be used as reference values of the dynamic optimization in lower layer to realize the real-time optimization control of the FCC main fractionator.The upper layer,that is,the steady-state target calculation(SSTC)layer,calculates the setpoints for the lower layer(dynamic control layer).For diverse operating conditions,different control input settings can be obtained to minimize the exergy cost.

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3.2.Exergy equations

The basic equations for calculating the exergy cost are defined as follows:

Symbol cpis specific heat,Te=101.325 kPa and Te=298K.

Because the above equations are not conducive to the calculation of exergy cost in practice,they are simplified to the following form.

For the petroleum of gaseous state,approximate equation of exergy cost is:

Taking into account the specific heat will vary with temperature,it is more convenient and accurate to calculate exergy using enthalpy difference.Then(17)can be changed into:

For the petroleum of liquid state,approximate formula of exergy cost is shown below.

As can be seen from Eq.(1),the effective enthalpy of oil and gas is related to enthalpy and entropy.The enthalpy and entropy of oil are related to the temperature and the physical properties of oil itself.Petrochemical components are complex.Enthalpy and entropy values change continuously.Thus,under certain conditions,the values need to be fitted.Because the exergy cost equations fitting involves enthalpy calculation and heat capacity calculation,enthalpy and heat capacity equations should be fitted.

For the petroleum of liquid state,approximate formula of heat capacity is:

For the petroleum of gaseous state,approximate formula of heat capacity is:

where the symbol d1155..66indicates the relative density,which means the ratio of 15.6 oil density to 15.6 water density.Alternatively,approximate equation of exergy cost for the petroleum of liquid state can be expressed as:

The enthalpy approximate equation is fitted based on Lee-Kesle equation[9],similar to the heat capacity fitting equation method above.Therefore there will not be too many details about it here.Based on the physical and chemical parameters of the oil and gas components of the main fractionator in Jiujiang No.2 catalytic cracking unit,the equation for calculating the effective energy at different temperatures was obtained.

3.3.Optimization objective function and algorithm for FCC main fractionator

Combined with the operable valves and instruments of the main fractionating tower in Jiujiang Petrochemical Complex No.2 catalytic cracking reactor,the operating variables whose optimal values are needed to obtain at certain operating conditions are amount of steam rising from column bottom,mass flow rate of overhead recycle,mass flow rate of one middle cycle,mass flow rate of two middle cycle,return temperature of overhead recycle,return temperature of one middle cycle,feed temperature,naphtha withdrawal amount from the 1st tray and diesel withdrawal amount from the 6th tray.On the basis of these control variables to be optimized,designing an objective function which can reflect the exergy loss in the process of oil separation is the innovation of this paper.

It is found that the exergy balance equations,the enthalpy fitting equations and the equations of specific heat capacity are all related to temperature and pressure.The main fractionator in Jiujiang Petrochemical Complex No.2 FCCU is a vacuum tower and the change range of whole tower pressure is not large,which can be seen as a linearly increasing variable from the top to the bottom of the tower.However,the temperature changes rapidly on plates of fractionating tower.In order to optimize operating variables more accurately and reduce exergy cost,it is necessary to estimate the temperature of each tray first.According to the first law of thermodynamics,energy is conserved.The enthalpy balance equation can be used to estimate the temperature of each tray of main fractionator.

After calculating the temperature of each plate,the exergy can be calculated accordingly.Under the constraint of each petroleum product yield of main fractionator,the optimization problem function for steady-state optimization can be set as Eq.(23).

In order to simplify the calculation,the exergy cost can be summed by calculating the exergy difference of the in flows flowing into and those flowing out of the large-scale system instead of accumulating the cumulative efficiencies.In other words,for a large system with multiple subsystems,it is not necessary to separately calculate the exergy cost of each small subsystem,but can only focus on the exergy flow in and out of the overall system,thus simplifying the analysis and calculation.For the product quality and other yield indicators,the desired products to be drawn out of the tray should meet product quality requirements.The boundary conditions of each product are used to regulate the concentration of the oil and gas components,that is,critical operation.The optimization objective function of the optimization problem is shown as follows.Meanwhile,the constraint Eqs.(2)–(13)should be satisfied in order to guarantee the steady state FCC main fractionator model.

Symbol E denotes exergy.This optimization objective function takes the energy loss under certain operating conditions in FCCU main fractionator into consideration.

Optimization objective function f(E)is a function to calculate exergy cost.The exergy cost of the main fractionator includes three parts:the exergy cost between the raw materials and the products of the fractionating tower Efuel,in?Efuel,out,the exergy cost caused by the circulating reflux heat extraction ΔEcycleand the exergy cost due to stripping stream produced by the tower bottom reboiler as well as cooling of gaseous naphtha by the condenser at the top of the tower|ΔEcondenser|+|ΔEreboiler|.The exergy cost caused by the circulating reflux heat extraction ΔEcycleconsists of three parts,representing the exergy loss of overhead recycle,one middle cycle and two middle cycle.The exergy cost of oil and gas reacting in the main fractionator is equivalent to the sum of energy loss on each tower plat.Furthermore,the exergy coston each layer of main fractionating tower can be expressed as the sum of the exergy of each component flowing into the column plate minus the sum of the exergy of the components flowing out of the column plate.However,in order to simplify the calculation,the exergy loss can be calculated by focusing on loss of exergy of the material entering and withdrawing from the main fractionator,instead of accumulation plate by plate.

As for the product yield performance,the concentration of the desired product on the plate from which the product is drawn should satisfy product quality requirements.The boundary conditions of each product are used to restrain the quality of this component.

With the performance index function proposed in this paperas(23),we can put emphasis on the optimization of exergy cost of different operating conditions while ensure products quality is met.Significant improvements have been made with respect to only considering quality and ignoring exergy in many previous studies.

A flow diagram of the exergy cost optimization algorithm under operating conditions in main fractionator of FCCU proposed in this paper is demonstrated in Fig.3 as follows.

Fig.3.A flow diagram of the exergy cost optimization algorithm.

4.Simulation and Analysis of Exergy Cost Optimization

According to feed temperature of the main fractionating tower in Jiujiang Petrochemical Complex No.2 catalytic cracking reactor as well as the energy conservation of each plate,the temperature of each plate can be estimated based on the law of conservation theory.Fig.4 demonstrates the temperature of each tray as follows.

Fig.4.Temperature of each tray.

On the basis of actual working condition of the main fractionator in Jiujiang Petrochemical Complex No.2 catalytic cracking reactor,two different operating conditions are used for simulation.The parameters of the two conditions are shown in the table below(Table 2).

Table 2 Parameters of Two Simulation Conditions

Exergy cost of corresponding operating condition is measured in objective function via fmincon function of MATLAB simulation software.Combined with the actual operating conditions of Jiujiang petrochemical,the upper and lower bounds of control variables are set as follows.

The solution algorithm mentioned in Fig.3 can be used to find the minimum value of the objective function,which is the minimum of exergy cost.The optimal steady-state mass fraction distribution of each component under certain operating condition in the main fractionating tower is demonstrated in Fig.5.A desired separation can be achieved for each oil component.

Fig.5.Steady state concentration curve(mass fraction).

The optimal control variables and objective function values obtained are shown in Table 3.

Table 3 Control variables and objective function values

The minimum value of the objective function under condition A is 1.7771 × 108kJ·h?1and that under condition B is 2.4557 ×108kJ·h?1.In view of the existing rectifying operating conditions of the main fractionator in Jiujiang Petrochemical Complex No.2 FCCU,exergy balance calculation is carried out.It can be seen that the exergy cost is1.7791 × 108kJ·h?1for condition A and2.4580 × 108kJ·h?1for condition B under original working condition without optimization when control valuable set is shown below.

For working condition A the exergy costis reduced by 2×105kJ·h?1and for working condition B the exergy cost is reduced by 2.3×105kJ·h?1.Therefore,after the exergy cost optimization of varied operating conditions in the main fractionator system,the exergy cost is reduced accordingly.

Table 3 shows that the exergy loss due to heat exchange of the condenser and reboiler accounts for the largest proportion.On the premise that the purity of the product meets the requirements,the amount of stripping steam from the tower bottom should be minimized.From the point of view of energy saving,it is also necessary to increase the heat transfer of the one middle part with high temperature.Meanwhile,under the condition of ensuring the quality of the products of fractionator,the reflux return temperature can be properly increased to save exergy.However,when other devices in the FCCU are taken into account together with the main fractionating tower,distributed optimization calculation will be adopted and different results will be obtained.Furthermore,according to the structure and composition of the main fractionator in FCC,the operating variables should be adjusted.The optimal values of the control variables under different operating conditions should be optimized,which is the result of enhanced exergy cost optimization.

Furthermore,when operating conditions switch frequently,the enhanced exergy cost optimization strategy proposed in this paper can track the working conditions and provide corresponding control scheme.In the following simulation,10 different operating conditions are provided.Fig.6 reveals the mass fraction of products,which is naphtha at layer 1st,diesel at layer 6th,recycle oil at layer 13th and slurry at layer 13th when the system of the current operating condition is stable.The control variables and objective function values can be obtained correspondingly.Fig.7 is a typical example of optimized varying control input u6under different operating conditions.Table 4 shows the exergy cost under different operating conditions.When operation conditions get changed continually,the in put variables optimized vary correspondingly,to ensure the optimization of objective function and minimize energy cost.Thanks to the enhanced exergy cost optimization of operating conditions 1 to 10 during the simulation time domain,exergy cost is reduced from 1.9213×109kJ without optimization to 1.9087×109kJ,as can be concluded from Table 4.

Fig.6.Mass fraction at steady-state of varied operating conditions.

Fig.7.Return temperature of one middle cycle of 10 operating conditions.

Table 4 Exergy cost objective function values of operating conditions

5.Conclusions

In this paper,by means of equation derivation,the mechanism model of main fractionator in Jiujiang Petrochemical Complex No.2 FCCU is built.The concept of exergy and exergy balance analysis method are demonstrated combined with the established nonlinear model.By using enthalpy balance,the whole tower temperatures are estimated,preparing for the following energy calculation effectively.Because the value of oil exergy varies with temperature and pressure,the exergy cost equations are fitted.For the sake of reducing available exergy loss and ensuring product quality,a new enhanced exergy cost optimization algorithm of operating conditions based on exergy analysis is proposed and simulated.The simulation results are in agreement with the actual operating conditions of Jiujiang petrochemical plant,confirming the correctness of the enhanced exergy cost optimization.It is of great economic and environmental significance to optimize the exergy at the control aspect.