Dynamic Modeling and Economic Model Predictive Control with

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and Economic Model Predictive Control with Production Mode Switching for an Industrial Reforming Process Min Wei, Ming-Lei Yang, Feng Qian, Wenli Du, Wangli He, and Weimin Zhong Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b02610 • Publication Date (Web): 11 Jul 2017 Downloaded from http://pubs.acs.org on July 14, 2017

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Industrial & Engineering Chemistry Research

Dynamic Modeling and Economic Model Predictive Control with Production Mode Switching for an Industrial Catalytic Naphtha Reforming Process Min Wei, Minglei Yang, Feng Qian*, Wenli Du, Wangli He, Weimin Zhong

Key Laboratory of Advanced Control and Optimization for Chemical Processes, Ministry of Education, East China University of Science and Technology, Shanghai 200237, China *. Corresponding Author： E-mail address: [email protected]

Abstract Catalytic naphtha reforming is a crucial process in producing gasoline or aromatic compounds. The characteristic of two production modes give rises to different economic optimization and control objectives. In the present work, we design an economic model predictive control (EMPC) with a production mode switching strategy to cope with these problems. Firstly, a rigorous dynamic process model is established to simulate the naphtha reforming process. Then, we formulate different economic objective functions and simplify the process model for each production mode, and also enable the EMPC controller to switch the production mode automatically according to empirical equations. Three case studies are presented to test the performance of our proposed control strategy. The results show that the designed EMPC controller with production mode switching can successfully overcome the economic disturbances and improve the production profits in different

ACS Paragon Plus Environment


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production modes. In addition, it also has fast response time to drive the system to a new economic optimal operating point.

1. INTRODUCTION 1.1. Background Catalytic naphtha reforming is one of the most profits making processes in the refining industry owing to its large capacity (over one million tons/year) and high product values. In an industrial naphtha reforming unit, its economic profits are affected by many factors, such as the market conditions, the changing quality and flowrate in the naphtha feedstock, and the selection of production modes between producing high octane number oil and aromatic compounds. In this sense, the economic optimization problems herein require the model based controller to have the ability to predict the detailed components of product accurately, at the same time can cope with the varying economic objectives in different production modes. For all of these reasons, the conventional RTO/MPC control framework can no longer be applied directly. Instead, the economic model predictive control (EMPC) is applied in this study, which is a one layer approach integrating economic dynamic optimization and control, to achieve the optimal operating for an industrial naphtha reforming process. 1.2. Literature review The naphtha reforming units applying operating optimization and advanced control methods have been extensively studied over the past decades1-5. In 1997, Taskar and Riggs studied the optimization of the octane number over the catalyst life of a semi-regenerative catalytic naphtha reformer, and located the optimum inlet temperature configuration6. Stijepovic and Linke proposed an efficient


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process model, and operated the optimization based on a quasi-steady-state assumption, which is computationally more effective than the models applying a system of partial differential equations (PDEs)7. For the applications of advanced control, Li and Shah proposed an inferential control framework for the octane quality control of a reforming process, and extended a popular model-based predictive control algorithm to the control framework8. Lid and Skogestad utilized data reconciliation for the estimation of process condition, and suggested a “self-optimizing” control structure for the optimal operation9. Although a signification number of publications have appeared about the applications of optimization and control for the naphtha reforming process, to the best of our knowledge, seldom results took the economic factors into consideration. The EMPC is a feedback control technique that attempts to integrate economic dynamic optimization and control in one layer10. In recent years, as the closed-loop stability and performance under EMPC has been considered and proved for various EMPC formulations, many researches about the application of EMPC were proposed in industrial processes11~17. Huang et al. proposed two economic MPC schemes for cyclic processes, and applied the Lyapunov techniques to establish the nominal stability of the closed-loop system18. In 2012, Heidarinejad et al. proposed a Lyapunov-based centralized economic MPC (LEMPC) scheme which has two operation modes considering the different periods that EMPC driving the system. Therefore, the pre-defined Lyapunov-based controller can be taken to achieve feasibility and characterize the closed-loop stability region19. Chen et al. proposed a sequential distributed economic model predictive control design method for large-scale process networks, and applied this method to a catalytic alkylation of benzene process network, which consists of four continuously stirred tank reactors and a flash separator20. While, considering the complexity of dynamic process model, the dynamic optimization



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problem in the EMPC controller can’t be solved fast enough to control an industrial process in real time. In this sense, frameworks of hierarchical economic optimization and control have been proposed21~ 24. Sildir and Arkun developed a hierarchical control structure, including EMPC and regulatory MPC, and applied to an industrial fluid catalytic cracker (FCC) unit. In their control strategy, EMPC is utilized in the supervisory control layer, which provides economic optimal reference trajectories to regulatory control layer25. 1.3. Motivation and novelties of this work This work aims to design an EMPC controller to improve the economic performance of an industrial naphtha reforming process accounting for different production modes which switch from one to another frequently. In an industrial naphtha reforming process, the production modes (producing reformate oil for gasoline blending or aromatic compounds for downstream processes) are decided by many factors, including the operating conditions of upstream processes, the feedstock quality, the market demands and so on. The EMPC controller should have the ability to cope with different economic objectives and constraints, and the frequently switching of production modes. Considering the design of an EMPC controller, it is a necessary step to build a rigorous dynamic process model, which should be detailed enough to predict each profit related information accurately, such as the aromatic components, the octane number of reformate oil, and even the energy consumed in furnaces. On the other hand, to meet the requirements of real time control, the process model has also to be simplified to reduce the computational cost. The novel contributions of this work can be summarized as: a). A first-principle dynamic model of a continuous catalytic regeneration reforming process is


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established. b). Different model simplification strategies are proposed according to the requirements of each production modes. c). The EMPC controller with production mode switching is designed to achieve the improvement in the economic performance of an industrial naphtha reforming process. 1.4. Outline This paper is organized as follows: the development of the process dynamic model is introduced in Section 2. The next Section describes the control problem formulation and the framework of the EMPC controller. In Section 4, the EMPC controller with production mode switching is designed, including the economic objective functions and constraints, and the control flowsheet. In Section 5, we conduct three case studies contain different industrial control problems to test the control performance of the proposed method. A conventional RTO/MPC controller is also introduced to make a comparison. The paper finished with Section 6 in which a general conclusion is summarized. REACTOR 1

REACTOR 2

REACTOR 3

REACTOR 4 Recycle Gas

Naphtha

HEATER 1

HEATER 2

HEATER 3

HEATER 4 Reformate

Figure 1. Simplified flow diagram of the CCR process

2. DYNAMIC MODEL DEVELOPMENT ACS Paragon Plus Environment


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There are three naphtha reforming technics, in which the continuous catalytic regeneration reforming (CCR) is the most popular which is adopted by >95% of new refinery plants. In this work, we put emphasis on this technic. Figure 1 shows a simplified flow diagram of the CCR process. The feedstock of this unit is a blend of mainly two streams: naphtha (from crude oil distillation units), and heavy naphtha (from hydrocracking units). Then, the mixed feedstock is reformed through the reformer. Consequently, the effluent is sent to the separation unit to give aromatic products and high purity hydrogen. In the CCR process, the reformer is composed of four cascade reactors so that the heat loss can be compensated by equipping one furnace in front of each reactor. In this sense, the four reactor inlet temperatures can be regarded as the manipulated variables to control reforming reactions in the reformer. For predicting the industrial reforming productions as close as possible, we herein propose a detailed first principle CCR process dynamic model. 2.1 Reaction kinetics Considering the characteristic of two production modes in the CCR process, we herein choose our previously proposed detailed reaction network to describe the reaction kinetics shown as Figure 2. This reaction network considered the following assumptions: a) Paraffin cannot directly translate into C6 naphthene and aromatic compounds. b) The reaction of isoparaffin to C6 naphthene is neglected. c) Aromatic hydrocracking occurs only on the side chain. d) Cracking reaction among naphthenes can be neglected because rate of naphthene isomerization and dehydrocyclization is extremely fast. e) Dehydrogenation, dehydrocyclization, and isomerization are reversible reactions, while


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paraffin hydrocracking is regarded as irreversible.

Figure 2. Modified 33 lumps reaction network ( NPi donates normal-parffins with carbon number i, and IPi donates iso-parffins with carbon number i, i=[5,…,10]) 33 pseudo components, and 4 types of reaction are taken into consideration, which are dehydrogenation, dehydrocyclization, isomerization, and hydrocracking. This model has been proved to have a good performance both in predicting the yields of different aromatic compounds and the octane number. Readers can refer to 26 for more information of the proposed reaction network. 2.2 Model equations Dynamic models of reactors, furnaces are established in this work, and these units were modelled based on the gPROMS Advanced Model Library. 2.2.1

Reactor model

The dynamic equations describing the behavior of the reactors, obtained through material and energy balances under standard modeling assumptions27-32. The mass balance and heat balance provide the variation of the components and temperature along the reactors. They are both nonlinear partial differential equations in space and time given as Material balance



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∂X i ∂X − LHSV ⋅ Vcat =− i⋅ + K r ,i ⋅ X i ∂t ∂rb 2π rb ⋅ H

(1)

∆H r ,i ⋅ ri ∂T ∂T − LHSV ⋅ Vcat ) =− ⋅ + ∑( ∂t ∂rb 2π rb ⋅ H C p ,i ⋅ X i

(2)

Heat balance

Where X i is the molar flowrate of component i in the proposed 33 lumps reaction network, rb is the bed radius coordinate of reactor, T donates the temperature in reactor, LHSV is the liquid hourly space velocity which is associated with the feedstock residence time in each reactor, ri and

K r ,i are the reaction rate and reaction rate constant of component i , Vcat and H donate the catalyst loading volume and height of the catalyst bed, C p ,i and ∆H r ,i donate the gas specific heat capacity and the heat of reaction of component i , respectively. The initial and boundary conditions for eq.1 and eq.2 are given as

X i (t , 0) = X i feed , X i (0, rb ) = X i s

(3)

T (t , 0) = T feed , T (0, rb ) = T s

(4)

Where X i feed and T feed donate the molar flowrate of component i in feedstock and inlet temperature, X i s and T s donate the static values of X i and T respectively. 2.2.2

Furnaces model

As the reforming reactions are strongly endothermic, the heat loss should be compensated to the effluent before entering the next reactor. In the present work, dynamic furnace models are also established to simulate the process of temperature change and predict the energy consumption during the production. The main component in fuel gas is methane, the reaction equation is given as


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CH 4 + 2O2 → CO2 + 2 H 2O + Q

(5)

In furnaces, the heater is largely affected by the radiation both from the fuel gas and furnace walls. Moreover, there are convection sections in the furnace. These issues make the dynamic behaviors in the furnace too complicated to model. In this sense, a simplified version of dynamic furnace model is proposed as other works do, where the heat transfer efficiency of the furnace is assumed to be a constant32. 2.3 Controllers of the process In this work, all the data used in the simulation are collected from an industrial refinery plant. The control schemes are illustrated in Figure 3. The feedstock of naphtha is made up of 49wt% paraffin, 41wt% naphtene, and 10wt% aromatic. The mass flowrate is controlled at 123.0t/h with naphtha 110.0t/h, and heavy naphtha 13.0t/h. Then the feedstock is sent to the reformer with recycle hydrogen at 2.4 hydrogen-to-oil molar ratio. The reacting pressure is controlled at about 0.24MPa. For the furnaces, 520℃ is a common value of all the four reactor inlet temperatures. The temperatures are detected and controlled by manipulating the fuel gas flowrate of each furnace.

Figure 3. Controller of the CCR process



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3. ECONOMIC MODEL PREDICTIVE CONTROL Consider a state-space model of a nonlinear system x& = f ( x, u, w) , where x is the state vector, u is the manipulated input vector, w is the disturbance vector, and x& denotes the time derivative of the state. The economic optimal operating condition of the system can be defined to be a steady state optimization problem as: max l ( xs , us ) s.t. f ( xs , us , 0) = 0 g ( xs , u s ) ≤ 0

(6)

g e ( xs , u s ) ≤ 0

Where l is the economic cost function, g is the process constraints including input and state constraints, ge denotes economic constraints. xs* and u s* are considered as the unique optimal solution of eq. 6, and the system is steady state because of f ( xs , us , 0) = 0 .

Figure 4. Vertical structures for process control In an industrial process, a conventional method accounting for the economic optimization and control is the hierarchical RTO/MPC framework which is shown as Figure 4(a). In the RTO layer, a steady state economic optimization problem of eq. 6 is solved, and the calculated value xs* and u s* are sent to MPC as the set-points. Then, MPC tracks the optimal reference trajectories by implementing changes in the control inputs.


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Although the RTO/MPC control structure is a successful method, which is widely applied in industrial chemical plants. The drawbacks of this method are also obvious and discussed10. As the process model is usually of great complexity with a mount of components and reactions, RTO has to use a detailed nonlinear steady state model to guarantee the optimizing accuracy. On the other hand, in the MPC control layer, a linearized model is often applied to meet the requirement of real time control. Consequently, the different models will lead to a model mismatch which makes the optimal operating condition computed by the steady state RTO unreachable for the MPC controller. Moreover, since an industrial process is dynamic and influenced by variety of disturbances, the actual optimal operating condition will move during the period of RTO calculating the optimization problems. Thus adversely affects the control performance. For this reason, the idea of using the economic cost function directly in an MPC scheme is proposed, which is named economic MPC (EMPC). The framework of EMPC is shown is Figure 4(b). Instead of using a quadratic criterion as in the classical MPC33, 34, an economic objective function is designed in EMPC with a discrete-time model as follows: N

min

∑ l ( x% ( j ), u( j )) j =0

s.t. x% ( j + 1) = f d ( x% ( j ), u ( j )) g ( x% ( j ), u ( j )) ≤ 0

(7)

g e ( x% ( j ), u ( j ) ) ≤ 0 It can be observed that in the EMPC controller a dynamic economic optimization problem is calculated instead of a steady state one. In addition, it converts the open-loop optimization into feedback control strategy by calculating the dynamic problem and updating the system states at each sampling time. Similar to a conventional MPC, the strategy of EMPC is implemented by solving the cost function



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in a receding horizon algorithm. In one sampling period, EMPC is initialized by receiving a state measurement of the current industrial process. After solving the economic optimization of eq. 7, an optimal piecewise control trajectory is computed over prediction horizon. Then, the first control action is sent to the control actuator to be implemented over the sampling period. At the next sampling period, the optimization is repeated after estimating the new optimum operating conditions based on outputs measurements.

4. EMPC DESIGN FOR THE CCR PROCESS For the economic optimization and control of an industrial CCR process, an advanced control strategy has to solving the following problems: a) It is time consuming to calculate the first-principle dynamic model in model based controller. b) The controller should be able to cope with economic disturbances from different production purposes (two production modes). In this work, we design an EMPC controller with production mode switching, the flow diagram of which is shown as Figure 5. The design procedure is described below.

Figure 5. Flow diagram of the EMPC controller with production mode switching

4.1 Two production modes Since the reformate oil is a very important material both in gasoline and aromatic producing, there are usually two production modes in an industrial CCR unit, named as the gasoline mode and the


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aromatic mode. In the gasoline mode, reformate is regarded as a high quality component oil, because it contains aromatic compounds and iso-paraffin which have relatively high octane number. It is used to improve the octane number of the gasoline without supplying any oxygen elements additionally. In the aromatic mode, reformate will be separated into aromatic products with different carbon numbers, and then stored or sent to downstream chemical processes. In fact, the prices and market demands of the aromatics are varying with their carbon numbers. Therefore, the aim of the aromatic mode is to produce the aromatics with higher value as much as possible, such as benzene (A6) and xylene (A8). Obviously, the two production modes give rise to different economic objectives, and require varying operating conditions. Among them, higher inlet temperatures are usually adopted in the aromatic mode, which can promote the dehydrogenation reaction to produce more aromatics. On the other hand, in the gasoline mode, owing to the limitation of feedstock quality, excessively high aromatic content in reformate is unnecessary and will also lead to an extra energy consumption. Thus, the reactor inlet temperatures in this mode are relatively lower as compared with the aromatic mode. The selection of production mode can be determined by many factors, including the scheduling orders, the feedstock properties, and the market demands. Moreover, the production mode switches from one to the other in a high frequency. For all these reasons, the control of mode switching is not negligible in the design of EMPC controller.

4.2 Dynamic model simplification To design an EMPC controller for the CCR process, the computational cost is a key factor that have to be taken into account. Model simplification is an effective method to improve the efficiency



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of the EMPC controller. In this work, we propose two simplified versions of the CCR dynamic model for each production purpose, respectively. In the gasoline mode, the aim of the dynamic model is to accurately predict the octane number in the reformate oil. Therefore, we classify the aromatics with similar octane number in to a single lump, such as xylene (XY) and ethylbenzene (EB) in aromatics with carbon number 8 (C8A). In other words, these components will be replaced with one lump in the reaction network. As a result, the reaction equations will decrease without reducing the accuracy of predicting octane number. The refinery version of dynamic model is formulated as

x% ( j + 1) = f refinery ( x% ( j ), u ( j ))

(8)

ON ( j ) = g refinery ( x% ( j ), u ( j ))

(9)

[ XY , EB ] → A8

(10)

[TMB , MEB, PE ] → A9

(11)

Where, ON is the vector of octane number, and we herein use RON (research octane number) to indicate the reformate octane number. In the aromatic mode, the process puts emphasis on the benefits generated by each kind of aromatic. In this sense, simplifying the aromatic lumps in reaction network will definitely reduce the accuracy of predicting aromatic compositions. Fortunately, we find that normal-paraffin and iso-paraffin can be classified into one lump for which with the same carbon number, because the profits of paraffin are not taken into consideration in this mode. In this case, the aromatic version of dynamic model can be formulated as follows with 27 lumps


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x%( j + 1) = f aromatic ( x%( j ), u( j ))

(12)

M ( j ) = g refinery ( x% ( j ), u ( j ))

(13)

[nPn , iPn ] → Pn

(14)

Where, n indicates the carbon number, n=5,…,10. M is the vector of products mass flowrate (in ton / hr ).

4.3 The EMPC controller with production mode switching The design of an EMPC controller accounting for the characteristic of production mode switching is the key section for the economic optimization and control of the CCR process. As shown in Figure 5, EMPC firstly collects the producing information and the operating constraints such as feedstock properties, market supply and demand. Then it calculates the economic dynamic optimization problem subject to these constraints. Considering the different production modes, we define the following two economic cost functions: The gasoline mode

N

min J gasoline = ∑ ( RON ( j ) − RON sp ) 2 + W U j =0

s.t. x% ( j + 1) = f gasoline ( x% ( j ), u ( j ))

(15)

RON ( j ) = g ( x% ( j ), u ( j )) g e ( x% ( j ), u ( j )) ≤ 0 Where, the gasoline version of dynamic model f gasoline ( x%, u ) is calculated, RON ( j ) is the vector of predicted research octane number. RON sp is the constraint information values from the gasoline blending process. U is the utility cost (in $ / h ), and W is the weighted value. In the CCR process, the utility cost herein mainly comes from the energy consumption in furnaces. As a component oil in



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gasoline blending, the toxicity of benzene should be controlled. Therefore, the limit of benzene content is added in constraints

Tmin ≤ Tn ≤ Tmax

(16)

CBen,min ≤ CBen ≤ CBen,max

(17)

Where, Tn is the inlet temperature of reactor n (in o C ), n = 1,..., 4 . CBen is the benzene content in the reformate oil. The aromatic mode N

4

max J aromatic = ∑ (∑ PM i i ( j ) − Pfeed M feed ) − U j =0

i =1

s.t. x% ( j + 1) = f aromatic ( x% ( j ), u ( j )) M i ( j ) = g ( x% ( j ), u ( j ))

(18)

g e ( x% ( j ), u ( j )) ≤ 0 The aromatic version of dynamic model faromatic ( x%, u) is used here. Where, Pi is the price of product i (in $ / ton ), i = 1,..., 4 . i indicates aromatics with different carbon numbers which are listed in Table 1. M i is the mass flowrate of product i (in ton / h ), the value of which can be calculated by the dynamic model. Pfeed is the price of naphtha feedstock (in $ / ton ). M feed denotes the mass flowrate of the feed (in ton / h ). The inlet temperatures of the four cascade reactors are the manipulated variables u in EMPC controller. In this case, the inlet temperatures subject to the following constraint

Tmin ≤ Tn ≤ Tmax

(19)

Table 1. Price of aromatics No 1

product Benzene

price $793.83/ton


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2 3 4

Toluene

$703.96/ton

Xylene

$1407.90/ton

A9+

$599.12/ton

Production mode switching function A logic module is designed to realize switching the production modes automatically, and it can be programmed as

If F < Fcri or NA < NAcri Then MODE = 1; else

(20)

MODE = 2; end Where F is the feedstock flowrate, and NA is the potential aromatic content. Fcri and NAcri are the two critical values, they depend on the operating conditions of a certain CCR unit. In our case,

Fcri = 115t / h and NAcri = 40 . MODE=1 donates the EMPC controller is operated at the gasoline mode, while MODE=2 is the aromatic mode, both of which are illustrated in Figure 5. Operators can also switch the production modes manually according to the current operating conditions and market demands. As the plant model solved in the EMPC controller is a detailed dynamic CCR process model, the optimization is very time consuming. Meanwhile, the time interval for the process providing the product detailed composition as the EMPC feedback information is no less than 5 minutes. Therefore, sampling time for the EMPC layer is 5min and the predictive horizon (N) is 2. With these considerations, plant dynamics allow enough time to track the temperature trajectories, and the need of feedback control is satisfied. Either eq. 15 or eq. 18 is solved at each sampling time to deliver the set points of the inlet temperatures of four reactors to the MPC layer.

4.4 Regulatory MPC



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In the MPC layer, the optimal temperature trajectories from the EMPC are tracked by manipulating the fuel gas flowrate in each furnace. The optimization objective for MPC is given as M

4

min J MPC = ∑ (∑ Tn − Tnsp j =0

n =1

4 Qc

+ ∑ ∆Fn

Rc

)

n =1

s.t. x% ( j + 1) = f furnace ( x% ( j ), Fn )

(21)

Fn ,min ≤ Fn ≤ Fn ,max ∆Fn ,min ≤ ∆Fn ≤ ∆Fn ,max Tn ,min ≤ Tn ≤ Tn ,max

Where Fn is the fuel gas flowrate of furnace n (n = 1,..., 4) , which is the manipulated variables of the MPC controller. ∆ Fn donates the rate of change in fuel gas flowrate at time k. Constraints include total and rate on the manipulated variables and the four reactor inlet temperatures. As MPC is used to overcome the fast disturbances, a rigorous nonlinear dynamic model can’t satisfy the computational efficiency in this layer. In this sense, a linearized dynamic furnace model is calculated in the MPC controller. Furthermore, the control frequency of MPC choice 30 seconds and can filter the noisy data at each control action. As a result, the predictive horizon and control horizon are chosen as P=20 and M=10, respectively.

4.5 Implementation Generally, the implementation of the proposed EMPC controller can be summarized as follow: a) At tk , EMPC collects the economic information and system state xk , and checks the production mode. b) For t ∈ [tk , tk + N ) , The EMPC controller computes the economic cost function under the current production mode, and provides the inlet temperatures of the four cascade reactors as the set points to the MPC layer.


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c) From t k to tk + t ' (one EMPC sampling time), the MPC layer tracks the optimal temperature trajectory by manipulating the fuel gas flowrate of four furnaces. d) Go back to step a, and tk = tk + t ' .

5 CASE STUDY AND DISCUSSION To test the control performance of the proposed EMPC controller in an industrial CCR unit, we herein present 3 case studies (CS) with different economic disturbances. Model parameters are calibrated based on the industrial data26. In addition, to simulate the fast disturbances in the manipulated variables of the regulatory MPC layer, a new random number with zero mean is generated and introduced over each MPC sampling period. The conventional RTO/MPC control structure is also involved in the 3 case studies, the structure of which is shown in Figure 4(a). In RTO/MPC, a 33 lump steady state CCR process model is applied in the RTO layer, and the sampling time is 1 hour, and a 5 lump dynamic model is used in the MPC controller to track the RTO. In the regulatory control layer, we use PID to control the four furnaces. The comparison results between EMPC and RTO/MPC are also discussed in the following case studies.

5.1 CS 1: disturbances in product prices In CS 1, we introduce the step disturbances in aromatic prices to model the market effect when the process is being operated in aromatic mode. For this purpose, at t=1 hour, we increase the prices of benzene, toluene, and xylene by 5%, and reduce the price of heavy aromatic (A9+) by 15%, respectively. The detailed product prices are listed in Table 2. Table 2. Disturbances in product prices No

product

Price



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

0-1 hour

1-3 hour

1

Benzene

$793.83/ton

$833.52/ton

2

Toluene

$703.96/ton

$739.15/ton

3

Xylene

$1407.90/ton

$1478.29/ton

4

A9+

$599.12/ton

$509.25/ton

The simulation results show that the CCR process is working at an economic optimal steady state from time t=0~1 hour. Then, at t=1hour, the disturbances are introduced in the system. After the EMPC controller detects the price changes within one sample time (5min), it begins to solve the economic dynamic optimization problems. Consequently, the calculated reference trajectories of the four reactor inlet temperatures are provided to the regulatory MPC controllers as shown in Figure 6. It can be observed that, affected by the economic disturbances, all the four inlet temperatures are raised to different extent. More specifically, the increasing amplitude of the last two reactors inlet temperature are relatively larger than the values in reactor 1 and reactor 2. This is because a higher reaction temperature will promote dehydrogenation reactions to form more aromatics. In addition, the hydrocracking reactions will be promoted by further increasing last two reactor temperatures, which promote the removal of alkyls of heavy aromatics to produce more aromatics with lower carbon number, and so as to increase the profit. This conclusion can also be supported the steady state optimization in reference 26. The yields of aromatic products during the optimization are shown in Figure 7. It can be observed that the yields of benzene, toluene, and xylene are increased because their prices become higher from t=1 hour. Simultaneously, the A9+ yield becomes lower because the conversion to light aromatics is accelerated. Figure 8 shows the comparison of the profits controlled by EMPC and RTO/MPC method. It can be observed that RTO and EMPC calculate the same process optimal profit shown as the red line in


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Figure 8, as their models have similar steady state performance and accuracy. However, since a 5 lump dynamic model is used in the lower layer of the RTO/MPC structure, the result shows that the MPC controller failed to drive the system to the set-point. Consequently, it provides a lower

528

528

526

526 T2( oC )

T1( oC )

economic profits than the EMPC controller does.

524 522

524 522

0

0.5

1

1.5 time ( h )

2

2.5

520

3

528

528

526

526 T4( oC )

T3( oC )

520

524 522 520

0

0.5

1

1.5 time ( h )

2

2.5

3

0

0.5

1

1.5 time ( h )

2

2.5

3

524 522

0

0.5

1

1.5 time ( h )

2

2.5

520

3

8

Tol( wt% )

Ben( wt% )

Figure 6. Reference trajectories and process value of inlet temperatures (case 1)

7.8 7.6 7.4

0

0.5

1

1.5 time ( h )

2

2.5

21.2 21 20.8 20.6

3

0

0.5

1

1.5 time ( h )

2

2.5

3

0

0.5

1

1.5 time ( h )

2

2.5

3

20.8 A9+( wt% )

23.8 A8( wt% )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


23.6 23.4

20.6 20.4 20.2

23.2

0

0.5

1

1.5 time ( h )

2

2.5

3



Figure 7. Aromatic product yields with different carbon number 4

8.3

x 10

8.2 profits( $/h )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

8.1 8 RTO-SP RTO-PV EMPC

7.9 7.8 7.7

0

0.5

1

1.5 time ( h )

2

2.5

3

Figure 8. Comparison of the profits controlled by EMPC and RTO/MPC

5.2 CS 2: production mode switching As mentioned above, the feedstock of an industrial CCR unit is usually a blend of two types of naphtha streams. Among the two streams, heavy naphtha from hydrocracking units accounting for 10 percent of the total feedstock usually has much higher NA compared with the naphtha from crude distillation units. We herein simulate the case that the heavy naphtha shut down at t=1 hour, and the flowrate and the compositions of the feedstock change immediately which are listed in Table 3. For an industrial CCR process, the production mode switching occurs frequently due to the unstability of the heavy naphtha from hydrocracking. Commonly, the production mode will be switched to producing gasoline manually, because the feedstock without heavy naphtha is no longer suitable for producing aromatic products. Table 3. Disturbances in the flowrate and the compositions of the feedstock time 0~1h

1~3h

F (t/h)

124.00

110.00

P (wt%)

52.00

62.00

N (wt%)

38.00

30.00

A (wt%)

10.00

8.00

Figures 10~11 indicate the simulation results of CS 2. Affected by the disturbance introduced at


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t=1 hour, the calculated profits dropped over 1500$/h immediately which can be observed from Figure 10(a). Then, the EMPC controller switches the production mode from producing aromatics products to gasoline mode automatically. By doing this, the objective function in gasoline mode will be calculated to drive the system to produce high quality reformate oil for gasoline blending process instead of pursuing the maximum profits of aromatic products. In other words, the system began to track the new optimal objective shown as the solid red line in Figure 10(b). While, the red line in Figure 10(a) becoming dashed from t=1hour indicates that the former economic objective is no longer work. The reference trajectories of the four reactor inlet temperatures to regulatory controllers is shown in Figure 9. It can be seen that all of the four reactor inlet temperatures are reduced by around 4 o C , and the EMPC controller drove the system to the new steady state within half an hour (6 sample time). As there is no switching mode functions in the RTO/MPC controller, the simulation results cannot be compared in this case. Considering the industrial naphtha feedstock changes

524

524

522

522 T( oC )

T( oC )

frequently, the simulation results can provide strategies for the reforming operating.

520 518 516

520 518

0

0.5

1

1.5 time ( h )

2

2.5

516

3

524

524

522

522 T( oC )

T( oC )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


520 518 516

0

0.5

1

1.5 time ( h )

2

2.5

3

0

0.5

1

1.5 time ( h )

2

2.5

3

520 518

0

0.5

1

1.5 time ( h )

2

2.5

3

516

Figure 9. Reference trajectories and process value of inlet temperatures (case 2)



4

8.5

x 10

110

8

108

7.5 RON

profits ($/h)

7

106 104

6.5 102

6 5.5

0

0.5

1

1.5 time ( h )

2

2.5

100

3

0

0.5

1

1.5 time ( h )

2

2.5

3

Figure 10. Comparison of the profits controlled by EMPC and RTO/MPC

5.3 CS 3: disturbances in feedstock quality The feedstock quality of the CCR process is affected greatly by the operation of the upstream processes. However, in the gasoline mode, the RON of the reformate oil should be controlled close to a constant value 102.2. The RON lower than that value will lead to unqualified gasoline, while higher will lead to quality excess. In CS 3, we introduce a disturbance of changing feedstock quality to test the EMPC control performance, which is shown in Figure 11. 40 39 NA (wt%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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38 37 36 35

0

0.5

1

1.5 time (h)

2

2.5

3

Figure 11. Disturbance in feedstock quality The simulation results are illustrated in Figure 12 and Figure 13. It can be observed that with the value of NA changing during t=1 to 2 hour, the product RON is controlled at around 102.2 by the EMPC controller with a fluctuation less than 0.1. In the last 1 hour, as the final value of NA is fixed at 36wt%, all the four reactor inlet temperatures are raised by different degree centigrade to make


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sure that the product RON can be controlled properly with the lowest energy consumption which is also taken into account in the objective function. The control performance of the TRO/MPC method is also illustrated as the black line marked * in Figure 13. Comparing with the result of the EMPC controller, it can be observed that the product RON controlled by RTO/MPC is higher than the desired value 102.2. That may lead to the quality excess of reformate for the downstream gasoline blending process. Meanwhile, during the simulation time t=1 to 2 hour, RTO/MPC also fail to compensate the disturbances in feedstock quality as the sampling time in RTO is much longer than the disturbances changing frequency.

520 T2( oC )

T1( oC )

520 518 516 0.5

1

1.5 time ( h )

2

2.5

3

0

0.5

1

1.5 time ( h )

2

2.5

3

0

0.5

1

1.5 time ( h )

2

2.5

3

520 T4( oC )

520 T3( oC )

518 516

0

518 516

518 516

0

0.5

1

1.5 time ( h )

2

2.5

3

Figure 12. Reference trajectories and process value of inlet temperature (case 3) 102.6 5.7 Ben (wt%)

102.4 RON

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


102.2 102 101.8

EMPC RTO-PV 0

0.5

1

1.5 time ( h )

2

2.5

3

5.65 5.6 5.55

0

0.5

1

1.5 time ( h )

Figure 13. Process values of product RON and Ben yield


2

2.5

3


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

6 CONCLUSIONS In the present work, we design an EMPC controller to improve the economic performance for an industrial CCR process. For this purpose, a rigorous CCR dynamic model with a 33-lump reaction network is proposed to predict the aromatic yields and RON of the reformate oil. To reduce the computational cost, the proposed dynamic model is simplified accounting for the different requirements of the two production modes. Then, the EMPC controller with production mode switching is designed. In the EMPC layer, we apply specific economic objective function and dynamic model for each production mode. In the regulatory controller layer, the MPC controllers are used to control the four reactor inlet temperatures and guarantee the process safety and stability by manipulating the fuel gas flowrate in furnaces. Three case studies are presented to test the control performance of the proposed EMPC controller in which variety of disturbances are introduced including aromatic prices, production mode switching, and feedstock quality. The simulation results show that the CCR process applying our proposed EMPC controller is able to overcome the economic disturbances and operate the system running at the economic optimal operating point. Compared with the conventional RTO/MPC method, the EMPC controller requires less response time to reach a new operating point. Furthermore, it can also obtain higher economic performance for the industrial CCR unit. Generally, the proposed EMPC strategy has a relatively more effective in coping with the economic disturbances in the industrial CCR process. Moreover, it also has the capacity to keep the system running at the economic optimal operating point. The presented results provide new strategy to operate the CCR process to gain remarkable economic profits under different production modes.


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Acknowledgements This work was supported by National Natural Science Foundation of China (21376077, 61422303, 21403066, 61503138).



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Table of content graphic


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Dynamic Modeling and Economic Model Predictive Control with

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